At the column voltage is changed to -D ( k = - 1 ) , corresponding to the off state. This results in a r.m.s. voltage ( Vgray), which is intermediate - 1
~
~~-~ -~ ~
208
3
Applications
interval resulting in a r.m.s. voltage across a pixel given by
42S2 - 4 k S D + 2 N 9 (Vpixel) = N
(14)
PHM allows the generation of a larger number of gray levels than FRC and PWM and can also be used in fast responding STN displays [36, 371.
Figure 11. Schematic illustration of frame rate control (FRC) for the case of five pixels and a superframe consisting of four frames resulting in five different gray levels.
between those given by Eq. (1 1)
i
f(S +
(%ray) =
m2+ (1- f )
(s - D ) +~(N - 1) D* N
(12)
The voltage reversal of the column voltages requires higher operation frequencies and limits the number of gray levels to 16 due to the low-pass filtering action of the panel [351.
3.1.4 Supertwisted Nematic Displays As described above, the slope of TN displays, described by the ratio V,,/V,, for a NB mode operated cell, is in the range of 1.4- 1.6, which is only sufficient for displays with a maximum number of multiplexedrows N= 16-32. Forhigherinformation content displays an increase of the slope is necessary to achieve a reasonable contrast ratio. In this subsection the influence of a twist angle >90° and other cell and material parameters on the midlayer tilt angle as a function of the reduced voltage, the socalled electrodistortional curve, is considered.
Gray Levels with Pulse Height Modulation In PHM gray levels are achieved by setting the column voltage to an intermediate value between + D and -D. With respect to Eq. (1 1) this mean that the parameter k is set of values -1 < k < + l to achieve a voltage between (V0J and (V&. However the r.m.s. voltages across the other pixels in the same column (Vpixel) are changed to J(S
+ D)2+ (kD)2+ (N - 2) 02
3.1.4.1 Influence of Device and Material Parameters Figure 12 shows calculated curves of the midlayer tilt angle as a function of the reduced voltage, for different twist angles, @ from 90"-360" [17, 28, 38, 391. Increasing twist angle, @, results in
- an increase of the reduced threshold voltage
(13)
- an increase of the slope of the electrodis-
This can be avoided by choosing the column voltage to be (k+(l-k2)) D in one time interval and (k-(1-k2)) D in another time
tortional curve an infinite slope for a twist angle of 270" a bistable region for twist angles above 270"
(Vpixel) =
N
-
3.1 90
n
0
05
10
15
20
25
30
Reduced voltage
Figure 12. Influence of different twist angles from 90" to 360" on the electrodistortional curve.
A twist angle @>90" can be achieved by doping the nematic liquid crystal mixture with a cholesteric liquid crystal. For a cell with zero pretilt the twist angle @ depends on the ratio of the cell-thickness d to the pitch p of the doped liquid-crystal mixture:
The reduced threshold voltage V,, for a cell with arbitrary twist angle @and zero pretilt is given by [40]
TN, STN Displays
209
slope of the electrodistortional curve and the threshold voltage is shown in Fig. 13. The standard condition, common to all figures, refers to the parameter set consisting of a twist angle @=210", a pretilt angle 8=5", K,,IK, I = 1.5, K2,IK1 =0.6 and y=2.5 [ 171. The curves of Fig. 13 were calculated assuming that an applied electric field only results in a reorientation of the local optical axis perpendicular to the layer (Freedericksz configuration). However, in a highly twisted structure an applied electric field may also lead to an additional reorientation of the local optical axis parallel to the layer, which was first described by Chigrinov [4 11. This additional reorientation causes the occurrence of striped domains resulting in a destabilization of the twisted structure [42-441. In Fig. 14 microscopic photographs of a domain-free STN cell and a STN cell with striped domains are shown. Table 2 summarizes the influence of increasing twist angle @, pretilt angle 6, d/p ratio, K,,IK,,, K221K,l and y o n the slope of the electrodistortional curve and the stability of the Freedericksz configuration. From Table 2 it follows that a variation of twist angle 0, K,,/K, K2,/K, I and A€/&, towards a steeper electrodistortional curve will result in a destabilization of the Freedericksz configuration. A simultaneous increase of the slope and the stability of the Freedericksz configuration can only be achieved by an increase of the pretilt angle [451 and a decrease of the d/p ratio. Decreasing the d/p ratio below a certain value however results in the formation of a twisted structure with a twist angle @- 180". In the following typical values for the different parameters will be given:
,,
For a TN-cell with twist angle @=90" and d/p=O, Eq. (16) reduces to Eq. ( 5 ) . The stabilization of a twisted structure with twist angle d b 9 0 " requires a finite pretilt angle at the boundaries. Pretilt angles from 2" to 10" can be achieved using commercially available polyimides. An increasing pretilt angle results in a shift of the threshold voltage to values which are smaller than given by Eq. (16). The influence of different values of the pretilt angle, the d/p ratio, the ratios of the elastic constants K,,IK, and K2,1Kl and the dielectric parameter y=A&/E, on the
,
(a) For a twist angle of 180" a pretilt angle of about 2" is necessary. Typical STN displays with twist angle of 240" require pretilt angles in the range of 5". Pretilt
210
3 Applications
mj
0
90
p ?
80 70
0.5
1.5 2.0 Reduced voltage
10
25
dlp = 0 33
0
05
10
15
20
25
10
15
20
25
30
Reduced voltage
Figure 13. Influence of different values of (a) the pretilt angle, (b) the d p ratio, (c) the ratio of the elastic constants K3,IK1I , (d) the ratio of the elastic constants K22/K1 and (e) the dielectric parameter, y= on the electrodistortional curve. The standard condition, common to all figures, refers to the parameter set consistingof a twist angle @=210", apretilt angle 8=5", K 3 3 / K 1=1 1.5, K22/K11=0.6 and y=2.5.
Table 2. Influence of increasing parameters of twist angle, @, pretilt angle, 8, d/p ratio, elastic constant ratios K3,IK1 and K2,IK1 and dielectric parameter y=A&I% on the slope of the electrodistortional curve and the stability of the Freedericksz configuration.
90
80
.
U
05
30
Reduced voltage
g
0
3.0
70
Increase of parameter ~~~~
Slope of the electrodistortional curve
Stability of the Freedericksz configuration
Increasing Increasing Decreasing Increasing Decreasing Decreasing
Destabilizing Stabilizing Destabilizing Destabilizing Stabilizing Stabilizing
~
10
K33/K1 = 0 5
/
0
05
10
15
20
25
30
Reduced voltage
Twist, @ Pretilt, 8 dP K331K1 I
K22IKI 1 y= A&/% K z z / K i i = 0 T4-
o, 60
5 %
50
L
30
:
20 10
0 0
05
10
15
20
25
30
Reduced voltage
angles of 2" to 10" are achieved using adequate polyimides [46 -481. Increasing temperature will result in a decrease of the pretilt angle.
(b) The d/p ratio for twist angles ranging from 180" to 270" is between 0.35 and 0.55. Increasing temperature results in a decrease of the upper limit of the d p value, defining the transition from the Freedericksz configuration to the formation of striped domains. The lower limit of the d/p value corresponding to a transition to a twist of a- 180" remains relatively unchanged with increasing temperature.
3.1 TN, STN Displays
12
F
I
I 11
~
~~
10 -~
a"
9
iI
-
8 7
-
-
I
: * *! - .
. . + *. . .,. . I
1
*.
1
+
*+'***
-,
'&&a +*.
~~
+Lob&
'c
2.- *
Figure 14. Microscopic photographs of (a) a domain-free STN-cell and (b) an STN-cell with striped domains.
I
'+*
~~
1
21 1
-
6
(c) The elastic ratio K33/K11an be influenced in the range 1-2.5 by the mixture composition. Polar compounds display higher K33/K11values than neutral singles. The introduction of double bonds in the core structure or the side chains results in a further increase of K 3 J K I 1 [49,50] (see also Sec. 3.1.5). Increasing temperature results in a slight decrease of K d K ,1 . (d) The elastic ratio K2,1K, is typically about 0.5-0.6 and the temperature dependence is rather weak. The dielectric parameter y=A&kI as a function of A& at room temperature for mixtures with similar clearing point is plotted in Fig. - 15. It becomes obvious that the problem of the destabilization of the Freedericksz configuration is more severe in mixtures with large threshold voltages (smaller A&values). Increasing temperature decreases AE due to the decrease of the nematic order parameter
Figure 15. Dielectric anisotropy A& as a function of the dielectric parameter at room temperature of liquid crystal mixtures with similar clearing point
while the changes of &Iare rather weak. Consequently the probability for the formation of striped domains is higher for increasing temperature. Summarizing these facts it follows that the different parameters need to be optimized to obtain a required slope of the electrodistortional curve for a certain application and avoid the occurrence of striped domains or the formation of a twisted structure with a twist of @-180" for the temperature regime of operation.
3.1.4.2 Configuration and Transmission of a Supertwisted Nematic Display A typical STN configuration with orientations of rubbing directions and polarizer directions for a cell with a twist angle of 240", dAn=0.85 and d/p=0.53 is shown in Fig. 16. The orientation of the rubbing directions of the polyimide layers of front and
212
3 Applications rear polarizer , 1 , , 1 p ) C
rear glass plate
front glass plate
,/*
/
rubbing direction
front polarizer
-/'
Figure 16. Typical STN-configuration consisting of front and rear polarizers and front and rear glass plate with orientations of rubbing directions and polarizer directions for a cell with twist angle 240°, dAn=0.85 and dlp=0.53.
A'
rear substrate depend on the twist angle @. The contrast ratio and the brightness are optimized by setting polarization axis of front and rear polarizers at an angle of (30-60)" with respect to the rubbing directions [5 11. For a cell with zero pretilt and an orientation of both polarizers at 45" to the rubbing directions the transmission of a STN-LCD is given by [52]
In Fig. 17 the transmission is plotted as a function of dAnlA for different twist angles @= 180"-270". The positions of the transmission minima are given by
Regarding the maximum of the spectral eye sensitivity curve (A=0.555 pm) this results in a retardation value q=dAn = 1.1-0.73 for twist angles @= 180"-270". The retardation value is about twice as large as for the 1st minimum condition of a TN-display. For a display with layer thickness d = 6 pm
a liquid crystal mixture with An=0.14 would be required for a STN display with twist angle @=240" while An=0.088 would be requested for a TN display operated in the 1st minimum condition. For general STN applications liquid crystal mixtures with An in the range 0.12-0.2 are necessary. As described in Sec. 3.1.2.2 the orientations of the front and rear polarizers of a TNcell are either parallel or perpendicular to the rubbing direction. For operation in a minimum condition, according to the Gooch and Tarry curve, the outcoming light is linearly polarized. Due to the off-axis orientation of polarizers and rubbing directions in a STN-cell, necessary to optimize the contrast ratio, the outcoming light is elliptically polarized. In combination with the large retardation values d An this leads to strong interference colors. The complementary color state can be achieved by turning one polarizer by 90". The STN-configuration shown in Fig. 16 appears yellow in the unactivated state and dark blue in the activated state. Black and white operation necessary to produce a colored STN display with RGB filter technology can not be achieved
3.1
TN, STN Displays
213
08
32
0 0
05
1
15
2
2 5
u = din//
in the standard STN-configuration and requires additional compensation techniques (see Sec. 3.1.4.5). Noncompensated STN displays are normally optimized for operation in yellow mode or the complementary blue mode. The designations yellow mode and blue mode correspond to the nonselect state. Different operating temperatures will change the product d A n due to a change of A n which is proportional to the nematic order parameter S. This causes coloration of the display which becomes more dominant with increasing operation temperature. The effect of unwanted coloration can be reduced by using a liquid crystalline mixture with a clearing point at least (30-40) K higher than the maximum operation temperature.
3.1.4.3 Electro-optical Performance of Supertwisted Nematic Displays According to Scheffer and Nehring the transmission spectra of the nonselected and select states of the yellow mode and the complementary blue mode for twist angles @=210" and @=270" show the following characteristics [ 171: -
The transmission spectra of the nonselect state of the yellow mode (blue mode) show a broad peak with a maximum (minimum) for wavelength A=(SOO-
-
-
Figure 17. Transmission as a function of u = 2 d A n l L for different twist angles @= 180" - 270" calculated according to Eq. 17.
550) nm. For twist angle @=270" the yellow mode is greenish-yellow and the blue mode shows a dark, purplish-blue colour. The yellow mode for a twist angle of 210" is greener than for 270". The wavelength dependence of the select state is nearly constant in the visible range above A = SO0 nm. For wavelengths below A=SOO nm an increase (decrease) of the transmission spectra for the yellow mode (blue mode) is observed. For twist angle @=270" the yellow mode appears black and the blue mode is bright and colorless. The yellow mode for a twist angle @=210" is dark purple. The application of a voltage intermediate between the nonselect and the select state also changes the wavelength of the peak maximum (minimum) for the yellow mode (blue mode) of operation.
The increase of the twist angle @ from 210" to 270" results in an increase of the range of viewing directions with high contrast and a decrease of the areas showing contrast reversal at large viewing angles.
3.1.4.4 Dynamical Behavior of Twisted Nematic and Supertwisted Nematic Displays Equations for the switching on time z,, and the switching off time zoffunder static driv-
214
3
Applications 1000
ing conditions for a cell with arbitrary twist angle and zero pretilt angle were calculated by Tarumi et al. [53]: v)
a"
.-
E 100 L
10
yl is the rotational viscosity, U,,, the operating voltage and U, the Freedericksz threshold voltage. The denominator of Eq. (20) is related to the elastic constants K , K22and K33,the d/p value and the twist angle @by the following equation [53]: EO A&U i
=
The switching time, z, can be decreased by decreasing the rotational viscosity, yl, the layer thickness, d, and by an optimized balance of elastic constants and dielectric anisotropy, A&.Polar materials generally show higher rotational viscosities than neutral substances of similar clearing point. Consequently mixtures with lower threshold voltage will show a higher rotational viscosity yl due to the larger percentage of polar materials. The rotational viscosity of neutral increases with increasing clearing point, TN. I (see Fig. 18). Consequently an increase of TN-Iof a mixture without affecting the polarity will in a first approximation result in an increase of the total rotational viscosity and the switching time. The product dAn has to be kept constant for an optimum contrast ratio. Consequently for a decrease of the cell thickness, d, to achieve a smaller switching time, liquid crystal mixtures with increased birefringence An are necessary.
0
' ' ' ' 50I " ' '
100
150
200
250
T, I O C
Figure 18. Rotational viscosity, y,, as a function of the clearing point TN.Iof different neutral single materials.
For STN laptop and monitor applications showing switching speeds of (250- 300) ms, liquid crystal mixtures with An = (0.12 0.14) are used according to a layer thickness of (6-7) pm. For fast switching STN displays, liquid crystal mixtures with An = (0.17 -0.21) are required. This increase in An and subsequent decrease of d results in a switching time reduction by a factor of about three. However, even switching speeds of (80- 100) ms are still two slow for video presentation. Figure 19 shows the contrast as a function of time for the switching on process, corresponding to an increase of the contrast ratio from 0% to 100% followed by the switching off process. The switching onprocess consists of a so-called turn on delay and the rise time characterized by a change of the contrast from 10% to 90%. The switching off process consists of a turn-off delay and the decay time for the change of the contrast from 90% to 10%. The rise time and the decay time are generally not identical. The rise time is determined by an interaction of elastic constants and the dielectric anisotoropy while the decay time only depends on the elastic constants. The response
3.1
time strongly increases with decreasing temperature as shown in Fig. 20 for the rise time, the decay time and the delay time. This
TN, STN Displays
215
effect is mostly due to the quasi exponential increase of the rotational viscosity, y,, of liquid crystal mixtures with decreasing operation temperature (see Fig. 21). Under multiplex operation increasing operating voltage results in a decrease of the switching on time zOnand an increase of the switching off time zOff.The crossover condition Ton
(22)
=
can be fulfilled for a defined operating voltage which is smaller than for achieving an optimum of the contrast ratio.
3.1.4.5 Color Compensation of STN Displays Figure 19. Contrast as a function of time for the switching-on and the switching-off process.
Black and white operation of STN displays, necessary to produce a color display with the typical color filter technology, requires a compensation of the interference colors of a standard STN device. In this subsection several compensation techniques will be described.
Black and White Operation by Decreasing the Product d An I
I 0
1 1
- 50
1 100
50
Temperature I
O C
Figure 20. Dependence of the rise-time, the decaytime and the delay-time on the operation temperature.
The transmission spectra of the nonselect state for the yellow mode (and the complementary blue mode) are characterized by a broad interference peak with a maxi-
100000 I
10000
-I
~
-
v,
a
. E
'
1 100 230
240
250
270
260
TIK
280
290
300
Figure 21. Dependence of the rotational viscosity, yi, of a liquid crystal mixture on the operation temperature, T.
216
3 Applications
mum (respectively minimum) for wavelength of about 500-550nm. Black and white operation can be achieved by shifting this interference peak to shorter wavelengths. This requires a shift from the optimized retardation value d An - 0.9 pm to d A n -(0.4-0.6) pm [54, 551. The remaining transmission spectra is relatively flat. However this results in a reduction of the luminance by 50% and the brightness by 75%. The transmission can be enhanced by the so-called extended viewing angle (EVA) cell requiring a twist of 270' and a pretilt angle of (12-15)'. For a cell with layer spacing d=4 pm, a large viewing angle and switching time in the range of 10 ms were reported [56].
phase compensating element restores the linear polarized state. The principle of phase-compensation is to use a retarder foil placed between the STN-layer and the polarizer, with the same absolute value of the phase retardation A q but with its optical axis perpendicular to the optical axis of the STN layer. This implies an additional phase retardation A 9 of
Supertwisted Nematic Cell with Dichroic Color Sensitive Polarizer
Double Layer Compensated Supertwisted Nematic Displays
In this technique one standard polarizer is replaced by a dichroic color sensitive polarizer. For the yellow mode this results in a compensation of the off state and only slight influence on the on state. This mode of operation is called the neutral STN-mode (NSTN). For the complementary blue mode a compensation of the on state is achieved. A disadvantage of this technique is the low polarization efficiency of only (50-75)%. This limits its use to low-multiplexed displays with moderate requirements of contrast and viewing angle.
The double layer compensated configuration [57], (DSTN) shown in Fig. 22, consists of a stack of two STN-cells with identical values of d A n , but opposite handedness of the helices. At the interface between both cells the directors must meet at right angles. In the bright off state the polarizers are oriented parallel to each other. In the dark off state the orientation of polarizer and analyzer is perpendicular. The angle between rubbing direction and polarization axis is about (30-60)'. Assuming that both cells contain the same liquid crystal mixture the DSTN configuration has the following advantages:
Phase- Compensation Light propagating through a STN-cell will undergo a phase retardation A q given by
This phase retardation results in a transformation of the incoming linear polarized light into elliptically polarized light. A
Consequently the overall retardation is zero (Soleil- Babinet compensator) resulting in a black and white operating LCD configuration.
-
-
LC mixture parameters such as clearing point, birefringence, rotational viscosity, dielectric anisotropy and elastic constants can be optimized for a special applications without affecting the compensation effect. The compensation effect should be wavelength independent owing to the same dispersion in both cells.
3.1
n i
1" STN layer
\
polarizer
217
2 ~ STN 4
I
layer
i n
90 0-J
. U
I
............._.._,, ..__
..',._....-
"..._ h
polarizer
light propagation
Figure 22. Principal configuration of a double layer compensated STN (DSTN) display. The 1st STN layer is an active layer, the 2nd STN layer is a passive layer.
-
TN, STN Displays
The temperature dependence of the birefringence, An, is the same in both cells resulting in a temperature independent compensation. Due to this effect DSTN displays are mostly used in automotive applications where a maximum operating temperature of up to 85 "C is necessary.
The compensation becomes nonperfect if the products d A n of both layers are different due to deviations of the layer thickness. These deviations should be less than 50 nm [58]. Generally the second STN layer is a so-called passive layer, as it is not addressed. As can be seen from Fig. 23 the deformation profile in the nonselected state and the field free state is rather similar. The birefringence of the active layer is smaller in the nonselected state than in the field free state. Consequently the retardation value d A n of the passive layer, which is held in a field free state, should be adjusted to the retardation value of the active layer in the nonselected state to optimize the contrast ratio. This requires a liquid crystal mixture for the passive layer with a retardation value about (2- lo)% smaller than for the active layer in the field free state [59-611. The range of viewing directions of a DSTN cell with a twist angle of 210" is similar to a noncompensated cell with twist angle of 270". A DSTN cell offers higher
Relative distance dd
Figure 23. Tilt angle as a function of the reduced distance d d (O
contrast, black and white operation and is about 50% brighter than an conventional STN cell. Disadvantages of the DSTN configuration are the increased thickness, weight and cost compared to the standard STN cell. The replacement of the second passive STN layer by a cholesteric polymer film with the same value of d A n and twist was described and commercialized [62,63].
Film Compensated Supertwisted Nematic Displays Compensation can be achieved by replacing the second passive STN cell of a DSTN display by an anisotropic, nonliquid crystalline polymer film made of polycarbonate (PC), polypropylene (PP) or polyvinyl alcohol (PVA). This type of compensated STN cell is the so-called film compensated STN (FSTN) cell [64]. The films of about 0.1 mm thickness are uniaxially stretched to obtain a retardation value of (200 - 800) nm. The configuration of a stretched film with refractive indices n, (parallel to the stretching direction) and n y , n, is shown in Fig. 24. Generally the films are slightly biaxial with n,>ny>n,. An even higher viewing angle can be achieved if n, > ny, which, however, requires a biaxial deformation [65]. Compensation can be performed by using one or two foils stacked between the STN layer and
218
3
Applications
for laptop displays where the required maximum operation temperature is about 50 "C. Further improvement of the film compensation technique was reported for FSTNLCDs with four films [72]. Figure 24. Configuration of a stretched film with refractive indices n, (parallel to the deformation axis) and nY,n, (perpendicular to the deformation axis).
the polarizer [66-691. In the case of two foils these can either be stacked on one side or on both sides of the STN cell. The first case results in a better viewing angle dependence while for the second case an enhancement of the contrast ratio and less coloration at oblique viewing angle are observed [70,7 11.Compared to the DSTN display, the FSTN display offers the advantages of reduced price, weight and an easier manufacturing. Film compensation is mostly used in portable applications such as laptop displays. A limiting factor of the compensation is the different dispersion of the liquid crystal mixture and the polymer foil. The wavelength dependency of the retardation is significant for polycarbonate while it is rather weak for polypropylene. The compensation effect can be adjusted by laminating polymers with different wavelengths dependencies. Another approach is to choose the retardation between the liquid crystal mixture, R ~and, the polymer foil, cpp, to be
p ~ c - @ = n -a- , with n=l,2,3,4,.. 2
(25)
This results in a wavelength independent phase difference given by
Acp = ApLC- Acpp = n z
(26)
A further problem of the film compensation technique is the different temperature dependence of the liquid crystal and the polymer foil, which limits the maximum operation temperature. However, it is sufficient
3.1.4.6 Viewing Angle and Brightness Enhancement In addition to the described compensation techniques, several other techniques have been reported to enhance the viewing angle dependency and the brightness. A system, suitable for the enhancement of the viewing angle of TFT and STN displays by external means consists of a specially designed collimated backlight and diffusing screen with the liquid crystal cell placed in between [73, 741. Recent studies on two- and four-domain structures have shown the potential improvement of the viewing angle dependence in TN and STN displays [75]. Reflective polarizers consisting of a wide waveband cholesteric film and a quarter wave foil can be optimized in their optimal properties to achieve improvement of the brightness by (70-80)% [76].
3.1.4.7 Color Supertwisted Nematic Displays For transmissive displays, color operation can be achieved by RGB (red, green, blue) color filter technology. RGB filters are manufactured on the interface between the I T 0 layer substrate and the polyimide layer by dyeing, pigment-dispersion, printing or electrodeposition. The thickness of the color filters varies around (0.8-3.5) pm depending on the production technique. The color filters are arranged as parallel stripes on the substrate, which increases the number of necessary columns by a factor of three. With three colors and n different achievable gray levels n3 different colors can be displayed. The transmission of such
3.1
a colored STN display is only (4-5)% of a black and white operated STN-display and consequently the use of color filters is not suitable for reflective operation. An alternative method to achieve a transmission of about 10% is the so-called subtractive color mixing [77-791. However, even this transmission ratio is not sufficient for a colored reflective display. One technique for the realization of a reflective colored STN display showing four colors (White, orange, blue and green) without the need for colorfilters makes use of the electrically controlled birefringence technology [ 801, Figure 25 shows the luminance as a function of the applied voltage. The applied voltage across a pixel results in a specific orientation of the molecules which determines the color. The requirements for the realization of a reflective colored STN display are: a large retardation, cp=dAn, value of about 1.5, - an optimization of polarizer orientations, and - a compensating foil to achieve a black and white status. -
3.1.4.8 Fast Responding Supertwisted Nematic Liquid Crystal Displays As described in Sec. 3.1.4.4, the response speed of a STN display can be reduced by decreasing the layer thickness and adequate increase of the birefringence of the liquid crystal mixture to obtain the necessary retardation value for an optimized contrast. However, in fast responding STN displays operated with Alt -Pleshko addressing the r.m.s. condition is not fulfilled and a phenomenon called frame response becomes apparent [8 11. Frame response means that the liquid crystal molecules in an activated pixel undergo a significant relaxation towards the unactivated state within the frame period, resulting in reduced contrast and
TN, STN Displays
219
White Orange
Green
+
_ _ _ _ _
u,,
Us
Voltage
Figure 25. Luminance as a function of the applied voltage for a reflective colored STN display.
flicker of the display. The transmission behaviour of a pixel of a slow- and a fast-responding LCD switched to the activated light state by Alt-Pleshko addressing is shown in Fig. 26 [17]. The fastest acceptable response speed to suppress frame response using Alt-Pleshko addressing is about 120 ms for dual scan VGA (Mux 240) and about 175 ms for dual-scan XGA (Mux 384) [8 11. The occurrence of frame response can be reduced by an increase of the frame frequency. However, this is limited by the low pass filtering action of the panel meaning that the pixel does not receive any voltage at high frequencies. In the Alt-Pleshko technique every row is addressed once per frame with a selection pulse of amplitude, S . The effect of frame response can be reduced by splitting the select pulse, S, into many pulses of smaller amplitude which are distributed over the frame period without the necessity to increase the frame frequency. Addressing techniques for fast responding STN displays are: active addressing (abbreviation is AA), where all rows are selected at a time [82, 831, - multi-line addressing (abbreviation is MLA), where several rows are selected at a time [84].
-
N scanning lines are divided into N/L subgroups, where each subgroup contains L scanning lines. For Alt - Pleshko addressing
220 liaht
3
I
Applications
slow LCD \
mation state of the display. The r.m.s. voltage across a pixel element is given by
fast LCD
I
(Uu) = F J 1- 2c Zu + Nc2
(29)
where F is given by
4
I
IT
16.7177s
Figure 26. Transmission behavior of a pixel of a slowand a fast-responding LCD switched to the activated ‘light’ state by Alt-Pleshko addressing.
L= 1, for active addressing L = N , while typically for multiline addressing the value of L =4 ...7. AA and MLA require a different set of row and column signals from Alt -Pleshko addressing. These will be considered in the following: The signal for row i and columnj at time t are described by functions F,(t) and Gj(t). The voltage across pixel ij is given by Uij(t) = F , ( t ) - Gj(t)
(27)
A detailed mathematical analysis shows that the row functions F,(t) must be a set of orthonormal functions to obtain an optimum selection ratio. The time dependent column signals Gj(t) must be calculated by summation of the product of a matix element Zii and the row functions Fi(t) over the number of scanning lines L per subgroup N/L: L
Gj (t)=
CC1~E ( t ) i=l
The matrix elements are set Zij =+ 1for anonselected state and Zii=-l for the selected state. The coefficient, c, is a proportionality constant, which is independent of the infor-
and T is the frame period. Equation (30) has the value F , i f j = k and is zero, if j # k. Setting c = 1/ f l the optimized selection ratio is given by
which corresponds to Eq. (10) for AltPleshko addressing. Detailed information about row waveforms for multiple-line addressing are given by Scheffer and Nehring [17]. In general AA will require more drivers than MLA. For MLA with seven selected rows at a time the lower driving limit is 30 ms for a dual-scan VGA and 50 ms for a dual-scan XGA display [73]. These values are smaller by a factor four than for the Alt - Pleshko addressing technique.
3.1.5 Liquid Crystal Materials for Twisted Nematic and Supertwisted Nematic Display Devices The quality of any LC-display is strongly determined by the physical properties of the LC-material. To achieve the highest display quality it is essential to select and optimize the materials for the given LC-cell parameters and requirements. On the other hand it is impossible to find one single LC-materia1 which fulfills all the material require-
3.1
ments. Therefore mixtures of up to 20 LCcomponents are usually used in LC-devices. Some of these materials are universal useful basic components, others are ‘specialists’ for the adjustment of properties such as birefringence An, dielectric anisotropy A&, ratio of elastic constants K,,/K, I etc. Commercially used LC-structures can be divided into the following groups: materials with high optical anisotropy, An materials with high positive A& (benzonitrile type) materials with moderate A& (fluoro aromatics) materials for the adjustment of the elastic constant ratio K3,1K, dielectic neutral two and three ring basic materials materials with extreme high clearing point In Tables 3 to 11, mesophases, dielectric anisotropies A&, birefringence values An, rotational viscosities yl and ratios of elastic constants K,,IK,, are given. All data was experimentally evaluated in the laboratories of Merck KGaA. The values of A&, An and yl were determined by measurement in a nematic host mixture (ZLI-4792) and extrapolation to 100%. The ratios of K33/K11 are those measured in a nematic host mixture while the values in brackets are those determined from mixtures of homologues.
3.1.5.1 Materials with High Optimal Anisotropy As described in Sec. 3.1.22 and 3.1.4.2 it is essential to adjust the birefringence, An, for a given cell gap, d, to achieve an optimal display performance. Since the switching time, z, strongly depends on d (Eqs. 19 and 20) materials with high A n are required. The refractive indices (ne, no) of liquid crystals are determined by the molecularpo-
TN, STN Displays
22 1
larizabilities and therefore depend mainly on the extent of conjugated x-bonding throughout the molecule [ 181. The optical anisotropy (An=ne-no) of LC materials increases with the increasing number of aromatic rings and x-bonded linking- or terminal groups (compare Table 5, Structures 3.1, 3.3 and 3.4). The main problem in the design of high An materials is the insufficient UV-light stability of such highly conjugated structures [85]. Commercially used high An LC materials (Table 3) are mainly based on cyanobiphenyl (Structures 1.1 and 1.2) and tolane structure (Structures 1.3 to 1.7).
3.1.5.2 Materials with Positive Dielectric Anisotropy The dielectric anisotropy A&of LC-materials is defined by A&= E,,- E ~where , E~~and are the dielectric constants parallel and perpendicular to the director. From the Maier and Meier theory it can be seen that both the polarizability anisotropy A a and the per, of the LC molemanent dipole movement U cule determine the dielectric anisotropy [86]. As given in Eqs. (3), (4),(19) and (20), A& is a quantity of paramount importance, as its magnitude directly determines the interaction between LC and the electric field. The A& value of LC-mixtures has to be adjusted for the desired threshold voltage. Currently available materials with highly positive A& are mainly based on benzonitrile structures (Tables 4 and 5). Introduction of heterocyclic ring systems (Structures 2.5 and 2.6) or ester links (Structures 2.7 and 3.5) lead to an increase of A&compared with the corresponding non-heterocyclic and directly connected systems. Unfortunately, the effectivity regarding A& of the benzonitrile structures is decreased by a local antiparallel ordering of the dipole moments [87]. The degree of antiparallel correlation
222
3 Applications
Table 3. Commercially used materials with high optical anisotropy. Structure
No.
1.1
C
5
H
l
w
C
Mesophases ["C]
Birefringence, An
Ref.
C 23 N 35 I
0.237
[911
C 131 N 240 I
0.324
[92,931
C 65 N (61) I
0.301
[941
C 109 N 205 I
0.223
[951
C 99 N 245 I
0.255
W, 961
C 96N 240 I
0.21 1
I971
C 8 4 N 1441
0.240
t971
N
Table 4. Commercially used two-ring materials with high positive dielectric anisotropy. Mesophases ["C]
A&
An
y, [mPas]
K,-,IK,,
C 23 N 35 I
22
0.237
112
(1.66)
C 45 N 46 I
21
0.136
116
2.0
C 68 N 74 I
23
0.170
180
2.1
C39N(-Il)I
26
0.123
98
1.83
-
C 59 N (42) I
29
0.124
121
(1.71)
c 5 H , <:ecN -
C 71 N (53) I
36
0.228
171
1.73
0.194
126
(1.82)
0.182
237
(1.78)
No. 2.1 2.2
Structure c
5
,
w
c
N
-
C3H7=CN
2.3 W 2.4
H
C
N
C,H7 C -N F
2.5 2.6
C5Hl
Ref.
3.1
223
TN, STN Displays
Table 5. Commercially used three-ring materials with high positive dielectric anisotropy. No.
Structure
yl [mPasJ K,,IK,,
Mesophases ["C]
A&
An
C45N242I
15
0.122
C53 N2041
20
0.123
C96N2191
17
0.210
C 131 N 240 I
Ref
1.95
[lo51
859
1.89
[I061
1338
1.92
[107, 1081
0.324
[931
C lllN226I
25
0.162
1227
C 9 1 N 1931
36
0.161
1424
[108, 1091
1.95
[110]
Table 6. Commercially used fluoro-aromatic materials with moderate dielectric anisotropy. No.
4.1
4.3
Structure C
7
H
i
w
Mesophases ["C]
A&
An
y, [mPas]
Ref.
C 36 N [-561 I
4
0.07
27
( 1 111
C 9 0 N 1581
3
0.08
156
11121
C 4 6 N 1241
6
0.08
160
[I131
C 25 SmB (51) N 119 I
5
0.08
229
(1141
C 3 9 S m B 7 0 N IS51
7
0.09
142
[115]
C 6 6 N 1021
8
0.14
194
[116]
F
C3H7+-J-o-QF
F
4.5
C3H7 3O C F*
-
F
4.7
C
,
H
7
W
:
OF
C 71 SmB (51) N I83 I
is a function of temperature and depends on the composition of the LC mixture. This fact often leads to a deterioration of the temperature dependence of LC mixtures. A predominantly parallel ordering of the molec-
ular dipoles and further increase of A& is possible with the introduction of ortho-fluorinated benzonitrile moieties [88] (Structures 2.4, 2.8 and 3.6).
224
3 Applications
Table 7. Influence of double-bonds on the elastic constant ratio K33/Kll. No
5.1 5.2
Mesophases ["C]
x KmPas1
C -3 SmB 68 I [N 17 I]
23
1.47
~901
C 23 SmB 33 N 34 I
34
1.59
[901
C 33 SmB (20) N 46 I
32
1.65
[901
C 29 N 44 I
26
1.68
~901
C 52 N 63 I
32
1.79
POI
Structure
%
5.3
5.4
5.5
% %
K33fKll
Ref.
Table 8. Commercially used materials with large elastic constant ratio K33/Kll. No
Structure
6.1
% -H I
6.2
m/
6.3
m\
6.4
F*/
6.5
F*
C C
H-
3
H -
-
3
C -9 SmB 52 N 63 I
39
1.53
[I181
C 66 N 162 I
118
1.72
[I 191
C 54 SmB 104 N 177 I
159
1.65
[1181
C 85 N 145 I
101
1.99
11181
C 47 N 109 I
115
1.95
[1181
F
Compared with the corresponding neutral structures the rotational viscosity, yl, of polar substituted LC - structures is increased (compare Structures 2.2/7.4, 3.3/8.3 and 3 3 8 . 6 ) . As given in Eqs. (19) and (20) this leads to an unwanted increase of the switching time. Therefore it is practice [89] in the design of mixtures for TN cells to include compounds with both large and small positive A&. The use of polar three ring materi-
als (Tables 5 and 6) in mixtures for multiplexed TN devices is restricted due to a deterioration of the frequency dependence of A&. Fluoroaromatic polar LC-materials (Table 6) with low to moderate A&show a better ratio of yl to clearing point. Owing to their high resistivity even at higher temperature these materials are especially useful in active matrix devices (TFT).
3.1
225
TN, STN Displays
Table 9. Commercially used basic two-ring materials. ~
No.
Structure
~~~
Mesophases ["C]
An
'/1 [mPas]
7.1
C -5 SmB 97 I
0.04
34
1.47
[I201
7.2
C 49 N 50 I
0.05
46
1.59
[121]
7.3
C 3 N [-751 I
0.08
14
1.47
[122, 1231
7.4
C 42 N (38) I
0.10
44
1.4
~1231
7.5
C 53 N [7] I
0.19
31
1.24
[I241
7.6
C 14 SmB 22 N 36 I
0.04
7.7
C 34 N (31) I
0.08
58
1.46
[I261
7.8
C 48 N 78 I
0.09
84
1.64
[I261
7.9
C 35 N (12) I
0. I5
58
7.10
C 32 N 42 I
0.15
3.1.5.3 Materials for the Adjustment of the Elastic Constant Ratio K33/KI1 All deformations in LCs can be expressed as a combination of the basic operations of splay, twist and bend of the director, mediated by elastic constants K,,, K22 and K33. As indicated in above it is particularly the elastic constants ratio K3,1K,,, that has received most attention because of its effect on the shape of the electro-optical switching curve in TN and STN cells. In TN devices it is essential to optimize the ratio of K,,IK, to low values, while for STN devices high values of K,,IK, are required to
K,,IK,,
Ref.
~251
~
7
11281
achieve a steep electro-optical contrast curve. A low value of K33IK11 can best be obtained by using heteroaromatic ring systems (structure 7.5). Compared with the neutral alkyl-chain substituted structures the introduction of a nitrile moiety leads to an increase of K,,IK, In general, a variation of K,,IK, can be obtained by the introduction of double bonds into the alkyl chain of LC-basic structures [49]. In Table 7 it is demonstrated that K,,/K, increases with the increasing number of double bonds introduced in basic structure 5.1 [90]. In addition the ratio of y,
,
1
226
3 Applications
Table 10. Commercially used basic three-ring materials. No.
Mesophases ["C]
An
fi [mPas]
C 62 SmB 109N 178 I
0.08
141
~ 9 1
C 51 SmB 129 N 157 I
0.08
275
[ 1301
C 66 SmB 134 N 166 I
0.16
100
[131,1081
0.15
154
11321
C 59 SmB 154 N 190I
0.04
313
[108, 1091
C 64 SmB 150 N 199 I
0.07
231
[log, 1091
0.12
274
[log, 1091
Structure -
8.1 3C3H7 HC*
Ref.
-
\ /
8.3 C53HH 2C 7*
-
8.5 1-7H3C
8.6 C
3
H
7
W
,
Table 11. Commercially used materials with extreme high clearing point. Structure
No.
C,H,
Mesophases ["C]
"/1 .. [mPasl
Ref.
C 158 SmB 212 SmA 223 N 327 I
491
[133,134]
C 133 N 302 I
651
~1321
C 110 SmB 212 N 325 I
911
[I351
F
9.3
C
3
H
7
W
I
to clearing point is improved. Commercially available materials used for STN devices are presented in Table 8.
3.1.5.4 Dielectric Neutral Basic Materials Tables 9 and 10 give an overview of basic materials used in TN and STN mixtures. The
choice is largely dictated by a compromise between clearing point and viscosity even at low temperatures, but other factors such as birefringence, elastic behavior or volatility play an important role. Structure 7.1 combines a low optical anisotropy with an excellent ratio of "/1 to clearing point. Structures 7.3 and 7.4 are very effective to suppress the formation of smectic phases at low
3.1 TN, STN Displays
temperatures. Table 11 shows effective basic materials for the increase and the adjustment of the clearing point of the nematic liquid crystal mixture. As an example the mixtures clearing point is enhanced by 3 K by adding only 1 % of Structure 9.1. Acknowledgements The authors wish to express their appreciation to T. J. Scheffer and J. Nehring for permission to reproduce figures from their publications [17, 191.
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[64] T. Nagatsuka, H. Yoshimi, Proc. SID 1991,32/2, 125 - 13 1. [65] Y. Fujimura, T. Nagatsuka, H. Yoshimi, T. Shimomura, SID Digest of Technical Papers 1991, XXII,739-742. [66] H. Odai, T. Hanami, M. Hara, K. Iwasa, N. Tatsumi, Proc. 8th International Display Researh Conference 1988, 195- 198. [67] I. Fukuda, Y. Kotani, T. Uchida, Proc. 8th International Display Research Conference, 1988, 159- 160. [68] S. Matsumoto, H. Hatoh, A. Murayama, T. Yamamoto, S. Kondo, S. Kamagami, Proc. 8th International Display Research Conference, 1988, 182-183. [69] S. Matsumoto, H. Hatoh, A. Murayama, T. Yamamoto, S. Kondo, S. Kamagami, Proc. SID 1989,30, 1 1 1- 115. [70] M. Ohgawara, T. Kuwata, H. Hasebe, M. Akatsuka, H. Koh, K. Matsuhiro, Y. Souda, K. Sawada, SID Digest of Technical Papers 1989, X X , 390 - 393. [71] A. H. Potma, P. H. M. Verheggen, Th. L. WelZen, Proc. 10th International Display Research Conference (EURODISPLAY)1990,348-351. [72] T. Miyashita, Y. Miyazawa, Z. Kikuchi, H. Aoki, A. Mawatari, SID Digest of Technical Papers 1991, XXII, 743 -746. [73] S. Zimmerman, K. Beeson, M. McFarland, J. Wilson, T. J. Credelle, K. Bingaman, P. Ferm, J. T. Yardley, SID Digest of Technical Papers 1995, XXVI,793 -796. [74] M. McFarland, S. Zimmerman, K. Beeson, J. Wilson, T. J. Credelle, K. Bingaman, P. Ferm, J. T. Yardley, Proc. 15th International Display Research Conference (Japan Display) 1995, 739 -742. [75] J. Li, E. S. Lee, H. Vithana, P. J. Bos, Jpn. J. Appl. Phys. 1996,35, 1446- 1448. [76] D. Coates, M. J. Goulding, S. Greenfield, J. M. W. Hanmer, S. A. Marden, 0. L. Parri, M. Verrall, J. Ward, International Display Works IDW 1996,2, 309-312. [77] A. Conner, Proc. 10th International Display Research Conference (EURODISPLAY) 1990, 362 - 365. [78] A. Conner, SID Applications Session Notes 1992, 109-112. [79] A. Conner, T. Johnson, SID Digest of Technical Papers, 1992, XXIII, 236-238. [80] M. Ozeki, H. Hori, E. Shidoji, Y. Hirai, H. Koh, M. Akatsuka, SID Digest of Technical Papers 1996, XXVII, 107- 110. [81] Y. Nakagawa, Semicon Korea 1995,83-88. [82] T. J. Scheffer, B. Clifton, SID Digest of Technical Papers 1992, XXIII, 228-233. [83] T. J. Scheffer, B. Clifton, D. Prince, A. R. Conner, Displays Technology and Applications 1993,14,74-85.
3.1 TN, STN Displays
1841 S. Ihara, Y. Sugimoto, Y. Nakagawa, T. Kuwata, H. Koh, H. Hasebe, T. N. Ruckmongathan, SID Digest of Technical Papers 1992, XXIII, 232- 235. 1851 V. Reiffenrath, U. Finkenzeller, E. Poetsch, B. Rieger, D. Coates, Proc. SPlE-Ind. SOC.Opt. Eng. 1990,84-94. [86] W. Maier, G . Meier, 2.Nuturforsch. A 1961, 15A, 262. [87] W. H. De Jeu, Phil. Trans. R. Soc. London Ser. A 1983,309, 217. 1881 K. Toriyama, D. Dunmur, Mol. Phys. 1985,56, 479. [89] K. Toriyama, K. Suzuki, T. Nakagonu, T. Ishibashi, K. Odawata, in The Physics and Chemistry of Liquid Crystal Devices (Ed.: G. Sprokel) Plenum Press, New York, 1976. 1901 E. Poetsch, V. Reiffenrath, B. Rieger, 24. Freiburger Arbeitstugung Fliissigkristalle 1995, P-I. [91] G. W. Gray, K. J. Harrison, J. A. Nash, Electron Lett. 1973, 9, 13. [92] G. W. Gray, J . Phys. (Paris) Suppl. 1975, 36 (Cl), 337. 1931 G. W. Gray, K. J. Harrison, J. A. Nash, J. Chem. Soc.; Chem. Commun. 1974,431. 1941 J. Malthete, J. Canceill, J. Gabard, J. Jacques, Tetrahedron 1981,37, 2815. [95] H. Takatsu, K. Takeuchi, Y. Tanaka, M. Sasaki, Mol. Cryst. Liq. Cryst. 1986, 141, 279. [96] B. Scheuble, G. Weber, A. E. F. Wachtler, V. Reiffenrath, J. Krause, R. Hittich, German Patent DE 3 71 1 306, Merck GmbH 1988. 1971 Y. Goto, K. Kitano, T. Ogawa, Liq. Cryst. 1989, 5, 225. 1981 R. Eidenschink, D. Erdmann, J. Krause, L. Pohl, Angew. Chem. 1977,89, 103. [99] M. Petrzilka, MoZ. Cryst. Liq. Cryst. 1985,131, 109. [loo] E. Poetsch, V. Meyer, H. Boettcher, German Patent DE-OS 3 736489,1987, Merck GmbH. [ l o l l H. Sorkin, Mol. Cryst. Liq. Cryst. 1980,56,279. [I021 A. Boller, M. Cereghetti, M. Scbadt, H. Scherrer, Mol. Cryst. Liq. Cryst. 1977,42, 1225. [I031 A. Boller, H. Scherrer, German Patent DE-OS 2 4 15 929,1974, Rocbe AG. [ 1041 S. M. Kelly, Helv. Chim. Actu 1984, 67, 1572. [lo51 T. Kojima, M. Tsuji, S. Sugimori, German Patent DE-OS 3 223 637, 1982, Chisso Corp. [ 1061 S. Sugimori, T. Kojima, Y. Goto, T. Isomaja, K. Nigorikdwa, European Patent EP 119 756, 1984, Chisso Corp. 11071 R. Eidenschink, J. Krause, L. Pohl, German Patent DE-OS 2701 591,1978, Merck GmbH. 11081 R. Eidenschink, J. Krause, L. Pohl, J. Eichler, Liq. Cryst. Proc. Int. Con$ (Ed.: S. Chandrasekhar), Heyden, London, 1980,515. [I091 R. Eidenschink, J. Krause, L. Pohl, US-Pat. 4 229 3 15. Merck GmbH 1980.
229
[I101 S. M. Kelly, M. Schadt, Helv. Chim. Acta 1984,67, 1.580. [ l 1 11 R. Eidenschink, L. Pohl, European Patent Application 14840, Merck GmbH 1980. [ I 121 S. Sugimori, T. Kojima, M. Tsuji, German Patent DE-OS 3 139 130, 1981, Chisso Corp. 11131 Y. Goto, T. Ogawa, S. Sawada, S. Sugimori, Mol. Cryst. Liq. Cryst. 1991,209, 1. [114] M. Romer, R. Eidenschink, J. Krause, B. Scheuble, G. Weber, German Patent DE 3 3 17 597B, Merck GmbH 1984. 11151 H. A. Kurmeier, B. Scheuble, E. Poetsch, U. Finkenzeller, German Patent DE 3 732 284, Merck GmbH 1989. [116] R. Eidenschink, L. Pohl, German Patent DE 3042391, Merck GmbH 1982. [ I 171 S. Sugimori, UK Patent GB 2070593, 1981, Chisso Corp. 11181 M. Schadt, R. Buchecker, A. Villinger, Liq. Cryst. 1990, 7, 519. [119] M. Petrzilka, M. Schadt, European Patent, EP 0122389B, Roche AG. [120] R. Eidenschink, M. Romer, G. Weber, G. W. Gray, K. J. Toyne, German Patent DE-OS 3321373,1983, Merck GmbH. [121] R. Eidenschink, G. W. Gray, K. J. Toyne, A. E. F. Wachtler, Mol. Cryst. Liq. Cryst. (Lett.) 1988,5, 177. [122] R. Eidenschink, Mol. Cryst. Liq. Cryst. 1983, 94, 119. 11231 R. Eidenschink, J. Krause, L. Pohl, German Patent DE-OS 2636684,1978, Merck GmbH. [124] H. Zaschke, German Patent DE 2429093, VEB - W F. [125] M. A. Osman, L. Revesz, MoZ. Cryst. Liq. Cryst. 1980,56, 157. 11261 H. J. Deutscher, B. Laaser, W. Dolling, H. Schubert, J. Prakt. Chem. 1978, 320, 191. 11271 J. P. Van Meter, B. H. Kanderman, Mol. Cryst. Liq. Cryst. 1973, 22, 27 I. [128] R. Steinstrasser, Z. Naturforschung 1972,27b, 774. 11291 S. Sugimori, T. Kojima, M. Tsuji, European Patent EP 62470, 1982, Chisso Corp. [I301 E. Poetsch, V. Meyer, H. Bottcher, German Patent DE-OS 3 736489, Merck GmbH 1989. [131] R. Eidenschink, D. Erdmann, J. Krause, L. Pohl, German Patent DE-OS 2927277, Merck GmbH 1981. 11321 R. Eidenschink, Mol. Cryst. Liq. Cryst. 1985, 123, 57. 11331 R. Eidenschink, L. Pohl, M. Romer, F. del Pino, German Patent DE-OS 2 948 836, 1979, Merck GmbH. (1341 W. H. De Jeu, R. Eidenschink, J. Chem. Phys. 1983, 78,4637. [I351 R. Eidenschink, J. Krause, G. Weber, German Patent DE 3 206 269, Merck GmbH 1983.
Handbook ofLiquid Crystals D. Demus, J. Goodby, G. W. Gray, H.-W. Spiess, V. Vill Copyright 0WILEY-VCH Verlag GmbH. 1998
3.2 Active Matrix Addressed Displays Eiji Kaneko
3.2.1 Thin Film Diode and Metal-Insulator-Metal Matrix Address [1 -201 The simplest way to overcome the scanning limitations encountered in passive matrix liquid crystal display panels is to provide one or more nonlinear circuit elements at the intersection of the gate and data electrodes, thus producing sharper threshold characteristics for each pixel. Presently, diodes and intrinsic nonlinear devices are used for these nonlinear circuit elements.
3.2.1.2 Back-to-back Diode Matrix Address [S- 101 Double threshold characteristics using two diodes which are connected, in series in opposite directions, can be constructed on a planar a-Si layer. Zener breakdown characteristics are used in this connection which is referred to as the back-to-back diode configuration. This connection provides larger threshold voltages in comparison with the diode ring connection. However, it is very difficult to control the Zener breakdown voltage of the diodes precisely.
3.2.1.1 Diode Ring Matrix Address [3-71 The double threshold addressed matrix liquid crystal display panel uses a two-terminal device that accomplished both set and reset functions for each pixel with appropriate signal pulses from the gate electrode drivers. To realize this panel, an amorphous silicon (a-Si) PIN thin film diode (TFD) matrix construction is used. The circuit diagram of a matrix panel addressed by these diodes is shown in Fig. 1 [4]. Each pixel is composed of a pair of diodes and one liquid crystal cell connected in series between a gate electrode bus and a data electrode bus. The diode pair is referred to as a diode ring, because the connection is a ring.
VI
In
I 3 )
-Pixel w
7J
<
e
+ m
-
Diode
ring
W
... m
0
c7
YI
Y2
Data
Ya
electrode
---
YM
buses
Figure 1. Circuit diagram of diode ring matrix addressed liquid crystal display panel.
3.2.1 Thin Film Diode and Metal-Insulator-Metal Matrix Address
23 1
3.2.1.3 Two Branch Diode Matrix Address [l,2, 11-13]
3.2.1.4 SiN, Thin Film Diode Matrix Address [14-691
In the two-branch configuration of Fig. 2, the liquid crystal pixel is charged when the diode is forward biased during the select period. Leakage from the pixel through the diode during the nonselected period is prevented by keeping both diodes reverse biased. One disadvantage of this configuration is that areas of the gate electrode buses are large on the substrate, and as a consequence, the pixel aperture ratio decreases greatly as compared with other diode addressing configurations.
Nonlinear current-voltage (I-V) characteristics can be obtained with a silicon nitride (SIN,) layer. Figure 3 shows across sectional view of a system which consists of metalloff-stoichiometric-SiN,/ITO formed on a glass substrate. The transparent electrode (ITO) film is deposited on the lower glass and photo-etched to form a separate pixel electrode. Afterwards, a SIN, layer is deposited by RF-plasma CVD (chemical vapor deposition). I-V characteristics for a conventional TFD are not completely polarity-symmetric due to differences between the upper and lower SIN, interface barriers. In order to cancel these differences and to obtain symmetric I-V characteristics, the
'
Aperture ratio: the ratio of the actual display area to the occupied area of one pixel in a matrix liquid crystal display panel.
Data v o l t a g e
-Lr
n_._ -u-
Figure 2. Circuit diagram of two-branch diode matrix addressed liquid crystal display panel.
c Upper glass substrate
M e t a l electrode
( C r : 150nrn) ( D a t a electrode bus)
- - - - - - - - - - -
- - -
-
-
(Gate electrode bus) Liquid crystal layer
Transparent p i x e l electrode
SiN,
layer
( IOOnrn)
Lower g l a s s substrate
Figure 3. Cross-section of an SIN, ma. trix addressed liquid crystal display panel.
232
3.2 Active Matrix Displays
Figure 4. An image displayed with the thin film diode switch matrix addressed liquid crystal display panel. (Courtesy of Philips Research Laboratories).
bridge structure TFD was developed. This structure consists of two conventional SiN,TFDs, connected to each other in back-toback series. Figure 4 shows an example of a displayed image obtained on an SiN,-TFD matrix drive liquid crystal display panel. The actual display are has a 10.4 inch diagonal and there are 480 x 1920 pixels.
3.2.1.5 Metal-Insulator-Metal Matrix Address [21-361 Highly nonlinear current-voltage characteristics can be obtained with an anodically formed tantalum pentaoxide (Ta,O,) layer. These characteristics result from the PooleFrenkel conduction mechanism [21, 221.
The characteristics of this layer can be used to drive matrix liquid crystal display panels instead of the SIN, diode device. It is called a metal-insulator-metal (MIM) diode. A serious problem in fabricating the MIM diode addressed matrix liquid crystal display panel which has a large number of gate electrodes is to reduce stray capacitances which are parallel to the MIM diodes. An ingeneously designed lateral MIM diode device which reduces the parallel capcitance is shown in Fig. 5 [27]. This MIM diode is constructed along the fringe of a thin tantalum (Ta) layer. The isolating layer is converted with a chromium (Cr) conducting layer. The obtained lateral sandwich construction of (Ta layer/Ta,O5 isolating layer/Cr) layer shows bidirectional non-
Figure 5. Diagram of lateral metal-insulator-metal diode device.
3.2.2
CdSe Thin Film Transistor Switch Matrix Address
233
Figure 6. An image displayed with the metal-insulator-metal switch matrix addressed liquid crystal display panel. (Courtesy of Seiko-Epson Co. Ltd.).
linear characteristics. The current flowing through this MIM diode flows primarily through the Ta,O, layer, if the polyimide insulator is sufficiently thicker than the Ta,O, layer. An example image displayed on the MIM diode addressed matrix liquid crystal display panel is shown in Fig. 6 [27]. The actual display area is 100x 96 mm. There are 240 gate and 250 data electrodes which provide a resolution of 25 lines cm-'. The contrast ratio obtainable is very high.
3.2.2 CdSe Thin Film Transistor Switch Matrix Address [37-561 Figure 7 (a) shows a top view of a matrix liquid crystal display panel which is addressed with thin film transistor (TFT) switches.
The gate and data electrode buses are located on a glass substrate and separated by a thin isolating layer inserted at their intersection. The rectangular shaped transparent pixel electrode is surrounded by the gate and data electrode buses. A tiny TFT is placed at each intersection of the gate and data electrode buses. Its drain and source electrodes are connected to the data electrode bus and the pixel electrode, respectively. The TFT gate electrode is connected to the gate electrode bus. Thus, each TFT is used to control the optical characteristics of the associated liquid crystal pixel of the matrix. A glass substrate, which has a transparent common electrode on its inner surface, is placed facing this matrix pixel substrate as shown in Fig. 7 (b). A liquid crystal molecular alignment layer is provided on the Glass s u b s t r a t e
Sate electrode
DU
TFT D a t a electrooe
DU
Srorclge capacitor
FTand pixel m a t r i x
loss substrate (a)
Top v i e w of p i x e l p o r t
( b l Cross sectional view of panel
Figure 7. Construction of thin film transistor switch matrix addressed liquid crystal display panel.
234
3.2 Active Matrix Displays
Insulating layer Gate electrode bus Source electrode and p i x e l e l e c t r o d e
D a t a electrode bus and d r a i n electrode
Gate e l e c t r o d e
Semiconductor (Cd S e )
( a ) Top view Semiconductor ( Cd Se 1
-,
Y
G
a
t
e
e lectrode
D o t o electrode bus
a n d d r a i n electrode
Source electrode and p i x e l e l e c t r o d e
Gate electrode bus
Glass substrate
I n s u l a t i n g layer
2 ( b ) Cross s e c t i o n a l view of
A-A'
inner surface of these two substrates. The liquid crystal material is introduced into the space between these glass substrate. Figure 8 shows the construction of an original TFT for the matrix liquid crystal display panel in which a cadmium-selenium (CdSe) TFT is used as the switch. Figure 8 (a) is a top view of the switch structure and its accompanying liquid crystal pixel electrode. Figure 8 (b) shows a cross-sectional view of the switch and pixel electrode. The CdSe semiconductor layer is used as a channel between the drain and source of the TFT.
Figure 9. An image displayed with the CdSe-thin film transistor switch matrix addressed liquid crystal display panel. (Courtesy of Stuttgart University).
Figure 8. Construction of CdSe thin film transistor for addressing a matrix liquid crystal display panel.
Figure 9 shows a black and white image displayed with a CdSe TFT switch matrix addressed liquid crystal display panel [56]. There are 128 gate and 192 data electrodes on this panel.
3.2.3 a-Si Thin Film Transistor Switch Matrix Address The field effect mobility of carriers in the a-Si thin film is very low, owing to many dangling bonds on the surfaces of silicon grains which constitute the film. This problem is significantly lessened by hydrogenization of the a-Si film which decreases the density of dangling bonds from about lo2' cmP3to about 1015cm-3 [57-581. There are two major types of a-Si TFT structures used in matrix liquid crystal display panels presently [59-721. One is a bottom-gate staggered structure and the other is top-gate staggered structure, with the former being more popular. The bottom gate structure is shown in Fig. 10. Several steps are needed for layer deposition and etching to fabricate the bottom-gate staggered structure. They are outlined as follows. First, a metal (sch as Cr) layer is sputtered onto a glass substrate and etched to form a
3.2.3
D a t a e l e c t r o d e bus-
Drain
3N
a-Si Thin Film Transistor Matrix Address
235
Gate e t e c t r o d e b u s
-
I T 0 pixel electrode Source Light s h i e l d l a y e r ( i s not shown
( a ) Top v i e w
Light s h i e t d Layer
D a t a electrode bus n+. 0 - S i l a y e r
i .a-Si layer
1
G a t e e l e c t r o d e Aw/
.”””
IT0 layer %SiNx layer -Glass substrate
( b ) A-n’ c r o s s - s e c t i o n a l view
rectangular gate electrode. To prepare the TFT array, a nondoped a-Si(i . a-Si) layer is deposited as an active layer by a glow discharge technique. Then, a phosphorus doped n+ . a-Si is deposited successively by plasma enhanced CVD. The i . a-Si layer and the n + . a-Si layer are etched into islands. The n+ . a-Si layer is used to prevent holes from being injected. Another metal layer is deposited and etched to form the data electrode bus and pixel contact. After that, an I T 0 layer is deposited and etched to form the pixel electrode. Finally, a passivation layer is deposited onto the layers to protect them. Figure 11 shows the structure of the topgate staggered TFT. Although the top gate
a-Si thin film transistor and pixel in a matrix liquid crystal display panel.
type TFT has many advantages, its application to active matrix liquid crystal displays has been limited for a long time, because of difficulties in making uniform ohmic contacts between a channel and two electrodes. As explained above, the present TFT fabrication requires may complicated steps with many photolithographic processes. To simplify fabrication and increase process yields, a fabrication with fewer mask processes are being developed [73-831. Figure 12 shows the fabrication flow for the two-mask-step a-Si TFT. DC sputtered Cr is deposited onto a substrate glass and patterned to form gate electrodes (a). SIN,, intrinsic amorphour Si (i . a-Si) and phosphorus doped n+ . a-Si are deposited succes-
,D a t a
( a ) C u t a w a y view ( A -A‘)
Figure 10. Construction of bottom-gate staggered
( b ) Top v i e w
e l e c t r o d e bus
lectrode bus
Figure 11. Construction of top-gate staggered a-Si thin film transistor and pixel in a matrix liquid crystal display panel.
236
3.2 Active Matrix Displays
Deposition
(0)
n m ~
Patterning Cr: Gate metal Deposition SIN,: Insulator Deposition 1.a- Si/nta-Si : c hannel
Developing OFPR-800 Patterning a-Si layer
(d 1
Deposition Patterning ITO: Source : Drain : Pixel
(e)
Spin coating photo resist :OFPR-800
Etching (nfa-Si remove) :channel
(f
(
Photo mask is used i n s t e p ( a ) and ( e l
sively by plasma enhanced CVD (b). The photoresist is spin coated and exposed to UV light from the back side of the substrate glass (c). After development of the photoresist, the n+ . a-Si and the i - a-Si are etched away except for the semiconductor layers on the gate electrodes (d). An I T 0 layer is deposited and patterned to form drain, source and pixel electrodes (e). The n+ . a-Si and a part of the i . a-Si are etched by the reactive ion etching method (f). In this way, the twomask-step TFTs is obtained. The SiN, on the gate electrodes to be connected to peripheral driver ICs is etched away after the liquid crystal cell assembly process. In this fabrication flow, the gate electrode is used as a mask for back side exposing light. This method is referred to as a self aligned method and it has been widely investigated as a way to reduce number of masks needed in photolithographic processes. To reduce the TFT area, the self-aligned method is probably the most suitable means of fabricating a large number of TFTs uniformly on a large substrate. And reducing the gate length, which is equal to the channel length, will keep the drain current high even in a small TFT.
)
Figure 12. Fabrication flow for the twomask step a-Si thin film transistor.
Typical values for field effect electron mobility and threshold voltage obtainable with the a-Si TFTs are around 0.6 cm2 V-' s-l and 2-4 V, respectively. The TFT area is usually covered with a black layer mounted on the opposite glass substrate of the liquid crystal panel to shield light, since an a-Si layer is a photosensitive material and a large off leak current flows under the illuminated condition [84-861. Sometimes, a light shield layer is mounted on the TFT as shown in Fig. lO(b). Figure 13 shows an example image displayed with an a-Si TFT addressed liquid
Figure 13. An image displayed with the a-Si thin film transistor switch matrix addressed liquid crystal display panel. (Courtesy of Hitachi Ltd.).
3.2.4
p-Si Thin Film Transistor Switch Matrix Address
237
aV= C G S . 2 V D
c,,+y
CLC
VO
I
Figure 14. Change in source voltage while the gate and drain (data) voltage are being ON/OFF driven.
crystal matrix display panel. There are 640x(480x3) pixels on this 10.4 inch diagonal panel. Figure 14 shows the change in source voltage (V,) while the gate voltage (V,) and drain (data) voltage (V,) are switched [87-891. The pixel must be charged to the drain voltage in a very short gated period of z ~ if ~the ,maximum contrast ratio is required in a displayed image. In order to obtain this condition, resistance of the drain electrode bus must be reduced as low as possible. To reduce the transient voltage drop AV, gate-source capacitance (C,,) must be small enough as compared with pixel capacitance and storage capacitance (CLC+C,). Off resistance of the TFT must be high enough in order to reduce the pixel voltage drop owing to leakage current during the unselected period of z ~ ~ ~ . Sometimes pixels are divided into two domains in which liquid crystal molecules are aligned differently [90-931. This divided domain TN mode can offer symmetric viewing-angle characteristics, since the two domains mutually compensate for the asymmetric viewing characteristics in the vertical direction. Thus, very wide viewing angles can be obtained for the image displayed with this panel. A huge number of TFTs must be mounted on high definition, large area liquid crys-
tal display panels. Many defective TFTs are apt to be present among them, which causes faults in the image on the panel. To prevent the faults, two TFTs are sometimes used for driving one pixel to increase redundancy [94]. For the same purpose, a butterfly drains architecture have been examined [95,96].
3.2.4 p-Si Thin Film Transistor Switch Matrix Address Field effect mobility of carriers in an a-Si layer is not high enough to apply a-Si TFTs as the gate and data electrode bus drivers for matrix liquid crystal display panels on which quick moving images are displayed. The field effect mobility can be increased if the a-Si layer is changed into a polycrystalline silicon (p-Si) layer, because the mean free path of the carriers can be increased in the latter. Furthermore, photo current of the p-Si TFT is lower than that of the a-Si TFTs, but it requires a quartz or high temperature glass substrate because of its high temperature fabrication processes [97, 981. There are two major methods which are presently -being used to producq the p-Si layer.
238
3.2
Active Matrix Displays
Electron mobility of more than 100 cm2 V-' sC1 can be obtained with this method. Figure 16 shows an example displayed image on the p-Si TFT addressed matrix liquid crystal display panel. There are 6 4 0 x 4 8 0 ~ 3pixels on this panel. The display area is 5 inches diagonal.
3.2.4.1 Solid Phase Crystallization Method [99-1191 A schematic cross-sectional view of the TFT and associated pixel electrode structure is shown in Fig. 15, which employs a conventional coplanar structure TFT with a double gate. Fabrication is done by the following procedure. First, the a-Si layer is deposited by low pressure chemical vapor deposition (LPCVD) on a substrate. Following photolithographic formation of the a-Si channel, the substrate is furnace annealed to convert the a-Si to p-Si through solid phase crystallization. An SiOz layer is deposited by atmospheric pressure chemical vapor deposition (APCVD). Chromium is then deposited and patterned to form the gate electrodes. After insulator deposition of SiO,, contact holes are opened photolithographically. Finally, TFT fabrication is completed by deposition and patterning of the I T 0 pixel electrode and the aluminum data electrode bus. The fabrication process required no hydrogenization step and has a maximum temperature of 600 "C which makes it ideal for low cost glass substrates.
I n s u La tins
Layer (Si 0,)
-,
3.2.4.2 Laser Recrystallization Method [120-1331 Figure 17 shows a cross-sectional view of the pixel constructed from a laser recrystallized p-Si TFT and I T 0 electrode. The fabrication process is as follows. After deposition of polysilicon by LPCVD, phosphorus ions are implanted in order to determine the threshold voltage. A finely focused CW argon laser beam was scanned on the layer. Successive fabrication steps are carried out by the standard N-channel MOS LSI technology. The pixel electrode is formed with the I T 0 layer. Usually, the gate and data driver circuits are mounted on the periphery of the p-Si TFT switch matrix addressed liquid crystal display panel.
G -/a et
electrodes P i x e l electrode (IT01
Dota electrode b u s p-Si layer
Lass substrate
( a ) C r o s s sectional view
/////////,-
Gate eiectrode bus
Drain contoctSource c o n t a c t -Pixel e l e c t r o d e Data e l e c t r o d e
(b)
Top view
Figure 15. Construction of a solid phase recrystallized p-Si thin film transistor and pixel for matrix liquid crystal display panel.
3.2.5 G l a s s substrate
Metal-oxide Semiconductor Transistor Switch Matrix Address
A
L i a h t schield /
-Color ,~
:TO
.ayer
239
\
\
~
’
,
-/--
.
\
- --
filter
A . anment .ayer
-Liquid
crystal
I gnment
“‘!‘~ITo
//
Glass substrate
”‘p-si
ibyer
Electron mobility of 320 cm2 V-‘ s-l is obtained, and the ON-OFF current ratio is about 10’. An XeCl excimer laser crystallization method is also very effective for field effect mobility enhancement of TFTs.
3.2.5 Metal-oxide Semiconductor Transistor Switch Matrix Address For driving matrix liquid crystal display panels, the silicon metal-oxide semiconductor field effect transistor (MOSFET) fabricated on a silicon monolithic wafer has been investigated by several groups [134-1501. The MOS transistor circuit fabrication techniques are well developed and have been used to produce various LSI devices. A dynamic scattering mode, a planar type GH mode or a polymer dispersed (PD) mode are used in these displays because the silicon wafer is intrinsically opaque. The circuit configuration of the panel is essentially the same as that of the p-Si TFT switch matrix addressed liquid crystal display panel as shown its equivalent circuit in Fig. 18(a). The physical arrangement of a prototype matrix liquid crystal display panel is shown in Fig. 18(b). Within the square area formed
//
layer
Layer
Figure 17. Construction of a laser recrystallized p-Si thin film transistor addressed liquid crystal pixel.
by the intersections of two adjacent gate electrode buses and two adjacent data electrode buses, there is an MOS transistor and a pixel. The MOS transistor source electrodes also serve as the pixel electrode. The pixel parts are usually sputtered with a white metal layer in order to obtain good diffused reflection of light. Reflective type MOS transistor drive liquid crystal display is being studied as an image mirror-cell of the liquid crystal projection TV display. In this cell, a PD mode is adapted to change cell light reflectivity. Figure 19 shows a projected picture on a 75 inch screen using the PD mode MOS transistor addressed liquid crystal display cell. The display area of the cell is 2.0 inch diagonal and the number of pixels is 640 x 480 x 3 [ 1501.
240
3.2 Active Matrix Displays
Figure 16. An image displayed with the solid phase recrystallized p-Si thin film transistor switch matrix addressed liquid crystal display panel. (Courtesy of SeikoEpson Co. Ltd.).
MOS transistor
Storage capacitor
Data electrode bus Gate electrode b u s
(a)
Equivalent
circuit
(b) M a t r i x MOS t r a n s i s t o r chip
3.2.6
Figure 19. An image displayed with the metal-oxide semiconductor thin film transistor switch matrix addressed liquid crystal display panel. (Courtesy of Hitachi Ltd.).
Figure 18. Metal-oxide semiconductor transistor switch matrix addressed liquid crystal display panel and its equivalent circuit.
References
[l] J. A. van Raalte, Proc. IEEE 1968, 56, 21462149. [2] G. J. Lechner et al., Proc. IEEE 1971,59, 15661579. [3] D. G. Ast, IEEE Trans. Electr. Dev. 1983, ED-30,532-539. [4] S. Togashi et al., SID 84 Digest 1984,324-325. [5] S. Togashi et al., Eurodisplay '84 1984, 141144. [6] S. Togashi et al., Proc. SID 26 1985,9-15. [7] K. H. Nicholas et al., Eurodisplay '90 1990, 170-173. [8] N. Szydlo et al., J. Appl. Phys. 1982, 53, 5044-505 1. [91 N. Szydloet al.,jpn. ~ i'83 1983,416418. ~ ~ [lo] T. Sat0 et al., SID 87 Digest 1987, 59-62. [l 11 Z. Yaniv et al., SID 86 Digest 1986, 278-280.
l
3.2.6 I121 K. E. Kuijk, Eurodisplay '90 1990, 174-177. [13] R. Hartman et al., SID 91 Digest 1991,240-243. [ 141 M. Suzuki et al., Japan Display '86 1986, 7274. [I51 J. W. Osenback, W. B. Knolle, J. Appl. Phys. 1986,60, 1408-1416. [16] K. Ohira et al., Japan Display '89 1989, 452455. [ 171 Y. Hirai et al, SID 90 Digest 1990, 522-525. [18] E. Mizobata et al., SID 91 Digest 1991, 226229. [19] A. G. Knapp IDRC Rec. '94 1994, 14-19. [20] J. M. Shannon et al., IDRC Rec. '94 1994, 373-376. [21] J. G. Simmons, Phys. Rev. 1967,155, 657-666. [22] H. Matsumoto et al., Jpn. J. Appl. Phys. 1980, 19,71-77. [23] D. R. Baraffet al.,SID80Digest1980,200-201. [24] D. R. Baraff et al., Tech. Dig. Int. Electron Devices Meeting 1980, 707-710. [25] D. B. Baraff et al., IEEE Trans. Electr. Dev. 1981, ED-28,736-739. [26] R. W. Streater et al., SID 82 Digest 1982, 248-249. [27] S. Morozumi et al., Japan Display '83 1983, 404-407. [28] K. Niwa et al., SID 84 Digest 1984, 304-307. [29] R. L. Wisnieff, IDRC Rec. '88 1988, 226-229. [30] H. Aruga et al., Japan Display '89 1989, 168171. [31] V. Hochholzer et al., SlD 90 Digest 1990, 526529. [32] V. Hochholzer et al., Eurodisplay '90 1990, 1 82- 1 85. [33] K. Aota et al., SID 91 Digest 1991, 219-222. [34] K. Takahashi et al., IDRC Rec. '91 1991, 247250. [35] V. Hochholzer et al., SID 92 Digest 1992,5 1-54. [36] V. Hochholzer et al., SID 94 Digest 1994, 423425. [37] A. G. Fischer et al., IEEE Conf. Record of 1972 Conf. on Display Devices 1972,64-65. [38] T. P. Brody et al., IEEE Trans. Electr. Dev. 1973, ED-20,995-1001. [39] T. P. Brody, F. C. Luo, SID Intr. Symp. Tech. Papers 1974, 166-167. [40] T. P. Brody et al., IEEE Trans. Electr. Dev. 1974, ED-22,739-749. [41] A. G. Fischer, Electr. Lett. 1976, 12, 30-31. [42] F. C. Luo et al., SID 78 Digest 1978, 94-95; Proc. SID 1978, 19,63-67. [43] J. C. Ershine, P. A. Snopko, IEEE Trans. Electr. Dev. 1979, ED-26, 802-806. [44] A. Van Calster, Solid State Electr. 1979, 22, 77-80. [45] T. P. Brody, P. R. Malmberg, Inr. J. Hybrid Microelectron. 1979, 2, 29-38. [46] W. Frash et al., Freiburger Arbeitstagung Flussigkristalle 1980, 20, 1-9.
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[47] F. C. LUO,W. A. Hester, IEEE Trans. Electr. Dev. 1980, ED-27,223-230. [48] F. C . Luo et al., IEEE Trans. Electr. Dev. 1981, ED-28,740-743. [49] F. C. Luo, D. Hoesly, SID 82 Digest 1982, 46-47. [50] A. G. Fischer et al., IDRC Rec. '82 1982, 161165. [ S I ] F. C. Luo, SZD 83 Digest 1983, 184-185. [52] T. P. Brody, IEEE Trans. Electr. Dev. 1984, ED-31, 16 14-1 628. [53] P. R. Malmber et al., SID 86 Digest 1986, 281284. [54] A. Van Calster et al., Japan Display '89 1989, 408-4 11. [55] J. De Baets et al., IDRC Rec. '91 1991, 215218. [56] D. Lueder, IDRC Rec. '94 1994, 30-38. [57] M. Milleville, W. Fuhs, Appl. Phys. Lett. 1979, 34, 173-174. [58] P. G. Le Comber et al., Electron. Lett. 1979, 15, 179-1 8 1. [59] H. Hayama, M. Matsumura, Appl. Phys. Lett. 1980,36,754-755. [60] A. J. Snell et al.,Appl. Phys. 1981,24,357-362. [61] A. I. Lakatos, IDRC Rec. '82, 1982, 146-151; Proc. SID 1983,24, 185-192. [62] D. G. Ast, IDRCRec. '82 1982,152-160; Proc. SID 1983,24, 192-198. [63] Y. Ugai et al., SID 84 Digest 1984, 308-3 1 1. [64] T. Snata et al., Proc. SZD 1986,27, 235-238. [65] S. Hotta et al., SID 88 Digest 1986, 296-297. [66] T. Ukawa et al., Japan Display '89 1989, 506-509. [67] Y.Nanno et al., SID 90 Digest 1990,404407. [68] T. Wada et al., Eurodisplay '90 1990, 370-373. [69] T. Yanagisawa, SID 93 Digest 1993,735-738. [70] A. Lewis et al., SID 94 Digest 1994, 251-254. [71] F. R. Libsch, H. Abe, SID 94 Digest 1994, 255-258. [72] W. E. Howard, IDRC Rec. '94 1994, 6-10. [73] S. Kawai et al., Proc. SID 1984, 25, 21-24. [74] Y. Nasu et al., SID 86 Digest 1986, 289-292. [75] Y. Lebosq et al., IDRC Rec. '85 1985, 34-35. [76] H. Tanaka et al., SID 87 Digest 1987, 140-142. [77] Y. Miyata et al., SID 89 Digest 1989, 155-158. [78] M. Akiyama et al., SlD 91 Digest 1991, 10-13. [79] N. Hirano et al., Japan Display '92 1992, 213216. [80] J. Gluck et al., Eurodisplay '93 1993, 203-206. [ 8 1 ] Y. Chouan et al., Eurodispluy '93 1993, 207-2 14. [82] J. Glueck et al., SZD 94 Digest 1994, 263-266. [83] N. Hirano et al., IDRC Rec. '94 1994, 369372. [84] S . Kawai et al., SID 82 Digest 1982, 42-43; Proc. SID 1982,23,219-222. [85] K. Suzuki et al., SID 83 Digest 1983, 146147.
242
3.2 Active Matrix Displays
[86] M. Ikeda et al., Japan Display '83 1983, 352354. [87] Y. Miyataet al., SID 88 Digest 1988,314-317. 1881 K. Suzuki, SID 92 Digest 1992, 39-42. [89] N. Nakagawa et al., SID 92 Digest 1992,781784. [90] K. H Yang, IDRC Rec. '91 1991,68-79. [91] Y. Tanaka et al., SID 92 Digest 1992,43-46. [92] Y. Koike et al., SID 92 Digest 1992,798-801. [93] T. Suzuki et al., SID 94 Digest 1994,267-270. [94] Y. Matsueda et al., SID 89 Digest 1989, 238241. [95] N. Bryeret al., JapanDispluy '86 1986,80-83. [96] J. F. Clerc et al., Japan Display '86 1986, 84-87. [97] M. Matsui et al., Appl. Phys. Lett. 1980, 37, 936-937. [98] F. Morin et al., Eurodisplay '81 1981,206-208. [99] A. Juliana et al., SID 82 Digest 1982, 38-39. [loo] T. Nishimuraet al.,SID82 Digest 1982,36-37; Proc. SZD 1982,23,209-213. [loll M. Matsui et al., J. Appl. Phys. 1982,53,995998. [lo21 S. Morozumi et al., SID 83 Digest 1983, 156157. [I031 M. Matsui et al., Jpn. J. Appl. Phys. 1983, 22 (Suppl. I), 497-500. [lo41 S. Morozumi et al., SID 84 Digest 1984, 316319. [lo51 S. Morozumi et al., SID 85 Digest 1985, 278281. [ 1061 N. Bryeret al.,Japan Display '86,1986,80-83. [lo71 S. Morozumi et al., Japan Display '86, 1986, 196- 199. [108] J. Ohwada et al., SZD 87 Digest 1987, 55-58. [lo91 S. Aruga et al., SID 87 Digest 1987, 75-78. [110] H. Ohshima et al., SID 88 Digest 1988, 408411. [ l l l ] J. Ohwada et al., IDRC Rec. '88 1988, 215219. [112] M. Takabatake et al., Japan Display '89,1989, 156-159. [113] K. Nakazawa et al., SID 90 Digest 1990,311313. [114] R. G. Stewart et al., SID 90 Digest 1990, 3 19-322. [115] U. Mitra et al., IDRC Rec. '91 1991,207-210. [116] T. W. Little et al., IDRC Rec. '91 1991, 219222. 11171 Y. Matsueda et al., Japan Display '92 1992, 56 1-5 64. [I 181 H. Ohshima et al., SID 93 Digest 1993, 387390.
[119] S. Chenet al., Eurodisplay '93 1993, 195-198. [120] A. F. Tasch Jun et al., Electron. Lett. 1979,15, 435-437. [121] T. I. Kanins et al., IEEE Trans. Electr. Dev. 1980, ED-27, 290. [I221 A. Ishizu et al., SID 85 Digest 1985, 282-285; Proc. SID 1985,26,249-253. [I231 E.Kaneko, Ext. Abs. of 1990 Int. Conf. on SSDM 1990,937-940. [I241 Y. Mori et al., SID 91 Digest 1991, 561-562. [125] S. Okazaki et al., SID 91 Digest 1991, 563564. [126] H. Hayama et al., SID 91 Digest 1991, 565566. [ 1271 H. Asada et al., IDRC Rec. '91 1991,227-230. [128] M. Kobayshi et al., SID 94 Digest 1994, 7578. [129] M. Matsuo et al., SID 94 Digest 1994, 87-90. [I301 H. Ohshima, IDRC Rec. '94 1994,26-29. [131] T. Hashizume et al., IDRC Rec. '94 1994,418421. [I321 A. Lewis et al., SID 94 Digest 1994,251-254. [133] K. Suzuki, SID 92 Digest 1992,3042. [I341 L. T. Lipton, SID 73 Digest 1973,44117. [135] M. N. Ernstoff, SID Technical Meeting Paper 1975, 1-9. [136] C. P. Stephens, L. T. Lipton, SID 76 Digest 1976,44-45. [137] L. T. Lipton et al., SID 77 Digest 1977,6445. [I381 L. T. Lipton et al., SID 78 Digest 1978,96-97. [139] M. N. Ernstoff, Proc. SID 1978, 19, 169-179. [140] K. Kasahara et al., 1980 Biennial Display Research Conf. Rec. 1980, 96-101; Proc. SID 1981,22,318-322. [141] M. Pomper et al., IEEE J. Solid-State Circuits 1980, SC-15,328-330. [142] T. Yanagisawa et al., SID 81 Digest, 1981, 110-112. [143] W. A. Crossland, P. J. Ayliffe, SID 81 Digest 1981, 112-113; Proc. SID 1982,23, 15-22. [144] M. Hosokawa et al., SID 81 Digest 1981, 114115. [145] K. Kasahara et al., SID 83 Digest 1983, 150151. [146] S. E. Shield et al., SID 83 Digest 1983, 179179. [147] K. Kasahara et al., Japan Display '83 1983, 408-411. [148] J. P. Salemo, SID 92 Digest 1992,63-66. [I491 J. P. Salemo, IDRC Rec. '94 1994, 39-44. [I501 T. Nagata et al., Tech. Rep. of IEICE, EID 9477,1994,97-101.
Handbook ofLiquid Crystals D. Demus, J. Goodby, G. W. Gray, H.-W. Spiess, V. Vill Copyright 0WILEY-VCH Verlag GmbH. 1998
3.3 Dynamic Scattering Birendra Bahadur
3.3.1 Introduction and Cell Designing The dynamic scattering effect is observed in nematic liquid crystals having low to moderate conductivity (resistivity < 10" ohms cm) and with mainly negative dielectric anisotropy. In the off mode and below a threshold voltage Vthw, the cells remains clear. When the voltage is increased beyond Vthw, striped patterns [ 1, 21 called Williams domains appear. On further increasing the voltage, these regularly shaped patterns are destroyed, giving way to a turbulent state called dynamic scattering [3, 41. Although the credit for discovering the dynamic scattering mode (DSM) and conceiving its electrooptical applications goes to Heilmeier et al. in 1968 [3, 41, a similar effect was reported much earlier in 1918 by Bjornstahl [ 5 ] . The dynamic scattering mode resulted in the first successful commercial application of liquid crystals in emerging flat panel display technology [6]. This in turn revitalized the scientific and technical interest in liquid crystals. The DSM effect and Williams domains are part of electrohydrodynamic instability, as these involve fluid motion. The physics of the DSM is still not fully understood because of its complex nature, and many of its effects are explained
on the basis of Williams domains, which are very well understood. The dynamic scattering effect is a classic example of chaos [7]. Electrohydrodynamic effects and DSM are summarized briefly here due to a shortage of space. For a detailed description, the reader is advised to read the review articles by Goossens [8], Dubois-Violette et al. [9] Bahadur [lo], Chandrasekhar [ l I ] and de Gennes and Prost [12]. In DSM cells, nematic liquid crystals of negative dielectric anisotropy with positive conductivity anisotropy are used. The LC (liquid crystal) mixture should have high birefringence, low viscosity, and a wide temperature range. The resistivity of the material should be about 10'- lo9 Ohms cm, which can be achieved intrinsically using materials such as Schiff bases or by doping the material with organic salts such as ternary amines, pyridinium salts, or HMAB (hexamethylaminobromide) [ 10, 131. The liquid crystal mixtures used were mainly composed of Schiff bases, azoxy, and esters [ 141. Dynamic scattering is usually not observed in very thin cells ( 4 5 pm). A cell gap of -10-30 pm is preferred. Cells are made with either homogeneous or homeotropic surface alignment [ 10, 151 for uniformity, although surface treatment is not essential to show DSM effects. For reflective mode,
244
3.3 Dynamic Scattering
Glass plates
Edge sealant
Tra nspa r e nt >conducting electrode pattern
Gasket
1 Liquid crystal
Reflector
a metallic reflector is used. Sometimes this reflector is put inside the cell to reduce double imaging and to form the back electrodes. The reactive nematic materials are separated from these electrodes by applying a nonconductive alumina or Si02 coating. A dynamic scattering mode cell is shown in Fig. 1.
3.3.2 Experimental Observations at DC (Direct Current) and Low Frequency AC (Alternating Current) Fields DSM cells exhibit the following sequence of regimes with an increasing DC or low frequency AC voltage. For simplicity, let us assume that glass plates were treated for unidirectional homogeneous alignment in the x direction.
3.3.2.1 Homogeneously Aligned Nematic Regime At low voltages (-1 V), the molecules are aligned normal to the electric field and therefore parallel to the glass plates, as expected for a material of negative dielectric anisotropy. In this regime we have a nematic single crystal.
3.3.2.2 Williams Domains When the rms (root mean square) voltage reaches a critical threshold Vthw ( - 5 V), a periodic distortion of nematic alignment is
Figure 1. Schematic diagram of a dynamic scattering mode LCD.
observed [S-12, 16-29]. Usually it is a simple one-dimensional type of distortion, as was.first observed by Williams [l]. A similar phenomenon was also independently reported by Kapustin and Larionova [2]. This perturbed state, observed only above a well-defined threshold, V,, at low frequencies, is optically characterized by regular parallel striations perpendicular to the original direction of the director. The separation between the parallel strips is approximately equal to the thickness of the liquid crystal layer, d, or cell gap. This domainpattern (Fig. 2) is known as the Williams domain mode (WDM). The visible domain pattern is closely connected with the existence of a regular pattern of cellular or vortex fluid motion that can be observed by means of tracer dust particles. A schematic drawing of the flow pattern is given in Fig. 3a. Vortices extend in the y direction and the fluid motion is antiparallel in adjacent cells. The periodicity of motion, A,, is roughly equal to 2 d. The hydrodynamic motion is not visible directly, but becomes manifest due to the anisotropy in the refractive indices of the liquid crystal. When the sample is illuminated from the bottom, an observer above the sample sees a series of bright domain lines extending in they direction. Two sets of domain lines can be observed by focusing the microscope on the top and bottom of the cell, respectively. The lines are shifted over about half of their spacing when the focal plane is moved down to the bottom of the surface plane. The pattern is only visible for light polarized in the
3.3.2
Experimental Observations at DC and Low Frequency AC Fields
245
Figure 2. Domain pattern in p-azoxyanisole (PAA) observed in transmission. A 38 pm sample has been subjected to a 7.8 V driving voltage at 130"C.The rubbing direction (x) is horizontal and the voltage is applied perpendicular ( z ) to the page. The microscope is focused near the top electrode and has a & 10 pm depth of focus. The top set of bright domain lines are visible and have a spacing of 31 pm or 4 1 2 . When the microscope is focused at the bottom of the sample, another set of bright domain lines are visible. Several dislocations are visible in the domain patterns, as are many particles of dust, some badly out of focus. After Penz [19].
( C )
Figure 3. (a) Flow and (b) orientational patterns of Williams domain [ I I , 191; (c) light focusing by the periodic orientational pattern of a nematic liquid crystal. The molecular arrangement in mid layer is represented by line MM'. Plane parallel light is sent through the bottom plate. The initial wave front S is flat [12].
246
3.3 Dynamic Scattering
x direction, which is perpendicular to the domain walls, implying that the director is located in the plane xz, perpendicular to the wall. The director pattern, as deduced from the domain lines, is given in Fig. 3 b. The domain lines above the sample are the real images of the light source below the sample [ 191. The bottom lines are the virtual images. Figure 3 c shows the light focusing and formation of Williams domains strips. With light polarized in the x direction, the sample may be used as a periodic grating. At low frequency, the distortion in molecular alignment is static, the pattern remaining the same with the field reversal. The threshold voltage is usually a few volts and is practically independent of the sample thickness. However, it is strongly dependent on the frequency. There is a cutoff frequency f,(=0,/2n) above which Williams domains do not appear. The cutoff frequency,
f,, increases with the conductivity of the sample. The regions below and above the f, are called the conduction and dielectric regimes, respectively. Below f,, i. e., in the conduction regime, the regular Williams domain pattern becomes unstable at about twice the threshold voltage, Vth,and the medium goes over to dynamic scattering mode. Abovef,, i. e., in the dielectric regime, another type of instability called the chevron pattern is observed. Figure 4 shows the conduction and dielectric regime for p-methoxybenzylidene-p-n-butylaniline (MBBA).
3.3.2.3 Dynamic Scattering When the voltage V is increased above Vt, in the conduction regime, the distortion amplitudes and the associated flow velocities increase. Finally, at some higher voltage, Vthd, which is roughly 2 Vthwf a new regime
/*'
("')
200
400
Frequency ( Hz )
600 -3
Figure 4. Threshold voltage V,, of the AC instabilities for MBBA. Region I conduction regime (Williams domains); Region I1 - dielectric regime (chevrons). Full line from DuboisViolette, de Gennes, and Parodi model. After Orsay Liquid Crystal Group [17,23].
3.3.4 Theoretical Explanations
247
is observed [lo-12, 25-29] with the following characteristics: The Williams domains become completely disordered and mobile - the flow is turbulent - the long range nematic alignment is completely upset, and - the nematic layer scatters the light very strongly -
This new fluctuating disordered state can be observed in normal light without any specific polarization, implying that the molecules are no longer confined to the xz plane. Microscopic observations also show a number of disclination loops nucleating near the limiting surface. In this mode, the molecular motions are turbulent and the light is scattered strongly. The turbulent liquid crystal contains violently moving birefringent regimes several micrometers in size, and the diffuse optical scattering comes from the irregular refractive index gradients that are present. In a display, the activated areas look milky white on a clear, nonactivated background. DSM mode also depolarizes the polarized light.
3.3.3 Observations at High Frequency AC Field The optical pattern of the perturbed state in the high frequency ( f > f c ) region is characterized by periodic parallel striations of a much shorter period (a few micrometers) than the Williams domains [23]. Above the threshold, these striations move, and bend and give rise to what has been called a chevronpattern(Fig. 5 ) [8-12,17,23-261. In this regime, the threshold is determined by a critical field rather than a critical voltage. The threshold field strength increases with the square root of the frequency. The spatial periodicity of the chevron pattern is also frequency dependent; it is
Figure 5. Chevron pattern. After de Gennes [ 121.
found to depend inversely on the square root of the frequency. The relaxation time of the oscillating chevron pattern is very short, of the order of a few milliseconds, while that of the stationary Williams domain is 100 ms for a 25 pm thick sample. The oscillatory domain regime is therefore sometimes called a fast turn off mode [ 1 1,12,30]. This regime is also called a dielectric regime, as space charges are not able to followthefieldinthisregime[lO-l2,28].The chevron pattern also gives way to turbulence at about twice the threshold field. An applied magnetic field parallel to the initial orientation of the director increases the threshold voltage in the conduction regime, but has no effect on the dielectric regime except to increase the spacing between the striations.
-
3.3.4
Theoretical Explanations
The basic mechanism for electric field induced instabilities is now very well understood in terms of the Carr-Helfrich model based on field induced space charges due to conductivity and dielectric anisotropies [ 16, 3 I]. Helfrich [ 161 made derivations for only DC fields, which were further extended to AC fields by Dubois-Violette and co-
248
3.3 Dynamic Scattering
workers [17, 181. Another somewhat accepted model, applicable only to DC fields, is the Felici model [32], which is based on charge injection in the liquid crystal and not on its dielectric and conductivity anisotropies. DC and low frequency AC voltages produce electrohydrodynamic instabilities in the isotropic phase of liquid crystals also, the threshold being comparable to that in the nematic phase. The Felici model is applicable only for DC fields. When the frequency becomes more than llt, (usually 10 Hz), where t, is the transit time of the ions, charge injection does not take place, showing that this is not the primary mechanism for AC field instabilities in the nematic phase.
-
3.3.4.1 Carr - Helfrich Model The current carriers in the nematic phase are ions whose mobility is greater along the preferred axis of the molecules than perpendicular to it. Because of conductivity anisotropy, space charges will accumulate with signs as shown in Fig. 6 at the distortion maxima and minima. The applied field acts on the charges to give rise to material flow in alternating directions, which in turn exerts a torque on the molecules. This is reinforced Ez
t
/
by the dielectric torque due to the transverse field created by the space charge distribution. The torque increases with an increase in the electric field. With increasing field, the torque may offset the counterbalancing normal elastic and dielectric torques, and the system may become unstable. The resulting cellular flow pattern and director orientation are sketched in Fig. 3. Based on this physics, Helfrich developed the theoretical model for Williams domains and explained most of the experimentally observed phenomena [lo- 12, 16,28, 311. He calculated the threshold voltage for Williams domains, V,,
K33
(1)
<
and is a dimensionless quantity called the Helfrich parameter [ 10, 11, 231 given by
where ql, and ol,, 0, are the dielectric constants and electrical conductivity (11, I) respectively, Al and ;tZ are the shear coefficients, A& is the dielectric anisotropy, and qois a function of the viscosity coefficients. The quantity (C2-1)A& is also called the Helfrich parameter by some authors. This equation shows that the threshold of Williams domains is independent of the thickness. must be more than 1 in order to obtain an instability. The results of the Helfrich theory have been verified experimentally by several workers [ l 1,12,28,33, 341. Earlier it was thought that Williams domains could only be observed in materials
<’
Figure 6. Charge segregation in the applied field E, as caused by a bend fluctuation in a nematic of positive conductivity anisotropy. The resulting transverse field is Ex.
(z)
(=)
where V t= - 4 7c3
249
3.3.4 Theoretical Explanations
having negative dielectric anisotropy. However, Blinov [28] and de Jeu et al. [35-381 showed that Williams domains can also be observed in materials having positive dielectric anisotropy. They showed that the Carr-Helfrich theory is capable of explaining this fact. In calculating the threshold voltage, Helfrich assumed that the spatial periodicity of the fluid deformation was proportional to the thickness of the cell. Penz and Ford [ 19 - 2 1] solved the boundary value problem associated with the electrohydrodynamic flow process. They reproduced Helfrich’s results and showed several other possible solutions that may account for the higher order instabilities causing turbulent fluid flow.
3.3.4.2 Dubois-Violette, de Gennes, and Parodi Model
Low Frequency or Conduction Regime
17, 181. The equation also shows that the threshold voltage is independent of the thickness of the cell and increases with an increase in the frequency, finally becoming very large on approaching the cut-off frequency, oc, where
The theoretical curve using Eq. ( 3 ) is in good agreement with the experimental results on MBBA. Williams domains are stable below o,and are not observed above 0,. From Eq. (3) we find that the relaxation frequency (l/z) increases linearly with the conductivity, which agrees with the experiments. In the low frequency regime (a5 o,), charges oscillate but domains or molecular patterns remain stationary. Therefore, this regime is also called the conduction regime.
High Frequency or Dielectric Regime
The Helfrich theory was extended by Dubois-Violette, de Gennes, and Parodi [ 171 to cover the AC field. The geometrical conditions are still the same. In the distorted state, the molecules are deflected by a small angle @ in the xz plane. The most important parameter from the point of view of charge accumulation is not exactly @, but rather the curvature ty=d$/dx of the molecular pattern; ty and the charge density, q , are used as fundamental variables. Their calculation yielded the threshold voltage Vthw
When o reaches the cut-off frequency the threshold field becomes very large, oT reaches -1 and the curvature ty becomes time dependent; hence the low frequency calculations are not valid
where E and q are a suitable combination of the dielectric and viscosity coefficients, K,, is the bend elastic constant, and T is the decay or relaxation time of the curvature ty. Equation ( 5 ) concludes that the threshold field, E,, -o”* E, is thickness-independent, i. e., the phenomenon is field-dependent rather than voltage-dependent - the spatial period of striations .n/k 1 / 6 -
(3) with zthe dielectric relaxation time and w the angular frequency. With very low frequency or oz=O, Eq. ( 3 ) reduces to Helfrich Eq. ( 1 ) [8- 12,
-
In the high frequency regime (a> a,), the molecular pattern oscillates while the charges are static; for this reason, the regime
250
3.3
Dynamic Scattering
is often called a dielectric regime. It is also called the fast turn off, i. e., if AC voltage is turned off from slightly above V, to 0, the striation pattern disappears rapidly. A simple explanation is that the relaxation time in zero field ( T =q/K,, k 2 ) in the Dubois-Violette et al. model is very small due to the large value of the wave vector k. The Carr-Helfrich theory and its extension to AC field by the Orsay group have been verified experimentally by several workers and they found good agreement with the theory [8-12, 16-28, 33, 34, 39 -411. Besides the above-mentioned theories, attempts have been made by other workers [41-431. Some of these are beautifully reviewed by Goosen [8], DuboisViolette et al. [9], Chandrasekhar [ l 11, and Blinov [28].
3.3.5 Dynamic Scattering in Smectic A and Cholesteric Phases It has been observed that a homeotropically aligned appropriate SmA material with +A& exhibits dynamic scattering on the application of a suitable voltage [44-471. In Carr - Helfrich nematic electrohydrodynamic instability, the conduction and dielectric forces are usually required to be orthogonal to each other and the usual nematic materials exhibiting dynamic scattering are of -A& and +AD. Therefore, for SmA material with +A&, we require -AD. Fortunately, the smectic geometry provides this configuration as, contrary to nematics, the ions would move faster in the direction of the smectic layer compared to that perpendicular to it. A net negative conductive anisotropy is achieved either by doping SmA with ions or electric field dissociation of impurities. In the homeotropically aligned SmA state, the cell is clear in the quiescent mode. On application of a low frequency electric
field, it is converted to a turbulent light scattering state. When the field is removed, the scattering texture persists for a long period, but the intensity decreases slightly. By applying a high frequency electric field or a low frequency rms voltage less than the threshold voltage for scattering, the scattering can be erased. The cell becomes clear as the molecules adopt homeotropic texture due to dielectric orientation. The initial and final stages consist of homeotropically arranged molecules, whereas the scattering state consists of small focal conic groups (scattering centers) which are continuously agitating in the presence of a field. These displays have a very long memory and a wide viewing angle. However, they did not become popular due to high voltage (-100- 150 V) addressing, the need of special drivers, and the advent of supertwisted nematic and ferroelectric LCDs. A scattering effect similar to dynamic scattering has been observed in long pitch cholesterics with negative dielectric anisotropy [48]. Electrohydrodynamic instabilities in planar cholesteric texture leading to periodic grid type patterns have been reported in both negative and positive dielectric anisotropy materials [36, 49-53]. On further increasing the voltage, the grid structure is distorted to form a strong scattering state, which persists long enough even after the removal of the field. The scattering texture is approximately the same, i.e., focal conic texture with randomly distributed helix axes, as observed in the field-induced nematic -cholesteric transition of a long pitch cholesteric with positive dielectric anisotropy, although the mechanism for producing the scattering state is quite different. In this mode, randomly oriented focal conic textures are created due to the turbulent motion of the fluid, similar to dynamic scattering. The effect is used in storage mode devices [24, 48, 54, 551. The light scattered in stor-
3.3.6
25 1
Electrooptical Characteristics and Limitations
age mode is relatively independent of the cholesteric concentration, the direction of ambient light, and the cell gap. The scattering state can be erased by the application of an AC voltage having a frequency greater than the cut-off frequency. The cut-off frequency is proportional to the conductivity of the material. Helfrich [49] was first to propose electrohydrodynamic instability in cholesterics with negative dielectric anisotropy. Harault [S6], combining Helfrich theory with timedependent formalism, calculated a voltage frequency relationship similar to that observed for Williams domains. The existence of conduction and dielectric regimes was experimentally verified. The domain periodicity is proportional to ( pod)”2, where po is the quiescent pitch and d is the cell gap. The threshold voltage in the conduction regime is proportional to (d/p,)”2.
3.3.6 Electrooptical Characteristics and Limitations Recent studies by Japanese workers indicate that on increasing the voltage, the Williams domains do not pass directly to dynamic scattering mode but go through a succession of transitions [8, 24-29,57-751. The flow pattern passes from Williams domains (WD), a two-dimensional roll flow, to the grid pattern (GP), a three-dimensional conductive flow, to the quasi grid pattern, a three-dimensional time dependent flow, and finally to dynamic scattering mode (DSM), the turbulent flow mode [S7-591. These workers have also found that there are three types of turbulent flow: DSM-like, DSM1, and DSM2 [57-591.
3.3.6.1 Contrast Ratio Versus Voltage, Viewing Angle, Cell Gap, Wavelength, and Temperature Figure 7 shows the threshold characteristic of a dynamic scattering mode display for a material (N-014) for various cell gaps (6- 127 pm) [60]. With increasing voltage above the threshold v t h d , the transmission drops and scattering increases. The scattering starts to saturate at about 2 Vthd. Thinner cells are found to have higher contrast ratios, especially in reflective mode LCDs. The numerical value of the contrast ratio is found to be strongly dependent on measurement conditions, i. e., the angle of the light source and detector with respect to the display, the acceptance angle of the detector, the nature of the light (specular or diffuse), etc. The threshold voltage was found to have almost no thickness dependence, as predicted by the theory. The contrast ratio increases steeply above the threshold voltage (-7.5 V for N-014), but saturates above 20 V for a cell thicker than 12 pm. Unlike a twisted nematic (TN) display, scattering in a DSM LCD is symmetrical in a cone normal to the display. However, it decreases with increasing cone angles. Both
z401 1 N-014
25.C
I-
2
60
2 0
50pm
20
5W.n
l27pm
0 0
10
20
30
00
50
60
70
VOLTAGE
Figure 7. Contrast ratio of transmissive N-014 cells at 25°C vs. the applied DC voltage. After Creagh et al. [60].
252
3.3 Dynamic Scattering
the scattering and threshold characteristics are viewing angle dependent, and consequently the contrast ratio of a DSM display shows strong angular dependence. At a higher operating voltage, the viewing angle dependence of the light scattering is reduced. The contrast increases with voltage at higher angles due to an increase in the scattering. DSM displays have much higher brightness compared to standard TN displays, as they do not use polarizers. As dynamic scattering is a forward scattering phenomenon, a specularly reflective reflector or mirror has to be used to reflect the scattered light back to the observer for a reflective mode display. In this mode, glare is a major problem. Antiglare coatings have to be used to minimize this effect. The threshold characteristic of dynamic scattering mode displays satisfies the requirements to display some gray scale and intrinsic multiplexing [6, 10, 621. Intrinsically multiplexed calculator displays were made using dynamic scattering LCDs in the 1970s [63]. Studies of spectral transmission of a dynamic scattering display in off mode showed nearly the same transmission through the entire visible region, except for the region below 420 nm [lo, 611. The decrease in transmission below 420 nm is due to strong absorption of near ultraviolet light by the organic liquid crystal molecules and glass. Dynamic scattering itself is more or less achromatic, [ 101. Detailed investigations of scattering versus applied voltage, wavelength, viewing angle, and light polarization have been reported by Wiegeleben and Demus [71]. The threshold voltage of the dynamic scattering mode is nearly independent of temperature, except for the close vicinity of solid - nematic and nematic - isotropic transitions. However, the contrast ratio of DSM shows a significant decrease with an increase in temperature.
3.3.6.2 Display Current Versus Voltage, Cell Gap, and Temperature Current in a DSM display is mainly resistive. The minimum current density should be about 0.1-0.5 pA/cm2 for the scattering to occur. Figure 8 shows the current density ( j ) vs. the applied voltage (V) for N-014 at 25°C for the cells with cell gaps ranging from 6- 127 pm [60]. Only a small deviation from ohmic behavior is observed. These data can be quite accurately described by the relation j = V” with n = 1.2. Current decreases with increasing thickness for the same applied voltage. The current and hence the power consumption increase drastically with an increase in temperature [lo, 601. A plot of l o g j vs. 1/T is not linear, so the temperature dependence of the current density cannot be described by j = e-A/j-.
I
I
I
l
l
I
I
I
*/ 10 -
u
-
N v)
-
I-
a
I
i
N-OIe
CELL THICKNESS:
.
N
E u
-
-
611m
U
-.2
l -
t ln
-
w
-
z
0
t-
z
12pm
25pm
-
W
a a u 3
50 pm
0.1
10
100
VOLTAGE (dc)
Figure 8. Current density ( j ) as a function of applied voltage (V) at 25 “C for DSM cells filled with N-014. After Creagh et al. [60].
3.3.6 Electrooptical Characteristics and Limitations
3.3.6.3 Switching Time The time for complete relaxation of the cell is much longer than the apparent decay time for scattering centers [lo, 29, 60, 61, 64671. If a display is operated repeatedly so that it does not reach a fully relaxed state, the measured delay time in rise, td,, and rise time, t,, are shorter. However, the decay time, t d , is not affected. This is sometimes useful, as it gives a shorter switching time. It has been found that the switching time can be expressed by the following relationship
where 17 is the viscosity, A& is the dielectric anisotropy, V is the applied voltage, cl, c2 are constants, and K is the elastic constant. As is evident from the equation, both the on and off switching times can be reduced drastically by reducing the cell gap. Moreover, a reduction in the viscosity also helps in producing faster switching. The time can be further reduced by operating the cell at a higher voltage. However, this increase the current consumption and requires higher voltage drive electronics. The typical turn on times is -10-50 ms, while turn off time is 100-200 ms. To achieve the faster turn off ( - 5 ms), a dynamic scattering mode display is sometimes operated in fast turn off mode, i.e., after removal of the operating signal, a high frequency (more than the cutoff frequency) voltage signal is used [28,29, 64, 651. Both the rise and decay times of a homeotropic DSM cell are - 5 times slower than those of a homogeneous display (all other factors such as the cell gap, LC mixture, etc., being the same) [29]. This is due to the fact that a homogeneous or quasi-homogeneous state is necessary for the onset of turbulence. In a homeotropically aligned cell, this state
-
253
has to be induced momentarily by an electric field each time the display is turned on, while with homogeneous alignment this state exists already. The decay time of a homogeneous display is also smaller because the elastic realignment force exerted by the undisturbed layer of the NLC (nematic liquid crystal) molecules adjacent to the cell walls is larger for homogeneous alignment. The response time of a DSM display is also dependent on its conductivity. t d , and t, are inversely proportional to both the density and the mobility of charge carriers. The greater the ion density and the quicker they acquire momentum, the faster the turbulence appears. tdr and t, therefore decrease with an increase in the charge carrier density (e. g., by additional doping) or its mobility (e. g., by heating to reduce the viscosity or by increasing the voltage). Both the turn on and turn off times increase with a decrease in temperature. The main contribution to the decrease in switching speed comes from the increase in the viscosity at a lower temperature. Homogeneous alignment also produces faster switching, while initial homeotropic alignment produces greater circular symmetry in the scattering distribution. Homeotropic alignment also generates a better cosmetic appearance by minimizing the scattering in the off state.
3.3.6.4 Effect of Conductivity, Temperature and Frequency Margerum et al. [68] have reported that the threshold voltage decreases with increasing O,~/O,, and the optical density of scattering is directly proportional to ( ql/o,).They also found that V,, can be expressed as (Vth)-2 =A(O~,/O,)-' + B
(7)
where A and B are constants depending on liquid crystals. With increasing conductivity, t,, and t, become faster.
254
3.3 Dynamic Scattering
Dynamic scattering mode displays can be operated by AC as well as DC. However, a DC field generates electrochemical degradations, shortening the life of the display. Hence an AC field is preferred. It is found that an AC field enhances the life of the display almost >50 times compared to that of a DC field [60]. Dynamic scattering mode displays can be operated at any frequency below the cut-off frequency. However, the use of higher frequency increases the current consumption. With temperature, the resistance of the liquid crystal decreases and the conductivity increases. Although this does not affect the contrast ratio significantly, it increases the current consumption and the cut-off frequency (f,).Asf, is directly proportional to the conductivity, which increases exponentially with temperature, the following relationship between the cut-off frequency and the temperature [69] is possible
where E is the activation energy for conduction, b is the Boltzmann constant, and T is the absolute temperature.
3.3.6.5 Addressing of DSM (Dynamic Scattering Mode) LCDs (Liquid Crystal Displays) DSM displays show rms response. They can be driven directly for unmultiplexed uses, or using the Alt-Pleshko scheme for multiplexed applications [62]. The addressing methods for a dynamic scattering LCD are almost the same as those for a TN mode, although the DSM operates at a higher voltage and consumes more power [6, 10, 24, 251. The applied voltage for turning on the DSM display should have frequency below the cut-off frequency. DSM LCDs can be driven by CMOS (complementary metaloxide semiconductor) chips and have the
capability of some gray scale and intrinsic multiplexibility. Muliplexing schemes with drive signals, having frequency components both below and above the cut-off frequency, enhance multiplexibility and reduce switching times of DSM displays [24, 26, 27,651. DSM displays can also be addressed using active matrix addressing [76].
3.3,6.6 Limitations of DSM LCDs Dynamic scattering mode displays consume more power, operate at higher voltage, and are less legible compared to TN displays. Another problem with DSM displays is the limited operating temperature range due to the exponential increase in conductivity (and hence current) with temperature. If doping was adjusted for the high temperature end to give the required conductivity and hence current to suit the driver, the cell would not produce dynamic scattering at low temperatures due to a drastic increase in the resistance. If the current drainage is adjusted for the low temperature end, it becomes too much for the battery and the driver at the high temperature end. Moreover, DSM LCDs have a limited life. These limitations of dynamic scattering mode displays have made them obsolete. Acknowledgements Thanks are due to Shivendra Bahadur for his assistance in preparing this manuscript.
3.3.7 References [ l ] R. Williams, J. Chern. Phys. 1963,39, 384. 121 A. P. Kapustin, L. S. Larionova, Krystallographia (Moscow) 1964,9,297. [3] G. H. Heilmeier, L. A. Zanoni, L. A. Barton, Appl. Phys. Lett. 1968, 13,46. 141 G. H. Heilmeier, L. A. Zanoni, L. A. Barton, Proc. IEEE 1968,56, 1162. [5] Y. Bjornstahl, Ann. Physik 1918,56, 161. 161 B. Bahadur, Mol. Cryst. Liq. Cryst. 1983, 99, 345; B. Bahadur, Liquid. Crystal Displays: Gordon and Breach, N. Y. 1984 as a special issue of Mol. Cryst. Liq. Cryst. 1984, 109, 1-98.
3.3.7 References [7] J. Gleick, Chaos - Making a New Science, Viking Penguin, New York, 1987. [8] W. J. A. Goossens, in Advances in Liquid Ctystal Vol. 3 (Ed. G. H. Brown), Academic, N. Y. 1978. [9] E. Dubois-Violette, G. Durand, E. Guyon, P. Manneville, P. Pieranski, Solid State Phys. 1978, 14, 147. [lo] B. Bahadur in Liquid Crystals - Applications and Uses (Ed.: B. Bahadur) Vol I, World Scientific, Singapore, 1990. [ 1 I] S . Chandrasekhar, LiquidCrystals, 2nded. Cambridge University Press, Cambridge 1992. [12] P. G. de Gennes, J. Prost, The Physics of Liquid Crystals, 2nd ed., Oxford University Press, Oxford 1993. [13] A. Sussman, Mol. Cryst. Liq. Cryst. 1971,14,183. [I41 Data Sheets on dynamic scattering mesogens and mixtures from E. Merck (Germany), Hoffman La Roche (Switzerland), American Liquid Crystal Company (Cleveland, U.S.A.), Chisso (Japan), etc.; A. M. Lackner, J. D. Margerum, Mol. Cryst. Liq. Cryst. 1985,122, 11 1; S. E. Petrie, H. K . Bucher, R. T. Klingbiel, P. I. Rose, Eastman Org. Chem. Bull. 1973,45, 2. [I51 J. Cognard, Mol. C y s t . Liq. Cryst., Suppl. 1 1981, 78, 1 . [16] W. Helfrich, J. Chern. Pkys. 1969, 51, 4092. [I71 E. Dubois-Violette, P. G. de Gennes, 0. Parodi, J . Physique 1971.32, 305. [IS] E. Dubois-Violette, J. Physique 1972, 33, 95. [I91 P. A. Penz, Phys. Rev. Lett. 1970,24, 1405;Mol. Cryst. Liq. Cryst. 1971, 1.5, 141. [20] P. A. Penz, G. W. Ford, Phys. Rev. A 1971, 6, 414; Appl. Phys. Lett. 1972,20,415. [21] P. A. Penz, Phys. Rev. A 1974, 10, 1300. [22] D. Meyerhofer, RCA Rev. 1974, 35, 433. (231 Orsay Liquid Crystal Group, Mol. C y s t . Liq. Cryst. 1971. 12, 251; Phys. Rev. Lett. 1970, 25, 1642. 1241 L. A. Goodman, J. Vac. Sci. Technol. 1973, 10, 804. [25] L. A. Goodman, RCA Rev. 1974,35,613. [26] A. Sussman, IEEE Trans. Parts, Hybrids Packuging 1972, PHP-8, 24. [27] R. A. Soref, Proc SID 1972, 13, 95. [28] L. M. Blinov, Electro-optical and Magnetooptical Properties of Liquid Crystals, Wiley, New York 1983. [29] M. Tobias, International Handbook of Liquid Crystal Displays, Ovum, London 1975. [30] G. H. Heilmeier, W. Helfrich, Appl. Phys. Lett. 1970, 16, 155. [31] E. F. Carr, J. Chem. Phys. 1963,38, 1536; 1963, 39, 1979; 1965, 42,738; Mol. Cryst. Liq. Cryst. 1969, 7, 253. 1321 N. Felici, Revue Gen. Electricite 1969, 78,717. [331 F. Gaspard, R. Herino, F. Mondon, Chem. Phys. Lett. 1974,25,449.
255
[34] M. 1. Barnik, L. M. Blinov, M. F. Grebenkin, S. A. Pikin, V. G. Chigrinov, Phis. Lett. 1975, S I A , 175. [ 3 5 ] W. H. de Jeu, C. J. Gerritsma, A. M. Van Boxtel, Phys. Lett. 1971, 34A, 203. [36] W. H. de Jeu, C. J. Gerritsma, P. Van Zanten, W. J. A . Goossens, Phys. Lett. 1972, 39A, 355. [37] W. H. de Jeu, C. J. Gerritsma, T. W. Lathouwers, Chem. Phys. Lett. 1972, 14, 503. [38] W. H. de Jeu, C. J. Gerritsma, J . Chem. Phjs. 1972,56,4752. [39] D. Meyerhofer, A. Sussman, Appl. Phys. Lett. 1972, 20, 337. [40] W. Greubel, U. Wolff, Appl. Phys. Lett. 1971,19, 213. [41] H. Gruler, Mol. Cryst. Liq. Cryst. 1973, 27, 31. [42] R. J. Turnbull, J . Phys. D. Appl. Phys. 1973, 6, 1745. [43] A. I. Derrhanski, A. I. Petrov, A. G. Khinov, B. L. Markovski, Bulq. Phys. J. 1974, 12, 165. [44] D. Coates, W. A. Crossland, J. H. Morrissy, B. Needham, J. Phys. 1978, D I I , 2025. [45] W. A. Crossland, S . Canter, SID Digest 1985, 124. [46] D. Coates, A. B. Davey, C. J. Walker, Eura Display Proc., London, 1987, p. 96. [47] D. Coates in Liquid Crystals Applications and Uses. (Ed.: B. Bahadur), World Scientific, Singapore 1990. [48] G. H. Heilmeier, J. E. Goldmacher, Proc. IEEE 1969, 57, 34. [49] W. Helfrich, 1.Chem. Phys. 1971, 55, 839. [50] F. Rondelez, H. Arnould, C. R. Acad. Sci. 1971, 273 B, 549. [51] C. J. Gerritsma, P. Van Zanten, Phys. Lett. 1971, 37A, 47. [52] H. Arnould-Netillard, F. Rondelez, Mol. Cryst. Liq. Cryst. 1974, 26, 11. [ 5 3 ] F. Rondelez, H. Arnould, C. J. Gerritsma, Phys. Rev. Lett. 1972, 28, 735. [54] W. E. Haas, J. E. Adams, et al., Proc. SID. 1973, 14, 121. [ 5 5 ) G. A. Dir, J. J. Wysocki, et al., Proc. SID 1972, 13, 105.
[56] P. J. Harault in Fourth In?. Liquid Crystal Conference, Kent, OH, 1972; J. Chern. Phys. 1975, 59, 2068. [57] H. Yamazaki, S. Kai, K. Hirakawa, J . Phys. Soc. Jpn 1983,52. 1878. [ S S ] H. Yamazaki, S . Kai, K. Hirakawa, Memoirs Fac. Eng. Kyushu Univ. 1984, 44, 317. 1591 H. Yamazaki, K. Hirakawa, S. Kai, Mol. Cryst. Liq. Cryst. 1985, 122, 41. [60] L. T. Creagh, A. R. Kmetz, R. A. Reynolds in IEEE Int. Conj: Digest, p. 630, N. Y. March 1971, IEEE Trans. Electron. Dev. 1971, ED-18, 672. [61] V. 1. Lebedev, V. I. Mordasov, M. G. Tomilin, Sov. J. Opt. Technol. 1976,43, 252.
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3.3 Dynamic Scattering
[62] P. M. Alt, P. Pleshko, IEEE Trans. Elect. Dev. 1974, ED21, 146; Proc. SID 1975,16,48. [63] K. Nakada, T. Ishibashi, K. Toriyama, IEEE Trans. Elect. Dev. 1975, ED-22, 725. [64] G. H. Heilmeier, L. A. Zanoni, L. A. Barton, IEEE Trans. Electron. Dev. 1970, ED1 7, 22. [65] P. J. Wild, J. Nehring, Appl. Phys. Lett. 1971,19, 335. [66] M. J. Little, H. S. Lim, J. D. Margerum, MoZ. Cryst. Liq. Cryst. 1977, 38, 207. [67] C. H. Gooch, H. A. Tarry, J. Phys. 1972, D5,
L-25. [68] J. D. Margerum, H. S . Lim, P. 0. Braatz, A. M. Lackner, Mol. Cryst. Liq. Cryst. 1977, 38, 219. [69] S. Matsumoto, M. Kamamoto, T. Tsukada, J. Appl. Phys. 1975,14, 965.
[70] D. Jones, L. Creagh, S. Lu, AppZ. Phys. Lett. 1970, 16, 61. [71] A. Wiegeleben, D. Demus, Cryst. Res. Techn. 1981, 16, 109. [72] G. Elliott, D. Harvey, M. G. Williams, Electron Lett. 1973, 9, 399. [73] J. Nakauchi, M. Yokoyama, K. Kato, K. Okamoto, H. Mikawa, S . Kusabayashi, Chem. Lett. (Jpn) 1973, 313. [74] E. W. Aslaksen, Mol. Cryst. Liq. Cryst. 1971,15, 121. [75] NPL, New Delhi, India, Bulletin No. NPL-7401, 1974. [76] F. C. Luo in Liquid Crystals Applications and Uses (Ed.: B. Bahadur) World scientific, Singapore, 1990.
Handbook ofLiquid Crystals D. Demus, J. Goodby, G. W. Gray, H.-W. Spiess, V. Vill Copyright 0WILEY-VCH Verlag GmbH. 1998
3.4
Guest - Host Effect
Birendra Bahadur
3.4.1 Introduction The phenomenon of the alignment of dye molecules by liquid crystal molecules and its applications were first reported by Heilmeier et al. in 1968. They termed this phenomenon the guest-host effect [l-31. Liquid crystals are excellent solvents for organic and organometallic molecules. Nonmesomorphic molecules may be incorporated in liquid crystals up to a fairly high concentration without destruction of the long-range order of the liquid crystalline matrix. More generally, the phenomenon of dissolving and aligning of any molecule or a group of molecules, such as dyes, probes, impurities, or even mesogenic molecules, by a liquid crystal can be called the guest-host phenomenon. Elongated molecules are aligned better than are spherical molecules. The molecules behave as guest molecules in a liquid crystal host. The host liquid crystal can be a single compound or a multicomponent mixture. The guest molecules couple to the anisotropic intermolecular interaction field of the liquid crystal, but can diffuse rather freely within the host. The anisotropic guest - host interaction leads to a highly anisotropic tumbling motion of nonspherical guest molecules in the liquid crystal ma-
trix. In the time average this anisotropic tumbling leads to an appreciable orientation of the guest with respect to the local director of the liquid crystal. These liquid crystalline solutions can be easily oriented by electric, magnetic, surface, or mechanical forces, resulting in highly oriented solute molecules. The molecular properties of the guests are not altered appreciably by the weak intermolecular forces, and they behave as an ‘oriented gas.’ This finding provides the basis for the application of liquid crystals as anisotropic solvents for spectroscopic investigations of anisotropic molecular properties [4 - 71. The ordering of probe molecules i n liquid crystals was in fact known much earlier than 1968. It is widely used to determine various parameters of the solute and solvent liquid crystal using nuclear magnetic resonance (NMR), electron spin resonance (ESR), ultraviolet (UV), visible, and other spectroscopic techniques. After the pioneering work of Saupe and Englert in 1963 [8], the NMR spectroscopy of molecules oriented in liquid crystals became very important in structural chemistry, as it provides the only direct method for precise determination of the molecular geometries in liquid phase. In addition to structural and confor-
25 8
3.4 Guest-Host Effect
mational studies of the molecules, NMR has been used to determine the chemical shift anisotropies and the anisotropies of the indirect spin - spin coupling [4 - 71. The field has been reviewed by many authors [4-71 and is the subject of a separate chapter in this book. Paramagnetic probe molecules (guest) dissolved in liquid crystals are used for EPR studies. The first EPR studies on radical ions in liquid crystals were done in 1964 using diphenylpicrylhydrazyl and tetracyanoethylene anion dissolved in PAA [9]. The guest-host effect has also been used in measuring linear and circular dichroism [4], the Mossbauer effect [lo], and many other spectroscopic and electro-optical properties. It is also used as an indirect method to determine the order parameter of the liquid crystal. The guest-host effect is also used to alter the reactivity of the dissolved solute for desired chemical reactions [ 1 11. In a broad sense, most of the commercially available liquid crystal mixtures may be regarded as being based on the guest host effect, as they incorporate some nonmesomorphic molecules to generate the desired effect in liquid crystal mixtures. These broad topics are covered in other chapters of this book, and hence are not described here. The general perception of the guest host effect is a system composed of a dye and a liquid crystal. The most valuable commercial application of this effect has been in electro-optical devices [ 12- 171. Hence, this chapter is devoted to dichroic liquid crystal mixtures and dichroic liquid crystal displays (LCDs). The dyes used in dichroic LCDs normally absorb in the visible spectrum. The present market for dichroic LCDs, including drive electronics in some cases, is estimated to be US$ 35 million, and is mainly in avionics, military, sign board, and games markets. The dichroic market has been stagnant and declining during the last few years. However, there is a
new emerging interest in dichroic LCDs due to the demand for low power consumption, direct view LCDs for use in consumer electronics and lap-top computers. If a small amount of an elongated dye is mixed with a liquid crystal, the dye molecules become aligned with the liquid crystal matrix and hence can be oriented from one position to another along with the liquid crystal molecules by the application of an electric field. This dichroic mixture absorbs light selectively. With proper surface treatment, in one state (quiescent or activated) the dichroic mixture does not absorb light strongly, while in another state it does (Fig. 1). The application of an electric field results in a nonabsorbing state if the quiescent state is absorbing, or in an absorbing state if the quiescent state is clear. This is the basis of almost all dichroic displays [12-171. The absorption is usually increased by using a polarizer [1, 2, 15, 161, or by adding a suitable amount of a chiral dopant in the nematic host [15-171. The most popular dichroic displays are the dichroic phase change effect [3, 12- 171 (White-Taylor mode [ 171) and Heilmeier type dichroic LCDs [l -3, 12- 161. Besides these quarter wave plate dichroic [16, 18-201, double cell guest - host dichroic [16, 21 -241, dye doped twisted nematic [15, 16, 25-28], supertwisted dye effect [29-3 11, dichroic ferroelectric [32 - 351, polymer dispersed dichroic [36-391, and dichroic SmA [40, 411 LCDs are also known. The performance of a guest - host LCD is greatly dependent on the dye parameters (such as UV stability, solubility, order parameter, absorption, etc.), the host liquid crystal properties (such as viscosity, dielectric anisotropy, birefringence, order parameter, temperature range, stability, etc.), and the compatibility of the dye and the host [12- 17,42-581.
3.4.2 Dichroic Dyes
narrow absorption spectrum, the wavelength of maximum absorption being designated as Amax. The color seen is basically the light which is not absorbed by the dye. Fluorescent dichroic dyes are slightly different. They absorb at a given wavelength (UV, blue, green, etc.) and emit at a longer wavelength [59-611. This emitted radiation determines the color of the dye and display. To make a black mixture one has to use several dyes having different A,, [IS,16, 55-58]. The dyes used in textile and other industries normally cannot be used in LCDs, as non-ionic dyes are required in order to avoid electrochemical degradation and to reduce the current consumption. The usefulness of dichroic dyes in guest-host LCDs is determined by the following properties 115, 16,461:
100
80
z
P
sa v,
259
60
v)
2 4 K !-
-
40
bp
10
0 380
460
540
610
700
780
WAVELENGTH (nm)
Figure 1. Operational principle of a dichroic display (Heilmeier display).
-
-
3.4.2 Dichroic Dyes Dichroic dyes absorb light more along one axis than the others. Usually, the major component of the transition moment of dyes is along the long molecular axis (pleochroic) or short molecular axis (negative dichroic). Pleochroic (positive dichroic) dyes [ 12- 16, 46, 541 absorb the E vector of light which is directed along the long molecular axis of the dye, while negative dichroic dyes absorb the E vector of light which is directed perpendicular to the long molecular axis [16, 46, 50-541. Normally, these dyes have a
-
The chemical and photochemical stability of the dye [15, 16, 46, 62-67]. Photochemical instability is also termed 'fading.' The color or hue (A,,,, wavelength of maximum absorption or emission). The spectral width (measured as the halfwidth). The extinction coefficient. The dichroic ratio [42]. The order parameter of the dye [421. The solubility of the dye in the host [ 16,46, 681. The influence of the dye on the viscosity of the host [ 16, 461. The nonionic nature. The purity and high resistivity. The compatibility of the dye with the host, which is usually determined by its order parameter, solubility, viscosity, and the absence of chemical reaction with the host.
260
3.4 Guest-Host Effect
3.4.2.1 Chemical Structure, Photostability, and Molecular Engineering The most widely used dichroic dyes in LCDs [16, 42-49] fall basically into two classes from a chemical structure point of view: azo [16,42-46,491 and anthraquinone [16, 42-48]. Besides these, methine [16,46], azomethine (Schiff base) [16,46], merocyanine [ 16, 44, 461, napthoquinone [ 16, 46, 56, 691, hydroxyquinophthalone [70], benzoquinone [46], tetrazine [52,53], perylene [70], azulene [46], and other types of dichroic dyes [ 16,461 have also been investigated. Fluorescent dyes are found to have many classes of chemical structures [59-611. Most of the dyes used are pleochroic dyes, as these exhibit a higher dichroic ratio and order parameter. Some of these dichroic dyes are listed in Table 1. Some good review articles on dichroic dyes have appeared recently [16,44-461, and these, especially the detailed articles by Bahadur [ 161 and Ivashchenko and Rumyantsev [46], should be consulted for more details on the chemical structures and physical properties of dichroic dyes and dichroic mixtures. Bahadur also provides extensive information about commercial dyes used in guest-host displays 1161. Attempts have been made to synthesize liquid crystalline dyes that exhibit both liquid crystalline and dichroic dye properties [46, 711. A few organometallic dichroic dyes have also been reported [72]. Some polymeric liquid crystals having light-absorbing groups have been reported [ 161. These can behave like a dichroic polymeric liquid crystal [ 161. Some dichroic dyes are also found to form a lyotropic liquid crystal phase [73]. However, they are not important for display applications. The vast majority of dichroic dyes used in LCDs are elongated in shape, and they more or less adopt the ordered arrangement of the host liquid crystal and exhibit
cylindrical symmetry. It is worth mentioning that many dichroic dyes, drastically differing from rod-like structure, have been synthesized, especially by Ivashchenko and Rumyantsev [4]. The color of the dye is basically dependent on the chromophoric and auxochromic groups present in the dye molecule. The angle of the transition moment of the dye determines whether the dye would be pleochroic or negative dichroic. Usually only one peak absorption wavelength (Amax) is observed. However, some dichroic dyes exhibit two or more peaks. Some of these dyes can exhibit both pleochroic and negative dichroic absorption bands [46]. Some prominent auxochromic groups are OH, NH,, NR,, NHR, NO,, C1, Br, F, -S-C,H4-R, and -S-C6H,,-R. To make a good black dichroic mixture, dichroic dyes in three colors (such as yellow, blue, and red; or magenta, cyan, and yellow; or violet, green-blue, and orange) with high order parameter, solubility, photostability, and absorption are required [ 161. Major efforts have been made in synthesizing these types of dichroic dye. Azo dyes with reasonable photostability can provide only red, orange, and yellow colors. Similarly, earlier anthraquinone dyes used to generate only blue, violet, or red colors. The photostability of dichroic dyes is one of the most important considerations for their use in LCDs [16,43-46,49, 62-67]. The photostability of many classes of dye is not sufficient for display applications [46, 64-66], this being particularly true for monoazo dyes with triazole and benztriazole rings, as well as bis(azo)dyes with theophelline and naphthalene fragments [46]. Monoazo and bis(azo) dyes without triazole and benztriazole rings have a sufficiently long lifetime [46]. Anthraquinone dyes are much more stabe than azo compounds. Naphthoquinone dyes have a photostability
Commercial Code
D35 D43 D46 D52 D54 D77
1.3 I .4 I .5 1.6 1.7 1.8 1.9 1.10
550 R, = ‘C,H~, R3= H, R, = tC4H9
R,=‘c,H~,
1.15
554 557 556 546 524 558
596 612
550
R=H Rxp-CH,
R=C,H, R=OC,Hl I R=OC,H,, R =N(CH3), R=N,C6HS R=CH(CH,), R = C6H, R =C,H,C,H,
R=OC,H,9 R=N(CH,),
L a x
(nm)
RI=H, R,=H, R3=H, R,=H
H2N 0 NH2
0 OH
drR
Structure
1.14
1.12 1.13
1.1 1
D16 D27
1.1 1.2
Antraquinone dyes
Dye No.
Table 1. Examples of various types of dichroic dyes and their physical parameters.
0.78
0.80
E43 (3.0%)
E43 (0.8%)
E7 E43 ZL1 1691 MBBA EN 24 ROTN 101 E 43 EN 24
0.7 1 0.76 0.78 0.31 0.52 0.56 0.68 0.65 0.79 0.80
E7 E7 E7 E7 E7 E7 ZLI 1132 ZLI I132
E7 E7
Host (solubility)
0.67 0.68 0.69 0.65 0.71 0.68 0.80 0.90
0.65 0.63
Order parameter
m
t 4
0
tl w
LCD 109
1.16
G 241
1.22
1.24
I .23
G 207
NC-@CH=N
C3H70-@
e
N= N*N=
CH3 CH3
N = N -@N
[email protected]~H~
N e C 4 H 9
N-
N = N*-N=
=N-@N<
1.20
1.21
& N = N * N = N e N = N G
1.19
N-@N
N = N+N=
1.18
@N=
@-N=
N-Q
Structure
1.17
Azo dyes
Commercial Code
Dye No.
Table 1. (continued)
n
L a x
455
566
39 1
500
400
359
450
(nm)
0.67
0.756
0.791
0.67 0.74 0.75 0.78
0.64
0.62
0.37
Order parameter
ROTN 101
ZLI 1840 (>3)
ZLI 1840 G-3)
E3 E7 E8 E9
E7
E7
E7
Host (solubility)
N Q\ N
3.4.2
263
Dichroic Dyes
r-
0 00
Y
8
r-
m
N N
c?
r-c: 0 0
0
c: 0
0 I
m
10
r-
m
00
In
0
d
-
I:
z 0
+
I
*i0 Q,
=* u
0 0 =v I
I
r -2
0
T
0
v =o
0
2
0 Q,
5 u
m N
-
0
-
3
-
c?'?
N
c?
264
3.4
Guest-Host Effect
0
m
zi
m
vl
*
v, d
P
6
=4
c1
€ Z = X
"\
\?
ir-n
r-n I
Q,
i-
I
(ri
r? 3
* r? 3
m r? 3
3.4.2
close to that of anthraquinone dyes [69]. Photostability of azo dyes depends on their La,,decreasing sharply with increasing Amax [49]. Only the yellow, orange, and red azo dyes have a satisfactory photostability, while the violet and dark blue mono and polyazo dyes seem to be unstable. The light degradation of azo dyes in the presence of oxygen and moisture is an oxidation reaction which generally proceeds by an attack on the azo group by a singlet oxygen molecule [64]. The singlet oxygen molecule is produced when the ground-state oxygen molecule receives the energy of the excited triplet state of the dye molecule. The photodecomposition of the dye is not only dependent on the intensity of the light source, but also on the spectral power distribution hitting the dye. Most of the photodecomposition is caused by the light with ;I< Lax of the dye. The deterioration can be reduced drastically by putting a UV cutt-off filter or just a UV barrier coating on the display [49]. Most dichroic LCDs involve glass substrates, which absorb most of the UV light. Glasses, films, and coatings having higher cut-off wavelengths (-400 nm) produce even better results. As this region has very low photopic response, the UV cut-off filters have no negative impact on the chromatic or electro-optical performance of the cell. Scheuble et al. [56] found a 20- to 30fold increase in the photostability of azo dyes by using a UV cut-off filter, giving a photostability comparable to that of stable anthraquinone dyes [56].Under this condition the photodecomposition of the dye basically takes place under the influence of visible light. The polarizers used in many dichroic LCDs also enhance the photostability, primarily due to its UV barrier coating, and secondly by reducing the transmitted light intensity to less than 50%. However, they would be effective only when the polarizer side faces the light before the di-
Dichroic Dyes
265
chroic mixture. The UV barrier coating increases the life of yellow to red azo dyes, but has little impact on the blue azo dye [49]. The photodecomposition of the dye is also dependent on the geometry and alignment in which the dichroic mixture is used. If the quiescent geometry is homeotropic with a pleochroic dye, the light absorption will be less, and consequently will lead to a longer lifetime. Although the light stability of dyes depends greatly on their structure, it is not an absolute property of the compound only [58]. It is also influenced by the compound’s environment and indeed it is a photoinduced reaction [ 5 8 ] . The lifetime of a dichroic mixture also depends on the host employed. In general, liquid crystals have an absorption edge lying above the glass cut-off which, in the absence of a dye, result in its photodecomposition [49]. A dye dissolved in a liquid crystal may be photosensitized as a result of the liquid crystal being excited. The effect of this process is to inhibit the degradation of the liquid crystal and to accelerate the decomposition of the dye. Liquid crystal mixtures exhibiting lower absorption above the glass cut-off generate longer lifetimes for dyes within them [491. In a mixture of dyes, the situation is more complex due to synergetic effects. This interaction may increase the light-fastness of the dyes, but may also have the opposite effect [ 5 8 ] . Since it is not easy to forecast how a photoinduced reactivity will develop, the correct photostability of the dye can be found only experimentally in the liquid crystal host. The excellent photostability of the anthraquinone dyestuffs are related to the introduction of a proton donor in the a-position of the anthraquinone molecule [58]. The anthraquinone molecule itself has no absorption band in the visible spectrum [46], so at least one of the 1 , 4 , 5 , or 8 (or 2,
266
3.4
Guest-Host Effect
3 , 6 , or 7) positions is occupied by a proper auxochromic group, such as OH, NH,, or NHR, to complete the chromophor system of the dye [45, 571. At the 1, 4, 5 , or 8 positions (i.e. a-positions) the introduction of two OH groups leads to a yellow dye, two amino groups generate red dyes, and two each of OH and NH, generate blue dyes [57]. These colors are affected by the bathochromic or hypsochromic elongated groups at a- or ppositions. The NH, substitutions are found to increase the order parameter, while OH substitutions decrease it. The substitution of all four a-positions by NH, group gives the highest order parameter, while substitution of all generate the lowest order parameter [58]. The order parameter drops from 0.69 to 0.53, and at the same time the hue changes from blue to red. In addition, the photostability decreases from excellent to poor [58]. The properties of the compounds between these two extremes correspond to those of their parent structures, depending on the permutations of the substituents [58].
served for some dyes. In the case of azo dyes, the long axis of the skeleton is usually the long axis of the molecule, and hence the transition moment making an angle with the skeleton usually reduces the order parameter of the dye. Before synthesis of a dichroic dye for display use, one should analyze the structure and estimate the order parameter (S), of the new dichroic dye, taking into consideration the bond lengths, valence angles, and transition moment direction. As the color of the dichroic dye is basically dependent on its auxochromic groups, proper auxochromic groups must be inserted into the molecule. Moreover, the structure has to be designed in such a way that for a pleochroic dye the transition moment should be more or less parallel to the long molecular axis of the dye. The solubility of the dye is also a critical parameter, so attempts should be made to insure that the dye chosen has good solubility in the liquid crystal. Moreover, the dye structure and the groups attached to it must have good photostability. It should be OH 0 NH,
Anthraquinone
S=0.69, blue
The auxochromic groups not only influence the color but also the angle of the transition moment in the dye molecule [46, 571. Whereas for a symmetrical substituted pattern the transition moment will be parallel (or perpendicular) to the long axis of the anthraquinone skeleton, the situation becomes quite complicated for an asymmetric substitution [74]. As the axis of alignment normally will not coincide with the axis of the skeleton, an oblique orientation of the transition moment with the skeleton axis may even be an advantage, and could provide an explanation for the high dichroic ratios ob-
S = 0.6 1, blue-violet
O H 0 OH
S=0.53, red
clearly understood that the change incorporated in the chemical structure of the dye to improve one property affects all the other properties simultaneously [ 16, 581. This is the reason why it is so difficult to produce a high-quality dichroic dye that satisfies most of the requirements.
3.4.3 Cell Preparation Cells are prepared by standard methods, as discussed by Bahadur [75, 761 and Morozumi [77]. For homogeneous alignment, poly-
3.4.3 Cell Preparation
vinyl alcohol, polyimide, obliquely evaporated SiO, and appropriate phenylsilane compounds are used [ 16,75-801. For homeotropic alignment, long-chain alkyl silane (such as steryltriethoxy silane), lecithin, specially formulated polyimide (such as RN-722 from Nissan Chemicals), or long-chain aliphatic chromium compounds, are used [ 16,75 - 79,8 1, 821. RN-722,being a polyimide material, provides a durable and strong homeotropic alignment. The homeotropic alignment achieved by silane compounds are not very stable, especially with regard to heat, humidity, and thermal cycling. After filling and end-plugging, the cell should be heated to the isotropic state and then cooled to room temperature to eliminate flow alignment defects. The structures of various dichroic cells are described in later sections. Most of the commercial dichroic displays use unidirectional homogeneous alignment produced by unidirectionally buffing the polyimide [ 16,75-80],as the latter is reliable, durable, low cost, and easy to apply. These displays include Heilmeier displays (negative mode), dye doped TN, ferroelectric dichroic, A/4dichroic, phase change dichroic, etc. For cases such as positive mode phase change dichroic displays using a dichroic mixture of negative dielectric anisotropy [12,13,15,161,homeotropic alignment [78,79,81,821 is required. For positive mode Heilmeier displays, which use homeotropic alignment and a pleochroic dye mixture in a negative dielectric anisotropy host, tilted homeotropic alignment [ 16,831 is usually preferred. Some supertwist dichroic effect displays may require highly tilted homogeneous alignment, which can be produced either by SiO coating or special polyimide [77,78,84,851. In normal phase change dichroic LCDs, some manufacturers prefer to use homeotropic alignment to reduce the memory effect. Occa-
267
sionally, hybrid alignment (i.e. homogeneous alignment on one plate and homeotropic on the other plate) is used in phase change displays [16,861.Homeotropic and hybrid alignments are also advantageous in the sense that they allow the dichroic mixture to retain its natural pitch in the cell and not to have a forced pitch as imposed by the homogeneous alignment on both plates [ 161. For ferroelectric dichroic displays, nylon and other polyamides are also being used [801. With regard to the dye-related parameter measurements, the dye concentration is usually kept at about 0.5-2%, depending on its absorption coefficient. For azo dyes the dye concentration is about 0.25-1% for dye doped TN, about 2-496 for Heilmeier displays, and about 2-5% for phase change displays. The cell thickness is usually about 5 pm for dye-doped TN at the first Gooch Tarryminimum[15,16,88],about7-10 pm for dye-doped TN at the second Gooch Tarry minimum [15,16,881, about 5-15 pm for Heilmeier, and about 10-20 pm for phase change dichroic displays. Usually, the dye concentration is increased by a factor of about 1.5-2 when anthraquinone dyes are used instead of azo dyes, as anthraquinone dyes have less absorbance than azo dyes. Sometimes combinations of azo and anthraquinone dyes are used [16,541. The cell spacing must be made uniform in the case of phase change displays with homogeneous alignment in order to avoid the Grandjean Cano disclination lines (also called pitch lines), which are quite visible because of the stepwise change in brightness appearing across them [16,75,891. These pitch lines are also visible in the case of homeotropically aligned cells, although to a lesser extent. Polarizers, color filters, and reflectors are usually mounted outside the cell, as dichroic displays do not have very high line reso-
268
3.4 Guest-Host Effect
lution. Color filters can be mounted inside the cell using normal materials (such as polyimide, acrylic, or gelatin-based color filter materials) and techniques used for TN LCDs [75 - 771. Efforts have also been made to develop internal reflectors [16, 901, but these are found to be inferior to external ones. For external reflectors in White-Taylor mode LCDs, BaSO,, Ti02,Melinex, and Valox (GE) films, etc., are used [91].
3.4.4 Dichroic Parameters and Their Measurement A dichroic mixture is basically a homogeneous mixture of dye(s) in a liquid crystal host. The various physical properties of dichroic mixtures are dependent on the physical properties of the dyes, the host, and their combination.
Figure 2. Geometrical relationship of a dye with its transition moment, the liquid crystal, and polarized light.
3.4.4.1 Order Parameter and Dichroic Ratio of Dyes The director of dyes in the host liquid crystal coincides with the director of the host, n. However, the direction of each dye molecule deviates from the director due to thermal fluctuations, in same way as individual liquid crystal molecules deviate from their own director [42,43]. The impact of thermal fluctuation may be different on dye and liquid crystal molecules, depending on their molecular lengths and geometries. The long molecular axes of the liquid crystal L, and the dye D , molecules make angles of 8 and @, respectively, with the director n,as shown in Fig. 2. The order parameters of the liquid crystal S, and dye S , molecules determined from the distribution of their long molecular axes are given by:
s, =
(3 COS2 8 - 1) 2
where (cos’8) and (cos2@)are the averages of cos28 and cos2@,respectively. The difference between 8 and @ is one of the reasons for the difference in the order parameters between the dye and the liquid crystal host. The main criterion for dichroic dye efficiency is the order parameter of the transition moment of the dye absorption S,, which is responsible for the color and absorption of the dye [14, 16,461. It must be clearly understood that the value of ST may differ from the order parameter of the long molecular axis of the dye SD. This is the case when the transition moment of the dye makes an angle with its long molecular axis. If the transition moment makes an angle & (not shown in Fig. 2) with the director of the liquid crystal, then by analogy with
3.4.4 Dichroic Parameters and Their Measurement
(2) If we assume that the direction of the transition moment, T, of the dye deviates from its long molecular axis D, by an angle p, the absorbance A of the incident polarized light, the electric vector P of which makes an angle ly with the director n, is given as [14,431 A ( P , l y ) = kcd [(?)sin'/i
+
(T) 1-s,
(3)
where k is the magnitude of the transition moment, and c and d are the concentration of the dye and the thickness of the liquid crystal layer, respectively. The dichroic ratio D is expressed as the ratio of the absorbance at y=O" and ly=90':
(4) The order parameter STof the transition moment is determined experimentally as:
269
ative dichroic dyes the transition moment order parameter is only half of that for a pleochroic dye. With OoIp<54'44'8'', S,>O and the dyes are pleochroic, while with p > 54"44'8", S, < 0 and dyes are negative dichroic dyes. The dyes with ST=O(p= 54'44'8" with $=Oo or p=0°1900 with $=54"44'8") are called 'phoney dyes,' because their optical densities A , , and A , are equal in magnitude [46]. For elongated pleochroic dyes, p is extremely small, or zero, making sinp almost negligible, and hence S,=S,. The order parameter measured by absorption measurements is always the order parameter of the transition moment of the dye, which is often referred to in the literature as the dye order parameter S. Hence, from here on we will use the symbol S for the dye order parameter or its transition moment order parameter ST. It is worth mentioning that Osman et al. [74] found theoretically that, in planar dyes, such as anthraquinone, the order tensor deviates strongly from cylindrical symmetry. The direction of the optical transition moment does not, in general, coincide with one of the principal axes of the order tensor. Based on their calculations they found that only those anthraquinone dyes that have a small angle between the transition moment and the molecular axis show a good dichroic ratio [74].
Using Eqs. (4) and ( 5 ) we get
3.4.4.2 Absorbance, Order Parameter, and Dichroic Ratio Measurement
From Eq. (6) it is clear that ST/SD decreases significantly as p increases, and hence p should be as low as possible in order to increase the dichroic ratio. One can also see that for p=Oo, ST=SD,while for p=9Oo, ST=-SD/2, which indicates that for the neg-
The dichroic mixture is put into cells having unidirectional homogenous alignment. A similar compensating cell is filled with the host liquid crystal. These cells are placed in a double-beam spectrophotometer and, by placing two identical high efficiency polarizers either parallel or perpendicular to the alignment direction, A , ,(absorption parallel to the long axis of the dye) and A , (ab-
270
3.4
Guest-Host Effect
the rub direction of the cell filled with pleochroic dye mixture having positive dielectric anisotropy, and then measuring the absorption in the quiescent (A,,)and fully excited (A,) state. However, A, obtained by this method results in a slightly higher value (Fig. 3) due to the absorption by the unoriented layers in the close vicinity of the glass surface. The order parameter Seffof a dye with a very wide absorption spectrum, or a black dye, can be calculated using Eq. ( 5 ) ,but the dichroic ratio is then evaluated over the whole visible spectrum:
sorption perpendicular to the long axis of the dye) are measured 1421. The reference cell compensates (and hence corrects for) the losses due to scattering, reflection, transmission, and polarization from the cell walls and host molecules [42]. The order parameter of the dye is calculated from the expression:
In the above expression the effect of the internal field is not taken into account. The correction to A,, and Al (or TI,and Tl) yields a slightly different value for the order parameter [42]:
andA,,(A)andA,(il) are the parallel and perpendicular absorbance of the dye at wavelength A. !A,,(A) dil and !A,(A) dA can be evaluated as the area under the absorbance curves in the 380-780 nm region; S,, and D,, provide the averaged values over the whole visible range. To account for the photopic response of the human eye for color [75], we may define the photopic order pa-
Usually the absorption (or transmission) spectrum is run and recorded in parallel or perpendicular geometry over the range 380-780 nm. From these measurements Amax,All, andA,aredetermined [42].A,,and A, are measured at A,, . Unless specified, the order parameter is usually calculated at Amax. A,,(A)and A,(& have also been calculated by keeping the polarizers parallel to
0.5 0.0 400
500
600 Wavelength (nm)
700
800
Figure 3. The absorption spectrum of a dichroic dye in a liquid crystal host.
3.4.6 Optical, Electro-Optical, and Life Parameters
rameter (S),
and the dichroic ratio (Dph)as:
and V ( A )is the value of photopic luminosity efficiency function at wavelength A. For these absorption and transmission measurements, polarizers must have extremely high polarization efficiency (as close as possible to loo%), otherwise the values of Seffand D,, will be too low, and even misleading in a few cases. Polarizers HN 32 or Sanritsu 9218 are good for this purpose [92]. Moreover, as the order parameter is temperature dependent, all measurements should be recorded at the same temperature. It is worth mentioning that, to obtain accurate results, the spectrometer beam should not carry any polarization. Unfortunately, however, most of them do. The absorbance measurement of a black dichroic liquid crystal mixture over the wavelength range 380-780 nm is shown in Fig. 3.
3.4.5 Impact of Dye Structure and Liquid Crystal Host on the Physical Properties of a Dichroic Mixture These parameters have been discussed in detail by the author and several other workers [14- 16, 42-49]. Studies have been done mostly on pleochroic dyes. In general, it has been found that the dye order parameter increases with increasing length of the dye, while it decreases with increasing breadth of the dye. The dye order parameter is heavily dependent on the host. Usually it increases with an increase in and decreases with a decrease in the host order parameter. Elongated dyes are found to have
27 1
higher order parameters, and shorter dyes lower order parameters than the host. Elongated dyes are also found to withstand thermal fluctuation better at higher temperature, and hence show less variation in order parameter compared to the host, with increase in temperature. The temperature range of a dichroic liquid crystal mixture is basically governed by the temperature range of the liquid crystal host. It has been noted that the addition of dichroic dyes increases or decreases the clearing point of the mixture slightly (-1 - 5 " C )depending on its compatibility with the host liquid crystal. The solubility of a dye depends greatly on its structure and host. In a multicomponent system (especially black dyes), the solubility of one dye is affected by the presence of others. Asymmetrically substituted dichroic dyes are found to have higher solubility than their symmetric analog [48]. The introduction of lateral alkyl substituents in dichroic dye molecules enhances their solubility in liquid crystals. An admixture of dichroic dyes absorbing in the same spectral range usually has higher solubility than does a single dye. The viscosity of host increases with increase in dye doping. The dielectric anisotropy, elastic constants, and refractive indices of dichroic mixtures are basically those of the liquid crystal host [ 161.
3.4.6 Optical, Electro-Optical, and Life Parameters As dichroic displays provide a man-machine interface through human eyes, their features and parameters must be optimized for human vision requirements [75]. For a clear understanding and detailed description of human vision, color and its measurement, visual requirements, and reliability issues of LCDs, the reader is referred to the article by Bahadur [75]. Some of the issues
27 2
3.4 Guest-Host Effect
related to dichroic displays are discussed very briefly here.
3.4.6.1 Luminance Luminance is the most important photometric quantity to define display performance. However, the perceived brightness does not bear a linear relationship with luminance, and depends also on the ambient lighting, the surroundings, etc. Luminance is usually measured with radiometric equipment using photopic filters or computer-controlled corrections for photopic response. The legibility of a character is not dependent entirely on contrast but also depends on luminance, the cone it forms on the retina, the color, background, etc. [75, 931. The sensitivity of the human eye to luminance discrimination (AL/L), and hence to the contrast between the pixel and the background, increases with increasing luminance level up to 100 Cd/m2 and then saturates [75]. Hence, for legibility of a display, luminance as well as contrast should be resonably high. A high luminance dichroic display with less contrast often looks better and more legible than a similar display with high contrast but very poor brightness or luminosity.
The background luminance can be taken to be either the luminance of the activated segment in its off mode or the luminance of the electro-optically inactive portion of the cell. Usually there is a small difference between the contrast in these two situations, which is neglected in most applications [75]. However, if the segment shows memory or reminiscent contrast (such as in the case of the phase change dichroic display) the value of the contrast calculated using these two procedures may be drastically different. The contrast ratio may be time dependent too. In the case of LCDs the contrast ratio is found to depend on the viewing angle and temperature. Dichroic LCDs exhibit a smaller reduction in contrast versus viewing angle compared to TN LCDs. In the case of dichroic (especially monochrome) displays, the contrast ratio is sometimes measured at Amax, which shows the maximum capability of the dye but does not correspond to the photopic response. The contrast ratios calculated using the radiometric equipment (or in arbitrary units of radiance) also differ from those evaluated using photometric equipment. Bloom and Priestly [94] therefore defined the perceived contrast ratio (PCR):
3.4.6.2 Contrast and Contrast Ratio The luminance contrast may be defined as the ratio of the difference between the symbol and background luminance, AL to the luminance of the symbol (or background, whichever is more luminous), i.e.
C=-AL L
The contrast ratio is defined as the ratio of greater luminance L,,, to lesser luminance Lminbetween the symbol and background. CR=- L a x Lin
where T'(A) and T,,(A)are the percentages of the light transmitted in the on and off states, respectively, and V(A) is the photopic luminous efficiency function. This equation is basically the same as Eq. (12) if the light intensities are measured in luminance (i. e. photopic response). Color is a combination of both chrominance and luminance, and hence to deter-
3.4.6 Optical, Electro-Optical, and Life Parameters
mine the contrast and contrast ratio of any colored pixel both these parameters must be used. However, there is no simple, exact, quantitative criterion for color that can be applied to color contrast in terms of legibility [75]. Some measurements have been reported in terms of color difference and color contrast [75].A more valuable approach would be to quantify the display’s visual performance with regard to its perception, from a human vision point of view [75].The threshold levels of luminance and chrominance detection are dependent on luminance level, target shape and size, search patterns, background, and other human vision parameters [75, 951.
3.4.6.3 Switching Speed The switching times of the LCDs are defined in the article by Bahadur [75].The rise and decay times Triseand Tdecayare given by the general equation [96]
17
T=
E~ A&E2 - kq2
where 17 is the viscosity, A& is the dielectric anisotropy, k is the appropriate elastic constant, E is the applied electric field, and q is the wave vector of the disturbance. The wave vector q can be expressed as q = -It
P where p is the pitch of the disturbance. In the case of cholesteric materials, q is the wave vector of the cholesteric helix and is also field dependent. Here p is the pitch of the material. In the absence of the field q=qo=n/po, where p o is the pitch in the quiescent state. In TN, dye-doped TN, and Heilmeier displays, where the decay time is determined by the propogation of the alignment from the cell walls, q will take the value of nld, where d is the cell
273
spacing. Hence,
Trise . =
17 d 2
E~ A&V 2- kIt2
and
where V is the applied voltage. Besides the rise and decay times, displays also exhibit turn-on and turn-off delays. The general equation (Eq. 15) becomes less accurate for the cholesteric -nematic transition, in as much as the reorientation to nematic is dependent upon the character of nucleation sites for the transition such that:
where B characterizes the nucleation sites, and is roughly a function of the inverse of the concentration of chiral material in the nematic host. Over a small range of pitch, the rise time is a relatively linear function of p-’ . Unlike the twisted nematic, the turnoff time of the cholesteric configuration becomes dominated by pitch rather than cell spacing as a result of the effect of the pitch on q . So phase change dichroic LCDs should have a much faster decay compared to TN displays. However, due to memory or reminiscent contrast the actual turn-off time perceived by the eye in the case of phase change dichroic LCDs is much slower than the predicted turn-off time. Cells having less memory, especially those formed with homeotropic or hybrid alignment, seem to have much faster turn off.
3.4.6.4 Life Parameters and Failure Modes As many of materials and processes are common to both dichroic and TN LCDs, most of the failure modes and defects observed in TN LCDs are also observed in
274
3.4 Guest-Host Effect
dichroic LCDs [16, 751. The defects and reliability issues in dichroic LCDs are basically related to the materials (such as dichroic mixture, glass, surface alignment, peripheral and end-seal, color filter, connectors, heater, polarizer, reflector, etc.) and their deterioration in adverse operating conditions (such as high temperature, intense light exposure, humidity, thermal shock, vibration, etc.). Even mild operating conditions over a period of time can have accumulated effects in certain types of defect. Some of these are blooming pixels, contrast loss due to dye bleaching, increase in power consumption, voids and air bubbles, and dye segregation. These, along with many others, have been discussed in the case of TN as well as dichroic LCDs by Bahadur (75) in an article that also includes a discussion of LCD failure modes, their causes, reliability, accelerated life testing and other life parameters of dichroic LCDs. The thickness nonuniformity, besides creating nonuniform contrast and switching, also creates annoying pitch lines, as discussed in Sec. 3.4.3. One noticeable defect in dichroic displays used in military and avionics applications, especially in deserts (high temperature, vibrations, and intense light) over a prolonged period is the development of gas bubbles in the displays [16]. This problem has been overcome to a great extent by cutting the light up to 400 nm by using appropriate glasses and filters. The problem of vacuum voids observed at low temperature is caused by the different coefficient of thermal expansion of liquid crystal and glass [75].
3.4.7 Dichroic Mixture Formulation Dichroic mixtures are usually formed in monochrome or black form. Dyes are mixed into the liquid crystal, and the mixture is
heated to about 10°C above its clearing point for sufficient time to dissolve the dyes completely. The dye concentration should be kept well below its solubility limit at the lowest required operating or storage temperature. If the dyes are near their saturation limit, their chromatographic separation during filling of the cell is observed more frequently. Usually the least soluble dye segregates first and acts as a nucleation center for further crystallization over time. The mixture should be degassed before use and should be kept under dry nitrogen or helium. A good method for degassing is a process where the surface area of the fluid is increased while applying ultrasonic agitation and heat simultaneously during degassing under high vacuum [97]. The absorption spectra of the dyes are found to be shifted when mixed in liquid crystals. The nature and the amount of the shift depends on the dye, its amount, and the liquid crystal mixture. Many monochrome and black dichroic mixtures are available commercially [54].
3.4.7.1 Monochrome Mixture Single dyes are usually used for forming monochrome mixtures. Sometimes it is necessary to mix two or more dyes to get a monochrome color if the color cannot be obtained with the desired properties by using a single dye. For example, a green dye can be obtained by mixing a yellow and a blue dye.
3.4.7.2 Black Mixture To make a black mixture, many dichroic dyes covering the whole visible spectrum are required [55-581. Besides the desired Amax and color, the three important criteria for choosing the dyes are their stability, solubility, and order parameter. Broad spectral band dyes are preferred over narrow band dyes.
3.4.8
Any given color can, in principle, be matched in two different ways: by spectral color matching or by metameric color matching [16, 5 5 , 931. In spectral color matching, colorants are mixed to reproduce the transmission (or reflection) spectrum of the given color. Spectrally matched colors have the advantage of staying matched under all conditions of illumination. However, they may require a large number of colorants to fit the spectrum. In the case of dichroic dyes the situation becomes a bit complicated as we require color matching in both quiescent and energized modes. In metameric color matching, dyes are mixed to achieve only the same sensation of the color to the human eye, and the resulting spectrum may be quite different than the original color [ 16, 55, 931. Any color can be matched metamerically using only three colorants. However, this color match is generally satisfactory only for one type of illumination. In dichroic display applications the color matching is usually done using 4-8 dyes. Efforts are made to achieve spectral matching of the colors as closely as possible in the quiescent state by using available dichroic dyes with high order parameter, photochemical stability, and solubility. Some tweaking is done to obtain finally the desired hue in the one state under given lighting conditions. It is extremely difficult to get exactly the same color matching in both the on and off states using different dyes from those contained in the specimen for all lighting conditions. For normal applications only two lighting conditions are required: one for daylight and one for nighttime applications. Usually incandescent lamps (source A) are used for phase-change type dichroic displays for night vision. For night vision goggle applications, commonly required in avionic displays, one has to filter out the infrared and most of the red light [98]. This can be done by using a fil-
Heilmeier Displays
275
ter. In large area displays the use of cold or hot cathode fluorescent lamps is becoming popular. Sometimes a minor correction for the desired chromaticity is done by using appropriate color filters behind the displays. To match the hue of a given dichroic mixture one can use a computer program [55, 561, or sometimes it can be achieved by 'tweaking' the existing mixture. In this case the absorption of both mixtures should be recorded using the same light source (or UVvisible spectrum) and the difference in the absorbance curves in various regions should be minimized by adjusting the dyes. The close spectral matching results in a close hue matching under various illuminations. Minor 'tweaking' may be required to match the on state chromaticities.
3.4.8
Heilmeier Displays
The Heilmeier display was the first dichroic display discovered [l-31 and can be made in transmissive, reflective, and transflective forms by appropriate choice of the reflector. However, these displays are used mostly in transmissive mode with a strong backlighting. Conventional Heilmeier displays use unidirectional homogeneous alignment and can be made with 0" or 90" twist [ 1, 2, 13- 161. The host liquid crystal has a positive dielectric anisotropy and the dyes are pleochroic. A Heilmeier display uses one polarizer mounted with its polarization axis along the long molecular axis of the dichroic mixture. The polarizer can be mounted on the front or the back of the display. The light, after passing through the polarizer, is polarized with its E vector along the long molecular axis of the dye and is absorbed. The cell looks dark colored or black depending on the dyes used. When the electric field is applied, the liquid crystal molecules, along with the dyes, become
276
20 l o0
3.4 Guest-Host Effect
c
I
/
TN display becomes saturated and achieves maximum contrast at lower voltage and its threshold characteristic is steeper compared to that of a Heilmeier display. In TN display the contrast ratio remains flat after saturation, while in Heilmeier displays the contrast ratio continues to increase with increasing voltage after becoming almost saturated. The reason for this is that TN LCDs are based on the capability to rotate plane polarized light and, once the central layer is aligned with the field, it is unable to rotate the plane of polarization of the light, and the display becomes full contrast. The contrast in a Heilmeier display is based on the alignment of more and more dichroic layers in the direction of the field. The central layer quickly becomes aligned after the threshold voltage, but layers in the vicinity of the glass plates are aligned more and more only with increasing field. Figure 4 also shows that for an optimized cell thickness both the contrast ratio and brightness are lower for Heilmeier displays than for TN displays. The contrast of a Heilmeier display can be made equal to or more than that of a TN display by increasing the amount of dyes in the mixture, but the transmission decreases drastically [ 15, 161. If transmission is matched, then the contrast ratio of the Heilmeier display decreases [ 15, 161. With increasing viewing angle both the contrast and transmission decrease drastically in TN displays, while these are little affected in Heilmeier displays (Fig. 5 and Table 2). Hence Heilmeier displays have a much wider viewing angle than do TN displays.
1
0
1
2
3
4
5
5
7
8
9
1
VOLTAGE ( V )
Figure 4. Threshold characteristic of Heilmeier display compared to those of a TN and a dye-doped TN display. The transmittance of the Heilmeier, dyedoped TN, and TN displays are 16.0%, 26.7%, and 35.5%, respectively. Operating voltage, 10 V.
aligned in the direction of the field. In this mode, the E vector of the light is perpendicular to the long molecular axis of the pleochroic dye, and light is not absorbed. The operational principle of Heilmeier displays is shown in Fig. 1. Although doping of the dichroic mixture with a chiral material is not necessary, occasionally (especially for 90" twist geometry) this is done. Heilmeier displays can also be made with (1) negative dichroic dyes in a liquid crystal host of positive dielectric anisotropy, or (2) pleochroic dyes in a host of negative dielectric anisotropy. These methods generate colored or black information on a clear background (see Sec. 13.1). The discussion below applies primarily to Heilmeier displays using pleochroic dyes in a host of positive dielectric anisotropy. The theoretical model for Heilmeier displays was proposed by many workers [16, 99, 1001.
3.4.8.1 Threshold Characteristic The threshold characteristic of Heilmeier displays and that of TN displays having the same polarizer and host liquid crystal are plotted in Fig. 4.The figure shows that the
0
3.4.8.2 Effects of Dye Concentration on Electro-optical Parameters With increasing dye concentration c , the contrast ratio of the Heilmeier display increases and its transmission decreases
3.4.8 Heilmeier Displays
277
Table 2. Contrast ratio and percent transmission of Heilmeier, dye doped TN, and TN displays versus viewing angle [16]. Viewing angle (")
TN
- 60 -54 -48 -42 -36 -30 - 24 -18 -12 -6 0 6 12 18 24 30 36 42 48 54
Dye-doped TN
Heilmeier
T (70)
CR
T (%)
CR
T (%I
CR
24.2 27.2 30.1 32.8 35.1 36.8 37.7 38.6 38.9 39.1 38.8 38.7 37.6 37.1 35.1 33.6 31.4 28.5 25.3 21.5
14.8 19.8 27.9 33.8 43.5 51.7 73.9 77.5 73.2 69.6 66.6 63.3 57.1 50.3 43.2 34.7 27.8 22.1 17.4 13.6
20.9 26.6 29.4 31.7 33.6 35.3 35.8 36.8 36.5 36.8 36.8 36.4 35.6 34.2 33.2 31.4 29.7 27.1 24.0 20.0
24.8 35.7 49.0 67.0 91.9 109.0 110.8 108.0 99.1 88.9 82.7 74.8 66.9 58.1 50.4 42.5 35.3 29.2 23.4 19.1
13.0 13.0 14.8 16.3 17.2 17.7 17.7 17.8 17.6 17.6 16.9 16.9 16.5 15.8 15.3 14.6 13.8 13.8 11.2 9.6
67.2 75.5 75.6 75.7 72.9 68.9 66.4 63.6 60.4 62.5 59.0 60.8 62.7 62.9 63.9 69.0 69.0 70.3 68.1 63.1
Figure 5. Contrast ratio versus viewing angle for Heilmeier, dye-doped TN (DDTN), first-minimum TN (FMTN), and second minimum TN (SMTN) LCDs. -60
-50
-40
-30
-20
-10
0
10
20
30
40
50
60
Viewing Angle (degrees)
[ 15, 16, 1001. The switching time of the dis-
play also increases a little due to the increase in viscosity of the liquid crystal. This increase in switching time becomes more significant at lower temperatures and very often restricts the lower operating temperature of the display. The threshold voltage does not seem to be affected significantly by
an increase in dye concentration. Figure 6 shows the dependence of electro-optical parameters of a Heilmeier display on the dye concentration. It can be seen that the contrast ratio increases exponentially with increasing dye concentration, while the transmission shows a more or less linear decrease. This means that with a small increase
278
3.4 Guest-Host Effect 40
180
160
sH 4
U
5
140
g
30 120
8
100
20 80
U
P4 2
60
8
10
40
Figure 6. Dependence of the constrat ratio and the percent transmission of a Heilmeier display on the dye concentration.
20
0
1
2
3
4
5
DYE CONCENTRATION(%)
in dye concentration one can get a high contrast without a heavy loss in transmission.
20
-
r
18 -
16-
14-
3.4.8.3 Effect of Cholesteric Doping A doped dichroic mixture (0.15%cholesterylnonanoate) produces an esthetically better cell, especially with a 90" twist, as it is free from reverse twist patches. There is little change in contrast or transmission, but the turn-off time To, without cholesterylnonanoate was found to be about 15%shorter (-50 ms instead of 60 ms).
8 5
1
2
5
10-
3
6 -
-1
~
8 -
C
2
4
6
8
10
12
14
16
VOLTAGE ( V )
Figure 7. Threshold characteristics of Heilmeier displays with 0" and 90" twisted homogeneous alignments.
3.4.8.4 Effect of Alignment The 90" twisted Heilmeier cells have sharper threshold characteristics and higher transmission than the parallel aligned versions (0" or 180") (Fig. 7). This can be explained by referring to Fig. 8 [13, 15, 161. In the field-off state the twisted layer absorbs nearly the same amount of light as the parallel aligned (or nontwisted) layer, as within the Mauguin limit the optically polarized mode propagating through the layer departs only very slightly from the linear polarized mode. The major axis of the ellipse follows very nearly in step with the twisted structure, and consequently remains more or less parallel to the optical (absorbing) axis. In the field-on state, however, the twisted layer
absorbs significantly less light than the nontwisted layer. The reason for this is that the orientation of the optic axis in the boundary region 2' on the lower substrate of the twisted cell is at right angles to the E vector of the polarized light and is, therefore, nonabsorbing. The transmission curve for the twisted Heilmeier display is much steeper at intermediate voltages than for the nontwisted layer, but the approach to saturation remains gradual at higher voltages because the upper boundary region 1' still absorbs the light. The threshold characteristic of 90" twisted Heilmeier cells is quite sharp from V,, to V,, (or V6& indicating that low-level multiplexing is possible. The nontwisted,
3.4.8
a)
-
Conventional Heilmeier
Incident Polarization
-
I---)
0
b)
Heilmeier Displays
279
Twisted Heilmeier
90"
0
0 0
-
Transmitted Polarization Field Off
II
0
-
Field On
-
0
U
0
Field Off
Field On
Figure 8. Molecular orientation in 0" and 90" twisted Heilmeier cells.
or 0" twisted, structure exhibits a higher contrast ratio compared to the 90" twisted structure, and is better suited for gray scale applications with TFTs. The isocontrast curves for 90" twisted and parallel aligned versions are shown in Fig. 9. The 180" twisted Heilmeier displays show switch-off behavior similar to n-cells. It takes a long relaxation time to return to the quiescent state after a very fast decay to an intermediate level. This long relaxation is undesirable, and a 180" Heilmeier shutter can function reasonably only after using a holding voltage similar to that of n-cells.
tioned earlier, due to strong surface anchoring, the molecules near the surface do not align with the field. So, even in an excited state, this layer d, is absorbing and therefore reduces the overall contrast of the display. The ratio of this inactive layer 2 d, to the active central layer d - 2 d S , which can be aligned by the field, should be kept small. The switching speed of the display is affected adversely with increase in thickness, as it is proportional to the square of the thickness (see Eq. 15).
3.4.8.5
As predicted from theory, the order parameter has a dramatic impact on the contrast ratio (Fig. 11). The order parameter of the dye is the only parameter that increases both the contrast ratio and the transmission simultaneously. Figure 11 shows that for a good Heilmeier display the dichroic order parameter should be as high as possible (preferably >0.75).
Effect of Thickness
Figure 10 exhibits the effect of the cell spacing d on the threshold characteristic, contrast ratio, and transmission using the same mixture. These measurements show that for an increase in the cell gap from 5 to 11 pm a significant gain in the contrast ratio (-7fold) is achieved with a small loss in transmission (7.6% overall and 32% of the initial transmission). This increase in contrast ratio is achieved primarily due to increase absorption in the off state of the cell due to increased cxd. A secondary reason for this increase can be explained as follows. As men-
3.4.8.6
3.4.8.7
Impact of the Order Parameter
Impact of the Host
As discussed in Sec. 3.4.2, the birefringence, dielectric anisotropy, elastic constant, and transition temperatures of dichro-
280
3.4 Guest-Host Effect
04
Figure 9. Isocontrast curves for (a) 90" twisted and (b) nontwisted Heilmeier cells.
3.4.8
28 1
Heilmeier Displays
70 60
2
r; 70
0
0
50
10
0
E
5
2
4
6
8
w
10
60
10
12
14
0
VOLTAGE 0
2
4
6
8
10
12
14
VOLTAGE (V)
Figure 10. Effect of cell gap on the threshold characteristic and contrast of a Heilmeier display. The transmittances of cells with 5, 8, and 1 1 prn cell gaps are 23.6%, 20.0%, and 16.0%, respectively. Operating voltage, 10 V.
Figure 12. Impact of polarization efficiency on the threshold characteristic of a Heilrneier display. The transmittance of the cells made with polarizers having polarization efficiencies of 65%, 75%, 85%. 92%, 96.9%, 99.5%, and >99.9% are 20.35%, 17.57%, 16.80%, 16.70%, 16.567~~ 16.02%, and 15.98%, respectively.
ciency of the polarizer (Fig. 12), and hence a high-efficiency polarizer with good transmission must be used for this application. The polarization efficiency should be kept above 99% and as close to 100%as possible. 0.60
0.65
0.70
0.75
0.80
Order Pameter
Figure 11. Theoretical calculation of contrast ratio versus order parameter. (After Ong [ 1001).
ic mixtures are more or less those of the host. The viscosity of the mixture and the order parameter of the dyes are also highly dependent on the host. The host should have low viscosity, high dielectric anisotropy, high birefringence, wide operating temperature range, and low K , I . Moreover, it must produce a very high order parameter and good solubility for the dye.
3.4.8.8 Impact of the Polarizer The contrast ratio of a Heilmeier display is highly dependent on the polarization effi-
3.4.8.9
Color Applications
For monochrome applications, one can either put a monochrome color filter inside the cell or use monochromatic back-lighting. For Heilmeier displays, there is another way to get a monochrome display: by using monochromatic pleochroic dyes [26]. For full-color display, color filters must be used. Heilmeier displays exhibit better color performance than TN displays, as the chromaticity of the pixels does not change much at large viewing angles.
3.4.8.10 Multiplexing Heilmeier displays can be multiplexed only for low levels, as the threshold characteristic is not sharp enough for high level multiplexing. The 90" twisted geometry provides
282
3.4 Guest-Host Effect
a better threshold characteristic for multiplexing compared to parallel (0") alignment. Positive mode Heilmeier displays, with pleochroic dyes in a negative dielectric anisotropy liquid crystal, exhibit sharp threshold characteristics and are good candidates for moderate-level multiplexing. Heilmeier displays also do not show unwanted memory effects. In active-matrix displays they can exhibit better gray scale characteristics than the TN mode. However, since the advent of first minimum TN LCDs, Heilmeier displays are rarely used in active-matrix LCDs.
3.4.9 Quarter Wave Plate Dichroic Displays The operational principle of the quarter wave plate dichroic display is shown in Fig. 13 [ 18- 201. The incident unpolarized light becomes almost linearly polarized after passing through the dichroic layer, as the pleochroic dye absorbs the component of the E vector of unpolarized light parallel to its long molecular axis. This linearly polarized light is then converted to circularly polarized light by passing through the quarter wave plate. Upon reflection from the metallic reflector the original circularly polarized light is changed to opposite-handed circularly polarized light which, after passing through the quarter wave plate, is converted to linearly polarized light with its polaDichroic Mixture
I I \ 'I,.
LO/J
i14plate
,
,
"
/
-
rization axis rotated by 90". This re-entrant reflected light has its electric vector parallel to the long molecular axes of the dye molecules, and hence is absorbed by the pleochroic dyes. In the quiescent state, the cell looks colored or black, depending on the dye composition. On application of the electric field, dye molecules, along with the liquid crystal, are aligned in the direction of the field. In this geometry, the electric vectors of the light are more or less perpendicular to the long axis of the dye, and hence the light is not absorbed. Therefore, in the activated state the cell looks clear. In place of parallel alignment on both pieces of glass, a 90" twisted or 270" twisted geometry can also be incorporated. In these geometries the display generates light or clear pixel information on a colored or dark background. By giving homeotropic alignment and using a liquid crystal host of negative dielectric anisotropy one can make a display exhibiting dark pixels on a light background. The procedure for making a good reflective quarter wave plate display (CR > 12 :1) has been described elsewhere [19]. To obtain a transflective mode quarter wave plate display [20] one can replace the reflector by a transflector, put another quarter wave plate at 45" to the rub, and put a high efficiency polarizer parallel to the rub. This cell basically operates as a reflective mode quarter wave plate cell with front lighting and a Heilmeier cell with backlighting.
Linear Polarizer
.
-
Transflactor
(a) QUIESCENT STATE
(b) ACIWATEDSTATE
Figure 13. The structure and operational principle of a transflective mode quarter wave plate LCD in reflective mode: (a) quiescent state; (b) activated state.
3.4.10 Dye-doped TN Displays
3.4.10 Dye-doped TN Displays Dye-doped TN has the same cell geometry as TN, except for the fact that the liquid crystal fluid is doped with a small amount of dye. The addition of dye increases both the contrast ratio and the viewing angle. Only a few studies on dye-doped TN LCDs have been reported [15, 16,25-27, 1021. Scheffer and Nehring [27] have given a detailed theoretical analysis of dye-doped TN LCDs. The threshold characteristic of the dyedoped TN display is very similar to that of a TN display (see Fig. 4). The contrast ratio of a dye-doped TN LCD is heavily dependent on the polarization efficiency of the polarizer, and thus polarizers with very high polarization efficiency (> 99%) should be used. The threshold and operating voltages also increase slightly with an increase in thickness. The contrast ratio shows a similar effect to the Gooch Tarry curve in TN displays. The contrast ratio has been found to maximize at the first and second Gooch Tarry minima [16, 881. It has been found that the incorporation of dyes broadens the Gooch Tarry minima [16, 271. The addition of a small amount of dichroic dye decreases the values of the maxima and increases
283
the values of the minima. The positions of maxima and minima are found to be essentially unaffected by the absorption. The effect of actually increasing the transmission for certain values of d A d Aby the addition of dye is a consequence of dichroism of the dye and does not occur for isotropic dyes. The dichroism of the dye causes the two eigenmodes to be absorbed in different amounts so that they do not interfere destructively so efficiently in the second polarizer [27]. This effect is even more pronounced at higher dye concentrations. At still higher concentrations the maxima and minima disappear altogether, leaving a monotonically decreasing function. Figure 14 shows the impact of the dye concentration on the contrast. It has been found that the contrast ratio of dye-doped TN with 90" twist is higher than or equivalent to TN for only a small amount of dye concentration. For higher dye concentration the contrast ratio decreases, primarily due to the fact that the cell tends to become more Heilmeier like rather than remaining in the TN mode. However, in spite of the lower contrast ratio and transmission, dye-doped TN cells with higher dye concentration provide wider viewing angles, and more achromatic background. The decrease in contrast ratio oc-
1 0
1
2
3
4
DYE (D12) CONCENTRATION (in %)
5
6
Figure 14. Impact of dye concentration on the contrast of a dye-doped TN display.
284
3.4 Guest-Host Effect
curs basically due to the different amounts of absorption of the two eigenmodes. It has been observed that, by reducing the twist angle below 90" in a dye-doped TN mode display, the contrast ratio can be increased further [27]. The threshold voltage does not shift appreciably in dye-doped TN but the operational voltage Vop does. Vop increases with dye concentration. The contrast ratio is found to increase for dye-doped TN compared to TN. Figure 5 shows the viewing angle dependence of dye-doped TN compared to TN and Heilmeier cells; it is better than TN but inferior to Heilmeier at large angles. The contrast of dye-doped TN is much higher than that of both TN and Heilmeier displays. Table 2 shows the percent transmission and contrast ratio of dyedoped TN, TN, and Heilmeier displays. It is clear from the table that the incorporation of dye reduces the percent transmission slightly, but improves the contrast greatly at large angles. This is because TN operates solely on birefringence, while dye-doped TN operates on absorption too. The switching time of dye-doped TN is slightly more than that of TN, but there is no appreciable difference (Table 3). To get the best results with dye-doped TN displays the liquid crystal fluid must have low viscosity, appropriate dielectric anisotropy, and birefringence. The dyes must have all the advantages already discussed in the Sec. 3.4.8 on Heilmeier displays.
3.4.11 Phase Change Effect Dichroic LCDs Phase change dichroic LCDs are the most widely commercialized displays of all the dichroic LCDs. They are based on the cholesteric-nematic phase change effect [ 1031061 and do not require polarizers. The liquid crystal mixture used is a long pitch (- 2- 5 pm) cholesteric material with an appropriate amount (- 2 -6%) of dichroic dyes [12, 15-17, 107-1141. The usual alignments on the glass plates are homogeneous, homeotropic, or hybrid. Homogeneous alignment could be nonunidirectional or unidirectional, with any angle between the buffing directions of the two plates (e. g. 0", 90" or 180"). The display also works without any alignment treatment on the glass. The theoretical treatment for phase change dichroic LCDs is given by White and Taylor [17], Saupe [107], and Scheffer and Nehring [12]. Figure 15 shows the Alp dependence of the eigenwave absorption constants a, and a, as calculated from the theory. For a detailed theoretical treatment of the subject, the reader is referred to the articles by Bahadur [16] and Scheffer and Nehring [12]. The unpolarized light entering the liquid crystal is propagated in polarized modes. For propagation of these modes in a cholesteric liquid crystal, there are four possible types of A versusp dependence [ 12, 16, 108-1101:
Table 3. Switching speed of Heilmeier, dye-doped TN, and TN displays [16]. (")
Tdelayin on (ms)
Trise (ms)
To, (ms)
Heilmer display (10.38 pm)
0 45
15 14.5
25 24.5
40 39
3 3
63 54
66 57
106 96
Dye-doped TN (5.00 pm)
0 45
10 6
26 23
36 29
12
I
29 28
41 35
77 64
TN (5.00 pm)
0 45
14 15
23 24
37 39
14 9
28 25
42 34
79 73
Display
Pitch
Tdelay in off (ms)
Tdecay
3.4.1 1 Phase Change Effect Dichroic LCDs
-
OO
I
1
I !
I
2
i
3
IVPIFigure 15. Alp dependence of the eigenwave absorbances a, .d and q . d for the typical case where n,=1.7, n,=1.5, ae.d=lO.O, q . d = l . O , il=500nm, and d= 10 Fm. The region between dashed lines is the selective reflection band. (After Scheffer and Nehring [121).
Case I: p % A This case, in the nonabsorbing mode, is described by Mauguin and Berreman [ 115 - 1171. The polarized modes follow the twist, and the nematic liquid crystal simply behaves as a waveguide. In a perfectly ordered system, the dichroic dye dissolving in a long-pitch host absorbs only a single component of the E vector. The absorption of unpolarized light is only 50% of maximum, limiting the contrast ratio of only 2: 1. This ratio can be increased to more than 2 :1 by using (1) one polarizer (Heilmeier mode), (2) two polarizers (dye-doped TN mode), ( 3 ) a dichroic dye mixture composed of pleochroic and negative dichroic dyes 11181, or (4) a double cell.
285
Case 11: p - Aln This case, analyzed by Fergason [ 1191 and others [ 1161, gives rise to irridescent colors due to Bragg reflection. We also see the reflection of this band in the case of an absorbing mode cholesteric (Fig. 15). However, one component of the polarized light always gets absorbed. Case III: p 5 A h , This case is described in White and Taylor 1171, Saupe [107], and by others [12]. In this case both the normal modes of the elliptically polarized light have a component parallel to the local liquid crystal director and the long axis of the dichroic dye. Hence more than 50% of the unpolarized light can be absorbed. As is clear from Figure 15, this region shows the maximum absorption (maximum average absorption occurring at Alp n,). The absorption depends on the pitch of the cholesteric which, along with the principal refractive indices nlland nl, determines the eccentricity of the polarized modes. The other important parameters include the order parameter of the dye, its absorbance, and the cell thickness. Although, theoretically, this is the most desired region for operating phase change displays, practical displays are not operated in this region as a very high operating voltage is required due to the very small pitch in this region (see Eq. 17).
-
Case IV: AAln, ( p - 1-5 pm) As is clear from Figure 15 in this region too, both the normal modes of elliptically polarized light get absorbed by the dyes, although q,d, in this case, is smaller compared than that in the region p IAln,. However, due to moderate operating voltages, this is the region in which phase change displays are operated. The cells are usually prepared with either ho-
286
3.4 Guest-Host Effect
mogeneous or homeotropic alignment, with a cell thickness of usually more than 4-5 times the pitch of the dichroic mixture (-2-5 pm). Sometimes hybrid alignment (homeotropic on one plate and homogeneous on the other) is given. Irrespective of the alignment, the central layers adopt the planar Grandjean arrangement, with the helix axis perpendicular to the glass surfaces.
3.4.11.1 Threshold Characteristic and Operating Voltage The threshold characteristic of a phase change dichroic display is shown in Fig. 16. With slowly increasing voltage, the cell seems to go from Grandjean to a scattering focal conic and from there to a homeotropic nematic texture. On reducing the voltage the same effect is observed in reverse order. The first major jump in the threshold characteristic corresponds to the transition from Grandjean or planar to fingerprint or focal conic texture, and the second is for focal conic to nematic texture. The critical unwinding voltage V, for the cholesteric -ne-
matic phase transition can be calculated as [103]:
This equation was derived for an infinitely thick cholesteric layer where there is no torque exerted by the boundaries and cholesteric material has its natural pitch. However, it holds reasonably well for practical devices with large d/p ratios, and in particular for White-Taylor displays with homeotropic boundaries having no forced pitch. The threshold characteristic shows a noticeable hysteresis. The winding voltage V, is given by (see Fig. 16)
where k22and k,, are the twist and bend elastic constants, respectively. V, is found to With homeotropic be smaller than V,.
Figure 16. Threshold characteristic of a phase change dichroic display: (--) homogeneous alignment; (- - - - ) homeotropic alignment. Voltage (V)
287
3.4.1 1 Phase Change Effect Dichroic LCDs
alignment the threshold characteristic shifts towards lower voltage. Homeotropic alignment generates lower threshold and operating voltages (see Fig. 16). Eq. (17) also shows that threshold and operating voltages are directly proportional to the cell gap and inversely proportional to the pitch of the mixture and the square root of A&.Thus, to reduce the operating voltage, the cell thickness must be reduced and the pitch and A& increased. However, increasing the pitch reduces the contrast. To obtain the appropriate contrast and operating voltage we recommended that dlp be kept at about 4-6 for directly driven applications, especially for avionic use. With smaller d/p ratios (d/p<2), the departure of the experimental curve from the theoretical values for the threshold characteristic shows the impact of increasing surface alignment with larger pitch [12, 161. For a value of dlp below a critical value for homeotropically aligned sample, the effect of boundaries is so strong that the critical voltage is zero and a homeotropic nematic structure is obtained [ 1201.
3.4.11.2 Contrast Ratio, Transmission, Brightness, and Switching Speed The impact of the other parameter and pitch on To, is shown in Fig. 17 [108]. It can be seen that To, is less for dyes having higher order parameters. The impact of the order parameter on To, becomes very significant at smaller pitches. For a very large pitch the elliptical waves are converted into linear ones, thereby reducing the absorption of the o-wave, and consequently the contrast. When the pitch is small, the dyes absorb more, yielding a higher contrast. Whenp becomes equal to A/rze,the values of a,and oc, become equal, and light propagates in circularly polarized mode. However, this increases the operating voltage drastically.
S
0.70 0.75
0.80
n,, = 1.77 nL =1.53
0 . 0 1 ” I ’
0
2
I ’ I 4 6 PITCH (rm)
‘
I 0
”
10
Figure 17. Semilogarithmic plots of the transmission To, in Grandjean texture at 550 nm versus the pitch as a function of the order parameter for field-on transmission of 50% and nll and n, of I .77 and 1.53, respectively. (After Cole and Aftergut [ IOS]).
So, one has to make a compromise between contrast and operating voltage. The light is significantly elliptically polarized in normal White-Taylor mode LCDs, as p is kept moderately large (much more than Bn,) in order to reduce the operating voltage and memory. The impact of birefringence on the contrast ratio can be seen from Fig. 18 [ 12, 15, 1081. This figure also shows the impact of the number of turns of the pitch (d/p) on the contrast ratio. The curve shows that a low birefringence material attains saturation of the contrast ratio with a low number of turns or with a low cholesteric doping. Hence, a lower value of An would also be preferable from an operating voltage point of view. Figure 18 also shows that the contrast ratio increases with an increase in the number of
288
3.4 Guest-Host Effect
d
NEUTRAL DYE R 1 6 . 7
I
I
I
I
I
2
3
4
NUMBER OF TURNS
-
turns of the cholesteric in a fixed cell thickness. For practical devices, a thicknesdpitch ratio of 4-6 is found to be more than adequate for dichroic mixtures having a birefringence of about 0.13 in a cell gap of about 10- 15 pm. The contrast ratio of a dichroic display can be increased by putting more dyes in the mixture. However, this decreases the brightness of the display and it looks dull. With increasing concentration of a black dye, the contrast ratio increases while the brightness of the display is reduced [ 12, 161. However, for single dyes the contrast ratio increases and becomes saturated. In fact, with a dye concentration above this saturation point, the contrast ratio starts to decrease for monochrome dyes. This surprising behavior is a general phenomenon for a dye that has practically no absorption in a wavelength region where the eye is still sensitive [12, 161. An extremely high concentration of any such dye would give a contrast ratio near 1.O. The impact of host birefringence and the number of helical turns on the contrast ratio of the display is illustrated in Fig. 19. The fact that these curves are nearly straight
I
5
I
6
Figure 18. Dependence of the contrast ratio on the number of turns of the cholesteric helix in the layer for different host birefringence An. (After Scheffer and Nehring [12]).
u)
z a
3
I-
0.2
-
anO.3
Figure 19. Curves of equal perceived contrast ratio for different numbers of helical turns and different values of host birefringence An. (After Scheffer and Nehring [ 121).
lines passing through the origin indicates that for a given cell thickness and a small enough An the contrast ratio is inversely proportional to the product pAn. For the same contrast, the operating voltage can be reduced by increasing the pitch and reducing An, as the operating voltage is inversely proportional to the pitch.
3.4.11 Phase Change Effect Dichroic LCDs
-I
289
HOMOGENEOUS
II
HOMOGtNEOUS
IW
w 300 TlMElmrJ
ZM
z-
41
v)
2-
z
I-I 0
0
\ ' -10
1
OFF STATE TRANSMISSION
I 20
0
I
I
1
40
Dichroic displays presently used in avionics have a reflective contrast ratio of >25 : 1 and a transmissive contrast of about 6: 1 with a brightness of over 18% at a 45" viewing angle. These displays operate from -30" to + 85 "C. The low-temperature operation is assisted by a heater. Scheffer and Nehring proposed a useful index f i for selecting a host material to give lower operating voltage by combining the linear relationship of p-l versus An for a fixed contrast and the threshold voltage relationship with material parameters. 1
I--(-)
-
1
&,,A&
An
k22
where kZ2 is the twist elastic constant and c0 is the permittivity of free space (=8.85 x MKS). Asf l does not include the impact of the order parameter S , or the viscosity 17 of the host on the performance of the dichroic display [15, 161, we define another parameter [ 151.
Higher values offl and f 2 would be advantageous. Usually, liquid crystals having
I 60
I
801
Figure 20. Switching speeds and memory effects in phase change dichroic LCDs in transmissive mode. The inset figures show the switching speeds on a shorter time scale.
TIME (sec)
lower An also have lower 17. Sometimes, in very simplistic terms, SLcan be replaced by T,, as nematic materials of the same family with higher T, have higher S, and the order parameter of the dye follows the order parameter of the host. The brightness of the display is found to be dependent on the reflector also. A diffuse BaSO, reflector and Melinex and Valox (GE) plastic films are good Lambertian reflectors. It has been found that bonding these reflectors on the rear of displays reduces the brightness slightly. Sometimes it is preferable to put BaSO, on another glass plate, keeping it separate from the LCD. The switching speed on the phase change dichroic cell is discussed in Sec. 3.4.6.3 and 3.4.1 1.3 (see also Fig. 20).
3.4.11.3 Memory or Reminiscent Contrast As mentioned earlier, with a slow increase in voltage the phase change display goes from a planar texture to fingerprint cholesteric and then to homeotropic nematic [12, 13, 15, 16, 1121, and vice versa when the voltage is reduced slowly. However, the
290
3.4 Guest-Host Effect
actual operating or dynamic situation produces significantly different results, as the voltage is applied or removed quickly without giving time for equilibrium conditions. With quick application of the voltage, the transition from planar cholesteric to homeotropic nematic is very fast, and no unwanted electro-optical effects are observed. However, when the excited pixel is turned off it does not decay quickly and retains a significant contrast over a long time in a few geometries, the worst being the transmissive mode homogeneously aligned sample. In this geometry, contrast decays from 100% to about 10- 15% very quickly, but it takes a long time to decay from about 15% to 0% and to merge completely with the background contrast (Fig. 20). This is a very undesirable feature as it gives the impression that turned-off segments are still partially on. The fast decay in contrast from 100% to 15% is due to a nematic to focal conic cholesteric phase transition, and that from 15% to zero is basically due to a focal conic to planar transformation. Usually it takes a long time to relax from a fingerprint to a planar cholesteric texture, resulting in an unwanted memory effect. If the scattering is high, the pixel looks noticeably excited for a long time after the voltage has been turned off. In the case of homeotropically treated phase change dichroic LCDs, the contrast from 100% to <5% decay instantaneously and then merges from 5% to zero reasonably quickly, exhibiting almost no memory. In the case of a reflective mode homogeneously aligned sample the residual level is reasonably low (<4-5%), probably due to increased absorption. Similarly, memory is completely unnoticeable in the case of homeotropically treated reflected mode displays. Some people find that the parallel boundary configuration is unsuitable for display applications because the Grandjean
texture in deactivated regions of the display is full of metastable disclination lines [12, 13, 15, 171. These disclination lines strongly scatter the incident light and give the display an objectionable ‘after image’, which persists from several seconds to several minutes after the segment has been deactivated. The cholesteric texture obtained with perpendicular boundary conditions is not a uniform texture and scatters the light very slightly. Under the microscope the entire field of view is filled with right-handed and left-handed spirals. This cholesteric texture is termed the ‘scroll texture’ and appears very much like an end-view of a bundle of rolled-up scrolls [91, 104, 105, 1121. The helix axis in this texture is still predominantly perpendicular to the glass surface in the bulk of the layers, similar to the Grandjean texture. Only the layers in the close vicinity of the glass surfaces have their helix axes parallel to the glass surface. It is noteworthy from an application point of view that the scroll texture is adopted without any significant disclinations immediately after a display element is turned off, and this structure, essentially a nonscattering scroll texture, is quite different from the highly scattering cholesteric focal conic texture that occurs at intermediate voltages. In the focal conic texture the helix axis is essentially parallel to the glass. The dichroic dyes embedded in this geometry absorb less compared to the case when they are embedded in a planar texture. The transition from fingerprint or focal conic to scroll texture is much faster compared to that from focal conic to planar. However, it has been found that homogeneous alignment generates a higher contrast ratio and is also more durable. The memory with homogeneous alignment is found to exhibit a regular pattern of peaks with the pitch of the mixture in the cells. Smaller pitches have higher peaks. The memory is also found to be strongly de-
3.4.12
pendent on the viscosity of the mixture. Low viscosity mixtures have less memory. Highly absorbing cells also seem to have less noticeable memory, as do cells with larger pitch. With proper adjustments to the cell thickness, pitch, birefringence, and viscosity one can make a very good cell with low memory using homogeneous alignment.
3.4.11.4 Electro-optical Performance vs Temperature The contrast ratio of the phase change dichroic display is found to decrease with an increase in temperature (see Fig. 22). This decrease is basically caused by the reduced absorption in the quiescent state that results from the decrease in the order parameter and pitch of the dichroic mixture at higher temperatures. The cells show faster switching speed and lower memory at higher temperature. The switching becomes slow at lower temperature due to an increase in the viscosity of the mixture, and a heater is usually required for low temperature operation.
3.4.11.5 Multiplexing Phase Change Dichroic LCDs Phase change displays are basically operated in direct drive mode. Some efforts have been made to operate them, especially the longpitch White-Taylor mode [16, 110, 1131 and positive mode nematic cholesteric phase transition with negative dielectric anisotropy host [ 16, 1211 in multiplexed mode. Efforts have also been made to drive phase change displays for high information content using special drive schemes [ I 221. These approaches did not achieve much popularity but, due to their high reflectance, there seems to be some emerging interest for their application in AMLCDs [123, 1241.
29 1
Double Cell Dichroic LCDs
3.4.12 Double Cell Dichroic LCDs A single cell guest - host nematic (with infinite or very long pitch) dichroic LCD, unassisted by apolarizer or quarter wave plate, can have a maximum contrast ratio of 2: 1 , as it absorbs only the E vector of unpolarized light parallel to the long molecular axis of the dye [ 14- 161. Even in the case of phase change transflective dichroic LCDs with reasonable reflective brightness (15- 18% at a 45" angle) [114], transmissive contrast ratio (typically 5: I to 6: 1) falls short of the requirements for many applications. To increase the contrast ratio without greatly sacrificing brightness, double cell geometry has been used. Basically there are three categories of double cell dichroic LCDs [14- 16, 21 -24, 125, 1261, nematic dichroic, one pitch cholesteric, and phase change dichroic.
3.4.12.1 Double Cell Nematic Dichroic LCD The geometry of a double cell nematic dichroic LCD [13-16, 21, 1261 is shown in Fig. 21. The liquid crystal mixture generally used is composed of pleochroic dyes in a nematic host of positive dielectric anisotropy. The first cell has a unidirectional homogeneous alignment in one direction, while the second cell has a unidirectional homo-
'on +
SURFACE LAYERS
( a ) OFF-STATE
( b) ON-STATE
Figure 21. Geometry of a double cell nematic dichroic LCD. (After Seki, et al. [22]).
292
3.4 Guest-Host Effect
geneous alignment perpendicular to the first cell. Making the double cell, using only three pieces of glass including a thin middle plate, reduces the parallax. The component of the unpolarized light parallel to the pleochroic dyes in the first cell is absorbed by the first cell, while the component of the light perpendicular to it is absorbed by the second cell. Thus, the double cell absorbs the unpolarized light very effectively in its quiescent state. On application of the voltage the dye molecules align in the direction of the field along with the liquid crystal, and hence the light, is not absorbed. The cell has a very high contrast ratio and wide viewing angle. The mixture may be either pure nematic (infinite pitch) or slightly doped nematic with very long pitch (pS-44. The cell geometries could be made either unidirectional homogeneous or twisted nematic. In 90" twisted geometry the alignment on the first surface of the second cell should be perpendicular to the alignment on the surface of the first cells. Recently, Ong [ 1261proposed a Heilmeier display having two asymmetric cells. This display has a high contrast and wide viewing angles, but low transmission. One can also use two separate Heilmeier cells with different dyes to make acomposite cell, and by controlling voltage differently a set of colors can be obtained. Two cells with different dyes and one polarizer, can also be used.
3.4.12.2 Double Cell One Pitch Cholesteric LCD The geometry is very similar to that of the double cell nematic dichroic LCD, with each cell having a single turn of cholesteric dichroic mixture [23, 241.
3.4.12.3 Double Cell Phase Change Dichroic LCD In double cell geometry [ 16, 114, 1251 two identical cells are placed together with a transflector in the middle. In reflected light or daylight mode, the cell behaves as a normal reflective cell, as most of the light (-95%) is reflected by the transflector. In daylight mode the first cells only, or both cells, are excited, while in transmissive mode both cells have to be excited together. The background in the quiescent transmissive mode looks much darker as the light is absorbed by the two layers of the dichroic mixture. When the field is applied the pixels become transmissive due to the alignment of pleochroic dyes in the direction of the field. The transmissive contrast in the double cell mode is very high (>15:1), which is good enough for almost all applications. The temperature variation of the contrast ratio of the double cell dichroic display is shown in Fig. 22.
3.4.13 Positive Mode Dichroic LCDs Most of the LCDs discussed in the preceding sections are negative mode LCDs, that is displays exhibiting colorless or white digits on a colored or black background. In many applications colored or black digits on a colorless background are preferred - these are positive mode dichroic LCDs [ 13 - 161.
3.4.13.1
Positive Mode Heilmeier Cells
Using Pleochroic Dyes The geometry of Heilmeier cells was discussed in Sec. 3.4.8. Using a liquid crystal mixture of negative dielectric anisotropy mixed with pleochroic dye initially in homeotropic geometry, we can make a posi-
3.4.13 Positive Mode Dichroic LCDs
z5
I
REFLECTWE
'
0 d
0
293
viewing
6 R H / l 5 * V viewing
20 viewing
2 0
3
15
10
z
8 5
0
Figure 22. Temperature variation of the contrast ratio of a double cell phase chan ge dichroic LCD. 20
40
60
80
100
120
TEMPERATURE ( "C )
tive mode display. In the off state the cell would look clear, as the long axis of the pleochroic dye is in the direction of propagation of the light. On application of the field liquid crystal molecules will stand perpendicular to the electric field due to their negative dielectric anisotropy, and consequently the dyes become parallel to the E vector of the light. Hence, the light is absorbed and colored or black information is displayed on a colorless background. Originally, this approach required high driving voltage as the materials had small -A&values (--0.5). However, recent syntheses of materials of high-A& (--4.5), such as E. Merck's ZLI 2806 (A&=-4.8), Chisso's two-bottle miscible mixtures LIXON EN 24 (A&=-5.6) and N24 (A&=-l.l), have solved this problem, Many black and colored dichroic mixtures with high negative dielectric anisotropy and high order parameters are also available commercially [54]. The host material should be free of ionic impurities in order to prevent the occurrence of electrohydrodynamic effects in the display. To get the best results one requires unidirectional homogeneous alignment of the
REDUCED VOLTAGE
Figure 23. Threshold characteristic of a positive mode guest-host cell using a negative dielectric host and homeotropic alignment. (After Scheffer [ 131).
dichroic mixture in the direction of the polarizer in the field-on state, which is achieved by treating the glass plates with tilted homeotropic alignment [83]. The transmission characteristic of the display is found to be quite steep [13] (Fig. 23), which makes it a good candidate for high level multiplexing. This is reasonable because, just above the threshold, the axis of maximum absorption is perpendicular to the layer where it can produce a large change in absorption for a small change in the tilt angle. Saturation is only approached gradual-
294
3.4
Guest-Host Effect
ly, as higher voltages are required before the boundary layers start absorbing light. Introduction of a 90” twist in the layer does not improve the transmission characteristic. Scheffer [ 131 has reported computed isocontrast curves for both transmission and reflection. In transmission mode an acceptable contrast ratio was found over a wide range of viewing angles, but in reflection mode the viewing angle uniformity is spoiled by ‘holes’ where the contrast is reversed. The holes occur at the angle of incidence for which the homeotropic layer acts like a quarter wave plate. This effect is also present in the on state of Heilmeier-type displays, but is not apparent as it affects only the character segments and not the display background. Using Negative Dichroic Dyes
A dye of negative dichroism can be mixed into a liquid crystal mixture of positive dielectric anisotropy and put in a cell having unidirectional homogeneous alignment [ 13- 16,52,53].A single polarizer is oriented in front of the layer, with its transmission axis parallel to the rubbing direction of the adjacent cell. The cell does not absorb in the quiescent state, as the transition moment of
the dye is in the direction of propagation of the light. On application of the electric field the transition moment of the dye becomes parallel to the E vector of the light. In this case light is absorbed. The major problem for this type of display is the availability of high order parameter negative dichroic dyes covering the whole spectral range. The various geometries for Heilmeier displays are listed in Table 4 [16,53]. Using Dual Frequency Addressing These nematic mixtures [ 161 show positive dielectric anisotropy below a critical frequency f, and negative dielectric anisotropy abovef,. In a dichroic cell (Heilmeier type) using such a host, negative contrast results if a display with homogeneous alignment is driven by low frequency voltage VL (fL4 f,),whereas positive contrast results if a display having homeotropic alignment is driven by a high frequency voltage VH(fH@fc). By driving the same display having homeotropic alignment with VL and VH one can get a dual frequency addressable positive mode display. This dual frequency mode addressing provides a much sharper threshold characteristic and is a good candidate for multiplexing [75].
Table 4. Guest-host variants in nematic hosts. No.
Starting orientation
A&
Aa
Planar Planar Homeotropic’) Homeotropic’) Twisted by d 2 Twisted by d 2
>O >O O >O
>O O O
Theoretical contrast ratioa) ~~
1 2 3 4 5 6
~
~~
Sign of the contrast
~~~~
(1 +2S) / (1 4) (2+S) / (2-2s) (1+2S)/(I-S) (2+S) / ( 2 - 2 9 (1+2S)/(l-S) (2+S) / (2-2s)
-
+ + -
+
Aa=q,-aL,dichroism of the dichroic dye. a) The contrast ratio is related to high voltages (V>Vth) and the use of polarized light. In planar cells the E vector is parallel to n. In homeotropic cells the E vector agrees with n after the dielectric reorientation. b, The director n is tilted by a small angle with respect to the layer normal.
3.4.13 Positive Mode Dichroic LCDs
3.4.13.2 Positive Mode Dichroic LCDs Using a i1/4 Plate
W4 displays do not need polarizers. One can get a positive mode A/4 display using the same two-cell geometries and materials as discussed in an earlier section.
Positive Mode Double Cell Dichroic LCD
3.4.13.3
The same geometry and materials can be used as discussed for single cell positive mode LCDs (see Sec. 3.4.13).
Positive Mode Dichroic LCDs Using Special Electrode Patterns
3.4.13.4
A positive mode dichroic LCD [16, 1271 can be demonstrated by using special electrode patterns even in the case of pleochroic dyes embedded in a liquid crystal of positive dielectric anisotropy. In this case the voltage is applied to the whole visible area and is removed only from the desired segmented areas. 3.4.13.5 Positive Mode Phase Change Dichroic LCDs
The molecular structure of a long-pitch cholesteric mixture is determined both by the cell gap and the type of alignment [ 13- 161. If the cell gap is sufficiently large, the structure is always helicoidal in the bulk of the layer, irrespective of the homeotropic or homogeneous alignment on the surface [ 13- 161. If the cell gap is below a critical thickness d,, where
the helix is unwound in the presence of a homeotropic alignment and the whole structure is homeotropic nematic [ 1201. Two versions of cells using this property have been proposed using a pleochroic dye
295
in a liquid crystal host of positive dielectric anisotropy [ 1281. The operational principle ofboth types of cell is that the area surrounding the picture element has homeotropic alignment and a cell gap less than d,, resulting in a nonabsorbing homeotropic nematic structure. In the first geometry the areas surrounding the pixels undergo homeotropic treatment, while the pixel areas receive homogeneous alignment [ 1291.The cell gap is less than d,. In the second geometry the alignment on the whole cell is homeotropic, but the cell gap is adjusted in such a way that the pixel areas have a cell gap more than d,, while the remaining area is less than d,. These proportions result in an absorbing helicoidal structure in the pixel areas and a nonabsorbing homeotropic one in the remaining area [ 1281. On application of the electric field, the helicoidal structure is destroyed and the liquid crystal molecules adopt a homeotropic structure, with the result that only the nonactivated pixels remain dark. The control logic for this display is inverted with respect to that required for the White-Taylor type with negative contrast. Another way of obtaining apositive mode phase change type display is to use a pleochroic cholesteric mixture of negative dielectric anisotropy [ 16, 1291. The surface treatment is homeotropic and cell thickness d is chosen to be less than d,. In the quiescent mode the cell is in the homeotropically aligned nematic state, and hence pleochroic dyes do not absorb the light. On aplication of the field, the molecules become parallel to the glass plates and also adopt the heliocoidal structure. In this situation the light is absorbed by the dyes. A display of this type has the advantages of positive contrast, brightness, wider viewing angle, lower operating voltage, and multiplexing capability [ 16, 1291, but has low contrast. A very high order parameter dichroic mixture with a very low optical anisotropy is need-
296
3.4 Guest-Host Effect
ed to obtain sufficient contrast for this display.
3.4.13.6 Dichroic LCDs Using an Admixture of Pleochroic and Negative Dichroic Dyes These dichroic LCDs have a dichroic mixture containing both pleochroic (L) and negative dichroic (T) dyes, these having absorption wavelengths in different parts of the spectrum [53, 1181. The display can be made in Heilmeier, TN, and phase change mode. If a liquid crystal mixture of positive dielectric anisotropy is used to make a dichroic mixture using these L and T dyes, and is filled in a cell having homogeneous alignment, both L and T dyes will absorb in the quiescent state, and the cell will have the complementary color of the dichroic mixture. This color can be changed by changing the ratio of L and T dyes. On application of the field, the dye molecules, together with the liquid crystal molecules, become aligned in the direction of the field. Only the T dye absorbs in this geometry, and its complementary color becomes the observed color. These displays do not require polarizers and can be operated at low voltage like TN displays. Their excellent brightness and contrast are much less dependent on the order parameter compared to other guest-host displays [ 1181. Schadt [ 1181 also derived the detailed analytical expressions describing the dependence of transmission and color effects on the dye order parameter, the direction of the dye’s transition moment, and the elastic and dielectric properties of the liquid crystal mixture. The viewing angle and threshold voltage have been calculated and compared with experimental values. Using tetrazine dye (T) and anthraquinone dye D27 (L), Schadt developed a display exhibiting bright-red characters on a bright-blue background [ 1181. This display
can also be operated with a single polarizer in the Heilmeier mode [ 1181.Pelzl et al. [54] have reported a similar display.
3.4.14 Supertwist Dichroic Effect Displays Supertwist dichroic effect (SDE) displays have a twist of approximately 3 x/2, instead of n/2 as in the case of the popular TN mode LCDs, and hence are called supertwisted LCDs 129-311, The 3n/2 twist imparts a very steep slope to the threshold characteristic of the cell. This means it has a lower value of AV/Vth, and hence can handle a higher level of multiplexing. However, the threshold characteristics of 3 n/2 displays, unaided by dye or the interference of ordinary and extraordinary rays, has low contrast. The dyes absorb the leakage and enhance the viewing angle and contrast. Two types of SDE display can be made, one by using a Heilmeier geometry (by using a single polarizer), and the second by using the phase change or White-Taylor mode. However, SDE displays did not become popular due to their lower contrast, lower brightness, and slower switching speed compared to other supertwist displays.
3.4.15 Ferroelectric Dichroic LCDs Surface stabilized mode ferroelectric LCDs [31-351 show bistability, i. e. both the 8and the -8 position are equally stable. A pulse of one polarity is used to switch from 8 to -8,while a pulse of opposite polarity is used to switch from -8 to 8. The molecules can remain in either of these states (8 or -8)for a long time without any applied voltage. In the case of GH ferroelectric LCDs, the ferroelectric mixture contains an appropriate
3.4.16 Polymer Dispersed Dichroic LCDs
amount of dichroic dyes. Ferroelectric dichroic LCDs have a very fast switching speed (-100 ps or less), wide viewing angle, and good contrast [35].
3.4.15.1 Devices Using A Single Polarizer For a dye dissolved in a ferroelectric host in a single polarizer device, the orientation is rotated through twice the tilt angle (28) of the guest - host material on changing from one switched state to the other. If the polarizer is aligned with the dye direction to generate maximum absorption (dark state), then the switched state ( @ = 2 8 )would be lighter. One can also make a display exhibiting dark characters on a light background by initially aligning the polarizers perpendicular to the long axes of the pleochroic dye molecules. For maximum contrast a tilt angle of 45" is required. Only a few ferroelectric liquid crystals have such a high tilt angle. Fortunately, a 10-90% change in intensity may be achieved with a tilt of only 27" [35], making commercially available ferroelectric host and dichroic mixtures, with a typical tilt angle of 22-25', useful for this application. Another single polarizer DGHFE mode LCD uses an anisotropic fluorescent dye in the ferroelectric mixture [35].
3.4.15.2 Devices Using No Polarizers
-
A ferroelectric liquid crystal with 8 22.5" and a high pleochroic content can be used entirely without a polarizer by using a 2 4 plate [32] with a reflector. In the off-state the incoming light is selectively absorbed along the homogeneous alignment n in the cell. A quarter wave plate is placed along or perpendicular to the director. The nonabsorbed radiation (- 50%)in the ideal case vibrates perpendicular to the dichroic director and is reflected back unaffected. In the onstate n is turned 45" to the axis of the A14 plate; the nonabsorbed orthogonal vibration
297
is thus split up and components retarded corresponding to a double pass 2 i1/4=A/2. The polarization plane is therefore rotated by 90" and the radiation is absorbed on its way back into the liquid crystal. Coles et al. [35] made another ferroelectric dichroic device without polarizer, using a double layer surface stabilized mode DGHFE. The optimum tilt angle required for this geometry is 22.5".
3.4.16 Polymer Dispersed Dichroic LCDs A polymer dispersed liquid crystal (PDLC) film [36-39, 130- 1321, with a pleochroic dye dissolved in it, possesses a controllable absorbance as well as a controllable scattering. This combination can be exploited to generate high-contrast displays. For polymer dispersed dichroic LCDs, Fergason's NCAP systems are found to be better than Doane's PDLC systems [36 - 391. Unlike to other dichroic LCDs where we strictly require dichroic dyes only, one can use isotropic as well as dichroic dyes in these kinds of devices. Vaz observed a larger than expected color change between the on and off states of dichroic PDLC shutters, even with dichroic dyes with small order parameters (0.2) and dichroic ratios (1.7) [37]. This is explained on the basis of increased path length (i.e. more than the film thickness) due to multiple scattering in the off mode, which consequently increases the off-state absorbance. The contrast ratio of the dyepolymer system can be improved significantly by incorporating dichroic dyes with high order parameters and extremely low solubilities in the polymer [36-39, 1311. These displays provide much higher brightness and wider viewing angles than TN displays. Two optical processes are at work in these displays: switchable absorbance due to dye alignment, and electrically controlled
298
3.4 Guest-Host Effect
light scattering. When the display is excited, the light entering the film experiences a low absorbance and minimal scattering. The color reflector in the back is seen clearly with high brightness and color purity. In the quiescent state, incoming light is both strongly absorbed and scattered. The strong absorption by the pleochroic dyes gives the film a dark appearance. The scattering effect enhances the absorption and causes a fraction of the light to be reflected before reaching the colored reflector. This ensures that the light reflected from the display in the unexcited state possesses a very low color purity and hence looks more neutral or black. The color difference properties of the film can be optimized by varying various parameters of the film, such as film thickness, dye concentration, dye order parameter, and the level of scattering. The scattering is controlled by the liquid crystal birefringence and the droplet size distribution.
3.4.17
Dichroic Polymer LCDs
It is now well established that polymer nematic liquid crystals can be aligned by an electric field and surface forces, in more or less the same way as low molecular weight nematic liquid crystals [ 133- 1351. To generate dichroic polymeric LCDs, either dichroic dyes are dissolved in nematic polymers, or side-chain dye moieties are attached in nematic copolymer structures [ 133- 1351.As the pleochroic dye has its absorption transition dipole defined relative to its chemical structure, rotation of the dye produces a change in absorption of the guest-host cell when observed in polarized light. Several types of effect have ben reported and many more are possible, analogous to the low molecular weight nematic counterpart (as discussed in Sec. 3.4.83.4.16). Some of these are: Heilmeier type,
using pleochroic dyes in liquid crystal polymer of positive dielectric anisotropy; guest-host cells, using a dichroic liquid crystal polymer in a low molecular weight liquid crystal host; and polymeric ferroelectric dichroic LCDs. However, their use in display devices is strongly restricted by their slow response time. The reason for this is that the viscosity of side-chain liquid crystals is some orders of magnitude greater (depending on the temperature) in relation to the glass transition temperature and the degree of the polymerization of the polymer. One of the most promising potential uses of liquid crystal polymers is in optical storage devices [133, 1351. The information is written using a He-Ne laser. Images are stable over a long period of time (at least 4 years under ambient conditions), and are erasable by applying an electric field. The absorption of the laser beam is facilitated by incorporating a dye into the polymer [ 1361. Ferroelectric polymeric materials are fascinating because, in principle, they can have the fast switching speed of ferroelectric materials together with the processibility of polymers. Dichroic properties can be achieved either by dissolving dichroic dyes in ferroelectric polymers or by inserting dichroic groups in the polymer. Using a little imagination one can form all types of dichroic ferroelectric LCDs using polymeric ferroelectric dichroic mixtures in place of ferroelectric dichroic liquid crystal mixtures.
3.4.18 LCDs
Smectic A Dichroic
In these displays usually a thin layer of SmA material (- 10- 15 pm) is sandwiched between I T 0 coated glass plates with homeotropic alignment. When the layer is heated above the isotropic temperature and
3.4.20
is cooled back to the SmA phase via a nematic phase, it generates: (1) a focal conic scattering texture in the absence of the field, and (2) a clear homeotropic texture if cooled in the presence of an electric field [137]. These properties of SmA phases have been used in making various kinds of laseraddressed [ 137, 1381 and thermal-addressed [40, 41, 1381 SmA displays. Incorporation of pleochroic dyes converts the scattering state into an absorbing state [40, 41, 137, 1381. The homeotropic state will remain clear in this case too. In spite of a lot of research and demonstrations, thermally and electrically addressed displays have not become a commercial product [40, 41, 1371. The main reasons for this are their high power consumption and limited operating temperature range. Moreover, the advent of supertwist displays closed the market sectors where they could have been utilized.
3.4.19 Fluorescence Dichroic LCDs Some attempts have been made to replace normal dichroic dyes with fluorescent type dichroic dyes [16, 59-61, 139- 1411. Fluorescence is a two-step process involving absorption at a given wavelength and reemission at a longer wavelength, and is associated with electronic transitions which, relative to dye-molecule geometry, are directional in space. Thus the change in the orientation of the fluorescent dye molecule changes the absorption and subsequent emission intensity. Depending on the polarization of the incident and transmitted light, sample thickness, and concentration, it is possible to produce an increase or decrease in the light level. These fluorescent dyes can be excited either by UV light or light of shorter wavelengths in the visible spectrum
References
299
(such as blue light for exciting green, and yellow for exciting red fluors). These fluors can be excited either directly or indirectly through a liquid crystal. For example, a green fluorescent dye can be excited directly by blue light or indirectly with ultraviolet light. In the latter case the UV energy is absorbed by an appropriately formulated liquid crystal host, and subsequently transferred to the fluorescent dye. The fluorescent LCDs combine the visual impact and good viewing angle of emissive displays with the desirable features of LCDs, such as long voltage operation and low power consumption. Both Heilmeier [ 1391 and phase change [61] type fluorescent dichroic displays have been reported. When stimulated from the rear, indirect excitation is preferred because the exciting light is invisible and the display then has a dark appearance on a bright colored background. The display can also be excited from the front. In the frontlit mode, the phase change version is preferred over the Heilmeier mode, as the polarizer blocks UV light and attenuates any blue light passing through it. Acknowledgments Thanks are due to Urmila, Shivendra, and Shachindra Bahadur for their untiring help in preparing this manuscript. This article is dedicated in loving memory to my aunt, Mrs Sushila Srivastava, who passed away recently after a brave fight against cancer.
3.4.20 References [ l ] G. H. Heilmeier, L. A. Zanoni, Appl. Phys. Lett. 1968, 13, 91. [2] G. H. Heilmeier, J. A. Castellano, L. A . Zanoni, Mol. Cryst. Liq. Cryst. 1969, 8, 293. [3] B. Bahadur, Mol. Cryst. Liq. Cryst. 1983, 99.
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3.4 Guest-Host Effect
161 C. Schumann, in Handbook of Liquid Crystals (Eds.: H. Kelker and R. Hatz), Verlag Chemie, Weinheim, 1980. [7] C. L. Khetrapal, R. G. Weiss, A. C. Kunwar, Liquid Crystals- Applications and Uses, Vol. 2 (Ed.: B. Bahadur), World Scientific, Singapore, 1991. [8] A. Saupe, G. Engler, Phys. Rev. Lett. 1963, 11, 462. [9] A. Carrington, G. R. Luckhurst, Mol. Phys. 1964,8,401. [lo] D. L. Uhrich, Y. Y. Hsu, D. L. Fishel, J. M. Wilson, Mol. Cryst. Liq. Cryst. 1973, 20, 349. [ I13 W. J. Leigh, in Liquid Crystals - Applications and Uses, Vol. 2 (Ed.: B. Bahadur), World Scientific, Singapore, 1991. [12] T. J. Scheffer, J. Nehring, in Physics and Chemistry of Liquid Crystal Devices (Ed. J. G. Sprokel), Plenum Press, New York, 1979, p. 173. [13] T, J. Scheffer, Phil. Trans. R. SOC., London Ser. A, 1983,309, 189. [14] T. Uchida, M. Wada, Mol. Cryst. Liq. Cryst. 1981, 63, 19. [15] B. Bahadur, Mol. Cryst. Liq. Cryst. 1991, 209, 39. [16] B. Bahadur, in Liquid Crystals - Applications and Uses, Vol. 3 (Ed.: B. Bahadur), World Scientific, Singapore, 1992. 1171 D. L. White, G. N. Taylor, J. Appl. Phys. 1974, 45,4718. [I81 H. S. Cole, R. A. Kashnow, Appl. Phys. Lett. 1977,30,619;SID Digest, 1977,8,96; GE-CRD Report No. 77CRD059,1977. [19] B. Bahadur, SPIE, Opt. Test. Meteorol. II, 1988, 954, 574. 1201 B. Bahadur, K. Wan, C. Prince, L. Krzymien, J. Tunnoch, Mol. Cryst. Liq. Cryst. 1992,220,155. [21] T. Uchida, H. Seki, C. Shishido, M. Wada, SlD Digest, 1980, 11, 192. [22] H. Seki, T. Uchida, Y. Shibata, Proc. SID 1984, 25, 275. 1231 K. Sawada, Y. Masuda, Proc. SID 1982,23,241. [24] K. Sawada, S. Kudoh, F. Kadoo, Y. Endoh, Y. Nakagawa, Y. Masuda, SID Digest 1985,78. 1251 G. A. Dir, V.J. Hull, Proc. Int. Disp. Res. Con$, 1985, 83. [26] B. Bahadur, Development of a High Resolution (Phase II) Liquid Crystal Display System - Llquid Crystal Mixture and Process Development, LSL Report, April 1989. [27] T. J. Scheffer, J. Nehring, J. Appl. Phys. 1984, 908,56. [28] K. Wan, D. Lewis, B. Bahadur, SID Digest 1994, 25, 601. B. Bahadur, K. Wan, US Patent 5589965,1996. [29] C. M. Waters, E. P. Raynes, V. Brimmell, Mol. Cryst. Liq. Cryst. 1985, 123, 303. [30] C. M. Waters, V. Brimmell, E. P. Raynes, Proc. SID 1984, 25, 261, Jpn. Displ. 1983,398.
1311 B. Bahadur, Supertwisted Dye Effect, Supertwisted Birefringence and Ferroelectric Liquid Crystal Displays, Litton Data Images Report, March 1986. [32] S. T. Lagerwall, J. Wahl, N. A. Clark, Proc. Int. Displ. Res. Con$ 1985,213. [33] K. Kondo, S. Era, M. Isogai, A. Mukoh, Jpn. J. Appl. Phys. 1985,24, 1389. [34] H. J. Coles, H. F. Gleeson, Mol. Cryst. Liq. Cryst. Lett. 1988, 6, 53. 1351 H. J. Coles, H. F. Gleeson, J. S. Kang,Liq. Cryst. 1989, 5, 1243. 1361 P. S. Drziac, R. Wiley, J. McCoy, SPZE, Liq. Cryst. Chem. Phys. Appl. 1980,41. [37] J. W. Doane, in Liquid Crystals - Applications and Uses, Vol. 1 (Ed.: B. Bahadur), World Scientific, Singapore, 1990. [38] J. L. Fergason, SZD Digest 1985, 68; US Patent 4435047, March 6,1984. 1391 P. S. Drzaic, Liquid Crystal Dispersions, World Scientific, Singapore, 1995. 1401 S. Lu, D. H. Davies, Mol. Cryst. Liq. Cryst. 1983, 94, 167. 1411 W. Harter, S. Lu, S. Ho, B. Basler, W. Newman, C. Otaguro, SID Digest 1984, 15, 196. [42] B. Bahadur, R. K. Sarna, V. G. Bhide, Mol. Cryst. Liq. Cryst. 1981, 75, 121. 1431 H. Seki, T. Uchida, Y. Shibata, Mol. Cryst. Liq. Cryst. 1986, 138, 349. 1441 R. J. Cox, Mol. Cryst. Liq. Cryst. 1979,55, 1. [45] G. W. Gray, Chimica, 1980, 34, 47; Dyes Pigments 1982,3,203. 1461 H . V. Ivashchenko, V. G. Rumyantsev, Mol. Cryst. Liq. Cryst., 1987, 150A, 1. [47] M. G. Pellatt, I. H.C . Roe, J. Constant, Mol. Cryst. Liq. Cryst. 1980, 59, 299. [48] F. C. Saunders, K. J. Harrison, E. P. Raynes, D, J. Thompson, Proc. SID 1983,24, 159. [49] J. Cognard, T. H. Phan, Mol. Cryst. Liq. Cryst. 1981, 68, 207. [50] X. Q. Yang, J. R. Wang, G. D. Ren, Mol. Cryst. Liq. Cryst. 1991, 199, 1. 1511 S. Imazeki, M. Kaneko, T. Ozawa, A. Mukoh, Mol, Cryst. Liq. Cryst. 1988, 159, 219. [52] G. Pelzl, H. Schubert, H. Zaschke, D. Demus, Krist. Techn. 1979, 14, 817. [53] G. Pelzl, H. Zaschke, D, Demus, Displays 1985, 141. [54] Literature on Dichroic dyes, Mixtures and Hosts from BDH (England), E. Merck (Germany), Hoffman La Roche (Switzerland) Mitsui (JaPan). [55] T. J. Scheffer, J. Appl. Phys. 1982, 53, 257. 1561 B. S. Scheuble, G. Weber, L. Pohl, R. E. Jubb, SIR Digest 1983, 176; Proc. SID 1984, 25, 25. [57] G. Heppke, B. Knippenberg, A. Moller, G. Scherowsky, Mol. Cryst. Liq. Cryst. 1983, 94, 191.
3.4.20 References [58] U. Claussen, A. Brockes, E. F. Kops, F. W. Krock, R. Neeff, SlD Digest 1984, 209; Proc. SlD 1985,26, 17. [591 E. Wolarz, D. Bauman, Mol. Cryst. Liq. Cryst. 1991, 197, 1. [601 S. Sato, M. M. Labes, J. Appl. Phys. 1981, 52, 3941. R. W. Filas, M. M. Labes, 1981,52,3949. [611 M. R. Lewis, M. C. K. Wiltshire, A. Cuddy, J. Stanford, I. Sage, J. Griffiths, S. Tailor, Proc. SlD 1988, 29, 233; Eurodisplay 1987, 149. [62] S . Aftergut, H. S. Cole, Jr., Mol. Cryst. Liq. Cryst. 1982, 89, 37. [63] H. Seki, C. Shishido, T. Uchido, M. Wada, Mol. Cryst. Liq. Cryst. 1981, 66, 209. [64] S. Ohmi, A. Watanabe, K. Hara, Jpn. Displ. 1986, 282; Proc. SlD 1987, 28, 123. (651 H. Seki, T. Uchida, C. Shishido, Jpn. J . Appl. Phys. 1980,19, L501. [66] S . Aftergut, H. S. Cole, Mol. Cryst. Liq. C y s t . 1990, 188, 147; Proc. SID 1990, 31, 317; SlD Digest 1990, 21, 95. [67] F. Jones, T. J . Reeve, Mol. Cryst. Liq. Cryst. 1981, 78, 201. [68] J. K. Foitzik, W. Haase, Mol. Cryst. Liq. Cryst. 1987,142,55; 1987, 149,401. [69] F. Jones, F. A. Kirby, Mol. Cryst. Liq. Cryst. 1984,108, 165. [70] S. Imazeki, A. Mukoh, T. Yoneyama, M. Kaneko, Mol. Cryst. Liq. Cryst. 1987, 145, 79. [71] A. Bloom, P. L. K. Hung, Mol. Cryst. Liq. Cryst. 1978,44, 323. [72] S. Yano, S. Kato, M. Kano, Y. Kamijo, Mol. Cryst. Liq. Cryst. 1985, 123, 179. [73] T. K. Attwood, J. E. Lydon, F. Jones, Liq. Cryst. 1986, I , 499. [74] M. A. Osman, L. Pietronero, T. J. Scheffer, H. R. Zeller, J . Chem. Phys. 1981, 74, 5377. [75] B. Bahadur, in Liquid Crystal -Applications and Uses, Vol. 2 (Ed.: B. Bahadur), World Scientific, Singapore, 1991. [76] B. Bahadur, Mol. Cryst. Liq. Cryst. 1984,109, 1. [77] S. Morozumi, in Liquid Crystals -Applications and Uses, Vol. 1 (Ed.: B. Bahadurj, World Scientific, Singapore, 1990. [78] J. Cognard, Mol. Cryst. Liq. Cryst. 1981, 7 8 (Suppl 11, 1. [79] T. Uchida, H. Seki, in Liquid Crystals - Applications and Uses, Vol. 3 (Ed.: B. Bahadurj, World Scientific, Singapore, 1992. [80] J. M. Geary, J. W. Goodby, A. R. Kmetz, J. S . Patel, J. Appl. Phys. 1987, 62, 4100. [81] S. Matsumoto, M. Kawamoto, N. Kaneko,Appl. Phys. Lett. 1975,27, 268. [82] Homeotropic aligning agents from E. Merck, Germany (such as ZLI-2570), and Nissan Chemical Ind., Japan (such as RN 722), etc. [83] H. Seki, Y. Itoh, T. Uchida, Y. Masuda, Jpn. J. Appl. Phys. 1990, 29, L2236; Mol. Cryst. Liq. Cryst. 1991, 199, 151.
30 1
[84] Low tilt (for TN) and high tilt (for STN) producing polyimides from Hitachi (Japan), Japan Synthetic Rubber (Japan), Nissan Chemicals Inc. (Japan). [851 H. Fukuro, S . Kobayashi, Mol. Cryst. Liq. Cryst. 1988, 163, 157. [861 M. R. Lewis, M. C. K. Wiltshire, Appl. Phys. Lett. 1987, 51, 1197; R. W. Filas, SID Digest 1984,206. [87] B. 0. Myrvold, Mol. Cryst. Liq. Cryst. 1991, 202, 123. [881 C. H. Gooch, H. A. Tarry, Electron. Lett 1974, 10, 2; J. Phys. D 1975, 8 , 1585. [89] P. Kassubek, G. Meier, Mol. Cryst. Liq. Cryst. 1969, 8, 305. [90] A. J. Hughes, D. G. McDonnell, S. Hedges, Displays, April 1987, 69. [91] M. Kawachi, K. Kato, 0. Kogure, Jpn. J. Appl. Phys. 1978, 17, 1245. [92] Information sheets for polarizers from Polaroid Corp., USA, Nitto, Japan, Sanritsu, Japan. [93] R. W. G. Hunt, Measuring Colouv, Ellis Horwood, Chichester, 1987. [94] A. Bloom, E. B. Priestley, ZEEE Trans. Electron. Dev., 1977, ED24, 823. [95] Euro-Fighter Project Definition Phase, Final Report-Report No. EFJ-R-EFA-000-107, October 1987. [96] E. Jakeman, E. P. Raynes, Phys. Lett. 1972, 39A, 69. [97] K. M. Bofingar, H. A. Kurmier, M. R. Romer, J. D. E. Beubert, German Patent 4699636 (E. Merck, Darmstadt, Germany). [98] US Military Standard MIL-L-85762. [99] F. Gharadjedaghi, J . Appl. Phys. 1983, 54, 4989. [loo] H. L. Ong,J. Appl. Phys. 1988,63, 1247; H. L. Ong, Proc. SlD 1988, 29, 161. [ l o l l G. Schauer, W. Wiemer, Eurodisplay 1990, 122. [lo21 D. Potzsch, H. Baeger, F. W. Nickol, E. Purtzel, H. Voss, Proceedings of 12th Freiburger Arbeitstagung Fliissigkristulle, Freiburg, Germany, 1982. [lo31 P. G. de Gennes, J. Prost, The Physics o f L i q uid Crystals, 2nd edn. Oxford University Press, London, 1993. [lo41 M. J. Press, A. S. Arrott,J. Phys. 1976,37,387. [lo51 B. Kerllenvich, A. Coche, Mol. Cryst. Liq. Cryst. 1985, 124, 149; 1983, 97, 103. [ 1061 P. R. Gerber, Z. Naturforsch. a 1981, 36, 7 18. [lo71 A. Saupe, J . Chem. Phys. 1980, 72, 5026. [ 1081 H. S. Cole, Jr., S . Aftergut, J . Chem. Phys. 1978, 68, 896. [lo91 S . Aftergut, H. S. Cole, Jr., Appl. Phys. Lett. 1981, 38, 599. [I101 T. Ishibashi, K. Toriyama, K. Suzuki, M. Satoh, Proc. lnt. Display Res. Conf. 1990, 186; Proc. SID 1983, 24, 152.
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[129] F. Gharadjedaghi, Mol. Cryst. Liq. Cryst. 1981, 68, 127. [130] J. L. West, R. Ondris, M. Erdmann, SPZE, Liq. Cryst. Disp. Appl. 1990, 57, 76. [ 1311 P. S. Drzaic, A. M. Gonzales, P. Jones, W. Montoya, SID Digest 1992, 571. [132] P. Jones, W. Montoya, G. Garza, S. Engler, SID Digest 1992,762. [133] H. Finkelmann, W. Meier, H. Scheuermann, in Liquid Crystals -Applications and Uses, Vol. 3 (Ed.: B. Bahadur), World Scientific, Singapore, 1992. [134] R. Simon, H. J. Coles, Liq. Cryst. 1986, I , 281. 113.51 H. J. Coles, Faraday Discuss. Chern. SOC. 1985, 79, 201. 11361 C. Bowry, P. Bonnett, M. G. Clark, presented at the Euro Display Conference, Amsterdam, September 1990. [ 1371 D. Coates in Liquid Crystals-Applications and Uses, Vol. 1 (Ed.: B. Bahadur), World Scientific, Singapore, 1990. [138] T. Urabe, K. Arai, A. Ohkoshi, J. Appl. Phys. 1983,54, 1552; Proc. SID 1984,2.5,299. [139] R. L. Van Ewyk, I. O’Connor, A. Moseley, A. Cuddy, C. Hilsum, C. Blackburn, J. Griffiths, F. Jones, Displays 1986, 155; Electron. Lett. 1986,22,962. 11401 L. J. Yu, M. M. Labes, Appl. Phys. Lett. 1977, 31,719. [141] D. Bauman, K. Fiksinski, Eurodispluy 1990, 278.
Handbook ofLiquid Crystals D. Demus, J. Goodby, G. W. Gray, H.-W. Spiess, V. Vill Copyright 0WILEY-VCH Verlag GmbH. 1998
Chapter IV Chiral Nematic Liquid Crystals
1 The Synthesis of Chiral Nematic Liquid Crystals Christopher J. Booth
1.1 Introduction to the Chiral Nematic Phase and its Properties Chiral nematic liquid crystals, as the name suggests, are optically active variants of nematic liquid-crystalline compounds; the incorporation of a chiral centre imparts properties which are unique to the chiral nematic phase and are responsible for their utilisation in a variety of differing display technologies and other related applications. The term cholesteric liquid crystal was originally used to describe this phase, and originates from the structural nature of the earliest chiral nematic liquid crystals which were derivatives of cholesterol [ 1,2]. Nowadays, the term chiral nematic is used primarily because the materials are clearly derived from nematic type liquid crystals [3, 41. Despite these differences in definition, the terms cholesteric and chiral nematic phase are interchangeable and it is common to find references to either term in the literature. The incorporation of a chiral centre into a formerly nematic structure (or alternatively of a chiral non-mesogenic dopant into a nematic host) results in the induction of a
macroscopic helical twist distortion in the bulk of the sample [ 5 , 6 ] .As a consequence the chiral nematic phase can be described as having helical orientational order or being a single twist structure [4]. The director ( n ) may precess through 360"; the distance over which this occurs is called the pitch length ( p ) , and this is shown simplistically in Fig. 1
1
pitch length, p
Figure 1. Diagram of the structure of the chiral nematic phase.
304
1 The Synthesis of Chiral Nematic Liquid Crystals
All interest in the unique optical properties of the chiral nematic phase stems from the two-fold optical activity of the phase [5, 6-91. That is, the mesophase displays (1) molecular optical activity - the phase being composed of optically active molecules and (2) macromolecular optical activity - arising from the macroscopic helical twist induced by the chiral molecules in the phase (sometimes termed form chirality). These features are of immense importance technologically, as many of the applications of such materials depend on one if not both of these phenomena. As would be expected for any optically active molecule, a chiral nematogen should rotate the plane of plane polarized light. This is indeed the case, but in contrast to other optically active materials (e.g. sugars), very large values of rotation are observed (ca. lo3 deg. mm-’ [5]); this may be attributed to the relative phase retardation of the right and left handed components of the plane polarized light as they encounter different refractive indices associated with the macroscopic helical twist of the phase. Rotation of the plane of polarized light usually occurs when the pitch length of the chiral nematic phase is very much longer than the wavelength of the incident light (i.e. p %-A).A second optical property associated with this phase is circular dichroism, whereby the chiral nematic phase will transmit one circularly polarized component of light whilst reflecting the other circularly polarized component. Which circularly polarized component becomes reflected or transmitted depends on the handedness of the macroscopic twist associated with the chiral nematic phase; a right handed helix will transmit the right-handed component whilst reflecting the left-handed circularly polarized component [4]. However, the most noted feature of the chiral nematic phase is its ability to reflect incident white
light selectively, provided that the incident light has a wavelength of approximately the same order as the pitch length of the phase (i.e. il= p ) . Coherently reflected light components experience constructive interference from other reflected wavefronts, giving rise to iridescent colour play (various analogies with Bragg reflection are possible, assuming normal incidence of the light beam). The wavelength or waveband of the reflected light is related to the pitch length by Eq. (1) [8]:
AA=An.p
(1)
where An = optical anisotropy of the phase (or birefringence). The optical purity (or the width) of the selectively reflected component ( A n ) may be modulated to some degree by manipulation of the optical anisotropy ( A n ) of the phase (this is usually achieved by controlling the sp2 or sp3 nature of the mesogen’s chemical structure). Special mention must also be made for the case of obliquely incident light on a chiral nematic phase; here the reflection band is shifted to shorter wavelengths and results in an angle-dependent effect to the viewer. However, this is outside the scope of this chapter and readers are referred to references [lo-121. These optical properties are observed only when the mesophase is in the planar or Grundjeun texture, that is where the helical/optical axis is perpendicular to the glass substrates when a sample is constrained between a microscope slide and cover slip [ 131, and the molecules lie in the substrate plane. There is a second common texture associated with the chiral nematic phase, where the helical axes of domains in the bulk sample are randomly aligned, and this is sometimes referred to as the pseudo focalconic texture; light undergoes normal scattering when the sample is in this texture [5, 131. This texture is easily mechanically
1.2 Formulation and Applications of Thermochromic Mixtures
disturbed to give the selectively reflecting planar texture. Certain chiral nematic liquid crystals (or mixtures) are found to exhibit thermochromism, that is, temperature dependent selective reflection; here the pitch length of such materials or mixtures is often found to have an inverse relationship with temperature and can depend on the nature of the material’s mesomorphism. Thermochromism is found to be at its most spectacular in materials which display chiral nematic phases and underlying smectic phases; this is exemplified for a material with an I-N*SmA* sequence (on cooling) and is shown schematically in Fig. 2. Here the pitch length gradually lengthens from the blue end of the electromagnetic spectrum (i.e. p = 0.4 pm), but an altogether more rapid increase in pitch length is experienced as the chiral nematogen is cooled towards the smectic A phase. This is best explained by the gradual build-up of smectic order on approach to the N*-SmA* transition, and results in startling colour play through to the red end of the electromagnetic spectrum (p=O.7 pm) as the helical structure of the phase becomes unwound (indeed the SmA* phase may be considered as having an infinite pitch length). It should be noted that not all chiral nematogens are either as responsive or behave in precisely
305
the same manner, and indeed some materials are notable for being exceptions to this rule of thumb [ 141. As an aside, it may be of interest to the reader that although selective reflection is usually a phenonemon associated with calamitic liquid crystalline systems, various multiyne materials have recently been demonstrated to show selective reflection as well as a helix inversion in chiral discotic nematic phases [15, 161.
1.2 Formulation and Applications of Thermochromic Mixtures Rarely, if ever, does one particular chiral nematic compound display “ideal” behaviour, which would make it suitable for use in a given application, and normally carefully formulated mixtures of a variety of mesogenic and non-mesogenic components, which may have very different thermodynamic properties, are used. Formulation of mixtures is frequently a complex trade-off of one property over another and is usually achieved by application of the Schrodervan Laar equation [ 17 -201, which allows the thermodynamic characteristics of a par-
1
I
I I I I
I I
Pitch
I I
Length
I
I
P)
I I I I
Smecuc A*
1 I I
I
C h i d Nematic
I
Temperature (“C)
I I
Isouoplc Liquid
Figure 2. The pitch length- temperature dependence of a chiral nematic liquid crystal.
306
1 The Synthesis of Chiral Nematic Liquid Crystals
ticular mixture to be predicted theoretically (with some accuracy) before recourse to actual experimental formulation of the mixture. Practical commercial thermochromic mixtures must have the following general characteristics: low melting points, wide operating ranges (i.e. -50- 150“C), short pitch lengths and underlying smectic A* phases to induce the spectacular pretransitional unwinding of the helix of the chiral nematic phase, which results in a visible thermochromic effect. It is usual to employ racemic or partially racemized compounds, as these have the effect of compensating the twist induced by other chiral components, enabling the fine tuning of the colour playtemperature characteristics, although this sometimes has the undesired side effect of extending the blue selective reflection range [3,5,21]. Similarly, the mixing of polar and non-polar liquid-crystalline components may result in the formation of injected smectic phases; these may also be exploited to give wider operating temperature ranges (they are also reported as preventing the extension of the “blue-tail’’ phenomenon) 1221. The colour purity of a thermochromic mixture (An),is related to the birefringence (An) of the mixture, and as mentioned earlier, this may be controlled by judicious selection of components which are either aromatic (sp2 hybridised), or alicyclic (sp3 hybridised) or a combination of the two (sp2- sp3) [ 171. The commercial synthesis of a wide variety of modern chiral nematic materials has made many of these points a little easier to address, in contrast to times when the choice of materials was limited to unstable cholesterol derivatives, azo-compounds, and Schiff’s bases; nevertheless, the final formulation of a mixture is still a complicated process. As may now be more clearly appreciated, the potential uses of chiral nematic liquid crystals depend on either the twisting pow-
er or the thermochromic response of the chiral nematic phase (N”). The former macroscopic property was initially the reason for most of the commercial interest in the use of chiral nematic liquid crystals; here chiral components were employed in electro-optic displays to counter reverse twist domain defects (in low concentrations ca. 1-10% wt.wt) and to sustain the helical twist induced by surface alignment in both the twisted nematic display and supertwist display modes [23, 241. Chiral nematic dopants may also be employed to induce short pitch lengths in White - Taylor Guest - Host displays (this prevents waveguiding of light in the off-state 117, 251) or as circularly dichroic filters 1261. However, the major applications of chiral nematic liquid crystalline materials are in thermometry, medical thermography, non-destructive testing, pollutant sensing, radiation sensing, surface coatings, cosmetics, and printing inks for decorative and novelty applications [3, 51; all of these applications employ either the selective reflective properties or the thermochromic response of the chiral nematic phase, or both. In many of these applications, the thermochromic liquid crystal mixture is rarely utilised as a thin, neat film, but rather as a microencapsulated slurry which is incorporated into a coating; microencapsulation of the thermochromic mixture is usually achieved by complex coacervation using gelatin and gum-arabic to form the microcapsule walls [27]. The reasons for microencapsulation are firstly economic and secondly to protect against and prevent attenuation of the optical properties of the chiral nematic liquid crystals, which are often prone to chemical and photochemical degradation during use. However, this may be reduced to some extent by use of UV filters or free-radical scavengers [3]. The availability of microencapsulated ‘inks’ have led to the increased use of the materials simply
1.3 Classification of Chiral Nematic Liquid Crystalline Compounds
because they may be applied to a variety of surfaces (paper, plastic, fabrics, and metal) by a variety of widely used techniques, e.g., airbrush, screenprinting, gravure, or flexographic means) [3, 281.
1.3 Classification of Chiral Nematic Liquid Crystalline Compounds Despite the wide variety of chiral nematic liquid crystals (and of course low molar mass chiral liquid crystals in general), it is possible to sub-divide them into three class types, according to the relationship of the chiral moiety and the liquid-crystalline core [29]. Firstly, we consider type I; here the chiral centre (or multiplicity of chiral centres) is situated in a terminal alkyl chain attached to the effective liquid-crystalline core. As will be seen later, it is entirely possible that the compound can have two or more chiral terminal groups associated with the molecule. Type I materials are probably the most frequently encountered chiral nematic liquid-crystalline compounds, often
3 07
because of their relative ease of synthesis and because of the availability of suitable chemical precursors. Secondly, type I1 materials: here the chiral centre may be trapped between two liquid-crystalline core units, and the structure resembles a dimer or a twinned molecule. Here, in principle, it is possible to modulate the properties of the molecule by variation of the length of the flexible spacer which carried the chiral group; this is believed to occur via processes which restrict the freedom of rotation about this central axis. However, this type of material has the disadvantage that the core units, which are usually polarisable in nature (i.e. sp2-hybridised carbon skeleton) are separated by a non-polar region (i.e. sp3hybridised carbon skeleton), preventing effective conjugation of the cores which usually leads to destabilisation of any liquidcrystalline characteristics. Thirdly and finally, type 111: here the chiral centre is in some way incorporated into the effective liquid-crystalline core: for example see Fig. 3 . In type 111 materials asymmetry may be achieved either by the presence of a chiral atom in the core or by a particular structural feature which results in gross molecular asymmetry. This stuctural type may be
Type I; terminal chiral chains appended to a liqmd-crystallme core
Type II: flexible chiral spacer chain between two liquid-clystalline cores
Type III: chiral point or structural molecular asymmetry within the liquid-crystalline core
Figure 3. The classification of chiral liquid crystals according to the position of the core unit and chiral moiety.
308
1
The Synthesis of Chiral Nematic Liquid Crystals
of use when attempting to gain the greatest coupling effect between the chiral centre and core to produce strongly twisting dopants. All three types of material are schematically illustrated in Fig. 3. Many of the compounds used as examples in this chapter to illustrate the three classes of chiral nematic structure are not necessarily compounds in which the presence of a chiral nematic phase or its properties were of primary importance to the researchers concerned in the work; for instance some of the materials were developed as potential ferroelectric dopants, but happened to show a chiral nematic mesophase. Also in many cases, the synthetic techniques used and the hazardous nature of some of the reagents employed, along with the poor chemical or photochemical stabilities of the mesogens, would almost automatically preclude their use in any commercial applications (i.e., thermography). However, such materials are of scientific interest in that they help to illustrate the many potential variations of novel molecular structures which may result in a chiral nematic mesophase.
1.3.1 Aspects of Molecular Symmetry for Chiral Nematic Phases Having defined the different forms of chiral nematogen structure with regard to the positioning of the chiral moiety relative to the liquid-crystalline core unit, it is now necessary to describe further and more precisely the exact nature of this structural relationship. It has been understood for many years that optical properties, such as helical twist sense and the direction of rotation of plane polarised light, depend intimately on the absolute spatial configuration of the chiral centre, the distance the chiral centre is sep-
arated from the core, the electronic nature of the substituents attached to the chiral centre and the overall enantiomeric purity of the system in question. These molecular features may be more clearly appreciated with reference to the schematic structure of a type I chiral liquid crystal shown in Fig. 4. Firstly, the absolute configuration of an organic compound is determined using the Cahn, Ingold and Prelog sequence rules which relate the atomic number of the groups attached to the chiral centre to their relative priority over one another (the higher the atomic number, the higher the priority; i.e. C1 has higher priority than H). The resulting order of increasing priority may then be designated as being either (R)- or (S)-; that is rectus or sinister (right or left forms) [4, 301. Additionally, it is necessary to define the distance of the chiral centre from the core (rn + l), as it has been found that the helical twist sense of the resultant chiral nematic phase alternates from odd to even numbers of atoms [ 311. This may be illustrated by considered the following two (S)-4-alkyl-4’-cyanobiphenyls(A and B), in Fig. 5 . Subsequent experimentation by contact studies with other chiral systems (R)- and (S)-, of differing parity revealed the following helical twist sense relationships, entries 1 to 4 in Table 1. These results form the basis of a set of empirical rules termed the Gray and McDonnell rules [ 3 2 ] and are particularly useful in predicting the properties of a chiral nematic phase of a given com-
X and Y may represent polar or non-polar groups; m and p = integers.
Figure 4. A representation of a type I chiral liquid crystal.
1.3 Classification of Chiral Nematic Liquid Crystalline Compounds
309
mathematically as
P = (P .C J 1 A
Abs. config ...(3)-;parity (m+1) ...2 (even, e); rotation of plane polarized light ...d; twist sense...LH.
B Abs. config ...(Sj-; parity (m+1) ...3 (odd, 0):
rotation of plane polarized light ...I; twist sense...RH
Figure 5. The relationship between twist sense, parity, and absolute configuration demonstrated for two chiral nematogens.
pound. The first four entries in Table 1 all correspond to materials which have an electron donating substituent at the chiral point (i.e. CH,-, +I). Electron withdrawing groups, such as C1 or CN (-1) were later demonstrated effectively to reverse these empirical twist sense rules; entries 5 to 8 in Table 1 all reflect this electronic structural change [ 3 3 ] . Finally, the other property which is also strongly dependent on molecular symmetry associated with the chiral centre is the twisting power, P, which is usually expressed Table 1. Rules relating twist sense to absolute configuration, parity and the electronic nature of the substituents at the chiral centre. Absolute configuration
Parity
Electronic nature of substituent
1. ( S ) (S)-
e
+I +I +I +I -I -I -I -I
2. 3. 4. 5. 6. 7. 8.
(R)(R)(S)(5’)(R)(R)-
0
e 0
e 0
e
o
Rotation of plane polarized light
Helical twist sense LH RH RH LH RH LH LH RH
(2)
where p =pitch length, c, = concentration of the chiral solute species, i; a right or left handed system is usually denoted by P being either positive (+) or negative (-), respectively [34, 3.51. This mathematical relationship is usually only applicable to systems which contain low concentrations of the chiral dopant (i), usually
(3)
If a compound possesses an ee of 1, its entirely composed of one enantiomer and may be termed optically pure; similarly, an ee value of zero corresponds to a racemic mixture and would show no net optical activity. The optical purity of a sample will not only influence the optical properties, but also the transition temperatures; this will be apparent in certain examples given in this chapter, where the racemate [(R,S)-]often has noticeably higher clearing temperatures
3 10
1 The Synthesis of Chiral Nematic Liquid Crystals
that the enantiomers [(I?)- or (9-1 [37]. The enantiomeric purity of chiral materials will also depend a great deal on their source, their stability towards racemization (or decomposition) and on their chemical history. It may be appreciated that by careful consideration of these empirical rules in relation to the structure of any prospective target molecule, it is possible to “build-in” certain inherent physical or optical properties, leading to materials which may be more precisely tailored to given specifications. This is particularly important in the preparation of materials which may be used in thermochromic formulations with specific colour play characteristics or in the formulation of a mixture with a given pitch length or twist sense characteristic for use in a display device.
1.4 Cholesteryl and Related Esters The term cholesteryl ester is employed in this chapter loosely to describe any sterol based liquid-crystalline system. Cholesteryl esters (2) are historically unique in that they
(RCO),O, pyridine, 100 ‘C
or
RCOCI, N,N-dimethylmiline, 100°C
where R = akyl
were the first materials to be classified as being liquid-crystalline [ l , 2, 38, 391; since then hundreds of examples of these cholesterol derivatives have been studied or utilised for thermography during the 1960s and 1970s [6-9, 14, 40-43, represent just a few]. The structural nature of cholesterol (1) gives some indication of why its esters form mesophases; its seventeen carbon atoms form four fused rings (three six-membered rings plus one five-membered ring), which form a relatively linear and quasi-rigid lathlike structure which has no centre of symmetry and cannot be superimposed on itself. Furthermore, of these seventeen carbon centres, seven carbons are chiral or asymmetric; as a direct consequence of this, the optically active, quasi-rigid core, may technically be classified as belonging to the type I11 structural family. Synthesis of these types of material is usually achieved by esterification reactions of the 3-hydroxy group, often using a suitable acyl chloride (e.g. propionoyl chloride or myristoyl chloride) [41]; this is illustrated in Scheme 1. Cholesterol (1) is not the only naturally occuring precursor whose derivatives display cholesteric phases; for example the lau-
(i) RCOCI, pyridine, benzene; (ii) H,, RO,,EtOAc
Scheme 1. Cholesteryl esters: structures and synthesis.
1.5 Type I Chiral Nematic Liquid Crystals
311
Table 2. The transition temperatures of selected sterol based mesogens. Ester name Cholesteryl benzoate (5) Cholesteryl butyrate ( 6 ) Cholesteryl myristate (7) Cycloartenyl palmitate (8)
Transition temperatures ("C) Cr 145.5 N* 178.5 I Cr 96.4 N* 107.3 I Cr 72 Sm 78 N* 83 I Cr 55 (N* 53) I
Ref.
[I1 ~411 [411 [461
-
rate, myristate, and palmitate esters (3 b) of 24-methyl cycloartenol(3a) and the palmitate ester (4b) of 4 a , 14a, 245-trimethyl9,19-cyclocholestan-3~-ol(3 b); these triterpenoids were first isolated from banana peel (rnusa sapienturn) 144-461. Other examples include esters of p-sitosterins, stigmasterins, and cholestans [47]. The transition temperatures ("C) of typical cholesteric phases given by a variety of sterol esters ( 5 - 8 ) are listed in Table 2. However, the use of sterol-based materials in technological applications has several drawbacks, which may be briefly summarised as follows; firstly, they tend to be photochemically unstable [5], a process thought to be facilitated by the presence of oxygen [ 3 ] .Secondly, cholesterol is a natural product and will be of variable quality depending on the source used; this could manifest itself both in terms of chemical purity and optical purity (it would be highly impractical to resort to synthesizing the sterol unit using advanced stereospecific organic techniques on an industrial basis !). Thirdly, cholesteryl esters are frequently solids at or around room temperatures [ 3 ] ; this presents the problem of crystallization at low temperatures which could destroy, the integrity of microencapsulated material [48]. Although formulation of multi-component mixtures does depress this solidification/crystallization temperature it does not easily enable systems to be developed for use below temperatures of 0 "C. Similarly, formulation of high temperature mix-
tures is difficult, despite the existence of individual esters which have clearing points in excess of 200°C. Fourthly, the fact that racemic modifications of cholesteryl esters are not available, means that the fine tuning of the colour play-temperature response is also not possible (211. Finally, comparatively thick films of cholesteryl based mesogens are necessary for acceptable colour play responses for a given application [ 5 , 2I ]. Despite these drawbacks cholesteryl esters still have a useful role to play commercially, particularly when precise temperature - colour play properties are not required, as for example in novelty applications.
1.5 Type I Chiral Nematic Liquid Crystals As the electro-optic display industry developed, great interest was centred on the development of suitable materials for use in twisted nematic or phase change displays, particularly as many of the first generation of materials frequently presented problems in practical usage. For instance, cholesteryl esters were deemed to be unsuitable for such applications for many of the reasons already outlined in Sec. 1.4 of this chapter, and also because of difficulties associated with optimising physical properties such as birefringence, viscosity, and dielectric anisotropy. Consequently, novel chiral materials based on known nematogenic materials
312
1 The Synthesis of Chiral Nematic Liquid Crystals
where X and Y = alkyl or alkoxy (chiral or racemic);
n and m = 1 or 2; A = -N=N-, -CH=N- or -CO2-.
Figure 6. The general structure of a non-sterol based chiral nematogen.
(hence the term chiral nematic liquid crystals) began to appear; these materials were not necessarily mesogenic, but because of their structural similarity to the host nematic mixtures of the time, this enabled formulation into suitable eutectic mixtures. These chiral nematogens may be divided into three kinds; the azobenzene derivatives, the azomethine materials (Schiff's bases), and the phenyl/biphenyl esters [18, 47, 491. All three classes may be represented by the general structure shown in Fig. 6. The central linking group (A) preserves the molecular linearity and increases both its polarisability (by allowing some degree of conjugation between the aromatic rings) and rigidity; however, as shall be seen, it can often be the weakest part of the mesogen [18, 491. The respective features of each of these three general classes of material will now be discussed with emphasis on the thermodynamic properties of the materials and the various synthetic routes employed.
1.5.1 Azobenzenes and Related Mesogens The use of the azo-linking group (- N = N -) in liquid crystal chemistry is now well documented, and hundreds of compounds of this class have been cited in the chemical literature [47]; the linkage is formed by an azo coupling reaction between a substituted aryl diazonium salt and a suitably activated substituted benzenoid compound [SO].
Typical examples of chiral azobenzenes are (R)-4-(2-methylbutyl)-4'-substituted azobenzenes (9- 13) which appeared with the emergence of synthetic methods which allowed the preparation of chiral precursors, such as (+)-2-methylbutylbenzene [5 1-54]. In the case of compound 12, the presence of two chiral terminal moieties was found to increase the helical twisting power (p) by a factor of two [51]. Both the compounds 9 and 10 show enantiotropic chiral nematic phases which have relatively low clearing points, unlike compounds 11 and 12 which are not liquid crystalline.
9;X=OC,H,,; Cr 31.8 N* 65.6 I ("C) [52] 10; X=OC,H,,; Cr 35.9 N* 58.2 I ("C) [52] l l ; X = C N ; C r 6 9 I ( " C ) ; p = l0.0[51]
12; Cr 112 I ("C);
fi = 4.7 [51]
13; n = 0, 1, 2 and 3 [54]
The azo group may be oxidized further, usually with a peracid such as 3-chloroperbenzoic acid to give azoxy linked materials; examples include compounds 14- 16 which are shown below [51, 54, 551, but only compounds 14 and 16 show chiral nematic phases.
14; X=OC,H,; Cr 4 N* 76 I ("C) [51] 15; X=CN; Cr 100 I ("C) [51]
16; Cr 24 SmB* 66 SmC* 79.3 N* 84.2 I ("C) [ 5 5 ]
313
1.5 Type I Chiral Nematic Liquid Crystals
Although early commercially available nematic mixtures for use in electro-optic displays were based on this class of material, they proved short lived because of their inherent strong yellow colour and because of their susceptibility to photochemical isomerization/degradation [IS].
1.5.2 Azomethine (Schiff 's Base) Mesogens
-
i
The azomethine group (or Schiff's Base linkage), like the azo linking group, has been widely employed as a linking group in many forms of mesogen [47] and was employed in the synthesis of a variety of early chiral nematic materials [52, 53, 56-62]. During the early seventies, a variety of optically active Schiff's bases were developed from the now readily available chiral precursor (S)-(-)-2-methyl- 1-butanol (17),via a series of reactions which avoided inversion of the chiral centre or any appreciable degree of racemization [53]. The route used to manipulate (S)-(-)-2-methyl- 1-butanol is outlined in the synthetic Scheme 2 and is of importance as it shows the versatility of the synthetic methods used to manipulate the chiral alcohol (indeed many of the steps are directly applicable to later types of chiral mesogen, see Sec. 1.5.3 of this Chapter). The alcohol is converted to (S)-(+)-l-bromo-2-methylbutane (18)using phosphorus tribromide; subsequent conversion to its Grignard reagent followed by treatment with solid carbon dioxide gives (S)-3-methylpentanoic acid (19).The higher homologs (S)-(-)-3-methyl- 1-pentan01 (20),(S)-(-)5-methyl-I-heptanol(21),(S)-(-)-4-methyl1-hexanol (22),and (S)-(-)-6-methyloctano1 (23)may be obtained from the Grignard reagent of compound 18 via a series of homologation steps involving the addition of either formaldehyde or ethylene oxide.
repeat above steps-:
x
i
OH
Scheme 2. Synthesis of optically active methyl branched primary alcohols.
The optically active alcohols (17,20-23) may then be brominated (PBr,) and used as alkylating agents for 4-hydroxybenzaldehyde. The resulting 4-alkoxybenzaldehydes (25)were then condensed with a variety of mono-substituted aromatic amines (26and 27) to give the two series of compounds shown in Scheme 3. These two ring azomethines gave chiral nematic phases which had relatively low thermal stabilities, but comparatively short phase ranges as demonstrated by compounds 28 and 29. The introduction of a third ring to give materials such as compound 30, led to markedly higher thermal stabilities. This compound is reported as having an optical rotation of 25000 degrees mm-' in its chiral nematic phase, further highlighting the extraordinary optical properties associated with the chiral nematic mesophase. However, despite showing promising thermal stability, this type of mesogen fell from widespread use simply because the azomethine linkage (- CH = N-) imparts colour to the material and proved too sus-
314
1 The Synthesis of Chiral Nematic Liquid Crystals PBr,
17,20-23
OHC
-W-
OH
24
where n = 1, 2, 3 or 4. 28; n = 1; (370.0 (N* 56.0) I ("C) [53]
29; n = 3;Cr 40.0 SmX*48.0 N* 66.0 I ("C) [531
1 1 ' 3
30; Cr 50 (SmX*43.5) N* 146 I ("C) [S3]
ceptible to water, making hydrolysis of the linkage and the subsequent degradation of the physical properties of the liquid crystal an ever present disadvantage during use U81.
1.5.3 Stable Phenyl, Biphenyl, Terphenyl and Phenylethylbiphenyl Mesogens During the early 1970s, the problem of manipulating a chiral substrate without adversely affecting the optical purity had largely been solved (in the main by use of readily available precursor (S)-(-)-2-methylbutan-1-01 17), but the problems associated with the poor chemical or photochemical stabilities and the inherently strong colours of the existing azo and azomethine derived materials were still to be addressed satisfactorily. The root of this problem lay with the linking group, which was recognised as being the weakest part of the liquid-crystalline molecule as a whole. The poor chemical
Scheme 3. Synthetic routes to optically active azomethine chiral nematogens.
stability and colouration of existing nematic materials was surmounted by elimination of the linkage, and resulted in the discovery of the now ubiquitous, stable, colourless nematic 4-alkyl- or 4-alkyloxy-4'-cyanobiphenyls, which are still the mainstay of many commercially based electro-optic mixtures [63]. It was subsequently discovered that chiral modifications of these materials, some of which had very low thermal phase stabilities, but had sufficient liquidcrystalline character, would be used successfully as reverse twist dopants in electrooptic mixtures for use in twisted nematic and later in supertwisted displays. Specific examples of such compounds are (S)-4-(2methylbutyl)-4'-cyanobiphenyl(31), which displays a N*-I transition at -30 "C and (S)-
4-(2-methylbutyloxy)-4'-cyanobiphenyl (32)which shows a monotropic phase at 9°C [64]; these materials are reported as having pitch lengths of 0.2 and 1.5 pm, respectively.
W
C
N
31; Cr 4 (SrnA* -54 N* -30) 1 ("C) [64]
*
O
W
C
N
32; Cr 53.5 (N* 9) I ("C) [64]
3 15
1.5 Type I Chiral Nematic Liquid Crystals
Whilst these chiral biphenyls fulfilled the needs of the display world, they were not immediately suitable for use in thermochromic applications, primarily because of their low N*-I transitions, which seriously restricted their use in higher temperature application environments. These low temperature restrictions were countered to some extent by the incorporation of either a further phenyl ring or by a CH,-CH, link between the existing rings, to give chiral terphenyl or phenylethylbiphenyl based structures [64]. In the case of the chiral terpheny 1, (S)-(+)-4 -(4-methylhexyl)-4”cyano-p-terphenyl (33), the clearing point of the the chiral nematic phase was raised to 186 “C; however, the material had a very high melting point of 120 “C, which again, not surprisingly, restricted its use. The use of the CH,-CH, link was much more successful in giving a compound with lower melting and clearing points; for example, ( S ) - ( + ) -1-[4’-(2-methylbutyl)biphenyl-4y1]-2-(4-~yanophenyl)ethane(34).
33; Cr 120 SmA* 163 N* 186 I (“C) 1641
+ \ /
CN
34; Cr 91.6 N* 110.8 I (“C) [641
This class of chiral nematic materials clearly demonstrated their potential, as they
form the basis of a number of stable experimental thermochromic mixtures [64]. The synthesis of the compound (S)-(+)4-(2-methylbutyl)-4’-cyanobiphenyl (31), shown in Scheme 4, typifies the route used to obtain these types of materials. The first step involves the FeC1, catalysed coupling of the magnesium derivatives of (S)-(+)-2methylbutyl bromide (18) and bromobiphenyl to give the chiral biphenyl fragment (35); this was then brominated to give
(S)-(+)-4-(2-methylbutyl)-4’-bromobiphenyl(36) which was eventually cyanated using copper cyanide to give the chiral biphenyl (31). Although the above route differs slightly from the synthesis of the related chiral biphenyls [i.e. (S)-(+)-4-(3-methylpentyl)-4’cyanobiphenyl (41, n = 1 and m = l ) ] , the other chiral methyl substituted alkanoic acids (37) are obtained by various transformations from (S)-(+)-2-methylbutyl bromide (18);the acyl groups are introduced into the aromatic core by conversion of the acids to their acid chlorides (38) followed by Friedel -Craft’s acylation and subsequent Huang - Minlon reduction of the chiral methyl substituted alkanoylbromobiphenyls (40). This general approach is demonstrated in Scheme 5. The ability of the chiral 2-methylbutyl moiety to generate very short pitch chiral nematic phases was by now widely recognised. It was not therefore surprising that a number of research groups should attempt (i) Mg, THF; (ii) Bromobiphenyl; (iii) FeCl,, THF;
wBr 18
Scheme 4. Synthesis of (S)-(+)-4-(2-Methylbutyl)-4’-cyanobiphenyl.
CuCN
31
-’cQQ
(iv) (+)-2-methylbutyl bromide, THF;
I
35
Br2,CHCl,, RT (in dark)
316
1 The Synthesis of Chiral Nematic Liquid Crystals
soc1, X n C O z H
38
37
H2NN2H.H20, KOH, diglyme.
H2S0,, AcOH, H,O.
where n = 1,2, or 3 and rn = 0 or 1.
to incorporate it into ester based structures, particularly as existing nematic esters were widely recognised as being both colourless and stable [65-671. The early materials (43-47) were relatively simple two ring materials often based on 4-substituted benzoic acids or trans-4-substituted cyclohexane- 1-carboxylic acids; the structures, relevant transition temperatures, and pitch lengths of a variety of such materials are given below.
w , 0
\ /
OCioHzi
43; Cr 36.0 (N* 32.0) I ("C); p = 0.23 pm [6S]
44; Cr 41.8 SmA* 42.2 N* 45.3 I ("C); p = 0.23 pm [66]
45;Cr 17 [N* -31 I ("C); p = 0.23 pm [66]
46; Cr 17.0 [N* 71 I ("C); p = 0.23 pm [66]
Scheme 5. Synthesis of higher homologues of chiral biphenyl mesogens.
0
mioHa
47; Cr 49.0 (SmA* 41.8 N* 45.41 I; p = 0.43 pm [66]
N.B. ( ) .. . denotes a monotropic transition, [ ] ... denotes a virtual transition SmA*
Cursory examination of the transition temperatures shown by these compounds, shows them to have rather low mesophase thermal stabilities; nevertheless, thermochromic mixtures composed of certain homologous of compounds 44 - 47 have been formulated, even if they have relatively low upper colour play limits which probably reduce practical applications. In most cases, the 2-methylbutyl group generates short pitch chiral nematic phases ( p = 0.23 pm), the only exception being the cyclohexyl compound 47 in which the pitch length is almost twice as long (p=0.43 pm). This loss of twisting power in this example is believed to be related to the fact that the chiral alkyl group is linked to a flexible moiety [66]. Vastly improved mesophase thermal stabilities were obtained on the introduction
1.5 Type I Chiral Nematic Liquid Crystals
317
Table 3. Transition temperatures and phase assignments for homologous (S)-4-(2-methylbutyl)phenyl4‘-alkoxybiphenyl-4-carboxylates.
Compound no.
n
Transition temperatures (“C)
Pitch lengths (km)
48 49 50
5 6 7
Cr 66 SmB* 77.3 SmA* 133.9 N* 156.0 I Cr 81 SmB* 71.0 SmA* 132.6 N* 146.2 I Cr 74.6 SmB* 75.0 SmA* 138.4 N* 147.6 I
0.23 0.23 0.23
of a third ring into these ester structures. This was achieved using a variety of chiral and achiral biaryl carboxylic acids and phenols, such as (S)-4’-(2-methylbutyl)biphenyl-4-carboxylic acid and 4-cyanophenol, many of which were by now readily available or were easily accessible from liquid crystal precursors (i.e. the hydrolysis of
pitch length of the chiral nematic phases [66]. The difference in mesophase stability is highlighted in the following members of two homologous series: the (9-(+)-4(2-methylbuty1)phenyl 4’-alkylbiphenyl-4carboxylates (compounds 48-50, see Table 3 ) and the 4-alkylphenyl (S)-(+)-4’-
(S)-4-(2-methylbutyl)-4’-cyanobiphenyl (31) to (S)-4’-(2-methylbutyl)biphenyl-4-
(compounds 51 -53, see Table 4). There are other differences between the series, notably that the (S)-(+)-4-(2’-methylbuty1)phenyl 4’-alkylbiphenyl-4-carboxylates (48-50) show smectic A* and smectic B* phases below the chiral nematic phases. The presence of an underlying smectic A* phase is advantageous, because it results in the startling pretransitional selective reflection effects as a selectively reflecting chiral nematic phase is cooled towards the smectic A* phase [ 5 , 171. Interestingly, the straight chain alkoxy analogues (compounds 54 and 55) of these materials, display chiral smectic C* phases which, although not iridescent, were successfully formulated into a number of broad range ( 1 13 “C) experimental thermochromic mixtures [64]. The nature of their N*-SmC* phase transition was to prove fascinating from the stand point of selective reflection.
carboxylic acid). Generally, speaking it was found that materials containing a (S)-4’-(2methylbutyl)biphenyl-4-carboxylatemoiety gave slightly lower thermal stabilities and shorter phase sequences than the materials which contained the chiral group in the ester function in as an (S)-4-(2’-methylbuty1)phenyl moiety. It should also be noted that this difference in behaviour did not have a corresponding detrimental effect on the
Table 4. Transition temperatures and phase assignments for homologous 4-alkylphenyl (S)-4’-(2-methylbutyl)biphenyl-4-carboxylates.
Compound no.
n
Transition temperatures (“C)
Pitch length (vm)
5 6 7
Cr 63.6 N* 138.2 I Cr 60.3 N* 132.0 I Cr 61.0 N* 133.4 I
0.23 0.23 0.23
(2-methylbutyl)biphenyl-4-carboxylates
~~
51 52 53
54; n = 8; Cr 78.0 Sm3 80.0 SmC* 128.3 SmA* 171.0 N* 173.2 I (“C): p = 0.23 l m [64]
318
1 The Synthesis of Chiral Nematic Liquid Crystals
55; n = 8; Cr 76.0 SmC* 88.6 N* 155.4 I (“C); p = 0.23 pm [64]
On cooling through the chiral nematic phase, the reflected colour of this mixture changes from blue through to red, then upon reaching and traversing the chiral nematic -chiral smectic C* phase transition, the reflected colour sequence reverses from red to blue (this corresponds to a shortening of pitch length of the smectic C* phase as the tilt angle increases [64]). Materials and mixtures which possess a chiral smectic C* phase as well as a chiral nematic phase, offer the opportunity for novel ‘reversed’ colour play of their thermochromic response (i.e., blue-redblue on cooling through a I-N*-SmC* sequence). The ready availability of the 2-methylbutyl and other related chiral alkyl or alkoxy substituted phenols and biphenyls resulting from this work made it possible to prepare esters which contained two chiral terminal chains easily [66]. Broadly speaking, providing the helical twist senses of both groups were identical, this had the effect of reinforcing the twisting influence of each group, often giving very highly twisted (short pitch) chiral nematic phases. Conversely, chiral groups with opposite helical twist senses, lead to compensation of the twisting influence of chiral nematic phases, giving longer pitch lengths. This may be illustrated using the following three compounds: (S)-4-(2-methylbutyl)phenyl (S)4’-(2-methylbutyl)biphenyl-4-carboxylate (56), (S)-4-(2’-methylbutyl)phenyl (S)-4’(2-methylbutoxy)biphenyl-4-carboxylate (57), and ( S ) -4 -(2’-methylbutyl)phenyl ( S ) 4’-(4-methylhexyl)biphenyl-4-carboxylate (58).
56; Cr 103 N* 115.5 I (“C) [66]; p = 0.10 pm [51
57; Cr 88 SmA* 124 N* 145 I (“C) [66]; p = 0.46 prn [ 5 ]
O
‘ /
58; Cr 83.4 (SmC* 74.3 SmA* 81.0) N* 113.5 I (“C); p = 0.23 prn [66]
Compounds 56 and 58, have chiral groups which may be described using Gray and McDonnell’s rules as ( S ) , e, d; therefore, the groups should reinforce one another. This is certainly the case with compound 56 ( p = 0.10 pm); the longer pitch of compound 58 ( p = 0.23 pm)is due to the increased distance between the chiral centre and the aromatic mesogenic core which effectively reduces any damping of rotation about the chiral centre [29]. On the other hand, the 2-methylbutoxy group of compound51 may be described by Gray and McDonnell’s rules ( S ) , 0,1, the opposite of the 2-methylbutyl group [ ( S ) , e, d], which leads to compensation and a longer pitch length (p=0.46 pm) [32]. It is worth drawing the reader’s attention to the elegant synthesis of the opposite enantiomer (i.e. the (R)-enantiomer) of (S)-(-)-4”-(2-methylbutylphenyl) 4’-(S)-2methylbutyl)biphenyl-4-carboxylate (56) (CE2); this was required for the detailed study of the Blue phase behaviour in binary mixtures [68, 691. The commercial unavailability of (R)-(+)-2-methylbu tan01 (or (R)-(+)-l-bromo-2-methylbutane) forced the authors to synthesize it from (S)-(+)methyl 3-hydroxy-2-methylpropionatevia
1.5 Type I Chiral Nematic Liquid Crystals
319
a five step route. The synthesis is also significant in that it successfully employed an efficient palladium (0) catalysed crosscoupling for the introduction of the valuable chiral side chain onto both the phenyl and biphenyl ring systems; this contrasts to the use of the inefficient ferric chloride catalysed cross coupling used 10 years earlier in the original synthetic route to this fragment of the molecule (see Scheme 4) [64]. In addition to these, a number of three ring esters which contained the more polar cyano group as a terminal group were prepared and evaluated (compounds 59 and 60); the thermodynamic properties of a selection of these materials is shown below ~641.
cially important, as many of these materials were very effective as reversed twist dopants for electro-optic devices, and also as the constituents of numerous thermochromic mixtures. A large range of mixtures is commercially available either in their neat forms or as microencapsulated inks or slurries, for a wide variety of different colour play ranges. It is also possible to obtain a particular set of mixtures and a partially racemized set of mixtures, the idea being to enable tailoring of the precise colour play properties to a specific requirement by the careful addition of a small quantity of the partially racemized mixtures in accordance with a specific set of temperature-composition directions [21].
59;Cr 96 N" 210 I ("C); p = 1.6 pm [64]
(R)-2-(4-Hydroxyphenoxy)propanoic Acid Derivatives 1.5.4
L
C
O
C
O
-
Q
-
Q
C
N
60; Cr 77.6 SmA* 138 N" 190.4 I ("C); p = 4.7 prn 1641
These materials show very much higher melting points and thermal stabilities of their chiral nematic phases than their tworing equivalents as a direct result of the increased polarisability of the liquid-crystalline core. The 2-methylbutyl group attached to the cyclohexyl ring is again notable in that this chiral moiety fails to give a tight pitch chiral nematic phase; indeed various studies performed on a variety of esters containing different ring systems has revealed that there is a marked order of twisting efficiency which is dependent on the nature of the ring system to which the chiral chain is attached. This may be summarised as follows, in descreasing order of twisting power: phenyl> bicyclo[2.2.2]octyl> cyclohexyl [5]. This entire class of stable, colourless chiral nematogens turned out to be commer-
During the late 1980s the highly optically pure intermediate (R)-2-(4-hydroxyphenoxy)propanoic acid (RHPP; ee >97% [70]) was employed as the basis of a series of novel thermochromic liquid crystals. RHPP is a bifunctional structure and theoretically allows for extension of the molecule along the molecular long axis at either terminal functional group, to give structures which may be classified as type I or type I1 materials. Additionally, the chemical nature of these groups could be modified to give other varieties of polar linkage (e.g. C 0 2 H converted to either CN or CH,OH), to give variation in the thermodynamic properties of the different structures. Initial work revealed that chiral nematic phases were only obtained when the carboxylic acid moiety of RHPP was converted into either a simple alkyl ester or a cyano group. This behaviour is highlighted by the ( R ) and (R,S)-alkyl 2-( 4-[4-(truns-4-pentylcy-
320
1 The Synthesis of Chiral Nematic Liquid Crystals
Table 5. Transition temperatures and phase assignments for a series of (R)-and (R,S)-2-{4-[4-(truns-4-pentylcyclohexyl)benzoyloxy]phenoxy) propanoates and a propanonitrile.
Compound no.
61 62 63 64
65
Z C02C3H7
Configuration
Transition temperature ("C)
(R)-
Cr 67.2 (SmA* 60.5) N* 77.9 I Cr 77.0 (Cryst B* 35.8 SmA* 67.9) N 82.0 I Cr 58.1 (SmA* 46.2) N* 67.3 I Cr 70.6 Cr 77.5 (Cryst B* 19.2 SmA* 51.4 N 70.9) I Cr 122.3 (SmA* 92.9) N* 151-6 I
C02C3H7 C02C4H9
(R)-
C02C4H9
(RS)-
CN
(R)-
clohexyl) benzoyloxy] phenoxy } propanoates (61 - 64) and (R)-2-{4-[4-(truns-4pentylcyclohexyl)benzoyloxy]phenoxy } propanonitrile (65) [71, 721, whose chemical structures and transitions are given in the Table 5. However, analytical determinations performed using 'H nmr and the chiral shift reagent, (+)-europium tris-(D-3-heptafluorocamphorate) revealed that these materials had inherently low enantiomeric excesses (ee). The ee values of the propyl (61) and butyl esters (63) were found to be between 0.69-0.75 on integration of the areas for the aromatic protons ortho to the carboxylate moiety of the trans-4-pentylcyclohexylbenzoate core. The low values of ee have been attributed to the presence of the electronwithdrawing carbonyloxy or cyano groups a to the chiral centre, which readily facilitates racemization, even during the relatively mild synthetic processes performed previously during the synthesis of the compounds. It is also interesting to note that the independently synthesized racemic modifications of these propyl and butyl esters (62 and 64) have noticeably higher melting points and clearing points when compared with their (R)-enantiomers (61 and 63). This behaviour has been noted before in other chiral systems and is an indication of the general influence and importance of enan-
tiomeric purity on a compound's physical properties [72]. This problem of low enantiomeric purity (ee) was circumvented by removing the electron withdrawing group. This was achieved by the reductive cleavage of a benzyl ester function to give the alcohol, using lithium aluminium hydride, and resulting in a series of materials derived from the compound (R)-2-(4-benzyloxyphenoxy)propan1-01(68) [73]. The synthetic route employed is outlined in Scheme 6. The first step involves heating (R)-benzyl 2-(4-hydroxyphenoxy)propanoate (66) with benzyl bromide and potassium carbonate in butanone to give the dibenzyl compound 67. Compound 67 was the reduced to (R)-2-(4-benzyloxyphenoxy)propan-1-01 (68) using lithium aluminium hydride in dry tetrahydrofuran at room temperature. The alkylation of compound 68 was then achieved using sodium hydride and the appropriate alkyl halide in dry N,N-dimethylformamide at room temperature to give the (R)-1-alkoxy-2-(4-benzyloxyphenoxy)propanes (69-75) as colourless oils. These compounds were then debenzylated using hydrogen and palladium-on-charcoal at room temperature and pressure to give the chiral phenols (76-82) which were then subsequently esterified with the appropriate two ring core acid using dicyclohexylcarbo-
1.5 Type I Chiral Nematic Liquid Crystals
32 I
PhCH?Br,
LiAM4, THF, Nr NaH, AlkylBr, H3C
H3C 6 8 0 H
OCnHznil
69-15
H2, Pd-C, EtOH Core Acid, DCC, DMAP, CH2C12,RT H3C
OCnHznil
76-82
83-101
H3C
OCnHzn+1
a = trans- 1,4-cyclohexyl, 1.4-phenyl or 2-fluorophenyl.
b = 1,4-phenyl or 2,3-difluoro-1,4-phenyl. n=lt06
diimide (DCC) and 4-N,N-dimethylaminopyridine (DMAP) to give the target compounds 83-101. Proton NMR and chiral shift reagent studies on various (R)-1-alkoxy-2-{4-[4-(truns4-pentylcyclohexyl)benzoyloxy]phenoxy ] propanes (83 and 84) failed to resolve the presence of any of the other enantiomer, indicating that the material was optically pure (ee 20.98, within experimental error) and that this system was now inherently stable to racemization.
Scheme 6. Synthesis of ( R ) -1alkoxy-2-[4-(4-substituted)phenoxylpropanes.
The methyl to hexyl terminal chain homologous all showed chiral nematic phases, although their phase ranges decreased from 15.2 to 4.4"C as the homologous series was ascended. The most interesting feature of the phase behaviour of these materials was the occurrence of Blue phases near the clearing points of the higher homologues of the series (butyl to hexyl, compounds 83 to 88). This is clearly the result of damped or restricted rotation of the bonds attached to the chiral centre caused by both the prox-
Table 6. The transition temperatures and phase assignments for the ( R ) -1-alkoxy-2- (4-[4-(tran.s-4-pentylcyclohexyl)benzoyloxy]phenoxy Jpropanes.
Compound no.
n
Transition temperatures ("C)
83
I 2 3 4 5 6
Cr, 69.3 Cr, 83.5 Cryst B* 85.5 SmA* 107.5 N* 122.7 I Cr, 43.4 Cr, 59.7 Cryst B* 80.1 SmA* 105.1 N* 112.4 I Cr 54.8 Cryst B 73.9 SmA* 95.8N* 100.8 I Cr 48.8 Cryst B* 73.6 SmA* 89.5 N* 93.7 BP 94.0 I Cr 46.3 Cryst B* 68.1 SmA* 83.2 N* 86.7 BP 86.7 I Cr 44.5 Cryst B* 62.8 SmA* 74.0 N* 78.4 BP 78.4 I
84
85 86 87 88
322
1 The Synthesis of Chiral Nematic Liquid Crystals
imity of the liquid-crystalline core and the presence of longer peripheral alkyl chains [29]. The transition temperatures and phase assignments are given in Table 6. The esters with 4’-pentylbiphenyl cores were somewhat disappointing in their phase behaviour; all materials showed smectic A* and crystal B* phases; and only the methoxy compound 89 displayed a short chiral nematic phase (3.8 “ C ) .
H3C‘
bCH3
89; Cr 73.3 CrystB* 93.3 SmA* 131.6 N* 135.4 I (“C) [73]
The use of lateral fluoro-substituents in liquid crystals chemistry is well known for influencing physical properties, particularly in supressing smectic phases, as well as depressing both melting points and clearing points [74-791. By use of 2’-fluoro- and 2,3-difluoro-substituents in the biphenyl core, it proved possible not only to reduce both the melting points and clearing points, but also drastically to lower the thermal stability of the smectic A* phases, often to such a degree that room temperature iridescent chiral nematic phases were observed for a number of compounds in two different, but related, series. The acids providing the two different fluoro-substituted cores (4’pentyl-2’-fluorobiphenyl-4-carboxylicacid and 4’-pentyl-2,3-difluorobiphenyl-4-carboxylic acid) were synthesized by well-documented techniques for low temperature lithiation, carboxylation and formation of the boronic acids from aryl bromides as well as palladium (0) catalysed cross-coupling procedures [80-831. It is important to stress the versatility of these methods, the increased use of which has led to the accessibility of numerous structures throughout liquid crystal chemistry, which were previously thought to be too difficult to synthesize easily.
In the first of these fluoro-substituted series, the (R)-1-alkoxy-2-[4-(2’-fluoro-4’pentylbiphenyl-4-carbonyloxy)phenoxy]propanes (90-95), it was found that the 2’-fluorosubstituent destabilizes the ability of the molecules to pack efficiently to such a degree that they prefer to form chiral nematic phases over the more ordered smectic phases observed in their non-fluoro-substituted parents (see compound 89) [841. The first five materials show monotropic smectic A phases at correspondingly low temperatures; furthermore the butyl, pentyl, and hexyl homologues did not crystallize above a temperature of -40 “C (potentially an advantage for microencapsulation). The transition temperatures of this series are shown in Table 7; the clearing points are seen to decrease very rapidly from 8 1.2 to -6.1 “C. A similar, but less rapid decrease in thermal stability of the SmA phase is also observed. The propyloxy and butyloxy compounds (92 and 93) are both of interest in that they show highly iridescent chiral nematic phases at or around room temperature. Spectroscopic measurements, indicate that the homologues of this series have pitch lengths which vary in magnitude between 0.30 and 0.32 ym. Table 7. The transition temperatures and phase assigments of (R)-1-alkoxy-2-(4-(2’-fluoro-4’-pentylbiphenyl-4-carbonyloxy)phenoxy]propanes. F
Compound no.
n
Transition temperatures (“C)
1
Cr 54.3 (SmA* 24.5) N* 81.2 I Cr 40.6 (SmA* 4.9) N* 50.1 I Cr 36.2 (SmA* 6.0) N* 47.4 I Cr -(SmA* -4.1) N* 18.6 I Cr - (SmA* -10.0) N* 7.7 I Cr N* -6.1 I
90 91 92 93 94
4 5
95
6
2 3
1 .5
Turning now to the second fluoro-substituted series, (R)-l-alkoxy 2-[4-(2,3-di-
Type I Chiral Nematic Liquid Crystals
323
propanonitrile [72] and (R)-1-methoxy-2( 4- [4-(trans-4-pentylcyclohexyl)-benzoylfluoro-4’-pentylbiphenyl-4-ylcarbonyloxy)- oxyl-phenoxy }propane (83) [73], revealed phenoxylpropanes (compounds 96 to 101), that they show opposite helical twist senses the transition temperatures listed in Table 8, (the compounds are left handed and right show that as would be expected, the inhanded, respectively) as would be predictsertion of a second fluoro-substituent aped for materials with electron acceptor and pears to have little extra effect on the cleardonor groups at the chiral centre [32, 33, ing point over that of the 2’-fluoro-substi851. Interestingly, certain composition mixtuted series [84]. tures displayed either TGBA* phases mediThe melting points, clearing points and ating the chiral nematic to smectic A* tranthe N*-SmA* temperatures are indeed all sitions or twist inversion phenomena in the slightly higher than for the corresponding chiral nematic phase. 2’-fluoro homologues; the SmA* phases all The use of the stable, optically pure ( R ) -1-alkoxy-2-(4-substituted-phenoxy)occur enantiotropically, indicating greater propane system in conjunction with the apthermodynamic stability, unlike the precedpropriately fluoro-substituted liquid-crysing SmA* phases of the 2’-fluoro series (90 talline cores offers great potential for mateto 95). This overall result may be partly due rials which are suitable for use in thermoto the shielding of the 3-fluor0 substituent chromic mixture formulations [SS]. by the carboxylate linkage and the fact that the second fluoro-substituent effectively makes the liquid crystal core no broader 1.5.5 Miscellaneous Type I (i.e. the second fluoro-substituent has little Chiral Nematic Liquid Crystals effect on the overall geometrical anisotropy of the molecule). The former examples of type I materials are Binary mixture studies involving the not the only examples of the class; many chiral nematogens (R)-2- [(2’-fluor0-4’other forms of novel side chains have also pentylbiphenyl-4-carbonyloxy)phenoxy lbeen investigated. These miscellaneous chiral nematic systems include the following types of material: (R)-and (5’)-l-methylalkTable 8. The transition temperatures and phase assignments of (R)-1-alkoxy-2-(4-(2,3-difluoro-4’-pen- oxy derivatives (102) [87, 881; derivatives of (S)-P-citronellol (103) [89]; (R)-2-chloty l biphenyl-4-carbonyloxy)phenoxy]propanes. ropropanol and (S)-2-ethoxypropanol(lO4) F F 190, 9 11; (S)-2-chloropropyl derivatives (105) [29, 921; (S)-2-halogeno-4-methylpentyl derivatives (106) [29, 931; materials with (2S,3S)-3-propyloxirane groups (107) Compound n Transition temperatures (“C) [29,94]; and (R)-4-(1-propoxyethyl)phenyl no. derivatives (108) [95]. These materials will 96 1 Cr 34.3 SmA* 41.4 N* 85.6 I not be covered in great detail, as many of 97 2 Cr 17.5 SmA* 45.6 N* 74.5 I them were synthesized as potential ferro98 3 Cr 18.2 SmA* 25.1 N* 54.1 I electric materials, nonetheless, they high99 4 Cr 1.4 SmA* 9.5 N* 32.8 I 100 5 Cr 2.6 SmA* 13.6 N* 35.8 I light the use of other novel chiral side 101 6 Cr 0.6 SmA* 15.8 N* 42.1 I chains.
324
1 The Synthesis of Chiral Nematic Liquid Crystals
102; (S)-Abs config.; Cr 71.8 SmC* 89.8 N* 137.4 I ("C) [87, 881 A
103; Cr 79.5 SmC* 116.6 N* 150.0 I ("C) [89]
OCzH5
104; Cr 27.9 (Sm2 16.9) SmA* 45.2 N* 50.3 I ("C) [90,91]
ci 105; Cr 102.6 SmA* 137.0 N* 166.0 I ("C) [29,92]
106;Cr 67.8 SmC* 79.9 SmA* 96.8 TGB A* 100.4N* 128.3 BP 129.4 I ("C) [29, 931
107; R=C,H,; Cr 59 (SmCg 46.2 SmCZ 46.8 SmCt) Ng 106.3 NE 112.1 NE 158.1 BPI 162.9 BPI1 164.6 I ("C) [29, 941
Some of these materials were readily available from commercial sources, others were not and have had to be synthesized from convenient precursors. This has often led to two distinct types of approach: firstly, by employing mild synthetic methods which somehow preserve the optical activ-
ity of a particular system; secondly, where the former method was not possible, asymmetric induction methods have been employed. Here the chiral moiety may be synthesized stereospecifically, for example by employing a-amino acids such as (S)-alanine, (S)-leucine, (S)-valine, or (2S,3S)-isoleucine [29, 92, 931, or by using chiral catalysts or auxiliaries [94,95]. These catalysts and auxiliaries allow a reaction to take place at one specific face of the transition state complex during the reaction, thereby leading to a preponderance of one isomer over others (see also the Sharpless asymmetric epoxidation in Sec. 1.7.3 of this Chapter). One of the more unusual and elegant examples of the uses of a chiral catalyst is in the synthesis of the novel mesogen (R)-1(4'-nonyloxybiphenyl-4-y1) 4-( 1 -propoxyethy1)benzoate (108) [95]; this is outlined in Scheme 7. The achiral starting material, methyl 4-acetylbenzoate (109) was enantioselectively reduced using borane in the presence of the chiral oxazaborolidine (110) (itself synthesized from (S)-(-)-2-diphenylhydroxymethy1)pyrolidine and BH3 : THF [96]) to give the optically active benzyl alcohol (lll),in 89% ee. The (R)-4-( l-propoxyethy1)benzoic acid (112) was then obtained in a 25% yield after the sequence of base hydrolysis, propylation and base hydrolysis procedures. Compound 112 was then esterified in the standard manner to give the target compound (108). (R)-1-(4'nonyloxybiphenyl-4-y1) 4-( 1-propoxyethyl)benzoate (108) showed only a very short chiral nematic (N*) phase of range 0.5 "C, after undergoing a direct SmC*-N* phase transition at 104.5 "C.
1.6 Type 11 Chiral Nematic Liquid Crystals
325
110, BH,, THF.
* H3CO&
H3C02C H:* 3
111
109
I NaOH, MeOH; (ii) NaH, CSH,I; (iii) NaOH, MeOH (I)
(i) SOCI,; (ii) ArOH, pyridine.
C9H,90 ~
O
Z
C
~
-
c OC3H7
H
3
H 0 2 c ~ c H 3 OC3H7
112 108; Cr98 SmC' 104.5 N* 105 I ("C) [95]
110 [961
Scheme 7. Asymmetric synthesis of (R)-l-(4'-Nonyloxybipheny1-4yl) 441-propoxyethyl)benzoate.
1.6 Type I1 Chiral Nematic Liquid Crystals
1.6.1 Azomethine Ester Derivatives of (R)-3-Methyladipic Acid
Achiral twin compounds, which possess two liquid-crystalline cores separated by a flexible spacer, are now well known and documented. As well as being pre-polymer model systems, they also give large variations in transition temperatures which are dependent on the length of the flexible spacer and frequently give incommensurate smectic phases [97- 1001. However, examples of chiral materials which may be categorized in this manner are not numerous, and the majority of these examples concern the use of flexible, chiral linking groups based upon (R)-3-methyladipic acid [ 1011051, derivatives of lactic acid [106, 1071or optically active diols 11081 between two liquid-crystalline moieties. This class of chiral materials, however, remain an interesting subject in that, in principle, it is possible to modulate and sterically restrict motion about the chiral centres by varying the length of the flexible linking spacer unit.
The first examples of this kind of material belong to a homologous series of bis-azomethines (113-114) which have the general structure represented in Table 9 [loll. The materials were prepared by esterification of (R)-3-methyladipic acid with 4-hydroxybenzaldehyde to the bis-[bforrnylphenyl] (R)-3-methyladipate. This was then condensed with the appropriate 4-alkoxyaniline to give the desired bis-azomethine dimer. In this homologous series, only the early members (ethoxy, butoxy and hexyloxy, compounds 113 to 115) showed chiral nematic phases; the transition temperatures of these materials are given in Table 9.
326
1 The Synthesis of Chiral Nematic Liquid Crystals
Table 9. The transition temperatures and phase assignments of diesters derived from the chiral3-methyl adipic acid and 4-hydroxybenzylidene-4'-alkoxyanilines.
Compound no.
n
Transition temperatures ("C)
113
2 4 6
Cr 156.3 N* 236.6 I Cr 154.6 Sml 158.5 Sm2 169.3 N* 210.9 I Cr 122.8 Sml 140.0 Sm2 174.7 SmA* 190.0 N* 195.5 I
114 115 ~~~
~
Where Sml and Sm2 represent unidentified smectic phases.
1.6.2 Novel Highly Twisting Phenyl and 2-Pyrimidinylphenyl Esters of (R)-3-Methyladipic Acid A more recent continuation of this theme using (R)-3-methyladipic acid, was the systematic study of dimeric or twin structures which are capable of forming highly twisted helical structures [ 102- 1051.These examples, differ from the previously mentioned bis-azomethines in that they employ 2-pyrimidinylphenyl (116 and 117) and phenyl core units (118); they were made simply by esterification of (R)-3-methyladipic acid with the appropriately substituted phenol using dicyclohexylcarbodiimide (DCC) and the catalyst 44,N-dimethylaminopyridine (DMAP). The structures and phase transitions of members of these two classes are given in structures 116 to 118.
The transition temperatures for the 2-pyrimidinylphenyl based compounds (116 and 117) clearly show that they display only rather short range, monotropic chiral nematic phases. Bearing this in mind, it is not surprising that the smaller twin with a phenyl core (118) does not form a chiral nematic phase. Studies which employed these three materials as dopants have shown conclusively that the chiral nematic phases of the test mixtures have particularly short pitch lengths ( p = 16- 22 pm) and right handed twist senses. This contrasts noticeably with the monomeric materials which have similar structures, for example (S)-4-(4-[2-(4hexyloxyphenyl) - 5 -pyrimidinyl] -phenyl } 3-methylpentanoate (119), which has a considerably longer pitch length ( p = 79 pm).
119; Cr 118.2 (SmC* 185.4) N* 195.8 I ("C); p = Fma, LH-helix [102, 1031
It has been suggested that the marked difference in pitch lengths between the twins and monomeric materials is due in part to the further restriction of rotational motion about the chiral centre caused by the presence of a second bulky core moiety, result-
116; n = 7; Cr 139.6 (N* 136.9) I ("C); p = 19 pm', RH-helix [102-1041 117; n = 8; Cr 130.9 (N* 127.7) I ("C); p = 22 pm",RH-helix [102-1041
C8H170 - @ 0 2 c & C 0 2 ~
OC,H
17
118; mp = 56.7"C, p = 16 pna, RH-helix [102-1041
a Corresponds to a measurement made with a 2 wt% mixture in 6CB.
1.7 Type 111 Chiral Nematogens
ing in a more tightly twisting helical structure. However, if this was entirely true, then a similar increase in spontaneous polarization of the induced SmC* phases, which are also present in the test mixtures doped with twins, should also be observed. This is not the case, and this may possibly be due to the transverse dipole of the twin aligning perpendicularly to the C2 axis of the chiral smectic C phase [ 1021.
1.6.3 Chiral Dimeric Mesogens Derived from Lactic Acid or 1,2-Diols
327
(R,R)-2,3-butandiol, has shown the diesters to have high helical twisting powers (p) when used as dopants in suitable nematic mixtures. However, only one of these materials is known to show a liquid-crystalline phase; this is a derivative of (R,R)-2,3-butanol (122) [IOS]. The high thermal stability of the chiral nematic phase is not surprising, considering the size of the liquid-crystalline core (4'-(trans-4-pentylcyclohexyl)biphenyl-4-carboxylic acid); the chiral nematic phase occurs between 212 and 255 "C. C5H11
C5Hll
Other attempts have been made to employ the (R)-2-oxypropanoyloxy moiety as a chiral spacer between identical [ 1061 and dissimilar [7 1, 1071 liquid-crystalline core systems, typical structures are given by compounds 120 and 121.
122; Cr 212 (SmX* 197) N* 255 I ("C) [lo81
This compound has been demonstrated to give highly twisted chiral nematic phases when used as a dopant and shows a helix in-
120; Cr 104.9 (SmA* 80.4 N* 83.7) I ("C) [lo61
Compound 120 shows a short monotropic chiral nematic and smectic A* phase, whilst 121 shows a short enantiotropic chiral nematic and a monotropic smectic A* phase. From this it may be concluded that the lactic acid derived (R)-2-oxypropanoyloxy moiety is not particularly suited to sustaining liquid crystal phases; this may either be partly due to poor conjugation between the liquid crystalline cores or because of the non-linear nature of molecules. Research on diesters derived from the optically active diols, (S)- 1,2-propandiol and
version at approximately 60°C in a commercially available wide range nematic mixture.
1.7 Type I11 Chiral Nematic Liquid Crystals This class of chiral mesogen contains many structurally unusual and interesting liquid
328
1 The Synthesis of Chiral Nematic Liquid Crystals
crystal materials. Here the chirality is imparted by the presence of either a chiral atom situated within the core, or by the generation of gross molecular asymmetry as a result of the core’s overall spatial asymmetry. It may also be recalled from an earlier section on molecular symmetry (Sec. 1.3.1), that the chirality of a liquid-crystalline system may be increased if the chiral centre is brought closer to the mesogenic core, due to restricted motion of groups around the chiral centre [29]. This increase in chirality may manifest itself in many ways, such as the shortening of helical pitch length or the increase in spontaneous polarisation of a chiral dopant. Therefore, it may be appreciated that incorporation of the asymmetric centre in the core, to create a chiral core, is an attractive method of trying to develop a mesogen capable of forming a very highly twisted helical structure (i.e. a short pitch chiral nematic phase). Examples of these less common systems include the following compound types: twistanol (or tricycl0[4.4.0.0~~~]decane) derivatives [ 1091; cyclohexylidene ethanones [ 110, 1111; chiral oxiranes [112,1131; chiral 1,3-dioxolan4-ones [ 1141; substituted stilbene oxides [ 1151; chiral dioxanyl derivatives [ 1161; nitrohydrobenzofuran derivatives [ l 171 and cyclohexanes [ 118,1191. Although many of these systems show chiral nematic phases, their usefulness is severely limited for a number of reasons; the awkward and expensive synthetic routes, the necessity for inefficient and frequently impractical resolution techniques, and in many cases their ultimate chemical or photochemical instability.
1.7.1 Tricyc10[4.4.0.0~~~]decane or Twistane Derived Mesogens
has been incorporated into a number of liquid-crystalline (R)-(+)-8-alkyltwistanyl 4-(trans-4-pentylcyclohexyl)benzoates or 4’-pentylbiphenyl-4-carboxylates(130-132), some of the members of these series are reported as showing chiral nematic phases [ 1091.The twistane ring system has D, symmetry and may be viewed as consisting of four fused boat form cyclohexyl rings which all twist in the same sense; using the Cahn, Ingold and Prelog selection rules, the two enantiomeric forms may be classified as having P- or M-helicity [30]. The (R)-(+)8-alkyltwistanol moiety was prepared by use of a six step synthetic route, starting from the disubstituted cyclohexan- 1,5dione (123) shown below in Scheme 8. The first two steps, that is the stereoselective cyclization in the presence of (S)-(-)proline to give the bicyclic diketone (124) and the hydrogenation of the double bond formation during the condensation step to give compound 125, are crucial in setting up the appropriate stereochemistry necessary for the acid-catalysed cyclization step which results in the formation of the basic twistance core (126). Of the five materials synthesized in this way, only three show chiral nematic liquid crystal phases, as listed in Table 10. It is also of interest to note that compounds 131 and 132 are reported to show anomalous pitch dependency in their chiral nematic phase; the pitches are both reported to increase from 1.1 to 1.6 pm with increasing temperature.
1.7.2 Axially Chiral Cyclohexylidene-ethanones
Solladie and Zimmerman have reported a series of novel chiral liquid crystals which The optically active twistane ring, more are believed to be the first to incorporate a correctly named tricyc10[4.4.0.0~,~]decane, molecular unit which possesses axial chiral-
1.7
128
329
126
127
I LiAlH4
Type 111 Chiral Nematogens
ArCOCI,
OH pyridine
C5Hll
129
130-132 where R = C3H7 or CSH11.
Scheme 8. Synthesis of (R)-(+)-8-twistanol containing mesogens.
Table 10. The mesomorphic behaviour of (R)-(+)-8twistanol derivatives.
where R1 = alkyl, alkoxy, nitrile and R2 = alkyl or mcthyleneoxy.
Compound no.
X
R
Transition temperatures ("C) H
130 131 132
Ph") Ph Ch")
C3H, C,H,, CSH,,
Cr 94.2 N* 119.2 I Cr71.8N" 126.41 Cr 65.0 N* 124.7 I
Figure 7. (a) The general structure of a cyclohexylidene ethanone. (b) Axial chirality of the cyclohexylidene moiety.
Where Ph denotes 1,4-phenyl and Ch denotes trans1,4-cyclohexyl.
')
ity; these are the substituted biphenylyl cyclohexylidene ethanones of the general structure shown in Fig. 7(a) [110, 11 11. The axial chirality is the consequence of two perpendicular planes associated with the R, and hydrogen substituents on the C-4 carbon atom of the cyclohexyl ring and the alkene substituents, R , and H; this is more clearly seen in Fig. 7(b). The optically active compounds were obtained by a series of elegant stereoselective reactions, outlined in Scheme 9. The chiral sulfoxide (134) was obtained from the reaction of the Grignard reagent of
a bromo-(4-substituted cyclohexy1)methane (133) and (S)-(-)-methyl sulfinate. Compound 134 was then stereoselectively acylated using lithium di-isopropylamide (LDA) at -78 "C with an appropriately substituted aroyl chloride, to give the diastereoisomeric sulfoxides (135- 136). The (R,R)-and (S,R)-diastereoisomers may both be obtained as either the thermodynamic or the kinetic product of the reaction process. The final step involves the stereoselective pyrolytic elimination of the sulfoxide group to give the ( S ) - or (R)-cyclohexylidene ethanones (137 and 138) from the diastereoisomeric (R,R)- or (S,R)-sulfoxides (135 and 136).
330
1 The Synthesis of Chiral Nematic Liquid Crystals
(i) LDA, THF, -78 OC; (ii) ArCOC1, -78 'C.
Table 11. Mesomorphic behaviour of a variety of arylcyclohexylidene ethanones.
Compound no.
Configuration
(0 (0
139 140 141
(9-
Rl
R2
Transition temperatures ("C)
C5H1 1
CHZOCZH,
CH3 CN
C5H1 1 C5H11
Cr 43 SmX* 63 N* 67 I Cr 65 N* 124 I Cr 102 SmX* 113 N* 135 I
SmX* = represents an unidentified smectic phase.
Of the seven optically active cyclohexylidene ethanones synthesized, only three showed chiral nematic phases; these materials are listed in Table 11 . However, the conjugated nature of these materials makes them particularly photochemically unstable; irradiation of a racemic cyclohexylidene ethanone with UV light has been shown to result in the rapid isomerization of its double bond in a few hours to give compounds of the general structure (142), as well as the oxidation product, 4'-pentylbiphenyl-4-carboxylic acid.
142
Nonetheless, despite this poor photochemical instability, these materials un-
equivocally prove that materials possessing axial chirality are capable of forming chiral nematic phases.
1.7.3 Chiral Heterocyclic Mesogens A number of heterocyclic type I11 systems have been investigated, primarily as ferroelectric dopants, but a number of the materials do display short (sometimes unstable) chiral nematic phases. Notable examples of systems based on three-membered ring heterocycles are probably best demonstrated by the materials containing the (2R,3S)-2oxirane carboxylic acid unit [ 1121 and trans-stilbene oxides [ 1 151. The synthesis of the oxirane units is of interest as it is achieved by use of the Sharp-
1.7 Type 111 Chiral Nematogens
less asymmetric epoxidation procedure by treatment of either cis- or trans-allylic alcohols with a stoichiometric mixture of L-(+)diethyl tartrate, titanium isopropoxide and t-butyl hydroperoxide at low temperature to give the appropriate epoxide [ 112,113,120, 1211. This process is demonstrated in the synthesis of (2R,3S)-(-)-4-heptoxyphenyl 3- [truns-4-(truns-4-pentylcyclohexyl)cyclohexyl]oxirane-2-carboxylate (146) shown in Scheme 10 [113]. The use of a further mild oxidation and neutral esterification methods ensure that ring opening of the epoxide ring is minimized. As can be seen from the transition temperatures of compound 146, the chiral nematic phase has quite a high thermal stability, presumably a direct result of the two cyclohexane rings which are known to promote high clearing points [49]; the material also has an underlying smectic A phase. Interestingly, this form of epoxide is somewhat more stable than other examples (i.e. compound 107 [94]) because the electron-withdrawing carboxyl moiety reduces the basicity of the oxirane ring, reducing the tendency towards ring opening processes.
-
CSHll
OH
143
Ti('OPr)4,L-(+)-DET, 'BuOOH, CH2Cl2,-23 "C.
144
C5hl
' I
RUC13, NaI04, CC14, CH,CN, H20, RT. 0 CO2H
* *
145
4-hcptoxyphenol, DCC, DMAP, C H Z C I ~RT. ,
33 1
Larger chiral heterocyclic core systems have been synthesized, for example chiral 1,3-dioxany1-4-ones (147) [ 1141 methyldioxanyl (148) [I 161 and 2-alkyl-2,3-dihydrobenzofuran (149) [ 1171 derived mesogens, and the phase behaviour and transition temperatures of these materials are shown below.
147: Cr 71 SmC* 75 N* 85 I ("C) [ I 141
148; Cr 52 SmA* 57.4 N* 100.5 I ("C) [ I 161
CeHi70
w z C6H13
149; Cr 115 SmC* 140 SmA* 183 N * 185 I ("C) 11171
1.7.4 Chiral Mesogens Derived from Cyclohexane A number of elegant attempts have also been made to employ chiral cyclohexane rings as part of the liquid-crystalline core; the approaches to these materials have usually involved the use of either enantiospecific aluminium trichloride catalysed Diels -Alder reactions (150) [ 1181 or the chiral reducing agent alpine boramine on unsaturated cyclohexyl derivatives (151) followed by palladium (0) catalysed coupling procedures [119]. However, the full development and potential of such mesogens still remains a relatively unexplored field.
146; Cr52.0 SmB* 121.0 SmA* 159.7 N* 167.5 I ("C) [I131
Scheme 10. Synthesis of (2R,35')-(-)-4-Heptoxyphenyl 3-[trans-4-(truns-4-pentylcyclohexyl)cyclohexyl Ioxirane-2-carboxylate.
150: Cr 79 S2 94 S , 113 SmC* I32 SmA* I33 N* 150 I ("C) [I181
332
1 The Synthesis of Chiral Nematic Liquid Crystals
H,CO‘
151; Cr 120.1 SmA* 127.4 N* 139.9 I (“C) [119]
1.8 Concluding Remarks As has been stressed throughout this chapter, the development of chiral nematic liquid-crystalline materials has often taken its lead from the inadequacies and unsuitability of many of the existing materials which have been employed in particular technological roles. This materials development process is perhaps most clearly evident in the development of the stable, colourless ester derivatives which utilise the (S)-2-methylbutyl side chain, particularly as this evolution is easy to trace from the early sterolbased mesogens, to the chiral azobenzenes through to the chiral azomethine mesogens. As well as being commercially successful, these materials also led to the development of ground rules which relate the nature of the chemical structure to the physico-chemical properties. This has most importantly led to a certain degree of selectivity in the manipulation of properties during the process of choosing a material for any given application. The fact that these materials have relatively simple structures, especially when compared with those of the ‘exotic’ chiral nematogens, is of benefit and importance in that is makes them more readily accessible and therefore more economically viable at a commerical level. Nevertheless, the advent of certain synthetic methods (i.e. the palladium (0) catalysed cross-coupling reactions) has led to a number of notable issues such as improvements in the synthesis of known materials, improvements of physical characteristics as a result of minor
structural modifications (i.e., use of lateral fluoro-substituents) and the generation of entirely novel and frequently exotic chiral mesogens (i.e., twistanol derivatives or cyclohexylidene ethanones). These ‘exotic’ chiral systems demonstrate the myriad of structural variations possible, despite some being highly impractical. Nevertheless they are of great interest from a purely scientific stand point; these materials have usually been used to probe experimentally some facet of the relationship between chirality and molecular structure.
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1 The Synthesis of Chiral Nematic Liquid Crystals
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[97] A. C. Griffin, T. R. Britt, J. Am. Chem. SUC. 1981,103,4957-4959. [98] J. W. Emsley, G. R. Luckhurst, G. N. Shilstone, I. Sage, Mul. Cryst. Liq. Cryst. 1984,102,223233. [99] J. L. Hogan, C. T. Imrie, G. R. Luckhurst, Liq. Cryst. 1988, 3, 645 - 650. [loo] G. S. Attard, S. Garnett, C. G. Hickman, C. T. Imrie, L. Taylor, Liq. Cryst. 1990, 7,795 -508. [loll J. Barberi, A. Omenat, J. L. Serrano, Mol. Cryst. Liq. Cryst. 1989, 166, 167-171. [lo21 A. Yoshizawa, I. Nishiyama, J. Muter. Chem. 1994,4,449-456. [lo31 I. Nishiyama, H. Ishizuka, A. Yoshizawa, Ferruelectrics 1993, 147, 193-204. [lo41 I. Nishiyama, A. Yoshizawa, Liq. Cryst. 1994, 17,555-569. [105] I. Nishiyama, M. Saito, A. Yoshizawa, Poster at the 15th ILCC, Budapest, Hungary, 1994. [lo61 M. Marcos, A. Omenat, J. L. Serrano, Liq. Cryst. 1993,13,843-850. [lo71 C. J. Booth, J. P. Hardy, J. W. Goodby, K. J. Toyne, Unpublished results. [lo81 G. Heppke, D. Lotzsch, F. Oestreicher, Z. Nuturforsch. 1987,42a, 279-283. [lo91 R. Ch. Geivandov, I. V. Goncharova, V. V. Titov, Mol. Cryst. Liq. Cryst. 1989, 166, 101103. [110] G. SolladiB, R. Zimmermann, J. Org. Chem. 1985,50,4062- 1068. [I 111 G. SolladiC, R. G. Zimmermann, Angew. Chem., Int. Ed. Engl. 1985,24, 64-65. [112] G. Scherowsky, J. Gay, Liq. Cryst. 1989, 5, 1253- 1258. [I131 G. Scherowsky, J. Gay, N. K. Sharma, Mol. Cryst. Liq. Cryst. 1990, 178, 179-192. [I141 G. Scherowsky, M. Sefkow, Mul. Cryst. Liq. Cryst. 1991,202,207-216. [115] B. F. Bonini, G. Gottarelli, S. Masiero, G. P. Spada, Liq. Cryst. 1993, 13, 13-22. [116] R. Buchecker, Oral Presentation at the 13th ILCC, Vancouver, British Columbia, Canada, 1990. [117] H. Matsutani, K. Sato, T. Kusumoto, T. Hiyama, S . Takehara, H. Takazoe, T. Furukawa, Poster at the 15th ILCC, Budapest, Hungary, 1994. [ 1181 Z. Li, B. M. Fung, R. J. Twieg, K. Betterton, D. M. Walba, R. F. Shao, N. A. Clark, Mol. Cryst. Liq. Cryst. 1991,199, 379-386. [ I 191 S. J. Lock, M. Hird, J. W. Goodby, K. J. Toyne, J. Muter. Chem. 1995,5,2175-2182. [ 1201 Y. Gao, R. M. Hanson, J. M. Klunder, S. Y. KO, H. Masamune, K. B. Sharpless, J. Am. Chem. SOC. 1987,109,5765-5780. [121] K. B. Sharpless, T. Katsuki, J. Am. Chem. SUC. 1980,102,5974-5976.
Handbook ofLiquid Crystals D. Demus, J. Goodby, G. W. Gray, H.-W. Spiess, V. Vill Copyright 0WILEY-VCH Verlag GmbH. 1998
2 Chiral Nematics: Physical Properties and Applications Harry Coles
2.1 Introduction to Chiral Nematics: General Properties The discovery of thermotropic liquid crystals is generally attributed to Reinitzer [ l ] who studied compounds such as cholesteryl benzoate and cholesteryl acetate and noted that the former compound exhibited two melting points and bright iridescent reflection colors between these points. Lehmann [2] coined the phrase “liquid crystal” for such materials as a result of his extensive work on liquid-like substances and there is a lot of interesting debate in the early literature as to who actually discovered liquid crystals [3]. Lehmann certainly constructed specialized polarizing microscopy apparatus which was of fundamental importance in recognizing the selective reflection properties of such materials. It is interesting to note that at much the same time as this discovery research was being carried out on the reflection colors of birds and insects, and that Michelson also noted [4] the selective reflection in ordinary daylight of circularly polarized light from the beetle Plusiotis resplendens. It is now generally thought that
this reflection layer is formed at the late chrysalis stage by a helicoidal liquid crystalline glandular secretion that hardens into a pseudomorph on the surface [ 5 ] . This reflecting layer has a thickness of 5-20 pm, which is typical of the reflecting cholesteric films discussed later. Further, Caveney showed that this reflection was enhanced by a nontwisted half-wave plate layer naturally formed between the two such helicoidal layers [6]. This biological example of enhanced selective reflection serves to show that we have many lessons to learn from Nature which is probably the true inventor of liquid crystals and, as noted in [7], “the farther backward you can look the farther forward you are likely to see”. Studies of the early thermotropic and biological systems have led to much of our present understanding of the general properties of cholesteric liquid crystals. These will be considered herein and we will show how such properties lead to optically linear and nonlinear devices, thermal imagers, radiation detectors, optical filters, light modulators, and other technologically interesting applications in Sec. 2.5 of this Chapter.
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Historically, the helicoidal liquid crystals recognized by Reinitzer, Lehmann, Michelson, Caveney et al. were called “cholesterics” after the original cholesterol esters studied by Reinitzer [l]. However, many other steroidal and nonsteroidal compounds exhibit these so-called cholesterical phases (see, for example, [8-121). Thermodynamically, the cholesteric phase is the same as the nematic phase described in the previous sections of this volume and, although both notations are often used, the cholesteric phase can be considered as just the chiral form of the nematic phase. This can be understood by considering a racemic mixture of exactly equal amounts of enantiomeric forms (S and R) of the same nematic molecule. Such a mixture would be achiral, however, a slight excess of one form over the other leads to a chiral nematic phase. It therefore seems more rational to use the notation “chiral nematic” or N*. Thus a chiral nematic phase (N*) is exhibited by neat nematic compounds or mixtures where at least one of the compounds is chiral (i.e., each molecule not superimposable on its mirror image) or where there is an excess of one enantiomer over the other. In this chapter we will not consider in depth chiral nematic systems where only a small percentage of chiral material is added to give a weak helical structure to prevent ‘reverse twist’, as in twisted nematic or supertwisted nemat-
ic devices [ 131. We will primarily be concerned with systems with a high twisting power, such that the N* helicoidal structure formed macroscopically has a pitch length ( p ) of the order of the wavelength of light (A) (see Fig. l), or more generally exhibits a high value of optical rotatory dispersion. For comparison, a typical N* material would give an optical rotation of >lo3 degrees/mm compared with -10 degreedmm for a typical sugar solution. Chiral nematic (or cholesteric) liquid crystals have the orientational order of achiral nematics, but the director (n)is constrained in a layer-like structure to precess around the helical axis perpendicular to n. A ‘layer’ one molecule thick would give a director rotation of -10-20 min of arc per layer. Thus successive ‘layers’, with molecules ‘on average’ preferring to sit at such an angle to each other, twist and describe a helix of pitch p over distances that are large in comparison to the molecular dimensions. Here it should be remembered that such ‘layers’ are composed of molecules in constant thermal agitation and the director only describes a mean macroscopic or continuum picture. Molecules can exchange between near neighbors in the N* phase just as in the N phase. The helix pattern described by the director then dominates the optical properties of the N* phase. Depending on the enantiomeric excess, the materi-
AXIS
Figure 1. Representation of the helicity in chiral nematic structures. The helix defines the z axis and the periodicity in the structure is pi2 due to the condition n =-n.
2.1
Introduction to Chiral Nematics: General Properties
als may have a right-handed (clockwise director rotation) helical structure, and there is a clear relationship between helical sense and molecular structure [ 141. If the director n (a unit vector) describes a right-handed screw along the z axis, in a right-handed coordinate system then the director in the N*< phase is given by
where @ is a constant defining an arbitrary angle with x in the x, y plane and p is the helix pitch, which is positive or negative for right-handed or left-handed materials, respectively. Note that the helix only extends in one direction and that in any one ‘layer’ the molecules appear nematic-like. Further, since n =-n the ‘true’ period of the N*phase corresponds to p12 or a 180” rotation of n . We may also define the helical wave vector k = 2 d p , which then appears in the twist term of the free energy density equation for an N* phase, i.e.,
+ X k2, ( n . V xn + k), +% k3, ( n x V xn),
,,
(2)
Here k, k,,, and k,, are the usual splay, twist, and bend elastic constants of Leslie [lS, 161 and Ericksen [17, 181 continuum theory. This theory will be considered further in Sec. 2.2.2. It is the dependency of k on p , dpld T, and d p l d P that leads to interesting reflection or transmission filters and thermometry devices or temperature and pressure ( P ) sensors, respectively. These will be considered further in Sec. 2.5. If an electric or magnetic field is applied to the system, then an additional term -W is also added to the Eq. ( 2 ) , where W=XArl ~ X ( E. n)2 or %AX ( H n12, respectively. This again has important ramifications
337
which will be considered in Secs. 2.2 and 2.4. The modified free energy density equation refers to static or time-independent properties. If pulsed fields are used, then transient changes lead to switchable bistable states, dielectric and hydrodynamic instabilities and flexoelectric phenomena [ 191, which again may be used in modulation devices. These will be considered in Secs. 2.3 and 2.5, respectively. The optical properties of chiral nematics are remarkable and are determined by the pitch, p , the birefringence, An, and the arrangement of the helicoidal axis relative to the direction and polarization of the incident light. Here we use the term light to indicate that spectral region between the material’s ultraviolet and infrared absorption bands, since this leads, for example, to the possibility of near-infrared modulators. The helical pitch may be much greater or much less than the wavelength &, provided we remain in the limit of high rotatory dispersion discussed briefly earlier. In an external field changes may occur in both the direction of the helix axis, which leads to a textural transition, or in the helical pitch p , which then leads to an untwisting of the helix itself. These effects have been reviewed recently [20, 211 and led to numerous device applications (see Sec. 2.5). The observed optical properties of chiral nematic films depend critically on the direction of the director at the surface interface and on how this propagates to the bulk material. If the director is oriented along the surface of the cell using suitable alignment agents, such as rubbed polyimide, PVA, or PTFE, then the helix axis direction (see Fig. 1) is perpendicular to the substrates, as shown in Fig. 2a. In this case, an optically active transparent planar texture is obtained. It is this texture that is normally used to observe the bright iridescent reflection colors initially observed by Reinitzer and Leh-
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2 Chiral Nematics: Physical Properties and Applications
mann. If, however, the molecules are oriented normal to the substrate using lecithin, quaternary ammonium surfactants (e.g., HTAB), or silane derivatives, the competition between the helix twist and the surface forces constrains the helix axis parallel to the substrate. This is turn leads to two possible textures, i.e., fingerprint and focal conic (Fig. 2 b, c). In the fingerprint texture the helix axis, z , is aligned uniformly and a side view of the helix is observed. As a result of the director rotation, the refractive index varies in an oscillatory manner and through crossed polarizers this appears as banding reminiscent of a fingerprint. On the other hand, if the helical axis is random in the horizontal plane, we would have a 'polycrystalline' sample which becomes focal conic if the axis of the helix tilts and forms ellipses or hyperbolae. We will discuss these textures further in Sec. 2.2.1. The focal con-
ic texture is highly light-scattering and for initially describing the optical properties of chiral nematics we consider optical phenomena observed with helically twisted planar textures. Under the conditions that the pitch @) is of the order of the wavelength (A) in the medium and that the incident light (Ao)propagates along the helix axis (z), we have two primary characteristic features: a) There is a strong selective reflection of circularly polarized light having the same handedness and wavelength as the pitch inside the chiral nematic medium (see Fig. 3). This corresponds to a snapshot of the E vector of the circularly polarized light matching the helicoidal structure. The reflected light is circularly polarized with the same handedness as the incident light, which is the exact opposite of a normal mirror reflection, which has a 7c phase change on reflec-
+ LINEAR
Figure 3. Schematic diagram of selective reflection from aright-handed chiral nematic planar texture for ;1=&ln inside the liquid crystal. The linearly polarized input light may be considered as counter-propagating right-handed (RH) and left-handed (LH) circular components. The RH component in which the E field matches the sense of the helicoidal structure is back reflected due to director fluctuations, whilst the LH component is almost totally transmitted. By convention, the handedness is defined in terms of the progression of the E field vector in time relative to the observer. The RH rotating wave therefore has the same spatial structure as the chiral nematic at any time.
2.1
Introduction to Chiral Nematics: General Properties
tion. Thus right circularly polarized light would be reflected by a right-handed helix. On the other hand, left circularly polarized light would be almost wholly transmitted through the medium without reflection. Thus if white light is normally incident on such a chiral nematic film, it appears vividly colored on reflection. The effect is best observed, as in thermometry devices, against a black background. The selective circularly polarized reflection occurs around the incident wavelength, &, (in air) as given by ;h=iip
(3)
with a bandwidth A L centered on A, given by
AA =Anp
(4)
where A n = n l ,-nl and E, the mean refractive index, is given by (n,,+ nJ2. Note that here rill is defined as parallel to the director and n1 as perpendicular to it in the same plane, and that the ratio An/& is defined only in terms of the birefringence and refractive indices of the chiral nematic material, i.e., An/;. This is of considerable importance in the design of narrow band optical filters. If p becomes very temperature-sensitive, such as, for example, when the N* phase approaches an SmA* phase on cooling, then since in the latter phase p +00 the wavelength & also diverges towards infinity. This is the basis of many thermometry devices [ 1 I]. At oblique incidence, the reflection band is shifted to shorter wavelengths and side-band harmonics appear [22]. This situation is complex to analyze because of the effect of the twisted refractive index ellipsoid associated with each ‘layer’ on the different polarization components of the incident light. We have in fact to deal with complex elliptically polarized light rather than circularly polarized reflec-
339
tions and their interactions with the refractive index. However, to a good approximation Fergason [22] showed that &, varies for polydomain samples as
where Oi and 8, are the angles of incidence and reflection at the chiral nematic polydomain sample and m is an integer. The equation is only approximate, since the derivation assumes small O,,, and A n . If Oi= Or, i.e., a planar N* sample then
4)= Pmk cos ~
[ (n)l sin
-I
sinO,
(6)
which is of the form of the often quoted ‘Bragg-like’ condition where
m A = p cos $r
(7)
where sin Oi=E sin $,., $r is the internal angle of refraction at the aidliquid crystal interface, and ilis the wavelength in the medium [23]. Experimentally, all orders (m= 1, 2,3, etc.) are observed and again the reflected polarizations are elliptical rather than circular [23-251. We will return to more exact derivations of the selective reflection properties of chiral nematic materials in Sec. 2.2.1 by solving Maxwell’s equations inside the structure. b) There is a strong optical rotatory power for incident wavelengths A,, away from the central reflection maximum at ;lo,subject to the two limiting conditions that Ai >>p or Ai<
340
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Chiral Nematics: Physical Properties and Applications
Figure 4. Schematic diagram of (a) the optical rotatory power and (b) the reflection spectrum from a planar chiral nematic texture.
RED
ROTARY DISPERSION
Figure 5. Schematic diagram of the rotatory power and dispersion of linearly polarized light incident on a chiral nematic along the helix axis.
cularly polarized light of opposite handedness but of the same frequency traversing the N* material. The right- and left-handed waves will travel with different velocities on passing through the material and there will then be a phase shift between the two components. If we now consider linearly polarized light as the superposition of two circular waves of opposite handedness then, after passage through the N* material, the two components are recombined to give linearly polarized light, but with its plane of
polarization rotated relative to the incident light due to the phase shift. Since different wavelengths will travel with different velocities, the different spectral components will show different rotations, i.e., dispersion (see Figs. 4 and 5). Thus a chiral nematic sample in the planar configuration will show different colors on transmission if placed between a crossed polarizer and analyzer using a white light source. If the analyzer is then rotated, there will be a shift in the transmitted color. As shown in Fig. 4,the specular reflection band separates the two regimes of opposite sign of rotatory power. On either side of the selective reflection band centered at & there are regions of strong rotation of the plane-polarized light. The optical rotation per unit length ty/d can be written [26] as
where A is the wavelength inside the medium and the condition that I A- &I > > AA/2
2.1
Introduction to Chiral Nematics: General Properties
applies. This equation also shows that the polarization plane rotates in the same sense as the helix for Ap. In the case of A c p (Mauguin's regime), the plane of the polarization actually follows the rotation of the director, and the angle of its rotation on emergence from the layer corresponds exactly to the number of turns of the helix. This is the waveguide regime used in twisted nematic (TN) devices [13], where the helical pitch is much greater than the wavelength of light. In this device the full twist in the director between the upper and lower plates is 90". Thus in the field off state linearly polarized light is rotated through 90" between crossed polarizers to give a transmission state. If the chiral nematic has a positive dielectric anisotropy (i.e., A E= - and E~~and are the dielectric constants parallel and perpendicular to the director at the frequency of an applied field E ) , then the planar texture on the application of E transforms to the homeotropic state and the twist ordering is lost. Thus the incident polarization is no longer rotated in the cell and the transmitted light intensity falls to zero, i.e., extinction between crossed polarizers. Although we will not consider such a 'dilute' regime ( A c p ) further, in great detail, it represents a major applications area of display devices and illustrates another reason why we prefer to call the present materials chiral nematic or N* rather than cholesteric. There is a further geometry of practical interest for light incident on chiral nematic films, related to the pitch of the helix in which we consider light propagating in a direction normal to the helix axis, i.e., as in the fingerprint texture, but with a pitchp less than A. In this short pitch chiral nematic case, the chiral optical tensor is averaged in space and the macroscopic optic axis is collinear with the helix axis [27]. The macro-
34 1
scopic refractive index, nia, for light waves with their polarization orthogonal to the helix axis is an average of the microscopic indices nI1and n I . Since in any one 'layer' nematic liquid crystals are optically positive (nll>n,), the short pitch chiral nematic is macroscopically optically negative, i.e., R ;;"< RY. Electric fields may then be applied to such short pitch systems to deviate the effective optic axis. At low fields this gives a linear electrooptic effect [28] due to flexoelectricity [29], whilst at higher fields dielectric coupling leads to a quadratic effect, i.e., the helix deforms as the pitch increases in the field to unwind completely above a critical field. We will consider these different dielectric and flexoelectric effects in Sec. 2.2.3, and their implications for light modulation devices in Sec. 2.5. In this introduction we have outlined the important physical properties, i.e., optical, elastic, etc., of chiral nematic liquid crystals and indicated the vital role that the pitch plays in determining these macroscopic properties. In the following sections we will present more rigorous derivations of the origins of these properties. Firstly we will consider the static properties, i.e., those exhibited at equilibrium either with or without an applied field (Sec. 2.2). We will then consider time-dependent or dynamic properties, where the systems are in continuous flux or responding to a transient field (Sec. 2.3). As outlined above, both the static and the dynamic properties lead to thermo-optic, electrooptic, magneto-optic (Sec. 2.4), and even opto-optic phenomena in chiral nematics, which in turn lead to devices where the chiral nematic pitch varies from much less than the wavelength of light to much greater than A. These applications will be considered in the Sec. 2.5, where we will also speculate on possible future developments.
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2 Chiral Nematics: Physical Properties and Applications
2.2 Static Properties of Chiral Nematics In the previous section we discussed the preferential use of the term chiral nematic over cholesteric. At zero pitch the chiral nematic (or cholesteric) becomes nematic. This is true on the molecular scale where the local twist is very small. In the simple 'layer' model, ignoring molecular fluctuations, the twist between layers is of the order of 0.1" for pitch lengths at optical frequencies. Therefore within this limit, and including fluctuations, the cholesteric behaves as a nematic and locally the order parameter definitions are the same for each system. For this reason, the definitions of local birefringence ( A n =q- nl) and dielectric anisotropy (A&= 6, - E ~ remain ) the same. Parallel (11) and perpendicular (I) refer to the local director inside the material. Macroscopically we consider the director, now averaged on a long length scale, to vary smoothly throughout the material, as depicted in Fig. 1. The local order parameter is described as for a nematic, i.e., S = -(3cos2 1 8 - 1) 2
(9)
where 8 is the angle between the long axis of each molecule and the local director. Here we ignore local molecular asymmetry to define the direction of the long axis. In chiral nematics we make the same assumptions, as in nematics, that (1) the centers of mass have no long range order, (2) there is local order as defined in Eq. (9) and therefore the director n has a direction, and (3) that the states n and-n are indistinguishable. For the chiral nematic, the director is no longer arbitrary but has a preferred helical conformation (Fig. l , as defined by Eq. (1)). The helical axis z and @ are arbitrary unless the director is aligned preferentially at
a surface. We will consider how this is done experimentally in the next section. As a result of the n =-n condition, the structure is periodic along z with a spatial variation of p/2, as previously discussed. The helical wave vector k (=2n/p) has magnitude and sign. The magnitude determines the macroscopic physical properties we are interested in herein, whilst the sign defines the handedness of the helix. As pointed out in reference [30] (p. 15) for materials in which k changes sign, the macroscopic properties, such as the specific heats, remain steady across the transition from -k through zero to + k . At k=O the material behaves like a conventional nematic. Further there is no evidence from X-ray scattering of any significant differences between cholesteric and nematic phases save a slight broadening on the cylindrical distribution curve due to reduced parallelism caused by the helical twist [31]. It was Friedel [32] who first noted the similarity between the local molecular arrangements of the so-called cholesteric (or N*)and nematic phases. This is further support for the use of the more general term chiral nematic in preference to cholesteric. For very tight pitch materials (i.e., when p approaches to within 10-100 times the molecular dimensions), the structure is more akin to a layered smectic phase; locally, however, it is still nematic although the scale of the repeat unit of the helix will give X-ray scattering peaks similar to SmA materials, but for a wider layer spacing [33]. These structures are then of considerable interest for flexoelectric and dielectric devices [29]. By definition then a racemic or achiral material leads to a nematic N phase, whilst a nonracemic or chiral material leads to a chiral nematic N*phase. In the preceding discussion chirality was used only to differentiate between righthanded and left-handed structures, that is, structures in which their mirror images can-
2.2
not be superimposed. This is the definition introduced by Lord Kelvin [34]. There is, however, no absolute measure of chirality and there is no obvious way of absolutely predicting how much twist comes from the molecular chirality. Chirality is important herein in that if the individual liquid crystals are chiral (assuming a nonracemic mixture) then there will be a tendency to form a helicoidal structure of the director superimposed on the local nematic order in the nematic (and tilted smectic) phase. As discussed above, the induced helicoidal structure has a defined axis orthogonal to the local director and a defined pitch p . It is the existence of this helix and the variation of p under different conditions that leads to the use of chiral nematics in many different applications and devices (see Sec. 2.5). Before such devices can be understood, it is necessary to consider how the bulk macroscopic properties are determined by this helicoidal structure. In this section we will consider the static properties, that is, those properties as observed at equilibrium in the presence of alignment forces, applied electric or magnetic fields, and at different temperatures and pressures. We have used the heading static to indicate, under any given conditions, that we are not considering transient changes between a ‘ground’ and an ‘excited’ state, but the conditions in either end state. Time-dependent phenomena will be considered in Sec. 2.3 under the general heading of dynamic properties. The static properties important in the following section will relate to how the helicoidal pitch is a) measured and b) influences the optical properties and leads to different textures and defects. We will then examine in detail the theoretical approach to optical propagation, Bragg reflection, and transmission for normal and nonnormal incidence in chiral nematic materials. We will outline how the
Static Properties of Chiral Nematics
343
bulk elastic properties are modified by the helicoidal structure by using the continuum theory to deduce a free energy density expression both for the quiescent state and in the presence of external fields. This will then allow us to determine the helicoidal pitch behavior in the presence of external influences such as temperature, pressure, and electric or magnetic fields. Finally, we will describe how these external fields lead to different dielectric, diamagnetic, and flexoelectric phenomena in chiral nematics.
2.2.1 Optical Properties As described earlier, the spectacular optical properties of chiral nematics are determined by the helicoidal pitch, the birefringence (and refractive index), the direction and polarization of the incident light, and the arrangement of the helix axis. For normally incident light the direction of the helix axis gives rise to the three classical textures depicted in Fig. 2, and typical photomicrographs taken with crossed polarizers are shown in Fig. 6; these are: a) The planar or Grandjean texture, in which the helix axis is uniformly orthogonal to the confining glass plates. The surface alignment is often induced by rubbed polymer films. b) The focal conic texture, in which chiral nematic domains are formed with the helix axes arranged in different directions. These may be achieved without surface treatment on rapid cooling from the isotropic phase. c) The fingerprint texture, in which the helix axes are parallel to the glass plates. Surfactants are often used to produce this texture, which may be uniform or polycrystalline depending on the degree of alignment control at the surface. The
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2 Chiral Nematics: Physical Properties and Applications
Figure 6. Photomicrographs of (a) planar, (b) focal conic, and (c) fingerprint textures in chiral nematics, and the schlieren texture demonstrating brushes in an apolar nematic (d); observations through crossed polarizers.
2.2 Static Properties of Chiral Nematics
name fingerprint arises, in the case of long pitch materials (i.e., p A) from the stripes observed as the helix pitch rotates through optically equivalent states with a period of p/2. IN.B. In short pitch mate-. rials ( p a i l ) , the pattern is not resolved and often takes on a fairly uniform colored appearance depending on the cell thickness, A n macroscopic (i.e., ni"-n;I"), and the direction of the input polarization.]
-
All of these textures may be switched to produce electro-, magneto, or flexo-electric effects, which will be discussed at the end of this section. The key to the use of these various effects and indeed observation of the optical properties lies in control of the director orientation at the liquid crystal-substrate interface. For the techniques to be described, we will be in the strong anchoring regime where we can ignore the k , , and k,, terms in the full free energy density expansion (see Sec. 2.2.2.1). As a result of the local similarity between nematic and chiral nematic phases, most of the alignment techniques that work for nematics [3S] work for chiral nematics. We are principally interested in two types of alignment of molecules at the surface, i.e., planar and homeotropic, in which the preferred orientation of the molecules pinned to the surface is parallel or perpendicular to the surface. Planar alignment in chiral nematics can normally be achieved by three well-known techniques: (1) SiO evaporation, (2) polymer rubbing, or (3) microgrooved surfaces. In (1), silicon monoxide ( S O ) is evaporated onto a surface to give a layer, typically 20-100 nm thick, at an oblique angle 8. For 8=60" the molecules align parallel to the evaporation plane, whilst for 0=80" they are perpendicular [36, 371. If random planar alignment is required, the SiO is evaporated at normal incidence. SiO gives a surface of
34s
very high thermal stability. In (2), i.e., polymer rubbing techniques [35, 381, a polymer such as PVA (polyvinyl alcohol), which is water soluble, or polyimide is spin-coated onto the substrate and then rubbed with a spinning velvet cloth in a unique direction. In these cases the molecules are aligned in the rubbing direction and, if necessary, speed and pressure may be used to control a small 1-5" surface pretilt. The commercially available polyimides have good thermal and chemical stability, whilst PVA is convenient for rapid testing in the laboratory. If a barrier layer is required for electrooptic applications to prevent ionic flow from the electrode layers, it is possible to evaporate the SiO normally and then spin-coat on top the polymer prior to rubbing, in order to obtain good planar alignment. A new polymer alignment technique [39] using frictiondeposited polytetrafluoroethylene (PTFE) gives excellent planar alignment of nematic and chiral nematic materials with almost zero surface tilt [40]. In ( 3 ) , as will be discussed in the thermochromic devices section (Sec. 2.5.2) fine microgrooved surfaces may be used in embossed laminated sheets [41] to give excellent planar alignment. Homeotropic alignment is usually obtained by coating the substrate surfaces with surfactants such as lecithin or HTAB [42, 431. A practical laboratory method is to deposit egg lecithin in ethanol or chloroform on the surface. The solvent evaporates to leave the surfactant with its polar head group stuck to the surface and the hydrocarbon chains pointed, on average, into the cell perpendicular to the substrates. The liquid crystal-hydrocarbon chain interaction then gives the desired homeotropic alignment. Via the elastic forces, the surface alignment then propagates into the bulk volume. Silane derivatives [44] or chromium complexes [4S] that chemically bind to glass surfaces have equally been used for homeotropic alignment.
346
2 Chiral Nematics: Physical Properties and Applications
The different optical textures induced by the different surface alignment conditions lead us to three common methods of measuring the helical pitch:
1. Fingerprint texture: Using homeotropic alignment and a polarizing microscope we can measure the distance between adjacent dark lines (see Fig. 6) provided the sample is illuminated with monochromatic light. As discussed earlier, the line separation is thenp/2. Since this is a visual technique, it is only easy to observe pitch lengths greater than -1.5 pm. If a polarized laser beam is used and the fingerprint texture treated as a diffracting (grating) element then this technique may be extended down to the diffraction limit to measure pitch lengths -0.6 pm, depending on the wavelength used. 2. Planar texture: Using planar alignment and by measuring the reflection or transmission spectrum of a chiral nematic
film it is possible to measure the Lax (re(transmitted) using a flected) or kin monochromator either to control the input light wavelength [ 101or using a white input light to monitor the reflected or transmitted spectrum. In the latter case we [46] have found it particularly useful to couple a simple single pass or spinning prism monochromator to a reflection microscope to measure such spectra for a large variety of materials. This is shown schematically in Fig. 7. This technique allows the spectrum to be monitored on an oscillocope instantaneously and allows pitch measurements in the range 0.2 p m < p < 1.O pm. The pitch p is related to &, by p=&,-n (see Eq. 3), where Z= (rill + n,)/2. This technique necessitates an independent measurement of nll and nI. Since these are normally measured for order parameter measurements using an Abb6 refractometer, this is no great problem. Simple diffracting ele-
Figure 7. Schematic diagram of a microscope spectrometer for measuring transmitted or reflected spectra from chiral nematic textures.
2.2
ments coupled to CCD arrays now make the detection simple and fast so that dynamic phenomena may be monitored [47]. A related technique for spectral measurement using phase-sensitive detection has also been presented [48]. 3. Focal-conic texture: Based on the diffraction equation derived by Fergason [22] for such a polydomain texture (Eq. 5 ) , e.g., HeNe laser at A=632.8 nm, the helix pitch can readily be determined. Again Z has to be determined independently, but the technique may be used for dynamic electrooptic studies. This method is limited to materials of small An,but the range of p readily measured is 1 p m < p < 2 0 pm. Supplemental to these techniques, it is also possible to use a wedge-shaped cell to measure the helical pitch in a chiral nematic [49, 501. This is a further example of the use of planar boundary conditions. In a wedge cell, with the angle a=h/L previously determined, the planar alignment produces the classical Grandjean-Cano texture with disclinations separated by a distance 1 (see Fig. 8). These disclinations arise since as the cell thickness increases the number of ‘half pitches’ through the cell also inreases to minimize the free energy. As a result of the alignment conditions, it can only do this in a quantized way. The increase thus takes
Static Properties of Chiral Nematics
347
place in steps where disclination lines are created every time the number of half pitches is increased by one (see Fig. 9). The pitch p is then given by p = 21a =
~
21h L
where I is the distance between two disclination lines and a is the wedge angle determined by interference fringes in an empty cell. Using this technique, pitch measurements can be made readily in the range 0.8 p m
DISCLINATION LmE
h
Figure 8. Schematic diagram of the Cano-wedge technique for measuring the pitch, where p = 2 1x a=2 1hlL, in a chiral nematic (see text).
348
2 Chiral Nematics: Physical Properties and Applications
Figure 9. Typical Cano-wedge textures for a chiral nematic. The Grandjean-Can0 disclination lines occur at the blue-yellow interface. The slightly curved distortion shows how sensitive the technique is to undulations in the glass of the wedge cell used here.
local director inside the liquid crystal. Macroscopically the ordinary (no)and extraordinary (n,) indices are measured, averaged in a chiral nematic over several turns or partial turns of the helicoidal distribution of n. This is contrary to the simple case of 'planar' nematics where no=nl and n,=nll. The case of the chiral nematic has been analyzed [52] for a planar texture with obliquely incident light which is necessary if using an AbbC refractometer to measure n, and no [53]. This analysis, under the condition of critical angles for internal reflection at the glasslchiral nematic interface, gives
n,=nl
and
ni= '2( n i +n:)
where n, is the refractive index in the direction of the helix axis and no is normal to this helical or optic axis. With an AbbC refractometer (as manufactured by Bellingham and Stanley [54]) it is possible to measure straightforwardly refractive indices between 1.3594 and 1.8559 (+O.OOOl) well within the range of most chiral nematics. Using planar alignment and a polarizer adapted into the eyepiece of the refractometer, n, and no are readily determined [53] over a temperature range of -10°C up to
80°C (kO.1 "C) using a circulating water system. This range may be extended by using dibutyl phthalate as the circulating fluid up to the softening temperature of the optical cements used in the prism optics, and down to below 0°C. The refractometer may readily be adapted to work at different monochromatic wavelengths, using mercury lamps or tunable He-Ne lasers to determine refractive index dispersions. Thus nI1 and nl may be determined from no and n, as a function of temperature and wavelength, from which the pitch may be determined, the relation Aillil=AnlE verified, and the diffraction analysis from focal conic textures carried out. A method using selective and total reflections with rotating cylindrical prisms has also been presented [55], which allows A n andp to be measured. Using this technique, p may be readily measured down to 400 nm. The refractive index data for all and nI, calculated from no and n, (Eq. 1 l), may also be used to calculate the order parameter (S) in the chiral nematic phase using the Haller [56] technique with the Vuks' local field correction factor [57] from
2.2 Static Properties of Chiral Nematics
where f (a) is the molecular polarizability correction factor, rill and nL are the local refractive indices parallel and perpendicular to the director (as before), and E is a mean refractive index given in this notation as X(n ;+2n:). The temperature dependence of S used in the Haller curve fitting technique is given by S=(l-$)p where all temperatures are in Kelvin, T* is the critical temperature for a second order chiral nematic to isotropic phase transition (note T* is normally 1-2 K above the clearing temperature T J , and p is used as a fitting parameter. From the techniques outlined above, it is possible to determine the optical textures (using a polarizing microscope), the specular reflection maximum (&),and the bandwidth (AA), the helical pitch @), the refractive indices (ne,no, nl, rill), the order parameter (S), and the temperature dependence of S(T). An optical polarimeter may be used to measure the optical rotation or, given the high rotatory powers, i.e., lo3 degreedmm or 1 degree/pm, this can readily be done using a planar texture and a polarizing microscope with monochromatic light and sample cells -10-50 pm thick. Thus we are in a good experimental position to measure all of the relevant optical properties of chiral nematic liquid crystals as a function of temperature and for a variety of textures. As discussed in the Sec. 2.1, it is the helicoidal twist structure of the director n that dominates the optical properties and makes for their use in a growing number of optically related applications (see Sec. 2.5 of this Chapter). It is useful to summarize 19, 58, 591 these unique optical properties, again assuming planar alignment:
349
1. For light of wavelength A, incident on a planar chiral nematic texture of pitch p, the optical rotatory power is extremely high (i.e., lo3 degreedmm) outside the specular reflection band, i.e., a,K~3 2. If the incident wavelength A, is of the same order as the chiral pitch p , then the light is selectively reflected. 3. The selectively polarized light (for A, - p ) is circularly polarized with the same handedness as the chiral nematic helix. The other circular polarization is almost totally transmitted. 4. The spectral bandwidth (Ail) back-reflected has a narrow bandwidth defined by the materials birefringence ( A n ) . AA is typically of the order of 10 nm. 5. In the region of the selective reflection, the optical rotatory dispersion is anomalous and changes sign approximately at the peak wavelength of the reflection band. 6. The wavelength of the reflected maximum & varies with the angle of incidence 8 approximately as d cos 8, if the length scale d ( = p 2 ) is comparable with the helix pitch p. This corresponds to a Bragg-like reflection.
a,.
These optical properties of chiral nematic materials have all been observed experimentally. There have been quite extensive theoretical studies carried out by Mauguin [60], Oseen [61], and de Vries 1261 to explain how these properties arise from the helicoidal structure. Kats [62] and Nityananda [63] have derived exact wave equations to explain the propagation of light along the optic axis and Friedel [32] has reviewed the main textures observed with chiral nematics. We will outline the important elements of these studies in the next sections (Secs. 2.2.1.1 -2.2.1.3). In Sec. 2.2.1.4 we will consider how the helicoidal pitch, and
350
2
Chiral Nematics: Physical Properties and Applications
therefore the optical properties, depend on external factors such as temperature, pressure, and chemical composition. The influence of an external electrical and magnetic field on the pitch will be discussed in Sec. 2.4, since this influence will depend greatly on the dielectric and diamagnetic anisotropies as well as the flexoelectric behavior. These discussions will then lead on to consideration of the device implications (Sec. 2.5).
2.2.1.1 Textures and Defects The basic textures observed in chiral nematics were introduced in 2.2.1 ;namely (a) planar or Grandjean, (b) focal conic, and (c) fingerprint. Typical textures are shown in Fig. 6 and the seminal review by Friedel [32] gives a lucid account of how these textures arise. Associated with these textures are a number of singular lines and defects, as observed using a polarizing microscope. It is useful here to recall the terminology used when observing such lines and defects in a thin (5-50 pm) layer. In classical nematics, in a schlieren texture, black or dark brushes are observed originating from point defects (see, for example, Fig. 1.16b in [59] due to Sackmann and Demus [64]). The points are due to line singularities perpendicular to the layer. In a modified form of Frank's [65] original notation, these defects are now referred to as disclinations, defined as a discontinuity in orientation or rotation. The dark brushes (Fig. 6d) are then due to regions where the optical axis, due to the director n, is either parallel or perpendicular to the polarization of the incident light, i.e., in these regions the polarization only interacts with n, or n,,. In nematics we observe either two or four brushes; in chiral nematics, because of the helical structure, the structure of the lines is often far more complex. For the moment it is useful to con-
tinue with the brief discussion of nonchiral nematics. If we rotate the crossed polarizers, the end of line disclinations or points remain unaltered; however, the brushes rotate. If the brush rotation follows the polarizer rotation direction, we have positive disclinations. If, however, the brush rotation is in the opposite direction, we have negative disclinations. The strength of a disclination is defined as s = !4 (x the number of brushes), and only disclinations of strengths s =f % and 21 are generally observed in nematics. These are depicted in Fig. 10 after Frank [65]. In this notation, if we assume an elastically isotropic material (i.e., k , =k,, =k,, =k and k=O, i.e., achiral) and a planar nematic structure in the x y plane with the line disclination along z, then in the plan view we can define the director orientation @ relative to x along any polar line radiating at an angle a to x from the point defect as
,
@=sa+c
(14)
where a=tan-' ( y l x ) and c is a constant for nx=cos @, ny=sin @, and n,=O. Equation (14) describes the director configuration around the point defect or disclination line L along z , and the director orientation changes by 27cs on rotation around this line. It is also interesting to note that neighboring disclinations joined by such brushes are of opposite sign, and that the sum of the strengths of all disclinations in the sample layer tends to zero. Further, if we rotate the polarizers, as described earlier, the two brush patterns will therefore rotate with twice the rate of the four brush patterns. These in turn have approximately the same rate as the rotation rate of the polarizers. In the so-called Volterra process [ 6 5 ] ,the topological defects of these disclinations can be visualized as follows: If the nematic material is cut by a plane parallel to the di-
2.2
Static Properties of Chiral Nematics
s=-l
s=-j
(@ s=
I , c=o
35 I
s= I , c= Rl4
rector n, then the limit of the cut is at the disclination line L. One face of the imaginary cut is then rotated with respect to the other about an axis perpendicular to the director by an angle 2 n s. Material is then removed from the overlapping regions or added to fill in voids and allowed to relax. If the axis of rotation is parallel to L, as is true here, then the disclinations are called wedge disclinations [66]. The textures for achiral nematics have been treated in great detail by Nehring and Saupe [68], following the pioneering theoretical work of Oseen [61] and Frank [65], and more recently comprehensive reviews have been presented [69, 701. We are now in a position to consider the more complex case of chiral nematics.
a) Planar or Grandjean textures: As discussed in Sec. 2.2.1, in a planar texture the director at the interfaces is constrained to be parallel with the alignment layers and an orthogonal helix axis. A typical planar texture is shown in Fig. 6a. In this figure the relatively braod lines between the apparent
s=
I , c= X I 2
Figure 10. Lines of equivalent director orientation in the neighborhood of s = + % and + I disclinations, where c is a constant (see Eq. 14).
platelets are known as oily streaks formed by focal conic bands, which correspond to regions of defects and poor planar alignment. These disappear if we use a Canowedge cell of the type depicted in Fig. 8 with the observed texture shown in Fig. 9. Here the thin disclination lines of strength s = !4 are clearly visible. The gradual variation in color from yellow to blue is due to distortion of the helix as it accommodates the wedge angle between disclinations. As discussed earlier, these textures allow us to determine the pitch via Eq. (10). To return to the parallel plate situation, if we make a contact preparation between a chiral and a nonchiral mesogen we form quite readily a concentration in the gradient along one axis, say x. The pitch p o of the chiral compound is then ‘diluted’ as a function of x towards the achiral compound. The real pitch is again quantized but tries very hard to stay close to the varying function p , ( x ) . This leads to a succession of similar domains (see Fig. I I a), separated by sharp discontinuities [71]. We will return to concentration gradients below.
352
2 Chiral Nematics: Physical Properties and Applications
Figure 11. Photomicrographs of concentration gradients with (a) planar and (b) fingerprint textures in chiral nematics. In both plates the high concentration of chiral compound is at the top left with the achiral compound at the bottom right.
b) Focal-conic texture: If a chiral nematic is cooled from the isotropic phase reasonably rapidly between the parallel glass plates, the bulk of the system does not have time to align in the planar texture and the helix axis is curved away from its direction at the surface interface to give the so-called focal-conic texture, where the director profile of any given repeat unit (i.e., any uniaxial direction at p / 2 ) orthogonally follows the same curvature. Since such directors are separated by p / 2 , this gives (macroscopically) a lamellar appearance which resembles a smectic A texture (Fig. 6 b). Microscopically the structure is still nematic (as discussed earlier) and Bouligand [72] has
discussed these similarities in detail. With good aligning agents, slow cooling, and, if necessary, a slight shear field, it is possible to align the texture into planar (with uniformly rubbed polymers) or fingerprint (with a homeotropic surface agent such as lecithin). c) Fingerprint texture: As discussed previously with respect to Fig. 6c, it is usually possible to obtain a fingerprint texture, in which the helix axis lies parallel to the substrates, using homeotropic surface alignment agents. In order to remove the degeneracy, a slight shear field is applied, in which case the helix axis aligns orthogonal to the
2.2
shear direction. This method is applicable tolong pitch systems (i.e.,p>afew microm-. eters). For shorter pitch systems, in which( case the fingerprint may be too fine to observe directly (other than by diffraction), an electric field [below the critical helix unwinding (see Sec. 2.2.3)] may be used in conjunction with the shearing process to unidirectionally align the helix for materials of positive dielectric anisotropy. This is particularly useful for chiral nematics used in flexoelectric switching [29]. Pate1 and Meyer [28] showed that rubbed polyimide layers could be similarly used (N. B. without shearing) and that, on cooling from the isotropic phase in the presence of an AC field, the helix could again be uniformly aligned in the plane of the substrates. Although, as discussed in Sec. 2.2.1, the fingerprint texture may be used to measure the helical pitch, care has to be taken lest the helix axis is inclined to the substrate plane or local distortions occur at the substratel liquid crystal interface [73]. An interesting use of the fingerprint texture is to examine pitch changes with concentration in a contact preparation between a chiral and an achiral nematic. As the pitch varies from infinity in the nematic to the value of p in the neat chiral compound, the fingerprints become closer together. This effect is shown in Fig. 11b for a very short pitch cholesta-
Static Properties of Chiral Nematics
353
nol-based organo-siloxane [74] in contact with pentylcyanobiphenyl (5CB). We will now consider in more detail some of the alignment or director field patterns around different defect structures in chiral nematics. Using the simple one elastic constant approximation (i.e., k as for the nematic case above) and the definition of the chiral director (i.e., n =(cos 6, sin 6, 0), 6 = k z , and @=O; see Eq. (1)) in the free energy density expression, (Eq. 2) gives
and V26=0. For X-screw disclinations (see the nematic wedge disclinations discussed earlier) there is a singular line along the z axis (i.e., parallel to the helix axis) and the director pattern is now given by
where m is integral as before. The simplified director patterns for s=X and 1 are shown in Fig. 12. If the elastic anisotropy is now included in the free energy density (see, for example, [59], p. 139 et seq.), then one
Optic Axis
/@//a/
/ s/I/
41t
/
/ e l f [a / /’ S=I/2
s=1
Figure 12. Representation of director patterns for s= X and 1 X-disclinations in a chiral nematic. The unfilled or filled dumbbells or pins denote the spiraling director.
354
2 Chiral Nematics: Physical Properties and Applications
particular value of c is favored for a disclination pair. This is important for chiral nematics where each layer may be regarded as nematic-like, but rotated about the twist axis. Since each layer is allowed only one value of c (0 or d 2 ) (see Fig. lo), the disclination pairs are expected, theoretically, to adopt a helicoidal configuration and this has been observed experimentally for s=% [75] and s= 1 [76] pair disclinations. For edge disclinations, the singular line disclination is perpendicular to the twist axis. On rotation around this line, an integral number of half pitches ( p / 2 ) are gained or lost and the pattern for s=% is as shown schematically in Fig. 13. The director pattern around such a disclination was first proposed by de Gennes [77], again in the one elastic constant approximation, with the following twist disclination type of solution
x
n = (cos 8,sin 8,o)
1
and m is again an integer. This approach has been extended to take into account elastic anisotropy by Caroli and Dubois-Violette 1781.
----c----OQ~cO----OCg.----OQCg
.............................. -*o--..o-.c+.o0
cs
-0-
4--cg
~rg-J-o-o-o.-o-o
cc
..........................
+-0.----0cOcO--o.0.c-c-c-c--mo-
...........................
h
L-c--c+-c-c-+
-----c------
@ - - - - a ~ ~ ~ o - - - - o o Figure 13. The director pattern for s = % X-edge disclinations in a chiral nematic. The filled in dots signify that the director is orthogonal to the plane of the figure, the dumbbells that it is in the plane, and the pins that it is tilted in a spiraling structure.
As for achiral disclinations, the Volterra process may be used to create screw or edge disclinations by cutting parallel or perpendicular, respectively, to the chiral nematic twist axis. As discussed when considering the focal conic texture, the chiral nematic may be considered as having a layered structure of period p / 2 for a given direction of n. This layered lattice can then have disclinations similar to SmA materials. In the Volterra process, if the cut is made such that the disclination line (L) is along the local molecular axis then the longitudinal (A) disclinations created are designated A+ (indicating material has to be removed) or d- (for material added) to arrive at the final configuration. If, however, L is perpendicular to the local molecular axis then these transverse (7) disclinations are similarly denoted z+ and z-. These configurations are shown schematically in Fig. 14, and it should be noted [59] that the coreless d disclinations have lower energies than the cored z structures in a chiral nematic. Also the and z(') disclinations occur in pairs to give five possible forms of dislocations and pincements or pinches (i.e., a transformation from a wall to a line) (see Fig. 15). These disclinations are most easily observed in the fingerprint texture (see Fig. 6 c), where many of these defects may be readily identified by the observant reader. As a result of the layered nature of the chiral nematic structure, like the smectic A, it can also exhibit focal-conic textures [79] and both phases exhibit screw and edge dislocations. A dislocation corresponds to a displacement of the layered structure in a - plane - o orthogonal to the layer and may be formed by the pairing of two disclinations of opposite sign. A screw dislocation has a singular line along the screw axis and is equivalent to ax-screw disclination in a chiral nematic. An edge dislocation corre-
2.2
2j.i .. 8 ::1
0-20-40-0~
................... =:'B ..................... b =..\
G-Qu-oo--o D-0C-c
L p ooo-*
q... %:;%
c+-oc-0
d........... -0 +---7F
..... o-. -6"
'
. . . .- . .0. . % .
t--S .......... -0
Y ...........
sponds to a line defect in the y direction for a planar (x, y ) chiral nematic with its helix axis in the z direction. This line defect then forces the layer (or planes of equivalent n ) to tilt with respect to the I or unperturbed helix axis. Schematic diagrams of such singular defects are shown in Fig. 16 a,b. These edge dislocations under favorable energetic conditions can combine (Fig. 16c,d) to form a 'grain boundary' with zig-zag and quadrilateral defects [79] in chiral nematics. These are clearly evident in Fig. 17 from
Static Properties of Chiral Nematics
355
Figure 14. The director configurations around defects leading to (a) X', (b) A+, (c) z-,and (d) r+ disclinations in a chiral nematic. The dumbbells, pins, and dots have the same significance as in Fig. 13 and the black star circles L represent the disclination lines.
Figure 15. Schematic representations of the pairing of iland z disclinations of opposite signs in a chiral nematic. The schematic diagrams show edge disclinations comprised of (a) il-and A+, (b) z-and T+, (c) r- and A+, (d) X and r+ and (e) pinches or pincements of z+ and 5-. The pins, dots, and layer lines represent the spiraling director field.
[80], where the dark banding is due to the layers of equivalent n in the chiral structure. The texture also shows in-plane linear and hyperbolic defects generated by coalescing edge dislocations in the z direction. These are similar to the focal conics formed in smectic A materials, but in the chiral nematics the length scale of the layers of equivalent n are separated by pI2, which is the order of micrometers rather than nanometers, i.e., it is a macroscopic rather than a microscopic feature.
356
2 Chiral Nematics: Physical Properties and Applications
I
(c)
(4
Figure 17. Optical micrograph of a chiral nematic texture exhibiting zig-zag and quadrilateral defects.
2.2.1.2 Optical Propagation (Wave Equation Approach) The large and anomalous optical rotations observed in the chiral nematic phase are not due to intrinsic spectroscopic properties, i.e., absorption or emission, of the constituent molecules, since they do not persist in the true isotropic phase (i.e., away from pre-
Figure 16. Simplified schematic diagram of (a) and (b) singular defects which combine to form grain boundaries with (c) zig-zag and (d) quadrilateral defects.
transitional effects [8 11). They must therefore be due to the transmission and reflection properties of light propagating in the helicoidal or twisted optically anisotropic liquid crystalline matrix. Based on the spiraling structure depicted in Fig. 1, this propagation has been examined theoretically in the seminal contributions of Mauguin [60], Oseen [61], and de Vries [26]. More recently Kats [62] and Nityananda [63] presented a highly accessible theoretical treatment of this work, and this will be considered below. This approach, based on the spiraling ellipsoid model for the dielectric tensor, gives ready access to the two experimentally interesting conditions of a) waveguiding in the Mauguin limit where p > >iland b) selective optical reflection when p=A. Solution of Maxwell’s equations in this formalism leads, not only to the conditions for strong reflection of circularly polarized light and anomalous optical rotatory dispersion, which are of interest in this chapter, but also to the treatment of absorbing chiral
2.2
nematic systems, e.g., dye guest-host [82]. In the present treatment we assume (1) am ideal helix (i.e., the director of n rotates regularly and sinusoidally, (2) a semi-infinite planar structure bounded on its upper surface by an isotropic dielectric medium of the same mean refractive index as that of the chiral nematic [i.e., E=X(nll+n,)l, (3) that the birefringence is small (An=nll-n,<<E), and (4) that the wave vector of the incident light has the same direction as that of the helix axis (i.e., z ) . Finally, we will outline the main theoretical predictions for light incident at oblique angles and normal to the optic (helix) axis. These three directions of the incident light are of interest experimentally for the behav-. ior of, for example, (1) planar films leading to optical transmissive and reflective filters or mirrors, (2) polydomain samples as used in microencapsulated thermometry devices, and ( 3 ) diffractive elements and flexoelectric displays. The incident electromagnetic lightwave represented by
where o is the angular frequency and c the velocity, interacts with the chiral nematic material via its dielectric permittivity tensor. Here, clearly, we are interested in optical frequencies, where ~ ~ ~ , ,211,1, = n and we represent this tensor by a 'spiraling ellipsoid' with its major axis parallel to the local director n and of principal value ql, with its minor axis perpendicular to the director and of value E ~ We . ignore any biaxiality as negligible for these systems (since E~-E lop4, ~if, E,; I is in the z direction) and we assume E,, and E, are in the x, y plane. Using the form of the director given in Eq. (l), the dielectric indicatrix spirals around the z axis through the medium. For
357
Static Properties of Chiral Nematics
convenience we take the major axis of the ellipsoid as parallel to x at the origin, which then defines the dielectric tensor E for any value of z as coskx -sinkz][~ll sinkz coskz 0 coskz sinkz -sink2 coskz
=[
1
E~ 0
]
]
E+(8~)cos2kz (6~)sin2kz (&)sin2kz 2 - (6e)cos2kz (19)
where E = X (E~~+ E ~ ) , (6 E ) = !4 (E~~- E ~ =) X(n;-n:)=EAn, assuming &=n2 at optical frequencies. Maxwell's equations then reduce to
If we introduce the variables E+= 2-'/* ( E + i E, ) and E-= 2-1/2(Ex-i E,), then E + is right circular and E- is left circular for a wave propagating along +z, and vice versa for propagation along -z (i.e., if E-=O then E , = i E, and Ex lags behind E ) by d 2 ) . The inverse of this transformation may then be represented in matrix form by
Equations (21) and (19) are then substituted into the wave equation for propagation (Eq. 20) to give
it["+] az3 E-
which has a solution of the form
358
2
Chiral Nematics: Physical Properties and Applications
and this is a superposition of two waves of opposite circular polarizations with wave vectors differing by 2 k. If the (k’+ k) component of Eq. (23) is substituted into Eq. (22),then this component experiences a wave vector shift of 2 k and it is converted into a (k’-k) wave and vice versa for the (k’- k ) component. Thus, due to the dependence of &onz, a right circular wave generates a left circular wave (and vice versa) with a wave vector shifted by -2 k (and +2 k), so that the two components form a closed set. Equation (23) therefore represents a true normal wave which, with a proper choice of A+ and A-, can satisfy the wave equation (Eq. 22). Substituting u (see Eq. 23) into Eq. (22) then gives
waves corresponding to the roots k, and k2, where each is dominated by one of the opposite circularly polarized components. Further, the mixing of these two components with wave vectors differing by 2 k is a consequence of the Bragg-like reflection. This equation may then be rewritten as
[
]
bei(K2+2k)z
u2 = eiK,z
1
(k’ + k)2- Zw2/c2 - ( & ) 0 2 / c 2 -(d€)02/C2 ( k ’ - k)2- Zw2/c2
I:;[.
2
47cik2+(a&) K
=0
4 112
]
}
If we rewrite the wave vectors as K (=w/c=2 nia) and K,, (= .P2 o / c =2 n: zia) for free space and the chiral nematic of average dielectric constant E, respectively, then the only nontrivial solutions occur when the determinant of the matrix is zero, i.e., the quadratic in k’2, given by
[(k’ + k)2 - ~ i ] [ ( k ’k)2 - - K;] (25)
-(a&)2K4 = 0
with roots k,, k, given by
4 ~ k2 ;
-(a&)2 K 4112 ] } (26)
From these two solutions we may obtain the ratios of Af/A- from Eq. (24) such that
Substitution of Eqs. (26) and (27) into Eq. (23) (i.e., the solution for u ) gives two
The difference between the wave vectors K~ and K~ (the dominant components of u1 and u2, respectively) gives rise to the optical activity of the chiral medium, i.e.,
d
=
1 ( K , - K2) radiandunit length. Further, 2
K, and K~ differ from K;, by terms of the order of (6 E ) ~and , hence a and b are small and of the order of ( 6 ~ )Equations . (28) and ( 2 9 ) mathematically describe the key optical properties of a chiral nematic planar texture for normally incident light [ 6 2 ] . We are now in a position to examine the behavior of the optical rotation as a function of K for different limiting conditions
2.2 Static Properties of Chiral Nematics
around, close to, and far away from k. A series expansion for K , and K~ within the limit of K~ - ~ ~ < < kand ignoring higher order terms [0(I?)] yields
d
=
2
which is the spectral width of the total reflection as given in Eq. (4) and [26]. In addition, Eqs. (31) and ( 3 2 ) give the following very simple but very important relationship for optical devices, namely,
(K1- K 2 )
q-(q2-(W - ______
)
~~
4k
AAAn -
; b n
2 K4 ‘I2
(30)
where q= K,-k2. 2 The optical rotation is complex if
(6 E ) +? ~ > q2, in which case the real part corresponds to the rotatory power and the imaginary part to circular dichroism. As stressed previously, there is no spectral feature contributing to this imaginary or loss term; therefore, the imaginary part of ydd has to be associated with the reflection of one of the components in a range bound by ( 6 ~2) 2 q to 2(6&) and centered at q=O,
359
(33)
For chiral nematics, this relationship has been satisfactorily verified [46] over a range of A n from 0.04 to 0.15 and bandwidths of 10-50 nm have been readily achieved. This is important for spectral filters and optical mirrors. We can now consider the optical rotation in a wave vector range away from the selective reflection, i.e., q>>(8&) K4, by making a series expansion of Eq. (30) and ignoring terms of 0 ( K’) or higher. This gives
-
(34) and from (6&)’=Ann, K=27G/jl, q= K k - k 2 , and k=23.c/p, we obtain
wavelength in vacuo (air). Therefore
p = E&
(31)
which is identical to Eq. (3). If we consider the reflection band and assume Km =k , then the bounds for reflections are given by
2 and, since 6 q = 6 ( K m ) = 2 K,6K,-2k6Km, where
then
whence AA=pAn
(32)
(35) which is the de Vries equation [26] derived using the formalism of Kats and Nityananda [62, 631 and is equivalent to Eq. (8). There are numerous studies in the literature that have confirmed the form of the function Wand that it changes sign at A=& [59], as shown schematically in Fig. 4. In summary for a planar texture and normal incidence we have outlined the derivation of the solution of Maxwell’s wave equation and this has led to explicit expressions forp(=iA,), AA(=pAn), and optical rotatory dispersion. We are now in a position to study special cases of normal and oblique incidence. The previous derivation assumes a semiinfinite layer thickness. Real chiral nemat-
360
2
Chiral Nematics: Physical Properties and Applications
ic films have a finite thickness and this modifies the reflection properties of the film, as shown in Fig. 18. The semi-infinite case gives a reflection spectrum with a flat top and sharp edges, whilst the finite slab gives a principal maximum at & with subsidiary side bands for A > & + p A n . For a perfect, but finite, chiral nematic layer with normally incident light the normalized intensity reflection coefficient '32 is given by
%=
R2 u2 + b2 coth2(mb)
(36)
where R = n: AnlE, u = -2 n: (1 -A/&, ~ = + ( R ' - u ' ) ~ ' ~and , m is a constant equivalent to the number of layers in the rotating slab model. If m j m , then %= 1 within the range AA=R &ln:=p An as before. The term R is determined by the local birefringence (rill -n,), u is essentially the wavelength-de-
pendent term, and [b2coth (mb)]limits the amplitude, oscillations, and decay rate of the side bands. The constants can then be determined by computer curve fitting. In the experimental world, it is rare to detect the side bands due to inhomogeneities in the substrates and alignment layers (on the length scale of A)and the possibility of polydomain planar samples. If side bands are observed at normal incidence, then this indicates an extremely well aligned sample! Berreman and Scheffer [83, 841 and Dreher et al. [85] have experimentally verified the validity of Eq. (36) in such samples. Surface undulations, surface pretilt, and polydomains of chiral nematic material lead to the more normally experienced, bell-shaped curves of Fig. 19. The theory of light propagation in a chiral nematic for directions other than that of the helix axis is complex. Whilst for normally incident light the transmitted and reflected waves are, to a good approximation, circularly polarized, for oblique incidence these waves become elliptically polarized
1
"
450
500 Wavelength (nm)
550
Figure 18. Reflection coefficient Yl as a function of wavelength for light normally incident on a chiral nematic planar film for (a) a semi-infinite and (b) a finite slab. The dots are experimental and the curves computed (see Eq. 36) (redrawn with data from [82]).
400
500 600 Wavelength (nm)
Figure 19. Selectively reflected light as a function of wavelength for the chiral nematic cholesteryl oleyl carbonate at different temperatures (a) 20.68 "C, (b) 20.55"C, (c) 20.44"C, and (d) 20.5"C (redrawn from [ 9 ] ) .
2.2
and refracted. The first attempts at numerically solving this problem were by Taupiri [25] and Berreman and Scheffer [83] who used a 4x4 matrix multiplication method and then compared, with excellent agreement, their computational method with the experimental results. The analysis again used the spiraling ellipsoid model for ~ ( r ) . i.e., E,
=E + ( ~ E ) c o s ( ~ ~ z )
E ~ = , E-(~E)cos(~~z)
= E , =(6~)sin(2kz) E,, = & - ( 6 E )
where all other components are zero and the ellipsoid is prolate. (This gave the best agreement between theory and experiment [83].) If the helix axis is in the z direction, it can be assumed that the incident and reflected wave vectors are only in the xz plane and the dependence on they coordinate may be ignored [83]. Writing the wave as E,=E: exp [i(ot-k’x)], etc., then Maxwell’s equations may be written in matrix form as
Static Properties of Chiral Nematics
plication is repeated many times, in small steps of 6 z , to give the matrix for a final slab of chiral nematic material, which incorporates the substrate boundary conditions to give the complex transmitted and reflected waves. Berreman and Scheffer [83, 841 included a number of simplifying cyclic and symmetry properties of 9( z ) to reduce the number matrix multiplications necessary. The model agreed very well with the spectral features of the experimental data and confirmed that the assumption of the dielectric ellipsoid as prolate was very reasonable. Indeed, this work established that locally the chiral nematic is uniaxial and not biaxial. In a later study, Takezoe et al. [48] showed that, for oblique incidence, the sideband behavior was not symmetric for left- and righthanded circularly polarized light and they also established the conditions under which there was a band of total reflection for any polarization of incident light. It is clear that such studies are of considerable importance for understanding the propagation of light in a locally rotating reference frame, i.e., the
E,Z
-i H ,
36 1
0
1
or
To a first order approximation
where E is the unit 4x4 matrix and 9 is a 4x4 propagation matrix. The matrix multi-
chiral nematic helix, with significant implications for wideband optical devices reliant on diffuse or oblique illumination. The extreme case of oblique incidence occurs for light propagating orthogonal to the helix axis. Light polarized along this axis alway experiences a refractive index of ni independent of the helix pitch p . Interesting optics occur for light polarized at
362
2 Chiral Nematics: Physical Properties and Applications
right angles to the helix axis (z) since, following n the local refractive index varies sinusoidally between the limits of rill and nL. For long pitch systems, i.e., p> A , the material behaves macroscopically as a variable birefringence film with A n (z) varying as a function of displacement of the orthogonal light beam relative to z, the helix axis. For p e a , the light wave interacts with many turns of the helix and the polarization experiences an average refractive index in, say, the x, y plane. In this case, if we define nfA as the macroscopic refractive index parallel to the helix axis (z) and n;OA as orthogonal, then the macroscopic birefringence is nfA-nroA. For this situation, nfA =nI in the local director n notation. The macroscopic orthogonal component is then given by (37) averaged over one pitch E(Z)= n2 (z>
where rill is parallel to the microscopic director n and e ( ~is) the in-plane (x,y ) angle between nI1(z=O) or y and n (z). Thus a microscopic positive birefringence material (A n =nI1-nl> 0) will become macroscopically negative, since nfA=nl
-
observed for
k = ki - k ,
(39)
ki and kd are for the incident and diffracted waves, respectively, and k is the grating wave vector; the angles of the diffraction allow us to determine the helix pitch. This technique was used in depth to study how the helical pitch varied as a function of the composition for a number of chiral nematic materials [86] and this has become a standard technique for pitch measurement if p > il. In the next section we will discuss the practical Bragg diffraction properties of chiral nematic films in more detail.
2.2.1.3 Optical Propagation (‘Bragg’ Reflection Approach) In the previous section we considered the propagation of light in a chiral nematic material by solving Maxwell’s equations under the limiting conditions of (a) a planar sample, (b) a perfect helicoidal structure with its axis orthogonal to the liquid crystal layer, and (c) for A e p - d a n d A-p. For A-p we showed that circularly polarized light is reflected in a wavelength range defined by & + p A n / 2 . This formalism is the only exact way of describing the reflective, refractive, and transmissive properties of light interacting with a chiral nematic. In the present section we will use a ‘Bragg’ diffraction approach to describe these properties in the practical situation where the chiral nematic material is polydomain in nature, and where these domains may be inclined to the direction of the incident light. The term Bragg reflection is used throughout the literature, but it must be stressed that this is only a convenience. True Bragg diffraction occurs when the radiation incident on a crystal lattice has the same order of wavelength as the repeat unit of the lattice, and where the density waves of the scatter-
Static Properties of Chiral Nematics
2.2
ing medium are discrete. In chiral nematics,, the material is in a continuum and it is the ‘local’ director that gives a layer-like structure as it precesses around the helix axis (2). Fluctuations ensure that the density wave is constant with respect to z along the axis and on the length scale of visible light. In the Bragg reflection approach, as in the figures that follow, the layers used to define the scattering or reflection geometries refer to planes of equivalent optical properties separated by d , where the local directors are orientationally aligned in the same direction with n=-n. There is a continuum of identical material, orientationally rotated ’in plane’, with respect to and in between these layers, separated byp/2 (see Eq. 1) and Anp defines the bandwidth of specularly reflected light at a wavelength A(=&/$ in the continuum. The simplest case of Bragg diffraction is shown in Fig. 20 a for an ideal planar chiral nematic. If k , is the scattering vector, arising from the structure in, and local fluctuation of, ~ ( r )the , dielectric tensor, then
k , = k1- k ,
363
and scattered light, respectively. A more exact treatment is given in Chap. 3 of [30]. If 19~=$~=0, then for ki=-k,=k, the only allowed nontrivial solution, we have
k,=2ik or
2d=A
(41)
which is the simple ‘Bragg’ condition. As discussed in the previous section, if k>O (i.e., a right-handed helix), then right circularly polarized light is back scattered or reflected whilst the left-handed circularly polarized light is transmitted. Secondly, there is only one order of back-reflected light. For Oi > $i= &, Eq. (40) gives solutions corresponding to
2d cos $i,s = rn A or piicos$=rn&
(42)
where rn is an integer and A=&/Z. In this case [84] higher orders are allowed and the reflected light is elliptically polarized. As discussed, when solving the wave equation, the propagation of light at oblique angles is complex, since the light polarization couples neither with nIl nor nI but with values
(40)
where ki and k , are the wave vectors, which are assumed to be coplanar with the incident
I
(a)
(b)
Figure 20. Geometry for selective reflection for plainar chiral nematic films for director layers (a) perfectly aligned for internal scattering and (b) inclined at an angle a to the surface interface. All rays are assumed to be in the plane of the figures.
364
2
Chiral Nematics: Physical Properties and Applications
of n given by an angled slice across the refractive index ellipsoid. For the following discussion we will ignore these complex polarization properties of the reflected light and consider only the wavelength behavior. Unless we are considering some of the specialized reflecting films to be discussed in Sec. 2.5 of this Chapter, from a practical point of view we are only interested in intensities and wavelength. One interesting consequence of Eq. (42) is that if the monodomain is illuminated with white light and reflects back normally, say, red wavelengths, then observation at angles of 8 (or Cp internal) leads to a blue shift and this is observed in practice. Indeed, this is used in security devices, since it is an effect that is impossible to photocopy. The angular dependence of the selective reflection is one of the key features of chiral nematic thin films. In the practical world we rarely have perfect semi-infinite planar samples. Surface imperfections, preparative techniques, etc., normally lead to polydomain samples in which the planar texture is locally inclined and Cpi#Cps. This is depicted in Fig. 20b. ' O oriented . There will be many polydomains with their helix axis at different angles (a) to the substrate or liquid crystal/air interface, and each domain will selectively reflect light at some specular angle [22]. In the original model, not so far from reality in microencapsulated or polymer-dispersed chiral nematic films, Fergason assumed fictitious chiral nematic domains embedded in a medium of mean refractive index <<= W(nll+ nL). Assuming that the birefringence is small (i.e., An<<<), Eq. 42) for the peak wavelength reflection, &, at the domain is given by p Z cosp=m;t,
(43)
and from the geometrical optics and refraction at the interfaces we have
2P = Cpi + Cps sinei = ii sin& sine, = Z sin&
(44)
which in terms of the external angles and parameters gives
[
. cos 1 sin . -1 sinei
+ sin-1 (T)] sine, (45)
This relation is identical to Eq. ( 5 ) and, as discussed in Sec. 2.2.1 allows us to determinep in polydomain samples. For large An we have to take into account form birefringence, which leads to multiple scattering and complex phase properties. For low An and thin samples, where such scattering may be ignored, the technique gives reliable pitch data [22]. If &=pl(Zm), for normal incidence (m = 1) then this equation clearly demonstrates the blue shift, since c0s-l of the argument of Eq. (45) is always less than unity for 6, or Os#O (see Fig. 21).
'
Wavelength (nm)
Figure 21. Reflection spectra as a function of viewing angle (6- 6,)for a chiral nematic reflecting green light at normal incidence. The data were taken [89] for ei= 6,using an isoenergetic white light source with a black, nonreflecting back substrate.
2.2 Static Properties of Chiral Nernatics
The angular or selective diffraction of light by chiral nematics allows for an interesting comparison between chiral nematic and smectic A focal conic textures. Both are normally observed in white light using crossed polarizers. Macroscopically, the texture from the director profile in a thin film of each looks similar. Microscopically, the layer-like structure forming Dupin cyclides, as discussed in Sec. 2.2.1.1, is very different, and this provides a method of dis-. tinguishing between the two phases if the pitch of the chiral nematic is of the same order as the wavelength of light. If the sample exhibiting the focal-conic texture is mounted on a partially reflecting substrate, then polydomains inclined at a high angle a (see Fig. 20 b) will selectively reflect light onto this substrate and the light will be back-reflected back towards the observer, who without polarizers would observe specular colors. A number of geometries that display this effect in chiral nematics have been discussed [89] and lead to the conclusion (see p. 447 of [ 3 3 ] )that in such textures the helix axis is predominantly, or on average, in the plane of the sample, as would be the case if the helix axis is parallel to the local normal of the Dupin cyclides. This provides a further useful example of the ‘Bragg’ reflection model in chiral nematic liquid crystals and allows us to differentiate between the two types of focal-conic texture. The achiral smectic A ‘molecular’ layers may give rise to incoherent scattering in the focalconic texture, but they should not give selective colored reflection or transmission unless contained between crossed polarizers.
2.2.1.4 Pitch Behavior as a Function of Temperature, Pressure, and Composition The optical properties of a chiral nematic depend initially on the helix pitch p . For
365
some applications, such as optical fillers, the selective reflection or transmission properties should either be independent of temperature or frozen in a glass phase, as found in chiral nematic polymers [88]. For a chiral nematic material far from a phase transition (i.e., within l0OC) either to the isotropic or a lower temperature smectic phase, the pitch generally decreases only slowly with increasing temperature. This will depend on the chemical or molecular characteristics, as has been discussed in [ 101. For materials that show a rapid change of pitch with temperature, this occurs as a phase transition is approached. In approaching the isotropic phase, the order parameter decreases rapidly and discontinuously towards zero and the pitch decreases equally, depending on the strength of this weak first order phase transition. The temperature dependence of S was given in Eq. (1 3 ) , and in this transitional region the behavior is complicated by the existence of the so-called blue phases [90,91]. These are of little practical importance in the present context, but they are of theoretical interest as far as the subtleties of twisting power and structure in low order parameter systems are concerned ~921. As the temperature is decreased the chiral nematic structure transforms to a higher order phase. The phase may go through a first order phase transition and crystallize in which case the optical properties are of little interest herein. It may transform to a glass, in which case the optical properties, such as birefringence, pitch, etc., are frozen and may be used in static, or time and environment-independent devices or applications (as discussed in Sec. 2.5 of this Chapter), or it may go through a second order or second order plus a weak first order phase transition to a higher order liquid crystalline phase. Here, for simplicity, we are not considering the so-called re-entrant phases [ 14)
-
366
2 Chiral Nematics: Physical Properties and Applications
in nematics, and a typical pitch dependency spanning the isotropic to smectic A phase transitions is shown in Fig. 22. Two main theories have been developed that predict the behavior of the pitch as it diverges from finite in the N* phase to infinite in a nonchiral smectic phase. If T* is a critical temperature just below the actual N* to SmA transition, the theory of Alben [95] predicts the pitch as p=PO+
U
(T - T*)'
where p o is the helix pitch well away from the phase transition, u is a constant, and y is a critical exponent of the order of 2. Keating's theory [96] predicts that (47) where A and p are constants and the theory is based on a rotational analog of thermal expansion. It should be noted that both the-
tSmA-N*
6oo-
400
[ i
550-
1
130
:
I
135
140
145
150
r
155
Temperature (Celsius)
Figure 22. Reflectance maxima as a function of temperature for a chiral nematic at normal incidence. The material is a mixture of chiral nematic esters from Merck and demonstrates the pitch divergence on approaching either the isotropic or smectic A phase from the N" phase (see [46]).
ories are phenomenological, based on the assumption implicit in Landau-de Gennes theory that some order-dependent property depends on (T-T*)-Y for a second order phase transition. The exponent ydepends on which theory is being used to model the molecular behavior [30] and experimentally there appears to be little difference between these two theories (p. 130 of [9], [46]). The striking prediction of either theory in accord with experiment [9, 10,461 is the divergent behavior of the pitch as the N* to SmA phase transition is approached with decreasing temperature. This behavior forms the basis of the thermographic devices described in Volume 1 of the Handbook [91] and in Sec. 2.5 of this Chapter. Further, it has been shown that the range of color play or region of pitch divergence is approximately inversely proportional to the square of the heat of transition (at TNA)for a homologous series of chiral nematic materials [46]. This range, corresponding to the width of the visible spectrum, may be spread over a temperature interval of 20-30°C down to as little as 10-20C [22], depending on the chemical composition of the chiral nematic material being studied. In achiral nematics exhibiting a nematic to smectic A phase transition (at TNA), it is well known that TNA increases with increasing hydrostatic pressure and typically ATIAP- 10-1 K bar-'. Thus, at constant temperature, a change in pressure of -100 bars ( lo7 N mP2)would shift the TNA phase transition by 10"C. For the typical chiral nematics discussed above, this would shift the selective color reflection or pitch right through the visible spectral range. Such increases in helical pitch length with pressure (see Fig. 23) have been recognized for some time [99-1011 and, provided suitably robust devices can be made that are not subject to mechanical deformation, this presents new opportunities for pressure sensor devices.
2.2
0
500
1000
1
D
367
Static Properties of Chiral Nematics
-0.3 30
I
34
Pressure (bar)
I
38 42 46 Temperature (Celsius)
L
50
Figure 23. Pressure dependence of the selective reflection maxima for different cholesteryl oleyl carbonate (COC) and chloride (CC) mixtures. Compositions (by weight) are (a) COC :CC 74.8 : 25.2 and (b) COC: CC 80.1 : 19.9 (data adapted from [99]. (One bar equals lo5 N m-2.)
Figure 24. Variation of inverse pitch ( p - ' ) with temperature for a chiral nematic composed of 1.75 : 1 (by weight) of cholesteryl chloride (RH) and mysistate (LH). Here the pitch lengths were determined by laser diffraction (see Sec. 2.2.1) (data redrawn from
The helical rotary senses of a number of nonsterol chiral nematics have been studied by Gray and McDonnell [ 1021, and from the results a simple rule relating molecular structure, absolute configuration, and twist sense was proposed. This was used successfully as a predictive tool for a number of new mixtures. This is important in the current context for it is clear that mixtures of rightand left-handed materials may be made to exhibit a linear dependence of p-' on T ; p-' changes sign (see Fig. 24) and varies regularly across the whole chiral nematic range [86]. As well as the pitch changing sign, so too does the rotatory power. If, however, the second component making up the mixture has a lower temperature smectic phase, then this dependence becomes strongly curved. This has to some extent been quantified [46]. When a small concentration of neat chiral nematic is added to an achiral nematic matrix, then a large pitch (p) mixture is
formed in which P K c-I. This result is quantified in the form
W1).
27c = +4@c k =P
where c is the number of solute molecules/cm3 and p, commonly known as the microscopic twisting power of the solute, is a constant with dimensions of area, which depends on the solvent-solute interactions. This parameter allows us to predict mixture composition and behavior and is useful in relation to materials produced for TN devices. For mixtures composed of many chiral components, each with its own dependency of k (T), then the resultant twist is approximately equal to the weight average sum [ 1031 of all the component twists, i.e.,
l k ( T )=
c ci ki ( T )
(49)
1
where ciis the weight concentration of the ith component. The different ki may have
368
2
Chiral Nematics: Physical Properties and Applications
positive or negative values, which allow for subtle k(T) mixtures over broad temperature ranges. There will be exceptions to this simple additivity rule if, for example, some of the components have lower temperature smectic phases. Re-entrant phases also become a strong influencing factor. The sign change in p leads to a double color play across the critical temperature at whichp =O and a change in handedness of the reflecting film (see Fig. 25 and [105]). It is also worth noting at this point that, although we have constantly referred to the visible spectrum, this range actually extends from ultraviolet absorption bands at -350 nm up to infrared absorption at 10 pm; Figure 26 shows a range of specular reflection bands recorded in the range 2-10 pm [ 1061.
.sc "0
h
1.5
B';
-Bz gz.$ d .-
5
1.0 0.5
0
2
3
4
5 6 7 Wavelength (pm)
8
9
10
Figure 26. Infrared helical absorption spectrum for a 1.71 : 1.OO chiral nematic mixture of cholesteryl chloride:cholesteryl myristate (redrawn from [ 1061). The dashed line corresponds to spectral regions of strong infrared absorption.
-
o
l
+
-3.0 0
SMECTIC CRYSTAL 40 60 80 Cholestelyl Chloride (mol.%)
20
100
Figure 25. Inverse of selective reflection maxima ( - p ) as a function of composition for a number of hinary chiral nematic mixtures. Here the components are: o cholesteryl formate/cholesteryl chloride (at 50 "C), A cholesteryl propionatekholesteryl chloride (at 60 "C), cholesteryl heptanoate/cholesteryl chloride (at 60"C), A cholesteryl lauratekholesteryl chloride (at 60°C) [105].
Finally, it should be mentioned that the chiral additive used to create a chiral nematic phase does not have to be a mesogen itself - it has to be soluble at reasonable concentration levels to produce the desired pitch, but since it is now acting equally as an impurity, the normal phase transition properties of the host material may also be altered. Chiral nematic liquid crystals are highly sensitive in their optical properties, and may therefore be used as contaminant detectors. Equally photoresponsive additives, such as azo-based dyes, may be incorporated into a chiral nematic structure and on photoexcitation they change shape; since they then behave as an impurity they can easily alter the pitch or selective reflection properties. Such effects are normally reversible because of the trans-cis and cis-trans back reactions available. This gives a simple imaging device.
2.2.2 Elastic Properties In the important physical properties we have discussed so far, the molecular structure contributes to the bulk optical, electrical, and thermal properties of the chiral nemat-
2.2
ic. Implicit in the use of the director n notation is that in order to consider the behavior of these properties we consider the material as behaving as a continuous medium. The liquid crystal differs from a normal liquid in that it is anisotropic in its properties along n despite the random motion of individual molecules, and in that the director is continuous throughout the medium except at defects (Sec. 2.2.1.1). The director is apolar (i.e., n = - n ) in the absence of spontaneous polar order or in the presence of strong fields. In order to discuss the elastic constants and viscosity coefficients of chiral nematics we make no reference to molecular structure and only consider phenomena on the length scale of the director field, i.e., the material is treated as a continuum. There are significant differences between elastic deformations in liquid crystals and solids, the most basic being that in a shear process there is no effective translational displacement of molecules in a liquid crystal, since they can interchange and ‘slip’ past one another. Consequently, a purely shear deformation in a liquid crystal conserves elastic energy. We are considering a liquid; there are therefore no permanent forces opposing a change in distance between two points, so that in a ‘bent’ liquid crystal, i.e., curved director profile, we must look for restoring forces that oppose such curvature. This is particularly true if we apply external fields or forces to produce orientational or translational motion of the director or fluid. In the next section we will derive the form of the Helmholtz free energy density, F d , for chiral and achiral nematics in terms of director deformations, the splay ( k , twist (k2*), and bend ( k 3 3 )elastic constants, and k the chiral nematic twist vector (k=2n/p). We will then show that application of external E or H fields leads to Frkedericksz (Frederiks) and other transitions depending on the sign of the dielectric anisotropy (A E ) , the diamag-
Static Properties of Chiral Nematics
369
netic susceptibility (Ax), the orientation of the helix axis ( z ) (with respect to the field off and on conditions), and the undisturbed pitch of the helix p ( E , H=O). The external field produces a torque on the director and a change in the free energy density, which in turn leads to new equilibrium structures. These new structures will depend critically on the magnitude (and sign) of the electromagnetic and optical properties as well as the elastic constants, and in chiral nematics specifically there exist a number of intermediate structures related to the twisted macroscopic nature of the phase. These will be discussed in some depth.
2.2.2.1 Continuum Theory and Free Energy The foundations of continuum theory were first established by Oseen [61] and Zocher [ 1071 and significantly developed by Frank (651, who introduced the concept of curvature elasticity. Erickson [ 17, 181 and Leslie [15, 161 then formulated the general laws and constitutive equations describing the mechanical behavior of the nematic and chiral nematic phases. In the continuum theory of liquid crystals, the free energy density (per unit volume) is derived for infinitesimal elastic deformations of the continuum and characterized by changes in the director. To do this we introduce a local right-handed coordinate (x,y , z ) system with ( z ) at the origin parallel to the unit vector n ( r ) and .x and y at right angles to each other in a plane perpendicular to z. We may then expand n ( r ) in a Taylor series in powers of x,y , z , such that the infinitesimal change in IZ ( r ) varies only slowly with position. In which case
n, = n , x + a2y + a3z + O(r2) n, = uqx + u5y + u g z + 0 ( r 2 ) n7 = 1 + 0 ( r 2 )(r2 = x2 + y2 2)
(50)
370
2 Chiral Nematics: Physical Properties and Applications
and
where
kIJ. . = kJ’. . with an a4 = 2, a5 = -, an, a, = -an, dz
ax
(51)
av
1 5 i, j 1 6 We can further invoke the following requirements:
Since we are considering infinitesimal changes, we may ignore 0 ( r 2 )terms and partial derivatives of n, are zero. The components of strain are then (see Fig. 27)
1. An arbitrary choice of coordinate system. We could therefore redefine a permissible system x’, y’ and z’ with new curvature components ki. As the free energy density, f, must be as before, this restricts the moduli kj and k,. 2. The only requirement on the x-axis was that it was perpendicular to z , and therefore to n . Hence any rotation of the coordinate system around z is allowed (i.e., in a uniaxial system, rotation about z does not change the phyiscal description, and F would be invariant).
Twist: a4 (= t l )= --dY a2 (= t 2 )= dn, JY
ax
~
( 51a) Free energy considerations allow us to postulate [59] for an incompressible fluid that the free energy F of the liquid crystal in any particular configuration, relative to that in a state of uniform orientation, is the volume integral off, a free energy density, which is a quadratic function of the six differential coefficients which measure the curvature ai
l$
= jf d z V
1 aiaj f = ki ai + -kd 2 Splay : 4= an 1
JY
-_.. --A Y
Bend :
&-k
-0,
an
x
4”
=1
dx
__---
1-
JY
-_-_.-.
&L
m
&-I-
Twist :
xA/---
__---
..-_-.
-_
---* Y
Figure 27. Graphical representation of the splay, twist, and bend elastic deformations in the chiral nematic phase; u l = s l ,u5=s2, u 4 = t l , u,=t,, u,=b, and a6=b2 (see Eq. 51a).
2.2 Static Properties of Chiral Nematics
A rotation of 45” gives the further equation ki2 -klS
-
(54)
k23 - k24 =
and rotation through an arbitrary angle gives one more equation kl2+ kl4=O 3
k1, = - k l 4 = k25 = -k45
(55)
Of the six hypothetical moduli, ki,two are zero and only two are independent
k; = ( k ,k2 0 - k2 k10)
(56)
Of the thirty-six moduli k,, eighteen are zero and only five are independent kll
‘62
k12
k22
I
k15
ki2
0
0
0 0
0 0
-k12
k15
k24
k12
-k12
kll
0
0
-
+ k2 = 0, k12 = 0
k33
where k , =k , - k 1 2- k Z 4 . So far we have only assumed that the system is a liquid with rotational symmetry. If the molecules are nonpolar with respect to the preferentially ordered axis (n),as is empirically the case in nematic and chiral nematic phases, or if polar molecules are distributed with equal probability in each direction, then the choice of the sign of n is arbitrary. Hence we can employ the condition n =-n, i.e., transform, such that x’=x, y’=-y, z’=-z, which gives
6:. = -alx’ + a2y’ + a32’+ 0(r2)
n;. = - q x ’ + asy’ + a,z’ + 0 ( r 2 )
(58)
and invariance offgives for first order terms
kl=O,
The effect of this condition of nonpolarity is that many of the terms in the matrices of moduli vanish. A further element of formalism in this argument is the arbitrary insistence on righthanded coordinates. Unless the molecules are enantiomorphic (i.e., chiral) or enantiomorphically arranged, this condition may also be relinquished. This is the case provided the phase is composed of nonchiral molecules. Thus we can cancel further terms contributing to the elastic moduli in both nematic and nonchiral smectic liquid crystals. From the condition of enantiomorphy (i.e., nonchirality) we have x’=x, y’=-y, z’=z giving
1
nx’=alx’-a3y’+ua3Z’+O(r ) n-,.. =uqx‘-u~y‘+agZ‘+O(r )
oj
k 5 = 0 , k,=O
as well as. for second order terms
37 1
5
(60)
Hence the most general dependence of free energy density on curvature in molecularly uniaxial liquid crystals is the matrix as given previously, but in the special cases of nonpolarity and in the absence of enantiomorphy, k2 and k I 2vanish. Hence to summarize, Eqs. ( 5 1a), (56) and (57) express the more general dependence of the free energy density on curvature in a uniaxial liquid crystal. Further restrictions then apply dependent on the physical properties, i.e., nonenantiomorphic and nonpolar kl = 0, k2 = 0, kI2 = 0 nonenantiomorphic and polar kl # 0, k 2 = 0, k l 2 = 0 enantiomorphic (chiral) and nonpolar k1 = 0, k2 # 0, k12 = 0 enantiomorphic (chiral) and polar k , # 0, k2 # 0, k12 # 0
(61)
The general expression for the free energy density is
372
f
2 Chiral Nematics: Physical Properties and Applications
= kl(s1+ s 2 ) + k2 (ti + t2 )
1 1 +kll(s1+ s2I2 + 5 k 2 2 ( t i + t 2 I 2 2 1 +k33 (b: + b? ) -k k12 (sl + s2 ( t l + t2 ) 2 (62) - (k22 + k24 )(s1 s2 + tl t2 and we note at the origin that
V .n = s1 + s2 -n . v x n = t2 + tl (n.V x n ) 2=b12+b?
I V . [(n.Q n - n ( V . n ) ] = s l s 2 + t 2 t 2 2
(63)
Equation (53) can be then further simplified using so = - kl l k l l , ko = - k2 lk22 1 kll so2 + 1 k22 t i and f,'= f + 2 2
(64)
which corresponds to a new, generally lower free energy density, including optimum splay and twist. This replaces the uniform orientation expression which we had earlier. Putting f into a coordinate-free notation, we have the more compact form
f , = 1 k11( V . ~t- SO ) 2 2 SPLAY -
+ 21 k22 (n . V XII + t o ) 2 -
TWIST
+1 k33 [(n . QnI2 2 BEND -kI2(V.n)(lt. V X ~ ) POLAR -
1
( k 2 2 + k24 )
.((V.n)2+(V~&)V 2 -L . V&) (65) SURFACE
The orientational elastic constants kl k2,, and k3, have magnitudes of typically lo-" N. Note that here we have described the bulk properties of the material and that in actual devices the free energy is modified by surface forces and electric or magnetic fields. We will return to this below. For both chiral and achiral nematic phases the materials are nonpolar, macroscopically, hence so=O and k12=0 from Eq. (61). Further, the last term of Eq. (65) has the form of a diver,gence, which may be converted into a surface integral [ 1081when integrating over the volume of the liquid crystal. This surface term is negligible when considering the bulk properties of the achiral or chiral nematic film. The reduced form of the free energy density then becomes Fd
1 k11( V . n ) 2 =2
+ 21 [(k22n . V x n )+ kI2 -
+-1
( k 3 3 n xV X ~ ) ~
(66)
2
which is in the form of the free energy in chiral nematic phases, given in Eq. (2), when the lowest energy structure has a finite twist of k radianslmeter [=27dp] and corresponds to the director field
[ t1 t 11
n = cos -z+$
,sin
-z+$
,O
(67)
given in Eq. (1) and Fig. 1 . If q = O we have an achiral nematic where
1 k12(divn)2+-1 k2, (n . ~ u r l n ) ~ Fd = 2 2 1 + 2 k33 ( n x ~ u r l n ) ~ (68) -
The usual depiction of the splay, twist, and bend deformations is shown in Fig. 28. The twisted nature of the chiral nematic phase often ensures that a number of differ-
2.2
00 00
000
ooanQ
00 00 00 TWIST
SPLAY
BEND
Figure 28. Schematic diagrams of (a) splay, . . (b) twist, and (c) bend deformations in a chiral nematic. (N. B. Although we use ellipses to represent the deformations they are director. not molecular, properties.)
ent equilibrium structures can be established in the presence of external fields of different magnitude, and often, frequency. The structures induced will also depend critically on the magnitude (and sign) of the dielectric, magnetic, and flexoelectric anisotropies and coefficients, respectively. The external fields couple with the macroscopic properties to alter the director field and to give extra terms in the free energy density expansion such that generally Fd
= Feldstlc
Fdielectric
+ Ftlexoelectric
+ Frnagnet~c
(69)
where: (1) Felastlc is the free energy density in the steady state due to the splay, twist, and bend deformations, and the helix twist, as given in Eq. (67),
(2) Fdlelectrlc is the contribution to the free energy density due to the coupling of the dielectric anisotropy A E (arising in nonpolar systems from the polarizability anisotropy) with the external electric field E , such that
and is the dielectric constant perpendicular to n. Note here that &Idoes not couple with n and therefore has no effect on the director field. The factor 4 7 ~ :has been includ-
Static Properties of Chiral Nematics
373
ed for consistency with the S . I. system of units. The sign of A & therefore defines the direction of preferential motion of n in the applied field, and the coupling gives rise to a quadratic effect in the external field due to the (n . E)2 term.
(3) Flnagnetlc is the contribution to the free energy density due to the coupling of A x , the magnetic anisotropy, defined as A x = ~ , ~ -with x ~ , the externally applied magnetic field B. A x is usually positive for aromatic ring structures (and some cholesteryl esters are negative), and arises from the diamagnetic anisotropy. The free energy density in the local magnetic field H is then given by ~ ~ a ~ n t . lI i c = - - [ x I ~ ~ + ~ x ( n(71) .H)~]
2 where again x L H 2 does not contribute to motion of the director field, and the coupling gives rise to a quadratic effect in the field due to the (n . H ) 2term. (4) FflexOelectrlcis the contribution to the free energy density due to the coupling of the flexoelectric polarization Pflexwith the applied electric field E , such that Fflexoelectric
=-E
. f'flex
(72)
where
Pflex= e,n( V .n ) + e , ( n x V x n )
(73)
and e, and eb are the splay and bend flexoelectric coefficients, respectively. e , and eb may differ both in sign and quite significantly in magnitude, thereby giving rise to quite different orientation effects of the director field n . In these cases, where the flexoelectric effect dominates over any dielectric term, the coupling is linear with E . In the above description we have limited ourselves to the main interactions that lead to large-scale deformations or reorienta-
374
2 Chiral Nematics: Physical Properties and Applications
tions of the director field and therefore marked changes in the optical properties of chiral nematic materials. These deformations lead to Frkedericksz transitions, helix unwinding, linear and nonlinear optical responses, etc., in the presence of an external coupling field and will be discussed in detail in Sec. 2.4. Other weak effects that might involve electroclinic phenomena in long (-) pitch chiral nematic systems are outside the scope of the present chapter. In the following section we will consider the time-dependent or dynamic implications of director deformations, which will lead us in turn to discuss field-induced transient phenomena in chiral nematic liquid crystals in Sec. 2.4.
2.3 Dynamic Properties of Chiral Nematics The static theory discussed in the previous section describes the equilibrium situation in chiral nematics very well - in general, theory and experiment are in good accord. The dynamic situation is less clear. On the molecular scale, the chiral nematic and nematic phases are identical; the question then becomes, ‘how does the macroscopic twist or helicity modify the vector stress tensor of the achiral nematic phase defined by the socalled [ 1091 Leslie friction coefficients a,- a,?’ Experimentally, viscosity coefficients that are then related to the Leslie coefficients are measured in a way that depends specifically on the experiment being used to determine them. The starting point for discussion of dynamic properties is to use classical mechanics to describe the time dependencies of the director field n (r, t), the velocity field v(r, t ) , and their interdependency. Excellent reviews of this, for achiral nematics, are to be found in [59,109,
1lo], and a concise overview of the derivation of static and dynamic properties based on continuum theory is given in [ 1111. The problem is encapsulated by the simple fact that in a dynamics experiment, such as viscometry, the coupling of hydrodynamic equations relating v ( r , t ) and it (r, t ) implies that n then, generally, becomes ill-defined. For example, the measured viscosity depends on shear rate, surface and flow-induced alignment, the presence of defects and instabilities, and a myriad of other experimental conditions, such as sample geometry, cell thickness, applied electric or magnetic field, etc. These experimental conditions are so important that apparent bulk viscosities may differ by several orders of magnitude from those predicted by continuum theory and applicable at the director level. With these observations in mind, we will present an outline of the main theoretical considerations and experiments where these predictions have been tested.
2.3.1 Viscosity Coefficients As discussed in Sec. 2.2.2.1, the foundations of the continuum model were laid by Oseen [61] and Zocher [ 1071 some seventy years ago, and this model was reexamined by Frank [65], who introduced the concept of curvature elasticity to describe the equilibrium free energy. This theory is used, to this day, to determine splay, twist, and bend distortions in nematic materials. The dynamic models or how the director field behaves in changing from one equilibrium state to another have taken much longer to evolve. This is primarily due to the interdependency of the director n (r, t ) and v (r, t ) fields, which in the case of chiral nematics is made much more complex due to the longrange, spiraling structural correlations. The most widely used dynamic theory for chiral
2.3
and achiral nematics is due to Ericksen [ 17, 181andLeslie [15,16,109],andthisisbased on the formulation of general conservation laws and constitutive equations to describe their mechanical behavior. It is assumed that the director field is a continuous function, whose direction can change systematically from point to point in the medium (ignoring singularities of the type discussed in Sec. 2.2.1. l), and that external fields can result both in director reorientation and a bulk translational motion of the chiral nematic medium. In the following outline we will use Leslie’s original nomenclature [ 109, 11 11 where possible and the Cartesian notation, in which repeated indices are subject to the usual summation convention, i.e., a comma followed by an index denotes partial differentiation with respect to the corresponding spatial coordinate, and a superimposed dot indicates a material time derivative, e.g., T,i=aTlaxi, v,=avilaxj, and V = d Vld t. The chiral nematic is considered incompressible, i.e., of constant density p with a nonpolar unit director n (i.e., n n = 1). This implies that the external forces and fields responsible for the elastic deformation, viscous flow, etc., are much weaker than the intermolecular forces giving rise to the local order, i.e., between the chiral molecules. We will consider a volume of material V bounded by a surface S ; v and w represent linear velocity and local angular velocity, respectively, i.e.,
w=n.ri
(74)
per unit time, and h as the flux of heat out of the volume per unit area per unit time. These are customary energy balance terms for a conventional isotropic liquid. For liquid crystals we introduce the following new terms to enable us to balance the conservation of energy equation: G is the generalized or director body force per unit volume (arising, for example, from a body couple created by an external magnetic or electric field), s is a generalized or director stress vector per unit area, which is related to the couple stress acting on liquid crystal surfaces, and o is a scalar which represents rotational kinetic energy of the material element (i.e., an intertial constant). With these assumptions we can now write the conservation laws for a chiral nematic:
1. Conservation of mass
2. Conservation of linear momentum Jp+dV=jFdV+jtdS V
V
(77)
S
3. Conservation of angular momentum [ ( p r x v) + (ori x %)]dV V
=
1[ ( r x f ) + ( n x G ) ] d V + 5 [ ( rx t )+ ( n x s)]dS V
s
4. Conservation of energy j ( p v .v +ori . n + U ) dV
and
v.v=0
375
Dynamic Properties of’ Chiral Nematics
V
(75)
due to the assumption of incompressibility. Further, we define f as the body force per unit volume, t as the stress vector per unit area, I/ as the internal energy per unit volume, Q as the heat supply per unit volume
=j(f.Y+G.ri+Q)dV V
+ j ( t . Y + s . ri - h ) dS
(79)
S
Equation (78) can be written [I091 as Oseen’s equation [59],i.e.
376
2
(G + g)dV + s dS
j OK dV = V
Chiral Nematics: Physical Properties and Applications
(80)
S
V
where g is the intrinsic director body force, with the dimensions of torque per unit volume, which is independent of G . Further ti=t,Vj, the surface force per unit area acting across the plane whose unit normal is vj and si=s, vj,the director surface force, as previously defined. Conversion of surface integrals into volume integrals and rearranging leads to the conservation laws in the following differential form, (i)
p = 0,
independent and arbitrary functions we obtain
and
with @i=aeyknj(Nk+dk,,np)and a i s a constant. Equation (85) then gives
(81)
(ii) ~ l i ~ = J ; : + t ~ , ~ ,
(82)
(iii) o E j = Gi+ gi + sij,j,
(83)
(iv) U = Q - hi,,+ t, dij + sij Nij - g, Nz,(84) where tij - ski n j , k
+ gi nj = tjj - skj ni,k g j ni NI. = k.I - w .I knk N.. v = n?I . - w .lk nk , J. 2d.. = v.1,J . + v J.. 1 . (I 2w.. = v.I , J . + v J.. 1 . (I
Here Ni may be interpreted as the angular velocity of the director relative to that of the bulk fluid, and it should be noted that to is asymmetric. From the Helmholtz free energy per unit volume (i.e., F= U - T S ) ,the form of the energy conservation given by Eq. (84), and the
Following the Leslie thermodynamic formulation for the constitutive relations, i.e., that t i j , gi, and p ian be resolved into separate static (elastic) and hydrodynamic (viscous) parts, namely t.. = t!!+.; . lJ
U
gi = gio + i z
pi = p;
dt v
the entropy per unit volume, we obtain the following entropy inequality for a system in isothermal equilibrium (85) t..d.. +s.. - g .1N .1 - p .1 T,1. - F - S T - @ . 1,z. >-O !J 1J 1J where &-hi- T p i is introduced as a dummy vector and pi is the entropy flux per unit area per unit time. Since T i , d, and nu are
+ ji
we obtain
SdV where S is
entropy inequality, i.e.,
lJ
with pq = 0
2.3
Dynamic Properties of Chiral Nematics
377
and the inequality (Eq. 86) simplifies to
+ ginj= Fji + gj ni and the entropy Further, tCj generation per unit volume is then T i = Q - h;,i + ff eijk [nj ( N k + dkp F Z p )] . ,1
+iji
dij
- i. Ni
(91)
The hydrodynamic components of and hi are then
tij
gi,
np dk, n; nj + a2 Ni nj +a3N j ni + a4dji + a5diknk n j +a6 djk nk ni + a7 eipqT qn j np
= a1 nk
(92)
+a8 e j p q T q ni np i i
ti,,
= -(YI Ni + ~2 dij nj
+
eipq
np Tq 1 (93)
h; = K I Ti + K 2 nk Tk nj +K3 eipq
np N q + K4 e;,, np dqr nr
(94)
(95) where a,-a, are the six Leslie coefficients, as defined for achiral nematics, a, and ag are two additional temperature-dependent viscosity coefficients that couple thermal and mechanical effects with K1-K4 (the coefficients of thermal conductivity in chiral nematics). The early experimental evidence for this coupling of thermomechanical effects in chiral nematics is due to Lehmann [ 1121. We will return to these experimental results along with a discussion of flow propertiey below and convective instabilities in Sec. 2.4.3. From Eq. (90), the entropy inequality gives
tl, dlJ - ii Nl - ki Ti - aa etjk nj
(Nk + dhp np) Ti
(96)
Clearly these inequalities underline the greater complexity involved in the analysis of the dynamic properties of chiral nematics in comparison with achiral nematics. Simplifications have been suggested [ 1 131 based on the work of Parodi [114], which, besides the relations in Eq. (95), suggests that K~ = K and K4 = a,+ ag. It remains true, however, that to date it has been difficult experimentally to define conditions that isolate these different viscosity coefficients and thermal properties, since this implies decoupling IE (r, t ) and v (r, t ) when n spirals relatively tightly on the optical length scale. Interesting experiments have, nonetheless, been carried out, which demonstrate the unusual viscometric (i.e., non-Newtonian) properties of chiral nematics with apparent viscosities that increase by five or six orders of magnitude on crossing from the isotropic to the chiral nematic phase 11 1-51.
2.3.2 Lehmann Rotation The first recorded example of thermomechanical coupling, as explained in the Les-
378
2 Chiral Nematics: Physical Properties and Applications
lie-Ericksen theory, in chiral nematics appears to be due to Lehmann [ 1121. In his experiments he observed droplets of chiral nematic, which on heating from below appeared to evolve a complex rotating and spiraling director pattern within the droplet walls. Following Leslie’s equations, this effect may be explained as follows: the temperature gradient acts as a directional or polar field, which in turn, through the lack of mirror symmetry in chiral nematics, leads to the thermomechanical cross terms. These produce a torque or axial vector, which then leads in turn to the director rotation and transport. In a parallel experiment using a polar electric (i.e., dc) field, similar ‘Lehmann’ rotations were observed [ 1161, which serves to underline the validity of the Leslie analysis. It is therefore interesting to follow this analysis further [ 1091. A chiral nematic film is assumed to be a semi-inifinite planar sample with its helix axis in the z direction bound by planes at z=O and z=d. The director n is described as in Eq. (1) with $=O, i.e., [cosO(z, t), sin e(z, t), 01. The boundary conditions are that there are (1) no external body forces, (2) no heat sources within the liquid crystal, and ( 3 ) that the velocity vector is zero, i.e., fi=Gi=dU=wU=O and that T = T ( z ) . Conservation of angular momentum [Eq. (83)] then gives
a2e ae a T 2 = Yl at - Y3 =&
0
at
where
and Fo is the free energy density in the ground state, or absence of elastic deformations. For such time-independent situations
a2e= ae = 0 ,
~-
and the above equations
at at simplify to
and
whence T
j q d< = A Z + B
0
and
where A , B, C, and D are all constants of integration set by the boundary conditions. If we assume the polar field comes from the temperature gradient between z =d and z=O, i.e., T, - To,and that the director is unbound at the surfaces (i.e., weak anchoring), then the surface torques or couple stresses r i l = f ? G k n i S l k are zero, which leads to
The energy balance per unit volume (Eq. 91) then gives
-
(
Y1,,-Y3-
aZ
-
at
(99)
If the material constants are assumed to be, in a first approximation, independent of
2.3
temperature (i.e., far from a phase transition), 8= w t + f ( z ) and T=g ( z ) ,then the conservation of angular momentum and the energy balance (Eqs. 98 and 99) give
and
a2.f
ag
k22 2- Y3 -+
az
az
Yl w = 0
with solutions g=
-
(
3
wz+Aexp y3-
+B
and
379
Dynamic Properties of Chiral Nematics
2.3.3 Macroscopic Flow The macroscopic flow properties of chiral nematics are very different from those of an achiral nematic, due primarily to the long range helicoidal structure. As shown in Fig. 29 [115], the apparent viscosity qapp can vary by a factor of lo6 at the same temperature in the same chiral nematic material, depending on the shear rate. The lower shear rates in capillary flow experiments lead to higher values of qappin comparison to the rotational shear field experiments. The reader can try a simple experiment by placing two drops of the same nematic base material, but one doped with a chiral twisting agent to give visible reflections, on a glass slide. On tilting the slide, the achiral nematic drop can be seen to flow at a significantly greater rate than the chiral compound. The flow of the chiral compound is
If 8=$ for z=O and T ( z )are as defined above. we have
and
CHOLESTERIC
Thus in Leslie's prediction [ 1 171, the director rotates about the helix axis with an angular velocity a.If the surface anchoring is strong, the solutions become static and result in a modified twisted helix configuration. Equally, if A T= ( T ,-To) =0, the solution for 8 leads to a static regular helix of pitch p = 2 7c k,,l(k- a).As we will see when studying capillary flow, the anchoring conditions are critical for observing the consequences of thermomechanical coupling in chiral nematic systems.
I10
i
ISOTROPIC
I20
130
140
Temperature (Celsius)
Figure 29. Apparent viscosity, qapp,of the chiral nematic cholesteryl acetate as a function of temperature for different shear rates. Capillary flow (s-I) 10 ( V ) , SO (x), 100 ( ), 1000 (v), SO00 ( );rotational shear (s-I) lo4 ( A ) , and normal liquid behavior at very high shear rate ( 0 ) (redrawn from [ 1 151).
380
2 Chiral Nematics: Physical Properties and Applications
much more akin to that of a smectic material, and the complete uncertainty of viscosity measurements in chiral nematic materials is encapsulated in this very simple experiment. Is the chiral nematic phase really so highly non-Newtonian or are these orders of magnitude differences in qappdue to more to the experimental environment? Do the Leslie coefficients, as extended to chiral nematics, have validity, and how might we examine them? There appears to be no concrete experimental evidence to answer these questions, but there are strong indications that support the base concepts, and so we will review some of the key experimental results to date. It is important, however, to remember at the outset that the boundary conditions, implicit in the Leslie theory, and the length scale of the experiment, as related to monodomain behavior, are fundamental in relating theory to experiment in these chiral nematic structures. One of the simplest experiments in ordinary liquids to measure viscosity is to measure the classical Poiseuille flow in a capillary tube. For a tube of radius R, with a mass flow of Q per second and a pressure drop of p per unit length, the apparent viscosity is given by
where p is the fluid density. Such pioneering measurements have been carried out on chiral nematics and lead to the high values of apparent or bulk viscosities referred to in references [ 115, 1181. In related torsional viscometry, consisting of parallel glass plates, similar high values of qapphave been obtained [ 1191. The latter authors have discussed [120, 1211 how the direction of the helix axis, relative to the substrates and in the bulk, depending on the shear rate, affect the data. Later results [122] have, via the Poiseuille flow techniques, established that
0.221
0
,
,
,
,
,
0.25
0.50
0.75
1.00
1.25
Shear Rate (lo3 s-l) Figure 30. Apparent viscosity, qaPp,in Poiseuille flow as a function of the shear rate for different chiral nematic pitch lengths (in micrometers); 1.9 ( O), 2.6 (x), 3 (+), 3.9 ( O ) , 6 (A), 9.1 ( 0 ) , and m ( V ) (redrawn from [122]). The helical axis was normal to the flow.
the flow normal to the helix axis is little different in chiral nematics from achiral nematics. These authors (Fig. 30) varied the helical pitch in a series of controlled experiments and showed that in their geometry the helix axis was orthogonal to the capillary walls and therefore to the flow direction at all points in the capillary. In this geometry, at long pitch lengths, the experiment would give an average of the Miesowicz [ 1231 viscosity coefficients q2 [= %(a,+ 2 a,+ a, + as)] and q3 (=%a,)for nematics. Hence for ‘in-plane’ shear, the viscosities for the achiral and chiral systems would not be expected to be so different, as indeed was observed [ 1221. In ‘thick’ capillaries, where R - 300500 ym, Helfrich [124] observed quite spectacularly different increased apparent viscosities, which he explained in terms of ‘permeation’. The Helfrich suggestion is that flow takes place along the helix axis ( 2 ) without the helical structure itself moving. In this model the director, n , is at all times orthogonal to the capillary cell walls (Fig. 31) and strongly anchored to them.
2.3
W
Figure 31. Schematic diagram of the Helfrich model of permeation in a chiral nematic. The flow is along the helix axis (z)at low shear rates and maintains the z direction distribution (see text).
The translational motion in the z direction is then achieved by the rotational motion of the director. (This can easily be visualized in terms of a corkscrew boring into a cork. The transverse view of the path in the cork is always the chiral screw, whilst the bulk of the corkscrew itself translates along the helix or screw axis.) In more mathematical terms, the energy dissipated by the motion due to the pressure gradient must equal that dissipated by the precessional or rotational motion. In this case, the viscous torque rexerted by the director is given by r = n x g where g in scalar form is given by -y, k v and v is the linear velocity in the z direction (see Eq. 93) and y, is negative in Leslie’s theory. For a pressure gradient of dpld z we have Yl
2
dp
(kv) =-vdz
The fluid flow, Q, ignoring edge effects or boundary layers, is Q=-
.nR2( d p l dz) Y1k2
which from Poiseuille’s law (see Eq. 105) gives
yl k2 R2
Vapp = - ___
8
-
Typical experimental dimensions R 300500 pm and k - 1-2 pm suggest that qaPp--lo6 yl, which is in good accord with
Dynamic Properties of Chiral Nematics
38 1
the experimental data [ 1151 for qapp.The Helfrich permeation model has been derived [ 1251 in an elegant use of the Leslie theory both for flow between parallel plates and in capillary tubes. In the latter case it has also been shown that the velocity profile is constant across the radius apart from in the interface region very close to the capillary walls. This interface and the production of quasi-infinite monodomain samples appears to be of considerable importance in experimental arrangements designed to test the theoretical predictions of the Leslie theory. It is an experimental observation that in capillary tubes the director configuration must always give either a disclination line at the center (along z ) for homeotropic surface alignment, or, in the Helfrich model, at the edges for either homeotropic or planar (x,y ) surface conditions. In the latter case, the dislocations would be bipolar in the x,y plane and spiral in the z direction. Measurements using capillaries are therefore always delicate. Either the radius is small and surface effects become important or the radius is large, in which case it is difficult to produce monodomain samples throughout the flow volume. Experimentally, we appear to be always in the situation in which it is extremely difficult to control, adequately, both n ( r , t ) and v (r, t ) independently. Techniques such as dynamic or quasielastic light scattering, in which director motion is probed at the local level, might be of great value in these helicoidal systems (see p. 295 of reference [30]). It is possible to simplify the problems posed by three dimensions by examining the flow between parallel plates, i.e., in two dimensions. This allows the director to be well controlled in ‘planar’ cells with a flow across the helix axis, and this has been considered analytically and numerically [126, 1271 as well as experimentally [ 1281, with qualitative agreement between the results. However,
382
2 Chirdl Nematics: Physical Properties and Applications
this still only leads to information on and ~ 2 rather , than the needed to test the theoretical predictions [lo91 of the LeslieEricksen theory. There is still clearly a great need for further experimental studies on chiral nematic systems if thermomechanical coupling is to be understood in these materials. This is of considerable importance if the dynamics of electro- and magneto-optical phenomena are to be exploited fully, either theoretically or practically, in chiral nematic systems. In the next section we will consider these field-induced distortions in more detail.
2.4 Field-Induced Distortions in Chiral Nematics The distortions induced by external fields applied to chiral nematic liquid crystals give rise to a remarkably wide range of electro-, magneto-, thermo-, and even opto-optic effects. These range from their use in twisted nematic devices, and a resulting technology that dominates the flat panel display market, through fundamental studies of magnetically and electrically induced Freedericksz transitions, thermometry, thermography, and imaging techniques, to their use as optical elements in laser technology. In the present sections we will review how the various static and dynamic properties, which we have already discussed, lead to such a wide range of uses and applications. The starting point is to reconsider Eqs. (1) and (2). In the presence of an external field, the free energy density is modified by a term involving the coupling between the electro-magnetic (or other) bulk anisotropic property and the field (see Eq. 69). This leads to reorientation of the director n in order to minimize this addition-
al term. In chiral nematics the director has a twist term, due to k in the free energy expression, which, in the general case of an applied field, will lead to distortion of the helix and therefore a change in the bulk and, particularly, optical properties. The helix pitch may be long @>>A), of the order of the wavelength of light (A-p), or short (Asp), and these three conditions lead to quite different types of response and, ultimately, devices. Equally, the coupling might be through the dielectric, conductive, magnetic, flexoelectric, or optical properties, which in turn may have anisotropies that are positive or negative relative to the applied field. The coupling will also then depend on the direction of this applied field relative to the helix axis and the director. Thus it is possible in chiral nematic materials to observe a very wide range of electro-magnetic phenomena, with implications for theoretical understanding and experimental or practical applications. For convenience, in the following sections, the major categories will be subdivided into the effects of magnetic and electric fields applied parallel or orthogonal to the helix axis, respectively. Under these four subclasses, the effects of helix pitch, positive or negative anisotropy, field frequency, and coupling mechanisms will be considered as appropriate.
2.4.1 Magnetic Fields Parallel to the Helix Axis We will first consider a planar chiral sample with a magnetic field H applied across the sample along the z or the initial helix axis direction. The diamagnetic susceptibilities are defined as xl, and i.e., parallel and perpendicular to the local director. Since n spirals around z (see Eq. l), this gives a value of parallel to H and %(xII+x1)orthogonal to H . If Ax(=xll-x1)
xL,
x1
2.4
Field-Induced Distortions in Chiral Nematics
xL>X(xrl+xL)
and the diis negative, then rector n stays normal to the field at all points and the sample remains planar. If, however, Axis positive (xll then X(xI, and the director can rotate to become parallel to H (or z ) and the helix axis will try to become horizontal (i.e., move into the x,y plane). Once the helix axis is horizontal, or predominantly so through the coupling of H with a second process starts to dominate known as helix unwinding [129]. The unequivocal threshold field for this will be discussed in the next section. Essentially in this mechanism, with the helix axis orthogonal to the field, the director now starts to unwind since xlI then xlI> !4(xll This continues until the directors n are aligned along H , in which case we have unwound the helix to give a homeotropic nematic texture. This gradual transformation is commonly known as the chiral nematic (cholesteric) to nematic transition. It is not a phase transition in the thermodynamic sense, but an orientational transition within a phase at a fixed temperature. On removal of the field, the structure reverts back to helical chiral nematic form. These changes can happen if the sample is considered thick or outside the length scale on which surface forces are considered strong. If this is not the case then there will be strong competition between the surface forces trying to keep the sample planar (i.e., the helix perpendicular to the substrate) and the applied field trying to reorient the helix into the x, y
>xL),
+xL)>xL
X(xlI+xL),
>xL
+xL).
383
plane. This competition, depending on the relative strength of the two mechanisms, leads to different director distributions or distortions. At low field strengths we may assume that the director remains on average in the x , y plane with the helix axis, therefore, ‘on average’ along z. Thermal fluctuations cause the director to oscillate around thex, y plane and in the presence of an external field the director, for systems where the cell thickness d is much greater than the pitch, can couple to give layer-like or ‘Helfrich’ [130, 1311 distortions. These are shown schematically in Fig. 32. As before, the socalled corrugated layers are planes in which the director directions are equivalent (i.e., at p / 2 remembering n =-n), but regularly periodic in the x, y plane. We will discuss the threshold for this effect below. At higher field strengths the directors become more uniformly tilted at higher angles, but still with the helix axis along z. The spiral nature of the chiral nematic forces the inclined director to trace out a ‘conical’ distortion [ 132, 1331. At higher fields the helix distorts into the horizontal plane and the director may unwind as described above. It should be stressed that not all chiral nematic liquid crystals clearly exhibit all of these effects. The critical fields for each distortion are not sharp, the distortions may co-exist, since the director field is at all times continuous (unless a ‘focal-conic’ phase is formed) and these fields depend on cell dimensions,
Distorted planes of uniform director orientation \
Magnetic field
Figure 32. Schematic representation of the Helfrich or periodic distortions in a planar chiral nematic due to a magnetic field acting parallel to the helix axis (z). The lines denote equivalent director fields (in the x , y) plane ( A x > O ) and the periodicity is 21rlk,.
384
2 Chiral Nematics: Physical Properties and Applications
pitch lengths, magnetic susceptibilities and anisotropies, elastic constants, and quality, i.e., homogeneity, of the initial planar alignment. We will first consider the ‘Helfrich’ instability mode [130, 1341. For an unperturbed planar chiral nematic with the helix along z, the director is given by Eq. (1). If we now assume small perturbations in @ and that the director layers undulate sinusoidally by an amplitude 8 (see Fig. 32), we have n, = cos(kz + @)=r cos kz + @ sin kz ny = sin(kz + @)= sin kz + @ coskz n, = 8 cos kz
I
(106)
&L L
Fl = [(kll sin2 k z + k33 cos2 kz)
[2 +
+ k22
2)
~
For a given undulation, 6, 3 is a minimum for -= 0 or a =0. Within the limit of small
a@
deformations, we may assume that the perturbations @ and 8 are dependent on x and z and given [ 1341 by (1 11)
where qz=m d d and m is an integer usually equal to unity. Practically, qZ<<4,<
-
sin kz cos kz -
+ k33 cos4 kz(
cos4 kz 7
8 = 80sin q,x cos qz @ = (q& + 43 cos2kx)cosqXxsin qz z
.(kf3+gr+kllcos
aZ k&J+
a2@ ax --k22 sin22kz a2e - (k22 - kll) 2 4 ax2 sin2kz- a2@ + kll ksin2kz-ae ax az aZ
-k33
a3
Equation (2) then gives the local energy density Fl as
- kll sin 2kz-
and
these limits. Thus for
ax
%I]
as a@
-= O
we have,
under the assumption of slowly varying a
(107)
If we assume that the total energy 3= F d V, V then
where
a = - (k, sin2 kz + k33 cos2 k z ) .
(2+ k g )
13)
(2 k22 + k33 - kll) cosq, zsinq, x (114)
2.4
Field-Induced Distortions in Chiral Nernatics
3 a5
Using the limitations of ql<
or again
which lead to $0
=
k8o 4x
Under these approximations, the free energy density, taking into acount undulations, is
If we now apply a magnetic field normal to the layers, the total free energy
Ft = F u m + Fmagnetic where -
A x ( n .H ) 2 2
Fmag - - -
( 1 19)
36 and if __ -0, we have
ae
The limiting conditions are if q?+O or 00 then H +03, remembering that qzis fixed by the cell dimensions. If qx+00, the bend (k33) mode is excited, whilst if qx 4 0 , the amplitude of the twist mode diverges rapidly with decreasing qn. The optimum wave vector [591 occurs for a mixture of twist and bend modes such that
Thus the periodic distortion depends critically on the relationship between the chiral nematic pitch and the cell dimensions. Therefore these phenomena are only observed for cells in which the thickness is considerably greater than the helix pitch [ 1351. For low threshold fields, the diamagnetic anisotropy should be high with low bend and twist elastic constants. For the conical distortion, Leslie [ 1 3 3 ] has derived a critical field, HcD, given by
H& = 1 (kl1 q: AX
+ k33 k 2 )
and as we shall see in the next section the critical field for the helix unwinding (chiral nematic to homeotropic nematic) transition HCNis given by
Since k > > q Z , the threshold field for the Helfrich periodic distortion is much lower than that for either the conical or the helix unwinding distortions. The inter-relation of, primarily, the bend and twist elastic constants defines which of the latter two modes
386
2 Chiral Nemdtics: Physical Properties and Applications
is observed in thinner cells or at higher field strengths. A further complication arises here in that the derivations of the different critical fields are calculated from the free energy expression (Eq. 2) with increasing field and for deformations induced in a texture that is initially planar. The critical fields vary [ 13 11 with decreasing field, depending on time and the ratio of dlp. On relaxing back for the helix unwound texture (H>H,,), the chiral nematic may form a metastable focal-conic texture with a long lifetime, even as H+ 0. Since these distortions are related to pitch changes, the reflection and transmission properties, both polarization state and wavelength, will alter with increasing and decreasing H. These optical changes are also observed in electric fields and will be discussed in the following sections. The more subtle deformations, as between the Helfrich and the conical distortion modes, are often more readily observed by capacitance measurements than by optical techniques for long pitch systems in thick cells [136]. The most spectacular optical changes occur for the chiral nematic to nematic field-induced transition and occur readily for a field applied across the helix axis for A x positive materials.
anchoring. The interesting case occurs for A x > 0 and planar alignment, since this leads to a clear chiral nematic to nematic helix unwinding distortion which involves only p , Ax, and k22 (see Eq. 126). This structural transition is depicted in Fig. 33. The director n in these experiments is orthogonal to z and spirals in the x, y plane (see Eq. 1). Since A x is positive (i.e., xII>xL),then j/2(xL+xI,)>xL and the director rotates in plane to minimize the free energy relative to H . The helix axis remains in the z direction, but gradually unwinds as H approaches a critical distortion field, HcN,to become planar nematic with an infinite pitch above HCN(Fig. 34). This results in the selected reflection color moving to longer wavelengths until the pitch becomes infinite [136,138]. This dependence of the pitch on the applied field has been examined theoretically [ 132,1391 and we will consider this further. Initially, the sample is assumed to be fairly thick (i.e., d > p ) and in a planar texture. For zero or low fields, the helix will be arranged as in Fig. 33 a. At intermediate fields
2.4.2 Magnetic Fields Normal to the Helix Axis In this section we will consider the magnetic field induced distortions for a field applied orthogonally (i.e., in the x, y plane) to the helix axis or z direction. For A x < 0, similar distortions to those discussed earlier will occur due to the director rotating in the field H to minimize the free energy, i.e., with the helix in the x, y plane and n in the z direction. The distortions will be the same, but with slightly different boundary conditions depending on the pitch, cell thickness, and
H=O
O
H'HCN
Figure 33. Schematic representation of the untwisting of a chiral nematic helix for a magnetic field H normal to the helix axis ( z ) with A x > O . A denotes regions where the helix becomes distorted and B denotes regions of 180" twist walls. For H>H,,, the helix has infinite pitch.
2.4
387
Field-Induced Distortions in Chiral Nematics
= L j [ [ s - k )2k 2 2 - A ~ H 2
+ const. where, as before, k=27clp, the undistorted helix wave vector. The equilibrium condition is then 10 0
I 0
H/Hm
Figure 34. Magnetic field dependence of the relative pitch p (H)/p(0) in a chiral nematic. These data come from [ 1371 and correspond to PAA doped with cholesteryl acetate.
H < H C N , with H in the x direction [i.e., H = ( H , 0, O)], the directors will deform to distort the helix, as shown in Fig. 33b. These directors originally pointing (on average) with a greater anisotropy component in the x direction will deform to be parallel to H , i.e., in the x direction (at B), having a tightly twisted region at the ‘points’ or positions (A) with the director along y , i.e., orthogonal to H . These correspond to a succession of 180” twist walls. With further increasing field, the regions or ‘walls’ such as B become unwound so that the directors realign along the field and the areas A on average expand, thereby increasing the effective pitch. The helix becomes fully unwound for H>H,. Mathematically this is described as follows. The field H is along z (i.e., H = h , 0, 0) and the director (see Eq. 1) is n = (cos v, sin v,0), where y = k z + $. For thick cells in which d>>p, $ is a constant defined by the surface alignment and can be ignored. We will consider pitch deformations ‘far away’ from the substrate. The free energy density of the system is then given by
k22(
d2W - A X H 2 s i n t y c o s v = 0 g)
(127)
which gives
z = 2a5,F, (a) for
and R12
dv
Fi(a)= j (I-a 2 sin . 2 y)Il2 In this notation, a is a constant determined from the condition that 3 is a minimum, z = p (H)/2, i.e., the half pitch of the field distorted structure or the distance between twist walls, F , ( a ) is a complete integral of the first kind, and 5, relates to the wall ‘thickness’, which is of the order of 2 t 2 ( H ) [30, 1391. The free energy is then given by
1
(q+p)
kz
kz
where
a2 = (I + p)-’ and h = (t2k)-’
(128)
388
2 Chiral Nematics: Physical Properties and Applications
and A12
fi (a)=
5 (1- a2sin2yl)1’2dyl 0
Here F2 (a)is an elliptic integral of the second kind. Minimizing the free energy as in the previous sections for A p= 0 leads to
For z(H=O)=n/p(O), i.e., the undisturbed helix, and z (H)=7t/p (H) we get
If z(H) +m, then a+ 1, F 2 ( a ) and for H=HCN,i.e., the helix unwinding field, we have h =7t/2 or -03,
where p=p(O), as defined in Eq. (126). Experimentally it has been verified that HCNis inversely proportional to p [ 1401 for relatively long pitch systems and that Eq. (131) is experimentally valid [137, 1401. It should also be noted that the pitch divergence only occurs close to HCNas the number of pitch walls rapidly decreases to zero. A further interesting observation is that for low field H<
2.4.3 Electric Fields Parallel to the Helix Axis Many of the magneto-optic effects described earlier are readily observed in electric fields when the magnetic free energy term Fmagnetic [=-Ax/2 (n . is replaced by the [=-Ad4 7t (n . HI2]. electric term Fdielectric Materials developments [ 144,1501in recent years have produced a wide range of nematic materials with high A& (positive or negative) with low voltage displays in mind. Access to their chiral analogs, through neat materials or mixtures, led to a similarly wide range of chiral nematic materials. These are now of such a high purity that many of the original conduction problems encountered with Schiffs-base materials, such as MBBA, have now disappeared. As a result of these highly significant improvements, it is generally easier to study distortions in chiral nematics in electric rather than magnetic fields. It is, however, instructive initially to study the general case where the free energy density includes a term Fconductive related to the conductivity anisotropy o(=oll-oL)as well to A& [134, 1511. Here o,, and o, are defined as relative to the local director n , as is usual. If we assume an initial planar texture, then the macroscopic conductivities will be q,and o,, with z defining the helix aixs as before and
a2]
provided the cell thickness d>p. Thus in the following analysis we are still in the coarse grain model [30]. Further, we ignore charge injection at the electrodes-simple SiO barrier layers prevent this experimentally. We first consider the case for E parallel to z, i.e., along the helix, and we assume a DC field. (Note that at high frequen-
2.4
Field-Induced Distortions in Chiral Nematics
cies 2 1 O3 Hz the dielectric phenomenon dominates in the distortions to be discussed later.) To analyze this we have to consider the Carr-Helfrich mechanism [ 124, 15215.51 due to mobile charges, as well as that due to the Helfrich distortion previously discussed for magnetic fields, i.e., layer fluctuations parallel to z , as defined in Eq. (1 1 1 ). (Note that in the de Gennes layer model [30] 8 = k, u.) Therefore we write the current J in terms of the total field Et due to the field applied externally E and that caused by the Carr-Helfrich charges, i.e.,
Jz0-E
where J z is a constant. The condition of charge conservation ( V .J = O ) leads to
ax
and E, due to the Carr-Helfrich mechanism is the lateral field component. The density of the mobile charge carriers, p,, is then 1 v.( E . E ) pc = 47t
and the vertical electric forcef, due to these carriers is then = PcE
and since fd=dTdldx
The total electric force felectricacting on the chiral nematic layers is
The elastic restoring force,fe,,,,i, is given by
and at the threshold (i.e., Eth) felectric+ felastic=O. The optimum wave vector k, is given by Eq. (120), q?=n/d, and k=2nlp, therefore
or
( 1 35)
.fc
structure distorts. This is determined from the dielectric torque acting on the structure, i.e.,
( 1 33)
For the distorted structure E the helix axis will have small components in the x direction as before, and therefore in the small deformation approximation we have
26:=o or J,=O
389
(137)
There is a further forcefd, due to changes in the dielectric tensor as the chiral nematic
and from Eq. (132) we have
Thus, as was shown for the magnetic case (see Eq. 124), the threshold field, Ep?, is proportional to ( ~ d ) - ' / For ~ . long pitch systems and thick cells, these effects are readily observed [ 156-1591 in moderate electric fields (-a few volts/micrometers) and this analysis has been extended to the general case of ac fields [ 1341 to give
390
2 Chiral Nematics: Physical Properties and Applications
1631. As o increases towards oc, then EPD diverges markedly [ 1641, and this differentiates between the two regimes (i.e., A&>O or < 0). So at low frequencies for AE < 0 the undulation modes are still observed, but at higher fields the conductivity mode domi(143) nates and again leads to a scattering texture. and On removal of the low frequency field, in thick cells, the texture relaxes back to focal (Sl - 01)(Ell + El) (144) conic with residual light-scattering proper(Sl + 01)(Ell - E l ) ties. This has been described as the storage In this regime, still with AE>O, the depenmode or memory effect in chiral nematic dence on o is relatively weak and E&, desystems [162]. If a high frequency ac field creases slowly with decreasing frequency. the dielectric torque is now applied (o>q), Above this threshold field, the periodic dorestores the nonscattering planar texture mains, to be discussed later, change [160, and, just as in smectic A materials, this ef1611 to a turbulent texture similar to the dyfect can be used in electrooptic storage namic scattering mode in apolar nematics. mode devices [ 1651, since we have a low In contrast to apolar nematics, this turbulent frequency ‘write’ and high frequency texture is stored on removal of the external ‘erase’ mechanism. field [162]. For high frequencies, at which To return to the mechanism where condielectric coupling dominates, the threshold ductivity is negligible, then dielectric field is given in a slightly different form coupling dominates the periodic domain formation (see Eq. 142). Optically, the ob(145) served texture between crossed polarizers appears as a square grid pattern [ 1571 with This has been derived [ 1341in the same way a periodicity of approximately d d . The grid as Eq. (123), and is directly equivalent to it arises from the competing mechanisms of with H replaced by E and A x by Ad4n in the elastic forces trying to maintain the the expression for the free energy density planar texture, whilst the field, through the (see Eq. 117). This derivation holds for dielectric coupling, is trying to induce a finsmall AE. For the more general case, as gerprint texture with the helix axis predomfound with current chiral nematics, i.e., not inantly in the x,y plane. The original alignbased on cholesterol compounds, the Ad47c ment direction sets x and y in this model, and term is replaced by E ~ E ~ [ ~ ~ C ( ~ + E ~the ) I‘grid . pattern’ results from the refractive In the derivation of Eqs. (141) and (142), index variations as the director follows it has been assumed that A&>O, i.e., these periodic undulations. If the pitch be! ~ ( E , ~ + E ~ ) For > E ~ A&.Within the where E”,(o) is the mean square value for the threshold field of frequency o for the conduction regime at low frequencies and zc is the dielectric relaxation time given by
2.4 Field-Induced Distortions in Chiral Nematics
limit of d
2.4.4 Electric Fields Normal to the Helix Axis The electro-hydrodynamic instabilities discussed previously are essentially independent of the sign of A E, since they are induced by the anisotropy of the conductivity. Thus applying fields perpendicular to the helix axis induces deformations dependent primarily on the sign of AD. In thick cells (d>p) the same instabilities are produced, depending on the sign of AD, in cells with E parallel or perpendicular to the helix axis. Obviously the effects for A o>O are inverted to those for A o
39 I
nar textures in which d>>p and (b) homeotropic surface alignment where flexoelectric coupling becomes important for p < A. In both cases the applied field E is parallel to n or orthogonal to the helix axis for such chiral nematic materials. For a chiral nematic with positive dielectric anisotropy and an electric field E orthogonal to the helix axis (z), then we observe a chiral nematic to unwound nematic transition for d>p. The analysis [ 132, 1391 of the unwinding mechanism is exactly the same as for the magnetic field case with the coupling - % A x ( n . H ) 2 replaced by -]/zA&(n . E ) 2 in the free energy density expression. The equilibrium condition (see Eq. 127) or Euler's equation then becomes
(z 7 )
kz2 d 2 y
-
AEE2sinycosy=0
(147)
Following the same solution route as for the magnetic field case leads to a coherence length given by
t2
and the pitch of the helix satisfies the condition of minimization of the free energy as given by
where F, (a)and F 2 ( a ) are complete elliptic integrals of the first and second kind as before (see Eqs. 129 and 130). Then as a+l, F , ( a ) + l , andF,(a)+.o, thecritical field for unwinding of the helix is given by
As discussed in Sec. 2.4.2, this helix unwinding corresponds to a decrease in the
392
2 Chiral Nematics: Physical Properties and Applications
number of regions of 180” twist or pitch walls (see Fig. 33). Thus the helix is no longer ideal and not only do the reflections occur at a longer wavelength, but higher order reflections occur and the polarization properties alter accordingly. Both second and third order reflections have been observed from such planar chiral nematic textures [168]. Further, the optical rotatory power as defined in Eq. (8) will be markedly altered to become inactive in the unwound state. Theoretically, if the influence of the cell walls is important, i.e., as in a ‘thin’ cell, then the helix unwinding is quantized and occurs in steps (of n 2dlp (0), where n is an integer) rather than as a continuous funciton with the applied field [169]. On removal of the electric field, the unwound structure relaxes to form a modulated optical structure of stripes or grids. The dynamics of the helix unwinding are described by ~1
~
A E E sintycosty=O ~ aty - k22 a2ty - ~
at
az2
4n
where tyvaries from 0 to 2 TC, with solutions [170] of the form
z, =
Yl
k22 q2 fA EE2 1 8 ~
and
where z,and z, are the response times for the field induced and relaxation processes, respectively, and q is the wave vector depending on the experimental configuration. In the denominator of Eq. (15 1) the positive sign refers to q 2 k and the negative sign to q Ik, where k =2 nlp as before. Flexoelectricity arises in liquid crystals due to their shape asymmetry, i.e., ‘pear’, ‘teardrop’, ‘banana’, etc., associated with a strong permanent dipole moment. Macro-
scopically, in the absence of a field, the system does not exhibit a bulk polarization. However, application of a field induces a polarization in the field direction, due to splay or bend deformations and the effect of the molecular shape asymmetry. This effect was recognized by Meyer [171] and is known as flexoelectricity. The most general form of the flexoelectric polarization, Pflex,is given [30] by P f l e x = e s n ( v ’ n ) + e b nx ( v x n )
(153)
where e , and ebare the splay and bend flexoelectric coefficients (which may be positive or negative), respectively. As briefly discussed in Sec. 2.2.2, this gives rise to a flexoelectric contribution to the free energy density as
(154) In chiral nematics this term is then added to the free energy density expression (Eq. 2) to determine the new equilibrium in the presence of this coupling. In the following analysis it is assumed that the dielectric anisotropic coupling is negligible. If this were not the case, then dielectric reorientation processes as described earlier, where helix unwinding takes place, could influence the electrooptic effect, although a weak A E has little significant effect and helps with the surface alignment [29, 1721. In the geometry to be considered, the chiral nematic is contained between cell walls in the x, y plane with the uniform surface alignment layers designed to align the helix axis along x with the electric field applied along z (see Fig. 35). In such a ‘sandwich’ like cell [29, 173-1751, the director spirals along the x direction in the z , y plane and is therefore described by
n = (0, sine (x,t ) cos 8 (x, t )
(155)
where we have assumed that the arbitrary term @ in Eq. (l), with transposed coordi-
2.4
Field-Induced Distortions in Chiral Nematics
393
system in an electric field then becomes
Helical axis, h, optical axis, O.A.
1 F ( E ) f= ~[ k l l ( V .n)* + k22 (n . V XII + k ) 2 2 + k33( n x V xn)2] - E . [ e , n ( V . n )+eb n x ( V x n ) ] (157) Using the rotated director coordinates (Eq. 156), and making the substitution that (sin2kx),,=(cos2kx)4'z= 1 , i.e., averaging 2 over the whole system, leads to the average free energy per unit volume, F(E),, given by
F (E)f = -1 (kl I + k33)k2 sin2$
E,=O
4
Figure 35. Representation of the director (y, z) plane and the helix axis ( x = h ) for a chiral nematic undergoing flexoelectric distortion in negative ( EO) polarity electric fields ( E ) .The z axis is out of the plane of the figure towards the observer.
+ 21 k22 k2(1- cos $)2 -
1 --(ef+%)E,ksin$ 2
(158)
To minimize F ( E ) , we take the derivative
aF(E)f =0, which leads to nates allowing for the helical geometry, is 0 or IT and O = k x . The helical wave vector along x is still given by k = 2 nlp and p is defined as positive or negative for right-handed and left-handed materials as before. The helical pitch is short, i.e., p < I , so that diffraction effects due to striped textures are not observed macroscopically (viewing along the z direction) and the material is therefore optically uniaxial along the x axis. On application of an external field E,, assuming flexoelectric coupling as the dominant mechanism, the directors rotate [ 1741 through an angle $ around z to new positions defined by n, = sin0 sin$ = sinkz sin$ n, = sin0 cos$ = sinkz cos$
n, = cos0
= cos k z
(156)
Thus the optic axis of the helix is also rotated through $. The free energy density of the
a@
Within the limit of small $, then tan$= sin$ = $, which gives
Thus the field-induced tilt is linear in E, and if (e,+e,,)>O and k > O this tilt follows the field direction and reversing the field polarity reverses the tilt angle. Therefore if such a material were placed between crossed polarizers with one polarizer aligned along +$ or -9, then maximum contrast is observed for $=22.5". For the more general case, the light transmitted through crossed polarizers is given by
394
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Chiral Nematics: Physical Properties and Applications
where Zo is the incident light intensity, p is the angle between the zero field optical axis (x) and the polarizer axis, A n is the macroscopic birefringence defined by (nFA-rzyA), where OA refers to the optical axis (i.e., parallel tox), d is the sample thickness, and A is the wavelength of light. The dynamics of this effect are described for small @ [172, 1741 by
where q is an effective viscosity for rotation of the optical axis around z , ksb=%(kll+k33),and esb=%(es+eb).Thus @ = 4, (1- exp-t’Zf)
(163)
where & is the saturation value of the rotation given by Eq. (160) for a pulsed field applied at t=O, and z, is given by Zf= q (ksb k2)-’
(164)
Thus the response time is independent of E, within the small angle limit of validity of Eq. ( 160). Experimentally, the electrooptic responseislinearupto-15’ [172,176,177], although for tilt angles greater than this the nonlinear behavior of Eq. (161) will dominate the optical response. Response times in the range of 10-100 ps have been recorded that have only a slight temperature dependence [ 1761. This can be seen from the form of Eq. (164), where it is desirable to have chiral nematic structures with a low ‘rotation’ viscosity and a high temperature independent pitch and mean splay bend elastic constant. These materials are very promising for fast electrooptic modulation [29, 1781, and in the following sections we will consider potential applications.
2.5 Applications of Chiral Nematics In the preface to the first edition of his seminal book entitled The Physics of Liquid Crystals, de Gennes wrote ‘Liquid crystals are beautiful and mysterious’ [30]. In the preface of his most comprehensive series on Liquid Crystals: Applications and Uses. Bahadur added to the de Gennes’ description the phrase ‘and extremely useful’ [ 1791. There is no liquid crystal phase to which these descriptions apply more aptly than the chiral nematic phase. The spectral reflection colors and the use of these phases in visual arts are certainly beautiful [89]. The exact solution of Maxwell’s equations for light obliquely incident on a chiral nematic film and of the Frank-Oseen and Leslie-Ericksen elastic and dynamic theories in the limit of large deformations in chiral systems, are all mysteries still to be solved. The applications of chiral nematics in twisted nematic displays [ 131, medical thermography [97], and imaging are certainly extremely useful. There are many other uses in linear and nonlinear optics, in thermal imaging, for sensors, and in novel electro- and magnetooptic devices and detectors. In the following sections we will review these applications based on the physical properties that we have already discussed. It is clear that, whilst the chiral nematic phase was the first thermotropic phase to be recognized or discovered [l-31, there are still many new inventions to be made and applications to be found [ l l , 19, 58, 147, 179-1811 for these curious chiral structures.
2.5.1 Optical: Linear and Nonlinear The optical properties of chiral nematic liquid crystals are unique in that, without ab-
2.5
sorption or energy loss, they can be used to filter or select, and reflect or transmit different polarizations and wavelengths of light spectrally from the near-ultraviolet to the near-infrared, in a range spanning -400 nm to 10 pm. In this mode they are used as passive ‘optical’ elements and if the polarization process only involves a coupling with the optical field Eoptthrough the polarizability, a, or linear susceptibility we classify this as a linear effect herein. If the coupling is with the field squared or higher, i.e., involves hyperpolarizability or n order susceptibility (n=2, 3, i.e., etc.), we will call this nonlinear. The coupling of optical effects with low frequency electric or magnetic fields will be considered in Sec. 2.5.3 as ‘active’ elements or extrinsic effects that involve director reorientation. With these definitions in mind we will outline some of the ‘passive’ or intrinsic optical applications of chiral nematics. The first application arising as a result of Eqs. (3) and (4) is in optical filters. Here the selective transmission or reflective properties are used to select a narrow spectral band [9, 181-1831, i.e., notch filters, or even a wide spectral band [ 1841,of optical frequencies. As a result of the circular polarization properties, this also leads to the production of polarizers and retardation plates [ 1811. The light reflected from a planar or Grandjean texture is either right- or left-handed circularly polarized at normal incidence. The combination of two such films of opposite handedness leads to notch and band pass filters capable of selecting bandwidths of a few nanometers or so, depending on Eqs. (3) and (4) from an unpolarized spectrum, i.e.,
xl,
x2,x3,
Thus An-0.01 and E-1.5 lead to AA 3 nm at optical wavelengths. Some
-
39s
Applications of Chiral Nematics
years ago [46] we studied a number of noncholesterol-based compounds, which verified the validity of Eq. (16.5) and demonstrated the role of Anlk in selective reflection devices. Band pass filters of this type, which required input polarizers, were described over two decades ago [ 1851, as was the ability to couple optically several of these filters to produce a multiband output [ 1811. Notch filters not requiring polarizers, but combining two films of opposite handedness, were produced [ 1851 more recently using polymeric variants [183]. A novel chiral nematic based color projection system has been demonstrated recently [ 1861, which clearly illustrates the advantages of liquid crystals. All of the functional parts, i.e., polarizers, band pass filters, and electrooptic modulators, were based on achiral or chiral nematic liquid crystals. In Fig. 36 we show the optical principles of the large aperture chiral nematic polarized light source. The conversion efficiency of the polarized color projector was close to loo%, due to the nonabsorbing nature of the chiral nematic materials used, and red-green-blue (RGB) polarized output was readily obtained from a white light source [ 1871 and used in colored twisted nematic (TN) cells. This has led to a compact efficient optical system suitable for projection TV. A different and quite remarkable application of chiral nematic wide band filters fol-
M
L
C
CNLH
QW
Figure 36. Schematic diagram of achiral nematic polarizedlight source [187], where L=lamp, M=spherical mirror, C=condenser lens, CN,, =left-handed chiral nematic filter, QW=quarter wave plate (A/4), I,=unpolarized light, I:=right-handed circularly polarized light, and Ia=polarized output light.
396
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Chiral Nematics: Physical Properties and Applications
lows from this work [ 1881. Using direactive chiral nematic low molar mass mesogens, achiral monoreactive mesogens, and UVabsorbing dyes, it has been possible to prepare polymer films with a pitch gradient from 450 nm to 750 nm, thus giving very wide band width, ‘white’ chiral nematic reflecting films [ 1891that are now being commercially exploited [ 1841 as brightness enhancers with 80% optical gain in TN and other displays. Storage films based on low molar mass organo-siloxanes exhibiting glass transitions [190-1921 have been used to prepare self-supporting films capable of withstanding typical continuum working laser intensities, as well as for use in visual arts [193]. Laser applications, for the selective reflection of light, represent a very technologically oriented use of chiral nematic liquid crystals. It has been shown that for a pulsed Nd:YAG laser cavity end mirrors may be produced which both maintain polarization on reflection and allow single longitudinal mode selection to be attained [194]. In solid state lasers, beam apodization, in which the laser beam profile is shaped to maximize gain in the active medium, is of major importance for high powered systems [ 1951. It has been shown [196] that such apodizers may be fabricated using two chiral nematic films based on cyanobiphenyl chiral mixtures in series, in separate devices, to give a linear apodizer, and in intimate chemical contact to give a circular apodizer using refractive index gradients to modify the reflection bands. The devices had damage thresholds of 5 J/cm2 for 1 ns pulses at A= 1.054 Fm with a 3 mm spot size. Chiral nematic materials have been used for over a decade in Nd:glass laser systems for the OMEGA project with beam diameters of up to 100 mm. The use of liquid crystals in this project has been reviewed [197], and it was shown that laser waveplates, circular polar-
izers, optical isolators, and notch filters, as well as the above soft apertures, could be readily used as high performance alternatives to conventional glasses, crystals, and thin films. The unique optical properties of chiral nematics were successfully used up to power densities of joules per squarecentimeter over an 18 month period without degradation problems. This is quite clearly an area where controlled organic structures, capable of being readily ‘tuned’ to the applications in mind, have a great advantage over inorganic systems that have to be prepared from large scale crystal growth facilities. Nonlinear optical effects have been predicted and demonstrated [ 198-2001 in chiral nematic materials. The n =-n condition in chiral nematics means, in this context, that the apolar order does not lend itself to second harmonic light generation (SHG), although, using external electric fields, it is possible to excite SHG through third order (THG) processes [201-2031. The electron conjugation of the noncholesterol based materials lends itself to THG applications. It is clear that with such synthesis and the degree of molecular engineering now available, this application presents an interesting growth area. The potential is there to use poled order in chiral nematics without fully unwinding the helix in a planar structure, to use the helix pitch to generate quasi-phase matching. This would of course require transverse electric fields, but the possibilities of using glass transitions to freeze the induced optical texture potentially lead to new NLO materials. Early experiments using organo-siloxane chiral nematic structures are very promising, leading to d coefficients of the order of 1-10 pmV-’ [204]. The application of chiral nematics to THG processes has long been recognized [ 198-2001. These are passive applications in which mirrorless optical bistability has been predicted [198] and the theory modi-
2.5
fied for retro-self-focusing and pinholing effects in these materials. The latter effects were also confirmed experimentally I2051 in the presence of intense optical fields. Four wave mixing of two circularly polarized counter-propagating waves has also been predicted [200] and discussed in detail [206]. This would seem to be a further potential growth area for 'frozen' optically clear, nonresonance enhanced chiral nematic phases.
2.5.2 Thermal Effects The thermo-optical properties of chiral nematics depend critically on the helix pitch, and it is the temperature variation of this, as described by Eqs. (46) and (47), that leads to many interesting applications. Initially, simple, inexpensive, digital thermometry devices were fabricated [207] using, for example, cholesterol-based materials with a fixed pitch, a narrow temperature range, and single strip elements (each with a different clearing temperature). Many early patents are described in [ 1801 and are well worth reading! These multiple legend devices have been used as room temperature thermometers, body temperature sensors [208], and for monitoring the postoperative progress of anaesthetized patients [209]. Of particular interest in temperature sensing are two features of chiral nematic phase transitions. Firstly, as a chiral nematic is cooled towards the smectic (A or C) phase, the helix pitch diverges markedly (see Eqs. 46 and 47). Since this temperature dependent reflected wavelength spectrum, or color play, can be chosen to be over the whole visible (or UV to near IR) spectrum and be as wide as 20-30"C, or even as narrow as a few degrees, it is possible to sense temperature spectrally (even by eye) to an accuracy of a few milli-Kelvin. Optical rot-
Applications of Chiral Nematics
397
atory power could similarly be used (see Eq. 8), because of thep ( t )dependency. Secondly, by using the optical texture and the quasi-permanent texture changes that occur during a heatingkooling cycle, which in turn lead to a planar to isotropic and then to a focal-conic texture sequence, it is possible to make 'maximum' thermometers [210]. The planar texture reflects light specularly, whilst the focal conic gives a scattering semi-opaque texture. The thermometer is reset by mechanical shear (i.e., weak bending of the device). A second example of this uses is in texture storage by rapid cooling into a glassy phase [21 I]. The applications of these materials and fabrication techniques have been extensively reviewed in an interesting historical sequence of decade steps [9, 11, 971. Herein we will only consider an outline of the thermal application areas and the avid reader is referred to these source references and the 700 plus references cited therein, as well as the early overviews [ 5 8 , 1801. Initially, it is useful to consider the availability of materials and preparation or fabrication techniques. Mixtures are now available [211, 2121 that cover a temperature range between circa -50°C and +150"C. Combinations of chiral nematic mesogens based on thermally stable chiral esters are used in these mixtures, and recent developments are described in the previous chapter [ 121. Essentially it is now easy to purchase A and B type mix and match materials for particular operating temperature ranges [211]. For many applications, it is the device fabrication technique that is the limiting factor rather than the availability and thermal or optical stability of the chiral nematic compounds. Chiral nematic liquid crystals are obviously fluids and in order to be used in an aligned state, they have to be contained. For good optical contrast, the background is usually black. The simplest
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2 Chiral Nematics: Physical Properties and Applications
‘encapsulation’ technique is to use glass substrates, as in TN devices or plastic laminates (see [97]). Plastic blisters have equally been used for low cost ‘throw away’ devices, as have filled fibers [2 131. By far the most popular fabrication process is to use microencapsulated chiral nematics [214, 2151, which may then be formulated in inks, sprays, and pastes. Typically, a gelatin and gum arabic combination is used to form spherulites of 1-10 pm diameter and, by careful production control, these can be optimized to a diameter of -5 pm, to reduce stray light-scattering effects from the smaller capsules. These optimized capsules are then suspended in a suitable polymer binder to be coated onto the black substrate. The optics of the confinement potentially pose two problems. Firstly, spherulitic droplets, as discussed in Sec. 2.2.1.1, will contain optical defects through disclinations or dislocations. Secondly, it is not obvious that the optimally reflecting planar texture will be obtained. This problem is accentuated if, in the preparative techniques, the chiral nematic cools from a blue phase into a supercooled blue phase or even a focal-conic texture. Although the angular viewing properties of the spherulitic droplets give fairly uniform color, the displays do not show the spectacular iridescence associated with the chiral nematic phase. Some of these problems are overcome if the droplets can be deformed into flattened oblate spheroids or discs. This helps to promote the planar texture, pins the bipolar dislocations at the edges, and leads to brighter devices. A second encapsulation technique is to use polymer dispersions [2 161,in which droplets of chiral nematics are suspended in a polymer matrix through processes such as temperature or solvent induced phase separation during the crosslinking of the polymer matrix. Essentially, any of the techniques used to produce polymer-dispersed
nematic liquid crystal devices (PDLC or NCAP) [2 17-2211 for electrooptic displays may also be used for chiral nematics. A further embodiment of encapsulation procedures, which produces very bright reflectance, is to use laminated polymer sheets in which the surfaces have been prepared to give planar alignment through microgrooved gratings [41]. These may then be used in a combination of RH and LH circularly reflecting films to enhance the narrowband or indeed broadband reflections. Within these different constructional constraints, we can now review, briefly, some of the key applications areas. Biomedical thermography [222] is used extensively as a thermal mapping technique to indicate a wide range of subcutaneous medical disorders. The first use of chiral nematics to indicate skin temperature was over 30 years ago [223]. Such devices are normally constrained to indicate temperature in the 30-33°C temperature range, over which the whole color play can be exhibited. Such films have been used to indicate breast cancer [224], for placental location [225], to identify vascular disorders [226], and for skin grafting [227]. The use of chiral nematics in such areas presents an inexpensive rapid screening technique which is only indicative, since local patient and environment conditions, e.g., room and patient temperatures and internal film pressure, may lead to some false readings. This is discussed in more detail in [97]. A particular application area of increasing importance is in the nondestructive testing [228] of inanimate objects. For example, local temperature variations may be caused by structural flaws [229,230] leading to local differences in thermal conductivity, by hot spots in electrical circuits due to short circuits (here the analysis of microchips [23 11 is particularly interesting) [232-2351, by heat transfer effects in aero-
2.5
dynamic models [236], boiler surfaces [237], cookware, etc., and by faults in spacecraft [238]. In many of these applications, it is possible to study transient changes with a resolution of lo--’ s [239]. The use of chiral nematic materials for nondestructive testing has been bibliographically reviewed in references [212,240], and [97] gives an excellent recent overview. Radiation sensing has been carried out using transducers of low thermal mass to detect infrared laser light [241, 2421, microwave leakage [2431, and ultrasound [244]. Power densities as low as 1Op3 W cm-2 have been detected [245]. In these applications, the incident radiation is converted to heat using backplanes of carbon black, gold black, or metal films. The choice of backplanes is led by the application and, in the case of long wavelengths (infrared or microwave above - 10 pm), the liquid crystal may itself have intrinsic absorption bands. A particularly useful application occurs in imaging infrared laser beam emission mode structures [246], and further such devices have been used in real time infrared holograms [237]. Similarly, microwave holograms [248] and acoustic images [244] have been formed. In the very near infrared (i.e., 680-800 nm), solid state lasers have been used for write once read many times optical data storage (WORMS) at rates of 100 MHz (i.e., 10 ns exposure times) with power densities of lop9J pm-* [249], using glassforming low molar mass chiral nematics. A further large market area for the use of chiral nematics is in decorative and novel product applications that use the visual appeal of the selective reflection properties. Mood-indicating jewellery and artifacts have been produced [250], as have images on fabrics and clothing [251, 2521. Wine bottles, coffee mugs, and drink mats are another area where chiral nematics have found amusing mass applications. Three dimen-
Applications of Chiral Nernatics
399
sional visual art effects [193] and stereoscopic images [253] have also been produced. The use of chiral nematic materials in this applications field is only limited, it appears, by the imagination of the inventor and the bounds of good taste!
2.5.3 External Electric Field Effects In the previous sections we discussed the static properites of chiral nematics, i.e., textures, optical propagation, ‘Bragg’ reflections, optical rotation, pitch variation, elastic constants, and dielectric, diamagnetic, and flexoelectric phenomena, and each and every one of these properties has been used in an electrooptic device of some form. At first sight this may seem surprising, since chiral nematics are normally associated with thermal and reflective ‘passive’ devices, as discussed in the previous two sections. However, as well shall see, the chiral nature of the phase imparts some very wide ranging electrooptic (and even magneto-optic) properties to the materials. The dynamic properties, such as viscosity, texture, and defects, are important for response times and memory effects. So the natural question is, ‘what is the main parameter that allows so many electrooptic devices to be produced?’ The answer lies in Eqs. (1) and (2). It is the pitchp, produced by different twisting powers, that leads to different effective electrooptic effects. For long pitch materials of p >> A, we have light-guiding phenomena leading to twisted nematic and supertwisted nematic (TN and STN) devices based on planar textures. For intermediate pitch lengths,p - A, we have scattering (conservative or consumptive) leading to dye guest-host (DGH) displays based on focalconic or Grandjean textures. In this regime the optical rotatory power (ORP) is anoma-
400
2
Chiral Nematics: Physical Properties and Applications
lously high, and this can also be switched in an electric field to produce devices. For very short pitch systems, p << A,we can use flexoelectric phenomena to switch 'homeotropic' chiral textures and produce optical modulators. The fabrication processes for chiral and achiral nematics are essentially the same, and this leads to interesting developments using polymer-dispersed liquid crystal (PDLC), droplet or network stabilized devices. Herein we will briefly review these different electrooptic device modes from the point of view of the chiral nature of the phase, and this will lead on to some recent innovations which appear to be quite promising for novel applications.
change. The operation of a conventional twisted nematic is shown in Fig. 37. The basic construction is to use two orthogonal planar alignment layers separated by a distance, d , so that the director, n, twists through 90" from one surface to the other. The twisted birefringent structure rotates the plane of polarization provided, according to the Mauguin limit dAn > 21
The threshold voltage, V,, (TN), for the transition from twisted structure to homeotropic alignment, above which polarization guiding is lost, is given [26] by &h
(TN)
2.5.3.1 Long Pitch Systems ( p >> A) The majority of current commercial liquid crystal displays are based on the twisted nematic electrooptic effect using active matrices to give, for example, complex computer lap-top screens [13]. It is often overlooked that these displays are based on long pitch chiral nematic materials to remove socalled reverse twist, and the original papers [254, 2551 referred to the effect as a positive planar cholesteric to nematic phase
I
White
( 166)
=";r'
1!kl 1 -k 41 ( k 3 3 - 2k22 EO
AE
4-
2k22 d / p
(167)
The rise, z,,and decay, z, times in response to a pulsed AC field are given by
z,=
17 d2 ~0 AE(V2-
I White Light I
I
Polarisers
1 Glass Panels Polarisers
U
Figure 37. Schematic diagram of a twisted nematic electrooptic cell for (a) zero voltage and (b) a voltage above threshold, V,,(TN). Note that some chiral nematic mesogens remain anchored in a planar arrangement on the alignment surface, which then provides the coupling for the field-off decay back to the twisted structure. The weak chiral nature prevents back flow.
2.5
where q is a twist viscosity and the other terms have their usual meaning (see Sec. 2.2). Thus the finite pitch, p , of the chiral nematic phase influences the electrooptic parameter through the 2 k,,dlp term. Normally only a few weight percent of chiral dopant is added to minimize this term, whilst at the same time eliminating reverse twist. The operating parameters, the role of surface pretilt, the viewing angle, the threshold curves, multiplexability, etc., are discussed in reference [13]. In a variant of this display, the twist is increased from 90" to 180"-270", i.e., as in the STN device, to sharpen the threshold intensity-voltage curves and thereby improve multiplexability. The STN, in comparison with the TN device, has better contrast and viewing angles, but slower response times and poorer grey scale. Here again the important influence of the chiral pitch can be seen from the threshold voltage V,, (STN)
where $ is the twist angle between the two alignment layers [N. B. This reduces to Eq. (167) for $=d2.]. In the STN device the chiral compound has to be twisting sufficiently to ensure 7t < @ < ~ 1 2depending , on the shape of the theshold curve required [257]. Here clearly the threshold voltage will be greater, because of the 4 k,, dlp and $ terms. The operating parameters of STN devices are discussed in detail in references [13, 2571. In a further example [25] of long pitch 90" twisted or chiral nematic displays, dyes have been added to sharpen the threshold curve of the planar Heilmeier display [258] with the advantage over conventional TN cells of requiring only one polarizer. This improves the optical throughput,
Applications of Chiral Nematics
40 1
but has also reduced contrast. Positive {J or negative ({,> dichroism (where 5 is the absorption coefficient parallel or perpendicular to n) may be used to give negative [259] or positive [260-2631 (i.e., dark symbols on a light background) optical contrast. In these devices the input polarization is the same as the alignment direction at the 'input' planar alignment layer.
2.5.3.2 Intermediate Pitch Length Systems ( p -A)
-
Intermediate pitch systems ( p A) give rise to focal-conic and planar or Grandjean textures (see Sec. 2.2.1.1), and these may be deformed in electric of magnetic fields (see Sec. 2.4). The earliest reports of electric field induced reorientation leading to electrooptic effcts are reported for scattering or focal-conic textures in [136, 1381 and for planar textures in [ 141,2641. Similar effects in magnetic fields were reported in [129, 137, 1401. The different optical effects observed at the time are accounted for by the direction of the applied field relative to the helix axis (see Sec. 2.4). As was discussed in Sec. 2.2.1.2,, for a chiral nematic phase exhibiting selective reflection, the ORD becomes anomalously large and therefore, if the helix pitch can be unwound or deformed in an electric field, the circular polarization and ORD should equally change. The latter was clearly observed and studied in some depth in [265]. These early observations set the scene for considering electrooptic devices in intermediate pitch ( p 2) chiral nematics. The focal-conic texture is inherently light-scattering in the forward direction [266] and this in itself does not provide sufficient optical contrast between 'off' and 'on' states when switched to the homeotropic texture, without the use of external polarizers. The planar to homeotropic field in-
-
402
2 Chiral Nematics: Physical Properties and Applications
Sec. 2.4.4) unwinds the helix to give a homeotropic state. The axis of the dye is then in the field direction and the device becomes nonabsorbing, assuming positively dichroic dyes (see Fig. 38a). In a second variant of this device, planar orientation is used to spiral the axis of the dye, following n , in the plane of the device and for zero fields this leads to a colored absorbing state. For such systems, where the pitch is too short to give light polarization guiding (see the Mauguin limit, Eq. (166)), the polarization becomes elliptical and this is readily absorbed by the dye (Fig. 38 b). For a high enough field the transition to homeotropic is again induced, and this leads to a nonabsorbing (or weakly absorbing, due to limiting 6)or clear state. The threshold voltage for helix unwinding is given by
duced transition does provide contrast with a suitable black background, but on field removal tends to relax back to a focal-conic rather than a planar texture in a fairly slow dynamic process. There have, however, been recent developments in which these effects have been utilized or improved upon to produce interesting displays. The first was the White-Taylor device [267] using anisotropic dyes and either homeotropic or planar surface alignment. The second is in using polymer-stabilized chiral nematic films to exploit the bistable nature of the planar and focal-conic textures [268]. In the White-Taylor device the chiral nematic ( p A) is doped with an anisotropic dichroic dye. With homeotropic boundary conditions and low voltages, the focal-conic texture becomes axially aligned in the plane of the device. The dye spirals with the director and the random directions of the helix axis in the plane of the device ensure that unpolarized light is absorbed uniformly in this state. Application of a high field (see
-
Input White Light c_ ____ j---____ mPolariser Glass Substrate .Transparent Electrode Homeotropic Alignment Layer Chiral Nematic (Focal Conic)
-
and for d - 10 pm and p 3 pm gives typical threshold voltages (to complete the un-
Input White Light
Input White Light
-_-I
output Coloured Light
Glass Substrate Transparent Electrode Planar Alignment Layr Chiral Nematic (Grandjean) outout Coloured Light
Output White Light
0 : LiquidCrystal With Little Attenuation Molecule
I (a) Unenergized State Focal Conic
(b) Unenergized State Grandjean
: DyeMolecule
(c) Energized State (Homeotropic)
Figure 38. Schematic operation of the White-Taylor dye guest-host chiral nematic electrooptic cell. In (a) for zero applied field the axis of each focal-conic domain is random in the x, y plane, as therefore is the dye, using homeotropic surface alignment. In (b) the texture is planar for the zero field state and therefore the dye spirals around the z direction. In (c) the focal conic (a) or planar (b) transition to homeotropic nematic has taken place above the threshold voltage V,, (WT). The black ellipses represent the dyes in the chiral nematic matrix.
2.5
winding) of the order of 1OV. These devices are polarizer-free and have better viewing angles than TN devices, although V,, (TN) < V,, (WT) (see Eq. 170). They can also be matrix-addressed to a limited extent, and the performance of the two modes has been compared in references [269]. Negamay also be used to protive dyes duce reverse contrast. It is not, however, possible to decrease the pitch ad infinitum in these devices because of the dependence of V,,(WT) on dlp. A recent innovation in the use of chiral nematic phases has been to stabilize the focal-conic or planar textures in situ with a polymer network [268]. The helix pitch may be chosen to give bright specular reflection, and that can then be switched into a focalconic (forward-scattering) texture. Using a black background, this has led to bright, high resolution colored images with high contrast and wide viewing angles, and without the need for backlights. Devices have been fabricated using flexible polymer substrates to make lightweight displays with a 320 x 320 pixel writable-erasable screen. Applications are foreseen in electronic publishing and, using a stylus, it is possible to hand write erasable information on these displays. As with the White-Taylor device, dyes can be incorporated into the polymerstabilized chiral nematic device [270] to improve contrast between the on and off states, and it is anticipated that such dyed PDN*LC devices will find use in projection displays. The use of flexible substrates without backlighting, combined with the specular reflection properties (in unpolarized light) of chiral nematics that may be electrically switched from one bistable state to another, seems to hold great promise in the search for the Holy Grail of an electronic newspaper (2711. In the latter reference, reflective chiral nematic liquid crystals were used to produce a 200 dpi full page, passive matrix,
(tl> t,,)
Applications of Chiral Nematics
403
bistable glass display with a 2240 row by 1728 column resolution. Whilst these are slow update displays, taking several seconds, they would seem ideally suited to this application. A further interesting use of the focal-conic to homeotropic texture transition is in infrared modulation [272]. Here it was found possible to modulate infrared light at A= 8 - 12 pm with a maximum transmission of 8796, a contrast of 93%, and turn on and off times of 1 ms and 125 ms, respectively. A further window examined was 3-5 pm, and this work suggests that other chiral nematic electrooptic effects could be exploited in the near infrared. In communications technology a 2x2 optical switch for fiberoptics has been developed [273] using a chiral nematic film and two switchable nematic waveplates. It has been demonstrated that this is suitable for LED or laser sources. The device worked at 1.3 18 pm and had switching times of 40 ms with -26 dB crosstalk between unselected fibers. There will clearly be further advances in this use of the unique optical properites of chiral nematics.
2.5.3.3 Short Pitch Systems ( p << 2) Short pitch chiral nematics in a planar alignment would, following Eq. (167), have very high threshold voltages compared with TN, STN, or WT displays and further, the switching would be from an isotropic optical texture with a tightly spiraling director to a homeotropic texture. Thus, unless a dye is included, there would be no optical contrast. If an aligned focal-conic texture is produced, however, in which the optical axis of the helix defines a macroscopic birefringent texture, then such a system could be switched to the homeotropic state through dielectric coupling, or tilted via flexoelectric coupling. The threshold voltage for the former effect would still be relatively high,
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and it is the flexoelectric effect that interests us here. Flexoelectric effects were observed in chiral nematic systems some 10 years age [28], and these have recently been reexamined theoretically [29, 1771 and experimentally [29, 1761to show that the flexoelectric tilt angle is linear in the applied field, independent of temperature, and gives -100 ps response times. This, therefore, has great potential for moderately fast electrooptic linear modulators. Tilt angles of y=22.5", i.e., optimum switching between crossed polarizers on field reversal, were readily obtained at 33°C for fields of 80 V p-' in 2 pm thick cells. For modulators, the optical signal needs to be restricted to angles 5 15" to ensure a linear response between crossed polarizers, i.e., for E150 V pm-'. The materials used in these studies were not optimized for flexoelectric responses, and in recent further studies [274] better materials in a polymer-dispersed geometry have been used to give tilt angles of 15" at 40 V pm-' with response times of -120 ps at 25 "C. On removal of the field, the polymer network ensured that the texture returned to the uniform uniaxial helix alignment of the off state, rather than a focal-conic texture. It is interesting that for the polymer-stabilized geometry, chiral nematics that exhibit dielectric rather than flexoelectric coupling for such short pitch systems ( p - 0 . 3 pms) give effective refractive index contol useful for phase, as well as intensity, modulators. Thus flexoelectric and related phenomena in controlled short pitch chiral nematic structures are clearly areas of great potential for holographic and modulation devices [178).
2.6 Conclusions and the Future The chiral nematic (or cholesteric) was the first of the recognized thermotropic liquid crystalline phases, and it has led to over a century of intensive study and research. As we have tried to outline in this chapter, the understanding of optical properties, textures, defects, and elastic and dynamic properties have all stemmed from the pioneering work carried out on chiral (and achiral) nematic phases. This has led to significant advances in the understanding of electro-magnetic properties, which in turn has led to a number of modern electro-, magneto-, and opto-optic devices. The twisted nematic is just one example amongst the more normally recognized thermal applications of chiral nematics. With the success of TN and STN devices in complex displays, it might be thought that everything there was to be done had been done with chiral nematics. Manifestly this is not true. The recent papers on 'active' flexoelectric and 'passive' optical components and devices adequately demonstrate that there is still much to be done. It is only now that we are really beginning to understand the complexity of chirality in liquid crystals. Mother Nature, as with the reflections from the beetle Plusoitis resplendens, got there before we did. To quote [27], we have a look 'back to the future' for our new inventions and exploitations. Acknowledgements The author thanks his wife Janet for sacrificing her summer holiday to this contribution, his son Marcus for producing many of the figures and always having the appropriate reflective comment, his research group for supporting his absence (probably with glee), and Leona Hope for interpreting the many squiggles meant to be super or subscripts, for preparing such a perfect manuscript (the errors are all down to the author), and devotion well beyond the call of duty. Finally, the author would like to thank George Gray and Jorn Ritterbusch for all their helpful guidance, support, and perseverence.
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[212] M. Parsley, The Hallcrest Handbook of Thermochromic Liquid Crystal Technology, Hallcrest Product and Information, Illinois, U.S.A. 1991. [213] N. Oguchi, I. Ikami, A. Hhe, Jpn. Patent 7 435 114,1970. [214] J. E. Vandegaer, Microencapsulation - Processes and Applications, Plenum, New York 1974. [215] T. L. Hodson, J. V. Cartmell, D. Churchill, J. W. Jones, U. S. Patent 3 585 381,1971. [216] EuropeanPatent, 1 161039,1968and3872050, 1973. [217] J. L. Fergason,SIDDig. Tech. Pap. 1985,16,68. [218] J. W. Doane, N. A. Vaz, B.-G. Wu, S. Zumer, Appl. Phys. Lett. 1986, 48, 269. [219] P. S. Drzaic, J. Appl. Phys. 1986, 60, 2142. [220] N. A. Vaz, G. W. Smith, G. P. Montgomery, Mol. Cryst. Liq. Cryst. 1987, 146, 1 and 17. [221] J. L. West, Mol. Cryst. Liq. Cryst. 1988, 157, 427. [222] I. Nyirjesy, M. R. Abernathy, F. S. Billingsley, P. Bruns, J. Reproductive Med. 1977, 18, 165. [223] J. T. Crissey, E. Gordy, J. L. Fergason, R. B. Lyman, J. Invest. Dermatol. 1964,43, 89. [224] M. Gautherie, C. M. Gros, Cancer 1980, 45, 51. [225] R. C. Margolis, L. S . Shaffer, J. Am. Obstetrics Assn. 1974, 73, 910. [226] C. Ambrosie, C. Bourcle, Gaz. Med. France 1975, 82, 628. [227] B. Y. Lee, S. S. Trainov, J. L. Madden, Arch. Phys. Med. Rehab. 1973,54, 123. [228] G. D. Dixon, Muter: Eval. 1977,35, 51. [229] W. E. Woodmansee, H. L. Southworth, Muter: Eval. 1968,26, 149. [230] H. E. Steinicke, D. D. Patent Appls. 224670A, 1984, and 236 175A, 1985. [231] M. Karner, U. Schaper, Jpn. J. Appl. Phys. 1994,33,6501. [232] P. L. Garbarino, R. D. Sandison, J. Electrochem. SOC.1973,120,834. [233] L. C. Mizell, AlAA Rep. 1971, A7-40738. [234] P. L. Garbarino, R. D. Sandison, IBM Tech. Discl. Bull. 1972, 15, 1738. [235] H. E. Shaw, U. S. Patent 3590371,1971. [236] P. Ireland, T. V. Jones, AGARD Con$ Proc. 1984, CP390. [237] A. A. Watwe, D. K. Hollingsworth, Experimental Thermal Fluid Sci. 1994, 9, 22. [238] P. G. Grodzka, T. C. Bannister, Science 1975, 187, 165. [239] K. W. Vantreuren, Z. Wang, P. R. Ireland, T. V. Jones, J. Turbomachinery Trans. ASME 1994, 116, 369. [240] M. A. Wall, UKAtom Energy Research Establishment, Bibliography, AERE-Bib, 1972,18 1. [241] R. D. Ennulat, J. L. Fergason, Mol. Cryst. Liq. Cryst. 1971, 13, 149.
2.7 [242] S. A. Hamdo, Electr: Eng. 1974, 46, 20. [2431 A. V. Tolmachev, E. Y. Govorun, V. M. Kuzkichev, Pis’ma Zh. Esper. Teoret. Fiz. 1972, 63, 583. [244] K. Hiroshima, H. Shimizu, Jpn. J . Appl. Phys. 1977,16, 1889. [245] R. G. Pothier, U. S. Patent 3713 156, 1970. [246] J. P. Leslier, M. C . Sexton, K. Vernon, J. Phys. D 1972, 5, 1212. [247] W. A. Simpson, W. E. Deeds,Appl. Opt. 1970, 9, 499. [248] K. Jizuka, Electron. Lett. 1960, 5, 26. [249] J. Pinsle, C. Brauchle, F. H. Kreuzer, J. Mol. Electron. 1987, 3 , 9. [2.50] B. G. James. U. S . Patent 3 802945, 1974. 12.511 A. Mace, J. Bersan, J. Luby, Fr. Patent 2461 008,1981. [252] K. Kurosawa, Jpn. Patent 81 118859, 1981. [253] D. Makow, Mol. Cryst. Liq. Cryst. 1983, 99, 117. [254] M. Schadt, W. Helfrich,Appl. Phys. Lett. 1971, 18, 127. [255] E. Jakeman, E. P. Raynes, Phys. Lett. 1972, 39A, 69. [2561 E. P. Raynes, Rev. Phys. Appl. 1975, 10, 117. [257] T. Scheffer, J. Nehring in Liquid Crystals: Applications and Uses, Vols. 1-111 (Ed.: B. Bahadur), World Scientific, Singapore 1990, p. 231. [ 2 5 8 ] G. Heilmeier, A. L. Zanoni, Appl. Phys. Lett. 1968, 13, 91. [2591 T. Uchida, H. Seki, C. Shishido, M. Wada, Mol. Cryst. Liq. Cryst. 1979, 54, 16 1.
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[260] G. Pelzl, H. Schubert, H. Zaschke, D. Demus, Kristull. Technik 1979, 14, 8 17. 12611 D. Demus, B. Kruecke, F. Kuschel, H. U. Nothnick, G. Pelzl, H. Zasche, Mid. Cryst. Liq. Cr-yst. 1979, 56, 1 15. [262] M. Schadt, J. Chem. Phys. 1979, 71, 2336. [263] T. Uchida. M. Wada, Mol. Cryst. Liq. Cryst. 1981, 63, 19. [264] W. J . Harper, Mol. Cryst. 1966, 1, 325. [265] R. Bartolino. F. Simoni, Opricu Acta 1980,27, 1179.
[266] J. W. Doane, W. D. S . John in Proc. SID: Asia Display 1995, p. 47. [267] D. L. White, G. Taylor,J. Appl. Phys. 1974,45, 47 18. 12681 J. L. West, M. Rouberoi, J. J. Franci, Y. Li, J. W. Doane. M. Pfeiffer in Proc. SID: Asia Display 1995, p. 55, and references therein. [269] T. J. Scheffer, Phil. Trans. R. Soc. London 1983, A309, 189. [270] D. K. Yang, Z. M. Zhu, C. Boulic in Proc. SID: Asia Display 1995, p. 5 1. 12711 Z. Yaniv, C. Catchpole, M. H. Lu, R. Bunz, E. Lueder, M. Pfeiffer, D. Y. Yang, J. W. Doane in Proc. SID: Asia Display 1995, p. 113. [272] J. G. Pasko, J. Tracy, W. Elser. Proc. SPIE 1979, 202. 82. [273] N. K. Shankar. J. A. Morris, C. P. Yakymyshyn, C. C. Pollock, IEEE Photonics Technol. Lett. 1990, 2, 147. [274] P. Rudequist, L. Komitov, S . T. Lagerwall, Liq. Cryst. 1997, in press. [275] R. Zemeckis, B. Gale, ‘Title of film’ 1985.
Handbook ofLiquid Crystals D. Demus, J. Goodby, G. W. Gray, H.-W. Spiess, V. Vill Copyright 0WILEY-VCH Verlag GmbH. 1998
Chapter V Non-Chiral Smectic Liquid Crystals
Synthesis of Non-Chiral Smectic Liquid Crystals John W Goodby
1.1 Introduction The synthesis of nonchiral smectic liquid crystals is a broad topic for discussion, however, it can be divided into subsections in two different ways. For example, smectic systems can be split into metallomesogens and nonmetallomesogens, alternatively, they can be divided into materials for (1) mesophase structure elucidation and classification [I], (2) property-structure correlations [2]; and ( 3 ) host systems for ferroelectric and antiferroelectric mixtures. In the following sections template structures used for the synthesis of smectic materials will be described, followed by discussions of the syntheses of materials that have extensive histories in the elucidation of smectic phase structures, and finally of the syntheses of smectogens that are useful in applications.
1.2 Template Structures for the Synthesis of Smectogens Smectic liquid crystal phases can be divided into phases that have structures where the long axes of the molecules are either inclined or orthogonal to the layer planes. In
addition, the molecules can have long range positional order as in crystal smectic phases (i.e., B, E, J, G, H, and K) or short range order as in smectic liquid crystal phases (i.e., SmA, SmB, SmC, SmI, and SmF) (see Chap. I of this Volume). Whether a material exhibits tilted phases or not, or long range positional order or not, has been found to be dependent to a large degree on the nature of the functional groups, the lengths of the peripheral aliphatic chains, and the length and breadth of the central rigid core region of the molecular structure of a smectogen. At a crude level the type of smectic mesophase formed by a smectogen depends on molecular shape, with the following subunits being important: (1) the rigid core, (2) polar functional groups, (3) laterally appended groups, and (4) peripheral substituents and chains. From property-structure correlations developed over many years of studying the relationships between molecular structure and mesophase formation, some idealized molecular shapes that support smectic phase generation have been identified [ 3 ] . A pictorial representation of a variety of molecular templates that have been found in smectic systems is shown in Fig. I . In this figure, the mesogenic core unit is depicted as an ellipsoid, but, it may con-
412
1
Synthesis of Non-Chiral Smectic Liquid Crystals
Cslamilic
Mesogenlc Pair
swallow-ta,led
Trtmer
Poly-calenar
LaterallyconnectedDtmer
Banana-shaped
Siamese Twin
Pyramidal or Bowl-shaped Core
~”
Telramer wilh Spherical Core
Figure 1. Some template structures for smectic liquid crystals.
Dendrimer
tain a number of carbocyclic, aromatic or heterocyclic rings and accompanying linking groups and lateral functional groups. The peripheral groups, which are essentially aliphatic chains are shown as ‘wiggly’ lines. The immediate impression from Fig. 1 is that smectogens do not necessarily have molecular shapes that are confined to being rod- or lath-like or calamitic! The molecules can have bent shapes, be bowlic or pyramidal [4], X- or cross-shaped [ 5 ] , or even spherical [6]. Essentially, examination of the varieties of molecular templates that support smectic phase formation indicates that molecules will find a number of ways,
through molecular deformation or by sharing space, to form lamellar structures. For example, consider the extreme case of the spherical dendrimers [ 7 ] , see Fig. 1. The mesogenic units in the periphery of the dendrimer will group together to give a quasirodlike molecular shape which will be more likely to stabilize smectic phase formation. Thus, the molecular architecture deforms in order to accommodate smectic phase formation, see Fig. 2. For compounds with less flexible structures, smectic mesophases can be formed if the molecules are able to share space, thereby reducing the void volume in the structure of the mesophase [8]. Typical
1.2 Template Structures for the Synthesis of Smectogens
413
Figure 3. Cross-shaped smectogens
Figure 2. An example of a dendritic smectogen.
examples of compounds with cross-shaped molecular structures that support smectic mesophase formation are metallomesogens, such as the asymmetrically substituted copper(I1) Pdiketonate complexes [ 5 ] (see Fig. 3). In the structure of the mesophase formed by these types of molecules, the shorter arms of the cross-shaped systems are thought to overlap, thereby allowing the molecules to pack tightly together. These systems have been shown to be optically uniaxial, which suggests that even if the local ordering is biaxial, any biaxiality does not persist over large distances. Given that there is a very wide variety of template structures that will support smectic phase formation, the object of this review
cannot be to discuss the syntheses of examples of compounds with molecular structures corresponding to each template. Instead, it is probably more important, and intuitive, to focus on the more significant types of smectic material. These materials tend to be drawn from the more traditional/conventional lath-like structural templates for smectogens, where the template incorporates a simple linear core that has one or two peripheral groups associated with it as shown at the top left of Fig. 1 . More detail concerning the molecular architecture of this simple template can be incorporated as shown in Fig. 4. In this template, the core structure is further divided to show the linking groups, terminal substituents, polar/apolar groups positioned at the termini of the core, and lateral groups attached to the core. Architecture (i) in Fig. 4 tends to be the template that will give the largest diversity of mesophase type in comparison to architecture (ii). For example system (i)
414
Synthesis of Non-Chiral Smectic Liquid Crystals
1
%(A)-
W
M Z is a linking group 'Rand 'R are aliphatic chains X and Y are lateral substiuenls A and B are usually polar linking groups W is alerminal group
(ii)
Examples:
2 = CHzCH,, (CH& CH=CH, C S , COO, COS, CH=CHCOO. N=N, CH=N, CH,O, COCH,, CONH, or nothing elc X and Y = H, CHs,C2H,. C.HPn+,. F, CI. Br, I,CF3,CCI,, CN. COOH. NO,, NH,, N(CH&. OH, or several of these
A and B = CH,, 0.S, Se, NH, NCH, elc W = H. C H , OCH,. CF3, C,Fs. CN. F, CI. Br, I. NO,, N(CHd,, COOH, OH etc Strunures of Some Common Core Ring Components
Figure 4. Architectural components of smectogens.
with two peripheral aliphatic chains will be more likely to support the formation of tilted mesophases in comparison to structure (ii). Thus, it is common when the two peripheral aliphatic chains are extended in length that there will be a cross-over from orthogonal phase to tilted mesophase formation. Only under specific architectural conditions will a system with a single aliphatic chain exhibit tilted mesophases [9]. For instance, Fig. 5 shows two cyano-terminated phenyl benzoates, when the polarity of the cyano group is reduced by the conjugation of the carbonyl function of the ester linking group, then tilted smectic C phases are seen, but where the polarity is reinforced by conjugation to the ether oxygen of the ester, only orthogonal phases are found. This result is relatively general and spans a wide
-
Cr79.SmA 79 N 86.5.
I
- -
Cr 67 (.SmC 33) SmA 98 I
Figure 5. Two cyano terminated phenyl benzoates.
variety of materials where the melting points and recrystallization temperatures are much lower than those shown in the example.
1.2.1 Terminal Aliphatic Chains For systems that have two terminal aliphatic chains that can be independently varied in length, tilted phases tend to occur when the two lengths are similar to one another. At short chain lengths, usually orthogonal phases such as smectic B, crystal B, and crystal E occur. In some cases the upper temperature transitions to the smectic A and smectic B phases can occur so close together that a transition from the nematic phase or the liquid phase to the smectic B phase appears to occur only through a transient smectic A phase. This transition is sometimes called a liquid or nematic to SmAB transition [lo] (Fig. 6 ) . As the chain lengths of both peripheral aliphatic groups are increased, tilted smec-
1.2 Template Structures for the Synthesis of Smectogens
-
SmA 106) .N 127 I
Cr 110
-
Cr 115 SmA 126 * I
C,oHaO
Cr 121 (. N 114) * I
Figure 6. Effect of terminal chain length on smectic phase formation.
tic C phases are usually observed first, followed by smectics I and F, underlying these phases there is the possibility of forming more ordered modifications such as J, G, H, or K. At very long chain lengths, the tilted phases sometimes, but not always, disappear to give systems that just exhibit smectic A phases [ I 11. Thus, if we were to plot the incidence of phase type, rather than transition temperatures, as a function of peripheral chain length for system (i) (i.e., varying R' and R2 in length) as shown in Fig. 4, then a graph would obtained that is similar to the one shown in Fig. 6. It should be emphasized that this figure is an idealized one and reflects data taken for a wide number of investigations, however, by no means do all material groups fit this picture; there are in fact many subtle variations. For systems where there is only one terminal alipahtic chain, typically no tilted smectic phases are observed, and orthogonal phases predominate. The smectic A phase is the commonest modification ob-
415
-
\ /
Figure 7. Three structures for comparison that have only one terminal chain.
served, followed by the smectic B, crystal B and E phases. Figure 7 shows a comparison of three materials that have only one terminal aliphatic chain, but where the terminal ring of the core has the possibility of the incorporation of a heteroatom (nitrogen) [ 121. It can be seen from this figure that the nematic phase still tends to dominate over smectic phases, and that the smectic phases observed are all smectic A in type.
1.2.2 Polar Groups Situated at the End of the Core The discussion above applies to most systems irrespective of core types, linking groups, and lateral groups, but not polar groups positioned at the termini of the core structures. The terminal core groups A and B (shown in Fig. 4 (i)) can be very important in determining whether or not tilted mesophases are formed. It was found over a large number of studies that when functional groups A and B are polar (but not hydrogen bonding) a higher incidence of tilted smectic phases is observed [ 131. Figure 8 demonstrates this effect for a set of substituted phenyl biphenyl carboxylates [ 141. In this family the oxygen atoms at the termini of the core are systematically removed. With both oxygen atoms present the mate-
416
1 Synthesis of Non-Chiral Smectic Liquid Crystals
Cr 110 * SmB 116. SmC 165 * SmA 200 - 1
Cr 110 * SmB 110.5 * SmC 132.5 SmA 184 * I
Cr98 * SmB 112 * SmC 125 *SmA 171 * N 173 * I
Figure 8. Effect of dipolar groups at the ends of the core.
rial exhibits a tilted smectic C phase, as the oxygen atoms are removed the temperature range and the upper transition temperature of the smectic C phase fall, and when there are no ether links present the tilted smectic C phase disappears. This result is typical of many material systems resulting in the experimental observations being made the basis for McMillan's theoretical model of the smectic C phase [ 151. In this model McMillan termed the dipoles associated
with the groups at the termini of the core as 'out-board terminal dipoles'. The coupling of the terminal outboard dipoles at the smectic A to smectic C phase transition was assumed to generate a torque which resulted in the molecules being tilted over in their layers, as shown in Fig. 9. However, as with most studies concerning the relationship between molecular structure and the types of smectic liquid crystal phase observed, this is not the whole story. If methyl branching points are incorporated into the terminal aliphatic chains without the inclusion of out-board dipolar groups, then tilted smectic phases can be returned, as shown in Fig. 10 [16]. This demonstrates the pronounced effects that can be produced from small changes in molecular structure and which affect of the packing of the molecules together. Thus, other theoreticians, most notably Wulf [17], attempted to relate the tilting of the molecules to the way in which the molecules pack laterally together side by side. Examination of the molecular shapes of compounds that form tilted phases showed most had zigzag shapes, and it was the way in which the bends in the structures of adjacent molecules nested together that produced the overall tilted structure (later suggested by X-ray diffraction) [IS]. Wulf's
Figure 9. McMillan model for the smectic C phase.
1.2 Template Structures for the Synthesis of Smectogens
tilted smectic C phase correctly reflected experimental observations: as the peripheral chain lengths are increased the molecular shape becomes zigzag thereby injecting and stabilizing the smectic C phase, at longer chain lengths the zigzag shape is less prominent and so the smectic C phase becomes less stable and disappears (Fig. 11).
-
Cr 102 (.G 67 * SrnB 98) SmA 153 - 1
1.2.3 Functional Groups that Terminate the Core Structure
Cr86 (.SrnC 78.1) * SrnA 96.1 * N 1185.1
Figure 10. Effect of branching in the terminal aliphatic chains.
model also showed that as the aliphatic chains are lengthened the molecular structure becomes increasingly zigzag shaped, however, as the aliphatic chain lengths are increased further the zigzag shape becomes less prominent. Thus, Wulf’s model of the
Zigzag shaped molecules pack together to form a tilted structure
This subsection applies specifically to materials with template structures such as the one shown in Fig. 4 (ii). Here the template has only one terminal chain attached to one end of the core and at the other end of the core is a functional group that can be either polar or apolar. Generally, terminal groups that are polar and conjugated to the aromatic core tend to form nematic phases, whereas nonpolar unconjugated groups lean towards forming smectic A and B phases [ 191. Figure 12 shows a property-structure correlation between mesophase type formed and the substituent in the 4-substitut-
ed(X)phenyl4’-n-octyloxybiphenyl-4-carboxylates [14]. The substituent was varied from being polar to apolar and its length was altered from hydro to fluoro to butyloxy. Tilted phases only occur when the substituent exceeds a certain length or size (equiv-
X
Mesophases Observed
H CI Br I
SmA. SrnB SmA, SmB SmA, SmB SmA. SmB SmA. SmB
CHO
K?
SNm!d,SmB N
COCH, COOC,H, C,H, C(CH,), OC,H,
SrnA, SmB
F
Smectic A
417
Smectic C
Figure 11. Wulf model of the smectic C phase.
SmA SmB SmA.SmB SmA. SmC SmA, SmC SmB
Figure 12. Phase types exhibited as a function of end group.
418
1 Synthesis of Non-Chiral Smectic Liquid Crystals
alent to butyloxy in this case). Nematic phaes are exhibited for the polar cyano and nitro substituents. A systematic study [14] of the variation in transition temperature with phase type for the 4-halogenophenyl 4’-n-octyloxybiphenyl-4-carboxylates is shown in Fig. 13. This particular family of materials have smectic A phases that exist over very long temperature ranges. Smectic B phases are found to occur but they are all monotropic. Interestingly, when the ester group is replaced by
X F CI Br I
Cr
* *
SmB 119 124 134 152
(. (* (. (*
I
SmA 110) 111) 130) 144)
* *
.
200 226 232 231
... .
Figure 13. Transition temperatures as a function of halogeno end group.
a Schiff’s base linkage crystal E phases appear and the smectic B phase is replaced by a crystal B phase. For polar terminal groups, such as the cyano group, the structure of the resulting smectic A phase differs from that of the lesspolar systems. In the less-polar systems the layer spacing in the smectic A phase is approximately equal to the molecular length, whereas for polar systems, and cyano systems in particular, the layer spacing is larger. Generally, for polar groups the layer spacing is approximately 1.4 times the molecular length, thereby generating a bilayer structure [20]. This increase in layer spacing is due to the formation of molecular pairs caused by a quadrupolar coupling between the longitudinal dipoles, as shown in Fig. 14.
1.2.4 Core Ring Structures It is generally understood that smectic liquid crystals are more likely to be formed in systems where the central core region has aromatic or heteroaromatic ring structures. Alicyclic ring systems, conversely, tend to disfavour smectic phase formation, see Fig. 15 for relative ordering, and in particular, they tend to depress tilted phases over orthogonal phases. For example, early work in the search for nematic materials for display devices resulted in development of the 4-substituted-phenyl benzoate unit as a suitable core for imparting mesogenic properties to a material
Decreasingability to form smectlc phases increasingpreferencelor orthogonal phases
Figure 14. Effect of cyano end groups on molecular packing.
Figure 15. Relative ordering of alicyclic ring systems.
1.2 Template Structures for the Synthesis of Smectogens
and for use in modifications to physical properties (most notably elastic constants). Extensions to the work on the 4-substituted-phenyl benzoate system included the replacement of either the phenyl or benzoate unit with the trans- 1,4-disubstituted cyclohexyl moiety or the corresponding bicyclo[2.2.2]octane unit. Investigations of transition temperatures in pure materials and in binary phase diagrams show that the alicyclic systems are prone to raising clearing temperatures while at the same time suppressing smectic phase formation. Figure 16 shows a comparison of various esters where one of the rings of the phenyl benzoate unit has been replaced by an alicyclic ring [21]. Although smectic phases are rarely seen in such systems, it still can be seen how the
Cr34 8 ("25 9) *
Cr42.8- N 51.7
Cr36
I
*I
SmA 29) * N 48 *
clearing temperature is enhanced by the inclusion of a bulky alicyclic system such as the bicyclooctyl moiety. Smectic phases are not seen in the phenyl benzoates because their melting points and clearing temperatures are so low. However, the cyclohexyl system does show weak smectic behavior, but the bicyclohexanyl systems, even though they have wide mesomorphic ranges, are not found to exhibit smectic phases. The study described above reflects a comparison for systems that would be expected to form monolayer structures in the smectic state. A similar comparison, however, can be made for systems that might exhibit bilayer smectic ordering. For example, the combination of a biphenyl core and a cyano terminal unit has been explored in depth because of its use in device applications [22]. Again one of the rings of the biphenyl unit can be systematically replaced by cyclohexyl [23] and bicyclooctyl [24] moieties. Figure 17 shows some comparative results for the 4-n-alkyl-4'-cyanobiphenyls,the trans1-n-alkyl-4-(4-cyanophenyl)cyclohexanes and the l-n-alkyl-4-(4-cyanophenyl)bicy-
I
-
n 7 8 9 Cr28 * N 70 *
419
SmA
Cr
28.5 21 40.5
* *
32.5
*
I
N
-
44.5
* * *
42 40 47.5
*
I
n Cr28 p N 22) *
I
Cr31 sN65.5.I
Cr50.5- N 93 5 - 1
SmX N 30(* 1 7 ) * - 3 3 * - 3 5 -
Cr
7 8 9
Figure 16. Effect of alicyclic rings located in the core on smectic phase formation.
n 7 8 9
Cr - 6 1
N
59 54 57
I ' * *
I
- 9 5
* 5 2 . 9 0 * 5 6 * 90
* *
Figure 17. Effect of alicyclic rings located in cyano terminated cores on smectic phase formation.
420
1
Synthesis of Non-Chiral Smectic Liquid Crystals
clo[2.2.2]octanes [19]. This comparison is more conclusive than the preceding one, and demonstrates clearly, at least for the formation of bilayer smectic phases, that the inclusion of alicyclic systems suppresses smectic phase formation and improves the likelihood of nematic phases being formed. Similar studies using other ring systems in the central core show that, by and large, the use of nonpolar cores results in the formation of smectic B phases or crystal B phases. Polar cores on the other hand enhance the formation of more disordered smectic phases such as the smectic A and smectic C modifications. Figure 18 shows comparisons for a variety of ‘biphenyl clones’ [ 19,251 (where possible for the hexyl and hexyloxy substituted derivatives). In this study, one of the phenyl units has been replaced with an alicyclic or a heterocyclic ring. Resulting cores that are relatively nonpolar tend to exhibit orthogonal ordered phases such as smectic B and crystal B and E phases. For symmetrical polar units (e.g., pyrimidine, tetrazine etc.) smectic A phases tend to predominate, and where one side of the core is more polar (e.g., pyridazine)
Cr 9 E 68 * B 84. I
-
Cr3E * B 52 I
smectic C phases are found. In addition to affecting mesophase type, the polarity of the core can also raise transition temperatures. In the case where a heterocyclic ring is coupled to an alicyclic ring with strong mesogenic tendencies (e.g., bicyclohexane linked to tetrazine) high clearing temperatures can be achieved. A wide variety of similar studies on three ring, fused ring, and two ring systems show that by careful control of the degree of polarity in the core, the direction of dipoles, the symmetry (or lack) of the charge distribution, the polarizability of the n-system, and the overall steric shape (bent or linear), the synthesis of smectic materials possessing phases of predicted type, structure, and accompanying transition temperatures can be achieved.
1.2.5 Linking Groups Usually the core system in smectogens contains a linking group positioned either between two ring units or between aring and an aliphatic chain. The linking group has been shown to have marked effects on
Cr25 * SmX 52.5 I
Cr 50 .SmA 57.501
Cr22 * SmX 66 N 69 -1
Cr 80 (.SmC 78) - 1
C 6 H i ~ O N-N ~ o c 6 H i 3 Cr69 (.N 47) - 1
Cr45 * SmA 75 I
-
Cr 87 SmC 106 I
%Hi3 4 N-N ~ = Cr44 .SmB 59 SmA 89 .I
Cr44 B 50 I
-
Cr34 * SmA 45 N 53 * I
~
r f f i (. N58.5) * I C&O~~=$+C~H1~ N-N
Cr45.Sm471.I
Cr 130 * SmX 189 I
~
o
c
5
H
i
1
Figure 18. Effect of heterocyclic and alicyclic rings located within the core on smectic phase formation.
1.2 Template Structures for the Synthesis of Smectogens
mesophase temperature ranges and type of mesophase formed. Some typical linking groups for use between rings (Z) or between aliphatic chains and rings (A or B) are shown in Fig. 4. Linking groups positioned at the end of the core system can also be analogous, under certain circumstances, to terminal polar groups (as described in Sec. 1.2.2). Linking groups serve to impart various functions to the structures of mesomorphic materials. For example, they can provide conjugated linking bridges between aromatic rings, or conversely they can interrupt conjugation between rings [9]. They can impart polarity or act as nonpolar groups, and in addition they can increase polarizability or decrease it. Linking groups also serve to increase the overall molecular length and breadth. By careful design, taking into account the effects of linking groups, smectic mesophases of any particular type can be achieved for a given molecular system or material type. The variety of linking groups utilized in smectic systems is exceptionally large, making it difficult to give a detailed description of the properties of each individual linkage. However, through the following examples, a number of effects can be described. First, consider the polarity of the linking group. Figure 19 shows the structure of two closely related biphenyl derivatives that only differ in the structure of the linking group: one is an ester whereas the other is a thioester [26]. Both linkages have strongly polar carbonyl groups, but conversely the thioester has a more weakly polar and more highly polarizable sulfur linking atom in comparison to the oxygen atom of the ester.
Cr65 p E60) * SrnBffi. SmA 84 7.
I
0 9 1*
B 121 * SrnA 1495 * I
Figure 19. Comparison of thioester and ester groups.
42 1
Thus the thioester will experience less strong lateral repulsive effects when like molecules pack together in layers. Consequently, molecules containing thioester linking groups will be able to pack together more tightly than esters; this will lead inevitably to thio esters forming more ordered phases than esters. This effect is exemplified in Fig. 19 which shows the thioester exhibits a crystal B phase which has long range positional order, whereas the ester exhibits a hexatic smectic B phase having short range order. The directionality of the linking group can also be used to effect in determining phase type and transition temperatures for a given system [9]. The direction of some linking groups, such as azo, is ineffectual because such groups are symmetrical, however, for linking units such as esters the directionality becomes important. Figure 20 shows a comparison between two pairs of compounds that possess ester linkages. For the first pair of phenyl benzoates, it can be seen that when the ester's carbonyl unit is conjugated to the cyano terminal group then smectic A and smectic C phase are observed, however, when the ether oxygen of the ester unit is conjugated to cyano group nematic and smectic A phases predominate [9, 271. Thus, the directionality of the conjugation of the ester to the rest of the core
-
Cr 79 * SmA 79 N 8 6 5 - 1
C r 6 7 (. SmC 56)* SrnA 98. I
Cr 79.SmA80.I
Cr 67.G107.SmF108S.I
Figure 20. Comparison of ester linkages
422
1 Synthesis of Non-Chiral Smectic Liquid Crystals
has a marked effect on the mesophases formed. When the carbonyl group is in conjugation with the nitrile moiety there is a competing effect (for the 7~ electrons) which reduces the polar effect of the cyano group. This increases the possibility of the molecules forming monolayer tilted phases. Where the conjugation reinforces the longitudinal dipole, antiparallel molecular pairing can take place similarly to that shown in Fig. 14, and as a consequence nematic and interdigitated bilayer smectic A phases are formed. When an ester linkage is positioned at the end of the core structure then the carbonyl group can be either conjugated to the aromatic n system or else it will not be conjugated at all. In the first case the n electrons of the carbonyl group will be part of an extended n system acting along the longitudinal axis of the core, but in the second the n system of the carbonyl group will be isolated. Thus in one case the ester will couple to the longitudinal dipole, whereas in the other it will tend to act laterally to the molecular long axis. In the example shown in Fig. 20, where the carbonyl group is conjugated, smectic A phases are formed, however, where it is unconjugated, and stronger lateral interactions can occur, more ordered smectic F and crystal G phases are produced [28]. The increased lateral interactions in the second case are possibly caused by the strongerholated dipole associated with the carbonyl group. Similar effects also apply to other linking groups such as Schiff's bases (CH=N), thio esters (COS), methoxy links (CH,O), and amides (CONH) etc. Results on these systems will not be discussed here, however comparisons are prevalent in the general literature [ l , 2, 19,291. Thus, when designing smectic materials that possess linking groups, the polarity, the ability to create an extended n system, the degree of pola-
rizability, the directionality, the bent or linear shape, and the location within or at the end of the core, must be taken into account when a particular mesophase is required. In addition, although not discussed here, the coupling of the linking group to other structural units can be of importance. For example, in certain phenyl benzoates which carry one normal aliphatic chain and one branched chain, when the carbonyl unit is attached to the same ring as the branched unit then high tilt smectic C phases are formed, whereas for the reverse case low tilt smectic C and smectic A phases are formed [30]. Thus, by predetermining the directionality of the central linkage some physical properties of mesophases (e.g., high tilt =45" versus low tilt = 25") can be controlled.
1.2.6 Lateral Substituents Lateral substituents may be attached to the core system or located in the terminal aliphatic chain. By and large, lateral substituents positioned on the core or in the terminal chain(s) disfavour smectic mesophase formation. Smectic mesophase formation is principally depressed more by the steric bulk of the lateral group than by its polarity. Thus for example, fluoro substituents at the core or in the chain(s) are less effective at depressing smectic mesophase formation than is a methyl substituent [14, 311, nevertheless fluoro substitution still lowers transition temperatures of the phase transition to the smectic state in comparison to the unsubstituted analogue. Lateral substitution in all of its forms, generally has the effect of increasing the lateral steric repulsion of the molecules within their layers. This has the effect of weakening the lateral interactions, thereby resulting in lower mesophase stability. Weakening of the lateral interactions will not only
1.2 Template Structures for the Synthesis of Smectogens
lower transition temperatures, but will depress the formation of ordered smectic and soft-crystal phases and increase the likelihood of observing more disordered phases such as smectic A and nematic phases. Figure 21 shows a comparison of some phenyl biphenylcarboxylates where a methyl substituent has been positioned in the phenyl ring [ 141. As noted, the methyl substituted systems tend to exhibit more disordered phases, but at lower temperatures, than their unsubstituted analogues. Thus, it can be seen that the more ordered smectic B and crystal G phases of the unsubstituted systems are lost in preference to smectic A and nematic phases in the methyl substituted analogues. However, the clearing temperatures are down by over 50°C in each case. When the degree of lateral substitution is increased by way of branching in the aliphatic chain, clearing points are lowered further and now all smectic phases are lost. The examples shown in Fig. 21 are typical of many systems, but in order to correctly gauge which mesophases will be formed and lost, the temperature range of the liquid crystal state should be taken into account for each compound. For instance, the last material given in the above example exhib-
-
-
423
its no smectic phases. However, this does not mean that smectic phases have been depressed altogether, they simply may not be observed because recrystallization prevents us from seeing any further phase transitions, and in fact smectic phases may be lurking just below the solidification point as virtual phases. A further example of lateral substitution, but this time with respect to extension of a lateral chain and change in substituent polarity, is shown in Fig. 22 for the 3-substituted- 1,4-bis-(4-n-octyloxybenzoyloxy)benzenes. It can be seen that for the parent system (X = H) smectic C and nematic phases are formed, but when a lateral substituent is introduced at the 3-position smectic phase behavior is suppressed. The clearing points are considerably lowered by increasing the length of a lateral aliphatic substituent, whereas for smaller polar substituents the reduction in clearing point is not as great [32]. Small polar lateral substituents have been made of considerable use in the development of materials that exhibit smectic C phases for applications as host systems for ferroelectric display devices [ 3 I]. Small polar groups do not depress mesophase formation greatly, and in addition they can be po-
Cr 110. SmB 110 5 * SmC 132 5 SmA 184.1
Cr 78 5 SmA 133 N 135 - 1
Cr 102 p G 67 * SmB 98) * SmA 153 * I
Cr51 .SmA 90"
H3C'
H,C'
H,C' Cr 40.5 * N 68.5 * I
97.5.1
Figure 21. Effect of lateral methyl groups on mesophase formation.
424
1 Synthesis of Non-Chiral Smectic Liquid Crystals
X
* * * *
H CH3 CpH5 CBH17
130.0 72.4
62.0 58.5 93.5 94.0
CI
CN
*
-
I
N
SmC
Cr
129.0
.. *
-
-
*
-
194.9
156.0 119.0 77.5 150.0 154.0
*
' * *
-
Figure 22. Effect of lateral substitution on mesophase formation.
sitioned laterally to the core in order to enhance the formation of certain phases over other unwanted phases, for example, tilted smectic C phases can be favored over orthogonal phases for ferroelectric applications. Figure 23 shows a comparison for fluor0 substituted and unsubstituted terphenyls [33]. The parent unsubstituted material melts at a very high temperature and only exhibits orthogonal smectic A and smectic B phases. The introduction of a single fluoro substituent can have the effect of re-
Cr 205 * SmB 216 * SmA 228.5 * I
G176.SmA 210.1
ducing the melting point by over 120 "C depending on its location, while at the same time only reducing the clearing point by 60 "C. In addition tilted phases can be introduced partly at the expense of orthogonal phases. The introduction of a second polar fluoro substituent results in the suppression of orthogonal smectic B and ordered smectic phases (tilted and orthogonal). The increased lateral repulsive effects caused by the interactions of the polar fluoro substituents lead to more disordered phases appearing culminating in the introduction of the nematic phase. Thus, the last material has an ideal phase sequence (for use as a host system in ferroelectric devices) of nematic smectic A and smectic C phases with no orthogonal and ordered phases being present. This particular phase sequence is important for aligning the material in rubbed polyimide cells. In cases where the lateral substituent has the potential for better or stronger lateral interactions, which would in turn stabilize smectic phase formation, the effect of the increased steric bulk caused by the lateral substituent itself weakens the other lateral interactions and so mesophase formation remains depressed. Figure 24 demonstrates this effect for chiral lateral hydroxy substitutedmaterials [34]. In this situation it might be expected that the lateral hydroxy groups
F
-
Cr 115 * SmC 131.5 N 166.5 - 1 E
-
C5Hll
\ /
\ /
OC6H13
-
Cr 68 Smc' 120 SmA' 172 * I
Cr70 * G 78. SmB 92 .Sml93-SmC 118. SmA 115 * N 166.5 - 1 c
-
c
-
-
-
Cr 101.5 SmC 156.5. SmA 167 N 171.5 - 1
Cr 28 SmC' 86 SmA' 141 - 1
Figure 23. Effect of lateral fluoro substitution on mesophase formation.
Figure 24. Effect of lateral hydroxy substitution on mesophase formation.
425
1.2 Template Structures for the Synthesis of Smectogens
of adjacent molecules would hydrogen bond, thereby stabilizing mesophase formation. However, with the possibility of intrarather than inter-molecular hydrogen bonding occurring, plus the possibility of poorer lateral interactions due to the steric bulk of the hydroxy group, a large reduction in clearing and melting points for the substituted over the unsubstituted material is found. Lateral substitution in the aliphatic chain region, like substitution in the core, can have dramatic effects on clearing and melting points. Systematic studies concerning directly comparable systems, however, are few. This is partly due to the availability of suitable starting materials and for systems required for display applications lateral substitution usually means high viscosity and so they are not so attractive for investigation. Nevertheless Fig. 25 shows a systematic comparable study for the alkyl4-n-octyloxybiphenyl-4'-carboxylates where the alkyl chain either carries a methyl substituent at the first position or does not [28, 351. In keeping with the previous discussion of lateral substituents, it can be seen from Fig. 25
n 1 2
3 4 5
E
Cr .
-
SmB
SmC
.
117 * 126 * 132 7 5 . 8 8 - 9 6 -
~ 5 - 6 6
-.
- ( . E l -
. 8 3 -
6 -
.
. .
..
-
.
I
SmA
-
. -
5 6 (55
. *
.
.)
132 112 101
-. *
8 6 . 88 *
that the clearing points are substantially reduced, conversely the melting points are not reduced as much. The branched systems, unlike the normal alkyl compounds, do not exhibit ordered orthogonal smectic B or E phases, but instead disordered tilted smectic C and orthogonal smectic A phases predominate. Examination of the data suggests that the introduction of tilted phases into this family of esters occurs at shorter alkyl chain lengths when a branching point is present. This shifting of the introduction of tilted phases to shorter alkyl chain lengths when a branch point is present is a relatively common occurrence in a variety of homologous series. The suppression of orthogonal phases however may be just an artifact of the reduced temperature range for which liquid crystal phases occur, that is they may be virtual rather than totally suppressed. The use of lateral substitution in the terminal aliphatic chain, therefore, can be used to stabilize the formation of tilted phases. This observation has been made use of in preparing materials that exhibit the alternating smectic C phase, which is the achiral analogue of the antiferroelectric phase [36]. Figure 26 shows a table of a series of compounds where the branching chain is increased in length until it matches the length of the terminal aliphatic chain [37]. It can be seen from this table that the alternating smectic C phase becomes more stable as the chain length of the lateral substituent is increased, and eventually it replaces the
CnHzn+i n
Cr
1 2
*
3 4
.
-.
SmC
(*
75 67 43 4
9
I
SmA 41
*
69)
*
1: 2 : 2-1 :. .
.
-
Figure 25. Effect of a methyl branch in the terminal aliphatic chain on mesophase formation.
n
Cr
4 5 6
*
Sml 402
(a
- 6 2 6 -
*
697
.
SmCan 355)
. .
*
-
(-
SmC 770
619)
-
-
SmA
689
-
--
945 874 81 0
Figure 26. Effect of branching in the terminal allphatic chain on mesophase formation.
426
1 Synthesis of Non-Chiral Smectic Liquid Crystals
smectic C phase. The more ordered smectic phases, such as smectic I, are suppressed, as expected, as the branching chain is increased in length. Thus lateral substitution in both the core region or in the terminal aliphatic chain can be used to control melting points, clearing points, and to some degree mesophase type formed.
1.3 Syntheses of Standard Smectic Liquid Crystals In the following sections, by way of example, the syntheses of standard and much investigated smectic liquid crystals will be described. These syntheses will give a general perspective on the synthesis of smectic liquid crystals from basic starting materials.
1.3.1 Synthesis of 4-Alkyland 4-alkoxy-4’-cyanobiphenyls: Interdigitated Smectic A Materials (e.g., 8CB and (80CB) Alkyl cyanobiphenyls provide classical examples of interdigitated bilayer smectic A phases [20]. These materials are also used in applications of smectic liquid crystals (see Sec. 3 of this chapter) in thermally addressed storage devices. Figure 27 shows
the synthesis starting from biphenyl [38]. Bromination followed by Friedel-Crafts alkylation and Huang-Minlon reduction gives the alkyl bromobiphenyl. Cyanation using copper(1) cyanide in N-methyl pyrrolidinone yields the appropriate cyanobiphenyl. The alkoxy analogue can be prepared in a variety of ways, one route involves the bromination of protected hydroxybiphenyl, subsequent deprotection and alkylation which results in the creation of the alkoxy bromobiphenyl, see the left-hand side of Fig. 28. Cyanation using copper(1) cyanide as above yields the final product. Alternatively, the alkoxy cyanobiphenyls can be prepared by a cross-coupling procedure as shown on the right-hand side of Fig. 28. Selective coupling of 4-iodo-bromobenzene with an alkoxyphenyl boronic acid in the presence of palladium(0) yields the alkoxy bromobiphenyl. Cynanation proceeds as described previously. This second example provides a comparison between two different synthetic strategies. One method uses a pathway that maintains the integrity of the core throughout, whereas the other, newer, method builds the core up with the substituents already attached and in place. This second technique is very powerful when complex core structures are required or where lateral substitution in the core is difficult to achieve using conventional electrophilic substitution techniques [39].
+ RW-Br
Figure 27. Synthesis of 4-alkyl4‘-cyanobiphenyls.
1.3 Syntheses of Standard Smectic Liquid Crystals
@
- 0O
W
E
427
r
Base RB\
Pd(Ph,),,
NaC03,
Figure 28. Synthesis of 4-alkoxy4’-cyanobiphenyls,
1.3.2 Synthesis of Alkyl 4-Alkoxybiphenyl-4’-carboxylates: Hexatic Smectic B Materials (e.g.,650BC) One of the most examined hexatic smectic B materials is hexyl 4-n-pentyloxybiphenyl4’-carboxylate (650BC). This material and related homologues can be prepared by the scheme shown in Fig. 29 [14, 28, 401. The synthesis uses bromo alkoxybiphenyls as useful intermediates. These intermediate compounds can be prepared as described in
the previous section. Cyanation and acid hydrolysis in glacial acetic acid or formation of the Grignard reagent using magnesium and entrainment followed by addition of solid carbon dioxide yields the alkoxy biphenyl carboxylic acids (these products are also smectic liquid crystals). Activation of any particular acid with distilled thionyl chloride to yield the acid chloride followed by immediate addition to the appropriate alcohol in dry toluene-triethylamine or toluenepyridine gives the desired product after chromatography over silica gel.
Figure 2Y. Synthesis of alkyl alkoxybiphenyl carboxylates.
428
1 Synthesis of Non-Chiral Smectic Liquid Crystals
This synthetic procedure describes a typical method for preparing alkyl esters and for the preparation of alkoxy biphenylcarboxylic acids. As with many liquid crystals, purification is important, and in this case chromatography can be used to produce products with better than 99.5% purity, which makes the materials eminently suitable for physical studies.
1.3.3 Synthesis of 4-Alkyloxybenzylidene-4'-alkylanilines: Crystal B and G Materials (e.g.,nOms) These materials provided the first classical examples of the crystal B phase. However, compounds such as 4 0 2 also provided an example of a G phase [4 11, 1 0 4 an example of a nematic phase at room temperature, and 506 an example of a crystal B-smectic F-crystal G phase sequence [42]. These compounds are relatively easy to prepare: but, their preparation requires very pure intermediates, and in addition the final products need to be rigorously purified before the materials can be used in physical studies. Part of the problem lies in the preparation of the 4-alkylaniline intermediates. Simple nitration of alkylbenzenes to give the 4-nitroalkylbenzenes followed by reduction to give the anilines is fraught with problems concerning the removal of unwanted 2-substituted isomers (for the higher homologues this has to be achieved using complex distillation techniques). In order to minimize this problem an alternative synthesis can be achieved through the 4-alkyl-acetophenones prepared by FriedelCrafts acylation of the alkylbenzenes (see right-hand side of the scheme in Fig. 30). Subsequent reaction with hydroxylamine yields the analogous oximes, and following rearrangement under Beckmann conditions,
R'=C,H,.
R =C8H17
= 408
R' = C5Hll. R = C7H15 = 507 R' = CsH11, R = C6H13 = 506
Figure 30. Synthesis of nOms
the 4-alkylacetanilides are obtained. Hydrolysis yields the corresponding anilines which can be condensed (in the presence of a trace of acid) with the appropriate 4-alkoxybenzaldehydes (prepared by alkylation of 4-hydroxybenzaldehyde with alkyl bromides in the presence of potassium carbonate) to give the final products. These materials, however, cannot be purified by chromatography because they decompose on the column, therefore they are purified by recrystallization (sometimes at low temperatures to prevent the products from dissolving back into the solvent).
1.3.4 Synthesis of Terephthalylidene-bis-4-alkylanilines: Smectic I, Smectic F, Crystal G and Crystal H Materials (e.g., TBnAs) These are an extremely important class of materials. Their mesophase properties have been extensively studied because they exhibit particularly rich polymorphism, for example TBlOA exhibits G, SmF, SmI,
1.3
Syntheses of Standard Smectic Liquid Crystals
SmC, and SmA phases [43]. In addition, unlike the nOms these materials are easily purified by recrystallization because of their higher melting points. However, they also suffer from similar problems of the presence of unwanted 2-substituted products, thus the resolution of this problem is the same as that used in the synthesis of the nOms. Thus two alternative synthetic pathways are shown in Fig. 3 1. These use the syntheses of the anilines as described in the previous section. Once the anilines have been prepared and purified they are condensed with terephthal-
Y
dehyde in the presence of a trace of acid. Repeated recrystallization from ethanol yields pure products.
1.3.5 Synthesis of 4-Alkoxyphenyl4-Alkoxybenzoates: Smectic C Materials Esters provide a wide range of stable smectic materials which are suitable for physical studies. In many instances they are more useful for investigations than Schiff's bases (nOms and TBnAs) because of their better stability and purity. Simple 4-alkoxyphenyl4-alkoxybenzoates are an interesting class of materials because they provide low temperature smectic C variants (often with the addition of smectic A and nematic phases). A synthetic pathway to the 4-alkoxyphenyl4-alkoxybenzoates is shown in Fig. 32. The pathway involves two alkylations: one of 4-hydroxybenzoic acid using an alkyl halide in the presence of sodium hydroxide and ethanol, and the other of 1,4-dihydroxybenzene using an alkyl halide in the presence of sodium hydroxide and dioxane. Activation of the acid with thionyl chloride to give the acid chloride and reaction with the alkoxyphenol in the presence of a base such as triethylamine yields the final esters.
JE"
R2Br,NaOH
IDioxane
I
S0Cl2 TEA
Figure 31. Synthesis of TBnAs.
429
Figure 32. Synthesis of phenyl benzoates.
430
1 Synthesis of Non-Chiral Smectic Liquid Crystals
1.3.6 Synthesis of 4-Alkylphenyl4-Alkylbiphenyl4’-carboxylates: Smectic C, Smectic I, Hexatic Smectic B Materials The synthesis of esters can be extended further to the preparation of systems with extended core sections (three rings instead of two). Synthetically, however, although more lengthy, the methods used are much the same as those described in the previous sections. The 4-alkylbiphenyl-4’-carboxylic acids can be prepared as described previously (see right-hand side of Fig. 33). The 4-alkylphenols, on the other hand, can be
JCGN
Figure 33. Synthesis of phenyl biphenylcarboxylates.
prepared from anisole as follows. First, anisole is acylated using Friedel-Crafts acylation techniques. This yields the 4-methoxyalkylphenones which can be reduced under Clemmensen conditions (zinc and mercury amalgam in the presence of strong acid) to give the 4-alkylanisoles. Demethylation in the presence of hydrobromic acid and glacial acetic acid or boron tribromide gives the desired 4-alkylphenols. Esterification using activation with thionyl chloride and reaction in the presence of a base such as triethylamine yields the appropriate esters.
1.3.7 Synthesis of 4-(2-Methylbutyl)phenyl4-Alkoxybiphenyl4’-carboxylates: Smectic C, Smectic I, Smectic F, Crystal J, Crystal K and Crystal G Materials (nOmIs, e.g., 8OSI) Extending the synthetic pathways for esters we arrive at one of the most well-known and researched compounds: 8OSI [44]. This ester is one representative of the family of 4(2-methylbuty1)phenyl 4-alkoxybiphenyl4’-carboxylates. The syntheses of these types of material follow much the same sequence of events as those described in the above two sections. The acids can be made from the corresponding 4-alkoxy-4’-cyanobiphenyls, see left-hand side of Fig. 34, whereas 4-(2-methylbutyl)phenol can be prepared starting from 2-methylbutanol, see right-hand side of Fig. 34.2-Methylbutanol is first oxidized in the presence of potassium permanganate to give the corresponding acid, which in turn is activated with thionyl chloride to give the acid chloride. The acid chloride is then used in a Friedel-Crafts acylation of anisole in an equivalent procedure to the one described in the preceding sec-
1.3 Syntheses of Standard Smectic Liquid Crystals
R
O
W
C
O
O
H+ SOCI, R
R = C,H,
O
W
C
O
C
I
+
43 1
HO-
= BOSl
Figure 34. Synthesis of nOSIs.
tion. The procedure then follows the same pattern, eventually yielding 4-(2-methylbuty1)phenol. Esterification via activation of the acid with thionyl chloride and reaction with the phenol in the presence of base yields the final product.
1.3.8 Synthesis of 2-(4-nAlkylphenyl)-5-(4-n-alkoxypheny1)pyrimidines: Smectic F and Crystal G Materials Pyrimidine containing materials are an important class of liquid crystals. 2-(4-n-Pentylphenyl)-5-(4-n-pentoxyphenyl)pyrimidine was the first compound to be found that exhibits the smectic F and crystal G
phases [45], and as a consequence it has been the subject of intense research. Pyrimidines used to be prepared via the construction of the heterocyclic ring as shown in Fig. 35. A 4-substituted-cyanobenzene is subjected to treatment with hydrogen chloride gas in an ethanolic solution, after the reaction is complete ammonia is bubbled into the solution to yield the amino-imine, which in turn is reacted with a suitably substituted phenyl diethyl malonate to give the dihydroxypyrimidine. The hydroxyl groups are removed by chlorination with phosphorus oxychloride followed by hydrogenation over palladium. The first part of this synthetic pathway is relatively straightforward, but the latter stages can result in poor yields if not performed correctly.
432
1
Synthesis of Non-Chiral Smectic Liquid Crystals
1
H+/H20
1""
Pressure
Figure 35. Synthesis of 2-(4-n-pentylphenyl)-5-(4n-pentyloxypheny1)pyrimidine.
Alternative routes to pyrimidines, that avoid the later hydrogenation steps, were developed at Hoffmann-La Roche [46]. This alternative synthetic strategy is shown in Fig. 36. An amino-imine can be prepared in the same way, but this time it is not reacted with a substituted phenylmalonate. Instead an alkoxybenzaldehyde is subjected to a Wittig reaction with the phosphorus ylide of chloromethoxymethane to yield 1-(4-alkoxyphenyl)-2-methoxyethane. Treatment with triethoxymethane in the presence of a Lewis acid such as boron trifluoride etherate gives the tetraethoxy derivative. Hydrolysis produces 2-(4-alkoxyphenyl)-3-methoxypropenal, reaction of this material with the imine results in the pyrimidine being formed directly.
Figure 36. Synthesis of 2-(4-n-alkylphenyl)-5-(4-na1koxyphenyl)pyrimidines.
For this synthetic pathway, when there is a need to prepare a wide variety of homologues, the synthetic procedure can be made more efficient by preparing the cyano substituted product. The cyano product can then be derivatized in a number of ways to give different alkyl substituents in the terminal position of the core. The cyano moiety is created by starting with the methyl ester and treating with ammonia under pressure. This results in the formation of the amide which is subsequently dehydrated in the presence of phosphorus oxychloride to give the nitrile.
1.3 Syntheses of Standard Smectic Liquid Crystals
1.3.9 Synthesis of 3-Nitro- and 3-Cyano-4-n-alkoxybiphenyl4’-carboxylic Acids: Cubic and Smectic C Materials 3-Nitro- and 3-cyano-4-n-alkoxybiphenyl4’-carboxylic acids provide examples of interesting materials that can exhibit cubic phases between smectic A and smectic C phases. The way in which a cubic phase is formed between two smectic phases is intriguing, and as a consequence these materials have been the subject of intense investigations [2, 471. The synthetic route to the 3-nitro- and 3cyano-4-n-alkoxybiphenyl-4’-carboxylic acids is shown in Fig. 37. The 4-n-alkoxybiphenyl-4’-carboxylic acids (the hexadecyloxy and the octadecyloxy homologues in the case of the preparation of materials that exhibit cubic phases) are prepared as de-
433
scribed previously in Sec. I .3.2. Bromination followed by cyanation yields the 3cyano-4-n-alkoxybiphenyl-4’-carboxylic acids. Alternatively, direct nitration using a mixture of concentrated nitric and sulphuric acids yields the 3-nitro-4-n-alkoxybiphenyl-4’-carboxylic acids. There are alternative routes to the 4-nalkoxybiphenyl-4’-carboxylic acids, but these usually involve acylation of an appropriate 4-n-alkoxybiphenyl with acetyl chloride. However, oxidation of the resulting 4n-alkoxybiphenyl with hypobromite solution can result in some bromination of the biphenyl occurring. In the preparation of the 3-ni tro-4-n-alkoxybiphenyl-4’-carboxylic acids small amounts of the 3-bromo-impurity can have adverse effects on transition temperatures and phase formation. Thus, in order to obtain materials suitable for physical studies, the intermediates need to be rigorously purified.
1.3.10 Synthesis of bis-[ 1-(4’-Alkylbiphenyl-4-y1)3-(4-alkylphenyl)propane1,3-dionato]copper(II): Smectic Metallomesogens
R
1
CuCN
O
W
C
O
O
H
-
Figure 37. Synthesis of 3-nitro- and 3-cyano-4alkoxybiphenylcarboxylic acids.
Metal-containing smectic materials are of considerable interest because, as they carry metal atoms or ions, they can be effectively studied by X-ray diffraction techniques. In addition, their unique shapes and physical properties make them ideal candidates for the study of biaxiality and conductivity in smectic liquid crystals. One class of materials that stands out are the copper(I1) complexes of B-diketones. These materials can exhibit columnar as well as smectic mesophases. Figure 38 shows the general synthesis of unsymmetrical copper(I1) complexes of a
434
1 Synthesis of Non-Chiral Smectic Liquid Crystals
1
H+/AcOH
1
H~C~HSOH
1
CH3COCI AlCl3
Figure 38. Synthesis of a symmetric p d i ketonates.
family of Pdiketones [ 5 ] .As with many of the other syntheses described in the previous sections, the preparations of the 4alkyl-4’-cyanobiphenyls and the 4-alkylbiphenyl-4’-carboxylic acids are of fundamental importance. Esterification of the 4-alkylbiphenyl-4’-carboxylic acids with ethanol yields the corresponding ethyl 4alkylbiphenyl-4’-carboxylates.These materials can be allowed to react with 4-alkylacetophenones in the presence of a suitable base such as sodium hydride to yield the corresponding pdiketone, and reaction with copper(I1) acetate yields the final complex.
The complexes so far studied have either been shown or assumed to be in the trans form. The above syntheses were selected for discussion because they demonstrate a common ancestry; that is many of the syntheses involve common intermediates or starting materials. Secondly, many of the synthetic procedures used are common, and coupled with common starting materialshntermediates, this makes synthesis efficient. Lastly, the materials selected for discussion are all historically important materials (with almost household names and reputations)
43s
1.4 Synthesis of Smectic Materials for Applications
from the viewpoint of the elucidation of the structures of smectic mesophases. In the following section we will turn to the synthesis of materials for practical applications.
1.4 Synthesis of Smectic Materials for Applications Generally the applications of achiral smectic liquid crystals fall into three categories as follows: materials with nematic and smectic A phases and strong positive dielectric anisotropies for storage display applications, - host materials for ferroelectric displays, and - potential host materials for antiferroelectric displays. -
Requirements for materials with strong positive dielectric anisotropies for storage applications are usually met by the availability of the 4-alkyl and 4-alkoxy-4'-cyanobiphenyls. The syntheses of these materials have been discussed in the above sections and so will not be discussed further in this section. The demands of ferroelectric and antiferroelectric applications, however, require that the syntheses of host systems are discussed in more detail.
perature. The materials must be able to dissolve a suitable chiral dopant or combination of dopants which will induce the necessary symmetry breaking operation in order to generate ferroelectric properties. The host materials must also have low viscosities in order to produce mixtures that have fast responses to weak electrical fields. They must also be chemically and photochemically stable and have a tilt angle of about 22"-28" in the smectic C phase (see Chap. VI, Sec. 2 of this volume). The properties required of ferroelectric hosts therefore means that materials such as esters, Schiff's bases, and azo compounds are unsuitable because of their slow response times and poor stability. The best materials discovered so far, rely on removal of any functional or linking groups which might increase the viscosity or lower the stability. Figure 39 shows a variety of families of host materials [3 1,33,48-S I]. These materials have a number of attributes in common. First, they are devoid of linking groups, thus the aromatic or heterocyclic rings in the core are directly linked. Second, only alkyl or alkoxy terminal chains are used in order to maintain as low a viscosity as possible. Third, some materials carry lateral fluoro substituents in order to increase
1.4.1 Synthesis of Ferroelectric Host Materials Ferroelectric host systems are mixtures composed of materials that are achiral, and when blended together they exhibit a nematic-smectic A-smectic C phase sequence for the purposes of ease of alignment with the smectic C phase being available over a temperature range that includes room tem-
F
F
F
F
F
F
F
F
Figure 39. Achiral host materials for ferroelectric liquid mixtures.
436
1 Synthesis of Non-Chiral Smectic Liquid Crystals
the dielectric anisotropy and biaxiality. Fourth, the selective positioning of the fluor0 substituents or the inclusion of heterocyclic rings can be used to stabilize the formation of tilted phases. In addition modifications to the terminal end-chains by the introduction of alkenic moieties have been used extensively to moderate phase transition temperatures and physical properties 1521. The fact that all of the best host materials have no linking functional groups and that most of the core rings are directly linked
means that in order to generate materials with appropriate substituents and substitution patterns or appropriate ring types, the coupling of rings together to yield suitable core structures is very important [39].Under these circumstances the coupling of boronic acids with suitable bromides or iodides in the presence of palladium(0) is extremely important. Figures 40 and 41 show the syntheses of the phenyl pyrimidines and the difluoroterphenyls respectively. Each synthetic route makes use of a selective boronic acid coupling in the presence of palladi-
64
F
(MeO)& THF 10% HCI
3 F
(HO),B
F
Br
F.
Pd(Ph&. NaC03. CH3OCH2CH2OCH3.H20 F.
F'
R3-C=CC-ZnCI
E
F
BuLi, THF (MeOLB. THF
Figure 40. Synthesis of difluorophenyl pyrimidines.
1.4 Synthesis of Smectic Materials for Applications
437
Figure 41. Synthesis of difluoroterphenyls.
um(0) to an iodide rather than a bromide. In addition, each route includes the derivatization of difluorobenzene via a boronic acid intermediate. Apart from these two innovative steps, the coupling of an alkynic zinc chloride in the presence of palladium(0) to an aromatic bromide in order to introduce an alkynic chain to the terminal position of the core is noteworthy. These steps apart, many of the other procedures are similar to those discussed in previous sections. The use of cross-coupling methods for both the creation of the core structure and for the introduction of aliphatic substituents is very flexible. Particularly, the ability to use boronic acids to selectively couple to iodides or bromides releases the chemist to prepare materials systematically and with any particular substitution pattern they require.
1.4.2 Synthesis of Antiferroelectric Host Materials This particular area of research is still in its infancy, but it might be expected that the requirements of antiferroelectric host systems might be similar to those of ferroelectric host materials. However, it is not yet clear whether or not this presumption is valid. Nevertheless, the ability to produce low viscosity materials with reasonably high tilt angles seems a reasonable demand. Yet at the same time there are no design rules developed for the creation of antiferroelectric templates, and the only correlations available show that most chiral antiferroelectric materials contain three aromatic or heterocyclic rings with at least two ester linking groups; a combination of units that is not likely to produce low viscosity and fast switching.
438
1
Synthesis of Non-Chiral Smectic Liquid Crystals
appropriately substituted alkoxyphenyl bromide (see left-hand part of Fig. 42), followed by lithiation and treatment with solid carbon dioxide. The biphenol required for the final esterification with the appropriate phenylpropiolic acid is prepared starting from 4-hydroxybiphenyl-4’-carboxylicacid and protecting the hydroxyl group with methylchloroformate. Esterification of the free acid function followed by deprotection yields the biphenol which can be esterified in the presence of dimethylaminopyridine (DMAP) and dicyclohexylcarbodiimide (DCC) to give the final product.
The synthesis of the first achiral host material that exhibits a smectic Caltphase [36] (achiral version of the antiferroelectric phase) is shown in Fig. 42. It can be seen that this material has three aromatic rings and two ester groups, but in addition it has a swallow-tail unit. This unit (for no apparent reason at the moment) stabilizes the formation of smectic Caltphases. The material like a ferroelectric host can be doped with a chiral dopant to give an antiferroelectric mixture. The synthesis of the novel achiral host material can be achieved in a variety of ways. Using the Corey-Fuchs method, which involves a modified Wittig reaction of 4-alkoxybenzaldehydes with carbon tetrabromide, phenylpropiolic acids can be prepared by lithiation and treatment with solid carbon dioxide (see center of Fig. 42). Alternatively, this can also be achieved using a palladium(0) mediated coupling between 3-methyl-3-hydroxybutyneand an
H O G C H O
H
O
1.5 Summary The area of the synthesis of smectic liquid crystals is too large to cover in a single article of this type. Nevertheless, a number of common areas of interest in the synthesis of
~
C
O
O
H
(i)CH30COC1, NaOH (ii)HCI
OH
Pr,NH. N2
I
I
Figure 42. Synthesis of swallowtailed materials for antiferroelectric applications.
1.6 References
smectic materials with simple molecular structures have been touched upon. Templates used in the design of simple systems have been discussed in detail, but again it should be remembered these guidelines do not extend to complex systems. Many of the systems described use common starting materials and intermediates, which is important in the efficient use of resources and maximization of the number of synthetic targets achieved.
1.6 References See, for example, G. W. Gray, J. W. Goodby, Smectic Liquid Crystals; Textures and Structures, Leonard Hill, Glasgow and London, 1984; A. W. Hall, J. Hollingshurst, J. W. Goodby in Handbook ofLiquid Crystal Research (Eds.: P. J. Collings, J. S. Patel), Oxford University Press, New York and Oxford, 1997, pp. 17-70. See, for example, G. W. Gray in Liquid Crystals and Plastic Crystals, Vol. 1 (Eds.: G. W. Gray, P. A. Winsor), Ellis Horwood, Chichester 1974, pp. 103-1.52. D. Demus, Liq. Cryst. 1989, 5, 75. S. Tantrawong, Ph. D. Thesis, University of Hull, 1994. N. J. Thompson, Ph. D. Thesis, University of Hull, 1991; N. J. Thompson, G. W. Gray, J. W. Goodby, K. J. Toyne, Mol. Cryst. Liq. Cryst. 1991,200, 109; N. J. Thompson, J. W. Goodby, K. J. Toyne, Mol. Cryst. Liq. Cryst. 1992, 213, 187; N. J. Thompson, J. W. Goodby, K. J. Toyne, Mol. Cryst. Liq. Cryst. 1992, 214, 81. G. H. Mehl, J. W. Goodby, Chem. Ber. 1996, 129, 521; G. H. Mehl, J. W. Goodby, Angew. Chem. 1996,108,2791;G. H. Mehl, J. W. Goodby, Angew. Chern., lnt. Ed. Engl. 1996,35,2641. U. Stebani, ti. Lattermann, M. Wittenberg, J. Wendorff, Angew. Chem., Int. Ed. Engl. 1996, 35, 1858; S. A. Ponomarenko, E. A. Rebrov, A. Y. Bobrovsky, N. I. Boiko, A. M. Muzafarov, V. P. Shivaev, Liq. Cryst. 1996,21, I ; K. Lorenz, D. Holter, B. Stuhn, R. Mulhaupt, H. Frey, Adv. Mater. 1996, 8, 414. J. W. Goodby, MoL Cryst. Liq. Cryst. 1981. 75, 179. N. H. Tinh, F. Hardouin, C. Destrade, J . Phys. (Paris) 1982,43, 1127; F. Hardouin, N. H. Tinh, M. F. Achard, A,-M. Levelut, J. Phys. (Paris) Lett. 1982,43,327; P. E. Cladis, P. L. Finn, J. W. Goodby, Liquid Crystals and Ordered Fluids,
439
Vol. 4 (Eds.: J. Johnson, A. C. Griffin), Plenum, New York, 1984, pp. 203-231; J. W. Goodby, T. M. Leslie, P. E. Cladis, P. L. Finn, Liquid Crystals and Ordered Fluids, Vo1.4 (Eds.: J. Johnson and A. C. Griffin), Plenum, New York, 1984, pp. 89-1 10. D. Coates, G. W. Gray, The Microscope 1976, 24, 117. J. W. Goodby, Ph. D. Thesis, University of Hull, 1978; J. W. Goodby, G. W. Gray,Mol. Cryst. Liq. Cryst. 1978,48, 127. D. J. Byron, D. Lacey, R. C. Wilson, Mol. Cryst. Liq. Cryst. 1980,62, 103; B. K. Sadishiva, Mol. Cryst. Liq. Cryst. 1979, 55, 135. W. H. de Jeu, J. Phys. (Paris) 1977, 38, 1265; J. W. Goodby, G. W. Gray, J. Phys. (Puris) (Suppl.) 1976,37(C3), 17; J. W. Goodby, ti. W. Gray, J. Phys. (Paris) (Suppl.) 1979, 40 (C3), 27-36. J. W. Goodby, Ph. D. Thesis, University of Hull 1978. W. L. McMillan, Phys. Rev. A 1973, 8, 1921. J. W. Goodby, G. W. Gray, D. G. McDonnell, Mol. Cryst. Liq. Cryst. (Lett.) 1977, 34, 183. A. Wulf, Phys. Rev. A 1975, 1I , 365. R. Bartolino, J. Doucet, G. Durand, Ann. Phys. 1978, 3, 389. See, for example, D. Demus, H. Zaschke, Flussige Kristalle in Tubellen, Vol. 2, VEB Deutscher Verlag fur Grundstoffindustrie, Leipzig, 1984, and references therein. A. J. Leadbetter, F. P. Temme, A. Heidemann, W. S . Howells, Chem. Phys. (Lett.) 1975, 34, 363; A. J. Leadbetter, J. L. A. Durrant, M. Rugman, Mol. Cryst. Liq. Cryst. (Lett.) 1977, 34, 231; D. H. Bonsor, A. J. Leadbetter, F. P. Temme, Mol. Phys. 1978, 36, 1805. M. E. Neubert, L. T. Carlino, D. L. Fishel, R. M. D'Sidocky, Mol. Cryst. Liq. Cryst. 1980,59,253; H.-J. Deutscher, B. Laaser, W. Dolling, H. Schubert, J . Prakt. Chem. 1978,320, 19 1; H.-J. Deutscher, Dissertation B, Halle, 1980; W. Weissflog, G. Pelzl, D. Demus, Cryst. Res. Techno/. 1981, 167, K79; G. W. Gray, S . M. Kelly, J. Chem. Soc., Chem. Commun. 1980, 465; G. W. Gray, S. M. Kelly, Mol. Cryst. Liq. Cryst. 1981, 75, 95. G. W. Gray, K. J. Harrison, J. A. Nash, Electron. Lett. 1973, 9, 130; G. W. Gray in Advances in Liquid Crystals (Ed.: G. H. Brown), Academic Press, New York, 1976; H. Hirata, S. H. Waxman, J. Teucher, Mol. Cryst. Liq. Cryst. 1973, 20, 334; D. S. Hulme, E. P. Raynes, K. J. Harrison, J. Chem. Soc., Chem. Cornmun. 1974, 98; G. W. Smith, Mol. Cryst. Liq. Cryst. 1979, 41, 89. R. Eidenschink, D. Erdmann, J. Krause, L. Pohl, Angew. Chem. 1977, 89, 103; R. Eidenschink, J . Krause, L. Pohl, DE-OS 2 636 684, 1978;
440
1 Synthesis of Non-Chiral Smectic Liquid Crystals
T. Szczucinski, R. Dabrowski, Bid. Wojsk. Acad. Techn. 1981,30, 109. [24] G. W. Gray, S. M. Kelly, Angew. Chem., Int. Ed. Engl. 1981,20,393; G. W. Gray, S. M. Kelly, J. Chem. SOC., Perkin I1 1981, 26. [25] D. Demus, L. Richter, C. E. Rurup, H. Sackmann, H. Schubert, J. Phys. (Paris) 1975, C36, 349; R. Eidenschink, J. Krause, L. Pohl, DE-OS 2636684, 1978; G. W. Gray, S. M. Kelly, UK Pat Appl GB 2065 104; H. Zaschke, H. M. Vorbrodt, D. Demus, W. Weissflog, German Patent DD-WP 139852, 1979; H. M. Vorbrodt; S. Deresch, H. Kresse, A. Wiegeleben, D. Demus, H. Zaschke, J. Prakt. Chem. 1981, 323, 902; A. I. Pavluchenko, V. V. Titov, N. I. Smirnova in Advances in Liquid Crystal Research and Applications (Ed.: L. Bata), Pergamon Press, Oxford, 1980, p 1007; H. Zaschke, Dissertation B, Universitat Halle, 1977; H. Zaschke, C. Hyna, H. Schubert, Z. Chem. 1977, 17, 333; D. Demus, B. Krucke, F. Kuschel, H. U. Nothnick, G. Pelzl, H. Zaschke, Mol. Cryst. Liq. Cryst. Lett. 1979,56, 115; D. Demus, H. Zaschke, Mol. Cryst. Liq. Cryst. 1981, 63, 129; R. Paschkonene, Yu. Daugwila, Abstracts ofthe 4th Liq. Cryst. Conj of Soviet Countries 1981, C36. [26] J. W. Goodby in Liquid Crystals and Ordered Fluids, Vol. 4 (Eds.: J. Johnson, A. C. Griffin), Plenum, New York, 1984, pp. 175-201. [27] R. E. Cladis, P. L. Finn, J. W. Goodby in Liquid Crystals and Ordered Fluids, Vol. 4 (Eds.: J. Johnson, A. C. Griffin), Plenum, New York, 1984, pp. 203-231; J. W. Goodby, T. M. Leslie, P. E. Cladis, P. L. Finn in Liquid Crystals and Ordered Fluids, Vol. 4 (Eds.: J. Johnson, A. C. Griffin), Plenum, New York, 1984, pp. 89-1 10. [28] J. W. Goodby, G. W. Gray, J. Phys. (Paris) 1976, 37 (C3), 17. [29] See, for example, D. Demus, H. Demus, H. Zaschke, Fliissige Kristalle in Tabellen, Vol. 1, VEB Deutscher Verlag fur Grundstoffindustrie, Leipzig, 1974, and references therein. [30] J. S. Patel, J. W. Goodby, Mol. Cryst. Liq. Cryst. 1987,144, 117. [31] M. Hird, Ph. D. Thesis, University of Hull, 1990. [32] R. A. Lewthwaite, Ph. D. Thesis, University of Hull, 1992; D. Demus, H. Demus, H. Zaschke, Fliissige Kristalle in Tabellen, VEB Deutscher Verlag fur Grundstoffindustrie, Leipzig, 1974, Vol. 1, p. 82 and 84; W. Weissflog, D. Demus,
Res. Technol. 1984,19,55;W. Weissflog, H. Heberer, K. Mohr, H. Zaschke, H. Kresse, S. KOnig, D. Demus, German Patent DD-WP 116 732, 1975. [33] G. W. Gray, M. Hird, K. J. Toyne, Mol. Cryst. Liq. Cryst. 1991, 204,43. [34] R. A. Lewthwaite, Ph. D. Thesis, University of Hull, 1992. [35] J. W. Goodby, G. W. Gray, Mol. Cryst. Liq. Cryst. 1976, 37, 157. [36] I. Nishiyama, Ph. D. Thesis, University of Hull, 1992; I. Nishiyama, J. W. Goodby, J. Matel: Chem. 1992,2, 1015. [37] Y. Ouchi, Y. Yoshioka, H. Ishii, K. Seki, M. Kitamura, R. Noyori, Y. Takanishi, I. Nishiyama, J. Matel: Chem. 1995,5,2297. [38] See, for example, P. J. Collings, M. Hird, Introduction to Liquid Crystals: Chemistry and Physics, Taylor and Francis, London, 1997, p. 152. [39] N. Miyaura, A. Suzuki, J. Organomet. Chem. 1981,213,C53; N. Miyaura, K. Yamada, H. Suginome, A. Suzuki, J. Am. Chem. SOC.1985,107, 972; G. W. Gray, M. Hird, D. Lacey, K. J. Toyne, J. Chem. SOC.,Perkin Trans. I1 1989, 2041. [40] J. W. Goodby, R. Pindak, Mol. Cryst. Liq. Cryst. 1981, 75, 233. [41] A. de Vries, D. L. Fishel, Mol. Cryst. Liq. Cryst. 1972, 16, 3 11. [42] J. W. Goodby, G. W. Gray, A. J. Leadbetter, M. A. Mazid, J. Phys. (Paris) 1980,41, 591. [43] L. Richter, D. Demus, H. Sackmann, Mol. Cryst. Liq. Cryst. 1981, 79, 269. [44] J. W. Goodby, G. W. Gray, J. Phys. (Paris) 1979, 40 (C3), 27. [45] D. Demus, S. Diele, M. Klapperstuck, V. Link, H. Zaschke, Mol. Cryst. Liq. Cryst. 1971, 15, 161. [46] A. Villiger, A. Boller, M. Schadt, Z. Naturforsch. 1979,34b, 1535;A. Boller, M. Cereghetti, H. Scherrer, Z. Naturforsch. 1977,33b, 433. [47] G. W. Gray, B. Jones, F. Marson, J. Chem. SOC. 1957,393. [48] G. W. Gray, M. Hird, D. Lacey, K. J. Toyne, J. Chem. SOC., Perkin Trans. I1 1989, 2041. [49] H. Zaschke, J. Prakt. Chem. 1975,317, 617. [50] C. Dong, Ph. D. Thesis, University of Hull, 1994. [51] U. Finkenzeller, A. E. Pausch, E. Poetsch, J. Svermann, Kontakte 1993, 2, 3. [52] S. M. Kelly, Liq. Cryst. 1996, 20, 493.
Handbook ofLiquid Crystals D. Demus, J. Goodby, G. W. Gray, H.-W. Spiess, V. Vill Copyright 0WILEY-VCH Verlag GmbH. 1998
2 Physical Properties of Non-Chiral Smectic Liquid Crystals C. C. Huang
2.1 Introduction Smectic (from the Greek opqypa = soap) is the name first coined by Friedel [ I ] for certain mesophases with mechanical properties similar to those of the layer phase of soaps. From a structural point of view, all smectics have a layered arrangement with a somewhat weak interlayer interaction and a welldefined interlayer spacing that can be measured by X-ray diffraction. Only one smectic mesophase, namely the smectic A (SmA) phase, was recognized by G. Friedel. To date, more than 20 different phases of the smectic type have been clearly identified, some now classified as crystal phases. Many of them were discovered among the chiral or polar liquid crystal compounds. Figure 1 illustrates the molecular order in the most common smectic phases found in non-chiral smectic liquid crystals. Some of the crystal phases which, unlike true smectics, possess long-range translational order are included for completeness. Traditionally, they have been called smectic phases because the interlayer interactions are fairly weak. This discussion is limited to the SmA, hexatic smectic B (SmBh,,), smec-
tic C (SmC), smectic I (SmI), and smectic F (SmF) phases. According to the intralayer interactions, the traditional smectic mesophases can be divided into the following two categories. The first group consists of the smectic phases that lack long-range positional order. Various SmA phases, SmBhex,SmC, SmF, and SmI, plus the possible new lyotropic phase, smectic L (SmL) are some examples. In the first group, the SmA and SmC phases possess a liquid-like intralayer arrangement, while the remaining phases display longrange bond-orientational order. The members of the second group possess long-range positional order, but the interlayer interactions remain fairly weak. To accentuate this important distinction between these two groups, we will call the latter the crystal phases, e.g. crystal B (B), crystal E (E), crystal G (G), crystal H (H), crystal J (J), and crystal K (K), plus possible new phases, crystal M (M), and crystal N (Nc,.). The typical molecular shape of compounds exhibiting any of the above mesophases is highly anisotropic. The molecules are well-described as long rods, roughly 2.5 nm long and 0.5 nm in diameter. The
N
H
a
EI
2.2 Smectic A Phase
Thus the frequency of thermal creation of holes of critical radius R,(=NZ0/2) per unit area will be
j = f o exp(-E,/k,T)
structure. Assuming the layers to be incompressible, the closed loop integral
$n . d r = O (3)
-
443
(5)
Here n is the molecular director. Consequently,
Taking y=21 dyn/cm [4], Zo=2.5 nm and assuming that f o (speed of sound)/[(molecular diameter) (molecular cross section)], one obtains
Hence,
f= 2x
(4)
n . ( V x n ) = O and n x ( V x n ) = O (6)
For N = 1, f - 109/(s . cm2), while for N=2, f - 10-"/(s.cm2). Thus the N 2 term in the exponent is of tremendous consequence. This indicates that while a one-layer film is extremely unstable, thicker films ( N 2 2 ) will last almost forever. On the other hand, liquid crystal molecules with y=27 dydcm [4] and /0=3.0 nm are not that uncommon, and in these circumstances,f- 10-6/(s. cm2) for N = I and one-layer films can be stable enough for many experimental measurements. At the very least, this heuristic argument provides a useful guide for finding compounds that can yield stable one-layer films. These uniform free-standing films offer a well-defined smectic layer structure in which the layer normal is perpendicular to the plane of the film. As a result, the films have proven to be very beautiful systems for investigating numerous physical properties, in particular two-dimensional behavior, related to various smectic mesophases.
In other words, both twist and bend distortions, which form important parts of the nematic free energy, are absent. This leaves only the splay term in the nematic free energy expression. It is seen that by merely bending or corrugating the layers a splay deformation can be readily achieved without disrupting the over-all layer structure Y5, 61. In order to give a better description of the SmA phase, one needs to take into account the compressibility of the layers. Based on this observation, de Gennes [7] put forward a continuum theory for the SmA phase. The parameter which describes such a deformation of the smectic phase is the layer displacement, u (I), along the layer normal ( z axis). In the case of the SmA phase, the displacement gradients of the director fluctuation 6n (r) are equal to -V,u (r),where V, is the gradient in the layer plane (x,y ) . The free energy density per unit volume can be written as
e x p ( - 4 2 ~ ~ ) / ( cm') s.
Vxn=O
f = (1/2) [B(i3u/i3z)2
2.2
Smectic A Phase
2.2.1 Macroscopic Properties Due to the layer structure of a smectic liquid crystal, some types of deformation commonly found in the nematic phase are prohibited. Consider a defect-free SmA
+ K(d2u/i3x2+ i32u/i3y2)2]
(7)
The coefficient B is the elastic constant associated with the layer compressions. This represents the solid-like term along the layer normal. The second term (nematic-like) describes how much energy is required to bend the layers. In describing the SmA phase, both elastic constants K and B are very important. The former, which is higher order,
444
2 Physical Properties of Non-Chiral Smectic Liquid Crystals
is believed to be about the same value as the splay elastic constant in the nematic phase which does not exhibit any divergent behavior at the nematic-SmA transition. The definitions of B and K yield a unique length scale in this problem, namely, the penetration length il=(K/B)'l2 which is typically of the order of a molecular length and characterizes the distance over which curvature is comparable to compression. In discussing the effect of thermal fluctuations, let us consider wave-vector space
[Bq; + K ( q ; + q;)2]IV2(4)I (8) Employing the equipartition theorem, one obtains (9) (1 u'2(q)1) = kB T / { rBq; + K(q: + q;)21 1 F = (1/2)
4
V is the sample volume. The thermal average of the square of the real-space displacement, (u2(r)),becomes
0 2 ( r )= (u2(r)) (10) = [kB T / ( ~ x ( K B ) " ~. ln(AD/d2) )] in which D is the sample size (D= V ' / 3 ) , and d is a typical molecular dimension. Thus the mean square displacement diverges logarithmically with the sample size. This is the well-known Peierls -Landau instability. The divergence is extremely slow. For typical values of liquid crystal compounds, i.e., A = 2 nm, (KB)'l2 = 5 dyn/cm, d = 0.5 nm erg, Eq. (10) yields a and kB T = 5 X layer fluctuation amplitude o=0.85 nm for a sample size D = 1 cm. Since these fluctuations are smaller than the layer-spacing, l0=3.0 nm, the layer structure in a 1 cm3 sample remains reasonably well-defined. To appreciate how slow the logarithmic divergence is, we can ask the following question: what will be the size of the system such that o=Zo/2? It turns out that the sample size has to be approximately that of the sun. Consequently, the higher order dif-
fraction maxima from bulk samples are extremely weak, lov4the intensity of the main peaks, if they are not absent altogether [8, 91. This intrinsic thermal fluctuation allows us to describe the smectic layer structure as a one-dimensional sinusoidal density wave. On the other hand, in a finite experimental system, the smectic layer structure is reasonably well-defined. Furthermore, both the anchoring effects from sample cell walls or free surfaces and any applied field (e.g. magnetic field) will reduce the amplitude of the fluctuations. X-ray diffraction offers the most powerful tool to investigate the effect of this instability. In the harmonic approximation, Caille [ 101 first calculated the effect on the X-ray structure factor. It is related to the Fourier transformation of the correlation function (exp [i qo(u 0-1 - u (0))l) = exp [-qo2((u - u (0)>2)/21
(1 1)
Here qo = 27c/Z0, the wave vector related to the layer thickness. Unlike (u2(r)),this quantity converges. Rather than a Bragg peak like a delta junction for a crystal, the calculated X-ray peaks should exhibit the following profile:
~ ( q=) l/[q,
qx = q y = 0 (12a)
- q0l2-" 2 2-11
I ( q ) cc 1/[q,2+qy1
9
q2=0
(12b)
where
17
= q i k B T/[8Z(KB)'/2]
(13)
This theoretical prediction has been confirmed by detailed X-ray diffraction studies which also enable accurate measurements of [ 111. Figure 2 displays the X-ray diffraction intensity Z(q,) as a function of the scattering wave vector qz obtained at two temperatures in the SmA phase of 8 0 C B [4'-n-octyloxy-4-cyanobiphenyl].The quasi-long-range smectic layer order gives the
2.2
I I
deviation of the experimental data from the dashed line which represents the scattering profile for a system with true long-range order. The best fits of the data to Eq. (12) convoluted with the resolution function are shown as two solid lines. The values of 77 determined from the best fits agree with the experimentally determined values of qo, K , and B. This absence of true long-range smectic order is a result of the simultaneous existence in the free energy of a solid-like elastic term for wave vectors perpendicular to the layers and a nematic term for wave vectors parallel to them. Such a system exhibiting quasi long-range order in three dimensions is at the lower marginal dimensionality below which long-range order no longer exists.
445
Smectic A Phase
Previous discussions demonstrate the importance of the compressional elastic constant B in characterizing the SmA phase. Moreover, the critical behavior of B in the immedite vicinity of the nematic (N)-SmA transition remains an important and unresolved issue. To obtain high resolution measurements of B , several experiments have been designed, (e.g. second-sound resonance [ 121 and the line width of Rayleigh scattering [13]). Well into the SmA phase, the typical value of B is about lo8 dyn/cm2. The most recent sets of experimental data resemble a power-law approach to a finite value at a continuous N-SmA transition. Figure 3 displays the compressional elastic contant B versus temperature just below the N - SmA transition temperature of SOCB. The data were obtained from the line width of Rayleigh scattering measurements [ 13). Whether the value of B approaches a finite value or zero at the SmA - N transition remains an experimentally and theoretically important question. The enhancement of surface ordering at the liquid crystalhapor interface has been well documented experi-
-m
7,8........................................................
7.4..............................
0
7
-<.5
-5
d5
2
-3.5
-3
-2.5
-2
-1 5
1
Wt)
Figure 3. Log-log plot of B versus the reduced temperature (t=(Tc- T)/T,) for 80CB in the immediate vicinity of the nematic- SmA transition. The solid line is the fit to the power-law expression, i.e., B = B , ] + B , (Tc-T)’, with @=0.50.(Adapted from [13]).
446
2 Physical Properties of Non-Chiral Smectic Liquid Crystals
mentally. Failure to take this important effect into consideration in the data interpretation may be the origin of the inconsistency among existing results.
2.2.2 X-ray Characterization of Free-Standing Smectic Films Free-standing liquid crystal films are unique model systems because they combine the properties of controlled size and a high uniformity in the SmA ordering [ 141. In practice, utilizing appropriate liquid crystal materials, uniform films of two to a few thousand molecular layers in thickness can be easily prepared [3]. Since these films are substrate-free and stable down to only two layers in thickness, they provide an important and unique physical system to investigate the evolution from three dimensional (thick films) to two dimensional (two-layer films) behavior, the nature of two dimensional phenomena and the effect of free surfaces as well as reduced dimensionality. Theoretical models of free-standing smectic films have been recently developed [ 151 that extend the smectic bulk free energy to include the effect of the surface tension y at the free surfaces. For an ( N + 1)-layer freestanding film, the free energy can be written as
H = (112) . { Jdr[B(du/dz)2
(14)
+ K(d2u/dx2+ d2u/dy2)2] + yJd7c dy [(du(x, y, z = O ) / ~ X ) ~ + cau (x,y, 2 = 0)/ay)2 + (au (x,y, 2 = Nd)/dx)2 + (du (x.y, z = Nd)/dy)2]} The second integral describes the additional energy associated with the increase in surface area of the two outermost surfaces at z=O and z=Nd. Both finite size and the surface tension will suppress the bulk smec-
tic layer fluctuations. Modern X-ray diffraction, utilizing high intensity sources, nevertheless, offers sufficient resolution to address these problems. The fluctuation profile depends on the ratio v = y/(BK)”’. For most of the ordinary liquid crystal compounds with saturated alkyl chains, one has v > 1 which indicates stronger surface damping of the layer fluctuations. Holyst et al. [15] first carried out the numerical analysis on a discrete version of the free-energy (see Eq. 14). The model offers a satisfactory explanation for the X-ray scattering data obtained from the SmI/C phase of free-standing 70.7 films at 72.5 “C [16]. The 70.7 compound is one member of the homologous series of N-(4-n-aZkyZoxybenzylidene)-4-n-aZkylanilines(n0.m).The phase consists of monolayer two dimensional SmI surface layers on SmC interior layers [ 171. High resolution data from four film thicknesses, namely 3-, 5-, 15-, and 35-layers, were obtained. The data can be fitted by a model including molecular tilt angle profiles to account for the finite tilt angle of both the SmI and SmC phases. However, the effect of surface hexatic order was not considered. Consequently, the critical test of the model should be conducted on a simpler system, namely, free-standing SmA films. Shalaginov and Romanov [ 181 have recently developed a continuum model and obtained an explicit formula for the displacement-displacement correlation function. Furthermore, both the uniaxial properties of the SmA phase and multiple reflection from the interfaces have been included in this theoretical model. It offers excellent agreement with the X-ray scattering data [9] acquired at a temperature well into the SmA phase of FPP (or H7F6EPP) [5-n-heptyl-2(4-n-perfluorohexylethanophenyl)pyrimidine]. Both the specular reflectivity and offspecular diffuse diffraction from 4-, 20-, and
2.3
Hexatic Smectic B Phase
447
[9]. Nevertheless an independent measurement of the compressional elastic constant would be extremely important. The low value of y is due to the perfluorinated tail. Subsequently, a direct measurement of surface tension confirmed this value of y [ 191. In comparison with terminal aliphatic compounds, the reduction of yand enhancement in B leads to v(=y/(BK)"2)< 1. Thus surface damping of layer fluctuations is weaker.
2.3 Hexatic Smectic B Phase Figure 4. Log-log plot of the X-ray scattering intensity versus transverse scans at fixed qz for 4- and 34layer H7F6EPP films. The films are in the SmA phase. Circles and crosses indicate positive and negative q x , respectively. The values (in ,k ') of qL are 0.235 (a), 0.292 (b), 0.348 (c), 0.448 (d), 0.216 (e), 0.287 (0, 0.355 (g), and 0.429 (h), respectively. Data have been shifted for clarity. The solid lines are the best fits to the model. (Adapted from [9]).
34-layer films were measured. Figure 4 shows transverse scans obtained from 4- and 34-layer films at various fixed qz's. A broad peak with a long tail is characteristic of the Peierls -Landau instability. The theoretically fitted results are shown as solid lines. The best fitting results for both film thicknesses and various qz values yield K = l . O x IO-'dyn, B = l . O x 10'' dyn/cm2 and y= 13.0 dyn/cm. The value of K is approximately the same as that for the ordinary nematic elastic constant. The coefficient B is about two orders of magnitude larger than for ordinary liquid crystal compounds with saturated alkyl groups [ 12, 131. The more rigid part of the perfluorinated tail in the H7F6EPP compound may be the origin of this enhancement. This is consistent with the fact that the layer structure of this perfluorinated compound is better defined. The evidence is that the specular reflectivity exhibits pronounced second order peaks
2.3.1 Macroscopic Properties In 1971 Demus et al. [20] first reported the existence of the SmF phase in 2-(4-npentylphenyl)-5-(4-n-pentyloxyphenyl)pyrimidine. About eight years later, utilizing X-ray diffraction, Leadbetter et al. [21] and Benattar et al. [22] studied the molecular arrangement in this mesophase. A pseudohexagonal molecular arrangement was found within the smectic layers in both the SmF and SmI phases. The basic understanding of this observed pseudo-hexagonal molecular arrangement required the concept of hexatic order, developed in the context of the two-dimensional melting theory which was proposed at about the same time by Halperin and Nelson [23]. While the theorists put forth these exciting hypotheses, experimentalists [24], performing X-ray diffraction studies on various liquid crystal compounds, also demonstrated the existence of two different types of B phases with different ranges of interlayer positional correlation lengths. This observation was subsequently followed by several high resolution X-ray diffraction investigations on free-standing liquid crystal films [24-271. First, the conventional B phase in 4 0 . 8 (N-(4-n-butyloxybenzyli-
448
2 Physical Properties of Non-Chiral Smectic Liquid Crystals
dene)-4-n-octylaniline) was demonstrated to be a three-dimensional crystalline phase [25, 261. The more interesting liquid crystal mesophase exhibiting long-range bondorientational order, but only short-range positional order, the SmB,,, phase, was subsequently identified in 650BC [27]. In Fig. 5, the X-ray scattering scan along one of the “crystalline” axes (Q,, scan) displays short-range positional order, while the QI scan exhibits very weak interlayer coupling, similar to that for the SmA phase. The development of a six-fold modulation in an angular scan (with the rotation axis parallel to the layer normal) becomes apparent below the transition temperature TAB=67.9 “C (determined by high resolution heat-capacity measurements by Huang et al. [28]). This six-fold modulation indicates that the phase below TABexhibits 3 D long-range bond-orientational order. However, the size of the hexatic order domain is about 1 mm2, which was much smaller than the X-ray beam size. Extensive averaging is required to demonstrate the existence of six-fold modulation
4
650
using X-ray diffraction. This makes quantitative studies and analyses of the bondorientational order practically impossible. Employing electron diffraction with a beam size of about 1 pm2, Ho and coworkers [29, 301 obtained beautiful six-fold arcs. Figure 6 displays a reproduction of one of these photographs [30] obtained from the (a) SmA, (b) SmB,,,, and (c) B phases of
BC
Figure 5. %-averaged X-ray scattering intensity for a Qll scan (solid dots) and a QL scan (open circles) in the HexB,, phase of 650BC. Note that different scales are used for the QII and QI axes. The inset illustrates the directions of three different scans, namely Qll and QI scans. (Adapted from [27]).
x,
Figure 6 . Electron diffraction patterns from a 9-layer 54COOBC film. The entire film is in the SmA phase (a), in the HexB phase (b), and in the crystal B phase (c). (Adapted from Ref. 30).
2.3
a nine-layer 54COOBC [n-pentyl 4’-n-
pentanoyloxybiphenyl-4-carboxylate]film. The constant intensity ring found in the high temperature SmA phase indicates the liquid-like in-polar molecular arrangement. Such a diffraction pattern is seen ubiquitously in fluids. The low temperature crystal B phase gives one set of six sharp spots. Sharp diffraction peaks are the signature of a crystal. However, much weaker second order diffraction peaks, which cannot be seen in this photograph, demonstrate that the Debye-Waller factor is very small; that is, the crystal is very “soft”. The intermediate SmB,,, phase yields the characteristic six-fold arc for the hexatic order. Although the inplane translational order remains short-ranged, the positional correlation length shows a significant increase (from approximately 2 nm to 7 nm for 650BC) through the SmA-SmB,,, transition [27]. As a result of this experimental evidence, the traditional smectic B phase has been reclassified into two different phases: the SmB,,, and B phases. By employing a symmetry argument, the existence of long range positional order in the B makes the SmA-B [28,3 11 and SmB,,,-B [30] transitions first order. The order parameter associated with the SmA- SmB,,, transition is bond-orientational order. It can be represented by YH= YHoexp (i 6 06).This order parameter places the SmA - SmBh,,-transition in the XY universality class. Thus the transition can be continuous in three dimensions and should, furthermore, exhibit Kosterlitz Thouless-like behavior in two dimensions [32]. Mechanical responses obtained from a low frequency torsional oscillator yield a finite in-plane shear modulus for 4 0 . 8 films in the crystal B phase [33, 341 indicative of a solid-like response. The hexatic B phase of 650BC yields no in-plane shear modulus, just like a liquid [35].
Hexatic Smectic B Phase
449
The molecular bond direction is defined by an imaginary line between one pair of the nearest neighbour molecules [23]. This means that the measurement of bond-orientation correlation requires a four-point correlation function. To date no appropriate experimental tool allows us to conduct this kind of measurement. Thus the degree of bond-orientation correlation can only be inferred indirectly. Moreover, no available physical field exists which can couple directly to the hexatic order in the hexatic B phase. Consequently, the heat-capacity measurement is one of the most powerful experimental probes used to investigate the nature of the SmA-SmB,,, transition and to complement structural identification by X-ray or electron diffraction. The pioneering X-ray work on 650BC also revealed the existence of herringbone order 1271,but a detailed investigation to determine the range of the herringbone order has not yet been performed. Despite the indication of the herringbone order, this phase is simply denoted as the SmB,,, phase. Subsequent electron diffraction studies on 8-layer 3(10)OBC films also revealed the characteristic diffraction pattern due to herringbone order [36]. As a consequence, the hexaticB phase found in nmOBC compounds may be more complicated. To test the theoretically predicted thermal properties [37,38]related to the two-dimensional liquid-hexatic transition critically, we have carefully characterized the hexatic B phase in compound 54COOBC 1301 and found that it does not display herringbone order. To make a clear distinction between these two cases, we propose to use hexatic B to denote the phase found in 54COOBC and use SmB for the phase found in the nmOBC compounds which has a clear indication of some degree of herringbone order.
450
2 Physical Properties of Non-Chiral Smectic Liquid Crystals
ian proposed by Bruinsma and Aeppli [43] to describe the three-dimensional SmASmB,,, transition, we considered the two dimensional version of the Hamiltonian. In the appropriate parameter space of this model, a single transition from the disordered phase to the phase with hexatic and herringbone order can be identified. Furthermore, the heat capacity anomaly can be characterized by a=0.35. Although this coupled XY model provides a plausible explanation for the liquid-hexatic transition found in the nmOBC's, no existing theory is suitable to explain the results from 54COOBC two-layer films, which lack any indication of herringbone order. Thus, our experimental results offer a unique contrast. The structural data clearly demonstrate the existence of the liquid-hexatic transition predicted by the two-dimensional melting theory [23], while the calorimetric results disagree with the related theoretical prediction. Heat capacity data from thin 3(10)OBC free-standing films of various thicknesses are shown in Fig. 8. Using information from specular X-ray diffraction [ 161,electron diffraction [44], and the evolution of this set of
2.3.2 Thin Hexatic B Films Employing our state-of-the-art ac differential free-standing film calorimeter [39 -411, we have conducted high resolution heat capacity and optical reflectivity measurements on liquid crystal films as thin as two molecular layers (thickness approximately 2.5 ndlayer). Figure 7 displays the results from two-layer films of 3( 10)OBC [41] near the liquid-hexatic transition. This heat capacity anomaly shows divergent behavior, while the optical reflectivity displays a sign change in curvature in the immediate vicinity of the heat capacity peaks. These heat capacity data are very different from the theoretical prediction [37,38] which shows only an essential singularity at the two-dimensional liquid-hexatic transition temperature and a broad hump on the high temperature side. Moreover, these heat capacity data can be well-characterized by a simple power-law expression with the heat capacity critical exponent a = 0.30 f 0.05. Using Monte-Carlo simulations, we have investigated the role of herringbone order on the liquid-hexatic transition of nmOBC [42]. Based on the coupled XY Hamilton-
~"
"
73
'
"
"
'
"
'
"
'
75 76 TEMPERATURE ("C)
74
"
"I
Figure 7.Temperature variation of heat capacity and optical reflectivity obtained from 2-layer films of 3(10)OBC. The inplane molecular density was obtained directly from the optical reflectivity data. (Adapted from [41]).
2.3 7.5
5.2
(0
1
(d)
64
1 f
N=7
N=5
68 72 TEMPERATURE (“C)
76
t 9
3.2
(b)
64
N=3
68 72 TEMPERATURE (“C)
76
Figure 8. Temperature dependence of heat capacity near the SmA-SmB,,, phase transition of 3( l0)OBC. The data were obtained from 2- (a), 3- (b), 4- (c), S- (d), 6- (e) and 7-layer (f) films. Both layer-by-layer transition and sharpness of the heat capacity peaks are clearly shown.
heat capacity data from free-standing films, we can draw the following conclusion. Upon cooling from the high temperature SmA phase, hexatic order is established at the outermost layers and proceeds toward
Hexatic Smectic B Phase
45 1
the interior layers in a layer-by-layer fashion, for at least the first four sets of the outer layers [45]. The fact that three-layer films show two well separated transitions indicates that only two-layer films possess twodimensional thermal behavior. Careful thermal hysteresis measurements on various samples indicate that the SmA - SmB, transitions in bulk nmOBC samples and thin free-standing films are continuous [40, 41, 461. The following is a list of several counterintuitive, yet salient features: (1) Distinct layer-by-layer transitions are found associated with this continous transition. This suggests no interlayer coupling. (2) The layer-by-layer transition can be characterized by an exponent v =: 113, suggesting van der Waals-type interlayer interaction (see the discussion below). (3) Under the influence of the surface hexatic order, the transitions associated with the interior layers remain as sharp as the surface transaction. This also suggests no interlayer coupling. (4) The lower temperature heat capacity peak of 3-layer films is more than four times smaller than that of 4-layer films. This indicates a strong interlayer interaction for 3-layer films, but not for the 4-layer ones. Further experimental and theoretical advances are required to address these counterintuitive questions. Although surface enhanced order is commonly found for various liquid crystal transitions, the layer-by-layer transitions have only been characterized in the following five cases: the SmA-SmI transition of 90.4 1471, the SmA-SmB,,, transition of nmOBC [45], the SmA-SmB,,, transition of 54COOBC [48], the SmA-B transition of 40.8 [49] and the SmA-isotropic transition [50, 511. Thus far the sequence of the transition temperatures can be described by the following simple power law [ 5 2 ] :
452
2
Physical Properties of Non-Chiral Smectic Liquid Crystals
2.4
Smectic C Phase
2.4.1 Physical Properties near the Smectic A-Smectic C Transition
\
I
* '4
lo-'
IO-~
lo-*
lo-'
(T(L) -To)/To Figure 9. The number ( L ) of layers of a 90.4 thick film in the SmI phase which form at the SmA/vapour interfaces on cooling is plotted as function of the layer transition temperature (T(L)).The temperature Tois a freezing temperature which is one of the fitting parameters in Eq. (15). (Adapted from [47]).
Here L gives the separation (measured in units of layers) between the nearest film/ vapor interface and the layer in question. The fittings yield L0=0.24k0.01, u=O.37 k0.02 for 90.4 [47], L0=0.31 k0.02, u=0.32k0.02 for 3(10)OBC [45], L0=0.34 k0.05, u=0.30k0.05 for 54COOBC [48] andLo=0.32k 0 . 0 1 , =0.36 ~ k0.02 for 40.8 [49]. The experimental data and fitting results near the SmA-SmI transition of 90.4 are shown in Fig. 9. The critical exponent u = 113 indicates that simple van der Waals forces are responsible for the interlayer interaction. Although the layer-by-layer transition near a first order transition has been theoretically predicted [52], that near a second order transition is totally counterintuitive. Further experimental and theoretical work is necessary to address this unresolved puzzle.
2.4.1.1 Bulk Properties
The major difference between the SmA and SmC phases is that the latter exhibits a finite molecular tilt angle from the layer normal. While the SmA phase possesses uniaxial properties, the SmC phase shows biaxial properties. Upon heating, one usually finds the following three possible transitions from the SmC phase: SmC-isotropic, SmC-N, and SmC- SmA. In the first two cases, more than one degree of order vanishes in the given transition. For example, both the layer structure and molecular tilt disappear at the SmC-N transition. These cases are, in general, first-order transitions. Even though pretransitional behavior is not uncommon, the tilt angle shows a finite jump at the transition temperature. The order parameter associated with the SmC - SmA transition can be written as Yc= Oo exp(i4,) [53]. The amplitude Oo is the molecular tilt angle relative to the layer normal and the phase factor GC denotes the azimuthal angle of the molecular director. In 1972, de Gennes [53] argued that the SmA - SmC transition should belong to the three-dimensional XY universality class (helium-like) and might be continuous. This important observation stimulated numerous experimental efforts to investigate the nature of this transition. However, the novelty of this phase transition was revealed ten years later by careful X-ray diffraction studies [54]. Subsequent high resolution calorimetric studies by Huang and Viner [55] enabled them not only to confirm the meanfield nature of this transition, but also to pro-
2.4
pose an extended mean-field model to characterize this transition fully. The majority of the SmA - SmC transitions are found to be mean-field [56-611 and also to be in the close vicinity of the mean-field tricritical point. Thus, to describe the physical properties associated with this transition, we need the following extended mean-field free energy expansion [55, 621.
G = Go + a t I YCl2 + b I YCI4+ c JYclh (16) Here t (=(T-T,)IT,) is the reduced temperature with T, being the transition temperature. The coefficients a and c are usually positive constants. For a continuous SmA-SmC transition b > O and for a first order one b < 0. The special case, b = 0, is the mean-field tricritical point. Huang and Viner [55] proposed a dimensionless parameter to=b2/(ac) to describe the crossover temperature between the mean-field tricritical region (I t l 9 to) and the ordinary meanfield regime ( I t 1 4 to). The value of to is usually very large for most other mean-field transitions [55], (i.e. paraelectric-ferroelectric, conventional normalsuperconducting, Jahn-Teller-type transitions). Thus the I YCI6 term can be ignored. To our great surprise, most of the SmAor even as SmC transitions have to < low as to= lo-'. Thus they are extremely close to a mean-field tricritical point. Various research groups have not only characterized continuous and first order SmASmC transitions, [63] but also identified systems in which the transition is tricritical [64-661. The width of the critical region may be estimated from the following Ginzburg criterion [67]:
Due to the unusually large value of the meanfield heat capacity jump (AC > lo6 erg/ cm3 K), the critical region of the SmA-SmC
Smectic C Phase
45 3
transition becomes experimentally inaccessible (tc < lo-') provided that > 1.3 nm which is slightly larger than the effective size of the molecules. Since the SmC ordering is presumably not driven by long-range interactions and the SmA-SmC transition is not at or above the upper critical dimensionality (d,=4 for the XY universality class), it is very difficult to explain the observed mean-field behavior. If the coupling to the layer undulation could be neglected, the SmA- SmC transition would be helium-like. Although the effect of layer undulation on the nature of the SmA - SmB,,, transition was considered by Selinger [68], it is extremely important to conduct extensive studies of the effect of the quasi-long-range SmA order on the molecular tilt order (SmA- SmC transition) and the bond-orientation order (SmA -SmB,,, transition). Meanwhile, it is very important to identify experimentally a system showing criticalfluctuations associated with the SmA-SmC transition [69]. In principle, with sufficient resolution, the SmA- SmC transition should exhibit an extremely rich series of cross-over behavior in an appropriate liquid crystal compound: mean-field tricritical-like ( 1 t (> to) - ordinary meanfield (to> I t I > tc) - Gaussian fluctuations (I tl= tc)-critical fluctuations (tc> I t l ) upon approaching the transition temperature. In light of the abnormal behavior of ultrasound velocity and attenuation near the SmA-SmC transition [70, 711, Benguigui and Martinoty [72] advanced a theory to explain the experimental data. They concluded that the Ginzburg crossover parameter ( t G ) determined by the static properties, (e.g. heat capacity) could be much smaller than that obtained from the measurement of the elastic constant. However, a quantitative comparison between the theoretical prediction and the experimental data is still lacking.
tetf
454
2
Physical Properties of Non-Chiral Smectic Liquid Crystals 8
From Eq. (16), one can calculate the temperature variation of tilt angle, heat capacity (C) and susceptibility They are given as follows:
(x).
For T > T,,
eo= o c=c,
L
0 -1.0
(184 (194
-0.6
-0.2 0
0.2
0.6
1.0
T-Tc (lo
a)
and
x-'= 2 a t
(20 4
For T < T,, 00 = { [-b+b
(1 + 3 I tI/to)'/2]/(3~)} 1'2 (18 b)
c = co+ TA((T, - T)/T,)-'/~ and .. .
x-' = 8 a ( t l + (8ato/3)
305
. [ l -(1 +31tl/to)]"2
(20b)
b)
310
31 5
320
325
TEMPERATURE ( K )
Figure 10. (a) Temperature variation of tilt angle
Here Co is the non-singular part of the (circles) for T < T, and reciprocal of the susceptibility heat capacity. A = L Z ~ / ~ / [ ~ ( ~ C )and ' ~ ~ T (triangles) ~ / * ] for T>T, near the SmA-SmC transition of 40.7. The transition temperature Tc=49.69"C. T, =T, (1 + t0/3). These equations demonThe tilt angles are measured by X-ray (open circles) strate that the effect of mean-field triand light (solid circles) scattering. The solid line is the criticality only shows up in the region T < T, best fit to Eq. (18) with to= 1 . 3 ~ (Adapted from in which I Ycl is non-zero. Except for the [56]).(b) Heat capacity in J/cm3K versus temperature temperature variation of for T < T, many near the SmA-SmC transition of racemic 2M450BC. The solid curve is the best fit to Eq. (19) with high resolution experiments [55 -611 have to= 3 . 9 ~ 1 0 - ~ (Adapted . from [58]). been conducted to test these predictions critically. Temperature variation of both Oo(TT,) obtained from 40.7 is shown in Fig. 10 (a). Experimentally, it is non-trivial to measure in the resharp rise of the heat capacity on the low gion T < T,. temperature side indicates the closeness Since heat capacity is a second derivative of this transition to a mean-field tricritiof the free energy, its temperature variation cal point. Equation (19) offers an excellent provides the most critical test of the model. fit which yields a very small value of One such result obtained near the SmAto(=3.9X 10-3). SmC transition of racemic 2M450BC is Because the molecule consists of a rigid shown in Fig. 10(b) [57]. Here 2M450BC central core and semiflexible tail(s), the defrefers to 2-methylbutyl 4'-n-pentyloxyinition of the tilt angle is somewhat ambigbiphenyl-4-carboxylate. The experimental uous. In particular, X-ray diffraction probes data display a characteristic mean-field the electron density of the entire molecule jump at the transition temperature. The to yield the smectic layer spacing; optical
x
x
2.4
probes are more sensitive to the orientation of the core part of the molecule. In 1978, Bartolino et al. [73] reported the temperature variation of the tilt angle obtained from both X-ray diffraction and conoscopy of four liquid crystal compounds with a large range of chain lengths. The optical tilt angle is always found to be larger than the tilt angle derived from the layer spacing. The difference increases with the alkyl chain length. This demonstrates that the melted alkyl chains are on average closer to the layer normal. Qualitatively, all the X-ray and optical data from these four compounds in the immediate vicinity of the SmA - SmC transitions are consistent with the ordinary mean-field prediction, (i.e. 8:" I t l ) . To measure the layer spacing, high resolution X-ray work requires high quality, well-aligned samples in a beryllium sample cell. In addition, the measurement is fairly time consuming. To date, only a limited amount of such work has been performed [54, 561 and most tilt angle data have been obtained from various optical techniques [56, 60, 611. Consequently, in the light of the extended mean-field model, critical comparisons between X-ray and optical tilt angles remain to be made on compounds of various chain lengths. The existence of bulk polarization in the ferroelectric smectic C (SmC*) phase makes switching the azimuthal angle (Cp,) from Cp,, to Cpco+nfairly easy through a change in the polarity of a moderate applied electric field. As a result, the clear optical contrast between the state of Cpc=Cpc, and Cpc = Cp,, + n greatly facilitates high resolution optical tilt angle measurements. It has been experimentally demonstrated that the tilt angle but not the polarization is the primary order parameter for the SmA* - SmC* transition [74]. The fact that the SmA-SmC (or SmA* SmC*) transition is mean-field like and the
Smectic C Phase
455
tilt angle is the primary order parameter yields the following singular part of the free energy expansion [75], G = at1 y,i2 + AG(Y,, 1x1)
(21)
Here AG( Y,, (x))represents all higher order expansion terms with temperature independent expansion coefficients and x is any set of relevant physical parameters characterizing the phase transition other than the primary order parameter Y,. For example, to characterize the SmA* -SmC* transition, we need at least two additional parameters, for example, polarization and helical pitch. From measured heat capacity data (C), after subtracting the non-singular par (C,), one can calculate the following inte gral:
From the general mean-field free energy expression, Eq. (21), one can show that 80,cal should be proportional to 8,. To check this unique relationship for a mean-field transition, high resolution calorimetric and optical measurements were carried out near the SmA*-SmC* transition of DOBAMBC [ p - ( n-decylox ybenzy1idene)-pamino-( 2methylbutyl) cinnamate]. Figure 11 displays the ratio 80/80,ca, which remains constant over a temperature range of more than two and a half decades in reduced temperature [75]. The data clearly confirm this important prediction. Most importantly, the free energy expansion (Eq. 21) holds for a mean-field transition, but not for a critical fluctuation one. This unique relationship has been used to demonstrate that the SmA SmC transition in AMC11 is mean-field [69] and not XY-like, as suggested by the detailed tilt angle measurements [77]. Here the AMC 11 compound refers to azoxy-4,4'di-undecyl-a-methylcinnamate.
456
2 Physical Properties of Non-Chiral Smectic Liquid Crystals
-
c 6
h
M
m
1E
1
W c-,
l ?
-
2 Y
0.5
0.
F?
g o
0.1 1 TEMPERATURE (T,-T)(K)
10
Figure 11. The ratio @o/Oo,cal plotted as a function of (Tc- T ) for the SmC* phase of DOBAMBC (TC=94.15”C). (Adapted from [75]).
rest of the interior layers, respectively. The film is taken to be symmetric about a plane passing through its center so that IYC.J= Several research groups have investigated I Yc,N+l-il.The leading coefficients in the the temperature variation of the tilt angle free-energy expansion A = a ( T - T c , B ) / T c , B as a function of film thickness near the continuous SmA* - SmC * transition of and A ‘ = U ’ ( T - T ~ , ~ ) / Tare , , ~ different for DOBAMBC [78, 791 and the first order the surface and interior layers. T c , B and Tc,s SmA-SmC transition of C7 [go]. Here, C7 are the bulk and two-layer (surface) transirefers to 4-(3-methyl-2-chloropentanoyl- tion temperatures, respectively. This free oxy)-4’-heptyloxybiphenyl. Figure 12 disenergy gives fairly reasonable fitting replays the average tilt angle versus temperasults. There exist systematic deviations ture data for various DOBAMBC film thickfrom the experimental data of lo-, 7-, and nesses. The average tilt angle was deter5-layer films. From the observation that surmined by observing the change in the polaface penetration length is larger than one rization state of the laser light transmitted layer, separate free-energy expressions for through the film. The data clearly exhibit a the outermost layers and the rest of the surface enhanced transition. In the case of interior layers may not be a sufficiently 7- and 10-layer films, separate “surface” good approximation. Further experimental and interior transitions are discernible. The work is required to address this question. data strongly suggest that the characteristic The experimental data also indicate that the thickness of the “surface” layers is more 2-layer films display a precipitous drop in than one molecular layer. Unlike most other the tilt angle.(see the inset of Fig. 12). The transitions involving the smectic phases, no authors speculated that the drop might be layer-by-layer transition is observed near the due to the presence of two-dimensional SmA-SmC transition [69, 78-80]. We do fluctuations. It should be noted that such a not understand the origin of this difference. drop in the measured average tilt angle was For N 2 3 , the data can be described by a also reported by Amador and Pershan [79] mean-field model consisting of the followfor 3-, 4-, 5,6-, and 11-layer DOBAMBC ing free energy contributions [78]: an interfilms. Thus, an obvious difference exists layer coupling term, and two separate sets between the data from these two research of parameters for the extended mean-field groups. High resolution measurements on model within the outermost layers and the thermally more stable liquid crystal com2.4.1.2
Thin Free-standing Films
2.4
Smectic C Phase
457
Figure 12. Average tilt angle versus temperature near the SmA*-SmC* transition of free-standing DOBAMBC films as a function of film thickness ( N ) . The solid curves are the fit to a mean-field model. The inset shows the result from a 2-layer film. A jump in the tilt angle at the transition temperature is shown. (Adapted from [78]). I00
80 T
120
(“C)
pounds are needed to address this important issue.
2.4.2 Macroscopic Behavior of the Smectic C Phase 2.4.2.1 Bulk Properties Well into the SmC phase the fluctuations of the tilt angle become energetically unfavorable since they are non-hydrodynamic. Then the predominant elastic effects are deformations described by the two “extra” hydrodynamic variables of the SmC phase. The first one is u ( r ) which, just as in the SmA phase, describes undulations of the layer structure. The new variable in the SmC phase describes the azimuthal position of the local molecular tilt. This corresponds to the azimuthal angle q& in the SmC order parameter. To describe this new degree of freedom, de Gennes [ 5 ] introduced a new director, the C-director, which is a unit vector along the projection of the molecular director onto the layer plane. Nearly all the light scattering in the SmC phase is due to the fluctuations of these two variables. The Orsay group [81] has discussed the elastic theory of the SmC phase by introducing a rotation vector, $2(r),to describe the possible distortion. Its direction gives the
axis of rotation of the layer structure and its magnitude gives the amount of rotation. In a uniform state the coordinate system is chosen so that the layer normal is along the z-axis, and the C-director points along the x-axis. Then Q Z represents the rotations of the C-director away from the x-axis, and its magnitude indicates the local azimuthal angle @c. $2, and QY involve rotations of the layer structure and are related to the layer undulation variable u , namely, $2, =auldy, $2,=-au/ax. All of the long wavelength elastic distortions of the SmC phase can be described in terms of this rotation vector. The SmC phase possesses a mirror symmetry plane (the z-x plane) and a two-fold rotation axis along they axis. With these two symmetries the distortion free energy density (up to second order) takes the following form:
,Ll= { A
(an,
+ A (an,
+A2,(&2,1ay)2}/2
+ { Kb(aa,lax)2 + K,(an,/ay)’ + K,(aa,/az)2 + 2Kb,(an,lax) (an,laz))/2 + D , (aa,lax)
(23)
The A terms are associated with the curvature of the layers and are analogous to layer
45 8
2 Physical Properties of Non-Chiral Smectic Liquid Crystals
undulation in the SmA phase, which requires only one elastic constant (see Eq. 7). The K terms describe the distortion of the C-director, and the D terms represent the coupling between the layer undulation and C-director. At a given temperature, the C-director in the SmC phase is similar to the nematic director. The significance of the K terms for the C-director is similar to that of Frank elastic constants for the nematic director. The coefficients Kb, K, and Kt correspond to the bend, splay, and twist elastic constants, respectively. Notice that there are nine elastic constants to describe the SmC phase in contrast to three in the nematic phase and only one in the SmA phase. Thermally excited fluctuations of S are responsible for light scattering in the SmC phase. Of particular interest are the fluctuations of the C-director, since this is the distinctive feature of the SmC phase. Applying the equipartition theorem to the Fourier transform of Eq. (23), one obtains
this number increases to thirteen [5]. Nevertheless, it is still possible to interpret dynamic experiments by assuming a simple viscous relaxational behavior characterized by an effective viscosity qeff. As mentioned previously, the light scattering intensity with q in the plane of the layers (this is the case in the SmA phase) involves all nine elastic coefficients and is difficult to interpret. For this reason the light-scattering studies that have been done for the SmC phase have probed only the fluctuations of the C-director. Using a lightbeating spectroscopic technique, Galerne and coworkers [82] measured the intensity and damping time of thermally excited twist fluctuations of the C-director in DOBCP [di-(4-n-decyloxybenzylidene)-2-chloro-14-phenylenediamine]. From Eq. (24) with qy=O, the scattering intensity can be simplified as
(a,(4)0, (-4))
or, equivalently, one can write the denominator as
=kBT/[Kbq:+
(24) Ksqg+KtqZ+2Kbtqxqzl
This result indicates that the light scattering from C-director fluctuations is significant for all 4.This is in contrast to the situation in the SmA phase, where the scattering was restricted to the region near the q,=O, and provides an explanation for the nematic-like turbidity of the SmC phase. The scattering from layer undulation in the SmC phase is also restricted to the region near q,=O, but experiments probing this mode are difficult since the intensity depends on all nine elastic coefficients. Another important difference between the SmC and SmA phases is the number of the dissipative coefficients involved. In the SmA, SmB,,, and nematic phases, which are uniaxial systems, there are only five independent viscosity coefficients. In the SmC phase, which is biaxially symmetric,
2
OC
l/[Kbq: + K t q z + 2Kbtqxqzl
(25)
[& cos28 + Kt sin28 + 2 ~ , , ,cos 8 sin el q2 2 = K ( 8 )q (26) and thus
~ ( 6q2z ) = constant
(27)
Here 8=tan-'(q,/q,). K ( 8 ) is the elastic constant associated with the twists of the smectic layers of wave vectorq along 8. A plot of qzZ1/2versus qxZ1/2should yield an ellipse. At a fixed temperature, by varying q, part of this ellipse has been experimentally demonstrated as shown in Fig. 13. The experimental data show an ellipse with its major axis inclined at eel=35" from the layers (x-axis). This angle is close to the direction of the molecular tilt 8m01, which is the assumed tilt angle of the molecules resulting from the alignment procedure. The alignment is achieved through mechanical
Smectic C Phase
2.4
459
rT'".
1
1
Figure 13. Plot of 9,1'/2 versis qX1'I2.The DOBCP liquid crystal sample is in its SmC phase. The inset shows the relative orientation of wave vector q with respect to the layer structure. The smaller axis of the ellipse corresponds to K,,,. (Adapted from [82]).
rubbing of the glass plates and the application of a magnetic field (20 kG) at a 45" angle of the plates during the cooling into the SmC phase. Gel is the angle of the experimental ellipse with respect to the smectic layers. The finite difference, 8mol-0e1, characterizes the lower symmetry of the SmC phase than the SmA phase. For each direction 8 of q, the distance between the origin and the experimental point on the ellipse should be proportional to K ( 8 ) . From a least-squares fit of the data, the authors ex2.3, comtract the ratio K(8)max/K(8),,,in= parable to the corresponding ratio K33/K22 (=2) found in a typical nematic liquid crystal. The damping time of these fluctuations should, if the relaxation is viscous, be of the usual form,
I- = z-'= K ( 8 )q2/qcff(8)
(28)
where qeff(8)is the effective viscosity. The results of the damping time measurements
c.g.s.ulo-')
., " / .
..
Figure 14. Plot of qiz"* versus q , ~ "(in ~ cgs units). The triangles and dots are data obtained from two different scattering configurations. The sample is in its SmC phase. (Adapted from [82]).
of Galerne et al. [82] are displayed in Fig. 14, where the separation between the origin and the data points gives the quantity, [ ~ e ~ f ( 8 ) / K ( 61'2). 1 An analytic form for qeff(8)is given [82] which involves three viscosity coefficients and two directions. One of them, 8,(-40°), is the direction of the maximum flow-orientation coupling and is experimentally found by employing the K ( 8 ) data in the damping time measurement. Estimates of the absolute magnitudes of both K(8),,, and K(8)mi, and three viscosity coefficients in q,,(8) were also made by observing the decrease in damping time when a magnetic field was applied in the symmetry plane along the layers. The elastic constants were: K(8),,,,, = 1.1 x lop6dyn and K(8),i,=S x dyn, which are slightly larger than typical nematic values [5, 61. By utilizing these values, the calculated viscosity coefficients are one order of magnitude larger than those in a typical nematic at an equivalent temperature.
460
2 Physical Properties of Non-Chiral Smectic Liquid Crystals
2.4.2.2 Thin Free-standing Films As discussed previously the extra hydrodynamic mode due to the molecular tilt in the SmC phase can be described by the variable Qz. As demonstrated by Meyer et al. [141, free-standing films offer a unique geometry to single out this variable. For wavelengths that are large compared to the film thickness (approx. 2.5 nrdlayer) and at a temperature far away from other transitions, without the complications of the surface-enhanced order, SmC free-standing films behave essentially like two-dimensional nematics. The free energy per unit area within each layer may be written as f = [ K $ ( a Q , l a ~ )+~K,* (aQ,lay)2]/2
(29)
the range of 4 K - T, - T I 2 0 K. Using 1,=3.3 nm for the SmA layer spacing, one obtains K , = 1 x loA5dyn which is about an order of magnitude larger than the typical value for a nematic liquid crystal. Figure 15 shows the thickness dependence of K$lsin2 8, and K$ obtained from bend mode fluctuations, as well as K:lsin28, and K,* from splay mode fluctuations. For N 2 4 , both K$lsin28, and K:lsin2Bo show a linear dependence on the film thickness. The deviation from the linear relation in the thin film region is most likely due to the surface enhanced ordering as shown in Fig. 12. To date, this is the only measurement in which one-layer films have been characterized. Numerous efforts have been aimed at pre-
where I '
K,* = h ~ , sin200 , and K$ = h [K22sin200cos2f3,
(30)
7
-
( b ) BEND
MODE
(31)
+ K33sin48,]
h(=Nl, cos O0) is the film thickness of an N-layer film, I, the layer spacing in the SmA phase, and 8, the molecular tilt angle. The coefficients Kii are the three bulk Frank elastic constants K,, (splay), K22 (twist), and K33(bend). Employing the equipartition theorem, one obtains the mean-square amplitude of these fluctuations, (W7)Qz(-!2))
= kEJl[K$d+K,*qy21 (32)
By employing a high electric field to quench the molecular orientation fluctuations in the DOBAMBC films, the light scattering enables absolute determination of elastic constants K$ and K,* as a function of temperature [83] and film thickness [84]. For the thinnest film stable in both time and over a wide temperature range, namely, a three-layer film, the results yield h K1 = Kf/sin2 8, = 1 x lo-' erg. This is relatively insensitive to temperature in
I
t 1
2
I
J
I
I
I
I
I
3
4
5
6
7
8
9
NUMBER OF LAYERS ( N I
Figure 15. Elastic constants ((a) splay and (b) bend) versus layer number (N) at T=91.5"C in the SmC* phase of DOBAMBC films. The average molecular tilt angle 8,(N) is determined by ellipsometry. The solid (a) and dashed (b) lines emphasize the linear dependence of Klsin28, at large Nand the reduced contribution of the surface layers. (Adapted from [83]).
2.5
paring stable one-layer films in order to investigate physical properties (e.g. heat capacity, optical reflectivity, electron-diffraction etc.). So far, significant achievement has been accomplished [85, 861.
2.5 Tilted Hexatic Phases Because of the existence of the quasi-hexagonal lattice in the tilted hexatic phase, there are three possible molecular tilt directions. The molecular tilt points towards the nearest neighbor for the SmI phase, towards the next nearest neighbor for the SmF phase, and towards an intermediate site for the novel SmL phase (see Fig. 1). Thus the former two have a higher symmetry than the SmL phase, which was first discovered in a lyotropic liquid crystal system [87]. The most common tilted hexatic phases found in thermotropic liquid crystal compounds are SmI and SmF. As mentioned previously, the pseudo-hexagonal molecular arrangement which is the characteristic feature of the hexatic phase, was first identified for the SmI phase.
2.5.1 Identification of Hexatic Order in Thin Films Due to the symmetry of the order parameters associated with the molecular tilt ( Y', = Oo exp (i 4,)) and bond-orientational order ( YH= YH0exp (i 6 O,)), the model Hamiltonian describing the SmC-tilted hexatic phase can be written as [88]
C C O S ( ~-O6O6j) ~~
H = - 56
(id
- JI
C cos($ci - $cj>
(id
-g
c c0s(6(P6i i
- 6@ci)
(33)
Tilted Hexatic Phases
46 1
The first and second terms describe the nearest neighbor interactions of the bondorientation and molecular tilt angle. The existence of the last coupling term between Ycand YHproduces a unique feature associated with this transition. The molecular tilt will induce a finite bond-orientational order, unless the coupling constant g incidentally vanishes. Thus, the SmC phase which is followed by a tilted hexatic phase is usually not a genuine thermodynamic phase. It only differs from the tilted hexatic phase by the strength of the bond-orientational order. Accordingly, the SmC-tilted hexatic phase transition is similar to the paramagnetic-ferromagnetic transition under a finite applied magnetic field and is always suppressed to some degree. An elegant experiment conducted by Dierker et al. [89] resulted in the first confirmation of the existence of the bond-orientational order in thin SmI films of racemic 2M4P8BC (or SSI) [4-(2'-methylbuty1)phenyl 4'-n-octylbiphenyl-4-carboxylate]. In the SmC phase, a 27-c point disclination in the director field is a fairly common defect (Schlieren texture) in which the orientation of the molecular director forms a circular pattern around the defect. Cooling into the SmI phase, the coupling between the molecular tilt and bond-orientational order will cause a tight distortion near the defect core and create a large strain in bond-orientationa1 order. This strain can be relaxed, at the expense of director disclination line energy, by producing radial lines of 60" disclinations which separate regions of relatively uniform director orientation. Employing depolarized reflection microscopy, Dierker et al. [89] observed this kind of defect in very thin films at a temperature well into the SmI phase. A magnificent star defect of five radial arms growing from the center of a 2z disclination can be seen. The existence of this five-arm star defect demonstrates that
462
2 Physical Properties of Non-Chiral Smectic Liquid Crystals
the initially 2 n disclination (rn = 1) of the bond-orientational order (locked on to the tilt order) has split into five rn = 116 disclinations at the arm endings, plus one m = 1/6 at the defect core. Upon approaching the crystal J phase, the arm length seems to grow continuously to infinity. The temperature dependence of the star-defect arm length for a two-layer film near the SmIcrystal J transition has been obtained. Qualitatively, this can be explained in terms of the temperature dependence of the bond-orientational elastic constant in a two-dimensional system [23].
2.5.2 Characterization of Hexatic Order in Thick Films As previously mentioned, no physical field exists which can act as an ordering field for the bond-orientational order in the SmB,,, phase. Thus, to date, no monodomain SmB,,, sample has ever been prepared. The situation is very different in the case of tilted hexatic phases. The coupling between the bond-orientation and molecular tilt order (see Eq. 33) provides a unique opportunity to prepare a single domain tilted hexatic sample in free-standing liquidcrystal films. Cooling down a free-standing film through the SmA- SmC transition under an off-axis magnetic field will create a uniformly tilted SmC sample. Upon further cooling into the tilted hexatic phase, one obtains a single domain tilted hexatic sample. Brock et al. [90] have prepared such a monodomain sample and investigated the evolution of the bond-orientational order near the SmC - SmI transition of racemic 2M4PSOBC (or SOSI) [4-(2'-methylbuty1)phenyl 4'-n-octyloxyphenyl-4-carboxylate]. Upon cooling, this compound exhibits an extremely rich sequence of mesophases, namely, nematic, SmA, SmC, SmI, crys-
40
60
80
100
120
140
X (degrees) Figure 16. X-ray scattering intensity versus the angle of x-scan along the peak of the form factor and structure factor near the SmC-SmI transition of a thick 2M4P80BC film. Solid curves are the results of nonlinear least squares fits to Eqs. (34) and (35). (Adapted from [go]).
tal J, and crystal K with the SmC - SmI transition temperature at 79.9 "C. Figure 16 displays the X-ray scattering intensity as a function of angular scans (X-scan) over a window of 100" for five different temperatures in the immediate vicinity of the SmC - SmI transition. The sample is a thick 2M4P80BC film, cooled from the SmA phase under an off-axis magnetic field (roughly 1 kG). The six-fold modulation in this X-scan is very clear. The X-ray scattering intensity shows a very fast increase within 3 K of the transition temperature. This single-domain SmI sample enables one to obtain high quality X-ray data describing the bond-orientational order. In order to characterize the bond-orientational order quantitatively, a nonlinear leastsquares fit of the data between 60" and 120" to the following Fourier cosine series [90]
2.5
has been made:
I ( X ) = Zo (112) C C,, cos[6n(9Oo - X)]
{
1
I1
+ IBG
(34)
x
Here is the angle between the in-plane component of the scattering vector q and the magnetic field H . I,, is the background term. Below the transition temperature, one expects to see harmonics. The coefficients C,, measure the strength of n-fold harmonics. Each of the C,, yields an independent degree of bond-orientational order. The temperature dependence of the first seven members of the set { CG,} is obtained from such a fit and plotted in Fig. 17. The results explicitly show that as the temperature decreases the sample smoothly develops first C , order, then C,2 order, then C1gorder and so on. This transition evolves smoothly and
If
0
A
TemperaturePC
Figure 17. First seven Fourier coefficients (Eq. 34) describing the bond-orientational order in a thick 2M4P80BC film. The inset shows the scaling exponents onversus harmonic number n. They are determined from the best fit of the data to Eqs. (34) and (35). (Adapted from [91]).
Tilted Hexatic Phases
463
continuously. In particular, even at 80 “C (in the SmC phase), the coefficient C6 is finite. This observation confirms the theoretical prediction that a finite coupling between the molecular tilt and bond-orientational order induces small but finite hexatic order in the SmC phase [SS]. There exists no symmetry change between the SmC and tilted hexatic phases. The C,,’S are found to satisfy the simple scaling relation [90] c6,= (C,)O”. The average values of 0,as a function of n are plotted in the inset of Fig. 17 [91]. Subsequently, starting from the idea that the bondorientational order can be expressed as an XY-like order parameter, Aharony et al. [92] have developed the following harmonic scaling relation:
The solid lines in Figs. 16 and 17 are results of a non-linear least-squares fit by using Eqs. (34) and (35) [91]. The parameter A ( T ) is found to be independent of n and temperature and close to the theoretical asymptotic value, A = 0.3 -0.008 n [92]. The remarkable achievement of these experimental and theoretical advances is that, in a single experiment, eight cross-over exponents which previously required separate measurements on different systems, or could not even be obtained, can be measured simultaneously. Nevertheless, recent high resolution calorimetric results [93] obtained from 2-layer DOBAMBC, 4-layer 2M4P80PC and other thin free-standing films near their SmCSmI transitions do not agree with the theoretically predicted heat-capacity anomaly associated with the two dimensional XY transition. To the best of our knowledge, no one knowns why the XY-type order parameter for bond-orientational order is so successful in explaining the structural data, but fails to give a proper account for the heat capacity data. Note that both 3-layer
464
2 Physical Properties of Non-Chiral Smectic Liquid Crystals
DOBAMBC and 4-layer 2M4PSOBC films show two separate heat capacity anomalies near their SmC - SmI transitions; therefore we believe that only two-layer films of DOBAMBC or 2M4P80BC with a single heat capacity peak exhibit two-dimensional behavior.
2.5.3 Elastic Constants Employing quasielastic light scattering, Dierker and Pindak [94] have measured elastic constants and viscosity of two-layer SmI films of 2M4P8BC in the vicinity of the weakly first order SmC* - SmI* transition. With the help of an applied magnetic field (along the x-axis), monodomain SmC* and SmI* samples were prepared. Similar to the case for the SmC phase, the intensity of depolarized light scattered by thermal molecular orientation fluctuations can be written as, I = l/[K,* 4x2 + K,* q," + 2nPp,2qx1
(36)
In the SmC* phase, K,* and KZ are the Frank elastic constants for bend and splay distortion of the C-director. In the tilted hexatic phase, they are the sums of the director and bond-orientational elasticities. The last
term is a space-charge contribution due to the permanent dipole moment, Po, of the chiral molecules. The existence of the last term enables one to calibrate the scattering intensity and determine absolute values for the elastic constants. The measured elastic constants from a two-layer film near the SmC* - SmI* transition temperature (TC,=77.3"C) are plotted in Fig. 18. Both splay and bend elastic constants show a large jump through the first order SmC*SmI* transition. As the temperature decreases, the increase in the elastic constants in the SmI* phase is mainly due to the increase in the short range positional correlation length as indicated on the left of the vertical axis. The experimental data in the tilted hexatic phase are above the theoretically predicted hexatic stability limit K2=72 k, TcI/n[23].
2.6 Surface Tension Our previous discussions demonstrate the importance of the surface tension to our heuristic argument of the film stability, interpretation of the surface-enhanced or-
C " " I ' " ' I " " I " " I " " I " " I
w
150
I
100
W
2
* J
Y
50
HEX AT I C STABILITY LIMIT--
J
--- --
W
a a
0
a
V
J
w
10- 3 :
60.0
SPLAY BEND 0
70.0
72.0
74.0
TEMPERATURE
76.0
("C)
78.0
80.0
Figure 18. Temperature variation of the splay and bend elastic constants of a 2-layer 2M4P8BC film in the SmC* and SmI* phases. The SmC*SmI* transition occurs at 77.4 "C. The stability limit on the hexatic elasticity for an isotropic hexatic is indicated. The equivalent positional correlation lengths in the hexatic phase are shown as the right vertical axis. (Adapted from
W1).
2.6 Surface Tension
dering, and fundamental understanding of the Peierls- Landau instability from the X-ray diffraction of free-standing smectic films. Employing the Wilhelmy plate technique, Gannon and Faber [95] conducted high resolution surface tension measurements as a function of temperature mainly on the nematic and isotropic phases of bulk 8CB and 5CB. These two liquid crystal compounds are members of the nCB series [4-n-alkyl-4’-cyanobiphenyls].In contrast to the majority of liquids, the surfac tension increases as temperature increases in the nematic phase, as well as in the low temperature range of the isotropic phase. Employing the well-known Maxwell relation dy/dT = -(dS/dA), = -0,
(37)
one is led to the important conclusion that surface entropy per unit area, o,,is negative. This implies that the molecular arrangement must be more ordered near the free surface than in the interior and suggests that there exists surface-enhanced order. Since then, various experimental techniques [96-991 have been developed to obtain the surface tension as a function of temperature or film thickness. To reduce the free energy contributed by the surface tension term, the molecules at the liquid crystal/vapor interface favor a layer structure. In the smectic phase, the outermost layers favor a better molecular packing than exists in the interior. The enhanced surface order has been reported for various liquid crystal phases, for example: the surface SmA order on the bulk isotropic or nematic sample [50];the surface SmI order on a SmA film [47]; the surface SmB,,, order on a SmA film [45,48]; the surface SmI on a SmC film [ 17,931;the surface B on a SmA film [49]; the surface crystal E order on a SmB,,, film [ 1001. Realizing the importance of the surface tension in characterizing the liquid crystal free-standing films, we
465
have established a novel and simple experimental set-up which enables us to conduct high resolution measurements of the surface tension in such a system. The film thickness ranges from two to a few hundred molecular layers. Two salient features have been discovered by our investigations [4].
1. Within our resolution of 1.5%, the values of surface tension obtained from more than ten different liquid crystal compounds are independent of the film thickness in films ranging from 2 to about 100 layers. Moreover, our measured results from CBOOA thin films agree very well with the existing bulk data obtained from the pendant drop technique [ l o l l . Here CBOOA refers to p-cyanobenzylidenep’-n-octyloxyaniline. This indicates that the origin of surface tension is localized at the two outermost molecular layers. One of the results obtained from 12CB films is shown in Fig. 19. So far we have been trying to prepare stable one-layer, free-standing films from various compounds, but have not yet been successful. Once stable one-layer films can be prepared, it would be extremely important to measue their surface tension and compare the results with those from thicker films. The principle of independent surface action [102], proposed by Langmuir, stated that one could suppose each part of a molecule to possess a local surface free energy. Current available data point to the fact that the origin of surface tension is fairly localized at a small part of a liquid crystal molecule near the interface. Critical experimental evidence is needed to address this fundamental principle. 2. Different values of surface tension have been obtained from the following three distinct groups of liquid crystal compounds:
466
2 Physical Properties of Non-Chiral Smectic Liquid Crystals
15
-
-
10
-
-
5
-
-
0 " " " " " " " " " " '
The compounds, (e.g. 3( 1O)OBC,650BC, 70.7, and 40.8) exhibiting the ordinary SmA phase (layer spacing = molecular length) yield a surface tension of 21 dynkm. This value agrees very well with the critical surface tension (22 dynkm) of a hydrocarbon surface consisting of -CH3 groups (crystal) [103]. The agreement points to the fact that the aidliquid crystal surface of this SmA phase consists mainly of -CH3 groups. b) The molecules in the second group (CBOOA, 8CB, and 12CB) possess a large dipole moment associated with the cyano group. As a result, the smectic phase is a bi-layer antiferroelectric phase (the SmAd phase) wherein cyano groups form pairs and constitute the center portion of this somewhat bulgy bi-layer structure (see Fig. 20) [104]. The alkyl chains point outward. In the smectic phase, the bulgy parts are lined up in a plane, which leaves more open space for the alkyl chains. This molecular packing offers an intuitive and plausible explanation for the existence of the re-entrant nematic phase below the SmAdphaSe [ 1051. Consequently, the -CH,- groups (critical surface tension of about 31 dynkm)
Figure 19. Surface tension versus film thickness for 12CB free-standing films. The film temperature was at 54 "C in the SmA, phase. (Adapted from [4]).
should have greater opportunity to be exposed to the liquid crystal/air interfaces and enhance the surface tension. The measured surface tension is around 27 dynkm, which is approximately equal to the average values of the -CH3 and -CH,- groups.
Figure 20. Schematic diagram of antiparallel local structure in 12CB resulting in a layer spacing of about 1.4 times in molecular length. When an nCB gives a smectic phase, it is called the SmA,.
2.7 References
The third group consists of perfluorinated compounds, for example, H6F5EPP, H 1OFSMOPP [5-n-decyl-2-(4-n-(perfluoropentylmethy1eneoxy)phenyl)pyrimidine]. The measurements yield a thickness independent surface tension of 14 dynkm. Again this value is between the critical surface tensions of the -CF, [I031 and -CH, groups. This suggests that on average, the liquid crystal/air interface consists of approximately 50% of hydrocarbon tails and 50% of fluorocarbon tails. This is consistent with both steric and entropic considerations of the SmA structure of this unique new group of liquid crystal compounds. The special features of liquid crystal freestanding films should offer a unique opportunity to give a critical examination of the principle of independent surface action. Acknowledgements The liquid crystal research at the University of Minnesota has been supported by the Donors of the Petroleum Research Fund, administered by the American Chemical Society, and the National Science Foundation, Solid State Chemistry, Grant No. 93-00781.
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467
fairly strong second order Bragg peak. This indicates that the layer structure in this kind of liquid crystal compound is more well-defined. J. D. Shindler, E. A. L. Mol, A. Shalaginov, W. H. de Jeu, Phys. Rev. Lett. 1995, 74, 722-725. [lo] A. Caille, C. R. Acad. Sci., Paris 1972, 274B, 89 1- 893. I l l ] J. Als-Nielsen, J. D. Litster, R. J. Birgeneau. M. Kaplan, C. R. Safina, A. LindegaardrAndersen, S . Mathiesen, Phys. Rev. B 1980, 22, 312-320. M. R.Fisch,P. S . Pershan, L. B. Sorensen,Phys. Rev. A 1984,29,2741-2750. M. Benzekri, T. Claverie, J. P. Marcerou, J. C. Rouillon, Phys. Rev. Lett. 1992,68,2480-2483. C. Y. Young, R. Pindak, A. N. Clark, R. B. Meyer, Phys. Rev. Lett. 1978, 40, 773 -776. R. Holyst, D. J. Tweet, L. B. Sorensen, Phys. Rev. Lett. 1990, 65, 2153-2156. D. J. Tweet, R. Holyst, B. D. Swanson, H. Stragier, L. B. Sorensen, Phys. Rev. Lett. 1990, 65,2157-2160. S . Amador, P. S . Pershan, H. Stragier, B. D. Swanson, D. J. Tweet, L. B. Sorensen, E. B. Sirota, G. E. Ice, A. Habenschuss, Phys. Rev. A 1989, 39, 2703-2708; E. B. Sirota, P. S. Pershan, S. Amador, L. B. Sorensen, Phys. Rev. A 1987,35,2283-2287. A. N. Shalaginov, V. P. Romanov, Phys. Rev. E 1993,48, 1073- 1083. T. Stoebe, P. Mach, C. C. Huang, Phys. Rev. E 1994,49, R3587-3590. D. Demus, S . Diele, M. Klapperstuck, V. Link, H. Zaschke, Mol. Cryst. Liq. Cryst. 1971, 15, I61 - 174. A. J. Leadbetter, J. P. Gaughan, B. Kelly, G. W. Gray. J. Goodby, J. de Physique 1979, 40, C3 - 178- 184. J. J. Benattar, J. Doucet, M. Lambert, A. M. Levelut, Phys. Rev. A 1979, 20, 2505-2509. B. 1. Halperin, D. R. Nelson, Phys. Rev. Lett. 1978, 41, 121 - 124. D. R. Nelson, B. I. Halperin, Phys. Rev. B 1979, 19, 2457 -2482. A. J. Leadbetter, M. A. Mazid, B. A. Kelly, G. W. Gray, J. W. Goodby, Phys. Rev. Lett. 1979, 43,630-633. D. E. Moncton, R. Pindak, Phys. Rev. Lett. 1979, 43,701 -704. P. S . Pershan, G. Aeppli, J. D. Litster, R. J. Birgeneau, Mol. Cryst. Liq. Cryst. 1981, 67, 205 -214. R. Pindak, D. E. Moncton, S . C. Davey, J. W. Goodby, Phys. Rev. Lett. 1981,46, 1135-1 138. C. C.Huang, J. M. Viner,R.Pindak, J. W. Goodby, Phys. Rev. Lett. 1981, 46, 1289- 1292. M. Chen, J. T. Ho, S. W. Hui, R. Pindak, Phys. Rev. Lett. 1987,59, 1 112- 1 1 15. A. J. Jin, M. Veum, T. Stoebe, C. F. Chou, J. T. Ho, S . W. Hui, V. Surendranath, C. C. Huang, Phys. Rev. Lett. 1995, 74, 4863 -4866.
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2 Physical Properties of Non-Chiral Smectic Liquid Crystals
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blatt, L. J. Yu, J. Goodby, Phys. RevA 1983,27, 1251- 1254. [57] M. Meichle, C. W. Garland, Phys. Rev. A 1983, 27,2624-2631. [58] S. C. Lien, C. C. Huang, J. W. Goodby, Phys. Rev. A 1984,29,1371- 1374. [59] C. C. Huang, S. C. Lien, Phys. Rev. A 1985,31, 2621-2627. [60] A. Seppen, I. Musevic, G. Maret, B. Zeks, P. Wyder, R. Blinc, J. Phys. (Paris) 1988, 49, 1569-1573. [61] F. Yang, G. W. Bradberry, J. R. Sambles, Phys. Rev. E 1994,50,2834-2838. [62] C. C. Huang, S. C. Lien, Phys. Rev. Lett. 1981, 47, 1917- 1920. [63] Ch. Bahr, G. Heppke, Mol. Cryst. Liq. Cryst. 1987,150,313-324. [64] H. Y. Liu, C. C. Huang, Ch. Bahr, G. Heppke, Phys. Rev. Lett. 1988,61, 345 - 348. [65] R. Shashidhar, B. R. Ratna, G. G. Nair, S. K. Prasad, Ch. Bahr, G. Heppke, Phys. Rev. Lett. 1988,61,547-550. [66] T. Chan, Ch. Bahr, G. Heppke, C. W. Garland, Liq. Crystals 1993, 13, 667-675. [67] V. L. Ginsburg, Sov. Phys. Solid State 1961, 2, 1824-1834. [68] J. Selinger, J. Phys. (Paris) 1988, 49, 13871396. [69] L. Reed, T. Stoebe, C. C. Huang, Phys. Rev. E 1995,52,2157-2160. [70] D. Collin, J. L. Gallani, P. Martinoty, Phys. Rev. Lett. 1988, 61, 102-105. [71] D. Collin, S. Moyses, M. E. Neubert, P. Martinoty, Phys. Rev. Lett. 1994, 73, 983-986. [72] L. Benguigui, P. Martinoty, Phys. Rev. Lett. 1989,63,774-777. [73] R. Bartolino, J. Doucet, G. Durand, Ann. Phys. 1978,3,389- 396. [74] C. C. Huang, S. Dumrongrattana, Phys. Rev. A 1986,34,5020-5026. [75] S. Dumrongrattana, G. Nounesis, C. C. Huang, Phys. Rev. A 1986,33,2181-2183. [76] G. Nounesis, C. C. Huang, T. Pitchford, E. Hobbie, S. T. Lagerwall, Phys. Rev. A 1987, 35, 1441- 1443. [77] Y. Galerne, J. Phys. (Paris) 1985,46,733-742. [78] S. Heinekamp, R. A. Pelcovits, E. Fontes, E. Y. Chen, R. Pindak, R. B. Meyer, Phys. Rev. Lett. 1984,52, 1017- 1020. [79] S. M. Amador, P. S. Pershan, Phys. Rev. A 1990, 41,4326-4334. [80] Ch. Bahr, D. Fliegner, Phys. Rev. A 1992, 46, 7657-7663. I811 Orsay Group on Liquid Crystals, Solid State Commun. 1971,9,653-655. [82] Y. Galerne, J. L. Martinand, G. Durand, M. Veyssie, Phys. Rev. Lett. 1972,29, 562-564. [83] C. Rosenblatt, R. B. Meyer, R. Pindak, N. A. Clark, Phys. Rev. A 1980,21, 140- 147.
2.7
(841 C. Rosenblatt, R. Pindak, N. A. Clark, R. B. Meyer, Phys. Rev. Lett. 1979, 42, 1220- 1223. [85] C. F. Chou, J. T. Ho, S . W. Hui, Phys. Rev. E 1997,56, 592-594. [86] M. Veum, C. C. Huang, C. F. Chou, V. Surendranath, Phys. Rev. E 1997,56, 2298-2301. [87] G. S . Smith, E. B. Sirota, C. R. Safinya, N. A. Clark, Phys. Rex Lett. 1988, 60, 813-816. [88] R. Bruinsma, D. R. Nelson, Phys. Rev. B 1981, 23,402-410. [89] S. B. Dierker, R. Pindak, R. B. Meyer, Phys. Rev. Lett. 1986,56, 1819- 1822. [90] J. D. Brock, A. Aharony, R. J. Birgeneau, K. W. Evans-Lutterodt, J. D. Litster, P. M. Horn, G. B. Stephenson, A. R. Tajbakhsh, Phys. Rev. Lett. 1986,57,98- 101. [91] J. D. Brock, R. J. Birgeneau, J. D. Litster, A. Aharony, Contemp. Phys. 1989, 30, 321 -335. (921 A. Aharony, R. J. Birgeneau, J. D. Brock, J. D. Litster, Phys. Rev. Lett. 1986, 57, 1012-1015. [93] T. Stoebe, C. C. Huang, Phys. Rev. E 1994, 50, R32 - 35. [94] S . B. Dierker, R. Pindak, Phys. Rev. Lett. 1987, 59, 1002- 1005. [95] M. G. J. Gannon, T. E. Faber, Philos. Mug. A 1978,31, 117-135.
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1961 C. H. Sohl, K. Miyano, J. B. Ketterson, Rev. Sci. Intrum. 1978,49, 1464- 1469. [97] A. Bottger, J. G. H. Joosten, Europhys. Lett. 1987,4, 1297- 1301. [98] P. Pieranski, L. Beliard, J.-Ph. Tournellec, X. Leoncini, C. Furtlehner, H. Dumoulin, E. Riou, B. Jouvin, J.-P. Fenerol, Ph. Palaric, J. Hewing, B. Cartier, 1. Krdus, Phjsica A 1993, 194,364-389. [99] M. Eberhardt, R. B. Meyer, Rev. Sci. Instrum. 1996,67,2846-2851. [IOO] R. Geer, T. Stoebe, C. C. Huang, R. Pindak, G. Srajer, J. W. Goodby, M. Cheng, J. T. Ho, S . W. Hui, Phys. Rev. Leu. 1991, 66, 1322- 1325. [lo11 S . Krishnaswamy, R. Shashidhar, Mol. Cryst. Liq. Cryst. 1977, 38, 353-356. [ 1021 I. Langmuir, J. Am. Chem. Soc. 1916,38,2221 2295. [ 1031 W. A. Zisman in Contact Angle, Wettabilityand Adhesion, (Ed.: F. M. Fowkes) Advances in Chemistry Series, No. 43, American Chemical Society, Washington, D. C. 1964, p. 1-51. 11041 A. J. Leadbetter, R. M. Richardson, C. N. Colling, J . Phys. (Paris)1975, 36, CI -37-43. [ 1051 P. E. Cladis, Phys. Rev. Lett. 1975,35,48-5 1.
Handbook ofLiquid Crystals D. Demus, J. Goodby, G. W. Gray, H.-W. Spiess, V. Vill Copyright 0WILEY-VCH Verlag GmbH. 1998
3 Nonchiral Smectic Liquid Crystals - Applications David Coates
3.1 Introduction This chapter is concerned with the application of both tilted and orthogonal smectic phases that do not contain a chiral center, within these constraints it is the smectic A phase ( S m A ) that is of most interest and has been most widely studied. The simple, popular picture of a smectic phase (Sm) consisting of elongated molecules in sharp, distinct layers is rather misleading; amore realistic picture is one where the molecules are arranged to provide a single sinusoidal density wave [1] with its wave vector either parallel to the molecular director (orthogonal phases such as SmA, SmB, etc. - see Fig. 1) or at some angle to it (tilted phases such as SmC, SmI, etc.). However, it is often convenient to refer to the layered nature of the smectic phase to help explain phenomena such as conductivity anisotropy. In thin films, smectic phases can adopt one of several microscopic textures [2] depending on the preceding liquid crystal phase, the nature of the substrate (whether any aligning layer has been used), and on the type of smectic phase. Of particular relevance are the homeotropic and the focal conic textures shown by the orthogonal
phases (SmA, SmB) (Fig. 1). Smectic phases in which the molecules are tilted within the layers form schlieren textures and, if emanating from an orthogonal smectic phase in its focal conic texture, a ‘broken’ focal conic texture is observed under the same conditions, e. g., SmC phases forming from an SmA phase. The homeotropic and schlieren textures arise when the substrate surfaces are treated with a homeotropic aligning agent as this encourages the molecules to orient with their molecular long axes, essentially perpendicular to the substrate; this is usually achieved using lecithin, hexadecyltrimethyl ammonium salts, alkylcarboxylate chromium complexes, and 1,1,l -triall chloro- or 1,1,l-trimethoxy-alkylsilanes,
Figure 1. Sinusoidal distribution function of molecules in the homeotropic orientation (A) and the focal conic texture (B) (after Gray and Goodby [ 2 ] ) .
3.2 Smectic Mesogens
of which are deposited from very dilute solutions. Vacuum-deposited inorganic layers deposited orthogonal to the substrate also promote homeotropic alignment. In some cases, when the molecules of the liquid crystal phase contain a strongly polar terminal group, such as cyano, they naturally form homeotropic aligned phases. Unless specifically aligned, compounds not containing a polar group usually form random focal conic textures. Random focal conic textures can be induced when the substrate is treated with an alkyl dicarboxylate dichromium complex, a dichlorodimethylsilane solution, or a polymer film such as poly(viny1 alcohol) or polyimide. In the case of polymer films, when the polymer surface is unidirectionally rubbed using a velvet cloth, the focal conic groups are aligned in the rubbing direction and become very elongated; in small areas and in thin ( 5 - 15 micrometer) films they can give the appearance of a homogeneous texture containing no focal conic groups. Obliquely evaporated SiO also provides focal groups that have excellent alignment. In some cases a combination of these techniques has led to a high tilt alignment [ 3 ] . It is energetically unfavorable to alter the ‘layer’ thickness of the smectic phase, therefore any process that relies on this feature is very unlikely to occur. However, bending of the smectic layers is possible, because this need not cause a change in the layer thickness; thus the molecules can undergo a splay ( K ,,) distortion. In a smectic film, any point distortion of the layer, e. g., arising from a surface feature, propagates for some distance into the film; this feature is important for electrically addressed dynamic scattering devices. Bend ( K 3 3 ) and twist (K22)elastic constants approach infinity at the nematic (N) to smectic transition.
47 1
In contrast to the more commonly used and less ordered nematic phase, the smectic phase exhibits a high, non-Newtonian viscosity; however, this belies the fact that there is still considerable motion of, and movement potential for the molecules within the smectic phase. Once the molecules have been moved by an external stimulus, the bulk viscosity of the smectic phase usually inhibits further bulk movement of the phase and thus bistability is usually enountered. Surprisingly, in some cases very little external force is required to cause these changes, but still more than for the less ordered and less viscous N phase. For many years this potential was not recognized, but in the early 1970s this oversight was corrected. Due to the high viscosity of smectic phases, they cannot be flow-filled into conventional glass cells by capillary action, and it is thus essential to heat the liquid crystal into a less viscous phase (N or isotropic) so that it can be flow-filled into a preheated cell. The dielectric anisotropy and birefringence values for the smectic phase are very similar to, or perhaps slightly lower than, those of the corresponding N phase [4]. There is a larger degree of error associated with the measurement of the dielectric anisotropy and birefringence properties of the smectic phase compared to the N phase, because this phase is more difficult to align in a perfect configuration. For example, ‘planar’ textures usually consist of very long, elongated focal conic groups which necessarily contain discontinuities not present in well-aligned N phases.
3.2 Smectic Mesogens Within the field of liquid crystals, most chemistry effort has been devoted to the synthesis of materials exhibiting an N phase; in
47 2
3 Nonchiral Smectic Liquid Crystals - Applications
the last 10 years this has been extended to materials giving chiral SmC phases. Very little research has been devoted to the synthesis of materials that would selectively exhibit smectic A or B phases. However, many compounds exhibiting a smectic A, B, or C phase are known, but very few have low melting points and wide range smectic phases. In general smectic phases are promoted by longer alkyl chain members of an homologous series. Some types of linking groups between ring systems are particularly useful, for instance, azomethines [5], which can in some cases give rise to a plethora of smectic phases in compounds with reasonable melting points. Simple mixtures of these compounds (1) were used in some of the first applications of smectic phases; mixtures [6,7] based on 4-cyano-4'-octylbenzylideneaniline can exhibit useful transition temperatures, e. g., Cr-SmA, 24°C; SmA-N, 73.5"C; N-I, 74 " C .
However, this class of compound is unstable to hydrolysis and has been replaced by the more stable 4-cyano-4'-alkylbiphenyls (2); the longer alkyl chain homologs Table 1. Transition temperatures for the longer alkyl chain homologs of 4-cyano-4'-alkyl- and -4'-alkoxybiphenyls.
R
Cr-NISmA
SmA-N
("C)
("C)
28.5 21 40.5 44 53.5 54.5 65 61
32.5 44.5 67 77
are very useful low melting point smectogens [8,9] (Table 1). The alkoxy analogs [9] also exhibit smectic phases (Table 1). The terphenyl analogs (3) exhibit smectic phases with higher transition temperatures [ 5 , 101: Cr-E, 127°C; E-SmB, 128 "C; SmB-SmA, 133 "C; SmA-N, 197 "C;N-I, 216°C.
Mixtures of (2) and (3) have provided SmA phases with very wide temperature ranges and low melting points [ l l ] (Table 2). In some cases, a narrow temperature range N phase is desirable and this has been achieved either by careful formulation of the mixtures of homologs of (2) or by adding other compounds [12, 131, such as 4'-cyano- or 4'-bromo-biphenyl-4-y1 3,5-alkoxybenzoates, which reduce the N phase stability. Mixtures of mesogens often exhibit spread transition temperatures which manifest themselves as biphasic regions; for some applications, such as laser-addressed devices, this feature is undesirable. To overcome this problem, several mixtures have been specifically developed [111 to have narrow temperature range transitions from Sm to N and from N to isotropic, i. e., S6 in Table 2. Other biphenyl based compounds such as the esters (4) (Table 3) also exhibit smectic phases [14] and have been formulated into low melting smectic mixtures [ 151.
SmA or N-I ("C) 42 40 47.5 51.5 75 75 79.5 84.5
Table 2. Physical properties of some SmA mixtures [ 1I] based on 4-cyano-4'-alkylbiphenyls.
s1 s5 S6
Cr-SmA ("C)
SmA-N
5 1 16.1
40 55.5 -55.1 58.9-59.2
("0
SmA or N-I ("C)
43 57.5 -61 .O 59.5-60.0
3.3 Laser-Addressed Devices Table 3. Transition temperatures of some 4'-cyanobiphenyl-4-yl alkanoates.
6 7 8 9 a
57.9 77.9 53.5 51.5
58 76
68.8 (74.I ) " 76 76.5
compound (7) [which exhibits the physical constants, Cr-SmC, 44.7 "C; SmC-SmA (41 "C); SmA-I, 146 "C; A ~ z - 3 1 . Smectogens based on tropolones have also been synthesized [20].
F
F
c
Monotropic transition
More recently, disiloxane units have been incorporated [ 161 into the alkyl chain of 4cyano-4'-alkoxybiphenyls. The disiloxane unit (in compound 5 ) appears to stabilize the 'smectic layer' arrangement, such that even in short chain length homologs, only SmA phases occur (Table 4). X-ray analysis indicates [ 171 that the siloxane units group together into a bilayer arrangement. Although most applications use smectogens of positive dielectric anisotropy, there are some wide temperature range smectogens of negative dielectric anisotropy. Some notable examples are the lateral cyano phenyl benzoates [ 181 (6) and the 2,3-difluorobiphenyl carboxylic acid esters [ 191, e. g.,
Table 4. Transition temperatures for some disiloxane derivatives of 4'-cyano-4-alkoxybiphenyls.
n
Cr-SmA ("C)
3 4 5 6 8 10 11
73.2 39.1 30.4 36.0 37.0 41.0 30.0
SmA-I ("C) ( 32.6) (28.7)" 50.3 53.8 60.9 68 73
Virtual transition temperatures obtained from mixtures by extrapolation.
"
473
3.3 Laser-Addressed Devices Laser-addressing of liquid crystal films was initially 11211,but only briefly, carried out on N and cholesteric films in 1972; it was soon determined that SmA phases offered [7, 81 advantages, such as better bistability, higher resolution [22], and the possibility of selective erasure. Considerable effort was expended to optimize this technology during the 1970s and 1980s, and commercial devices were developed.
3.3.1 Basic Effects Two modes of operation have been studied; normal mode refers to the writing of lightscattering lines on a clear transparent background, and reverse mode refers to the writing of clear lines on a light-scattering background. Many of the basic techniques used in one mode have been used in the other mode.
3.3.1.1 Normal Mode A thin layer, typically 12- 14 pm, of SmA liquid crystal is sandwiched between two homeotropically [23] aligned glass plates to produce a transparent single crystal film
474
3 Nonchiral Smectic Liquid Crystals - Applications
(Fig. 2). Homogeneous [24] and hybrid [25] alignments have also been used, but less often. To achieve good initial alignment, the material is heated to the isotropic phase and slowly cooled via an N phase (which aligns very readily) into the smectic phase. It may not be essential to have an N phase present, but its presence makes the alignment more reliable than a direct transition from the isotropic liquid into the smectic phase, and is useful in subsequent operations. When a laser beam is scanned over this film, and provision made to absorb the laser energy, which converts it to heat, the liquid crystal is locally heated into the isotropic phase. After the laser beam has passed, the film quickly cools back into the liquid crystal phase, due to the heat sinking action of the substrates. On fast cooling such as this, and especially if the N phase has only a very narrow temperature range, the liquid crystal phase does not align into a single crystal, but forms a myriad of tiny focal conic groups which are of such a size that they scatter visible light, and thus an opaque line is produced where the laser beam irradiated the film. Although it is expected that the entire thickness of the film is changed to a scattering texture, this need not be so, and often is
not, and in this way intermediate levels of scattering can be produced giving rise to ‘grey levels’. The glass substrates carry transparent conducting layers such as indium tin oxide (ITO); this can act to absorb the laser energy and/or as an electrical conducting layer. For example, total erasure of the image can be achieved in several ways (Fig. 2): 1 . By applying a sufficiently sized DC pulse to one of the I T 0 coated substrates, which in this case has to be of low resistance, i. e., 110 SZcm-2, followed by slow cooling; however, in practise slow cooling is not very easy to control reproducibly. 2. If an I T 0 layer is used on each substrate, a small voltage ( 3 0 V ) can be applied across the film during the cooling cycle (after it has been heated to the isotropic liquid by a method such as (l)), so that homeotropic alignment of the transient N phase is electrically aided; this then causes alignment of the smectic phase [261. 3. A short (1 s) high voltage pulse of 100 V at 1 - 1.5 kHz can be applied to align the smectic phase homeotropically [27]. In this case, heating to the isotropic liquid is not necessary.
-
m I
HOMEOTROPIC
I
ISOTROPIC WRITTEN AREA 1. HEAT, SLOW COOL
2. HEAT, COOL f 30V 3. lOOV lkHz
FOCAL CONIC SCATTERING
Figure 2. Schematic drawing of a normal mode laser-addressed SmA device showing the initial clear state (homeotropic alignment) and the laseraddressed and storage (focal conic) states. Methods 1- 3 are alternative processes for erasure.
3.3 Laser-Addressed Devices
Selective erasure is also possible by re-scanning over an isolated area while a small electric field (-20-30 V) is applied to the entire cell; this quickly aligns the transient N phase, formed on cooling, into a homeotropic texture. Localized heating, produced by supplying a DC current to a local electrode, followed by cooling and the application of a small AC field can also provide localized erasure. Another way to produce grey scales is to apply a 5 - 15 V field during the cooling cycle to partially align the Smectic phase such that it does not scatter light so intensely [28]. It has also been reported [25] that applying a very small voltage (= 1 V) during cooling can induce better light scattering. Such films have indefinite storage unless the ambient storage temperature reaches the clearing temperature of the smectic phase.
3.3.1.2 Reverse Mode In the reverse mode device, the entire cell is initially converted into a light-scattering state. This can be achieved by fast cooling LASER
FOCAL CONIC SCATTERING
from the isotropic liquid to give a randomized focal conic texture (Fig. 3). However, the production of a uniform light scattering texture has proven difficult to achieve. The film can be heated to the isotropic liquid using a controlled high current DC pulse [26, 27, 291 via the I T 0 layer, followed by fast cooling. Alternatively, the smectic phase, doped with a small amount of ionic dopant, can be electrically induced to undergo dynamic scattering [26, 301, although the subsequent laser writing speed on films made scattering using the dynamic scattering method is slower than in films made scattering using the thermal method [26]. Another neat method [31] uses the energy from a camera flash gun placed directly over the cell; the light energy can be absorbed by a dye dissolved in the smectic liquid crystal and converted to heat, which heats the liquid crystal to the isotropic phase. In the write mode, immediately after or during the laser writing, a modest voltage (= 20- 30 V) is simultaneously applied to the entire cell to align the transient N phase homeotropically in the written areas; this
+ 20V
ISOTROPIC WRITTEN AREA
HOMEOTROPIC
II
T I
HEAT PULSE, FAST COOL DYNAMIC SCATTERING FLASH GUN
475
Figure 3. Schematic diagram of a reverse mode laser-addressed SmA device showing the initial lightscattering state, the isotropic laseraddressed region, and the clear storage state produced by simultaneously cooling and applying a small field across the film. Three alternative processes for erasure are shown.
476
3
Nonchiral Smectic Liquid Crystals - Applications
small voltage does not affect the smectic phase not being heated by the laser beam. In this way, clear, transparent lines on a light-scattering background are formed. This mode is attractive because it offers the possibility to use simpler projection optics to provide bright lines on a dark background, and is the mode usually employed.
3.3.2.2 Lasers and Dyes
3.3.2 Materials 3.3.2.1 Liquid Crystals SmA liquid crystals that exhibit a small temperature range N phase (1- 3 "C) are desirable). To increase the intensity and opacity of the light-scattering state, it is desirable to use high birefringence materials; this allows thinner films to be used, which in turn allows faster write speeds and finer line resolution. A positive dielectric anisotropy is essential so that electrical reorientation can be accomplished. A low melting point and a fairly high clearing temperature (- 50 60 "C) are needed to give an adequate storage temperature range; if the clearing temperature is too high this has a negative effect on the laser writing speed. The first materials used [7, 81 were Schiff's bases such as (1) - they were the only low melting smectic materials available. However, most of the subsequent work has been carried out with mixtures of 4-cyano-4'-alkylbiphenyls (2), because they offer high birefringence values (An =0.22), high dielectric anisotropy (A&=>+7)and, in mixtures, good temperature ranges (i.e., S6 in Table 2). They are also stable to heat, moisture, and light. A chiral nematic dopant such as cholesteryl nonanoate [32] (8) or C15 [ l l ] (9) is also claimed to provide enhanced light scattering that is easier to achieve [33], but has the disadvantage that line shrinkage occurs, which in turn requires a slower scan speed to counter it.
Laser light has to be converted into heat so that it can heat the smectic liquid crystal film into the isotropic liquid. Initially this was accomplished by using an I T 0 layer to absorb the light energy from high power (20 mW [6] to 2 W [34]) Nd:YAG and YAG lasers emitting at 1.06 ym. The I T 0 could absorb about 35% of the laser's energy [6, 351. However, such lasers were large and required water cooling; they were replaced by He-Ne lasers (typically emitting 8 - 10 mW at 0.633 pm). The problem with He-Ne lasers is that the emission is in the visible light region, and if the device is to be used in projection devices the absorbing component (dye) will absorb some of the white light used during projection. In practice this was not too serious a problem, but there was a desire to use the new infrared lasers which would overcome this problem. These small compact semiconductor lasers based on GaAs or GaAlAs, emitting in the near infrared (0.75 - 1.2 pm), can produce about 10 mW of power. However, such lasers produced a divergent beam that was difficult to focus. With the move to smaller, shorter wavelength lasers, new dyes had to be found that could absorb the light energy. Initially, the dye was incorporated into a 1 ym thickpolymer film [36] (often polyimide), spin-coated onto the I T 0 electrodes; this was not without its problems, as the resistive polymer layer dictated that a higher voltage was required to cause dielectric reorientation of
3.3 Laser-Addressed Devices
the smectic phase. It was also calculated that if the dye could be dissolved in the liquid crystal itself, rather than coated onto the substrate, the efficiency could almost be doubled [37] and the line width reduced; a large proportion of the heat generated is dissipated into the substrate and wasted in heating the substrate, rather than the liquid crystal film, and causing line broadening [23]. However, when traditional dyes were tested it was found that they had poor solubility in the liquid crystal and poor stability; the first attempts were abandoned. Coincidentally, in the mid 1970s work had begun on dyed phase change displays and many new soluble, stabe dichroic dyes were being synthesized that could be used to absorb He-Ne laser light. Dyes that dissolve in the liquid crystal and have high extinction coefficients at the laser emission wavelength are required. If the device is for projection applications, the dye should not absorb at the wavelengths that may be used to project the final imageinfrared dyes and lasers are well suited for this. The dye will experience very high temperatures for very short time periods when addressed by the laser and should therefore be stable to heat and light. Dichroic dyes appear to give smaller spot widths than isotropic dyes, and so dyes with a modest order parameter (S=0.5-0.6) are desirable [231. For the commonly used He-Ne lasers, blue dyes based on anthraquinone [38, 391 (10) are particularly useful.
&* /I
0
10
I
NHCH3
Dyes absorbing at 0.75 - 1.2 pm tend to be of low solubility in liquid crystals, less stable, and often ionic or organometallic, thus undesirably drawing current during
477
electrical addressing schemes. However, some such dyes have been reported, for example, cyanine perchlorates [40] (11) (A=0.83 pm)andsquaryliumdyes [41] (12) (A=0.78 pm corresponding to the emission of GaAlAs lasers). Some liquid crystalline bis-dithio-a-dicarbonyl organometallic complexes (13) (;1=0.7-0.925 pm) have also been reported [42]. An interesting innovation was to create an electrochromic dye [43] within the cell by adding 0.3% of tetra-n-hexylammonium iodide to the cell and applying a 4 V DC voltage to create an absorption at 0.633 pm.
The use of dyes dissolved in the liquid crystal is obviously more efficient in the reverse mode effect, as the random orientation of the dye in the unwritten state provides a better chance for the dye to absorb the light energy.
3.3.2.3
Additives
In an attempt to improve the opacity of the light-scattering state, various additives have been tried [7] such as spherical molecules (e. g., adamantane), ortho-isomers of the usual para-substituted compounds, and chiral compounds [32, 33, 371.
478
3
Nonchiral Smectic Liquid Crystals - Applications
3.3.3 Physical Characteristics and Applications 3.3.3.1 Line Width and Write Speed The writing speed essentially depends on how fast the smectic film can be heated to the isotropic liquid. This is governed by the laser power, how well it is absorbed by the dye (concentration and extinction coefficient) how much liquid crystal has to be heated (film thickness), and at what temperature above ambient the clearing point transition temperature lies. To reduce the difference between ambient and the clearing point, the cell is often held at a bias temperature some 5 - 10 "C below the clearing temperature. The heat-sinking action of the relatively thick glass substrates is also likely to affect both the writing speed and the line width. Systems using YAG lasers are reported to have scan speeds of 40 cm/s [35] (using a 300 mW laser); He-Ne laser-addressed systems can provide about 40 mm/s (using an 8 mW laser) and 8 mW GaAs lasers also provide about 40 m d s . In the earlier work with YAG lasers, line widths of 15-20 pm were typical [6, 28, 351 (25 line pairdmm), while in later work, line widths down to 3 pm have been reported [23] in 9 pm thick films using a 12 mW He - Ne laser and a dye dissolved in the liquid crystal. However, 10 pm line widths are more typical [29]. A total erasure cycle, by electrical heating of the cell, is often accomplished in about 20 s [6, 351.
3.3.3.2 Contrast Ratios On screen, projected image contrast ratios of 8-2O:l have been reported [6, 28, 29, 351. The contrast of scattering systems is critically dependent on the collection angle of the optics used, and so comparing data
from different sources is not so useful. Reverse mode devices tend to provide higher contrast ratios [26]. Some commercial devices [29] have been reported that have 16 grey levels.
3.3.3.3 Projection Systems The fine resolution, sharp image quality and high light throughput in the clear state makes this device suitable for projection applications [35,44]. To convert the normal mode device to provide a bright image on a dark background, schlieren optics can be used [30]. The image from a cell can be projected either in a transmissive or a reflective mode; several types have been reviewed [45]. In practise, the reflective mode using the reverse mode effect (bright lines on a dark scattering background) is preferred; one reason for this is that it allows co-projection with another image. A typical [46] transmissive projection system is redrawn in Fig. 4.
3.3.3.4 Color Devices Full color devices have been demonstrated using three cells having red, green, or blue light projected through them; in a simplified version, two cells having red and green light shone through them were used [34]. However, later commercial devices [29] had four cells with red, green, blue, and white light shone through them; the projection beam was split into four, but imaged (reflection mode) onto one cell which was split into four quadrants, each responsible for a particular color, and then the projection beams were co-projected.
3.3.3.5 Commercial Devices This technology was principally exploited by Greyhawk Systems [29] who produced a range of projection devices whose images
3.3 Laser-Addressed Devices
479
LASER
LASER SCANNER
J
SMECTIC CELL
D’CHRo’C
used for laser-addressed displays [35, 461.
MIRROR
were drawn by deflecting a laser light beam using high speed reflection mirrors. An image could be drawn more quickly than on a paper plotter. The image was either projected onto a small screen [22” x 34” (55 x 85 cm)] suitable for engineering drawing work (Softplot) or onto very large screens where it could be overlaid onto other projected images (such as maps) and viewed by large audiences. In this system,
the laser energy was absorbed by a surface coating deposited beneath a reflective coating (Fig. 5 ) ; the other substrate carried an I T 0 layer by which an electric field could be applied across the cell. Such devices had 16 grey levels and provided 4096 colors, and with two 30 mW semiconductor lasers could be written at 2000” (5000 cm) a second (on screen) with a contrast of 16 : 1. The system was capable of local erasure using a
LASER SCANNING SYSTEM
\ SMECTIC FILM
REFLECTOR/ELECTRODE TRANSPAREN1 ELECTRODE
DICHROIC BEAM
PROJECTION LAMP
Figure 5. Simplified projection system and cell construction of a reflective laser-addressed SmA device (after Kahn et al. [29]).
480
3 Nonchiral Smectic Liquid Crystals - Applications
small electric field applied after the laser beam had heated the local area to the isotropic state; full erasure was achieved by applying a higher voltage. Additionally, similar laser-addressed devices could be used as a mask for circuit board manufacture.
3.4 Thermally and Electrically Addressed Displays In concept this device is similar to the laseraddressed device except that a heat pulse is electrically generated along a matrix of conducting tracks within the cell, rather than by the use of a scanning laser. An SmA liquid crystal film of positive dielectric anisotropy (e.g., 2) is held between conducting electrodes and DC electrical pulses (typically of 2 ms duration) are supplied along low resistivity (< 10 SZ) tracks on one substrate (typically made from 2 pm thick evaporated aluminum which also acts as a reflector on the back substrate, but within the cell); this is sufficient to cause local heating of the liquid crystal to the isotropic liquid (Fig. 6). As the material cools, a small AC voltage is applied between the aluminum tracks and an I T 0 front electrode to cause homeotropic alignment of the intermediate N phase to occur (clear state); when a voltage is not ap-
5
HEAT
plied, a light-scattering texture is produced [12, 131. Thus a transition between a lightscattering state and a clear state is possible. Optimizing the magnitude and duration of the heat pulses was found to be crucial [47]; 10 A for a few milliseconds being typical. In the original device [131, 25 rows were addressed at 10 ms per row. This effect was developed to provide a small (10 x 12 mm) projection device having 256 x 256 rows and columns with a line access time of 64 ps and 32 grey levels [48]. A development of this device (thermally addressed dyed display) incorporated a black, high order parameter dichroic dye such that a direct view (reflective mode) device having a contrast between white (homeotropic aligned state) and black (scattering state) was produced [49]. This was developed [50] into demonstration devices of 6 x 7" (15 x 21 cm) having 512 x 576 or 288 x 360 elements. The displays were characterized by good viewing angles (150') and contrast ratios (10: l), high multiplexibility, high brightness (35% of a standard white), and the possibility of a variety of colors. To eliminate parallax effects and give a wide viewing angle, the reflector was built inside the display by using a textured or faceted aluminum reflector. The cell thickness was 16 k 2 pm. To reduce the heat energy required for writing by as much as 60%, due to losses into the glass substrate, a polyimide layer was coated between the
electric anisotropy SmA phase being driven into a focal conic texture.
3.5 Dielectric Reorientation of SmA Phases
glass and the aluminum layer. To improve the cooling rate for total erasure (the production of a scattering texture), an aluminum heat sink was attached to the back of the display. In the initial device, 288 rows could be addressed in 1.4 s (5 ms per row), and a later device [5 11 was heat-sinked at 45 “C to reduce row write times to 50 ps. The materials used [52] in this device were mixtures of smectic A and chiral nematic 4-cyano-4’alkylbiphenyls (2).
3.5 Dielectric Reorientation of SmA Phases In the same way that the molecules of N phases can be electrically reoriented, the molecules of the smectic phase can be dielectrically reoriented by electric fields, albeit at a higher voltage. However, unlike in the N phase, when the field is removed, the bulk viscosity of the smectic phase inhibits relaxation and bistability is favored. This can be an advantage unless the procedure has to be reversed, because this cannot be achieved so easily. Reversal is accomplished by heating to either the less viscous N or isotropic liquid phases (as used in the laser and thermally addressed devices) or by causing electrohydrodynamic scattering to occur (see Sec. 3.6). In this section we shall specifically consider the dielectric reorientation effect. In itself it may not be particularly useful, but when combined with other techniques, it can lead to interesting devices. Due to the anisotropic nature of the liquid crystal phase, there are two dielectric constants or permittivities, one along the molecular long axis ( E , , ) and the other perpendicular ( E ~to) it. The difference between the two values is denoted as the dielectric anisotropy ( A E ) . In an electric field, the
48 1
higher dielectric constant aligns parallel to the applied field; thus depending on which E is higher, the molecules can align parallel or perpendicular to an applied field.
3.5.1 Materials of Negative Dielectric Anisotropy Under the influence of an applied electric field, these materials align with their molecular long axis perpendicular to the field. When a high frequency field (> 1 kHz) is applied to a 10- 20 pm thick film of a homeotropically aligned SmA phase (held between I T 0 coated glass plates), the molecules reorientate such that eventually, at a high enough voltage, they lie with their molecular long axes perpendicular to the field. In general, large focal conic groups form; these groups are too large to cause efficient light scattering, so the film appears as only very faintly light scattering (Fig. 6). Between crossed polarizers, a random multidomain birefringent texture is seen. The effect can be reversed by a heat pulse, causing the film to be heated to the N phase, which becomes realigned homeotropically. Typical materials that show this effect are (6) and (7).
3.5.2 Materials of Positive Dielectric Anisotropy These materials align with their molecular long axis parallel to the applied field. Most work [53, 541 has been concentrated on the reorientation of an SmA phase of positive dielectric anisotropy in its focal conic texture (often referred to as a planar texture when the focal conic groups are large and elongated) or in a light-scattering texture (probably caused by very small ‘micro’ focal conic groups), because in combination
482
3 Nonchiral Smectic Liquid Crystals - Applications
with an electrical method to induce the lightscattering texture, it is the basis for electrically addressed smectic scattering displays (Sec. 3.6). When the focal conic groups are well aligned (homeogeneous alignment, Sec. 3.1) and viewed between crossed polarizers, a fairly uniform birefringent film is seen, and upon applying a voltage the film appears black (Fig. 7). Dichroic dyes can be added to the smectic phase and a contrast between colored (focal conic) and clear (homeotropic) produced [55]. This seemingly simple transition is expected [56] to follow the relationship given by Eq. (1); however, the exact nature of the focal conic texture seems important. For example, with relatively large focal conic groups (obtained by cooling into the SmA phase), a V - f i relationship was found [53], but for a light-scattering texture (electrically induced) the relationship was [54, 581 V = d
where K , is the splay distortion elastic constant, d is the film thickness, % is the permittivity of free space, and il is a character-
istic length approximating to the layer spacing of the smectic phase used. The response time [58] can be quite fast, (
3.5.3 A Variable Tilt SmA Device A film of hexadecyltrimethyl ammonium bromide coated onto a layer of obliquely evaporated silicon monoxide can cause the SmA phase of 4-cyano-4'-octylbiphenylto exhibit a high (22" as measured from the normal to the cell using conoscopic methods) apparent tilt angle (Fig. 8). A retardation color of brown-yellow (450 nm) between crossed polarizers in a 20 pm thick cell was exhibited [59]. From neutron scattering experiments, the 'tilt' was found to be due to the smectic layers tilting (Fig. S), rather than to the molecules tilting within the layers [59]. When a voltage of more than 70 V was applied to the cell, the retardation color gradually changed through yellow then white and grey before becoming black; this corresponded to a decrease in the tilt angle to 12" (from the normal) at about 150 V.
Figure 7. Schematic drawing illustrating the dielectric reorientation of a focal conic positive dielectric anisotropy SmA phase being driven into a homeotropic texture. Figure 8. A positive dielectric anisotropy SmA phase with high tilt alignment showing a 22" layer tilt being electrically driven into a 12" tilt state.
3.6
Dynamic Scattering in SmA Liquid Crystal Phases
In thicker films (29.5 pm), the original color was sky blue changing to yellow when a voltage was applied. By removing the voltage, any retardation color attained could be indefinitely stored until either a higher voltage was applied or the film was heated to the N or isotropic phase, whereupon the original color was regained. This device was considered for use in variable and programmable color filters [3].
3.6 Dynamic Scattering in SmA Liquid Crystal Phases Dynamic scattering in N liquid crystal phases has been known for many years [60] and recently reviewed [61]. Indeed the first commercial liquid crystal displays made in the late 1960s used this effect. Dynamic scattering in smectic liquid crystal phases was first observed [62] by Tani in 1971 in N-p-cyanobenzy lidene-p-n-octylaniline; since then most research work has used 4-cyano-4’-octylbiphenyl (8CB or K24) or mixtures of this and its homologs. In 1976, Steers and Mircea-Roussel observed [63] a scattering mode produced by a pulsed field on K24 at 0.5 “C below the SmA-N transition. In 1978, the dynamic scattering effect in SmA phases was further studied and characterized by Coates et al. [58], who proceeded to combine the scattering mode produced by a low frequency field with the dielectric reorientation of the scattering texture, to produce the first electrically reversible smectic display (Fig. 9).
For dynamic scattering to take place, a conductivity torque must act against a dielectric torque which is attempting to align the molecules orthogonal to the conductivity (0)torque. In nematics, The Carr-Helfrich model was developed [64] to account for the experimental observations and is the basis for much of the theoretical treatment of dynamic scattering in smectic phases; the easy flow for ion motion in N phases is along the molecular long axis, and thus materials with A&< 0 and AD > 0 are required. In smectics, the easier direction for ion flow is along and between the smectic S ‘layers’, in which case materials with A&>O and A o < O are needed. In nematics, the ion flow gives rise to a vortex flow that is orthogonal to the electrodes, while in smectics the vortex is in the plane orthogonal to the field direction and is seen as a turbulent spiral motion characterized by many vortices [58]. When the electric field is removed, the vortices remain more or less intact, but not quite as intensely light-scattering [58] (Fig. 10). When the field is removed, perhaps micro focal conic groups form. It is energetically favorable for the layers to bend rather than compress, and hence the motion is due to the ions bending the smectic layers, causing refractive index variations through the film thickness. The occurrence of this scattering texture has been the subject of much research and speculation. The scattering, caused by ion flow, usually begins at the edge of electrodes or at point discontinuities formed by some topographical feature on the substrate. The importance of the substrate surface is clearly shown by reference to a study [58, 651 of
. . IOOHz, >1OOV
1 kHz, < lOOv
I
I
HOMEOTROPIC
483
FOCAL CONIC SCATTERING
Figure 9. Electrically reversible SmA display being driven from a clear state to a scattering state and back again.
484
3 Nonchiral Smectic Liquid Crystals - Applications
Figure 10. Micrograph ( ~ 4 magnification) 0 of the stationary vortex texture of 4-cyano-4’-octylbiphenyl after excitation at 50 V and 50 Hz.
the surface roughness of the substrate. I T 0 coatings that were very smooth (as measured by Talystep and scanning electron microscopy) required very high voltages (>290 V) to produce a scattering texture, which was not very intense, while rough surfaces with many large peaks [i.e., with peaks of =800 8, (80 nm) over a 1000 ym path length] required much lower voltages (110- 120 V) to produce intensely scattering films 1651. Films that had previously been electrically oriented into a homeotropic texture using a high frequency and a high voltage were also difficult to scatter [%I. This was presumably because the molecules and layers were homeotropically aligned too well - some degree of undulation of the layers is essential for ion motion to begin and then propagate. The conductivity of the smectic phase is important; rather than rely on impurities in the liquid crystal or degradation products of the dynamic scattering, it is desirable specifically to add ionic dopants. In the early work, the homeotropic aligning dopant [hexadecyltrimethyl ammonium bromide (HMAB)] conveniently also acted as the
ionic dopant. Typically, the resistivity (l/o) had to be below 1x lo9 R c m for scattering to occur [58]. A study 1561 of the conductivity ratio (CT,~/O~) [which should be large to reduce the threshold voltages for scattering to occur, see Eq. (2)] in 4-cyano-4’alkyl biphenyls and their mixtures showed that the nature and concentration of the cations is particularly important. At 100 Hz, the conductivity ratio varied between 0.4 for tetramethylammonium bromide to 0.8 for hexadecyltrimethyl ammonium bromide
The voltage to ‘scatter’ similar films of similar conductivity gradually decreased with increasing alkyl chain length for the homologous series of alkyltrimethyl ammonium bromides (from 230 V for the methyl homolog to 100 V for the hexadecyl homolog). Increasing the concentration of ionic dopant also increased the conductivity ratio (ql:oL)(from0.55at0.01% to0.72at 0.8% hexadecyltrimethyl ammonium bromide. The conductivity ratio is also frequency
3.6 Dynamic Scattering in SmA Liquid Crystal Phases
485
200
160 h
2
0
-
.
1
120
c
0 >
-0
.!I!80 Q
8 40
Figure 11. Plot of addressing frequency versus scattering threshold and clearing threshold.
0 10
100
1000
10000
Frequency (Hz)
(and temperature [56]) dependent; A o = O at about 1 - 1.5 kHz [56, 661. Hence, to remain within the essential regime of A o < O for scattering to occur, it is important to operate at low frequencies and over limited temperature ranges. Typically, 100-200 Hz was used. Figure 11 illustrates the effect of frequency on both the scattering threshold and the erasure (scattering to clear by dielectric reorientation) threshold [58]. The conductivity of the SmA phase is also dependent on the texture or molecular arrangement of the smectic phase. The scattering state (osc)has a different conductivity to the homeotropic state ( o T R ) ; it was then found that when oscis larger than oTR, dynamic scattering will occur [57] and that, as the ratio o S c / o T R increases, the threshold voltage decreases.
3.6.1
Theoretical Predictions
The threshold voltage (or field) for dynamic scattering in SmA liquid crystals was predicted in 1972 [Eq. (2)] by Geurst and Goosens [67] who extended the Carr-Helfrich model [64] for dynamic scattering in nematics.
However, these expressions consider only the torques acting on the molecules and not the ability of the dopant to disrupt the smectic layers; there are also some anomalies in the experimental work defining what is meant by the ‘threshold voltage’. Hence, it is not surprising that there are some problems in fitting experimental data to these predictions. For example, Eq. (1) predicts that V t h fi; ~ while experimentally a V,, 0~ d relationship is found [57, 581.
3.6.2 Response Times Light scattering caused by dynamic motion originates at ‘scattering centres’ and the speed at which this spreads will have a major influence on the response time. Chirkov et al. [57] predicted that the speed of spread will be faster at higher temperatures and voltages. Typical response times are =90 ms at 120 V and 50 Hz for a 20 ym thick film of K24 with a resistivity of 8 x lo8 Rcm. No consensus is found for a dependence on the ‘clear’ to ‘scattering’ response time, with time - voltage values varying between toc v-2.5 and t= V 5 being reported [57, 581.
486
3
Nonchiral Smectic Liquid Crystals - Applications
3.6.3 Displays Based on Dynamic Scattering By combining the dynamic scattering effect, to provide a light-scattering state, and then reversing this using the dielectric reorientation effect, Coates et al. [58] showed that it was possible to produce an electrically addressed smectic display. In the early to mid1980s, active matrix displays were still in their infancy (very small and expensive) and there was a need for a large size complex (many pixels) display, which was of good contrast and flicker free, to replace CRTs in exacting situations such as with CAD software packages. This technology was developed by STL Harlow and later by ITT Courier into many demonstration displays [68, 691. The display was first driven en bloc into a scattering mode (page blanking). The voltage required to cause light scattering to occur depended on the pulse time used. Longer pulses required lower voltages, typically a 40 ms (50 Hz square wave) pulse of over 250 V was used; this allowed page blanking in 40 ms. Additionally, if required, only several rows at a time could be blanked (caused to scatter). The information was then scanned into the display one line at a time by applying a square wave voltage Vs sequentially to each row, whilst a data voltage VD was applied to the columns. Selected pixels (those intended to be driven from scattering to clear) in the row being scanned received V, + V , (typically about 30-40 V in 12 pm thick cells), while unselected pixels received in-phase pulses (Vs- V,); when not being scanned, the pixels received only VD. The act of scanning in subsequent rows had no effect on the contrast of previous rows. A line of information could be written in 2 ms. Special high voltage drivers (350 V) were designed for this task [69]. A keyboard entry mode was also
featured, which meant that screen blanking was not necessary if additional characters were to be added to information already stored on the screen; this operation took 6 ms per line. Special low resistivity transparent conducting electrode materials were developed so that the high voltage and current could be transmitted along the rows and columns of a 12” (30 cm) diagonal panel. Ionic dopants and redox dopants were developed that would give long display lifetimes and good light scattering. Because the device has bistability, an infinite number of rows could be addressed; the addressing of 5000 rows without image degradation was demonstrated. Although the display had good brightness, it could also be illuminated using a perspex light guide optically coupled to the display; scattering centres in the display cause light to be directed from the light guide, and this gave a contrast luminance of 8: 1. A 12” (30 cm) display having 420x780 rows and columns (327600 pixels, 2275 characters) could be written in 840 ms. The operating temperature range was 15-55 “C and the display had the advantage of indefinite storage, no image flicker, and excellent direct view contrast with a wide and symmetrical viewing angle; it could also be used in a projection mode. The advent of STN displays and cheaper active matrix addressed displays took over this market, although it has been considered several times subsequently for other market sectors, but without a product being made.
3.7 Two Frequency Addressed SmA Devices Another example of an electrically reversible SmA display uses the two frequency
3.8
addressing technique [70], well known from work on N liquid crystals in the early 1970s. For liquid crystals of positive dielectric anisotropy (A&> 0, where A&=q,- EJ at the usual addressing frequency of 1 kHz, the parallel component is the larger. However, its magnitude is rather more sensitive to the frequency of the addressing field than is the perpendicular component; at high frequencies decreases and can become less than E ~ Thus, . in principle, all compounds could exhibit a negative dielectric anisotropy, but very often the frequency at which this change occurs is very high and almost unattainable. However, in some compounds this cross-over frequency (where =cl) is at relatively low frequencies (a few kilohertz). Materials that show this effect are often characterized by being viscous and having a long molecular structure, frequently containing several ester groups. Based on these observations, a mixture of diesters based on compound (14) was formulated.
487
Polymer-Dispersed Smectic Devices
01 25
I
I
30
35
I
40
45
50
55
Temperature ("C)
Figure 12. Plot showing the cross-over frequency as a function of temperature and liquid crystal phase.
large enough to produce a uniform birefringent texture - hence the film appears mottled (see Sec. 3.4). As a result of this poor contrast, difficult addressing schemes, and nonavailability of materials, this effect was not pursued.
3.8 Polymer-Dispersed Smectic Devices When a homeotropically aligned sample of (14) was viewed between crossed polarizers, subjected to an electric field of >lo0 V and the frequency of the field increased, a focal conic texture eventually appeared. This is the point at which the material changed from positive to negative dielectric anisotropy. This was repeated for a range of temperatures (Fig. 12). In nematics, this temperature dependence is a major problem, because addressing schemes have to be complex to cope with changing voltages and frequencies as the ambient temperature changes. In smectics, the additional problem is that in the negative mode (switching from homeotropic to planar or focal conic) the focal conics are too large to cause light scattering and yet not
Polymer dispersed liquid crystal (PDLC) devices usually contain N phases as the liquid crystal material [71] and are used in vision products [72], e. g., privacy windows, projection displays [73], and direct view displays [74, 751. Cholesteric liquid crystals have also been used [76]. All these devices relax back to the original ground state when the field is removed. Ideally such films consist of diroplets of liquid crystal in a polymer matrix; the reverse situation (reverse phase) consists of a liquid crystal continuum with polymer balls dispersed within it. The latter films are not desirable, because they do not provide reversible electrooptic effects. Ferroelectric SmC* liquid crystals have also been used [77], and these give bistable
488
3 Nonchiral Smectic Liquid Crystals - Applications
devices not too dissimilar to conventional FLC devices. The light scattering appearance of a thick (> 20 pm) film of an SmA liquid crystal provides an opaque film. If doped with a colored dichroic dye, an intense color can be produced. On heating this film to the isotropic liquid, the light scattering disappears and the light path through the film is reduced such that a fairly clear film is produced. An appropriately colored background, previously hidden by the scattering film, would now be visible. This is the basis for a temperature indicator. One problem with this concept is that the liquid crystal is fluid; this problem can be overcome by containing the smectic phase in a PDLC film. By heating a PDLC film made from a liquid crystal having a smectic and an N phase, it is possible to make an electrically addressed storage device [78]. The PDLC film is heated to the temperature at which the liquid crystal is nematic and a small electric field applied to the appropriate areas using I T 0 conductors; this homeotropically aligns the N phase into a clear state and on cooling with the field applied, a transparent image on a scattering background is produced. A PDLC film containing an SmA liquid crystal can also be addressed with light from a suitable laser to produce a clear line under the influence of an applied electric field when the film cools [79]. Very recently a ‘memory type liquid crystal’, which has the characteristics of an
SmA phase, has also been used to produce a memory type device [80]. Interestingly, this device uses reverse phase PDLC so that a finer line resolution can be obtained, reversal of the process being of no importance. This device consists of a thin (6 pm) film of memory type liquid crystal and has submicrometer sized polymer balls dispersed within it and then a polymer skin on top to give.a memory type liquid crystal polymer composite (M-LCPC) (Fig. 13). This film is prepared on top of an I T 0 coated glass substrate. The film switches from scattering to clear between 200 and 300 V to provide many grey levels. The film is used in the same way as a photographic film, but in a special camera. Held 10 pm above the M-LCPC layer is a structure consisting of an organic photoconductor and an I T 0 electrode mounted on a glass substrate. A large DC field (700 V) is applied between the two I T 0 layers. When an area of the photoconductor is exposed, its resistivity drops in accordance with the energy of light and allows a field to be applied to the M-LCPC layer, which responds to the strength and duration of the field applied to it. Typical exposure time is 1/250 s for the camera shutter and the field is applied for about 1/25 s. The camera contains a lens to separate the incident image into red, green, and blue images, each of which is captured on three M-LCPC films. The films are removed from the camera, scanned with a 5000-CCD line sensor with a pixel size of 6 pm and the analog signals converted to
Figure 13. Submicrometer polymer balls in a continuum of memory type liquid crystal and a polymer cover film.
3.10 References
digital data, enhanced, and the three images combined; the final image can then be displayed on monitors or printed on conventional color printers. A resolution of 6 ym was demonstrated and the sensitivity was about I S 0 10-50; future films are expected to be I S 0 100. Compared to conventional silver halide photographs (from negative film), the images produced were much less granular. Thus this system for capturing images provides high resolution color prints very quickly, and the master images can be stored indefinitely.
3.9
Conclusions
Basic research to discover how smectic liquid crystals are affected by heat and electric fields has resulted in several effects being found, and a few of them have been extensively studied and developed into working display prototypes and early commercialization. The property of bistability is both useful and, at the same time, a problem. As yet a really long term application involving smectic liquid crystals has not been found. However, they continue to hold a fascination because they can offer many unique properties which are continually being reexplored for new applications.
3.10 References A . J. Leadbetter in Therniotropic Liquid Crystals (Ed.: G . W. Gray), Society of Chemical Industry, Great Britain 1987, Chap. 1 . G. W. Gray, J. W. Goodby, Smectic Liquid Crystals, Leonard Hill, Glasgow 1984. D. Coates, W. A. Crossland, J. H. Morrissey, B. Needham, Mol. Cryst. Liq. Cryst. 1978,41, 151. D. A. Dunmur, M. R. Manterfield, W. H. Miller, J . K. Dunleavy, Mol. Cryst. Liq. Cryst. 1978,45, 127.
489
151 D. Demus, H. D. Demus, H. Zaschke, Flin’ssige Kristalle in Tabellen, VEB Deutscher Verlag fur Grundstoffindustrie, Leipzig 1974. 161 F. J. Kahn, Appl. Phys. 1973, 22, 1 1 1. 171 G. N. Taylor, F. J. Kahn, J. Appl. Phys. 1974,45, 4330. [8] G. W. Gray, K. J. Harrison, J. A. Nash, Electron. Lett. 1973, 9, 130. [ 91 G. W. Gray, Advances in Liquid Crystal Materiuls ,for Applications, BDH Chemicals, Dorset 1978. [ 101 G. W. Gray, K. J. Harrison, J. A. Nash, J. Chem. Soc. Chem. Commun. 1974,431. [ I 11 Merck Ltd., Licrilite Catalogue 1994. [ I21 S. LeBerre, M. Hareng, R. Hehlen, J. N. Perbert, Displuys 1981, 349. [ 131 M. Hareng, S. LeBerre, R. Hehlen, J. N. Perbert, SlD Digest of Technical Papers 1981, 106. [ 141 H. Scherrer, A. Boller, US Patent 3 952046,1976. [IS] I. Shimizu, K. Furukawa, M. Tanaka, EP Patent 037 468 B 1, 1988. [16] J. Newton, H. Coles, P. Hodge, J. Hannington, J . Muter: Chern. 1994,4(6), 869. [ 171 M. Ibn-Elhaj, H. Coles, D. Guillon, A. Skoulios, J . Phys. I / (France) 1993,3, 1807. [18] J. C. Dubois, A. Zann, A. Beguin, M o l . Cryst. Liq. Cryst. 1977, 42, 139. 1191 M. Chambers, R. Clemitson, D. Coates, S. Greenfield, J. A. Jenner, I. C. Sage, Liq. Cryst. 1989, 5(1), 153. 1201 K. Kida, M. Uchida, N. Kato, A. Mori, H. Takeshita, Chem. Express 1991, 6(7),503. [21] H. Melchior. F. Kahn, D. Maydan, D. B. Fraser, Appl. Phys. Lett. 1972, 21, 392. [22] D. F. Aliev, A. K. Zeinally, Zh. Tekh. Fiz. 1982, 52, 1669. [23] T. Urabe, K. Arai, A. Ohkoshi, J . Appl. Phys. 1983,54, 1552. [24] A. G. Dewey. J. T. Jacobs, B. G. Huth, SID Digest Technicul Papers 1978, 19. 1251 W. H. Chu, D. Y. Yoon, Mol. Cryst. Liq. Cryst. 1979, 54, 245. [26] R. Daley, A. J. Hughes, D. G. McDonnell, Liq. Cryst. 1989, 4(6), 585. [27] C. W. Walker, W. A. Crossland, Displuys 1985, 207. (281 M. Hareng, S . LeBerre, Electron. Lett. 1975, I / , 73. 1291 F. Kahn, P. N. Kendrick, J. Leff, J. Livioni, B. E. Lovcks, D. Stepner, SID Digest Technical Pupers 1987, 18, 254. [30] J. Harold, C. Steele, Proc. SID 1985, 2 6 , 141. 1311 D. Mash, GB Patent 2093206A, 1982. [32] A. Sasaki, N. Hayashi, T. Ishibashi, Jpn. Display 1983,497. [ 33] J. Harold, C. Steele, Eurodispluy Proc. (Paris) 1984, 29. [34] M. R. Smith,R. H. Burns, R. C. Tsai, Proc. SPIE 1980,200, 17 1.
490 [35] [36] [37] [38] [39] [40]
3 Nonchiral Smectic Liquid Crystals - Applications
A. G. Dewey, Opt. Engl. 1984,23, 230. G. J. Sprokel, US Patent 3 999 838, 1976. D. Armitage, Appl. Phys. 1981,52,4843. D. Coates, GB Patent 2091 1753 A, 1982. Eastman Kodak, US Patent 3 774 122, 1973. T. Nishizawa, R. Tukahara, R. Morinaka, T. Hidaka, GB Patent 2069518,1981. [41] T. Urabe, GB Patent 2 140023A, 1984. [42] V. T. Muller-Westerhof, A. Nazzal, R. J. Cox, A. M. Giroud, Mol. Cryst. Liq. Cryst. 1980,56,249. [43] K. Nakamura, 0. Yashuhiro, M. Sugimoto, J. Appl. Phys. 1989,59(2), 593. [44] A. G. Dewey, S. F. Anderson, G. Cherkoff, J. S. Feng, C. Handen, H. W. Johnson, J. Leff, R. T. Lynch, C. Marinelli, R. W. Schmiedeskamp, SID Digest Technical Papers 1983, 36. [45] A. G. Dewey, IEEE Electron Devices 1977,24, 918. [46] D. Mayden, N. Melchior, F. J. Kahn in Proc. IEEE Conference in Display Devices, 1972, p. 166. [47] M. Hareng, S. LeBerre, B. Mourey, P. C. Moutou, J. N. Perbert, L. Thirant in Proc. of the IEEE International Displays Research Conference 1982, p. 126. [48] M. Hareng, R. Hehlen, S. LeBerre, J. P. LePesant, L. Thirant in Proc. of the Electronics Displays Conference, Vol. 1 1984, p. 28. [49] S. Lu, D. H. Davies, R. Albert, D. B. Chung, A. Hochbaum, C. H. Chung, SID Digest Technical Papers, 1982, p. 238. [50] S. Lu, D. H. Davies, C. H. Chung, D. Evanicky, R. Albert, R. Traber in IEEE International Display Research Conference 1982, p. 132. [51] W. Harter, S. Lu, S. Ho, B. Basler, W. Newman, C. Otaguro in SID Symp. Digest. 1984, p. 196. [52] S. Lu, D. Buuvinhchu, US Patent 4461715, 1984. [53] M. Hareng, S. LeBerre, L. Thirant, Appl. Phys. Lett. 1974,25, 12. [54] M. Hareng, S. LeBerre, L. Thirant, Appl. Phys. Lett. 1975,27, 575. [55] W. A. Crossland, J. H. Morrissey, D. Coates, GB Patent 1569688, 1977. [56] D. Coates, A. B. Davey, C. J. Walker, Eurodisplay 1987, 96. [57] V. N. Chirkov, D. F. Aliev, G. M. Radzhabov, A. K. Zeinally, Mol. Cryst. Liq. Cryst.Lett. 1979, 49, 293.
(581 D. Coates, W. A. Crossland, J. H. Momssey, B. Needham, J. Phys. D: Appl. Phys. 1978, 11, 2025. [59] W. A. Grossland, J. H. Morrissey, D. Coates, GB Patent 1569686, 1977. [60] G. H. Heilmeier, L. A. Zanoni, L. A. Barton, Appl. Phys. Lett. 1968, 13,46. [61] B. Bahadur in Liquid Crystals - Applications and Uses (Ed. B. Bahadur) World Scientific, Singapore 1990, Vol. 1, Chap. 9. [62] C. Tani, Appl. Phys. Lett. 1971, 19, 241. [63] M. Steers, A. Mircea-Roussel, J. Physique Coll. 1976,37(3), 145. [64] W. Helfrich, J. Chern. Phys. 1969, 51,4092. [65] W. A. Crossland, D. Coates, GB Patent 1 601 601, 1978. [66] S. Matsumoto, M. Kawamoto, T. Tsukada, Jpn. J. Appl. Phys. 1975,14,7. [67] J. A. Geurst, W. J. A. Goosens, Phys. Letts. 1972,41(4), 369. [68] W. A. Crossland, P. J. Ayliffe, Proc. SID 1979, 23,9. [69] W. A. Crossland, S . Cantor, SID Digest Technical Papers 1985,16, 124. [70] D. Coates, Mol. Cryst. Liq. Cryst. 1978,49, 83. [71] J. L. Fergason, SID Digest Technical Papers 1985, 16,68. [72] Taliq Varilite and 3M Privacy Film. [73] Y. Nagoe, K. Ando, A. Asano, I. Takemoto, J. Havens, P. Jones, D. Reddy, A. Tomita, SID Digest Technical Papers 1995,26,223. [74] P. Nolan, M. Tillin, D. Coates, E. Ginter, E. Leuder, T. Kallfass, Eurodisplay 1993, 397. [75] P. Drzaic, R. C. Wiley, J. McCoy, Proc. SPIE 1989,1080,41. [76] P. P. Crooker, D. K. Yang, Appl. Phys. Lett. 1990,57,2529. [77] V. Y. Zyryanov, S. L. Smorgan, V. F. Shabanov, SID Digest Technical Papers 1992, 776. [78] M. Koshimizi, T. Kakinuma, Japanese Patent 07 36007 (95 36007), 1995; Chem. Abs. 1995, 123,70512. [79] T. Kakinuma, M. Koshimizu, T. Teshigawara, Jpn. Display (Hiroshima) 1992, 85 1. [80] M. Utsumi, M. Akada, E. Inoue, IS&T’s48th Annual Conference Proceedings 1995, p. 499.
Handbook of Liquid Crystals D. Demus, J. Goodby, G. W. Gray, H.-W. Spiess, V. Vill
VOl. 1: Fundamentals Vol. 2 A: Low Molecular Weight Liquid Crystals I Vol. 2 B: Low Molecular Weight Liquid Crystals I1 VOl. 3: High Molecular Weight Liquid Crystals
Further title of interest:
J. L. Serrano: Metallomesogens ISBN 3-527-29296-9
D. Demus, J. Goodby, G. W. Gray, H.-W. Spiess, V. Vill
Handbook of Liquid Crystals
8WILEY-VCH
D. Demus, J. Goodby, G. W. Gray, H.-W. Spiess, V. Vill
Handbook of Liquid Crystals Vol. 2 B: Low Molecular Weight Liquid Crystals I1
8WILEY-VCH Weinheim New York Chichester Brisbane Singapore Toronto
Prof. Dietrich Demus Veilchenweg 23 06 1 18 Halle Germany Prof. John W. Goodby School of Chemistry University of Hull Hull, HU6 7RX U. K. Prof. George W. Gray Merck Ltd. Liquid Crystals Merck House Poole BH15 1TD U.K.
Prof. Hans-Wolfgang Spiess Max-Planck-Institut fur Polymerforschung Ackermannweg 10 55 128 Mainz Germany Dr. Volkmar Vill Institut fur Organische Chemie Universitat Hamburg Martin-Luther-King-Plat2 6 201 46 Hamburg Germany
This book was carefully produced. Nevertheless, authors, editors and publisher do not warrant the information contained therein to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.
Library of Congress Card No. applied for. A catalogue record for this book is available from the British Library. Deutsche Bibliothek Cataloguing-in-Publication Data: Handbook of liquid crystals I D. Demus ... - Weinheim ; New York ; Chichester ; Brisbane ; Singapore ; Toronto : Wiley-VCH ISBN 3-527-29502-X Vol. 2B. Low molecular weight liquid crystals. - 2. - (1998) ISBN 3-527-29491-0
0 WILEY-VCH Verlag GmbH. D-60469 Weinheim (Federal Republic of Germany), 1998 Printed on acid-free and chlorine-free paper.
All rights reserved (including those of translation in other languages). No part of this book may be reproduced in any form - by photoprinting, microfilm, or any other means - nor transmitted or translated into machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law. Composition and Printing: Fa. Konrad Triltsch Druck- und Verlagsanstalt GmbH, D-97070 Wiirzburg. Bookbinding: Wilhelm Osswald & Co., D-67433 Neustadt Printed in the Federal Republic of Germany.
The Editors D. Demus studied chemistry at the Martin-Luther-University, Halle, Germany, where he was also awarded his Ph. D. In 1981 he became Professor, and in 1991 Deputy Vice-Chancellor of Halle University. From 1992-1994 he worked as a Special Technical Advisor for the Chisso Petrochemical Corporation in Japan. Throughout the period 1984-1991 he was a member of the International Planning and Steering Commitee of the International Liquid Crystal Conferences, and was a non-executive director of the International Liquid Crystal Society. Since 1994 he is active as an Scientific Consultant in Halle. He has published over 310 scientific papers and 7 books and he holds 170 patients.
J. W. Goodby studied for his Ph. D. in chemistry under the guidance of G. W. Gray at the University of Hull, UK. After his post-doctoral research he became supervisor of the Liquid Crystal Device Materials Research Group at AT&T Bell Laboratories. In 1988 he returned to the UK to become the Thorn-EMI/STC Reader in Industrial Chemistry and in 1990 he was appointed Professor of Organic Chemistry and Head of the Liquid Crystal Group at the University of Hull. In 1996 he was the first winner of the G. W. Gray Medal of the British Liquid Crystal Society.
G . W. Gray studied chemistry at the University of Glasgow, UK, and received his Ph. D. from the University of London before moving to the University of Hull. His contributions have been recognised by many awards and distinctions, including the Leverhulme Gold Medal of the Royal Society (1987), Commander of the Most Excellent Order of the British Empire (1991), and Gold Medallist and Kyoto Prize Laureate in Advanced Technology (1 995). His work on structure/property relationships has had far reaching influences on the understanding of liquid crystals and on their commercial applications in the field of electro-optical displays. In 1990 he became Research Coordinator for Merck (UK) Ltd, the company which, as BDH Ltd, did so much to commercialise and market the electro-optic materials which he invented at Hull University. He is now active as a Consultant, as Editor of the journal “Liquid Crystals” and as authorleditor for a number of texts on Liquid Crystals.
VI
The Editors
H. W. Spiess studied chemistry at the University of FrankfurVMain, Germany, and obtained his Ph. D. in physical chemistry for work on transition metal complexes in the group of H. Hartmann. After professorships at the University of Mainz, Miinster and Bayreuth he was appointed Director of the newly founded Max-Planck-Institute for Polymer Research in Mainz in 1984. His main research focuses on the structure and dynamics of synthetic polymers and liquid crystalline polymers by advanced NMR and other spectroscopic techniques.
V. Vill studied chemistry and physics at the University of Miinster, Germany, and acquired his Ph. D. in carbohydrate chemistry in the gorup of J. Thiem in 1990. He is currently appointed at the University of Hamburg, where he focuses his research on the synthesis of chiral liquid crystals from carbohydrates and the phase behavior of glycolipids. He is the founder of the LiqCryst database and author of the LandoltBornstein series Liquid Crystals.
List of Contributors Volume 2B, Low Molecular Weight Crystals I1
Boden, N.; Movaghar, B. (IX) Centre for Self-Organising Molecular Systems (SOMS) Dept. of Chemistry University of Leeds Leeds LS9 9JT U.K.
Fukuda, A.; Miyachi, K. (VI:3) Shinshu University Faculty of Textile Science and Technology Dept. of Kansei Engineering Tokida 3-15-1, Ueda-shi Nagano-ken 386 Japan
Bushby, R. J. (VII) University of Leeds Leeds LS2 9JT U.K.
Giroud, A.-M. (XIV) Chimie de Coordination Unit6 de Recherche AssociCe au CNRS N. 1194 CEA Grenoble-DRFMC/SCIB 17, rue des Martyrs 38054 Grenoble Cedex France
Cammidge, A. N. (VII) University of East Anglia Norwich NR4 7TJ U.K. Chandrasekhar, S. (VIII) Centre for Liquid Crystal Research P. 0. Box 1329 Jalahalli Bangalore - 560 013 India Diele, S.; Goring, P. (XIII) Martin-Luther-Universitat Haile-Wittenberg FB Chemie Inst. f. Physikal. Chemie 06099 Halle Germany
Imrie, C. T. (X) University of Aberdeen Dept. of Chemistry Meston Walk, Old Aberdeen AB24 3UE U.K. Kato, T. (XVII) University of Tokyo Institute of Industrial Science 7-22- 1 Roppongi, Minato-ku Tokyo 106 Japan
VTII
List of Contributors
Kelly, S. M. (V1:l) The University of Hull Liquid Crystals & Advanced Organic Materials Research Group Dept. of Chemistry Hull HU6 7RX U.K . Lagerwall, S. T. (VI:2) Chalmers University of Technology Physics Department Liquid Crystal Group 41296 Goteborg Sweden Luckhurst, G. R. (X) University of Southampton Dept. of Chemistry Highfield Southampton SO17 1BJ U.K. Lydon, J. E. (XVIII) University of Leeds Dept. of Biochemistry & Molecular Biology Leeds LS2 9JT U.K. MalthCte, J. (XII) Institut Curie Section de Recherche UMR - CNRS 168 1 1 , Rue Pierre et Marie Curie 75231 Paris Cedex 05 France
Nguyen, H. T.; Destrade, C. (XII) Centre de Recherche Paul Pascal Avenue A. Schweitzer 33600 Pessac France Praefcke, K.; Singer, D. XVI TU Berlin IOC StraBe des 17. Juni 124 10623 Berlin Germany Sadashiva, B. K. (XV) Raman Research Institute CV Raman Avenue Bangalore - 560 080 India Weissflog, W. (XI) Max-Planck-Gesellschaft Arbeitsgruppe Flussigkristalline Systeme Martin-Luther-Universitat Mahlpforte 1 06108 Halle Germany
Outline Volume 1
..................
Chapter I: Introduction and Historical Development . George W Gray
1
Chapter 11: Guide to the Nomenclature and Classification of Liquid Crystals . . . . . 17 John W Goodby and George W Gray Chapter 111: Theory of the Liquid Crystalline State . . . . . . . . . . . . . . . 1 Continuum Theory for Liquid Crystals . . . . . . . . . . . . . . . . Frank M . Leslie Molecular Theories of Liquid Crystals . . . . . . . . . . . . . . . . 2 M. A. Osipov Molecular Modelling . . . . . . . . . . . . . . . . . . . . . . . . . 3 Mark R. Wilson Chapter I V General Synthetic Strategies . Thies Thiemann and Volkmar Ell
. . . . 25 . . . . 25 . . .
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40
. . . . 72
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115
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133
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189 189
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204
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215
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23 1
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253
Chapter V Symmetry and Chirality in Liquid Crystals. John W Goodby
Chapter VI: Chemical Structure and Mesogenic Properties Dietrich Demus Chapter VII: Physical Properties . . . . . . . . . . . Tensor Properties of Anisotropic Materials 1 David Dunmur and Kazuhisa Toriyama 2 Magnetic Properties of Liquid Crystals . . David Dunmur and Kazuhisa Toriyama 3 Optical Properties . . . . . . . . . . . . . David Dunmur and Kazuhisn Toriyama 4 Dielectric Properties . . . . . . . . . . . . David Dunmur and Kazuhisa Toriyama 5 Elastic Properties. . . . . . . . . . . . . . David Dunmur and Kazuhisa Toriyama 6 Phase Transitions. . . . . . . . . . . . . .
87
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..
... ... .....
. ... .. ..
. . . . . . . . . . . . . . . . . 28 1
X
Outline
6.1 6.2 6.2.1 6.2.2 6.2.3 6.2.4 6.3 6.4 7
8 9 10 11
12 13
Phase Transitions Theories . . . . . . . . . . . . . . . . . . . . . . . . . . Philippe Barois Experimental Methods and Typical Results . . . . . . . . . . . . . . . . Thermal Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jan Thoen Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wolfgang Wedler Metabolemeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wolfgang Wedler High Pressure Investigations . . . . . . . . . . . . . . . . . . . . . . . . . P. Pollmann Fluctuations and Liquid Crystal Phase Transitions . . . . . . . . . . . . P. E . Cladis Re-entrant Phase Transitions in Liquid Crystals . . . . . . . . . . . . . . P. E . Cladis Defects and Textures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Y: Bouligand Flow Phenomena and Viscosity . . . . . . . . . . . . . . . . . . . . . . . Frank Schneider and Herbert Kneppe Behavior of Liquid Crystals in Electric and Magnetic Fields . . . . . . . Lev M . Blinov Surface Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Blandine Je'rSme Ultrasonic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Olga A . Kapustina Nonlinear Optical Properties of Liquid Crystals . . . . . . . . . . . . . . R Pal&-Muhoray Diffusion in Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . . l? Noack
'
281
. 310 310 334 350 355
. 379 . 391 406 454
. 477 535 549
. 569 582
Chapter VIII: Characterization Methods . . . . . . . . . . . . . . . . . . . . . . . . 595 1 Magnetic Resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595 Claudia Schmidt and Hans Wolfgang Spiess X-Ray Characterization of Liquid Crystals: Instrumentation . . . . . . . . 619 2 Richard H . Templer Structural Studies of Liquid Crystals by X-ray Diffraction . . . . . . . . . 635 3 JohnM.Seddon 4 Neutron Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 680 Robert M . Richardson Light Scattering from Liquid Crystals . . . . . . . . . . . . . . . . . . . . 699 5 Helen E Gleeson Brillouin Scattering from Liquid Crystals . . . . . . . . . . . . . . . . . . 719 6 Helen E Gleeson Mossbauer Studies of Liquid Crystals . . . . . . . . . . . . . . . . . . . . 727 7 Helen F. Gleeson
Outline
XI
Chapter IX: Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 731 1 Displays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 731 Ian C. Sage Nondisplay Applications of Liquid Crystals . . . . . . . . . . . . . . . . . 763 2 William A . Crossland and TimothyD . Wilkinson 823 Thermography Using Liquid Crystals . . . . . . . . . . . . . . . . . . . . 3 Helen F: Gleeson Liquid Crystals as Solvents for Spectroscopic. Chemical 4 Reaction. and Gas Chromatographic Applications . . . . . . . . . . . . . 839 William J. Leigh and Mark S. Workentin Index Volume 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
897
Volume 2 A Part I: Calamitic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
Chapter I: Phase Structures of Calamitic Liquid Crystals . . . . . . . . . . . . . . . . . 3 John W Goodby Chapter 11: Phase Transitions in Rod-Like Liquid Crystals . . . . . . . . . . . . . . . 23 Daniel Guillon Chapter 111: Nematic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Synthesis of Nematic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . 47 1 Kenneth J . Toyne 2 Physical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 Elastic Properties of Nematic Liquid Crystals . . . . . . . . . . . . . . . . 60 2.1 Ralf Stannarius Dielectric Properties of Nematic Liquid Crystals . . . . . . . . . . . . . . . 91 2.2 Horst Kresse Diamagnetic Properties of Nematic Liquid Crystals . . . . . . . . . . . . . 113 2.3 Ralf Stannarius 2.4 Optical Properties of Nematic Liquid Crystals . . . . . . . . . . . . . . . 128 Gerhard Pelzl 2.5 Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 Herbert Kneppe and Frank Schneider 2.6 Dynamic Properties of Nematic Liquid Crystals . . . . . . . . . . . . . . 170 R. Blinc and Z. Mus'evic' 3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 199 TN, STN Displays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Harald Hirschmann and Volker Reiffenrath Active Matrix Addressed Displays . . . . . . . . . . . . . . . . . . . . . . 230 3.2 Eiji Kaneko
XI1 3.3 3.4
Outline
Dynamic Scattering . . . . . . Birendra Bahadur Guest-Host Effect . . . . . . . Birendra Bahadur
.......................
243
.......................
257
Chapter IV: Chiral Nematic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . 303 The Synthesis of Chiral Nematic Liquid Crystals . . . . . . . . . . . . . . 303 1 Christopher J. Booth Chiral Nematics: Physical Properties and Applications . . . . . . . . . . . 335 2 Harry Coles Chapter V: Non-Chiral Smectic Liquid Crystals . . . . . . . . . . . . . . . . . . . . Synthesis of Non-Chiral Smectic Liquid Crystals . . . . . . . . . . . . . . 1 John W Goodby Physical Properties of Non-Chiral Smectic Liquid Crystals. . . . . . . . . 2 C. C. Huang Nonchiral Smectic Liquid Crystals - Applications . . . . . . . . . . . . . 3 David Coates
41 1 41 1 441 470
Volume 2B Part 2: Discotic Liquid Crystals. . . .
.........................
Chapter VI: Chiral Smectic Liquid Crystals . . . . . . . . . . . . . Synthesis of Chiral Smectic Liquid Crystals. . . . . . . . 1 Stephen M. Kelly Ferroelectric Liquid Crystals. . . . . . . . . . . . . . . . 2 Sven i? Lagerwall Antiferroelectric Liquid Crystals . . . . . . . . . . . . . 3 Kouichi Miyachi and Atsuo Fukuda Chapter VII: Synthesis and Structural Features. . . Andrew N. Cammidge and Richard J. Bushby
49 1
. . . . . . . . . 493 . . . . . . . . . 493 .
........
. . .
5 15
. . . . . . 665
..................
693
Chapter VIII: Discotic Liquid Crystals: Their Structures and Physical Properties . . . 749 S. Chandrasekhar Chapter IX: Applicable Properties of Columnar Discotic Liquid Crystals Neville Boden and Bijou Movaghar
,
. . . . . . 781
Outline
XI11
Part 3 : Non-Conventional Liquid-Crystalline Materials . . . . . . . . . . . . . . . . 799 Chapter X: Liquid Crystal Dimers and Oligomers . . . . . . . . . . . . . . . . . . . 801 Corrie 7: Imrie and Geoffrey R. Luckhurst Chapter XI: Laterally Substituted and Swallow-Tailed Liquid Crystals . . . . . . . . 835 Wolfgang Weissflog Chapter XII: Phasmids and Polycatenar Mesogens . . . . . . . . . . . . . . . . . . . 865 Huu-Tinh Nguyen. Christian Destrade. and Jacques Malth2te Chapter XIII: Thermotropic Cubic Phases . . . . . . . . . . . . . . . . . . . . . . . Siegmar Diele and Petra Goring
887
Chapter XIV Metal-containing Liquid Crystals . . . . . . . . . . . . . . . . . . . . Anne Marie Giroud-Godquin
901
Chapter XV: Biaxial Nematic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . B. K. Sadashiva
933
Chapter XVI: Charge-Transfer Systems . . . . . . . . . . . . . . . . . . . . . . . . Klaus Praefcke and D . Singer
945
Chapter XVII: Hydrogen-Bonded Systems . . . . . . . . . . . . . . . . . . . . . . . Takashi Kato
969
Chapter XVIII: Chromonics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . John Lydon
981
Index Volumes 2 A and 2 B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1009
Volume 3 Part 1: Main-Chain Thermotropic Liquid-Crystalline Polymers . . . . . . . . . . . . . 1 Chapter I: Synthesis. Structure and Properties . . . . . . . . . . . . . . . . . . . . . . 3 Aromatic Main Chain Liquid Crystalline Polymers . . . . . . . . . . . . . . 3 1 Andreas Greiner and Hans- Werner Schmidt Main Chain Liquid Crystalline Semiflexible Polymers . . . . . . . . . . . . 26 2 Em0 Chiellini and Michele Laus Combined Liquid Crystalline Main-Chain/Side-Chain Polymers . . . . . . . 52 3 Rudolf Zentel BlockCopolymers Containing Liquidcrystalline Segments . . . . . . . . . 66 4 Guoping Ma0 and Christopher K. Ober
XIV
Outline
Chapter 11: Defects and Textures in Nematic Main-Chain Liquid Crystalline Polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Claudine Noel
93
Part 2: Side-Group Thermotropic Liquid-Crystalline Polymers . . . . . . . . . . . . 121 Chapter 111: Molecular Engineering of Side Chain Liquid Crystalline Polymers by Living Polymerizations . . . . . . . . . . . . . . . . . . . . . . . . . . Coleen Pugh and Alan L. Kiste
123
Chapter I V Behavior and Properties of Side Group Thermotropic Liquid Crystal Polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jean-Claude Dubois, Pierre Le Barny, Monique Mauzac, and Claudine Noel
207
Chapter V: Physical Properties of Liquid Crystalline Elastomers . . . . . . . . . . . 277 Helmut R. Brand and Heino Finkelmann
Part 3: Amphiphilic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . . .
303
Chapter VI: Amphotropic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . Dieter Blunk, Klaus Praefcke and Volkmar Vill
305
Chapter VII: Lyotropic Surfactant Liquid Crystals . . . . . . . . . . . . . . . . . . . 34 1 C. Fairhurst, S. Fullec J. Gray, M. C. Holmes, G. J. 7: Eddy Chapter VIII: Living Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Siegfried Hoffmann
393
Chapter IX: Cellulosic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . . Peter Zugenmaier
45 1
Index Volumes 1 - 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
483
Contents Volume 2 A
Part I: Calamitic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . .
1
Chapter I: Phase Structures of Calamitic Liquid Crystals . . . . . . . . . . . . . . 3 John W Goodby 1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
Melting Processes of Calamitic Thermotropic Liquid Crystals . . . . . . . . . 4
3 3.1 3.2 3.3 3.3.1 3.3.2 3.3.3 3.3.4 3.4 3.4.1 3.4.2 3.4.3 3.4.4 3.4.5
Structures of Calamitic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . 6 The Nematic Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Structures of Smectic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . 7 The Structures of the Orthogonal Smectic Phases . . . . . . . . . . . . . . . 7 Structure of the Smectic A Phase . . . . . . . . . . . . . . . . . . . . . . . . 7 Structure in the Hexatic B Phase . . . . . . . . . . . . . . . . . . . . . . . . 10 Structure of the Crystal B Phase . . . . . . . . . . . . . . . . . . . . . . . . 10 Structure of Crystal E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Structures of the Tilted Smectic Phases . . . . . . . . . . . . . . . . . . . . . 13 Structure of the Smectic C Phase . . . . . . . . . . . . . . . . . . . . . . . . 13 Structure of the Smectic I Phase . . . . . . . . . . . . . . . . . . . . . . . . 16 Structure of the Smectic F Phase . . . . . . . . . . . . . . . . . . . . . . . . 16 Structures of the Crystal J and G Phases . . . . . . . . . . . . . . . . . . . . 17 Structures of the Crystal H and K Phases . . . . . . . . . . . . . . . . . . . . 18
4
Long- and Short-Range Order . . . . . . . . . . . . . . . . . . . . . . . . . .
18
5
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
3
Chapter 11: Phase Transitions in Rod-Like Liquid Crystals . . . . . . . . . . . . . 23 Daniel Guillon 1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 2.1 2.2 2.3 2.4
Isotropic-Nematic (Iso-N) Transition . . . . . . . . . . . . . . . . . . . . . 23 Brief Summary of the Landau-de Gennes Model . . . . . . . . . . . . . . . . 23 Magnetic Birefringence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Light Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Deviations from the Landau-de Gennes Model . . . . . . . . . . . . . . . . . 25
23
XVI
Contents
3 3.1 3.2
Nematic-Smectic A (N-SmA) Transition . . . . . . . . . . . . . . . . . . . . 26 26 The McMillan-de Gennes Approach . . . . . . . . . . . . . . . . . . . . . . Critical Phenomena: Experimental Situation . . . . . . . . . . . . . . . . . . 26
4 4.1 4.2 4.3 4.4 4.5 4.6
Smectic A-Smectic C (SmA-SmC) Transition . . . . . . . . . . . . . . . . . 29 29 General Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Critical Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Experimental Situation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Smectic A-Smectic C* (SmA-SmC*) Transition . . . . . . . . . . . . . . . . 32 The Nematic-Smectic A-Smectic C (NAC) Multicritical Point . . . . . . . . 33 35 SmA-SmC Transition in Thin Films . . . . . . . . . . . . . . . . . . . . . .
5 5.1 5.2
Hexatic B to Smectic A (SmBhex-SmA) transition . . . . . . . . . . . . . . 36 General Presentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 SmBhex-SmA Transition in Thin Films . . . . . . . . . . . . . . . . . . . . 37
6 6.1 6.2 6.3
Induced Phase Transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Mechanically Induced SmA-SmC Transition . . . . . . . . . . . . . . . . . . 38 Electrically Induced Transitions . . . . . . . . . . . . . . . . . . . . . . . . 39 39 Photochemically Induced Transitions . . . . . . . . . . . . . . . . . . . . . .
7 7.1 7.2 7.3 7.4
Other Transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Smectic C to Smectic I (SmC-SmI) Transition . . . . . . . . . . . . . . . . Smectic C to Smectic F (SmC-SmF) Transition . . . . . . . . . . . . . . . Smectic F to Smectic I (SmF-SmI) Transition . . . . . . . . . . . . . . . . Smectic F to Smectic Crystalline G (SmF-SmG) Transition . . . . . . . . .
8
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
Chapter 111: Nematic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . .
47
1 1.1
1.2 f.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 1.12
. . . .
41 41 41 42 42
47 Synthesis of Nematic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . Kenneth J. Toyne Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Benzene. Biphenyl and Terphenyl Systems . . . . . . . . . . . . . . . . . . . 48 49 Cyclohexane Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1,4-Disubstituted-bicyclo[2.2.2]octanes. . . . . . . . . . . . . . . . . . . . 50 51 2,5.Disubstituted.l, 3.dioxanes . . . . . . . . . . . . . . . . . . . . . . . . . 2,5.Disubstitute d.pyridines . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 2,5.Disubstituted.pyrimidines . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3,6.Disubstituted.pyridazines . . . . . . . . . . . . . . . . . . . . . . . . . . 52 52 Naphthalene systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unusual Core Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Ester Linkages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 54 Lateral Substitution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Contents
1.13 1.14 1.15
XVII
4.c.(trans.4.A1kyicyc1ohexyl).1.alkyl.r.1.cyanocyclohexanes . . . . . . . . . 55 Terminal Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 56 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
60 Physical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Elastic Properties of Nematic Liquid Crystals . . . . . . . . . . . . . . . . . 60 Ralf Stannarius 2.1.1 Introduction to Elastic Theory . . . . . . . . . . . . . . . . . . . . . . . . . 60 2.1.2 Measurement of Elastic Constants . . . . . . . . . . . . . . . . . . . . . . . 63 64 2.1.2.1 Frkedericksz Transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 2.1.2.2 Light Scattering Measurements . . . . . . . . . . . . . . . . . . . . . . . . . Other Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 2.1.2.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 Experimental Elastic Data 2.1.3 71 2.1.4 MBBA and n-CB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 2.1.5 ‘Surface-like’ Elastic Constants . . . . . . . . . . . . . . . . . . . . . . . . . 79 2.1.6 Theory of Elastic Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.7 Biaxial Nematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 2.1.8 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 2 2.1
2.2 2.2.1 2.2.2 2.2.3 2.2.4 2.2.5 2.2.6 2.3 2.3.1 2.3.2 2.3.2.1 2.3.2.2 2.3.2.3 2.3.2.4 2.3.2.5 2.3.3 2.3.4 2.3.5 2.3.6 2.4 2.4.1 2.4.2
Dielectric Properties of Nematic Liquid Crystals . . . . . . . . . . . . . . . . 91 Horst Kresse 91 Rod-like Molecules in the Isotopic State . . . . . . . . . . . . . . . . . . . . Static Dielectric Constants of Nematic Samples . . . . . . . . . . . . . . . . 92 The Nre Phenomenon and the Dipolar Correlation . . . . . . . . . . . . . . . 98 99 Dielectric Relaxation in Nematic Phases . . . . . . . . . . . . . . . . . . . . Dielectric Behavior of Nematic Mixtures . . . . . . . . . . . . . . . . . . . 102 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 Diamagnetic Properties of Nematic Liquid Crystals . . . . . . . . . . . . . Ralf Stannarius Magnetic Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Measurement of Diamagnetic Properties . . . . . . . . . . . . . . . . . . Faraday-Curie Balance Method . . . . . . . . . . . . . . . . . . . . . . . . Supraconducting Quantum Interference Devices Measurements . . . . . . NMR Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Magneto-electric Method . . . . . . . . . . . . . . . . . . . . . . . . . . . Mechanical Torque Measurements . . . . . . . . . . . . . . . . . . . . . . . Experimental Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Increment System for Diamagnetic Anisotropies . . . . . . . . . . . . . . Application of Diamagnetic Properties . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 113 113 . 116 116 . 116 117 117 118 118 . 124 125 126
Optical Properties of Nematic Liquid Crystals . . . . . . . . . . . . . . . . 128 Gerhard Pelzl Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
XVIII 2.4.3 2.4.4 2.4.5 2.4.6 2.4.7 2.4.8 2.4.9 2.5 2.5.1 2.5.2 2.5.2.1 2.5.2.2 2.5.2.3 2.5.2.4 2.5.2.5 2.5.3 2.5.3.1 2.5.3.2 2.5.3.3 2.5.3.4 2.5.4 2.5.4.1 2.5.4.2 2.5.4.3 2.5.5 2.6 2.6.1 2.6.2 2.6.3 2.6.4 2.6.5 2.6.6 2.6.7 2.6.8 2.6.9 2.6.10 2.6.1 1 2.6.12 2.6.13 2.6.14
Contents
Temperature Dependence of Birefringence and Refractive Indices . . . . . . 132 133 Dispersion of ne. no and An . . . . . . . . . . . . . . . . . . . . . . . . . . Refractive Indices of Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . 135 136 Birefringence in Homologous Series . . . . . . . . . . . . . . . . . . . . . Determination of Molecular Polarizability Anisotropy and Orientational 136 Order from Birefringence Data . . . . . . . . . . . . . . . . . . . . . . . . Relationships between Birefringence and Molecular Structure . . . . . . . . 137 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Herbert Kneppe and Frank Schneider Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Determination of Shear Viscosity Coefficients . . . . . . . . . . . . . . . General Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mechanical methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Light Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Other Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Determination of Rotational Viscosity . . . . . . . . . . . . . . . . . . . . . General Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental Methods with Permanent Director Rotation . . . . . . . . . Relaxation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Leslie Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Determination from Shear and Rotational Viscosity Coefficients . . . . . . Determination by Means of Light Scattering . . . . . . . . . . . . . . . . Other Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
142 142
. 142 142 143 147 1SO 150 155 155 . 156 157 160 165 . 165 . 166 167 167
Dynamic Properties of Nematic Liquid Crystals . . . . . . . . . . . . . . . R. Blinc and I . MuSevic' Quasielastic Light Scattering in Nematics . . . . . . . . . . . . . . . . . . . Nuclear Magnetic Resonance in Nematics . . . . . . . . . . . . . . . . . . . Quasielectric Light Scattering and Order Fluctuations in the Isotropic Phase Nuclear Magnetic Resonance and Order Fluctuations in the Isotropic Phase . Quasielastic Light Scattering and Orientational Fluctuations below Tc . . . Nuclear Magnetic Resonance and Orientational Fluctuations below Tc . . . . Optical Kerr Effect and Transient Laser-Induced Molecular Reorientation . . Dielectric Relaxation in Nematics . . . . . . . . . . . . . . . . . . . . . . . Pretransitional Dynamics Near the Nematic-Smectic A Transition . . . . . . Dynamics of Nematics in Micro-Droplets and Micro-Cylinders . . . . . . . Pretransitional Effects in Confined Geometry . . . . . . . . . . . . . . . . . Dynamics of Randomly Constrained Nematics . . . . . . . . . . . . . . . . Other Observations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
170 170 173 174 175 177 177 181 182 183 184 188 189 190 191
Contents
3 3.1 3.1.1 3.1.2 3.1.2.1 3.1.2.2 3.1.2.3 3.1.3 3.1.3.1 3.1.3.2 3.1.3.3 3.1.3.4 3.1.4 3.1.4.1 3.1.4.2 3.1.4.3 3.1.4.4 3.1.4.5 3.1.4.6 3.1.4.7 3.1.4.8 3.1.5 3.1.5.1 3.1.5.2 3.1.5.3 3.1.5.4 3.1.6 3.2 3.2.1 3.2.1.1 3.2.1.2 3.2.1.3 3.2.1.4 3.2.1.5 3.2.2 3.2.3 3.2.4 3.2.4.1 3.2.4.2 3.2.5 3.2.6
XIX
Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 199 TN. STNDisplays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Harald Hirschrnann and Volker Reiffenrath Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 200 Twisted Nematic Displays . . . . . . . . . . . . . . . . . . . . . . . . . . . Configuration and Operation Principles of Twisted Nematic Displays . . . . 200 Optical Properties of the Unactivated State . . . . . . . . . . . . . . . . . . 200 Optical Properties of the Activated State . . . . . . . . . . . . . . . . . . . 202 204 Addressing of Liquid Crystal Displays . . . . . . . . . . . . . . . . . . . . 205 Direct Addressing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 Passive Matrix Addressing . . . . . . . . . . . . . . . . . . . . . . . . . . . The Improved Alt-Pleshko Addressing Technique . . . . . . . . . . . . . . 207 Generation of Gray Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 208 Supertwisted Nematic Displays . . . . . . . . . . . . . . . . . . . . . . . . Influence of Device and Material Parameters . . . . . . . . . . . . . . . . . 208 Configuration and Transmission of a Supertwisted Nematic Display . . . . . 211 Electro-optical Performance of Supertwisted Nematic Displays . . . . . . . 213 Dynamical Behavior of Twisted Nematic and Supertwisted Nematic Displays 2 13 Color Compensation of STN Displays . . . . . . . . . . . . . . . . . . . . . 215 Viewing Angle and Brightness Enhancement . . . . . . . . . . . . . . . . . 218 218 Color Supertwisted Nematic Displays . . . . . . . . . . . . . . . . . . . . . Fast Responding Supertwisted Nematic Liquid Crystal Displays . . . . . . . 219 Liquid Crystal Materials for Twisted Nematic and Supertwisted Nematic 220 Display Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Materials with High Optimal Anisotropy . . . . . . . . . . . . . . . . . . . 221 Materials with Positive Dielectric Anisotropy . . . . . . . . . . . . . . . . . 221 Materials for the Adjustment of the Elastic Constant Ratio K33/Kll . . . . 225 226 Dielectric Neutral Basic Materials . . . . . . . . . . . . . . . . . . . . . . . 227 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Active Matrix Addressed Displays . . . . . . . . . . . . . . . . . . . . . . Eiji Kaneko Thin Film Diode and Metal-Insulator-Metal Matrix Address . . . . . . . . . Diode Ring Matrix Address . . . . . . . . . . . . . . . . . . . . . . . . . . Back-to-back Diode Matrix Address . . . . . . . . . . . . . . . . . . . . . . Two Branch Diode Matrix Address . . . . . . . . . . . . . . . . . . . . . . SiNx Thin Film Diode Matrix Address . . . . . . . . . . . . . . . . . . . . Metal-Insulator-Metal Matrix Address . . . . . . . . . . . . . . . . . . . . CdSe Thin Film Transistor Switch Matrix Address . . . . . . . . . . . . . . a-Si Thin Film Transistor Switch Matrix Address . . . . . . . . . . . . . . . p-Si Thin Film Transistor Switch Matrix Address . . . . . . . . . . . . . . . Solid Phase Crystallization Method . . . . . . . . . . . . . . . . . . . . . . Laser Recrystallization Method . . . . . . . . . . . . . . . . . . . . . . . . Metal-oxide Semiconductor Transistor Switch Matrix Address . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
230 230 230 230 231 231 232 233 234 237 238 238 239 240
xx 3.3 3.3.1 3.3.2 3.3.2.1 3.3.2.2 3.3.2.3 3.3.3 3.3.4 3.3.4.1 3.3.4.2 3.3.5 3.3.6 3.3.6.1 3.3.6.2 3.3.6.3 3.3.6.4 3.3.6.5 3.3.6.6 3.3.7 3.4 3.4.1 3.4.2 3.4.2.1 3.4.3 3.4.4 3.4.4.1 3.4.4.2 3.4.5 3.4.6 3.4.6.1 3.4.6.2 3.4.6.3 3.4.6.4 3.4.7 3.4.7.1 3.4.7.2 3.4.8 3.4.8.1
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Dynamic Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 Birendra Bahadur Introduction and Cell Designing . . . . . . . . . . . . . . . . . . . . . . . . 243 Experimental Observations at DC (Direct Current) and Low Frequency AC (Alternating Current) Fields . . . . . . . . . . . . . . . . . . . . . . . . . . 244 Homogeneously Aligned Nematic Regime . . . . . . . . . . . . . . . . . . 244 Williams Domains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244 Dynamic Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 Observations at High Frequency AC Field . . . . . . . . . . . . . . . . . . 247 247 Theoretical Explanations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248 Carr-Helfrich Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dubois-Violette, de Gennes, and Parodi Model . . . . . . . . . . . . . . . . 249 Dynamic Scattering in Smectic A and Cholesteric Phases . . . . . . . . . . 250 Electrooptical Characteristics and Limitations . . . . . . . . . . . . . . . . 251 Contrast Ratio Versus Voltage, Viewing Angle, Cell Gap, Wavelength, and Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 Display Current Versus Voltage, Cell Gap, and Temperature . . . . . . . . . 252 Switching Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 Effect of Conductivity, Temperature and Frequency . . . . . . . . . . . . . 253 Addressing of DSM (Dynamic Scattering Mode) LCDs 254 (Liquid Crystal Displays) . . . . . . . . . . . . . . . . . . . . . . . . . . . Limitations of DSM LCDs . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 Guest-Host Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Birendra Bahadur Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dichroic Dyes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chemical Structure, Photostability. and Molecular Engineering . . . . . . . Cell Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dichroic Parameters and Their Measurement . . . . . . . . . . . . . . . . . Order Parameter and Dichroic Ratio of Dyes . . . . . . . . . . . . . . . . . Absorbance, Order Parameter, and Dichroic Ratio Measurement . . . . . . . Impact of Dye Structure and Liquid Crystal Host on the Physical Properties of a Dichroic Mixture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Optical, Electro-Optical, and Life Parameters . . . . . . . . . . . . . . . . . Luminance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Contrast and Contrast Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . Switching Speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Life Parameters and Failure Modes . . . . . . . . . . . . . . . . . . . . . . Dichroic Mixture Formulation . . . . . . . . . . . . . . . . . . . . . . . . . Monochrome Mixture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Black Mixture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Heilmeier Displays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Threshold Characteristic . . . . . . . . . . . . . . . . . . . . . . . . . . . .
257 257 259 260 266 268 268 269 271 271 272 272 273 273 274 274 274 275 276
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3.4.8.2 Effects of Dye Concentration on Electro-optical Parameters . . . . . . . . 3.4.8.3 Effect of Cholesteric Doping . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.8.4 Effect of Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.8.5 Effect of Thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.8.6 Impact of the Order Parameter . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.8.7 Impact of the Host . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.8.8 Impact of the Polarizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.8.9 Color Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.8.10 Multiplexing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.9 Quarter Wave Plate Dichroic Displays . . . . . . . . . . . . . . . . . . . . . 3.4.10 Dye-doped TN Displays . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.11 Phase Change Effect Dichroic LCDs . . . . . . . . . . . . . . . . . . . . . 3.4.11.1 Threshold Characteristic and Operating Voltage. . . . . . . . . . . . . . . 3.4.1 1.2 Contrast Ratio, Transmission Brightness, and Switching Speed . . . . . . 3.4.11.3 Memory or Reminiscent Contrast . . . . . . . . . . . . . . . . . . . . . . . 3.4.11.4 Electro-optical Performance vs Temperature . . . . . . . . . . . . . . . . 3.4.1 1.5 Multiplexing Phase Change Dichroic LCDs . . . . . . . . . . . . . . . . . 3.4.12 Double Cell Dichroic LCDs . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.12.1 Double Cell Nematic Dichroic LCD . . . . . . . . . . . . . . . . . . . . . . 3.4.12.2 Double Cell One Pitch Cholesteric LCD . . . . . . . . . . . . . . . . . . 3.4.12.3 Double Cell Phase Change Dichroic LCD . . . . . . . . . . . . . . . . . . 3.4.13 Positive Mode Dichroic LCDs . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.13.1 Positive Mode Heilmeier Cells . . . . . . . . . . . . . . . . . . . . . . . . 3.4.13.2 Positive Mode Dichroic LCDs Using a AJ4 Plate . . . . . . . . . . . . . . 3.4.13.3 Positive Mode Double Cell Dichroic LCD . . . . . . . . . . . . . . . . . 3.4.13.4 Positive Mode Dichroic LCDs Using Special Electrode Patterns . . . . . . 3.4.13.5 Positive Mode Phase Change Dichroic LCDs . . . . . . . . . . . . . . . . 3.4.13.6 Dichroic LCDs Using an Admixture of Pleochroic and Negative Dichroic Dyes . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.14 Supertwist Dichroic Effect Displays . . . . . . . . . . . . . . . . . . . . . . 3.4.15 Ferroelectric Dichroic LCDs . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.15.1 Devices Using A Single Polarizer . . . . . . . . . . . . . . . . . . . . . . . 3.4.15.2 Devices Using No Polarizers . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.16 Polymer Dispersed Dichroic LCDs . . . . . . . . . . . . . . . . . . . . . . 3.4.17 Dichroic Polymer LCDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.18 Smectic A Dichroic LCDs . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.19 Fluorescence Dichroic LCDs . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.20 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Chapter 1% Chiral Nematic Liquid Crystals . . . . . . . . . . . . . . . . . . . . 1 1.1
. 276
. . . . . . . . . .
278 278 279 279 279 281 281 281 282 283 284 286 287 289 291 291 291 291 292 292 292 292 295 295 295 295 296 296 296 297 297 297 298 298 299 299
303
The Synthesis of Chiral Nematic Liquid Crystals . . . . . . . . . . . . . . . 303 Christopher J . Booth Introduction to the Chiral Nematic Phase and its Properties . . . . . . . . . 303
XXII 1.2 1.3 1.3.1 1.4 1.5 1.5.1 1.5.2 1.5.3 1.5.4 1S . 5 1.6 1.6.1 1.6.2 1.6.3 1.7 1.7.1 1.7.2 1.7.3 1.74 1.8
1.9 2 2.1 2.2 2.2.1 2.2.1.1 2.2.1.2 2.2.1.3 2.2.1.4 2.2.2 2.2.2.1 2.3 2.3.1 2.3.2 2.3.3 2.4 2.4.1 2.4.2 2.4.3 2.4.4 2.5 2.5.1
Contents
Formulation and Applications of ThermochromicMixtures . . . . . . . . . . 305 Classification of Chiral Nematic Liquid Crystalline Compounds . . . . . . . 307 Aspects of Molecular Symmetry for Chiral Nematic Phases . . . . . . . . . 308 310 Cholesteryl and Related Esters . . . . . . . . . . . . . . . . . . . . . . . . . Type I Chiral Nematic Liquid Crystals . . . . . . . . . . . . . . . . . . . . 311 Azobenzenes and Related Mesogens . . . . . . . . . . . . . . . . . . . . . 312 313 Azomethine (Schiff’s Base) Mesogens . . . . . . . . . . . . . . . . . . . . Stable Phenyl. Biphenyl. Terphenyl and Phenylethylbiphenyl Mesogens . . . 3 14 (R)-2-(4-Hydroxyphenoxy)-propanoicAcid Derivatives . . . . . . . . . . . 319 Miscellaneous Type I Chiral Nematic Liquid Crystals . . . . . . . . . . . . 323 Type I1 Chiral Nematic Liquid Crystals . . . . . . . . . . . . . . . . . . . . 325 Azomethine Ester Derivatives of (R)-3-Methyladipic Acid . . . . . . . . . . 325 Novel Highly Twisting Phenyl and 2-Pyrimidinylphenyl Esters 326 of (R)-3-Methyladipic Acid . . . . . . . . . . . . . . . . . . . . . . . . . . Chiral Dimeric Mesogens Derived from Lactic Acid or 1.2.Diols . . . . . . 327 Type 111 Chiral Nematic Liquid Crystals . . . . . . . . . . . . . . . . . . . . 327 Tricyclo[4.4.0.03,8]decane or Twistane Derived Mesogens . . . . . . . . . . 328 Axially Chiral Cyclohexylidene-ethanones . . . . . . . . . . . . . . . . . . 328 330 Chiral Heterocyclic Mesogens . . . . . . . . . . . . . . . . . . . . . . . . . Chiral Mesogens Derived from Cyclohexane . . . . . . . . . . . . . . . . . 331 332 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chiral Nematics: Physical Properties and Applications . . . . . . . . . . . . Harry Coles Introduction to Chiral Nematics: General Properties . . . . . . . . . . . . . Static Properties of Chiral Nematics . . . . . . . . . . . . . . . . . . . . . . Optical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Textures and Defects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Optical Propagation (Wave Equation Approach) . . . . . . . . . . . . . . . Optical Propagation (‘Bragg’ Reflection Approach) . . . . . . . . . . . . . Pitch Behavior as a Function of Temperature, Pressure, and Composition . . Elastic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Continuum Theory and Free Energy . . . . . . . . . . . . . . . . . . . . . . Dynamic Properties of Chiral Nematics . . . . . . . . . . . . . . . . . . . . Viscosity Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lehmann Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Macroscopic Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Field-Induced Distortions in Chiral Nematics . . . . . . . . . . . . . . . . . Magnetic Fields Parallel to the Helix Axis . . . . . . . . . . . . . . . . . . Magnetic Fields Normal to the Helix Axis . . . . . . . . . . . . . . . . . . Electric Fields Parallel to the Helix Axis . . . . . . . . . . . . . . . . . . . Electric Fields Normal to the Helix Axis . . . . . . . . . . . . . . . . . . . Applications of Chiral Nematics . . . . . . . . . . . . . . . . . . . . . . . . Optical: Linear and Nonlinear . . . . . . . . . . . . . . . . . . . . . . . . .
335 335 342 342 350 356 362 365 368 369 374 374 377 379 382 382 386 388 391 394 394
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2.5.2 2.5.3 2.5.3.1 2.5.3.2 2.5.3.3 2.6 2.7
XXIII
397 Thermal Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399 External Electric Field Effects . . . . . . . . . . . . . . . . . . . . . . . . . 400 Long Pitch Systems (p>A) . . . . . . . . . . . . . . . . . . . . . . . . . . Intermediate Pitch Length Systems (p =A). . . . . . . . . . . . . . . . . . . 401 403 Short Pitch Systems ( p d ) . . . . . . . . . . . . . . . . . . . . . . . . . . 404 Conclusions and the Future . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405
Chapter V Non-Chiral Smectic Liquid Crystals . . . . . . . . . . . . . . . . . . 411 Synthesis of Non-Chiral Smectic Liquid Crystals . . . . . . . . . . . . . . . 411 John K Goodby Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411 1.1 Template Structures for the Synthesis of Smectogens . . . . . . . . . . . . . 411 1.2 414 1.2.1 Terminal Aliphatic Chains . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.2 Polar Groups Situated at the End of the Core . . . . . . . . . . . . . . . . . 415 1.2.3 Functional Groups that Terminate the Core Structure . . . . . . . . . . . . . 417 418 1.2.4 Core Ring Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420 1.2.5 Liking Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422 1.2.6 Lateral Substitutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Syntheses of Standard Smectic Liquid Crystals . . . . . . . . . . . . . . . . 426 1.3 1.3.1 Synthesis of 4-Alkyl- and 4-alkoxy-4’-cyanophenyls:Interdigitated Smectic A Materials (e.g., 8CB and (80CB) . . . . . . . . . . . . . . . . . 426 Hexatic 1.3.2 Synthesis of 4-Alkyl-4-alkoxybiphenyl-4’-carboxylates: Smectic B Materials (e.g., 650BC) . . . . . . . . . . . . . . . . . . . . . . 427 1.3.3 Synthesis of 4-Alkyloxy-benzylidene-4-alkylanilines:Crystal B and 428 G Materials (e.g., nOms) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.4 Synthesis of Terephthalylidene-bis-4-alkylanilines:Smectic I. Smectic F. Crystal G and Crystal H Materials (e.g., TBnAs) . . . . . . . . . . . . . . . 428 Smectic C Materials . . . 429 1.3.5 Synthesis of 4-Alkoxy-phenyl-4-alkoxybenzoates: Smectic C. 1.3.6 Synthesis of 4-Alkylphenyl-4-alkylbiphenyl-4’-carboxylates: 430 Smectic I. Hexatic Smectic B Materials . . . . . . . . . . . . . . . . . . . . 4-(2-Methylutyl)phenyl-4-alkoxybiphenyl-4’-carboxylates: Synthesis of I .3.7 Smectic C. Smectic I. Smectic F. Crystal J. Crystal K and Crystal G 430 Materials (nOmIs. e.g., 8OSI) . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.8 Synthesis of 2-(4-n-Alkylphenyl)-5-(4-n-alkoxyoxyphenyl)pyrimidines: Smectic F and Crystal G Materials . . . . . . . . . . . . . . . . . . . . . . 431 1.3.9 Synthesis of 3-Nitro- and 3-Cyano-4-n-alkoxybiphenyl-4’-carboxylic Acids: Cubic and Smectic C Materials . . . . . . . . . . . . . . . . . . . . 433 1.3.10 Synthesis of bis-[ 1-(4’-Alkylbipheny1-4-y1) -3- (4-alkylpheny1)propane- 1 3-dionato]copper(11): Smectic 433 Metallomesogens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Synthesis of Smectic Materials for Applications . . . . . . . . . . . . . . . 435 1.4 1.4.1 Synthesis of Ferroelectric Host Materials . . . . . . . . . . . . . . . . . . . 435 1
.
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1.4.2 1.5 1.6
Contents
Synthesis of Antiferroelectric Host Materials . . . . . . . . . . . . . . . . . 437 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438 439 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Physical Properties of Non-Chiral Smectic Liquid Crystals . . . . . . . . . . 441 C. C. Huang 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441 2.2 Smectic A Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443 443 2.2.1 Macroscopic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 X-ray Characterization of Free-Standing Smectic Films . . . . . . . . . . . 446 2.3 Hexatic Smectic B Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . 447 2.3.1 Macroscopic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448 450 2.3.2 Thin Hexatic B Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452 2.4 Smectic C Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1 Physical Properties near the Smectic A-Smectic C Transition . . . . . . . . 452 2.4.1.1 Bulk Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452 2.4.2 Macroscopic Behavior of the Smectic C Phase . . . . . . . . . . . . . . . . 457 457 2.4.2.1 Bulk Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461 2.5 Tilted Hexatic Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.1 Identification of Hexatic Order in Thin Films . . . . . . . . . . . . . . . . . 461 2.5.2 Characterization of Hexatic Order in Thick Films . . . . . . . . . . . . . . . 462 464 2.5.3 Elastic Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464 2.6 Surface Tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467 2.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
3 3.1 3.2 3.3 3.3.1 3.3.1.1 3.3.1.2 3.3.2 3.3.2.1 3.3.2.2 3.3.2.3 3.3.3 3.3.3.1 3.3.3.2 3.3.3.3 3.3.3.4 3.3.3.5 3.4 3.5 3.5.1
Nonchiral Smectic Liquid Crystals - Applications . . . . . . . . . . . . . . 470 David Coates Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 470 471 Smectic Mesogens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Laser-Addressed Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . 473 Basic Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473 473 Normal Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475 Reverse Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476 476 Lasers and Dyes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477 Additives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Physical Characteristics and Applications . . . . . . . . . . . . . . . . . . . 478 478 Line Width and Write Speed . . . . . . . . . . . . . . . . . . . . . . . . . . 478 Contrast Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478 Projection Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478 Color Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478 Commercial Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thermally and Electrically Addressed Displays . . . . . . . . . . . . . . . . 481 482 Dielectric Reorientation of SmA Phases . . . . . . . . . . . . . . . . . . . . Materials of Negative Dielectric Anisotropy . . . . . . . . . . . . . . . . . 482
Contents
3.5.2 3.5.3 3.6 3.6.1 3.6.2 3.6.3 3.7 3.8 3.9 3.10
xxv
Materials of Positive Dielectric Anisotropy . . . . . . . . . . . . . . . . . . 482 A Variable Tilt SmA Device . . . . . . . . . . . . . . . . . . . . . . . . . . 482 Dynamic Scattering in SmA Liquid Crystal Phases . . . . . . . . . . . . . . 483 Theoretical Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485 Response Times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485 Displays Based on Dynamic Scattering . . . . . . . . . . . . . . . . . . . . 486 Two Frequency Addressed SmA Devices . . . . . . . . . . . . . . . . . . . 486 Polymer-Dispersed Smectic Devices . . . . . . . . . . . . . . . . . . . . . 487 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 489 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 489
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Volume 2 B
Part 11: Discotic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . .
491
Chapter VI: Chiral Smectic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . 1 Synthesis of Chiral Smectic Liquid Crystals . . . . . . . . . . . . . . . . . Stephen M . Kelly 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Long Pitch Chiral Smectic Liquid Crystals or Dopants . . . . . . . . . . . . 1.2.1 Schiff’s bases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.2 Aromatic Esters with Alkyl Branched Alkyl Chains . . . . . . . . . . . . . 1.2.3 Aromatic Heterocycles with Alkyl-Branched Alkyl Chains . . . . . . . . . . 1.2.4 Esters and Ethers in the Terminal Chain . . . . . . . . . . . . . . . . . . . . 1.2.5 Halogens at the Chiral Center . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.6 Cyclohexyl a-Fluorohexanoates . . . . . . . . . . . . . . . . . . . . . . . . 1.2.7 Gyano Groups at the Chiral Center . . . . . . . . . . . . . . . . . . . . . . 1.2.8 Optically Active Oxiranes and Thiiranes . . . . . . . . . . . . . . . . . . . 1.2.9 Optically Active y-Lactones . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.10 Optically Active &Lactones . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.11 Miscellaneous Optically Active Heterocycles . . . . . . . . . . . . . . . . . 1.3 Short Pitch Chiral Smectic Liquid Crystals or Dopants . . . . . . . . . . . . 1.3.1 Optically Active Terphenyl Diesters . . . . . . . . . . . . . . . . . . . . . . 1.3.2 Optically Active Methyl-Substituted Dioxanes . . . . . . . . . . . . . . . . 1.4 Antiferroelectric Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . 1.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
493 493
2 2.1 2.2 2.2.1 2.2.2 2.2.3 2.2.4 2.2.5 2.2.6 2.2.7 2.3 2.3.1 2.3.2 2.3.3
Ferroelectric Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . . Sven T. Lagerwall Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Polar Materials and Effects . . . . . . . . . . . . . . . . . . . . . . . . . . Polar and Nonpolar Dielectrics . . . . . . . . . . . . . . . . . . . . . . . . The Nonpolarity of Liquid Crystals in General . . . . . . . . . . . . . . . Behavior of Dielectrics in Electric Fields: Classification of Polar Materials Developments in the Understanding of Polar Effects . . . . . . . . . . . . The Simplest Description of a Ferroelectric . . . . . . . . . . . . . . . . . Improper Ferroelectrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Piezoelectric Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Necessary Conditions for Macroscopic Polarization in a Material . . . The Neumann and Curie Principles . . . . . . . . . . . . . . . . . . . . . . Neumann’s Principle Applied to Liquid Crystals . . . . . . . . . . . . . . The Surface-Stabilized State . . . . . . . . . . . . . . . . . . . . . . . . . .
493 495 496 497 500 501 503 503 506 506 508 508 508 509 509 510 510 512 515
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515 520 520 522 523 527 531 536 539 541 541 542 544
Contents
2.3.4 2.3.5 2.3.6 2.3.7 2.4 2.4.1 2.4.2 2.4.3 2.4.4 2.4.5 2.4.6 2.4.7 2.4.8 2.4.9 2.5 2.5.1 2.5.2 2.5.3 2.5.4 2.5.5 2.5.6 2.5.7 2.5.8 2.5.9 2.5.10 2.5.11 2.6 2.6.1 2.6.2 2.6.3 2.6.4 2.6.5 2.6.6 2.6.7 2.6.8 2.6.9 2.7 2.7.1 2.7.2 2.7.3 2.7.4 2.7.5 2.7.6 2.7.7 2.7.8
XXVII
Chirality and its Consequences . . . . . . . . . . . . . . . . . . . . . . . . 548 The Curie Principle and Piezoelectricity . . . . . . . . . . . . . . . . . . . . 550 Hermann’s Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 552 The Importance of Additional Symmetries . . . . . . . . . . . . . . . . . . 553 The Flexoelectric Polarization . . . . . . . . . . . . . . . . . . . . . . . . . 555 Deformations from the Ground State of a Nematic . . . . . . . . . . . . . . 555 The Flexoelectric Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . 556 The Molecular Picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557 Analogies and Contrasts to the Piezoelectric Effect . . . . . . . . . . . . . . 558 The Importance of Rational Sign Conventions . . . . . . . . . . . . . . . . 559 The Flexoelectrooptic Effect . . . . . . . . . . . . . . . . . . . . . . . . . . 560 Why Can a Cholesteric Phase not be Biaxial? . . . . . . . . . . . . . . . . . 563 Flexoelectric Effects in Smectic A Phases . . . . . . . . . . . . . . . . . . . 564 Flexoelectric Effects in Smectic C Phases . . . . . . . . . . . . . . . . . . . 564 The SmA*-SmC* Transition and the Helical C* State . . . . . . . . . . . . 568 The Smectic C Order Parameter . . . . . . . . . . . . . . . . . . . . . . . . 568 The SmA*-SmC* Transition . . . . . . . . . . . . . . . . . . . . . . . . . 571 The Smectic C* Order Parameters . . . . . . . . . . . . . . . . . . . . . . . 573 The Helical Smectic C* State . . . . . . . . . . . . . . . . . . . . . . . . . 574 The Flexoelectric Contribution in the Helical State . . . . . . . . . . . . . . 576 Nonchiral Helielectrics and Antiferroelectrics . . . . . . . . . . . . . . . . . 577 Simple Landau Expansions . . . . . . . . . . . . . . . . . . . . . . . . . . 578 The Electroclinic Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583 The Deformed Helix Mode in Short Pitch Materials . . . . . . . . . . . . . 587 The Landau Expansion for the Helical C* State . . . . . . . . . . . . . . . . 588 The Pikin-Indenbom Order Parameter . . . . . . . . . . . . . . . . . . . . . 592 Electrooptics in the Surface-Stabilized State . . . . . . . . . . . . . . . . . 596 The Linear Electrooptic Effect . . . . . . . . . . . . . . . . . . . . . . . . . 596 The Quadratic Torque . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 599 Switching Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 600 The Scaling Law for the Cone Mode Viscosity . . . . . . . . . . . . . . . . 602 Simple Solutions of the Director Equation of Motion . . . . . . . . . . . . . 603 Electrooptic Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . 604 Optical Anisotropy and Biaxiality . . . . . . . . . . . . . . . . . . . . . . . 608 The Effects of Dielectric Biaxiality . . . . . . . . . . . . . . . . . . . . . . 610 The Viscosity of the Rotational Modes in the Smectic C Phase . . . . . . . . 613 Dielectric Spectroscopy: To Find the yand E Tensor Components . . . . . . 617 Viscosities of Rotational Modes . . . . . . . . . . . . . . . . . . . . . . . . 617 The Viscosity of the Collective Modes . . . . . . . . . . . . . . . . . . . . 618 The Viscosity of the Noncollective Modes . . . . . . . . . . . . . . . . . . 620 The Viscosity yq from Electrooptic Measurements . . . . . . . . . . . . . . 622 The Dielectric Permittivity Tensor . . . . . . . . . . . . . . . . . . . . . . . 622 The Case of Chiral Smectic C* Compounds . . . . . . . . . . . . . . . . . . 623 Three Sample Geometries . . . . . . . . . . . . . . . . . . . . . . . . . . . 625 Tilted Smectic Layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 626
XXVIII
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2.7.9 2.7.10 2.8 2.8.1 2.8.2 2.8.3 2.8.4 2.8.5 2.8.6 2.8.7 2.8.8 2.8.9 2.8.10 2.8.1 1 2.9 2.10
Nonchiral Smectics C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Limitations in the Measurement Methods . . . . . . . . . . . . . . . . . . . FLC Device Structures and Local-Layer Geometry . . . . . . . . . . . . . . The Application Potential of FLC . . . . . . . . . . . . . . . . . . . . . . . Surface-Stabilized States . . . . . . . . . . . . . . . . . . . . . . . . . . . . FLC with Chevron Structures . . . . . . . . . . . . . . . . . . . . . . . . . Analog Gray Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thin Walls and Thick Walls . . . . . . . . . . . . . . . . . . . . . . . . . . C1 and C2 Chevrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The FLC Technology Developed by Canon . . . . . . . . . . . . . . . . . . The Microdisplays of Displaytech . . . . . . . . . . . . . . . . . . . . . . . Idemitsu's Polymer FLC . . . . . . . . . . . . . . . . . . . . . . . . . . . . Material Problems in FLC Technology . . . . . . . . . . . . . . . . . . . . Nonchevron Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Is There a Future for Smectic Materials? . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
Antiferroelectric Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . 665 Kouichi Miyachi and Atsuo Fukuda Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665 Origin of Antiferroelectricity in Liquid Crystals . . . . . . . . . . . . . . . 665 Biased or Hindered Rotational Motion in SmC* Phases . . . . . . . . . . . 665 Biased or Hindered Rotational Motion in SmCA* Phases . . . . . . . . . . . 669 Spontaneous Polarization Parallel to the Tilt Plane . . . . . . . . . . . . . . 671 Obliquely Projecting Chiral AlkylChains in SmA Phases . . . . . . . . . . 673 Thresholdless Antiferroelectricity andV-Shaped Switching . . . . . . . . . 675 Tristable Switching and the Pretransitional Effect . . . . . . . . . . . . . . . 675 Pretransitional Effect in Antiferroelectric Liquid Crystal Displays . . . . . . 679 Langevin-type Alignment in SmCR* Phases . . . . . . . . . . . . . . . . . 682 Antiferroelectric Liquid Crystal Materials . . . . . . . . . . . . . . . . . . . 684 Ordinary Antiferroelectric Liquid Crystal Compounds . . . . . . . . . . . . 684 Antiferroelectric Liquid Crystal Compounds with Unusual Chemical Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 688 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 689
3.1 3.2 3.2.1 3.2.2 3.2.3 3.2.4 3.3 3.3.1 3.3.2 3.3.3 3.4 3.4.1 3.4.2 3.5
627 628 629 629 630 634 637 639 644 648 650 651 653 655 658 660
Chapter VII: Synthesis and Structural Features . . . . . . . . . . . . . . . . . . 693 Andrew N . Carnrnidge and Richard J . Bushby 1
General Structural Features . . . . . . . . . . . . . . . . . . . . . . . . . .
693
2 2.1 2.1. I
Aromatic Hydrocarbon Cores . . . . . . . . . . . . . . . . . . . . . . . . . Benzene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Esters and Amides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
694 694 694
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XXIX
2.1.2 2.1.3 2.1.4 2.2 2.3 2.4 2.5 2.5.1 2.5.2 2.5.3 2.5.4 2.5.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13
Multiynes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 697 Hexakis(alkoxyphenoxymethy1) Derivatives . . . . . . . . . . . . . . . . . 698 Hexakis(alkylsu1fone) Derivatives . . . . . . . . . . . . . . . . . . . . . . . 698 Naphthalene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 699 Anthracene (Rufigallol) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 700 Phenanthrene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 701 Triphenylene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 702 Ethers. Thioethers and Selenoethers . . . . . . . . . . . . . . . . . . . . . . 702 Esters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 703 Multiynes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 704 Unsymmetrically Substituted Derivatives . . . . . . . . . . . . . . . . . . . 705 Modifications of the Number and Nature of Ring Substituents . . . . . . . . 708 Dibenzopyrene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 712 Perylene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 712 Truxene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 713 Decacyclene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 714 Tribenzocyclononatriene . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715 Tetrabenzocyclododecatetraene . . . . . . . . . . . . . . . . . . . . . . . . 717 Metacyclophane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 719 Phenylacetylene Macrocycles . . . . . . . . . . . . . . . . . . . . . . . . . 719
3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.8.1 3.8.2 3.8.3 3.9 3.9.1 3.9.2 3.9.3 3.9.4 3.9.5 3.9.6 3.9.7 3.9.8 3.9.9 3.9.10 3.9.1 1
Heterocyclic Cores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 720 Pyrillium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 720 Bispyran . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 722 Condensed Benzpyrones (Flavellagic and Coruleoellagic Acid) . . . . . . . 723 Benzotrisfuran . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 723 Oxatruxene and Thiatruxene . . . . . . . . . . . . . . . . . . . . . . . . . . 724 Dithiolium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725 Tricycloquinazoline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 726 Porphyrin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 727 Octa-Substituted Porphyrin . . . . . . . . . . . . . . . . . . . . . . . . . . 727 meso.Tetra(p.alkyl.phenyl).porphyrin . . . . . . . . . . . . . . . . . . . . . 729 Tetraazaporphyrin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 729 Phthalocyanine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 730 Peripherally Substituted Octa(a1koxymethyl)phthalocyanine . . . . . . . . . 730 Peripherally Substituted 0cta.alkoxyphthalocyanines . . . . . . . . . . . . . 731 Peripherally Substituted Octa-alkylphthalocyanine . . . . . . . . . . . . . . 733 Tetrapyrazinoporphyrazine . . . . . . . . . . . . . . . . . . . . . . . . . . . 734 Peripherally Substituted Octa(alkoxycarbony1)phthalocyanines . . . . . . . 734 Peripherally Substituted Octa-(p-alkoxylpheny1)phthalocyanine . . . . . . . 735 Peripherally Substituted Tetrabenzotriazaporphyrin . . . . . . . . . . . . . . 735 Tetrakis[oligo(ethyleneoxy]phthalocyanine . . . . . . . . . . . . . . . . . . 736 Non-Peripherally Substituted Octa(alkoxymethy1)-phthalocyanines . . . . . 736 Non-Peripherally Substituted Octa-alkylphthalocyanine . . . . . . . . . . . 737 Unsymmetrically Substituted Phthalocyanines . . . . . . . . . . . . . . . . 739
xxx 4 4.1 4.2 4.3 5
Contents
Saturated Cores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cyclohexane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tetrahydropyran (Pyranose Sugars) . . . . . . . . . . . . . . . . . . . . . . Hexacyclens and Azamacrocyles . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
739 739 741 742 743
Chapter VIII: Discotic Liquid Crystals: Their Structures and Physical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S . Chandrasekhar
749
1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
749
2 2.1 2.1.1 2.1.2 2.2 2.3 2.4 2.5 2.6
Description of the Liquid . Crystalline Structures . . . . . . . . . . . . . . 750 The Columnar Liquid Crystal . . . . . . . . . . . . . . . . . . . . . . . . . 750 NMRStudies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 752 High Resolution X-Ray Studies . . . . . . . . . . . . . . . . . . . . . . . . 753 Columnar Phases of ‘Non-discotic’ Molecules . . . . . . . . . . . . . . . . 755 The Nematic Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 757 757 The Columnar Nematic Phase . . . . . . . . . . . . . . . . . . . . . . . . . 758 The Chiral Nematic Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . The Lamellar Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 759
3
Extension of McMillan’s Model of Smectic A Phases to Discotic Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
760
4
Pressure-Temperature Phase Diagrams . . . . . . . . . . . . . . . . . . . .
762
5
Techniques of Preparing Aligned Samples . . . . . . . . . . . . . . . . . . 764
6
Ferroelectricity in the Columnar Phase . . . . . . . . . . . . . . . . . . . .
7
The Columnar Structure as a One-Dimensional Antiferromagnet . . . . . . . 766
8
Electrical Conductivity in Columnar Phases . . . . . . . . . . . . . . . . . . 766
9
Photoconduction in Columnar Phases . . . . . . . . . . . . . . . . . . . . .
10 10.1 10.2 10.3 10.4 11 11.1 11.2 12 13 14
Continuum Theory of Columnar Liquid Crystals . : . . . . . . . . . . . . . 769 769 The Basic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acoustic Wave Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . 770 Fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 771 772 Mechanical Instabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 773 Defects in the Columnar Phase . . . . . . . . . . . . . . . . . . . . . . . . Dislocations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 774 Disclinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 774 The Properties of Discotic Nematic Phases . . . . . . . . . . . . . . . . . . 775 776 Discotic Polymer Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . 777 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
765
768
Contents
XXXI
Chapter IX: Applicable Properties of Columnar Discotic Liquid Crystals . . . . 781 Neville Boden and Bijou Movaghar I
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 2.1 2.2
Molecular Structure-Property Relationships . . . . . . . . . . . . . . . . . . 782 HATn Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 782 783 The Phthalocyanines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3 3.1 3.2
Electrical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . HATn Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chemically Doped Materials . . . . . . . . . . . . . . . . . . . . . . . . . .
784 784 787
4
Dielectric Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
788
5
Fluorescence Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . .
790
6
Gaussian Transit Characteristics . . . . . . . . . . . . . . . . . . . . . . . .
791
7 7.1 7.2
Anisotropy of Charge Mobility and Inertness to Oxygen . . . . . . . . . . . 792 Xerography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 792 Phthalocyanine Based Gas Sensors . . . . . . . . . . . . . . . . . . . . . . 792
8
Selforganizing Periodicity, High Resistivity, and Dielectric Tunability . . . . 792
9 9.1 9.2
Ferroelectrics and Dielectric Switches . . . . . . . . . . . . . . . . . . . . . Nematic Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ferro- and Antiferroelectric Phases . . . . . . . . . . . . . . . . . . . . . .
10
Novel Absorption Properties, Fluorescence. and Fast Exciton Migration . . . 795
11
Applications of Doped Columnar Conductors . . . . . . . . . . . . . . . . . 795
12
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
795
13
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
796
781
794 794 794
Part 3: Non-Conventional Liquid-Crystalline Materials . . . . . . . . 799 Chapter X: Liquid Crystal Dimers and Oligomers . . . . . . . . . . . . . . . . . 801 Corrie 7: Imrie and Geoflrey R . Luckhurst 1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 3 3.1 3.2 3.3
Structure-Property Relationships inLiquidCrysta1 Dimers . . . . . . . . . . 801
801
Smectic Polymorphism . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conventional Smectics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Intercalated Smectics . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
804 804 807
Modulated Smectics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
812
XXXII
Contents
4
Chiral Dimers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
Oligomeric Systems and Relation to Dimers . . . . . . . . . . . . . . . . . 813
6 6.1 6.2
Molecular Theories for Liquid Crystal Dimers . . . . . . . . . . . . . . . . 814 The Generic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 815 822 A More Complete Model . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
Molecular Shapes of Liquid Crystal Dimers . . . . . . . . . . . . . . . . . . 829
8
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
813
832
Chapter XI: Laterally Substituted and Swallow-Tailed Liquid Crystals . . . . . 835 Wolfgang Weissflog 1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 2.1 2.2 2.3
Laterally Alkyl Substituted Rod-Like Mesogens . . . . . . . . Long-Chain 2-Substituted 1.4.Phenylene bis(Benzoates) . . . . Further mesogens bearing one Long-Chain Group in the Lateral Two Long-Chain Substituents in Lateral Positions . . . . . . .
3 3.1 3.2
Mesogens incorporating Phenyl Rings within the Lateral Segments . . . . . 843 Mesogens with One Lateral Segment containing a Phenyl Group . . . . . . . 843 Mesogens with Two Lateral Segments each containing a Phenyl Ring . . . . 850
4
Swallow-Tailed Mesogens . . . . . . . . . . . . . . . . . . . . . . . . . . .
850
5
Double-Swallow-Tailed Mesogens . . . . . . . . . . . . . . . . . . . . . .
855
6
Further Aspects and Concluding Remarks . . . . . . . . . . . . . . . . . . . 857
7
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
835
. . . . . . . 835 . . . . . . . 835 Position . . 837
. . . . . . . 841
860
Chapter XII: Plasmids and Polycatenar Mesogens . . . . . . . . . . . . . . . . . 865 Huu-Tinh Nguyen. Christian Destrade. and Jacques Malth2te 1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
865
2
Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
865
3
Synthesis Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
866
4 4.1 4.1.1 4.1.2 4.1.3
Mesomorphic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . Polycatenars with Only Aliphatic Chains . . . . . . . . . . . . . . . . . . . Phasmids or Hexacatenar Mesogens 3mpm-3mpm . . . . . . . . . . . . . . Pentacatenars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tetracatenars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
866 867 867 869 869
Contents
XXXIII
4.2 4.2.1 4.2.2
875 Polycatenars with Polar Substituents . . . . . . . . . . . . . . . . . . . . . Polycatenars with Hydrogenated and Fluorinated Chains . . . . . . . . . . . 875 Polycatenars with Other Polar Substituents . . . . . . . . . . . . . . . . . . 877
5 5.1 5.2
The Core. Paraffinic Chains. and Mesomorphic Properties . . . . . . . . . . 879 879 Core Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 880 Number and Position of Chains . . . . . . . . . . . . . . . . . . . . . . . .
6 6.1 6.1.1 6.1.2 6.1.3 6.1.4 6.2
Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Structures of Mesophases . . . . . . . . . . . . . . . . . . . . . . . . . . . Nematic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lamellar Mesophases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Columnar Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cubic Mesophases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Crystalline Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
882 882 882 882 882 883 883
7
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
884
8
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
884
Chapter XIII: Thermotropic Cubic Phases . . . . . . . . . . . . . . . . . . . . . Siegmar Diele and Petra Goring 1 Historical Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
887 887
2
Chemical Structures and Phase Sequences . . . . . . . . . . . . . . . . . . 888
3 4
On the Structure of the Cubic Phases . . . . . . . . . . . . . . . . . . . . . Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
895 899
5
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
899
Chapter XIV Metal-containing Liquid Crystals . . . . . . . . . . . . . . . . . . 901 Anne Marie Giroud-Godquin 1 901 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Early Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3 3.1 3.2 3.2.1 3.2.1.1 3.2.1.2 3.2.1.3 3.2.2 3.2.2.1
Metallomesogens with Monodentate Ligands . . . . . . . . . . . . . . . . . 902 Organonitrile Ligands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 902 902 n-Alkoxystilbazole Ligands . . . . . . . . . . . . . . . . . . . . . . . . . . Distilbazole Ligands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 903 Palladium and Platinum . . . . . . . . . . . . . . . . . . . . . . . . . . . . 903 Silver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 903 Iridium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 903 903 Monostilbazole Ligands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Platinum 904
901
XXXIV
Contents
3.2.2.2 3.2.2.3 3.3 3.3.1 3.3.2 3.4 3.5
Rhodium and Iridium . . . . . . . . . . . . . . . . Tungsten . . . . . . . . . . . . . . . . . . . . . . . Other Pyridine Ligands . . . . . . . . . . . . . . . Rhodium and Iridium . . . . . . . . . . . . . . . . Silver . . . . . . . . . . . . . . . . . . . . . . . . . Acetylide Ligands . . . . . . . . . . . . . . . . . . Isonitrile Ligands . . . . . . . . . . . . . . . . . .
............. ............. .............
4 4.1 4.1.1 4.1.2 4.1.3 4.1.4 4.2 4.2.1 4.2.2 4.2.3 4.2.4 4.2.5 4.2.6 4.3 4.4 4.4.1 4.4.2 4.4.2.1 4.2.2.2 4.4.2.3 4.4.3 4.5 4.5.1 4.5.2 4.5.3 4.5.4 4.6 4.6.1 4.6.2 4.6.3 4.6.4 4.6.5 4.7 4.7.1 4.7.1.1 4.7.1.2 4.7.1.3
Metallomesogens with Bidentate Ligands . . . . . . . . . . . . . . . . . . Carboxylate Ligands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Alkali and Alkaline Earth Carboxylates . . . . . . . . . . . . . . . . . . . . Lead. Thallium. and Mercury Carboxylates . . . . . . . . . . . . . . . . . Dinuclear Copper Carboxylates . . . . . . . . . . . . . . . . . . . . . . . . Dinuclear Rhodium. Ruthenium. and Molybdenum Carboxylates . . . . . PDiketonate Ligands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Copper Complexes with Two or Four Peripheral Chains . . . . . . . . . . Copper Complexes with Eight Peripheral Chains . . . . . . . . . . . . . . Malondialdehyde Complexes . . . . . . . . . . . . . . . . . . . . . . . . . Dicopper Complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Other Metal Complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . Glycoximate Ligands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sulfur Containing Ligands . . . . . . . . . . . . . . . . . . . . . . . . . . . Dithiolene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dithiobenzoate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nickel and Palladium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zinc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Silver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Other Dithio Ligands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . N-0 Donor Sets: Salicylaldimine Ligands . . . . . . . . . . . . . . . . . Copper, Nickel, and Palladium . . . . . . . . . . . . . . . . . . . . . . . . . Platinum, Vanadyl, and Iron . . . . . . . . . . . . . . . . . . . . . . . . . . Rhodium and Iridium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Polymeric Liquid Crystals Based on Salcylaldimine Ligands . . . . . . . . Cyclometalated Complexes . . . . . . . . . . . . . . . . . . . . . . . . . . Azobenzene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Arylimines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Orthopalladated Diarylazines . . . . . . . . . . . . . . . . . . . . . . . . . Aroylhydrazine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Orthopalladated Pyrimidine Complexes . . . . . . . . . . . . . . . . . . . . Metallocen Ligands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ferrocene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Monosubstituted Ferrocene . . . . . . . . . . . . . . . . . . . . . . . . . . 1,1’Disubstituted Ferrocene . . . . . . . . . . . . . . . . . . . . . . . . . . 1,3 Disubstituted Ferrocene . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
....... ....... ....... .......
904 904 904 904 904 905 906
. 906 906 906 . 906 907 . 908 909 . 909 . 910 911 911 911 911 913 913 913 913 914 914 914 914 . 915 915 917 917 . 917 918 918 919 920 921 921 921 921 921 922 922
Contents
xxxv
Ruthenocene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Iron Tricarbonyl Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . .
923 923
5.1 5.1.1 5.1.2 5.1.3 5.1.4 5.2 5.3
Metallomesogens with Polydentate Ligands . . . . . . . . . . . . . . . . . . Phthalocyanine Ligands . . . . . . . . . . . . . . . . . . . . . . . . . . . . Copper Complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Manganese. Copper. Nickel. and Zinc Complexes . . . . . . . . . . . . . . Lutetium Complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Silicon. Tin. and Lead Complexes . . . . . . . . . . . . . . . . . . . . . . . Porphyrin Ligands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Other Amine Ligands . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
923 923 923 924 924 924 925 926
5
Lyotropic Metal-Containing Liquid Crystals . . . . . . . . . . . . . . . . . 926
7
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
927
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
928
Chapter X V Biaxial Nematic Liquid Crystals . . . . . . . . . . . . . . . . . . . . B. K . Sadashiva
933
1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
933
2
Theoretical Prediction of the Biaxial Nematic Phase . . . . . . . . . . . . . 933
3
Structural Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
934
4
Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
935
> 5.1 5.2
Characterization Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . Optical Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-Ray Diffraction Studies . . . . . . . . . . . . . . . . . . . . . . . . . . .
937 937 938
5
Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
941
7
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
942
Chapter XVI: Charge-Transfer Systems . . . . . . . . . . . . . . . . . . . . . . . K . Praefcke and D . Singer 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
945
2
Calamitic Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
946
3
Noncalamitic Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
952
4
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
964
4.7.2 4.7.3 )
945
XXXVI
Contents
Chapter XVII: Hydrogen-Bonded Systems . . . . . . . . . . . . . . . . . . . . . Takashi Kato Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
969 969
2 2.1 2.1.1 2.1.2 2.1.3 2.1.4 2.2 2.2.1 2.2.2 2.2.3 3 3.1 3.2
Pyridine/Carboxylic Acid System . . . . . . . . . . . . . . . . . . . . . . . Self-Assembly of Low Molecular Weight Complexes . . . . . . . . . . . . . Structures and Thermal Properties . . . . . . . . . . . . . . . . . . . . . . . Phase Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stability of Hydrogen Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . Electrooptic Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Self-Assembly of Polymeric Complexes . . . . . . . . . . . . . . . . . . . Side-Chain Polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Main-Chain Polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
969 969 969 972 973 973 973 973 974 974
Uracil/Diamino-pyridine System . . . . . . . . . . . . . . . . . . . . . . . Low Molecular Weight Complexes . . . . . . . . . . . . . . . . . . . . . . Polymeric Complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
975 975 975
4
Miscellaneous Thermotropic H-Bonded Compounds by Intermolecular Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
976
5
Lyotropic Hydrogen-Bonded Complexes . . . . . . . . . . . . . . . . . . .
977
6
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
978
981 Chapter XVIII: Chromonics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . John Lydon 981 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 A Well-Defined Family Distinct from Conventional Amphiphiles . . . . . . 981 982 1.2 The Chromonic N and M Phases . . . . . . . . . . . . . . . . . . . . . . . 982 1.3 Drug and Dye Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Molecular Structure of Chromonic Species . . . . . . . . . . . . . . . . . 983 2 2.1 2.2 2.3
The History of Chromonic Systems . . . . . . . . . . . . . The Early History . . . . . . . . . . . . . . . . . . . . . . . Disodium Cromoglycate and Later Studies . . . . . . . . . The 3-Way Link Between Drugs, Dyes, and Nucleic Acids
........ ........ ......... . . . . . . . . .
3 3.1 3.2
The Forces that Stabilize Chromonic Systems . . . . . . . . . . . . . . . . 986 Hydrophobic Interactions or Specific Stacking Forces? . . . . . . . . . . . 986 The Aggregation of Chromonic Molecules in Dilute Solution 987 and on Substrat Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
Phase Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
988
5
Optical Textures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
989
983 983 984 985
Contents
6
X-Ray Diffraction Studies . . . . . . . . . . . . . . . . . . . . . . . . . .
7 7.1 7.2 7.3 7.4 7.5 7.6
The Extended Range of Chromonic Phase Structures The P Phase . . . . . . . . . . . . . . . . . . . . . . . Chromonic M Gels . . . . . . . . . . . . . . . . . . . Chiral Chromonic Phases . . . . . . . . . . . . . . . . More Ordered Chromonic Phases . . . . . . . . . . . Chromonic Layered Structures . . . . . . . . . . . . . Corkscrew and Hollow Column Structures . . . . . .
8
The Effect of Additives on Chromonic Systems: Miscibility and Intercalation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . .
XXXVII
. . . . . . . . . . . .......... .......... .......... .......... .......... ...........
991 993 993 998 998 998 999 999 1000
9
The Biological Roles of Chromonic Phases . . . . . . . . . . . . . . . . . 1001
10
Technological and Commercial Potential of Chromonic Systems . . . . . . 1005
11
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1005
12
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1006
Index Volumes 2 A and 2 B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1009
General Introduction
Liquid crystals are now well established in basic research as well as in development for applications and commercial use. Because they represent a state intermediate between ordinary liquids and three-dimensional solids, the investigation of their physical properties is very complex and makes use of many different tools and techniques. Liquid crystals play an important role in materials science, they are model materials for the organic chemist in order to investigate the connection between chemical structure and physical properties, and they provide insight into certain phenomena of biological systems. Since their main application is in displays, some knowledge of the particulars of display technology is necessary for a complete understanding of the matter. In 1980 VCH published the Handbook of Liquid Crystals, written by H. Kelker and R. Hatz, with a contribution by C. Schumann, which had a total of about 900 pages. Even in 1980 it was no easy task for this small number of authors to put together the Handbook, which comprised so many specialities; the Handbook took about 12 years to complete. In the meantime the amount of information about liquid crystals has grown nearly exponentially. This is reflected in the number of known liquid-crystalline compounds: in 1974 about 5000 (D. Demus, H. Demus, H. Zaschke, Fliissige Kristalle in Tabellen) and in 1997 about 70000 (V. Vill, electronic data base LIQCRYST). According to a recent estimate by V. Vill, the cur-
rent number of publications is about 65000 papers and patents. This development shows that, for a single author or a small group of authors, it may be impossible to produce a representative review of all the topics that are relevant to liquid crystals on the one hand because of the necessarily high degree of specialization, and on the other because of the factor of time. Owing to the regrettable early decease of H. Kelker and the poor health of R. Hatz, neither of the former main authors was able to continue their work and to participate in a new edition of the Handbook. Therefore, it was decided to appoint five new editors to be responsible for the structure of the book and for the selection of specialized authors for the individual chapters. We are now happy to be able to present the result of the work of more than 80 experienced authors from the international scientific community. The idea behind the structure of the Handbook is to provide in Volume 1 a basic overview of the fundamentals of the science and applications of the entire field of liquid crystals. This volume should be suitable as an introduction to liquid crystals for the nonspecialist, as well as a source of current knowledge about the state-of-the-art for the specialist. It contains chapters about the historical development, theory, synthesis and chemical structure, physical properties, characterization methods, and applications of all kinds of liquid crystals. Two subse-
XL
General Introduction
quent volumes provide more specialized information. The two volumes on Low Molecular Weight Liquid Crystals are divided into parts dealing with calamitic liquid crystals (containing chapters about phase structures, nematics, cholesterics, and smectics), discotic liquid crystals, and non-conventional liquid crystals. The last volume is devoted to polymeric liquid crystals (with chapters about main-chain and side-group thermotropic liquid crystal polymers), amphiphilic liquid crystals, and natural polymers with liquid-crystalline properties. The various chapters of the Handbook have been written by single authors, sometimes with one or more coauthors. This provides the advantage that most of the chapters can be read alone, without necessarily having read the preceding chapters. On the other hand, despite great efforts on the part of the editors, the chapters are different in style, and some overlap of several chapters could not be avoided. This sometimes results in the discussion of the same topic from
quite different viewpoints by authors who use quite different methods in their research. The editors express their gratitude to the authors for their efforts to produce, in a relatively short time, overviews of the topics, limited in the number of pages, but representative in the selection of the material and up to date in the cited references. The editors are indebted to the editorial and production staff of WILEY-VCH for their constantly good and fruitful cooperation, beginning with the idea of producing a completely new edition of the Handbook of Liquid Crystals continuing with support for the editors in collecting the manuscripts of so many authors, and finally in transforming a large number of individual chapters into well-presented volumes. In particular we thank Dr. P. Gregory, Dr. U. Anton, and Dr. J. Ritterbusch of the Materials Science Editorial Department of WILEY-VCH for their advice and support in overcoming all difficulties arising in the partnership between the authors, the editors, and the publishers. The Editors
Part 2: Discotic Liquid Crystals
Handbook of Liquid Crystals Edited by D. Demus, J. Goodby, G. W. Gray, H.-W. Spiess, V. Vill Copyright 0 WILEY-VCH Verlag GmbH. 1998
Chapter VI Chiral Smectic Liquid Crystals
1 Synthesis of Chiral Smectic Liquid Crystals Stephen M. Kelly
1.1 Introduction Although it was known from seminal investigations early in this century [ 11 that smectic phases can be characterized by a one dimensional density wave, the exact layer structure was not known. Most smectic phases were characterized as smectic A, B or C (SmA, SmB and SmC) until the 1960s, depending on their optical characteristics under polarized light [2-4]. At this time it was known that in the SmA phase the timeaveraged director orientation is perpendicular to the layer plane. Therefore, uniformly aligned domains appear optically uniaxial. The structure of the SmB phase was unknown and this term was used to describe a range of orthogonal and tilted smectic phases [2-4], whose number and nature were determined much later [5, 61 The structure within the layers of the SmC phase, where the molecules are tilted at an azimuthal angle, 0, to the layer normal [7-91 giving rise to the observed optical biaxiality [8], had
just been determined [7-91. Liquid Crystals (LCs) incorporating an optically active center and exhibiting chiral smectic phases including the chiral smectic C phase (SmC*) had been synthesized along with nonoptically active LCs from the very beginning of LC research [lo-131. They were the result of investigations of the relationship between molecular structure and mesomorphic behavior and transition temperatures [ 10-1 31. The first SmC* compounds synthesized intentionally and recognized as such [ 141were prepared in order to study its structure. These were optically active versions [ 141 of laterally substituted Schiff's bases (see Structure 1) [7]. The lateral substituent had been introduced in order to reduce the high melting point (T,) of the original Schiff's bases [15,16], which probably also possess an SmC phase. Theoretical studies had indicated that the molecular orientation (i.e. the director) in an SmC* phase should spiral around an axis normal to the layer plane giving rise to a helical structure [ 171. If the pitch, p , the distance for a rotation of the di-
Cr-SmC* 29°C; SmC*-N* 94°C; N*-I 146.5"C [14] Structure 1
494
1 Synthesis of Chiral Smectic Liquid Crystals
Table 1. Comparison of the transition temperatures and spontaneous polarization measured at TSmC* - 10°C of (S)-4-decyloxybenzylidene-,(S)-a-methyl4-decyloxybenzylidene-, (S)-2-methylbutyl a-chloro 4-decyloxybenzylidene-, (S)-2-methylbutyl a-cyano 4-decyloxybenzylidene- and (S)-2-methylbutyl4-decyloxy-2-hydroxybenzylidene-4-amino-cinnamate[21, 351 and (S)-1-methylpropyl 4-decyloxybenzylidene-4-amino-cinnamate [37, 381.
c1
n 1 1 1
1 1 O
X H H H H OH H
Y H CH, C1 CN H H
""
I=\
v N Y& O (
CH 2)" ' C H ( C b
)C,H5
Cr-SmC* ("C)
H-SmC* ("C)
SmC*-SmA* ("C)
SmA*-I
P,
("C)
(nC crn-*)
76 45 51 92 88 82
(63)
92 68 (45) (70) 114 91
117 99 71 104 145 106
-
-
3
DOBAMBC
-
-
=3 10
HDOBAMBC DOBA- 1-MPC
Values in parentheses represent monotropic transition temperatures.
rector through 360°, is of the same magnitude as the wavelength of visible light, this can lead to the selective reflection of circularly polarized light in the visible part of the electromagnetic spectrum. 6 was found to be temperature dependent and normally increases with decreasing temperature [9]. The other tilted smectic (SmI* and SmF*) or crystal (J*, G*, H* and K*) phases or orthogonal smectic (hexatic SmB) or crystal (B and E) phases exhibit varying degrees of higher order within and between the layers [5, 61. The ordered chiral smectic phases can exhibit the same form chirality as the SmC* phase (see Sec. 2 and 3 of this chapter) [18]. The local C2 symmetry in tilted chiral smectic layers leads to a polar inequivalence within the layers due to the chiral and polar nature of the individual molecules despite a considerable degree of molecular reorientation about the long axis (see Sec. 2 and 3 of this chapter) [19-221. The consequence of this time-dependent alignment of the dipoles along the C2 axis is a spontaneous polarization (P,) parallel to the layer planes, which is averaged out macroscopically to
zero by the helical superstructure. However, a permanent polarization arises in an homogeneous monodomain, if the helix is unwound by an electric field or suppressed mechanically. Based on these symmetry arguments the ferroelectric properties of chiral smectic phases with a helical structure such as the SmC* phase were predicted and then found [21, 221 for the Schiff base 4-decyloxybenzylidene-4-amino-2-methylbutylcinnamate (DOBAMBC), see Table 1 . The first eight members of this series had already been prepared [12]. This was before the structure and optical characteristics of the SmC* phase had been established. Soon after the initial discovery of ferroelectricity in chiral smectic LCs it was predicted that, if the helix of an SmC* phase were suppressed by surface forces in very thin layers between two glass electrodes, then this would pin the molecules in their positions and allow switching between two energetically equivalent polarization directions, thereby giving rise to an electro-optic memory effect [22]. This is the basis of the electro-optic display device called the surface stabilized ferroelectric liquid crystal
1.2 Long Pitch Chiral Smectic Liquid Crystals or Dopants
device (SSFLCD) [23] utilizing ferroelectric LCs (see Sec. 2 and 3 of this chapter). In this device the helix is suppressed by surface forces, if the cell gap is considerably lower than the pitch of the SmC* helix. Therefore, long-pitch SmC* materials are used. Compounds exhibiting the SmC* phase are chosen due to the low rotational viscosity (li, of this phase compared to that of the more ordered tilted smectic phases. Chiral LCs with an SmA* phase are also receiving increased attention for potential applications utilizing the electroclinic effect, where the molecular tilt is coupled directly to the applied field [24].
1.2 Long Pitch Chiral Smectic Liquid Crystals or Dopants Although several attempts were made soon after the initial discovery of ferroelectricity in DOBAMBC to reduce T, and increase P, in order to facilitate the study of this new phenomenon at temperatures closer to room temperature, the vast majority of syntheses of chiral smectic LCs were undertaken later in order to provide stable SmC* materials with a defined spectrum of physical properties for SmC* mixtures designed for electro-optic display devices. Although the first eutectic mixtures created for prototype SSFLCDs consisted of purely optically active SmC* components [25], it was soon found that yand response time (z) for mixtures consisting of purely nonracemic SmC* components are generally too large for practical applications. It was also necessary to mix SmC* compounds with the same sign of P,, but opposing p , so that the P , values are additive and the p of the resultant mixture would be large. Both of these parame-
495
ters depend on the polar character of the substituents at the chiral center and the position of the chiral center in the terminal chain (see Sec. 2 and 3 of this chapter) [ 5 , 6, 181. Current commercially available SmC* mixtures designed for SSFLCDs consist of a nonoptically active base SmC mixture with a low value for a high TSmC* and low T , doped with at least one optically active (chiral) dopant [26-291. The chiral dopant should induce the desired value of P, and a long p in the base SmC mixture, in order to avoid the necessity of pitch compensation, without depressing TSmC* or increasing or the birefringence (An) of the mixture excessively. The dopant can also affect 6, which should be approximately 22" in order to produce a good optical contrast. All the mixture components must be chemically, thermally and photo- and electrochemically stable. The resultant induced P, of the mixture must also not be too large in order to avoid charge effects, but a large intrinsic value of P, for the chiral dopant allows smaller amounts to be used. Since many chiral dopants designed for LCD applications do not themselves possess a SmC* phase, parameters such as the P , or zoften have to be determined in a standard SmC mixture. This is often of more relevance to display device applications than the value for the pure dopant, if it does possess an SmC* phase, as the P, is matrix, concentration and temperature dependent. The P, in a mixture often reaches a maximum at a certain concentration and then remains constant or even decreases as more dopant is added [26-291. In contrast to the expectation that a higher P, necessarily means a shorter z an increase of P , which is due to an increase in 8,leads to longer z. If both z and P, increase (or decrease) upon changing the side chain within an homologous series of dopants, then this is probably a change of 8 of the mixture induced by the
496
1 Synthesis of Chiral Smectic Liquid Crystals
dopant. If zdecreases and P, increases, this is probably due to a change of Po (where P, = Po sine), which is a constant characteristic of the dopant, especially for low dopant concentrations, where changes of viscosity are small [30]. Both microscopic and steric models of the SmC phase postulate a zigzag shape for the terminal aliphatic chains of essentially symmetric compounds for SmC formation [20, 3 11. The microscopic model assumes additionally that antiparallel permanent dipoles at an angle to the molecular axis promote SmC behavior due to an induced torque 1201. It has been shown that while such dipole moments are not always absolutely essential for SmC formation, they are to be found in most SmC components and still mostly lead to higher SmC transition temperatures than those of the corresponding compounds without these dipoles [32, 331. This is not valid for compounds incorporating isolated, nonconjugated dipoles next to aliphatic rings [34]. There are also indications that alternately a cisltruns, linearly-extended conformation of the terminal chains is preferred in the SmC phase [34].
1.2.1 Schiff’s bases To facilitate the study of ferroelectricity in chiral smectics lateral substituents were introduced into the phenyl ring next to the cinnamate group of DOBAMBC and other members of the series. This was in order to reduce the degree of rotation at the chiral center and to increase the lateral dipole moment in the core of the molecule in an attempt to increase P, and at the same time lower the high T, of the original Schiff’s bases, see Table 1, [35]. Although the lateral substituents resulted in large decreases in T,, TSmC* and the clearing point ( T J , except for the nitriles, where T, increases, and the suppression of ordered smectic phases,
no significant effect on P, could be determined. This is most probably due to the relatively large d,istance between the substituents Y and the chiral center in the (9-2methylbutyl moiety. The introduction of a hydroxy group in a lateral position next to the central bond results not only in an improved stability , but the transition temperatures and the SmC* temperature range are also increased significantly, see Tables 1 and 2 [36-40]. This is caused by the formation of a pseudo-sixmembered-ring at the core of the molecule due to hydrogen bonding between the hydroxy group and the nitrogen atom of the central linkage. This gives rise to a higher degree of planarity of the aromatic rings, without leading to a broadening of the molecular rotation volume. However, the large dipole (2.58 D) associated with the hydroxy group in a lateral position does not lead to a significant increase in P,. This implies that a nonchiral dipole moment in the middle of the core of the molecule is of significantly less importance for the P , value than the dipole moment at the chiral center. Related Schiff’s bases incorporating commercially available optically active secondary alcohols such as (R)-2-butanol and (R)-2-pentanol instead of the primary alcohol (S)-2-methylbutanol exhibit a broad SmC* phase at high temperatures [37, 381, see Table 1 . A consequence of the closer proximity ( n = 0) of the methyl group to the 1core in 4-decyloxybenzylidene-4-aminomethylbutylcinnamate (DOBA- 1 -MBC) is a higher degree of coupling between the dipole moment at the chiral center and that of the core as well as a lower degree of free rotation. This results in a relatively high value for the P, and slightly lower transition temperatures than those of DOBAMBC ( n = 1) [21]. To further increase the chemical and photochemical stability and reduce T,, more to-
1.2 Long Pitch Chiral Smectic Liquid Crystals or Dopants
497
Table 2. Comparison of the transition temperatures, tilt angle and spontaneous polarization measured at 25 "C for (S)-4-(2-methylbutyl)-2-hydroxyresorcylidene4-octylaniline, (S)-4-(4-methylhexyl)-2-hydroxyresorcylidene 4-octylaniline and (S)-4-(6-methyloctyl)-2-hydroxyresorcylidene4-octylaniline 139,401.
~~
n 1 3 5
~
Cr-SmC* ("C)
Sm2-SmC*
36 -
=20
20
-
("C)
SmC*-SmA* ("C)
SmA*-I ("C)
8
50 17 86
57 -
8 =40
-
=5
wards room temperature to yield SmC* substances more suitable for use in SSFLCDs, new Schiff's bases without the cinnamate group were synthesized [39,40]. The effect of chain length and proximity of the point of branching to the molecular core, which are general for SmC* LCs, is shown for these Schiff's bases in Table 2. The TSmC* is highest for the compounds with the longest chain and the chiral center furthest from the molecular core ( n = 3). The steric effect of the methyl group at the point of branching decreases for positions further from the core due to the greater number of chain conformations possible. The P, also decreases due to the smaller energy difference between the various positions of the dipole moment and the lower degree of coupling with the dipoles of the core. This is shown more clearly when differences in 8 are taken into consideration. The low value for T , and wide SmC* temperature range of MHxRA 8 allowed studies of the ferroelectric properties of these LCs to be carried out at room temperature.
1.2.2 Aromatic Esters with Alkyl Branched Alkyl Chains To prepare stable SmC* LCs with comparable P , values to those determined for
PS
(degrees) (nC cm-') 3 2 =O. 1
P, I e (nC cm-' rad-I) 22.0 2.9 0.2
MBRA8 MHxRA8 MORA8
Schiff's bases, but with greater resistance towards hydrolysis, higher resistivity and better alignment properties a wide variety of aromatic esters with alkyl-branched and, above all, methyl-branched terminal chains were synthesized, see Table 3 [41-511. Several ester series with a nonracemic chiral center had already been prepared for thermochromic applications [44]. Several homologues also exhibited SmC* as well as N* phases at high temperatures. The optically active part of the molecules was usually derived form the same alcohols such as (S)-2-methylbutanol, (R)-2-butanol and (R)-2-pentanol as for the Schiff's bases, see Scheme 1 . Similar dependencies of the transition temperatures, P, and yon the nature of the methyl-branched chain were found. Additionally it was found that the value of P, increased with the number of carbon atoms in the chain after the point of branching, probably due to the dampening effect of the longer chain [6, 41-44]. Large substituents like an ethyl group at the point of branching reduce the transition temperatures substantially more than a methyl group. The absolute transition temperatures and the presence of other smectic phases or the nematic phase depends on the direction of the ester linkage in the molecular core, the presence and nature of polar groups between the core and the terminal chain and
498
1
Synthesis of Chiral Smectic Liquid Crystals
Table 3. General structures for typical smectic C* liquid crystals with nonracemic, methyl-branched terminal chains derived from primary and secondary alcohols. Structure
the number of rings in the core [6,41]. Aliphatic rings in the core such as l, 4-disubstituted cyclohexane [45], bicyclo(2, 2, 2)octane [46], dioxane rings [47] or dioxaborinane rings [48] lead to the elimination of the SmC* phase in two-ring compounds and to lower TSmC* in three-ring compounds compared to the corresponding fully aromatic analogs. However, yand/or An are lower [45]. This results in lower Tor allows thicker cells to be used. The introduction of a cis carbon-carbon double bond in the middle or in a terminal position of the alkoxy chains of two-ring and three-ring esters leads to lower transition temperatures in general and sometimes to broader SmC* phases close to room temperature [49].
Ref.
The additive effects of dipole moments near the chiral center and at the chiral center itself are demonstrated by a reference to Tables 4 and 5. The introduction of a large dipole moment in the form of a carbonyl function between the aromatic core and the chiral center to yield a number of alkanoylsubstituted (keto-) esters led to higher P, values than those of the corresponding ethers and esters, see Table 4 [50]. The presence of a second optically active group in the second terminal chain can also lead to additive effects and a still higher P,, although y can be expected to be considerable [50].A strong dependence of the observed P , values on the number of carbon atoms in both terminal chains and the presence and
1.2 Long Pitch Chiral Smectic Liquid Crystals or Dopants
499
H
Br
a) Mg/Et20 b) BrC4H$r
I
* H
HO
2
I
Br
NaOEt/EtOH/CH2(COZEt)z
o* OyO
f
HO
Ix
LiAIH4/Et20 H+/H20
H
O
A
HO
HO
Ai
HBr/H2S04
b)H+/H20 1 H
H
Br
O
A
1
HBr/H2SO4
position of various lateral substituents was also observed. Dipole moments incorporated in the form of lateral substituents in the aromatic core next to the terminal chain, but
Scheme 1. Typical reaction pathways to important reaction intermediates derived from naturally occurring (S)-2-methylbutanol and used to synthesize chiral smectic liquid crystals or dopants with nonracemic, methylranched terminal chains.
further away from the chiral center can also give rise to a higher p,, see Table 5 [28, 5 11. However, the effect is smaller for similar dipole moments and the increase is al-
500
1 Synthesis of Chiral Smectic Liquid Crystals
Table 4. Comparison of the spontaneous polarization measured at TSmC*-I 0 “C of (S)-4-([2-octyl]oxy)phenyl 4-octyloxy- l,l’-biphenyl-4’-yl-carboxylate(X = 0),(S)-2-octyl4-(4-octyloxy- l,l’-biphenyl-4’-yl-carboxy)benzoate (X = COO) and (S)-4-(2-methyloctanoyl)phenyl 4-octyloxy-l,l’-biphenyl-4’-yl-carboxylate (X = CO) [sol.
X -0-
0.68 1.23 1.99
-coo-co-
38 70 112
130 195 313
Table 5. Comparison of the transition temperatures, tilt angle and spontaneous polarization measured at TSmC*-10 “C of 4-octyloxy- l,l’-biphenyl-4’-yl 3-substituted-4-([(S)-2-octyl]oxy)benzoates [5 11. X
X
(D)
Cr-SmC* (“C)
SmC*-SmA*/N* SmA*-I (“C) (“C)
N*-I (“C)
0 (degrees)
PS
(nC cm-2)
Po (nC cm-2)
0 -1.47 -1.59 -1.57 -4.05
78 65 13 43 68
99 97 95 87 90
122 100 97 89
45 36 40 41 25
45 78 123 131 160
64 134 191 202 386
P
~
H F
c1 Br CN
-
105
most certainly also due to steric effects as the energy difference between the most stable, time-dependent conformations of the chiral center is increased. This is seen as p decreases and yincreases with the size of the lateral substituent [28,5 11. However, the small p requires pitch compensation for practical application in SSFLCDs. This contributes to the higher y and zvalues caused by the presence of the lateral substituents.
1.2.3 Aromatic Heterocycles with Alkyl-Branched Alkyl Chains A further development was the introduction of an optically active center into the terminal chains of two- and three-ring SmC com-
-
pounds with a phenyl-pyrimidine, pyrazine or pyridazine group in the molecular core to produce the corresponding methylbranched SmC* materials [52-551. Some of these new compounds exhibited a broad SmC* phase, sometimes close to room temperature (Structure 2). They were characterized by low yvalues. The corresponding alkenyloxy-substituted phenylpyrimidines with a cis-carbon-carbon double bond or a carbon-carbon double bond in a terminal position often possessed an SmC* phase closer to room temperature [56].
Cr-SmC*: 23°C; SmC*-N*: 34°C; N*-I: 47°C [ S 2 ]
Structure 2
1.2 Long Pitch Chiral Smectic Liquid Crystals or Dopants
NCfOH
NaCN
a) LiA1H4/Eb0
b) Ht/H20
\
TosCl/N(C,H,),
/
a)KOH/EtOH b)H+
/
A
l
2
\
\ H+/H20
a) LiA1H4/Et20
C02H CnHZn+lo-r(
1.2.4 Esters and Ethers in the Terminal Chain Large P , values can be achieved by increasing the polarization of the branching methyl group at the chiral center by the introduction of the electron withdrawing oxygen atom. Simple esters and ethers were usually prepared from naturally occurring alkyl L-(+)-lactates (alkyl (S)-2-hydroxypropa-
Cr-SmC*: 88°C; SmC*-I: 148°C [58]
Structure 3
50 1
Scheme 2. Typical reaction pathways to important reaction intermediates derived from naturally occurring alkyl L-(+)-lactates (alkyl (S)-2-hydroxypropanoates) and used to synthesize chiral smectic liquid crystals or dopants with nonracemic terminal chains with polar substituents.
noates), see Scheme 2 [57-601 or readily accessible, synthetic alkyl (R)-3-hydroxybutanoates [61]. More sophisticated syntheses of two- and three-ring phenylpyrimidines with an alkoxy group and a methyl group at the chiral center in the terminal chain (Structure 3) involved resolution of a prochiral ester into the corresponding optically active alcohol and ester by an enzyme catalyst [62]. Lactate ethers [60] exhibit higher P ,
Cr-SmC*: 51°C; Sx-SmC*: 46°C; SmC*-N: 69°C; N*-I: 91.5"C [60]
502
1
Synthesis of Chiral Smectic Liquid Crystals
Table 6. Comparison of the transition temperatures and spontaneous polarization of 4'-heptyloxy- 1, 1'-biphenyl-4-yl (S)-2-chloro-3-methylbutanoate, (2S,3R)-2-chloro-3-methylpentanoateand (S)-2-chloro-4-methylpentanoate r64, 651.
R
Cr-SmC*/SmA* ("C)
S3*-SmC*/SmA* ("C)
SmC*-SmA* ("C)
SmA*-I* ("C)
PS ( n c cm-2)
16
-
(71)
80
-98
48
(36)
56
66
-210
71
-
(65)
74
+S8
Values in parentheses represent monotropic transition temperatures.
a) NaN02/H2S04 a) LiAlH,
a) LiAlH,
b)
b) H+/H20
J H
NaN02/H2S04
O
T
c2H50H!Y
(CF3SO2)20
cF3s020~2"5
/U*N-F
a) LiAlH,
CHzOH
Scheme 3. Typical reaction pathways to important reaction intermediates derived from naturally occurring amino acids such as (2R,3s) or (2S, 3R)-2-amino-3-methylpentanoic acid (D- or L-alloleucine) and used to synthesize chiral smectic liquid crystals or dopants with nonracemic terminal chains with polar substitu-
503
1.2 Long Pitch Chiral Smectic Liquid Crystals or Dopants
Table 7. Comparison of the spontaneous polarization (extrapolated to loo%),response times (10 V,,/pm square wave, time to maximum current), pitch and tilt angle measured at 25°C for mixtures of 7 wt% 4-octyloxy-1,l’biphenyl-4’-yl (R)-2-fluorohexanoate and 7 wt% trans- 4-(4-octyloxyphenyl)cyclohexyl (R)-2-fluorohexanoate and a host mixture [69].
e
X
(degrees)
-Q-
56
a..,, 35
950
0.75
24.5
700
1.52
22
and higher y values than comparable lactate ester mixtures with similar 8 and TSmC* values. This results in similar z for similar mixtures containing one or the other chiral dopant. The high TSmC* temperatures for the pure lactate esters [58] are not reflected in high TSmC* values for mixtures containing them. This is typical of the nonlinear and nonideal behavior of chiral dopants in SmC* mixtures.
1.2.5 Halogens at the Chiral Center If the dipole at the chiral center is increased by replacing the methyl branching group by a more polar moiety such as a halogen atom, then Po increases due to the larger dipole moment perpendicular to the long axis of the molecule, see Table 6. Most ferroelectric LCs incorporating halogen atoms at the optically active center are esters or ethers derived either from naturally occurring lactic acid or amino acids, see Schemes 2 and 3 [63-671. There is still a considerable degree of freedom of rotation at the chiral center and the observed value for P, is still considerably lower than that
expected if the dipole moment at the chiral center is taken into account. For a large value of the P, it is important that the dipoles in the vicinity of the optically active center point in the same direction, see Table 6. The dipoles due to the two chiral centers in the (2S,3R)-2-chloro-3-methyl-pentanoyloxysubstituted esters are additive and lead to the highest P, values [63-671. The pure esters exhibit high negative P , values and enantiotropic SmC* phases. The values extrapolated to 100% from SmC* mixtures are often considerably lower. The small van der Waals radius (1.47 A) of fluorine and relatively large dipole moment (1.41 D) of the C-F bond lead to SmC* dopants with a relatively high P,, but with a lower y and higher TSmC* than the corresponding chloro- or bromo-substituted compounds [68, 691.
1.2.6 Cyclohexyl a-Fluorohexanoates Substitution of the aliphatic trans- 1, 4-disubstituted cyclohexane ring for the aromatic benzene ring leads to a lower electron density at the chiral center and to a higher
504
1 Synthesis of Chiral Smectic Liquid Crystals
degree of conformational mobility of the dipole moment, but P, is only reduced by about 40%, see Table 7 [30, 691. However, the cyclohexane ring gives rise to lower values for An, y and a substantially longer pitch, as expected. The data collated in Table 8 allow a valid comparison of the relative effects of either a fluorine or a chlorine atom attached directly to the optically active center of the chiral dopant [69]. The transition temperatures and P, of the mixture containing the Table 8. Comparison of the transition temperatures, spontaneous polarization and response times (10 V,,/pm square wave, time to maximum current) measured at 25°C for mixtures of 7 wt% of the truns4-(2',3'-difluoro-4'-decyloxy- 1,l '-biphenyl-4-yl)cyclohexyl (R)-2-fluorohexanoate and truns -4-(2', 3'Difluoro-4'-decyloxy- 1, l'-biphenyI-4-yl)cyclohexyl (R)-2-chlorohexanoate and a host mixture (SmC-SmA: 76°C; SmA-N: 81 "C; N-I: 103 "C) ~301. F
F CI
6.2 4.5
F
415 75.5 630 74.5
88.3 86.3
104.3 102.3
a-fluoroester are all higher than those observed for the corresponding mixture containing an equal amount of the otherwise identical a-chloroester. This could be due to the stronger electronegativity of the fluorine atom. Additionally, y of the a-fluoroester must also be lower than that of the a-chloroester as shown by the significantly lower 2, which is only partially due to the higher value of Po. This is a result of the smaller size of the fluorine atom and the shorter carbon-fluorine bond compared to that of chlorine. Despite the presence of the cyclohexane ring, which promotes SmB behavior, several optically active a-fluoroesters incorporating the aliphatic cyclohexane ring and a number of different cores possess an enantiotropic SmC* phase at elevated temperatures [69]. However, the tendency to form the SmC* phase is much reduced and a number of dipole moments in various parts of the molecular core are required, see Table 9. This is consistent with the microscopic, dipole-dipole theory of the SmC phase [20]. Only the combination of the phenylpyrimidine core and an alkoxy chain in the ester gives rise to the SmC* phase. Tworing compounds incorporating a cyclohexane ring do not generally exhibit an SmC phase.
Table 9. Comparison of the transition temperatures for the truns-4-(4'-decyI-l, l'-biphenyl-4-yl)cyclohexyl ( R ) 2-fluorohexanoate, truns-4-(4-[5-decylpyrimidin-2-yl]phenyl)cyclohexyl(R)-2-fluorohexanoate and rrans-4[4-(5-nonyloxypyrimidin-2-yl)phenyl]cyclohexyl(R)-2-fluorohexanoate (SmC*-SmA: 76 "C; SmA-N: 8 1 "C; N-I: 103 "C) [30].
R
X
C-SmB*/SmC*/I ("C)
SmB*-SmC*/SmA* ("C)
SmC*-SmA* ("C)
I16 90
108
SmA*-I ("C) I45
I65
1.2 Long Pitch Chiral Smectic Liquid Crystals or Dopants
505
Table 10. Comparison of the spontaneous polarization, response times (10 V,,/pm square wave, time to maximum current) and pitch measured at 25 "C for mixtures of 7 wt% of the ether rrans-4-[4-decyloxyphenyl]cyclohexyl (R)-2-fluorohexanoate and the ester truns-4-[4-decanoyloxyphenyl]cyclohexyl(R)-2-fluorohexanoate and a host mixture (SmC-SmA: 76°C; SmA-N: 81°C; N-I: 103°C) [30].
CHZ
co
3.8 5.7
460 400
64.5 68.0
82.6 81.5
97.8 97.1
Table 11. Comparison of the transition temperatures, spontaneous polarization and response times ( 1 0 V,,/pni square wave, time to maximum current) measured at 25 "C for mixtures of 7 wt% of the diester tuuns-4-[4-(2,3difluoro-4-decyloxybenzoyloxy)phenyl]cyclohexyl (R)-2-fluorohexanoate and 7 wt% of the ester truns-4-(2',3'difluoro-4'-decyloxy- l,l'-biphenyl-4-yl)cyclohexyl (R)-2-fluorohexanoate and a host mixture (SmC-SmA: 76°C; SmA-N: 81 "C; N-I: 103°C) [30]. F
coo -
5.4 6.2
F
650 415
The data collated in Table 10 allow the effect of an ester group in a terminal position in the core of a chiral dopant to be determined. The ether [30] and the diester [69] differ only in the presence of a carbonyl group (CO) instead of a methylene unit (CH,), that is, the chain lengths are the same. TSmC* for the mixture containing the ester (X = CO) is higher than that incorporating an equal amount of the ether (X = CH,). The P , is higher for the ester than for the ether, indicating a greater value for Po as shown by the shorter z. The effect of an ester group in a central position of a chiral dopant can be elucidat-
76.7 75.5
83.5 88.3
103.9 104.3
ed from the data in Table 11 [69]. TSmC* for the mixture containing the a-fluoro diester with a second ester group in a central position is higher than that incorporating an equal amount of the a-fluoro (mono-) ester. This is not surprising as the a-fluoro di-ester exhibits an enantiotropic SmC* phase at elevated temperatures in the pure state. The P, is higher for the ester than for the diester. This is probably due to a change of Po as well as of because of presence of the second carboxy (ester) group. Even if Po were constant and Owere fully responsible for the increase of P,, yof the mono ester would still be substantially lower.
506
1 Synthesis of Chiral Smectic Liquid Crystals
The P, values for related fluoro-alkyl- or alkoxy-substituted compounds are lower due to the lower dipole moment at the chiral center [70-751. The presence of the trifluoromethyl group at the chiral center in the side-chain of three-ring compounds leads to high P , values and an SmC* phase for the pure substances [76]. Although a trifluoromethyl group at the chiral center in the central linkage between two aromatic rings in the core of a similar three-ring phenylpyrimidine leads to very low transition temperatures and the absence of a SmC* phase for the pure substance and to a low TSmC* for mixtures containing these chiral dopants the values of P,, z and 8 are otherwise attractive [77].
1.2.7 Cyano Groups at the Chiral Center The large dipole moment and steric bulk of the cyano group at the chiral center gives rise to a larger energy difference between the most probable time-averaged conformations of the chiral center and therefore to a high P , value, although low transition temperatures are also observed [78-811. This is a consequence of the large steric effect of
CN
Cr-SmC*: 102°C; SmC*-SmA: 145°C;SmA-I: 155°C [79]
Structure 4
the cyano group close to the molecular core (Structure 4) leading to low transition temperatures for the pure compounds. Therefore, enantiotropic LC phases are only observed for three-ring compounds.
1.2.8 Optically Active Oxiranes and Thiiranes Another way to maximize P , is to limit the degree of free rotation at the chiral center and increase the energy difference between the two major conformations of the dipole at the chiral center. This can be achieved by incorporating the chiral center in a cyclic system such as in an oxirane 127, 82, 831. The molecular dipole associated with an epoxide moiety is oriented normal to the tilt plane. The rigidity of the epoxide ring minimizes the conformational averaging out of the dipole moment and should lead to a high value for the P,. Oxiranes are prepared by Sharpless epoxidation of ally1 alcohols,
Table 12. Transition temperatures and spontaneous polarization of mixtures of 7.37 wt% of 4-[(R)-l-fluor0-(2s, 3S)-epoxynonyl]pheny14-decyloxybenzoate(X = H;Y = F) or 7.58 wt% of 4-[(S)- I-fluoro-(2S, 3s)-epoxynonyllphenyl 4-decyloxybenzoate (X = F; Y = H) and a host compound (Cr-SmC: 35 "C; SmC-SmA: 70.5 "C; SmA-I: 72 "C) [83].
X
H F
Y
F H
Cr-SmC* ("C)
S mC *-SmA * ("C)
SmA*-I ("C)
ps (nC cm-2)
53 25
66 61
70 66
+2 -13
507
1.2 Long Pitch Chiral Smectic Liquid Crystals or Dopants
Table 13. Helical twisting power (HTP) (measured just above SmA*-N*), rotational viscosity, response time and spontaneous polarization measured at 25 "C for mixtures of 10 mol% of 5-([cis-(2S, 3S)-epoxy]octanoyloxy)phenyl-2-octyloxyprimidineor 5-([truns(2R, 3S)-epoxy]octanoyloxy)phenyl-2-octyloxyprimidine and a host mixture (C-SmC: 10 "C;SmC-SmA: 84.5 "C; SmA-N: 93.5 "C; N-I: 105 "C) [27].
Configuration
HTP pm-'
ps
z
y (mPa)
ps
(2S, 3s) cis (2R, 3s) trans
6.2 0.8
38 422
240 36
77 2.3
(nC cm-2)
which can be easily attached to a phenol, or oxidized to the corresponding acid and attached to the phenol in a normal esterification reaction [27, 821. If the dipoles associated with the fluorine atoms and the epoxy moiety in the two diastereomeric oxiranes shown in Table 12 [83] point in the same direction, then a high P, value is observed. If they are opposed, then they cancel each other out to some extent, and a low P, value is the result. Converting the ether linkage to an ester group
does not lead to a significant change in the observed P, value, see Table 13 [27]. However, changing the configuration at the second carbon atom of the epoxy group (i.e. changing from trans to cis) results in an enhanced stereo coupling between the chiral moiety and the lateral molecular dipole. Thus, significantly higher P, values are observed for the cis-substituted oxiranes [27]. The cis configuration at the epoxy moiety leads automatically to a nonlinear (i.e. fully extended) conformation of the chain. This leads to a substantially higher value for y However, y i s increased to a lesser extent than the P, is increased and this results in significantly shorter z for the cis-substituted esters. Replacement of the oxygen atom in the epoxy moiety by a sulfur atom to produce the analogous thiiranes [84] results not only in lower transition temperatures, but also significantly lower values for P,, if the optically active unit is situated on the periphery of the molecule. The opposite is observed with respect to P,, if the chiral entity is situated between two mesogenic units such as six-membered rings. A Walden inversion during the reaction produces an inversion of configuration at both asymmet-
Table 14. Transition temperatures, response time (10 Vpp/ymsquare wave, time to maximum current), tilt angle and spontaneous polarization measured at 25°C in a 2 pm cell with polyimide alignment containing mixtures of 2 mol% of the (2 S , 4R)-truns- (a-[4'-pentyl-l,l'-biphenyl-4-yl]-y-pentyl)lactone or (2R,4R)-cis- (a-[4'-pentyl- l,l'-biphenyl-4-yl]-y-pentyl)lactoneand a host mixture (Cr-SmC: <25 "C; SmC-SmA: 5 1 "C;SmA-N: 63 "C; N-I: 69 "C) 1851.
Configuration
2S, 4R (trans) 2R, 4R (cis)
SmC*-SmA* ("C)
SmA*-N* ("C)
N*-I ("C)
z (ps)
e
PS
(degrees)
(nC cm-')
52 52
61 61
68 68
655 100
17 21
<0.5 +5.3
508
I
Synthesis of Chiral Smectic Liquid Crystals
Table 15. Transition temperatures, response time (10 Vp&m square wave, time to maximum current), tilt angle and spontaneous polarization measured at 25 "C in a 2 pm cell with polyimide alignment containing mixtures of 2 mol% of the (2R, SR)-truns-(a-[4'-hexyloxy-l, l'-biphenyl-4-ylcarboxy]-&hexyl)lactone or (2S, 5R)cis-(a-[4'-Hexyloxy-l, l'-biphenyl-4-ylcarboxy]-6-hexyl)lactone and a host mixture (SmC-SmA: 5 1 "C; SmA-N: 61 "C; N-I: 68 "C) [86]. 0
Configuration
2R, 5R (trans) 2S, 5R (cis)
Cr-SmC* ("C)
SmC*-SmA* ("C)
SmA*-N* ("C)
N*-I ("C)
z
8
(ps)
(degrees)
p, (nC cm-')
2.5 2.6
53 53
60
67 67
19.5 126
21.0 22.3
-2.4 i4.2
59
ric carbon atoms resulting in an inverse absolute configuration. The thiiranes are significantly less thermally stable than the corresponding oxiranes.
C-SmC*: lll°C; SrnC*-I: 128°C [86]
Structure 5
1.2.9 Optically Active y-lactones
1.2.10 Optically Active &Lactones
In the optically active, 5-membered y-lactone ring there are two asymmetric (chiral) carbon atoms and a large dipole moment due to the carboxy function. The dipole moments associated with the carbonyl and ether components of the ester linkage are in the same plane, point in the same direction and are arranged perpendicular to the long axis of the molecule [85]. The degree of free rotation of the chiral centers and the dipole moments are greatly reduced. Therefore a large value for P , can be expected and this is indeed observed to be the case, see Table 14. It is clear from the data in the table that the values for p,, 8 and z, but not the transition temperatures, are strongly dependent on the configuration of the lactone ring (i.e. cis or trans). Both configurational isomers are generated as a result of the same reaction pathway [85].
A similar geometry is also observed for the related 6-membered &-lactone ring. Therefore similarly large values for P, are to be expected and this is observed to be the case, see Table 15 [86]. Large differences in P, are observed for the cis and trans configurations (Structure 5 ) , although the value for the trans-isomer is greater than that of the cis-isomer, where the opposite is the case for the ylactones. As the concentration of dopant is so low little difference is seen in the transition temperatures of the mixtures. [861
1.2.11 Miscellaneous Optically Active Heterocycles Dopants incorporating a series of optically active rings such as 1,3-dioxolan-4-ones
1.3 Short Pitch Chiral Smectic Liquid Crystals or Dopants
[87], 1,3-dioxolan-2-ones [MI, 2-oxetanones [89, 901, oxazolidines [27] and prolines [27] have also been prepared. These dopants generally induce lower P, values and/or higher z and y and/or lower transition temperatures in hosts than do the oxiranes, ylactones and &lactones discussed above.
1.3 Short Pitch Chiral Smectic Liquid Crystals or Dopants A major problem inherent to bistable FLCDs such as SSFLCDs and SBFLCDs [91] is the d.c.-bias, which results from the P, if an area of the display remains in one of the degenerate states for any length of time [92]. This may result in a build up of space charge in the FLC or in the alignment or insulating layers. These so called ghost images can be alleviated, but not completely eliminated, by sophisticated driving schemes and electrode designs. This is also valid for the inherent lack of grey scale in FLCDs based on bistable effects required for full color displays. An alternative technology utilizes the deformed helix ferroelectric effect DHFLCD [93] on an active matrix substrate driven via simple capacitive coupling in a symmetric, dipolar driving mode [94]. This eliminates the build up of space charges and of ghost images. Active addressing of each pixel is required due to the absence of bistability and of multiplexability. The DHFLCD effect is based on the distortion of a helix consisting of SmC* layers with p significantly shorter than the wavelength of visible light. The birefringence, An, is averaged out over the helical structure and can be modulated by an electric field. A good contrast necessitates a wide switching angle, 20. This requires optically active dopants with a significantly different spectrum of properties to those
509
Table 16. The pitch and spontaneous polarization measured at 25 "C of mixtures of 5 wt% of the bis(S)1-methylalkyl4,4"-terphenyldicarboxylates in 4-hexyloxyphenyl 4-octyloxybenzoate (Cr-SmC: 55 "C; SmC-N: 66 "C; N-I: 89.5" C ) [951. 0
CnH2n+' 1 2 6 8
or-
\ /
-
-
0
I/I/
01(CnH2
15.7 17.5 6.9 5 .O
n+'
4.4 9.4 8.8 3.1
for SSFLCDs such as very high P , and very short p .
1.3.1 Optically Active Terphenyl Diesters The ability to incorporate two or more chiral centers close to the rigid core of the molecule render 4, 4"-terphenyl dicarboxylates of interest for the above application. The usual optically active primary and secondary alcohols with various polar substituents at the chiral center have been used to prepare a multitude of diesters [95]. The usual trends found for mono-substituted esters were also found for the diesters, although most of them do not exhibit enantiotropic phases due to the combined effect of the two branching groups at the chiral centers. However, an advantageous combination of high P,, shortp, high solubility, good stability and low ywas found for the bis(R or S)-2-alkyl 4, 4"-terphenyl dicarboxylates, see Table 16. The P, rises as the length of the chain after the chiral center is increased, reaches a maximum and then decreases as also observed for SmC* dopants incorporating only one chiral center. A sim-
5 10
1
Synthesis of Chiral Smectic Liquid Crystals
Table 17. Comparison of the tilt angle, helical twisting power (HTP) and spontaneous polarization (extrapolated to 100%) measured at TSmC*-lS"C of a mixture of 7 wt% of the dioxanes in a host mixture [961.
high y of the tetracyclic dioxanes prohibit their use in more than small quantities.
1.4 Antiferroelectric Liquid Crystals n
1 2
e
HTP (pm-')
PS
(degrees)
29 30
9.1 -
27 59
(nC cm-*)
ilar trend is also observed for p . Thus the optimal combination of P, and short p is seen for intermediate chain lengths ( n = 8). This diester also exhibits a high virtual TSmC* which results in an increase in TSmC* of the mixture as the concentration of the dopant is increased [95]. The corresponding biphenyl-dicarboxylates lead to low transition temperatures and surprisingly long response times.
1.3.2 Optically Active Methyl-Substituted Dioxanes The optically active 2,5-disubstituted-4methyl-dioxane ring contains three chiral centers and is synthetically accessible [96]. A tetracyclic compound incorporating two such rings possesses a high P, value, which is approximately twice as large as that of corresponding monodioxanes, see Table 17. The lower value for the tricyclic dioxane infers that the optically active parts are not completely decoupled from each other. The high P,, high helical twisting power (HTP) and relatively large 8 render these compounds highly attractive as dopants for DHFLCDs. However, the low solubility and
The first antiferroelectric phases were found for chiral and racemic 2-octyl N, N'-terephthalidene-bis(4-aminocinnamate) and were classified as smectic 0 (SmC(a1t)) [97]. Both the chiral and achiral smectic phase possess a herringbone structure (Structure 6), where the molecules in alternating layers are tilted at an angle +8 or -8 to the layer normal [98]. The helical structure of the chiral phase results in a zero macroscopic P, as the very high P , of alternating ferroelectric layers point in different directions and cancel each other out. In an electric field the helix is unwound and a normal ferroelectric SmC* phase is produced. If the field is reversed then the FLC is switched into the second degenerate state as usual. On removal of the field the molecules relax to the intermediate position parallel to the rubbing direction. This behavior is characteristic of the phase denominated as the antiferroelectric smectic C (SmCX) phase, which has now been shown to be the same as the SmO phase [99-1011. The tristable switching in the SmCz phase [102, 1031is the basis of antiferroelectric liquid crystal display devices (AFLCDs) [104]. The use of an alternating bias prohibits the appearance of ghost or memory effects. The sharp threshold voltage and hysteresis allow a high degree of multiplexing. Several subphases have also been identified, at least one of which exhibits a ferrielectric structure [l05-1 I I]. Several of these compounds with a high P, and HTP also exhibit the recently discovered twisted grain boundary (TGB) phases [105].
51 1
1.5 Antiferroelectric Liquid Crystals
Several of the SmCz compounds collated in Table 18 were prepared during systematic studies of LCs exhibiting a high degree of molecular and form chirality [ 106-1 lo], while others were the product of attempts to synthesize optimized materials for SSFLCDs [51] and later for AFLCDs [ l l 1-1 171. The synthesis of SmCz LCs is
in its infancy and most of the compounds in Table 18 show a strong similarity. The chiral center is close to the aromatic core and the aliphatic chain after the chiral center is long. The necessity of a rigid aromatic core close to the chiral center for SmCz formation is illustrated by the comparison of the transition temperatures of cinnamates and
CI C& 3*CH(CY)O,CCH-CH~CH-N
&N=CH
~ C H = C H C O ~ * C H ( C H - & ~ H 31
C-SmO*: 95°C; SmO*-SrnQ*: 130°C; SmQ*-I: 133°C [97]
Structure 6
Table 18. Structures of typical antiferroelectric smectic SmC; compounds. Structure
Ref.
[51, 1111
[I 111 [112, 1131
~1031 [1031 F
~
3
1
[ I 141 [1081
~1151 [106, 1171
[109, 1171 [109, 1181
512
1 Synthesis of Chiral Smectic Liquid Crystals
the corresponding phenylethyl-carboxylates, where the conjugation has been broken by effective hydrogenation of the carbon-carbon double bond [ 1 161. However, it is noteworthy that the phenylethyl-carboxylates still exhibit an SmCZ phase, although at much lower temperatures. It is postulated that the SmC, phase of nonoptically active, swallow-tail compounds, which cannot be caused by chirality, is the result of the bent or zigzag shape of dimers formed by the steric interaction between the swallow tail of one molecule and the normal alkyl chain of a second molecule in an adjacent layer, although dipole-dipole interactions probably also make a contribution [118]. Similar steric interactions are probably responsible for the SmC, phase exhibited by some tetracyclic dimers [ 1 191. Acknowledgements. The author is grateful to Professor J. Funfschilling and Professor J. W. Goodby for many helpful and instructive discussions.
1.5 References G. Friedel, Ann. Phys. 1922, 18, 273474. H. Sackmann, D. Demus, Mol. Cryst. Liq. Cryst. 1966,2, 81-102. H. Arnold, Mol. Cryst. Liq. Cryst. 1966, 2, 63-70. H. Sackmann, Mol. Cryst. Liq. Cryst. 1989,5, 43-55. G. W. Gray, J. W. Goodby, Smectic Liquid Crystals: Textures and Structures, Blackie Press, Glasgow and London, 1984. J. W. Goodby in Ferroelectric Liquid Crystals (Ed.: G. W. Taylor), Gordon and Breach, Philadelphia, 1991, pp. 99-241. S. L. Arora, J. L. Fergason, A. Saupe, Mol. Cryst. Liq. Cryst. 1970,10, 243-257. T. R. Taylor, J. L. Fergason, S. L. Arora, Phys. Rev. Lett. 1970,24, 359-362. T. R. Taylor, S. L. Arora and J. L. Fergason, Phys. Rev. Lett. 1970,25, 722-726. F. M. Jager, Rec. Trav. Chim. Pays Bas 1906, 25,334-35 1. W. Urbach, J. Billard, C. R. Hebd. Sian. Acad. Sci. l972,274B, 1287-1290.
G. W. Gray, Mol. Cryst. Liq. Cryst. 1969, 7, 127-15 1. M. Leclercq, J. Billard, J. Jacques, Mol. Cryst. Liq. Cryst. 1969, 8, 367-387. W. Helfrich, C. S. Oh, Mol. Cryst. Liq. Cryst. 1971,14,289-292. G. W. Gray, J. Chem. SOC.1955,43594368. S. L. Arora, T. R. Taylor, J. L. Fergason, A. Saupe, J.Am. Chem. SOC.1969,91,3671-3673. A. Saupe, Mol. Cryst. Liq. Cryst. 1969, 7, 59-74. J. W. Goodby, J. Muter: Chem. 1991, I , 307-3 18. P. G. de Gennes, The Physics of Liquid Crystals, Oxford University Press, Oxford, 1974, p. 321. W. L. McMillan, Phys. Rev. 1973, A-8, 1921-1929. R. B. Meyer, L. Liebert, L. Strzelecki and P. Keller, J. Phys. (Paris) Lett. 1975, 36, L69-L7 1. R. B. Meyer, Mol. Cryst. Liq. Cryst. 1977,40, 33-48. N. A. Clark, S. T. Lagerwall, Appl. Phys. Lett. 1980,36, 899-901. S. Garoff, R. B. Meyer, Phys. Rev Lett. 1977, 38,848-851. J. W. Goodby, T. M. Leslie in Liquid Crystals and Ordered Fluids, Vol. 4, (Eds.: A. C. Griffin, J. F. Johnson), Plenum, New York, 1984, p. 1-32. T. Geelhaar, Ferroelectrics 1988,85, 329-349. H. R. Dubal, C. Escher, D. Gunther, W. Hemmerling, Y. Inoguchi, I. Muller, M. Murikami, D. Ohlendorf, R. Wingen, Jpn. J. Appl. Phys. 1988,27, L2241-L2244. F. Leenhouts, J. Funfschilling, R. Buchecker, S. M. Kelly, Liq. Cryst. 1989, 5, 1179-1 186. U. Finkenzeller, A. E. Pausch, E. Poetsch, J. Suermann, Kontakte 1993, 2, 3-14. S. M. Kelly, R. Buchecker, J. Funfschilling, J. Muter: Chem. 1994,4, 1689-1697. A. Wulf, Phys. Rev. A 1975,11, 365-375. J. W. Goodby, G. W. Gray, D. G. McDonnell, Mol. Cryst. Liq. Cryst. Lett. 1977,34, 183-188. J. W. Goodby, G. W. Gray, Ann. Phys. 1978,3, 123-1 30. S. M. Kelly, J. Funfschilling, J. Muter: Chem. 1994,4, 1689-1697. P. Keller, L. Liebert, L. Strzelecki, J. Phys. (Paris) Coll. 1976, 37, C3-C27. B. I. Ostrovski, A. Z. Rabinovitch, A. S . Sonin, E. L. Sorkin, Ferroelectrics 1980, 24, 309312. T. Sakurai, K. Sakamoto, M. Hanma, K. Yoshino, M. Ozaki, Ferroelectrics 1984,58, 21-32. K. Yoshino, T. Sakurai in Ferroelectric Liquid Crystals, (Ed.: G. W. Taylor), Gordon and Breach, Philadelphia, 1991, pp. 317-361.
1.S References A. Hallsby, M. Nilsson, B. Otterholm, Mol. Cryst. Liq. Cryst. Lett. 1982, 82, 61-68. B. Otterholm, M. Nilsson, S . T. Lagerwall, K. Skarp, Liq. Cryst. 1987,2, 757-768. J. W. Goodby, T. M. Leslie, Mol. Cryst. Liq. Cryst. 1984,110, 175-203. P. Keller, Ferroelectrics 1984,58, 3-7. G. Decobert, J. C. Dubois, Mol. Cryst. Liq. Cryst. 1984,114,237-247. G. W. Gray, D. G. McDonnell, Mol. Cryst. Liq. Cryst, 1976,37, 189-211. S. M. Kelly, R. Buchecker, Helv. Chim. Acta, 1988,271,451-460. R. Dabrowski, J. Dziaduszek, J. Szulc, K. Czuprynski, B. Sosnowska, Mol. Cryst. Liq. Cryst. 1991,209,201-21 1. Y. Haramoto, H. Kamogawa, Mol. Cryst. Liq. Cryst. 1990,182, 195-200. H. Matsubara, S . Takahashi, K. Seto, H. Imazaki, Mol. Cryst. Liq. Cryst. 1990, 180, 337342. S. M. Kelly, R. Buchecker, M. Schadt, Liq. Cryst. 1988,3, 1115-1113; and 1125-1128. A. Yoshizawa, I. Nishiyama, M. Fukumasa, T. Hirai, M. Yamane, Jpn. J. Appl. Phys. Lett. 1989,28, L1269-L1270. K. Furakawa, K. Terashima, M. Ichihashi, S . Saitoh, K. Miyazawa and T. Inukai, Ferroelectrics, 1988, 85, 451-459. H. Nonoguchi, H. Suenaga, K. Oba, M. Kaguchi, T. Harada in Preprints of the 12th Jpn. Liq. Cryst. Meeting, Japan, 1985, 1207, 54-55. H. Suenaga, K. Oba, M. Kaguchi T. Harada, S. Shimoda, in Preprints of the 12th Jpn. Liq. Cryst. Meeting, Japan, 1985, 3F01, 152-153; 2F13, 106-107. M. Murakami, S. Miyake, T. Masumi, T. Ando, A. Fukami, Jpn. Display ’86 1986,344-347. S. Matsumoto, A. Murayama, H. Hatoh, Y. Kinoshita, H. Hirai, M. Ishikawa, S. Kamagami, SlD 88 Digest, 1988,4144. S . M. Kelly, A. Villiger, Liq. Cryst. 1988, 3, 1173-1182. K. Yoshino, M. Osaki, K. Nakao, H. Taniguchi, N. Yamasaki, K. Satoh, Liq. Cryst. 1989, 5, 1203-1211. S. Sugita, S. Toda, T. Yamashita, T. Teraji, Bull. Chem. Soc. Jpn. 1993,66,568-572. E. Chin, J. W. Goodby, J. S. Patel, Mol. Cryst. Liq. Cryst. 1988, 157, 163-191. S. Sugita, S. Toda, T. Yoshiyasu, T. Teraji, Mol. Cryst. Liq. Cryst. 1993, 237, 399-406. J. Nakauchi, Y. Kageyama, S . Hayashi, K. Sakashita, Bull. Chem. SOC. Jpn. 1989, 62, 1685-1 691. C. Sekine, T. Tani, Y. Ueda, K. Fujisawa, T. Higasii, I. Kurimoto, S . Toda, N. Takano, Y.Fujimoto, M. Minai, Ferroelectrics 1993, 148, 203-212.
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[63] P. Keller, S. JugC, L. LiebCrt, and L. Strzelecki, Compt. Rend. Acad. Sci. 1976, 282, C639-C641. [64] T. Sakurai, N. Mikami, R. Higurchi, M. Honma, K. Yoshino, Ferroelectrics 1988, 85,469-478. [65] C. Bahr, G. Heppke, Mol. Cryst. Liq. Cryst. 1987,148,29-43. [66] G. Heppke, D. Lotsch, N. K. Sharma, D. Demus, S. Diele, K. Jahn, M. Neundorf, Liq.Cryst. 1994,241,275-288. [67] S . Arakawa, K. Nito, J. Seto, Mol. Cryst. Liq. Cryst. 1991, 204, 15-25. [68] J. Bomelburg, G. Heppke, A. Ranft, Z. Narurforsch. 1989, 44b, 1127-1 13I . [69] R. Buchecker, S. M. Kelly, J. Funfschilling, Liq. Cryst. 1990, 8,217-227. [70] S . Nakamura, H. Nohira,Mol. Cryst. Liq.Crysr. 1990,185, 199-207. [7 11 H. Nohira, S. Nakamura, M. Kamei, Mol. Crysr. Liq. Cryst. 1990,180, 379-388. [72] D. M. Walba, H. A. Razavi, N. A. Clark, D. S. Parma, J. Am. Chem. SOC. 1988, 110, 8686-8691. [73] M. D. Wand, R. Vohra, D. M. Walba, N. A. Clark, R. Shao, Mol. Cryst. Liq. Cryst. 1991, 202, 183-192. [74] K. Yoshino, M. Ozaki, H. Taniguchi, M. Ito, K. Satoh, N. Yamasaki, T. Kitazume, Jpn. J. Appl. Phys. 1987,26, L77-L78. [75] Y. Suzuki, T. Hagiwara, I. Kawamura, N. Okamura, T. Kitazume, M. Kakimoto, Y. Imai, Y. Ouchi, H. Takezoe, A. Fukuda, Liq. Cryst. 1989,6, 167-174. [76] A. Sakaigawa, Y. Tashiro, Y. Aoki, H. Nohira, Mol. Cryst. Liq. Cryst. 1991, 206, 147-157. [77] Y. Aoki, H. Nohira, Chem. Lett. 1993, L113-L116. [78] L. A. Beresnev, L. M. Blinov, Ferroelectrics 1981,33,129-138. [79] L. K. M. Chan, G . W. Gray, D. Lacey, R. M. Scrowston, I. G. Shenouda, K. J. Toyne, Mol. Cryst. Liq. Cryst. 1989,172, 125-146. [80] D. M. Walba, K. F. Eidman, R. C, Haltiwanger, J. Org. Chem. 1989,54,49394943. [81] C. J. Booth, J. W. Goodby, J. P. Hardy, 0. C. Lettington, K. J. Toyne, Liq. Cryst. 1994, 16, 925-940. [82] D. M. Walba, R. T. Vohra, N. A. Clark, M. A. Handschy, J. Xue, D. S . Parma, S. T. Lagerwall, K. Skarp, J. Am. Chem. SOC.1986,108,724-72s. [83] D. M. Walba, N. A. Clark, Ferroelectrics 1988, 84,6572. [84] G. Scherowsky, J. Gay, Liq. Crysr. 1989, 5, 1253-1258. [85] K. Sakaguchi, T. Kitamura, FerroelectricJ 1991,114,265-272. [86] K. Sakashita, M. Shindo, J. Nakauchi, M. Uematsu, Y. Kageyama, S. Hayashi, T. Ikemoto, Mol. Cryst. Liq. Cryst. 1991, 199, 119-127.
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1871 G. Scherowsky, M. Sefkow, Mol. Cryst. Liq. Cryst. 1991,202,207-216. [88] G. Scherowsky, J. Gay, M. Gunaratne, Liq. Cryst. 1992,11,745-752. 1891 G. Scherowsky, M. Sefkow, Liq. Cryst. 1992, 12,355-362. 1901 S. Takehara, M. Osawa, K. Nakayama, T. Kusumoto, K. Sato, A. Nakayama, T. Hiyama, Ferruelectrics 1993, 148, 195-202. 1911 J. Fiinfschilling, M. Schadt, SlD Digest 1990, 106-109. 1921 Y. Inaba, K. Katagiri, H. Inoue, J. Kanabe, S. Yoshihara, S. Iijama, Ferruelectrics 1988, 85, 255-264. 1931 L. A. Beresnev, V. G. Chigrinov, D. I. Dergachev, E. P. Poshidaev, J. Fiinfschilling, M. Schadt, Liq. Cryst. 1989, 5, 1171-1 177. [94] M. Schadt, J. Fiinfschilling, SID IDW’Y4 Hamamatsu City, Japan, 1994, 67-70. [95] M. Loseva, N. Chernova, A. Rabinovitch, E. Poshidaev, J. Narkevitch, 0. Petrashevitch, E. Kazachkov, N. Korotkova, M. Schadt, R. Buchecker, Ferroelectrics 1991,114,357-377. 1961 R. Buchecker, J. Fiinfschilling, M. Schadt, Mu/. Cryst. Liq. Cryst. 1992, 213, 259-267. 1971 A. M. Levelut, C. Germain, P. Keller, L. Liebert, J. Billard, J. Phys. (Paris), 1983, 44, 623-629. [98] Y. Galerne, L. Liebert, Phys. Rev. Lett. 1990, 64,906-909; and 1991,66,2891-2894. [99] P. Cladis, H. Brand, Liq. Cryst. 1993, 14, 1327-1 349. [loo] G. Heppke, P. Kleineberg, D. Lotsch, S. Mery, R. Shashidar, Mu!. Cryst. Liq. Cryst. 1993,231, 257-262. [loll Y. Takanishi, M. Johno, T. Yui, H. Takezoe, A. Fukuda, Jpn. J. Appl. Phys. 1993, 32, 4605-4610. [lo21 A. D. L. Chandani, T. Hagiwara, Y. Suzuki, Y. Ouchi, H. Takezoe, A. Fukuda, Jpn. J. Appl. Phys., 1988,27, L729-L732. 11031 A. Fukuda, J. Muter. Chem. 1994,4,997-1016. 11041 Y. Yamada, N. Yamamoto, K. Mori, K. Nakamura, T. Hagiwara, Y. Suzuki, I. Kawamura, H.
Orihara, Y. Ishibashi, Jpn. J. Appl. Phys. 1990, 29, 1757-1764. [lo51 J. W. Goodby, M. A. Waugh, S. M. Stein, E. Chin, R. Pindak, J. S. Patel, Nature, 1989,337, 449-452. [ 1061 I. Nishiyama, J. W. Goodby, J. Muter. Chem. 1993,3, 149-159. 11071 I. Nishiyama, E. Chin, J. W. Goodby, J. Muter. Chem. 1993,3, 161-168. 11081 J. W. Goodby, J. S. Patel, E. Chin, J. Muter: Chem. 1992,2, 197-207. [lo91 J. W. Goodby, I. Nishiyama, A. J. Slaney, C. J. Booth, K. J. Toyne, Liq. Cryst. 1993,14,37-66. [110] J. W. Goodby, A. J. Slaney, C. J. Booth, I. Nishiyama, J.D. Vuijk, P. Styring, K. J. Toyne, Mol. Cryst. Liq. Cryst, 1994, 243, 231-298. [I 111 N. Okabe, Y. Suzuki, I. Kawamura, T. Isozaki, H. Takezoe, A. Fukuda, Jpn. J. Appl. Phys. 1992,31, L793-L796. [112] Y. Suzuki, T. Hagiwara, I. Kawamura, N. Okamura, T. Kitazume, M. Kakimoto, Y. Imai, Y. Ouchi, H. Takezoe, A. Fukuda, Liq. Cryst. 1989,6, 167-174. [113] Y. Yamada, K. Mori, N. Yamamoto, H. Hayashi, K. Nakamura, M. Yamawaki, H. Orihara. Y. Ishibashi, Jpn. J. Appl. PhyJ. 1989, 28, L1606-L1608. [114] I. Nishiyama, A. Yoshisawa, M. Fukumasa, T. Hira, Jpn. J. Appl. Phys. 1989, 28, L2248-L2250. [ 1151 S. Inui, S. Kawano, M. Saitoh, H. Iwane, Y. Takanishi, K. Hiraoka, Y. Ouchi, H. Takezoe, A. Fukuda, Jpn. J. Appl. Phys. 1990, 29, L987-L990. [ 1161 S. Inui, T. Susuki, N. Iimura and H. Iwane, Mol. Cryst. Liq. Cryst. 1994, 239, 1-9. [117] C. J. Booth, D. A. Dunmur, J. W. Goodby, J. S. Kang, K. J. Toyne, J. Muter. Chem. 1994, 4, 747-759. [118] I. Nishiyama, J. W. Goodby, J. Muter. Chem. 1992,2, 1015-1023. [ 1191 J. Watanabe, M. Hayashi, Mukromulecules, 1989,22,4083-4088
Handbook of Liquid Crystals Edited by D. Demus, J. Goodby, G. W. Gray, H.-W. Spiess, V. Vill Copyright 0 WILEY-VCH Verlag GmbH. 1998
2 Ferroelectric Liquid Crystals Sven 7: Lagerwall
2.1 Introduction Ferroelectric liquid crystals are a novel state of matter, a very recent addition to the science of ferroelectrics which, in itself, is of relatively recent date. The phenomenon which was later called ferroelectricity was discovered in the solid state (on Rochelle salt) in 1920 by Joseph Valasek, then a PhD student at the University of Minnesota. His first paper on the subject [ l ] had the title Piezo-Electric and Allied Phenomena in Rochelle Salt. This was at the time when solid state physics was not a fashionable subject and it took several decades until the importance of the discovery was recognized. Valasek had then left the field. Later, however, the development of this branch of physics contributed considerably to our understanding of the electrical properties of matter, of polar materials in particular and of phase transitions and solid state physics in general. In fact, the science of ferroelectrics is today an intensely active field of research. Even though its technical and commercial importance is substantial, many breakthrough applications may still lie ahead of us. The relative importance of liquid crystals within this broader area is also constantly growing. This is illustrated in Fig. 1,
showing how the proportion of the new materials, which are liquid-crystalline, has steadily increased since the 1980s. h
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Ferroelectric Liquid Crystals
The general level of knowledge of ferroelectricity, even among physicists, is far lower than in the older and more classical subjects like ferromagnetism. It might therefore be worthwhile to discuss briefly the most important and characteristic features of solid ferroelectrics and polar materials, before turning to liquid crystals. This will facilitate the understanding and allow us to appreciate the striking similarities as well as distinctive differences in how polar phenomena appear in solids and how they appear in liquid crystals. One of the aims, of course, is also to make a bridge to existing knowledge. Those not aware of this important knowledge are apt to coin new words and concepts, which are bound to be in contradiction to already established concepts or even contradictory to themselves. When dealing with ferroelectric liquid crystals, we use the same conceptual framework already developed for solid polar materials. An important part of this is the Landau formalism describing phase transitions (still not incorporated in any textbook on thermodynamics), based on symmetry considerations. It is important to gain some familiarity with the peculiarities of this formalism before applying it to ferroelectric liquid crystals. In this way it will be possible to recognize cause and effect more easily than if both subject matters were introduced simultaneously. Concepts like piezoelectric, pyroelectric, ferroelectric, ferrielectric, antiferroelectric, paraelectric, electrostrictive, and several more, relate to distinct phenomena and are themselves interrelated. They are bound to appear in the description of liquid crystals and liquid crystal polymers, as they do in normal polymers and crystalline solids. Presently, great confusion is created by the uncritical use of these terms. For example, in the latest edition of the Encyclopedia Britannica [4]it is stated that pyroelectric-
ity was discovered in quartz in 1824. This is remarkable, because quartz is not pyroelectric at all and cannot be for symmetry reasons. To clarify such issues (and the confusion is no less in the area of liquid crystals), we will have to introduce some simple symmetry considerations that generally apply to all kinds of matter. In fact, symmetry considerations will be the basic guidelines and will play a probably more important role here than in any other area of liquid crystals. Chirality is a special property of dissymmetry with an equally special place in these considerations. It certainly plays a fundamental role for ferroelectric liquid crystals at least so far. Therefore we will have to check how exactly the appearance of polar properties in liquid crystals is related to chiral properties, and if chirality is dispensable, at least in principle. Finally, flexoelectricity is also a polar effect, and we will have to ask ourselves if this is included in the other polar effects or, if not, if there is an interrelation. Can liquids in which the constituents are dipoles be ferroelectric? For instance, if we could make a colloidal solution of small particles of the ferroelectric BaTiO,, would this liquid be ferroelectric? The answer is no, it would not. It is true that such a liquid would have a very high value of dielectric susceptibility and we might call it superparaelectric in analogy with the designation often used for a colloidal solution of ferromagnetic particles, which likewise does not show any collective behavior. An isotropic liquid cannot have polarization in any direction, because every possible rotation is a symmetry operation and this of course is independent of whether the liquid lacks a center of inversion, is chiral, or not. Hence we have at least to diminish the symmetry and go to anisotropic liquids, that is, to liquid crystals, in order to examine an eventual appearance of pyroelectricity or ferroelectricity. To
2.1 Introduction
search for ferroelectricity in an isotropic liquid would be futile, because a ferroelectric liquid cannot be isotropic. In order to have a bulk polarization, a medium must have a direction, the polarity of which cannot be reversed by any symmetry operation of the medium. On the other hand, an isotropic liquid consisting of dipoles may show a polarization during flow, because a shear diminishes the symmetry and will partially order the dipoles, thus breaking the randomness. This order will be polar if the liquid is chiral. However, we would not consider such a liquid ferroelectric or pyroelectric - no more than we would consider a liquid showing flow birefringence to be a birefringent liquid. It is clear that there may be lots of interesting polar effects yet to be explored in flowing liquids, particularly in fluids of biological significance (which are very often chiral). Nevertheless, these effects should not be called “ferroelectric”. They should not even be called piezoelectric, even if setting up shear flow in a liquid certainly bears some resemblance to setting up shear strain in a crystal. Are there magnetic liquids? Yes, there are. We do not mean the just-mentioned “ferrofluids”, which are not true magnetic liquids, because the magnetic properties are due to the suspended solid particles (of about 10 nm size). As we know, ferromagnetic materials become paramagnetic at the Curie temperature and this is far below the melting point of the solid. However, in some cases it has been possible (with extreme precautions) to supercool the liquid phase below the Curie temperature. This liquid has magnetic properties, though it is not below its own Curie temperature (the liquid behaves as if there is now a different Curie temperature), but it would be wrong to call the liquid ferromagnetic. The second example is the equally extreme case of the quantum liquid He-3 in the A1 phase. Just like
5 17
the electrons in a superconductor, the He-3 nuclei are fermions and have to create paired states to undergo Bose-Einstein condensation. However, unlike the electron case, the pairs are created locally, and the axis between two He-3 then corresponds to a local director. Thus He-3 A is a kind of nematic-like liquid crystal, and because of the associated magnetic moment, He-3 A is undeniably a magnetic liquid, but again, it is not called ferromagnetic. Thus, in the science of magnetism a little more care is normally taken with terminology, and a more sound and contradiction-free terminology has been developed: a material, solid or liquid, may be designated magnetic, and then what kind of magnetic order is present may be further specified. When it comes to polar phenomena, on the other hand, there is a tendency to call everything “ferroelectric”, a usage that leads to tremendous confusion and ambiguity. It would be very fortunate if in future we could reintroduce the more general concepts of “electric materials” and “electric liquids” in analogy with magnetic materials and magnetic liquids. Then, in every specific case, it would be necessary to specify which electric order (paraelectric, dielectric, etc.) is present, just as in the magnetic case (paramagnetic, diamagnetic, etc.). Coherent and contradiction-free terminology is certainly important, because vagueness and ambiguity are obstacles for clear thinking and comprehension. In the area of liquid crystals, the domain of ferroelectric and antiferroelectric liquid crystals probably suffers from the greatest problems in this respect, because in the implementation of ideas, concepts, and general knowledge from solid state physics, which have been of such outstanding importance in the development of liquid crystal research, the part of ferroelectrics and other polar materials has generally not been very well represented.
518
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Ferroelectric Liquid Crystals
Presumed ferroelectric effects in liquid crystals were reported by Williams at RCA in Princeton, U. S. A., as early as 1963, and thus at the very beginning of the modern era of liquid crystal research [S]. By subjecting nematics to rather high dc fields, he provoked domain patterns that resembled those found in solid ferroelectrics. The ferroelectric interpretation seemed to be strengthened by subsequent observations of hysteresis loops by Kapustin and Vistin and by Williams and Heilmeier [7]. However, these patterns turned out to be related to electrohydrodynamic instabilities, which are well understood today (see, for instance, [8], Sec. 2.4.3 or [9], Sec. 2.4.2), and it is also well known that certain loops (similar to ferroelectric hysteresis) may be obtained from a nonlinear lossy material (see [lo], Sec. 2.4.2). As we know today, nematics do not show ferroelectric or even polar properties. In order to find such properties we have to lower the symmetry until we come to the tilted smectics, and further lowering their symmetry by making them chiral. The prime example of such a liquid crystal phase is the smectic C*. In principle, the fascinating properties of the smectic C* phase could have been detected long before their discovery in 1974. Such materials were synthesized by Vorlander [ l I] and his group in Halle before the first World War. The first one seems to have been an amyloxy terephthal cinnamate with a smectic C* phase from 133 “C to 247 “C and a smectic A* phase from 247°C to 307 “C, made in 1909 [I 13 at a time far earlier than the first description of the smectic C phase as such [I21 in 1933. At that time it was not, and could not possibly have been realized as ferroelectric. The concept did not even exist. In a classic review from 1969, Saupe (at Kent State University) discusses a hypothetical ferroelectric liquid crystal for the first
time [13]. While a nematic does not have polar order, such order, he points out, could possibly be found in the smectic state. The ferroelectric smectic, according to Saupe, is an orthogonal nonchiral smectic in which all molecular dipoles are pointing along the layer normal in one single direction (a longitudinal ferroelectric smectic). He also discussed a possible antiferroelectric arrangement. Among the other numerous topics discussed in this paper (suggesting even the first blue phase structure), Saupe investigates the similarities between nematics and smectics C and introduces the twisted smectic structure as the analog of a cholesteric. In the same year, Gray in Hull [ 141 synthesized such materials (actually the first members of the DOBAMBC series), but only reported on an orthogonal smectic phase; no attention was paid to smectic polymorphism in those days. Actually, in the year before, Leclerq et al. [I51 (in Paris) had reported on a material having two distinct chiral and strongly optically active phases, which they interpreted as two distinct nematic phases. They were thus very close to discovering the helicoidal smectic. (Their material had a first order N*-C* transition.) A helicoidal smectic was then reported for the first time by Helfrich and Oh, at RCA in I97 1, who described the first smectic liquid crystal (“spiraling” or “conical” smectic) identified as optically active [16]. Like the substances in the above-mentioned examples, this one belongs to the category that is the topic of this chapter, but who could have expected them to have special polar properties? While the smectic C* phase was gradually becoming recognized, the question offerroelectricity was again brought up by McMillan at the University of Illinois, Urbana, U. S. A. In 1973 he presented a microscopic molecular theory of the smectic C phase [ 171 based on dipole-dipole interac-
2.1 Introduction
tions, which predicted three different polar phases. McMillan’s model molecules have a central dipole and two outboard dipoles perpendicular to the long axis. Either all three can line up or only the outboard ones with the central dipoles random, or the central dipoles can line up with the outboard dipoles random. The transition from the A phase to these polar phases is thought to take place through different rotational transitions where the rotational freedom is lost or frozen out due to the dipole-dipole interaction. The net polarization in the condensed phases lies in the smectic plane and gives rise to a two-dimensional ferroelectric. Actually, whether the order is ferroelectric or antiferroelectric depends on the sign of the interplanar interaction, which cannot be predicted. McMillan’s dipolar theory, which does not involve chirality at all, never really applied to liquid crystals and was rapidly superseded by the ideas of Meyer in the following year. In fact, the discovery and introduction of practically all polar effects in liquid crystals go back to the ideas of Meyer, at that time working at Harvard. In 1969 he published an epoch-making paper entitled Piezoelectric Efsects in Liquid Crystals [ 181. It must be said that the new phenomena described in that paper are beautifully analogous to piezoelectric effects in solids. Nevertheless they are of a different nature. Therefore de Gennes instead proposed the name flexoelectric [19], in order to avoid misunderstanding. Seven years later, together with his student Garoff, Meyer presented a new, original effect which he called the piezoelectric effect in smectic A liquid crystals [20]. The analogies between this effect and the piezoelectric effect in solids are here perhaps even more striking, as we will see. However, it is not the same thing and, after much consideration by the authors, the new phenomenon was finally published under
519
the name electroclinic effect [21], a term which has since been generally adopted. In the following twenty years, there were numerous publications, in which different workers reported measuring a piezoelectric effect in liquid crystals (normally without stating what it meant and why they used this term). Obviously, they meant neither the flexoelectric nor the electroclinic effect, because the meanings of these are by now well established. Therefore the question arises as to whether a third effect exists in liquid crystals, which would finally qualify for the name piezoelectric. Obviously, this state of affairs is not very encouraging. A critical review of the terminology is therefore necessary in this area and should contribute to clarifying the concepts. Ferroelectric liquid crystals have been a field of research for about twenty years, and have certainly been in the forefront of liquid crystal research, with an increasing number of researchers involved. The first state-of-the-art applications have recently appeared. This account concentrates on the basic physics, but also treats in considerable detail the topics of highest relevance for applications. Literature references have been given, as far as possible, for topics that, for space reasons, could not be treated [8 - 10, 22 - 581. A big help for finding access to previous work is the bibliography of [52], which extends to 1989, as well as the series of conference proceedings published by Ferroelectrics [54-581, covering a great deal of the work from 1987 to 1995. New ferroelectric liquid crystal materials are continually included in the Liqcryst-Database [59] set up by Vill at the University of Hamburg.
520
2
Ferroelectric Liquid Crystals
2.2 Polar Materials and Effects 2.2.1 Polar and Nonpolar Dielectrics A molecule that has an electric dipole moment in the absence of an external electric field is called a polar (or dipolar) molecule. Such a molecule will tend to orient itself in an electric field. In a material consisting of polar molecules, the induced polarization P due to the average molecular reorientation is typically 10-100 times larger than the contribution from the electronic polarization present in all materials. In contrast, a nonpolar molecule has its distributions of positive and negative charges centered at the same point. A characteristic of materials consisting of nonpolar molecules is that the polarization P induced by a field E is small and independent of temperature, whereas in the first-mentioned case, P i s a function P(T) with an easily observable temperature dependence. Hence the same goes for the dielectric constant E and the susceptibility If we write the relations between dielectric displacement D , induced polarization P, and applied electric field E , assuming that P is linear in E
x.
D = E ~ +EP = ~ Q =EE E
(1)
and we get
P = ( q -1)%E = x % E
(2)
equally use this term, the susceptibility, for its dimensional form q,x=aP/aE. As examples of nonpolar molecules we may take H,, 02,C02, CS2, CH,, and CCl,, and as well-known polar molecules CO (O.IO), NH3 (1.47), C,jHcjOH (1.70), H,O (1.85), C6H,N02 (4.23), where we have stated the value of the dipole moment in parentheses, expressed in Debye (D), a unit commonly used for molecules. One Debye equals lo-'* cgs units and, expressed in SI units, 1D=3.3x Cm. For a comparison, let us consider a dipole consisting of two elementary charges i-e (i.e., with e the C) at a charge of the electron, 1 . 6 ~ typical atomic distance of 1 A or 0.1 nm from each other. This gives a dipole moment ~ Cm p = q d = 1 . 6 x O-'9x10-'0= 1 . 6 0-29 equal to 4.85 D. Let us assume that we had a gas consisting of molecules with this dipole moment and that we had a field sufficiently strong to align the dipoles with the field. With a density N= 3 x 102s molecules/m3 this would correspond to a polarization of P = 5 x lo4 C m-, = 50 nC cmP2. However, this is a completely unrealistic assumption because the orientational effect of the field is counteracted by the thermal motion. Therefore the distribution of dipolar orientation is given by a Boltzmann factor e-"", where U = - p . E is the potential energy of the dipole in the electric field. Integrating over all angles for p relative to E gives the polarization P as a function of E according to the Langevin function L [which expresses the average of cos @,E)]
(g)
with q as the relative, E as the total dielecP = NpL (3) tric constant or permittivity, and q, the permittivity of free space, where q , = 8 . 8 5 ~ shown in Fig. 2. For small values of the arC/V m. The dielectric susceptibility gument, L [pEl(kT)] =pEl(3kT), and thus is then, like 5,a dimensionless number, and lies in the range 0- 10 for most materials, ~ although it may attain values higher than lo4 p=-N P E (4) for certain ferroelectric substances. We will 3kT
x
2.2
1
2
3
4
5
6
7
x=pEfliT
Figure 2. The Langevin function L(x) =coth x-llx.
corresponding to the linear part around the origin. However, even at a field E = 10’ V m-l, corresponding to dielectric breakdown, the value of p E / ( k T ) is only about 0.03 at room temperature, giving a resulting polarization of 1% of the saturation value. A similar result would be true for the liquid phase of the polar molecules. In liquid crystal phases, it will generally be even harder to polarize the medium in an external field. In the very special polar liquid crystals, on the other hand, the reverse is true: for quite moderate applied fields it is possible to align all dipoles, corresponding to polarization values in the range of 5500 nC cm-2 (depending on the substance). According to Eq. (4), the polarization, at constant field, grows when we lower the temperature. By forming aP/aE, we may write for the susceptibility
x=-C T
The fact that the susceptibility has a 1/T dependence, called the Curie law, is characteristic for gases and liquids, but may also be found in solids. Generally speaking, it indicates that the local dipoles are noninteracting. For another comparison, consider a crystal of rock salt, NaC1. It has a x value of 4.8. If we apply the quite high but still realistic field of 106Vm-’ (1 V/pm) we will, ac-
Polar Materials and Effects
52 I
cording to Eq. (2), induce a polarization of 4.25 nC cm-2 (or 42.5 pC m-2; the conversion between these units commonly used for liquid crystals is 1 nC cm-2 = 10 pC m-*). The mechanism is now the separation of ionic charges and thus quite different from our previous case. It turns out that the displacement of the ions for this polarization is about nm (0.1 A), i.e., it represents only a small distortion of the lattice, less than 2%. Small displacements in a lattice may thus have quite strong polar effects. This may be illustrated by the solid ferroelectric barium titanate, which exhibits a spontaneous polarization of 0.2 C mW2= 20 000 nC cm-2. Responsible for this are ionic displacements of about nm, corresponding to less than half a percent of the length of the unit cell. Similar small lattice distortions caused by external pressure induce considerable polar effects in piezoelectric crystals. When atoms or molecules condense to liquids and solids the total charge is zero. In addition, in most cases the centers of gravity for positive and negative charges coincide. The matter itself is therefore nonpolar. For instance, the polar water molecules arrange themselves on freezing to a unit cell with zero dipole moment. Thus ice crystals are nonpolar. However, as already indicated, polar crystals exist. (In contrast, elementary particles have charge, but no dipole moment is permitted by symmetry.) These are then macroscopic dipoles and are said to be pyroelectric materials, of which ferroelectrics are a subclass. Pyroelectric materials thus have a macroscopic polarization in the absence of any applied electric field. Piezoelectric materials can also be polarized in the absence of an electric field (if under strain) and are therefore sometimes also considered as polar materials, though the usage is not general nor consistent. Clearly their polarization is not as “spontaneous” in the pyroelectric case.
522
2 Ferroelectric Liquid Crystals
Finally, there seems to be a consensus about the concepts of polar and nonpolar liquids. Water is a polar liquid and mixes readily with other polar liquids, i.e., liquids consisting of polar molecules, like alcohol, at least as long as the sizes of the molecules are not too different, whereas it is insoluble in nonpolar liquids like benzene. If in liquid form, constituent polar molecules interact strongly with other polar molecules and, in particular, are easily oriented in external fields. We will also use this criterion for a liquid crystal. That is, we will call a liquid crystal polar if it contains local dipoles that are easily oriented in an applied electric field.
2.2.2 The Nonpolarity of Liquid Crystals in General The vast majority of molecules that build up liquid crystal phases are polar or even strongly polar. As an example we may take the cyanobiphenyl compound 8CB (Merck Ltd) with the formula
which has an isotropic -nematic transition at 40.1 "C and a nematic to smectic A transition at 33.3 "C. Whereas the molecules are strongly polar, the nematic and smectic A phases built up of these molecules are nonpolar. This means that the unit vector n, i.e., the director, describing the local direction of axial symmetry, is not a polar direction but rather one with the property of an optic axis. This means that n and -n describe the same state, such that all physical properties of the phase are invariant under the sign reversal of n
n
-+
-n, symmetry operation
(6)
Repeatedly this invariance has been described as equivalent to the absence of fer-
roelectricity in the nematic phase, whereas it only expresses the much weaker condition that n is not a polar direction. How can we understand the nonpolarity expressed by Eq. (6), which up to now seems to be one of the most general and important features of liquid crystals? Let us simplify the 8CB molecules to cylindrical rods with a strong dipole parallel to the molecular long axis. In the isotropic phase these dipoles could not build up a macroscopic dipole moment, because such a moment would be incompatible with the spherical symmetry of the isotropic phase. But in the anisotropic nematic phase such a moment would be conceivable along n. However, this would set up a very strong external electrostatic field and such a polar nematic would tend to diminish the electrostatic energy by adjusting the director configuration n(r) to some complex configuration for which the total polarization and the external field would be cancelled. Such an adjustment could be done continuously because of the three-dimensional fluidity of the phase. It would lead to appreciably elastic deformations, but these deformations occur easily in liquid crystals and would carry small weight compared to the energy of the polar effects which, as we have seen, are very strong. Thus it is hard to imagine a polar nematic for energetic reasons. Moreover, the dipolar cancellation can, and therefore will, take place more efficiently on a local scale. This is illustrated in Fig. 3 , where the local dipolar fields are shown for two molecules. Each dipole will want to be in the energetic minimum position in the total field of all its neighbors. If two molecules are end on, their dipoles tend to be parallel, but in a lateral position the dipoles will be antiparallel, as shown to the right. Now, on the average, there are many more neighbors in a lateral position, which is a result of the shape of the molecules, and hence the latter
2.2 Polar Materials and Effects
Figure 3. Why liquid crystals are in general nonpolar. Around any molecule a lateral neighbor molecule has the tendency to align with its dipole in an antiparallel fashion. This means that n +-n is a symmetry operation for liquid crystals.
configuration will prevail. We will therefore have an antiparallel correlation on a local scale. This leads to the fundamental property of liquid crystals of being invariant under sign reversal of the director, i.e., to Eq. (6). We may note that the argument given above is even more conclusive for smectic phases, which are thus characterized by the same nonpolar, “nematic” order. The oblong (or more generally anisotropic) shape of the molecules, which both sterically and by the anisotropy of their van der Waals interactions leads to the liquid-crystalline order, at the same time makes this order nonpolar. It has nothing to do with the strength or weakness of the dipolar interaction. Whatever strength such an interaction may have, it cannot be assumed that it would favor a parallel situation giving a bulk polarization to a liquid, nor even to a solid. Undeniably there is also an entropic contribution to this order, because a polar orientation has a lower entropy than an apolar orientation for the same degree of parallel
523
order. Thus, if we turn all dipoles into the parallel position, we diminish the entropy and increase the free energy. However, the electrostatic contribution seems to be the important one. This is confirmed by computer simulations [60], which show that the antiparallel correlation is quite pronounced, even in the isotropic phase of typical mesogenic molecules. Although the nematic phase is nonpolar, there are very interesting and important polar effects in this phase, in a sense analogous to piezoelectric effects in solid crystals. This was recognized by Meyer [18] in 1969. These so-called flexoelectric effects are discussed in Sec. 2.4 of this Chapter. Meyer also recognized 1611in 1974 that all chiral tilted smectics would be truly polar and the first example of this kind, the helielectric smectic C*, was presented [62] in 1975. Out of Meyer’s discovery grew the whole research area of ferroelectric and antiferroelectric liquid crystals, which is today a major part of liquid crystal physics and chemistry.
2.2.3 Behavior of Dielectrics in Electric Fields: Classification of Polar Materials All dielectrics become polarized if we put them in an electric field. The polarization is linear in the field, P E, which means that it changes sign if we reverse the sign of the field. When the field is reduced to zero, the polarization vanishes. For very strong fields we will observe saturation effects (and eventually dielectric breakdown of the material). The typical behavior of a normal (nonpolar) dielectric is shown at the top of Fig. 4. In a piezoelectric, an appropriate strains s will have a similar influence to the electric field for a normal dielectric. The effect is likewise linear around the origin and shows saturation at high strains. Converse-
-
5 24
2
Ferroelectric Liquid Crystals
''normal'' dielectrics P E (at origin)
PI
-
E+ non-polarpiezoelectrics P-s
converse piezoeffect
SI
typical for ordinary materials. The electrostrictive effect therefore has an entirely different character; the strain itself is not related to any polarization so no converse effect exists (i.e., an electric field cannot be generated in ordinary materials simply by applying mechanical pressure). The electrostrictive strain is always superposed on, but can be distinguished from, a piezoelectric strain by the fact that it is quadratic and not linear in the field, thus s E2. The linear and quadratic dependence, resepectively, of the piezoelectric and electrostrictive strain, of course applies near the origin for small fields. In the more general case, the effect is called piezoelectric if it is an odd function of E, and electrostrictive if it is an even function [63]. The piezoelectric effect can only be present in noncentrosymmetric materials. If we apply a field to a material with a center of symmetry, the resultant strain must be independent of the field direction, hence
-
piezo
P-E
4 - E
electrostriction s-E2
I
E
Figure 4.Response of nonpolar dielectrics (which do not contain orientable local dipoles) to an applied electric field. Piezoelectric materials react both with polarization and distortion and, because of the way these are related, they are also polarized by a distortion in the absence of an electric field.
-
ly, we can induce a strain s E by applying an external field. This is the converse piezoelectric effect, which is used to produce ultrasound, whereas the direct effect is used to transform a mechanical strain into an electric signal, for instance, in gramophone pick-ups. The linearity in P - s and s - E means that there is linearity between P and E, that is, a nonpolar piezoelectric behaves dielectrically just like a normal dielectric. In addition, all materials show the electrostrictive effect. This is normally avery small field-induced strain, which originates from the fact that the equilibrium distance between atoms and the distribution of dipoles are to some degree affected by an applied field. It corresponds to the small induced polarization and thus small dielectric constant
se =
a E 2 + d E 4 -I-...
(7)
whereas the reversibility of the piezoeffect will only admit odd powers sP = B E + PIE3 + ...
(8)
Sometimes care has to be taken not to confuse the two effects. If, for some reason, the sample has been subjected to a static field E, and then a small ac signal E,, is applied, the electrostrictive strain will be
se = a ( E o + E,,)2 = a E i
+ 2aEoE,,
(9)
giving a linear response with the same frequency as the applied field. An aligning field Eo may, for instance, be applied to a liquid crystal polymer, for which the electrostrictive coefficient is often particularly large and the signal coming from this socalled biased electrostriction may easily be mistaken for piezoelectricity. Therefore, in the search for piezoelectricity, which would
2.2
indicate the lack of a center of symmetry in a material, the direct piezoeffect should be measured, whenever possible, and not the converse effect. In Fig. 5 we have in the same way illustrated how polar materials may behave in response to an external electric field E. The P- E trace is the fingerprint of the category that we are dealing with and is also characteristic of the technological potential. At the top there is the normal dielectric response with P increasing linearly up to a saturation value at high fields. In principle this behavior is the same whether we have local dipoles or not, except that with local dipoles the saturation value will be high and strongly temperature-dependent. If the molecules lack permanent dipoles, the induced local polarization is always along the field and temperature-independent. Dipolar molecules may, on the other hand, align spontaneously at a certain temperature (Curie temperature) to a state of homogeneous polarization. On approaching such a temperature the susceptibility (aP/aE) takes on very high values and is strongly temperature-dependent. We will describe this state - which is unpolarized in the absence of a field, but with a high and strongly temperaturedependent value of the dielectric susceptibility - as paraelectric, independent of whether there actually is a transition to an ordered state or not. It should be noted from the previous figure that a piezoelectric material has the same shape of the P-E curve as a normal dielectric, but it often shows paraelectric behavior with a large and even diverging susceptibility. Next, the contrasting, very strongly nonlinear response of a ferroelectric is shown in Fig. 5. The two stable states (+ P , - P ) at zero field are the most characteristic feature of this hysteresis curve, which also illustrates the threshold (coercive force) that the external field has to overcome in order to
Polar Materials and Effects
p, femlectric
t t t t t
t t t t t
t t t t t
t t t t t
t t t t t
525
two stable states
+ '
two stable states
belielectric
._/_I
Figure 5. Response of polar dielectrics (containing local permanent dipoles) to an applied electric field; from top to bottom: paraelectric, ferroelectric, ferrielectric, antiferroelectric, and helielectric (helical antiferroelectric). A pyroelectric in the strict sense hardly responds to a field at all. A paraelectric, antiferroelectric, or helieletric phase shows normal, i.e., linear dielectric behavior and has only one stable, i.e., equilibrium, state for E=O. A ferroelectric as well as a ferrielectric (a subclass of ferroelectric) phase shows the peculiarity of two stable states. These states are polarized in opposite directions (+P)in the absence of an applied field (E=O). The property in a material of having two stable states is called bistability. A single substance may exhibit several of these phases, and temperature changes will provoke observable phase transitions between phases with different polar characteristics.
flip over from one state to the other. In the solid state this behavior may be represented by BaTiO,. The response of an antiferroelectric is shown two diagrams below. The initial macroscopic polarization is zero, just as in a normal dielectric and the P - E relation is linear at the beginning until, at a certain thresh-
526
2 Ferroelectric Liquid Crystals
old, one lattice polarization flips over to the direction of the other (the external field is supposed to be applied along one of the sublattice polar directions). This is the fieldinduced transition to the so-called ferroelectric state of the antiferroelectric. (Not ferroelectric phase, as often written - the phase is of course antiferroelectric. Transitions between different thermodynamic phases by definition only occur on a change of temperature, pressure, or composition, that is, the variables of a phase diagram.) The very characteristic double-hysteresis loop reveals the existence of two sublattices as opposed to a random distribution of dipoles in a paraelectric. From the solid state we may take NaNbO, as representative of this behavior. It is not without interest to note that the structure of NaNbO, is isomorphous with BaTiO,. The fact that the latter is ferroelectric whereas the former is antiferroelectric gives a hint of the subtleties that determine the character of polar order in a lattice. At the limit where the hysteresis loops shrink to thin lines, as in the diagram at the bottom, we get the response from a material where the dipoles are ordered in a helical fashion. Thus this state is ordered but has no macroscopic polarization and therefore belongs to the category of antiferroelectrics. It is called helical antiferroelectric or heliectric for short. If an electric field is applied perpendicular to the helical axis, the helix will be deformed as dipoles with a direction almost along the field start to line up, and the response P - E is linear. As in the normal antiferroelectric case, the induced P value will be relatively modest until we approach a certain value of E at which complete unwinding of the helix takes place rather rapidly. Although the helielectric is a very special case, it shares the two characteristics of normal antiferroelectrics: to have an ordered distribution of dipoles (in
contrast to random) and a threshold where the linear response becomes strongly nonlinear (see Fig. 5 ) . In the solid state this behavior is found in NaNO,. In the middle diagram of Fig. 5 we have also traced the P - E response for the modification of an antiferroelectric, which we get in the case where the two sublattices have a different polarization size. This phase is designated ferrielectric. Because we have, in this case, a macroscopic polarization, ferrielectrics are a subclass of ferroelectrics. It also has two stable states as it should, although the spontaneous macroscopic polarization is only a fraction of that which can be induced. If the polarization values of the sublattices are P, and P2
2.2
liquid, this might be an attractive way to rule out at least the second problem. This is one of the facts that make ferroelectric liquid crystals very promising. As a result of these inherent problems, solid state ferroelectrics have, strangely enough, not been used for their ferroelectric properties, but rather for their superior pyroelectric (heat detectors), piezoelectric, and dielectric (very high e) properties. In addition, they are the dominating electrooptic materials as Pockels modulators as well as for nonlinear optics (NLO), e.g., for second-harmonic generation.
2.2.4 Developments in the Understanding of Polar Effects The denominations dielectric, paralectric, and ferroelectric were of course created as analogs to the names of the previously recognized magnetic materials. In the first treatise on magnetism, De Magnete (1600), Gilbert (W. Gilbert, De Magnete, Engl. transl. Dover Publications, New York 1958) describes how iron loses its magnetic (like magnesian stone) properties when it is made red-hot. He also introduced the word “electric” (like amber) for bodies that seem to be charged (but differently than the magnetic ones) or may even produce sparks. It was Faraday who divided the magnetic materials into the groups diamagnetic, paramagnetic, and ferromagnetic and he also (1839) introduced the word dielectric for materials through which electric forces are acting (which could get polarized). Confirming Gilbert’s observation, Faraday (M. Faraday, Experimental Researches in Electricity, Vol. 1-3, Taylor&Francis,London 1839-1855) also found that iron loses its ferromagnetic properties at high temperature (770 “C) and becomes paramagnetic. This temperature is today called the Curie point, or Curie temperature, for iron.
Polar Materials and Effects
527
In his thesis (1895) Pierre Curie [64] investigated the magnetic properties of a number of different materials. He found that the magnetic susceptibility is independent of temperature for diamagnetic materials. For paramagnetic materials (like oxygen) he found a relation of the type of Eq. (5). A different relation
x=-
C T-T,
was found for such bodies that showed ferromagnetism, on approaching the ferromagnetic state from above. That is, the susceptibility does not diverge at T=O (in which case one would not observe a divergence), but at a finite temperature T,, which is the temperature below which the body is ferromagnetic. When Curie’s friend and colleague Paul Langevin in 1905 deduced the formulae corresponding to Eqs. (3), (4), and ( 5 ) it was the first microscopic physical theory relating to macroscopic phenomena [65], in this case to the measured magnetization M and magnetic susceptibility 8MI8H. Thus Langevin found for C, the Curie constant, the value Np2/3k where p is the magnetic moment of the atom. The electric case reflected in our Eqs. (3), (4), and (5) withp instead of p,is of course modeled in exact analogy to the magnetic case. One year later, in 1906, Weiss [66], at that time professor at the ETH in Zurich, attacked the problem of ferromagnetism by a phenomenological theory similar to that presented in 1873 by van der Waals in his thesis on the condensation of a gas to a liquid [J. D. van der Waals, On the Continuity of Gas and Liquid State, Engl. transl. in Physical Memoirs, London 18901. Weiss introduced the notion of a “molecular field”, the average field on a certain magnetic moment caused by its magnetized environment, and set this field proportional to the external field H . In doing this, he
x=
528
2
Ferroelectric Liquid Crystals
could account for the spontaneous magnetization of ferromagnets, and he was able to deduce a relation for the susceptibility corresponding to Eq. (lo), which since then has been called the Curie-Weiss law. The divergence of at the Curie temperature T, corresponds to the divergence of the compressibility of a fluid at the critical point. The approach by Weiss has been very successful and a longstanding model for descriptions of condensed matter phenomena which go under the name of “mean field theories”. The word dielectric is analogous to diamagnetic. Physically, however, dielectric does not correspond to diamagnetic in any other sense than, that the effects are very general, whereas paraelectric and paramagnetic effects can only be found where we have orientable electric and magnetic dipoles. In fact, there is no electric effect corresponding to diamagnetism, the origins of which (in the classical description) are induced atomic and therefore lossless currents (“superconductivity on an atomic scale”) and which therefore give a small magnetization against the applied field, corresponding to a negative susceptibility. As, in contrast, the general dielectric effect and the more special paraelectric effect do not differ in sign, the reason to make a distinction between them is not generally felt as very strong, except when we want to express the fact that in the dielectric effect (in the narrow sense) there is no temperature dependence, because the dipole does not exist prior to the application of the field, but is only created by the field, just as in the diamagnetic case. Dielectric and diamagnetic effects are therefore also always present in paraelectric and paramagnetic materials, but can on the other hand usually be neglected there. While electric phenomena connected to matter seem to have been observed, like the
x
magnetic ones, even in ancient times, their investigation and comprehension is of a more recent date. Curiosity about these phenomena was raised in about 1700, when Dutchmen in foreign trade brought tourmaline from Ceylon to Europe. They observed how these rodlike crystals acquired a force to attract light objects, like small pieces of paper, when heated. The first scientific description [67] was given in 1756 by the German Hoeck (Aepinus) working in Berlin and then mainly in Russian Saint Petersburg. Brewster in Scotland, who made a systematic study on a number of minerals [67], coined the name pyroelectric in 1824. However, it was necessary to wait until the present century to really get an understanding of the phenomenon, and the historical name (pyro etymologically related to fire) is a very unfortunate one. It is true that a change ATin temperature causes the appearance of a polarization P , and pyroelectricity is often defined this way. Still, it is not really the heart of the matter. Brewster’s colleague in Glasgow, Lord Kelvin, who worked out (1878 - 93) the basic thermodynamics of the pyroelectric effect and its converse, the electrocaloric effect (heat dissipation on applying an electric field) suggested [69] that pyroelectric materials have a permanent electric polarization. This is the basic thing: a pyroelectric has a spontaneous macroscopic polarization, i.e., it is an electric dipole in the absence of an external field. The pyroelectric effect, however, important it may be for applications, is only a secondary effect, just a manifestation of the temperature dependence of this polarization. The charged poles in a pyroelectric cannot normally be observed, because they are neutralized in a rather short time by the ubiquitous free charges which are attracted by the poles. (As there are no free magnetic charges, such a screening does not occur in a magnet, which makes magnetic phe-
2.2 Polar Materials and Effects
nomena simpler in many respects than the corresponding electric phenomena). However, the magnitude (and in rare cases even the direction) of the polarization is generally a function of temperature, P= P(T). Hence a change ATin temperature causes an additional polarization AP which is not compensated by the charges present and can be observed (normally in a matter of minutes) until the redistribution of charges to equilibrium has been completed. This is also one of the standard methods to measure polarization: the pyroelectric current is integrated through an external circuit after firing a heat pulse from an infrared laser. This gives aPIaT, which is determined as a function of T . From this, P(T) is deduced. Charles Friedel, the father of George Friedel, had studied pyroelectric phenomena in crystals since 1860 and in the 1870s published a number of papers on the topic with Jacques Curie, who was his assistant in the mineralogy laboratory at Sorbonne (and later went to Montpellier as a lecturer in mineralogy). When the brothers Jacques and Pierre Curie discovered piezoelectricity in 1880, their conjecture [70] was at first that when creating surface charges by compressing the crystal they had invented an alternative method for making a pyroelectric, because they believed that there was a correspondence between thermal and mechanical deformation. This was objected to by Hankel, professor of physics in Leipzig, Germany, who pointed out that the two effects must be fundamentally different in nature and proposed the name piezoelectricity [71], which was immediately adopted by the Curie brothers. Basically we can say that temperature, being a scalar, can never change the symmetry. Therefore the polarity must already exist and be intrinsic in a pyroelectric crystal. A strain, on the other hand, being a tensor, can alter the symmetry and thereby provoke the polarity.
529
The further theory of pyro- and piezoelectricity was later essentially worked out by Voigt (the man who also coined the word “tensor”) and summarized in his monumental Lehrbuch der Kristallphysik (Treatise of Crystal Physics), which appeared in 1910 [W. Voigt, Lehrbuch der Kristallphysik, Teubner, Leipzig 19101.Voigt, who had been a student of Franz Neumann in Konigsberg and then professor of theoretical physics in Gottingen from 1883, was able to show in detail how these polar phenomena were related to crystal symmetry. In particular he showed that among the 32 crystal classes, 20 have low enough symmetry to admit piezoelectricity and, within these 20 classes, 10 have the still lower symmetry to be polar, i.e., pyroelectric. We can therefore divide dielectric materials into hierarchical categories, and this is illustrated in Fig. 6. dielectric piezoelectric
Figure 6. The hierarchy of dielectric materials. All are of course dielectrics in a broad sense. To distinguish between them we limit the sense, and then a dielectric without special properties is simply called a dielectric; if it has piezoelectric properties it is called a piezoelectric, if it further has pyroelectric but not ferroelectric properties it is called a pyroelectric, etc. A ferroelectric is always pyroelectric and piezoelectric, a pyroelectric always piezoelectric, but the reverse is not true. Knowing the crystal symmetry we can decide whether a material is piezoelectric or pyroelectric, but not whether it is ferroelectric. A pyroelectric must possess a so-called polar axis (which admits no inversion). If in addition this axis can be reversed by the application of an electric field, i.e., if the polarization can be reversed by the reversal of an applied field, the material is called ferroelectric. Hence a ferroelectric must have two stable states in which it can be permanently polarized.
530
2
Ferroelectric Liquid Crystals
In this figure, the higher, more narrow category has the special properties of the lower ones, but not vice versa. Thus, for instance, a pyroelectric is always also piezoelectric. We have also inserted in the figure the very important subclass of pyroelectrics called ferroelectrics, to which we will return in detail below. For 35 years piezoelectric materials were rather a laboratory curiosity, but in 1916, during the first World War, Langevin started his epoch-making investigations in the harbour of Toulon in southern France, to range submarines and to develop navigation and ranging systems based on his technique of producing and detecting ultrasound by means of piezoelectric (quartz) crystals. He thereby became the founder of the whole industry of sonar and ultrasonics with very important military as well as civil applications. At the end of the war, Cady, in the United States, initiated the applications of piezoelectric crystals for oscillators and frequency stabilizers, which subsequently revolutionized the whole area of radio broadcasting, and set a new standard for the measurement of time prior to the arrival of atomic clocks (up until 1925, when quartz oscillators took over; the frequency of the electronic master clocks was still set by tuning forks). In the meantime Debye, who the year before had been appointed professor of theoretical physics at the University of Zurich, in 1912 introduced the idea of “polar molecules”, i.e., molecules with a permanent electric dipole moment (at that time a hypothesis) and worked out a theory for the macroscopic polarization in analogy with Langevin’s theory of paramagnetic substances. He found, however, that the interactions in condensed matter could lead to a permanent dielectric polarization, corresponding to a susceptibility tending to infinity for a certain temperature, which he
proposed to be the analog to the Curie temperature for a ferromagnet. In the same year, Schrodinger in Vienna, in his habilitation thesis [72] applied the model to solids and concluded that all solids ought to become “ferroelectric” at sufficiently low temperatures. Thereby he coined the word ferroelectric even before such a similar state was to be found eight years later. (The state in Schrodinger’s anticipation does not quite cover the concept in the sense it is used today.) After the first World War, the strategic importance of piezoelectric materials was fully recognized and research was intensified on Rochelle salt, whose piezocoefficients had been found to be much higher than those of quartz. It became the thesis subject for Valasek of the University of Minnesota. Valasek recognized the electric hysteresis in this material as perfectly analogous to magnetic hysteresis [I] and also used the word Curie point for the transition at 24 “C. Thereby the phenomenon of ferroelectricity was discovered (although it was not quite recognized in the beginning). After some time, it was found that ferroelectric materials were not only extremely interesting as such, but also had the most powerful piezoelectric and pyroelectric properties. Important research projects were started in Leningrad headed by Kurchatov who founded the Russian school and wrote the first treatise on ferroelectricity (or “seignette electricity” as it was previously often called after the French name on Rochelle salt) [73]. In Zurich, Busch and Scherrer (the latter initially studied both in Konigsberg and with Voigt in Gottingen) discovered [74] the important ferroelectric KDP (Curiepoint 123 K) in 1935. When Landau in 1937 presented his very general framework based on symmetry changes in phase transitions [75], it would gradually come to dominate the whole area of phase transitions and collec-
2.2
tive phenomena. Mueller at ETH, independently, worked out a similar theory [76] and applied it successfully to KDP. Finally, wartime research efforts during the second World War led to the discovery in 1945 of the very important perovskite class starting with barium titanate (BaTiO,, with the conveniently located Curie point of 120“C) by Wul and Goldman at the Lebedev Institute in Moscow [77,78] and, probably independently, in 1946 by von Hippel and his group at MIT in the U. S. A. [79]. In the same year, Ginzburg applied the Landau theory for the first time to the ferroelectric case (of type KDP) [80]. Today, still no unified microscopic theory is available for these different ferroelectrics. This is a good argument for using phenomenological theories, which we will do in the following. These theories also have the advantage that they can be applied to ferroelectric liquid crystals. Finally, a comment has to be made about the polar materials called electrets. The word itself was introduced by Heaviside at the end of the last century [8 I] to designate a permanently polarized dielectric, in analogy with the word magnet. It has, however, hardly been used in that general sense, but has instead acquired a special meaning. In current terminology, an electret is a dielectric that produces a permanent or rather quasi-permanent external field, which results from the ordering of molecular dipoles or stable, uncompensated surface or space charges [82]. The first electrets were prepared by Eguchi [83, 841 at practically the same time as the discovery of ferroelectrics by Valasek. Normally electrets are made by orienting dipoles, or separating, or injecting charges by a high electric field (for instance, in a corona discharge) acting on materials like natural waxes or resins or, in modern times, organic polymers, and then cooling down the material in the presence of the field such that the charges, or dipoles, stay
Polar Materials and Effects
53 1
trapped (thermoelectrets). A powerful modern method is to inject charge in the material directly by an electron or ion beam (charge implantation). Amorphous selenium and other inorganic materials can also be used as electrets in which charges are separated by illumination in the presence of the field (photoelectrets). Common to all electrets is the fact that the polarization or space charge is a non-equilibrium condition. These materials are therefore in a “glassy”, metastable state and their polarization in principle slowly decays with time, more rapidly at higher temperatures. However, for practical purposes their long-term stability can be very high and their industrial importance is enormous both for electroacoustic devices (electrets are used in almost all small earphones, microphones, and loudspeakers), sensors and transducers (ultrasound and touch devices). The typical electroacoustic electret is a thin foil of polyimide, polyethylene, or teflon (polytetrafluoroethylene), 5 - 50 pm thick, with one side metallized and charged to about 20 nC cm-2 (corresponding to 10 V/pm) and in extreme cases up to 500 nCcm-2. Although liquidcrystalline electrets are presently a subject of some research activity, especially in connection with NLO applications, electrets will not be considered further in this chapter. The development of ferroelectric materials and concepts has been reviewed by Fousek [3] and, with particular emphasis on historical details, by Busch [85] and Kanzig [861.
2.2.5 The Simplest Descriptions of a Ferroelectric As mentioned above, Debye concluded that the interaction between local dipoles could lead to a permanent dielectric polarization. The mechanism can be described as follows:
532
2 Ferroelectric Liquid Crystals
As long as the polarization is small, it is directly proportional to the applied field according to Eq. ( 4 ) . However, as P becomes large, it begins to contribute to the field at the site of the dipoles. If we consider one of them, it will be in a field E superposed by an average field created by the other dipoles, which will be proportional to P. If we call the proportionality constant 1,we can replace E in Eq. ( 4 ) by ( E + AP)to give P=
Np2 ( E + AI’) 3kT
Solving for P gives
p = - NP2 . E 3k T-;1Np2/3k and for the susceptibility
We see that the susceptibility diverges and becomes infinite when T approaches the value
which means that at this temperature we can have a nonzero polarization P even if the external field E turns to zero. T, is therefore the Curie temperature at which the dielectric goes from the paraelectric to the ferroelectric state. In Eq. ( 5 ) we introduced the Curie constant C equal to Np2/3k. With this inserted in Eq. (1 l), the susceptibility can be written as C &OX = -
T-T,
This corresponds to the Curie - Weiss law for magnetic phenomena and has the same name for polar materials. In fact, Eqs. ( 1 1) to ( 1 5 ) are just the mean field description by Weiss, applied to polar materials.
It may be pointed out that, although Eq. ( 1 1) correctly connects the ferroelectric state to an instability, the numerical value required for the phenomenological coefficient A turns out (just as in the Weiss theory of ferromagnetism) to be quite unrealistic. Most polar materials should also be expected to be ferroelectric according to this model, in disagreement with experience. On the contrary, the collective interaction of an assembly of dipoles may not mean that the lowest state is one where all dipoles are directed in the same manner. The general problem is still unsolved, but in 1946 Luttinger and Tisza [87] were able to show that an assembly of dipoles forming a simple cubic structure has a lower energy in antiparallel fashion (antiferroelectric order) than in one where all dipoles are in the same direction. As a matter of fact, antiferroelectrics are much more common in nature than ferroelectrics ! The paraelectric - ferroelectric instability is thus considerably more complex than indicated by the ideas behind Eq. (11). We may also notice that the instability described by this formalism corresponds to the very general concept of positive feedback, describing how an instability appears in a system. For instance, the diverging susceptibility describing the transition from paraelectric to ferroelectric at the instability point T, corresponds to the diverging gain when an electronic amplifier makes the transition to a self-sustaining oscillator at a certain feedback coefficient p (the fraction PV of the output voltage is fed back to the input voltage Vi). These analogous cases are compared in Fig. 7. It may be pointed out in advance that in liquid crystals there is no such instability connected with polar interactions. The Landau description, although in essence a mean field theory, is a phenomenological description of far greater generality
2.2
Polar Materials and Effects
533
gain CP ) spontaneous oscillator amplifier
Figure 7. Phase transition from paraelectric to spontaneously polarized state in a ferroelectric, compared to the state transition in an amplifier when the gain V/Vi =
1IA
\P
and penetration than our discussion so far. Even from its simplest versions, deductions of high interest can be made. We begin by introducing an order parameter, and in this case we naturally choose the polarization P , describing the order in the low temperature phase (P#O) and the absence of order in the paraelectric phase ( P = 0). The order parameter is a characteristic of the transition and should conform to the symmetry of the high temperature phase as well as to that of the low temperature phase. We expand the free energy in powers of P
G ( T ,P ) = G o ( T ) + r a ( T ) P 2 2
Often, the high temperature phase has a center of symmetry (for instance, the cubic paraelectric phase of BaTiO,). If the high temperature phase is piezoelectric (as in the case of KH,PO,, abbreviated KDP), the free energy nevertheless cannot depend on the sign of strain and polarization. It is also true that the two states of opposite polarization in the low temperature ferroelectric phase are energetically equivalent. G is therefore invariant under polarization reversal ( P + - P ) and only even powers can appear in the Landau expansion. It may be noted that no such invariance is valid for a pyroelectric material, and that a corresponding Landau expansion cannot be made. Sometimes expressions of this type (Eq. 16)
A diverges 1 - BA for p= 1/A. A is the amplificatidn at zero feedback. ~
are called Taylor series expansions, which is rather misleading because the coefficients bear no relation to Taylor coefficients. In fact (and we will see examples of this later) the expression is of a far more general nature and, in addition to powers of several order parameters and their conjugates and coupling terms, may contain scalar invariants of their components as well as their derivatives of different order. Generally speaking, the terms included in the Landau expansion have to be invariant under all symmetry operations of the high temperature phase. (Then they are also automatically invariant under those of the low temperature phase, whose symmetry group is here assumed to be a sub-group of that of the high temperature phase.) As for the coefficients, we have indicated a temperature dependence of a, which we will express with the simplest straightforward choice
u ( T )= cx ( T - T,) , cx > 0
(17)
It is further assumed that b and c in Eq. (16) are small and both positive in the first instance. The term Go(T)is often included in G on the left side. Equation (17) means that the coefficient a changes sign at the temperature T,. For T>T,, a is positive and the free energy (now with Go included) will be a simple parabolic function at the origin, according to Eq. (16), thus with a minimum for P= 0. For T < T,, the free energy will have a maximum instead (see Fig. 8 a). When P grows larger, however, the 9 term
534
2
Ferroelectric Liquid Crystals
Figure 8. The free energy as a function of the order parameter according to the Landau expansion Eq. (16) with Eq. (17). For T > Tc, G has a minimum for the order parameter of zero (P=O, corresponding to the paraelectric phase); for T
takes over and will yield two symmetrically situated minima, corresponding to a nonzero polarization which can take the opposite sign. At T,, the P2 term vanishes and G becomes -P4, giving a curve which is very flat at the origin (see Fig. 8 b). The equilibrium value of P is obtained by minimizing the free energy with respect to this variable, thus
If we apply an electric field, we have to include the term -PE in the Landau free energy. The field E is here the thermodynamic intensive conjugate variable to P. In the presence of a field, we have of course a nonzero polarization even in the paraelectric phase for T>T,. However, as P is small, we only keep the P2 term from Eq. (14) and write
ac =a(T ap
G = -1~ ( T - T , ) P ~ - P P E for T > T , (21) 2
- T,)P +
b$
+ cP5 = 0
(18)
which gives, if we disregard the fifth power,
P [ a ( T- T,)
+ bP2] = 0
(19)
For T > T,, the only real solution is P = 0, describing the paraelectric phase. For T < T,, we get
P=
JF
-(T,-T)
Minimizing the free energy now gives @=a
ap
describing how the spontaneous polarization increases smoothly from zero in a parabolic fashion when we decrease the temperature below the Curie point T,. This is characteristic for a second-order phase transition and qualitatively conforms well with real behavior in most ferroelectric materials. If b was negative instead and c positive, we would have had to include the original P6 term and would have found a (weakly) first-order transition with P making a (small) jump to zero at the Curie point, but we will not pursue this matter further.
(22)
i.e., a polarization proportional to the applied field according to
P= 112
(-~ T,) P - E = 0
E a ( T - T,)
and a corresponding susceptibility
ap = -
1
1
aE
a(T-T,)
i.e., the Curie-Weiss law describing the divergence of when we approach the Curie temperature from above. Let us compare this to the situation in the ordered (ferroelectric) phase ( T c T , ) . As P is now not small, we have to include the P4 term in G and therefore write
x
1 4 - PE G = -1a ( T - T,)P2 +-bP 2 4 for T < T,
(25)
2.2
Minimizing with respect to P gives @ = CX(T - T',)P ap
+ bP3 - E = 0
(26)
and, differentiating with respect to E (remembering that q,x=dP/aE)
a ( T - T c ) ~ x 3+b P 2 6 x = 1
(27)
Polar Materials and Effects
535
ity in the condensed phase is half of that in the disordered phase. The reason for their difference is evident: the effect of an external field on the polarization must be smaller in the condensed phase, due to the existing internal field (molecular field) in that phase, which has a stabilizing effect on the polarization. We may also write this as
If we insert P2=(alb)(T,-T), according to Eq. (20), into this expression we get
1 €Ox = 2a(T,- T )
Our results are summarized in Fig. 9. Analytically, we can express them as
P-IT-T',I P
(29)
x - 1 T - T, 1 - y x - =1p +
(30) (31)
with the so-called critical exponents p= 112 and y= 1, for the order parameter and susceptibility characteristic of the Landau description or, more generally, of mean field models. On approaching the Curie point from below, the susceptibility diverges just as on approaching from above, with the dif1 ference that x(T T,). This is 2 a general mean field result: the susceptibil-
T
because it also means that the Curie constant above and below the transition differs by a factor of two. Graphically this is most easily seen if we plot the inverse of the susceptibility as a function of the temperature, as in Fig. 10. In passing it may be mentioned that no such critical behavior (no divergence in would be observed if the low temperature phase has antiferroelectric order, corresponding to the fact that such a phase has zero macroscopic polarization. Finally, let us look a little closer at the behavior in an external field both above and below the Curie point. We will rewrite the free energy from Eq. ( 2 5 )in a slightly more expanded form (33) 1 2 1 4 1 6 G=Go+-aP +-bP +-CP +...- PE 2 4 6
x)
Minimizing the free energy with respect to P at constant external field E
T
Figure 9. The growth of the order parameter P(Q, in this case representing ferroelectric polarization below the Curie point TC,together with the corresponding 1 ap susceptibility x= above and below the phase EO FIE transition.
Figure 10. The inverse dielectric susceptibility following a Curie law with different Curie constants (C+/C-=2) above and below the Curie point T,.
536
2 Ferroelectric Liquid Crystals
yields
E = aP
+ bP3 + cP5 + ...
(35)
Sometimes this is written (including ~0 in 1P E =-
X
+ 5P3+ c P 5
x)
(36)
where the values of 5 and are given as measure of the dielectric nonlinearity. Let us again neglect the highest power and write E = a ( T - T,)P
+ bP3
(37)
When T > T, we may also discard the P 3 term and see that
E
- P (paraelectric state)
(38)
whereas for T = T, we get a purely cubic relationship
E-P3
(39)
A graphic illustration of Eq. (37) is given in Fig. 11. The P - E curves are analogous to van der Waals isotherms. For the isotherm at T= T,, instead of Eq. (39) we write p
-
(40)
introducing a third critical exponent 6, with
the value 6=3 for the critical isotherm of the order parameter. This value, 6=3 , is also a characteristic of mean field theories. For T< T,, we clearly recognize the shape of a hysteresis loop (emphasized in Fig. 1 1) connected with the presence of an instability. Whereas P follows the field in a normal fashion when we reverse the sign of E at T>T,, and much more dramatically at T= T,, P does not change sign at first below the Curie point. But P is now not a singlevalued function of E, and below the value -Ec, the decrease in P no longer follows the upper curve but continues, after a jump, along the lower curve. We also see that below T, there are two stable states for E=O. In Fig. 12 the free energy as a function of polarization according to Eq. (33) is sketched (the P6 term can here be neglected) for three different values of the external field. The stable states for P correspond to the minima of G. In a ferroelectric sample these are seen in the spontaneous domains. For a sufficiently high field, E, (corresponding to E, in Fig. 1l), the oppositely directed polarization state becomes metastable and the polarization is reversed.
G
E
Figure 11. Graphic representation of E=aP+bP3. This strongly nonlinear relationship P(E) describes the ferroelectric hysteresis (emphasized) appearing for T < T,. Two stable states of opposite polarization exist at E=O. A field superior to the coercive field E, has to be applied in order to flip one polarization state into the other.
Figure 12. The free energy as a function of polarization for different values of the external field. The symmetrical curve for E=O for which the two polarization states &,' are stable has been emphasized and E, > E , corresponds to the coercive field E, which destabilizes the -Po state.
2.2
2.2.6 Improper Ferroelectrics So far it has been assumed that the polarization is the variable that determines the free energy, but it may happen that the transition is connected to, i.e. occurs in a completely different variable, let us call it q, to which a polar order can be coupled. A polarization P appearing this way may affect the transition weakly, but it can only have a secondary influence on the free energy. We will therefore call q and P, respectively, the primary and secondary order parameters, and the simplest Landau expansion in those two Darameters can be written (41) G=-a(T)q2+-bq 1 1 4 1 - 1P2 -AqP 2 4 2
+-xo
We note, already from the presence of the coupling term -Aq P , that the Landau expansion is not a “power series”, cf. the previous comments made with reference to the expression (16). If q and P have the same symmetry, i.e., if they transform in the same way under the symmetry operations, then a bilinear term of the form -A4P must be admitted since it behaves like the other terms of even power. The minus sign means that the free energy is lowered due to the coupling between q and P. The coupling constant Ais supposed to be temperature-independent. The fact that q appears to the fourth power, but P now only to the second, reflects their relative importance. Instead of using c as the coefficient in front of the P2 term, it is convenient to introduce the symbol ~ 0 ’ We . assume that in contrast to the coefficient a(T) in front of q2,does not depend on temperature, which also reflects the fact that P is not as a transition parameter. In fact, it can often be shown thatx;’-T, which in practice means that it is temperature independent compared to a coefficient varying like T-T,, where T, lies in the region of experimental interest. As will be dis-
x;’,
Polar Materials and Effects
537
xo
cussed in detail later, takes the form of a special kind of susceptibility. The equilibrium values of q and P are obtained by minimizing G with respect to these variables. Let us begin with P. From
we see that P will be proportional to the primary order parameter (43)
p = Axoq Continuing with
&?= a ( T - TJq + bq3- Q = 0 a4
(44)
and inserting P from Eq. (43), we get
+ bq3 = 0
- A2xo]q
(45)
a(T- Ti)q + bq3 = 0
(46)
[ a ( T - T,) or
with (47) Equation (46) is the same relation as Eq. (19), hence q in the ordered phase will grow in the same way as the primary order parameter P in our previous consideration, i.e., according to Eq. (20), or q(T)
- (Ti - T)1’2
(48)
Equation (43) shows that this is also true for P as the secondary order parameter. However, we have a new Curie temperature given by Eq. (47), shifted upwards by an amount AT= Ti - T, (49) Thus the coupling between the order parameters will always raise the transition temperature, i.e., stabilize the condensed
538
2 Ferroelectric Liquid Crystals
phase. As we can see, the shift grows quadratically with the coupling constant A. Let us now look at the dielectric susceptibility in the high temperature phase (T> TL).Both the order parameters q and P are zero in the field-free state, but when an electric field is applied it will induce a polarization and, by virtue of the coupling between P and q, also a nonzero value of q. In the high temperature phase we will thus have a kind of reverse effect brought about by the same coupling mechanism: whereas in the low temperature phase a non-zero q induces a finite P, here a non-zero P induces a finite q. The values of P and q above TG are small, so we can limit ourselves to the quadratic terms for G and write
G =1 a q 2 +l xO'P2-Aq P - P E 2 2
(50)
We then find
giving
Because P is proportional to E , in the high temperature phase we induce a nonzero value of the order characteristic of the low temperature phase by applying a field, and this order is proportional to the field. In liquid crystals, the electroclinic effect is an example of this mechanism. This is not a normal pretransitional effect, because it is mediated by the kind of order that shows no translational instability and its susceptibility ~ x = ( a P f a E ) Sometimes . it will also be convenient to introduce a corresponding susceptibility for q, = aq/aE. If we minimize G with respect to P in Eq. (50)
xq
(53)
and insert q from Eq. (52),we find
P(l -
%)
= XOE
(54)
Therefore
(55) or Eo
x = x o TT--TT,',
Finally, with TL- T, =AT= A2xo/a, we obtain the expression &OX = xo
A2xo +T-T,
(57)
If the coupling constant ilis sufficiently large, we see that will satisfy the CurieWeiss law. Then the dielectric susceptibility will indeed show a divergent behavior, although P is not the transition parameter. If A is small, the susceptibility will instead be practically independent of the temperature except in the vicinity of T,, where we might observe some slight tendency to a divergent behavior. In conclusion, the case where q and P have the same symmetry in many respects resembles the case where P is the primary order parameter. When there is a strong coupling between the two order parameters we might not see too much of a difference. In the case where q and P do not have the same symmetry properties, the term -Aq P is not an invariant and cannot appear in the Landau expression. Therefore it must be replaced by some other invariant like -q2P (depending on the actual symmetries) or similar terms like q2PiP,. The coupling will then take on a different character. In the case where we have two order parameters q 1 and q2, which couple to P , we may have a term - q l q 2 P , and so on. In this last case, Blinc
x
2.2
and gek3 found ([30], pp. 45,58) that P will not be proportional to q1 and q2,but to their squares, which means that P will grow linearly below the transition point To
P-(To-T)
(58)
as in norinstead of parabolically [Eq. (20)], mal ferroelectrics. Furthermore, the susceptibility is found to be practically independent of temperature above To,as well as below it, and makes a jump to a lower value when we pass below To.The nondivergence of the susceptibility is due to the fact that the fluctuations in q1 and q2 are not coupled to those of P in the first order in the high temperature phase [30], hence does not show a critical behavior. Ferroelectrics in which the polarization P is not the primary order parameter are called improper ferroelectrics. The concept was introduced by Dvorak [88] in 1974. As we have seen in the last example, improper ferroelectrics may behave very differently from proper ferroelectrics. The differences are related to the nature of the coupling. If we write the coupling term -Aq"P, our first example showed that for n = 1, the behavior may, however, be very similar to that of proper ferroelectrics. This class of improper ferroelectrics for which IZ = 1 is called pseudoproper ferroelectrics. Ferroelectric liquid crystals belong to this class.
Polar Materials and Effects
539
stress. The stress (T is a "field" corresponding to the field E and in a thermodynamic sense the intensive conjugate variable to the extensive variable s, just like E is to P (or H to M , or T to S, etc.). If we suppose that the elastic energy is a quadratic function of the strain, we can write (for materials in general)
(59) so that we deduce the equilibrium strain from
x
or
Thus the strain is a linear function of the applied stress (Hooke's law). The Landau expansion for a paraelectric phase with piezoelectric properties will now contain this new term in addition to a coupling term 4 s P , of the same form as in our previous case
G = - 1u P 2
The paraelectric phase has higher symmetry than the ferroelectric phase. However, it might have sufficiently low symmetry to allow piezoelectricity. In the case where the paraelectric phase is piezoelectric, it will become strained when electrically polarized. In addition to the term -PE there will appear a term -so in the free energy, where s designates the strain and (T the applied
+-s
1
2
-AsP-s(T-PE
(62)
2x0
NOW,aG/aP= 0 and aG/& = 0 give the equilibrium values of P and s, according to
aP-L
2.2.7 The Piezoelectric Phase
2
-E
=0
or
E=aP-as and
1
-$
xo
-a p -0=
or 1 (T=---aP
xo
o
(63)
540
2 Ferroelectric Liquid Crystals
If we arrange the experimental conditions such that we apply an electric field at the same time as we mechanically hinder the crystal’s deformation (this is called the “clamped crystal” condition), then s = 0, and Eq. (64) gives
E=aP
(67)
Hence
ap l=az whence
Thus we see again that the coupling raises the transition temperature. As an example, the paraelectric - ferroelectric transition point in a “free” crystal KDP lies 4 “C higher than for a clamped crystal. The reason that the Curie point is lower in the clamped crystal is that the mechanical clamping eliminates the piezocoupling. Finally, we want to see how the piezocoefficients behave at the transition. These coefficients dijkare tensors of rank three defined by
p i = d.. CJk 0. Jk
Thus the Curie law is fulfilled. In this situation a stress will develop to oppose the effect of the field and its induced polarization. Its value is, from Eq. (66)
o=-aP (70) If instead we have the “free crystal” condition, there can be no stress and, with o=O
but as the tensorial properties do not interest us for the moment we continue to use a scalar description and write
Due to the appearance of the two conjugate pairs so and PE in the free energy expression (Eq. 62), a Maxwell relation
in Eq. (65), we get = axop
(79) (71)
The insertion of s in Eq. (64) now gives E =aP
-
a2xop
(77)
(72)
exists, which allows a very simple calculation of d. Rewriting Eqs. (64) and (66) to eliminate P in order to form d= (aslaE), yields
or, differentiating with respect to E (73)
and
Thus This gives or &OX =
1
a ( T - T,’)
~~
with a new Curie point
d=
(75)
ax0
a-
a2xo
If we compare this with Eqs. (74) and ( 7 3 , it is evident that it can be reshaped to ax0 d ( T )= -~ a(T-Ti)
2.3 The Necessary Conditions for Macroscopic Polarization in a Material
Hence the piezocoefficient diverges just like the dielectric susceptibility at the paraelectric - ferroelectric transition. This divergence has other consequences: because of the piezoelectric coupling between polarization and elastic deformation, it will influence the elastic properties of the crystal. If we look at the coefficient relating the strain to an applied stress, it can be measured under two different conditions, either keeping the electric field constant or keeping the polarization constant. In the latter case the crystal behaves normally, it stays “hard” when we approach the transition. In the former case the elastic coefficient diverges just like d, i.e., the crystal gets anomalously soft when we approach the transition. The formalism developed in this section was first used to describe the piezoelectric effect. It was later employed to treat the electroclinic effect in orthogonal chiral smectics. As will be seenin Sec. 2.5.7-2.5.8 there are very close analogies, but also some characteristic differences between the two effects.
2.3 The Necessary Conditions for Macroscopic Polarization in a Material 2.3.1 The Neumann and Curie Principles When we are dealing with the question of whether a material can be spontaneously polarized or not, or whether some external action can make it polarized, there are two principles of great generality which are extremely useful, the Neumann principle and the Curie principle. Good discussions of these principles are found in a number of books, for instance [24, 36, 891. The first of
54 1
these principles, from 1833 and named after Franz Neumann, who founded what must be said to be the first school of theoretical physics in history (in Konigsberg), says that any physical property of a medium must be invariant under the symmetry operations of the point group of the medium. The second, from 1894, after Pierre Curie, says that a medium subjected to an external action changes its point symmetry so as to preserve only the symmetry elements common with those of the influencing action. Symbolically we may write the Neumann principle as
KcP
(84)
i.e., the crystal group either coincides with P, the property group, or is a subgroup of P, and the Curie principle as
k=KnE
(85)
i.e., the point symmetry K changes to k: the highest common subgroup of K (the crystal group) and E (the external-influence symmetry group). This means that, in particular, if
KcE
(86)
then
K=K
(87)
i.e., if K is a subgroup of E, then the crystal symmetry is not influenced by the external action. The Neumann and Curie principles have long been the dominating symmetry principles in condensed-matter physics. Both can be formulated in a number of different ways. For instance, the Neumann principle may be stated as follows: ‘the symmetry elements of an intrinsic property must include the symmetry elements of the medium’. This formulation stresses that every physical property may and often does have higher symmetry, but never less than the medium.
542
2
Ferroelectric Liquid Crystals
A well-known example of this is that cubic crystals are optically isotropic, which means that the dielectric permittivity has spherical symmetry in a cubic crystal. Another example is that the thermal expansion coefficient of a cubic crystal is independent of direction. In fact, if it were not, the crystal would lose its cubic symmetry if it were heated. Thus, as far as thermal expansion is concerned, a cubic crystal “looks isotropic” just as it does optically. Since, according to Neumann’s principle, the physical properties of a crystal may be of higher symmetry than the crystal, we will generally find that they range from the symmetry of the crystal to the symmetry of an isotropic body. A more general example of higher symmetry in properties is that such physical properties characterized by polar second rank tensors must be centrosymmetric, whether the crystal has a center of symmetry or not, cf. Fig. 27. For, if a second rank tensor T connects the two vectors p and q according to p 1. = TIJ. . qJ .
(88)
and we reverse the directions o f p and q, the signs of all the components pi and qj will change. The equation will then still be satisfied by the same Tijas before. How can we know that the Neumann principle is always valid? Consider, for the sake of argument, that the crystal group K had a symmetry operation that was not contained in the property group P. Then, under the action of this operation, the crystal would on the one hand coincide with itself, and on the other, change its physical properties. This inherent contradiction proves the validity of the principle. This principle is often used in two ways, although it works strictly in only one direction. Evidently, it can be used to find out if a certain property is permitted in a medium, the symmetry of which is known. However, it may and has also been used (with caution) as an aid in the proper crys-
tallographic classification of bodies from the knowledge of their physical properties.
2.3.2 Neumann’s Principle Applied to Liquid Crystals The general application of the Neumann principle in condensed matter is normally much more formalized (for instance, involving rotation matrices) than we will have use for. Few textbooks perform such demonstrations on an elementary level, but there are exceptions, for example, the excellent treatise by Nussbaum and Phillips 1901. For a liquid crystal, we illustrate the simplest way of using the symmetry operations of the medium in Fig. 13. (The same discussion, in more detail, is given in [46]). We choose the z-direction along the director as shown in Fig. 13a and assume that there is a nonzero polarization P = (P,, Py, P,) in a nematic or smectic A. Rotation by 180 O around the yaxis transforms P, and P, into -P, and -Pz, and hence both of these components must be zero, because this rotation is a symmetry operation of the medium. Next, we rotate by 90 O around the z-axis, which transforms the remaining Py into P,. If therefore P , were nonzero, we would see that the symmetry operations of the medium are not symmetry operations of the property, in violation of Neumann’s principle. Hence Py=O and P will vanish. In Fig. 13.b we have illustrated the C phase, normally occurring at a second-order phase transition A +C at a certain temperature T,, below which the molecules start to tilt, and with an order parameter than can be written as Y= 8eiV,where 8is the tilt angle with respect to the normal and cp is the azimuthal angle indicating the direction of tilt in the layer plane. The variable cp is a phase variable (the transition is helium-like) with huge fluctuations; the director in the C phase
2.3 The Necessary Conditions for Macroscopic Polarization in a Material (a) Nematic
Smectic A n P
t
t
IIIIIIIIIIII IIIIII 11111111111 11111 111111 1111111111
f'
R$$ng180"
+ P1=0,P=o
-bk
Rotation90" around2
P=O
Symmetry operation: rotation 180 around $ $
A
k%
--*
+
"dF
qq]
Figure 13. Neumann's principle applied to ( a ) the nematic and smectic A, ( b ) the smectic C and smectic C* phases.
therefore has a large freedom to move on a cone with half apex angle Qaroundthe layer normal. In the figure, the tilt is chosen to be in the xz-plane. Hence, a 180" rotation around the y-axis is still a symmetry operation so P can have a component in the y-direction, whereas a 90" rotation around the z-axis is no longer a symmetry operation. However, if the xz-plane is a mirror plane, then Py must be zero, because a nonzero Py goes to -Py on reflection. On the other hand, if the medium lacks reflection symmetry, i.e., is chiral, such a component must be admitted. The important concepts chiral and chirality were introduced by Lord Kelvin, who derived them from the Greek word for hand. After having contemplated such symmetry - dissymmetry questions for at least a decade, he used them for the first time in his Baltimore lectures in the fall of 1884, pub-
543
lished twenty years later [91]. He there stated, "I call any geometrical figure or group of points chiral and say it has chirality if its image in a plane mirror ideally realized, can not be brought to coincide with itself'. These concepts are used, and should be used, in exactly the same manner today. Thus, in order to let Py survive, we can put "small propellers" on the molecules, i.e., make them chiral. We could for instance synthesize molecules with one or more asymmetric carbon atoms, but it would, in principle, also be sufficient to dissolve some chiral dopant molecule in the nonchiral smectic C in order to remove the mirror plane. This can, symbolically, be written
c+*+=c*
(89)
The smectic is now chiral and may be denoted C* (which is independent of whether there is any observable helix or not). Whether the constituent molecules are chiral or whether we make the medium chiral by dissolving chiral molecules to a certain concentration c > 0, in both cases the only symmetry element left would be the twofold rotation axis along the y-direction, and a polarization along that direction is thus allowed. The symmetry of the medium is now C2,which is lower than the symmetry of the property. The polarization P, like the electric field, is a polar vector, hence with the symmetry C, (or a m in the crystallographic notation). The fact that P,if admitted, must be 90 degrees out of phase with the director, could have been said from the very beginning. The fundamental invariance condition Eq. (6) means that if there is a polarization P in the medium, it cannot have a component along n , because the symmetry operation (6) would reverse the sign of that component, and thus P must be perpendicular to IZ
P l n
(90)
544
2
Ferroelectric Liquid Crystals
It was the Harvard physicist Meyer who in 1974 first recognized that the symmetry properties of a chiral tilted smectic would allow a spontaneous polarization directed perpendicular to the tilt plane [61]. In collaboration with French chemists, he synthesized and studied the first such materials (621. These were the first polar liquid crystals recognized and as such something strikingly new. As mentioned before, substances showing a smectic C* phase had been synthesized accidentally several times before by other groups, but their very special polar character had never been surmised. Meyer called these liquid crystals ferroelectric. In his review from 1977 [43] he also discussed the possible name antiferroelectric, but came to the conclusion that ferroelectric was more appropriate. We will call the polarization P permitted by the symmetry argument just discussed, the spontaneous polarization. Leaving out its vectorial property, it is often indicated as P,. The spontaneous polarization is so far a local property, not a macroscopic one.
2.3.3 The Surface-StabilizedState According to the symmetry argument already given, the spontaneous polarization P is sterically connected with the molecule, lying along +z x n. (The plus or minus sign is a characteristic of the material.) However, the prerequisite for the existence of P was that the molecules are chiral, and the chiral interactions between them lead to an incommensurate helical superstructure, as shown in Fig. 14. Actually there are two interactions involved in the helix, one chiral leading to a spontaneous twist and one nonchiral (steric) leading to a spontaneous bend deformation in the director field (see Sec. 2.4). The phase angle cp describes a right- or left-handed helix with a period of
Figure 14. The helical configuration of the sterically coupled variables n-P in the unperturbed helical C* state. The phase angle rp changes at a constant rate if we move in a vertical direction.The variables n, P, and q are all functions of z, the vertical coordinate. The twist is exaggerated about ten times relative to the densest possible twist occurring in reality.
typically several micrometers, whereas the smectic layer periodic length is several nanometers. The helical arrangement makes the macroscopic polarization zero for the bulk sample at the same time as satisfying V . P=O everywhere. It is therefore an alternative to the domain formation in a solid ferroelectric. However, there is no coercive force in such a structure, and if we apply an electric field perpendicular to the helix axis we will wind up the helix and turn more and more of the local polarization into the field direction (see Fig. 15). The P - E response is dielectric - in fact it has the shape of the curve shown at the bottom of Fig. 5 , corresponding to an antiferroelectric with an infinitely thin hysteresis loop. This behavior is also known in the solid state, e.g., in the chiral structure NaNO,, and the order is called helicoidal antiferroelectric. A shorter useful name is helielectric. The helielectric smectic C* has zero macroscopic polarization (like an antiferroelectric), no hysteresis, no threshold, and no bistability. However, by an artifice it can be turned into a structure with very different properties. This is illustrated in Fig. 16. If the smectic layers are made perpendicular to the confining glassplates, there is no boundary condition compatible with the
2.3 The Necessary Conditions for Macroscopic Polarization in a Material I /
E
Figure 15. The helical configuration of the director-polarization couple is unwound by a sufficiently strong electric field E. The increasing field induces a macroscopic polarization (which is thus not spontaneous) and finally polarizes the medium to saturation (all dipolar contributions lined up parallel to the field), as shown to the right.
Figure 16. Elastic unwinding, by the surfaces, of the helical twist in the bookshelf geometry of smectic C*. The helical bulk state is incompatible with the surface conditions and therefore can never appear in sufficiently thin cells. The surface acts as an external symmetry breaking agent, reducing the degeneracy of the bulk to only two selected states. In the most attractive case these are symmetric, which also leads to a symmetric bistability of the device. The two memorized director states, n , and n2 ( n ; and n ; in the case of a pretilt different from zero) represent polarization states of opposite (or nearly opposite) direction.
helical arrangement. Let us assume that we can prepare the surface in such a way that the boundary condition imposed on the molecules it such that they have to be parallel to the surface, but without specified di-
545
rection. As we make the distance between the surfaces smaller and smaller, the conflict between the helical order and the surface order will finally elastically unwind the helix via the surface forces, and below a certain sample thickness the helix cannot appear: the nonhelical configuration has now a lower energy. The physical problem has one characteristic length, which is the helical period z. We can therefore expect that for a sample thickness d < z , i.e., of the order of one micrometer, the only allowed director positions will be where the surface cuts the smectic cone, because here both the intrinsic conical constraint and the constraint of the surface are simultaneously satisfied. There are two such positions, symmetrical around the cone axis and corresponding to polarization up and down, respectively. Energetically these states are equivalent, which leads to a symmetric bistability. Indeed, when very thin samples of d= 1 pm are made with the appropriate boundary conditions, spontaneous ferroelectric domains all of a sudden appear in the absence of any applied field (Fig. 17). This second step was realized five years later than Meyer’s first paper [93]. By applying an external field we can now get one set of domains to grow at the cost of the other and reverse the whole process on reversing the field. There are two stable states and a symmetric bistability ; the response has the characteristic form of a ferroelectric hysteresis loop, as represented by the second curve of Fig. 5. We might therefore call this structure a surface-stabilized ferroelectric liquid crystal (SSFLC). The surface stabilization brings the C* phase out of its natural crystallographic state and transfers macroscopic polarization to the bulk. We may note that the polarization in the helical state of Fig. 14 is denoted P and not P,. This is because the local polarization in this state does not correspond to P,, but has
546
2
Ferroelectric Liquid Crystals
Figure 17. Spontaneous ferroelectric domains appearing in the surface-stabilized state.
a second contribution due to the flexoelectric effect. This contribution, which will be discussed in detail later, is of the same order of magnitude as P,. There are several different methods to measure P,, most of them involving the application of an electric field to saturate the polarization between the two extreme states, as represented to the right of Fig. 15, and the corresponding state with the field reversed. In such a state there is no flexoelectric contribution, hence P coresponds to P, except for a contribution due to the electroclinic effect. This is an induced polarization, Pi,connected to an extra tilt 68 of the director caused by the field. The electroclinic tilt is negligible compared to 8 for T e T , , thus Piis normally quite small, but
Figure 18. Polarization as a function of temperature, as often observed in a measurement. P corresponds to the spontaneous polarization P , except in a small region around T, where an induced polarization due to the electroclinic effect may influence the measurements.
may be observable at high fields near T = T,, and may then slightly change the shape of the observed polarization curve, as illustrated in Fig. 18. The helical smectic C* state has the point symmetry D, (m22), illustrated in Fig. 19, which does not permit a polar vector. It is therefore neither pyroelectric nor ferroelectric. Nor can it, of course, be piezoelectric, which is also easily realized after a glance at Fig. 14: if we apply a pressure or tension vertically, i.e. across the smectic layers (only in this direction can the liquid crystal sustain a strain), we may influence the pitch of the helix but no macroscopic po-
Figure 19. The point symmetry of the helical smectic C* state is D, ( ~ 2 2illustrated ) by a twisted cylinder. The principal rotation axis is along the smectic layer normal and there are an infinite number of twofold rotation axes perpendicular to this axis, one of them illustrated to the right. The symmetry does not allow pyroelectricity.
2.3
The Necessary Conditions for Macroscopic Polarization in a Material
larization can appear. On the other hand, if we do the same to the surface-stabilized structure (see Fig. 20), we change the tilt 8 and thereby the local polarization P , hence i n conformity with the statement according to the scheme of Fig. 6 that if a structure is ferroelectric it also, by necessity, has to be piezoelectric. That the SSFLC structure with symmetry C2 is also pyroelectric, as it must be, is also evident, because Band thereby P is a function of the temperature T. As there is now a macroscopic polarization in this state, we have a strong coupling with the external field leading to a high-speed response according to
r-'
P.E
I
__
Y where yis a characteristic viscosity for the motion around the cone. The difference 28 between the two optic axis directions (see Fig. 16) leads to an electrooptic effect of high contrast. The high available contrast and the very high (microsecond level) speed in both directions at moderate applied voltages, together with the inherent memory, make this a very attractive electrooptic effect for a variety of applications. While the basic idea behind the work of [93] was to get rid of the helical space mod-
547
ulation of the tilt direction (i.e., of the infinity of polar axes) and achieve bistability by fitting the director to satisfy the cone condition and the surface condition at the same time, it was soon recognized in subsequent papers [94, 951 that the bistable switching demonstrated in [93] and the observed threshold behavior, the symmetric bistability, and the shape of the hysteresis curve (see Fig. 21) all came very close to the properties of materials previously classified as ferroelectrics, whereas these properties are absent in the helical smectic C* state. Therefore the concept surface-stabilized ferroelectric liquid crystal (SSFLC) was coined and used for the first time in print three years later in [96] from 1983. This was also first paper in which acceptable monodomain samples were demonstrated, awakening the interest in the display industry and pointing to the future potential of the surface-stabilized smectic C* state. With the developing skill in alignment techniques the first simple device prototypes could also be demonstrated [96a] even before room temperature mixtures were available. Finally, the study
+ Figure 20. The surface-stabilized smectic C* has C, symmetry. It has a single polar axis. A pressure applied across the layers increases the tilt angle and thereby the polarization (P-0) along the twofold axis which is perpendicular to the paper plane.
Figure 21. Oscilloscope picture showing photodiode response (change in optical transmittivity of the cell) to triangular pulses of opposite polarity (4 V peak-topeak), demonstrating threshold, saturation, memory, and symmetry bistability; cf. Fig. 11. The material is DOBAMBC at 60°C. Horizontal scale 1.5 V/div (from 1951).
548
2
Ferroelectric Liquid Crystals
of the very characteristic defect structures which showed up in monodomain samples led to the discovery of the chevron local layer structure, which will be discussed in detail in Sec. 2.8. As already pointed out, one condition for achieving the fast bistable switching and all the additional characteristic properties is to get rid of the “antiferroelectric helix” (to use the expression employed in the 1980 paper 1931). Therefore, achieving the same properties by adding appropriate chiral dopants to the smectic C* could be imagined, in order to untwist the helical structure but, as the same time, keeping a residual polarization. This is illustrated by the structure to the left in Fig. 22. However, such a hypothetical bulk structure is not stable in the chiral case. It would transform to a twisted state where the twist does not take place from layer to layer, but in the layers, in order to cancel the macroscopic polarization. For this reason, surface-stabilization requires not only that d < z , but that the sample thickness is sufficiently small to prevent the ap-
(a)
(b)
Figure 22. Director configuration for (a) a nonchiral smectic C and (b) a chiral smectic C* in its natural (helicoidal) structure (after [97]).The first could also be imagined as the bulk structure for a chiral smectic Cy with infinite pitch, which would then correspond to a macroscopic polarization P pointing towards (or from) the reader. However, such a structure is not stable.
pearance of this different twist state, by forcing it to appear on such a small length scale that its elastic deformation energy is higher than the energy of the untwisted state. The first analysis of these questions was made by Handschy and Clark 1981.
2.3.4 Chirality and its Consequences Chirality is a symmetry concept. We note from Kelvin’s definition that being chiral is a quality and that this quality is perfectly general, regardless of the nature of the object (except that it must be three-dimensional, if we speak about chirality in three dimensions as Kelvin did). Thus we may speak of a “chiral molecule” and of a “chiral phase” or medium made up of chiral molecules or of chiral or nonchiral molecules ordered in a chiral fashion. Examples of nonchiral molecules ordered in a chiral fashion in the crystal state are a-quartz and sodium chlorate where, respectively, SiO, and NaC10, molecules are arranged in a helical order. We thus find right- and left-crystals of both substances. The reason for this is simply that the energy is lower in the helical state. Other examples are sulfur and selenium, which are found to form helical structures, thus ordering to a chiral structure although the atoms themselves are nonchiral. (Sometimes the designation “structure chirality” or “phase chirality” is used to distinguish this phenomenon where nonchiral obiects build UP a chiral structure.) In these examples we see the important one-wayness of chirality: a phase, i.e.9 an ensemble of molecules or atoms, may be chiral whether the constituents are chiral or not, but a phase built from objects is always chiral, i.e. it can never possess reflection symmetry. When we here talk about c h i d objects, we do not consider the trivial case which might
2.3 The Necessary Conditions for Macroscopic Polarization in a Material
be taken as an exception, when there are exactly as many right-handed as left-handed objects, which are each others mirror images (racemic mixture). We may also remember that when talking about a chiral phase, we consider its static properties for which all molecules are in their time-averaged configurations (organic molecules would otherwise have very few symmetry elements). This corresponds to considering atoms to be situated on regular points in a lattice, without considering individual displacements due to thermal motion. In the case where only the building blocks are chiral, the optical activity is relatively weak (as in liquid solutions), whereas if there is a helical superstructure, this activity can be large as in quartz, NaClO,, or immense as in liquid crystals, because the effect sensitively depends on d/A, the ratio of the stereospecific length to the wavelength of light, which is appreciable in the latter cases. When the building blocks have higher symmetry than the structure, as in NaClO,, there is, as we just mentioned, an inherent tendency to arrange them to a structure without a mirror plane and a center of symmetry. However, if we take a pure left-NaC10, crystal, dissolve it in water and let it crystallize from this solution, there is an equal chance to build up both mirror image arrangements. Thus from a solution of a left-crystal NaClO,, right- and left-crystals grow with equal probability. This is a local breaking of a non-chiral symmetry to chiral, although the symmetry is preserved on a global scale. A considerable number of such cases exist in solid crystals, although they are, relatively speaking, not very frequent. In principle, chiral “domains” or “crystallites” could be expected to be created in the same way in liquid crystals from nonchiral mesogens; see the discussion in Sec. 2.5.6. A chiral phase normally shows optical activity. On the other hand, if we observe op-
549
tical activity we know for sure that the phase is chiral. Whereas chirality is a property that does not have a length scale, optical activity is a global, bulk property and it can only be measured on a large ensemble of molecules. It is therefore less correct to speak about “optically active molecules”. Optical activity and chirality are of course strongly related, because the optical activity is one of the consequences of chirality. We might, for instance, have a chiral substance that does not show any optical activity, because different parts in the molecule give rise to antagonistic contributions. If we now mix this substance with a nonchiral substance, the result may very well be that we find an easily measurable optical activity, and we may even see immediately, in the case of liquid crystals, that the phase gets twisted, thus a clear manifestation of chirality. Descriptions of such a case as “the chiral molecule does not show any chirality in its pure state” are not uncommon, but should be avoided, apart from their lacking logic, because they confuse cause and effect. Optical activity (or more precisely optical rotatory dispersion) is a quantitatively measurable property, like the helical twisting power, and both are therefore very useful to quantify the manifestations of chirality. However, expressions like “more or less chiral” are just as devoid of sense as “more or less cubic”. A structure can have cubic symmetry, or else it does not, but there can be nothing in between. Likewise it is not the chirality that “goes down by a factor of five on raising the temperature” (to cite one of many similar statements), but rather the twisting power or a similar quantitative measure. Nevertheless, this common misuse of the word “chiral” points to a real problem. Now, let us go back to the example of the chiral smectic C, written C* whenever we want to emphasize the chirality. The symbolic relation (Eq. 89) means that if we have
550
2
Ferroelectric Liquid Crystals
added a concentration c#O of chiral dopant to our smectic layer then a local polarization P is permitted perpendicular to the tilt plane. If c = 0, no polarization is permitted. This corresponds to the qualitative character of chirality. Lack of reflection symmetry is thus a prerequisite for polarity. The argument does not say anything about the size of the effect and could not, because it is a symmetry argument. We have to take recourse to other arguments in order to say anything about the size of the effect. For instance, if we only add one dopant molecule, only the rotational motion of this molecule will be biased if we disregard its weak interaction with its neighboring molecules (see further discussion in Sec. 2.5.2), and a fraction of its lateral dipole moment will show up in P. If we increase the concentration, it is highly probable that P will be proportional to c, at least for small values of the dopant concentration. This is also borne out by experiment. This case is very similar to the case of dissolving noncentrosymmetric molecules in a liquid solution. Such a solution shows an optical activity that is, at least for low concentrations c, proportional to c. The sense of rotation depends on the solvent and is thus not just specific of the noncentrosymmetric molecule. We can expect the same thing to happen in the smectic C* case: the sense of optical rotation, the sense of P, and the sense of the helical twist will all depend on both the solute and the solvent, and cannot (so far) be predicted from first principles but have to be measured, at least until sufficient empirical data has been collected. We will define the polarization as positive if it makes a right-handed system with the layer normal and the director, and hence lies in the same direction as z x n (see Fig. 23). A priori, there are two classes of chiral smectics, those with P>O and those with P
2
7.
PoS
Figure 23. Spatial relation between layer normal, director, and local polarization for the two possible classes (+/-) of chiral smectics.
means that their opposite enantiomers would belong to the first class. A right-handed helix would also correspond to a lefthanded and vice versa between the enantiomers. However, there is no a priori relation between the sense of P and the sense of the helix in a certain compound. The recognition of chiral effects and their importance is growing and it is not improbable that chiral effects will bring new and important perspectives to liquid crystal research, as well as to physics and chemistry in general in the coming decades. Thus there is a great need to be able to quantify chirality and chiral effects in different ways. This might be done by introducing convenient order parameters for different chiral manifestations, but the problem is exceedingly complex because, while chirality itself does not have a length scale, the effects of chirality range from intramolecular to bulk.
2.3.5 The Curie Principle and Piezoelectricity If we want to investigate the conditions for an elastic stress to induce a macroscopic polarization, we have to turn to the Curie principle, which in a sense is a generalization of Neumann’s principle. It cannot be proven in the same way as that principle; in fact it is often the violations (or maybe seeming violations) that are the most interesting to study. Among these cases are the phase tran-
2.3
The Necessary Conditions for Macroscopic Polarization in a Material
sitions (spontaneous symmetry breakings) where the temperature is the “external force” in Curie’s language. As mentioned before, Curie’s principle can be stated in different ways and the earliest formulation by Curie himself is that “when a cause produces an effect, the symmetry elements of the cause must be present in the effect”. This means that the produced effect (the induced property) may have higher symmetry, but never less symmetry than the cause. In particular in this formulation, the principle has to be used with care. An example of this is related by Weyl in his book Symmetry [99]. Weyl here tells about the intellectual shock the young Mach received when he learned about the result of the 0rsted experiment (see Fig. 24 taken from the book). The magnetic needle is deflected in a certain sense, clockwise or anti-clockwise when a current is sent in a certain direction through the conducting wire, and yet everything seems to be completely symmetric (magnet, current) with respect to the plane containing the needle and the conductor. If this plane is a mirror plane, the needle cannot swing out in any direction. The solution to this paradox is that this plane is not a mirror plane, because of the symmetry properties of the magnetic field. The problem is that while we easily recognize the reflection properties of geometric objects, we do not know a priori the corre-
Figure 24. The symmetry paradox of the 0rsted experiment (after [99]).
55 1
sponding properties for abstract things, e.g., physical quantities. In fact, the magnetic field has reflection properties such that it is rather well illustrated by Magritte’s wellknown surrealist painting where a man is looking into a mirror and sees his back. A lesson to be learned from this is that we cannot rely on appearances when we judge the symmetry of various fields and physical properties in general. Pierre Curie was the first person to study these symmetries in a systematic way and, in order to describe them, he introduced the seven limiting point symmetry groups (also called infinite or continuous point groups), which he added to the 32 crystallographic groups. With this combination he could classify the symmetry of all possible media and all possible physical properties, illustrating the continuous symmetries with drawings related to simple geometric objects as, e.g., in Fig. 25. Obviously, these continuous symmetries have a special relevance for liquid crystals, liquid crystal polymers, and liquids in general, being continuous media without a lattice. Let us apply a stress to a general medium and ask under what conditions it could cause an electric displacement. The basic problem we then have to sort out is the proper description of the symmetry of stress. Clearly a stress cannot be described by a polar vector - there must be at least two. A simple illustration of this is given in Fig. 26. We see that in two dimensions a homogeneous tensile stress as well as a pure shear stress has two perpendicular mirror planes, one twofold rotation axis, and one center of symmetry (center of inversion). In three dimensions we have analogously three mirror planes, three twofold axes, and the center of symmetry, which we may enumerate as m, m, m, 2,2, 2, Z (see Fig. 27). These are the symmetry elements of the point group mmm (or D2J. This is the orthorombic point
552
-
2
-m
d n m m -1-
Ferroelectric Liquid Crystals
-22
mim
-I-mm
Figure 25. Pierre Curie’s seven continuous point groups illustrated by geometric “objects”. Among them we might distinguish mm representing a polar vector (like the electric field), and 4 m representing an axial vector (like the magnetic field). Three of these symmetries, -, -22, and -/m, can appear in a righthanded as well as in a left-handed form (enantiomorphic). Several equivalent ways of expressing the symmetry are in common use, for instance, the one in Fig. 19. Pyroelectricity (i.e., a macroscopic polarization) is only permitted by the first two groups (- and mm). They represent a chiral and a non-chiral version of a longitudinal ferroelectric smectic. If the continuous medium in question can sustain the mechanical strain, piezoelectricity would be allowed by the first three groups (M, mm,and ~22).The third of these (also written D-) represents the symmetry of the cholesteric (N*) phase as well as the smectic A* phase and the helicoidal smectic C* phase, and the effects are, respectively, inverse to the flexoelectrooptic effect, the electroclinic effect and the deformed helix mode - all one-way effects. If we polymerize these phases (i.e. crosslink them to soft solids), the effects would become truly piezoelectric (two-way effects).
group, which can be illustrated by a matchbox or a brick. Now apply the stress in the most general way, i.e., such that its three axes of two-fold symmetry and its three planes of reflection symmetry do not have the same directions as the axes and planes in the unstrained medium. Curie’s principle then says that the stressed medium will retain none of its symmetry axes and planes. However, if the unstressed medium has a center of symmetry Z, it will retain that center because the stress also has a center of symmetry. Therefore, in a medium with inversion symmetry, no effect representable by an arrow can be induced by the stress, and hence no electric displacement or polarization, whatever stress is applied. In other words, a medium with inversion symmetry cannot be piezoelectric. We could also have reasoned formally in the following way: If a property P (polarization in this case) should appear in the medium K as a result of the external action E (stress o i n this case), then P must be compatible with the symmetry of the strained medium, according to Neumann’s principle
but, according to Curie’s principle
K=Kno Figure 26. The symmetry of stress: (a) pure tensile stress, (b) pure shear stress.
If we now insert -m for P and m m m for 0, we get from Eqs. (92) and (93)
-m 2 K n m m m
a
b
Figure 27. Characteristic surfaces of second-rank polar tensors: (a) ellipsoid, (b) hyperboloid of one sheet, (c) hyperboloid of two sheets. (After reference 36.)
(93)
(94)
The symmetry elements to the right (mmm) contain a center of inversion, but those to the left (am)do not. Therefore, if Eq. (94) should be satisfied (i.e., the Neumann and Curie principles together), K must not have a center of inversion, i.e., -
1 P K
(95)
2.3
The Necessary Conditions for Macroscopic Polarization in a Material
Out of the 32 crystallographic groups, 11 have symmetry elements including a center of inversion. Piezoelectricity should therefore be expected to appear in the other 21, but it appears only in 20. The exception is 432 (=O), the octahedral group. However, this exception is sufficient to give the very important insight that the Neumann and Curie principles, and in fact all symmetry principles, only give necessary (never sufficient) conditions for a certain phenomenon to appear. The principles can only be used in the affirmative when they prevent things from happening.
2.3.6 Hermann’s Theorem It is often said that group 432 is “too symmetric” to allow piezoelectricity, in spite of the fact that it lacks a center of inversion. It is instructive to see how this comes about. In 1934 Neumann’s principle was complemented by a powerful theorem proven by Hermann (1898- 1961), an outstanding theoretical physicist with a passionate interest for symmetry, whose name is today mostly connected with the Hermann -Maw guin crystallographic notation, internationally adopted since 1930. In the special issue on liquid crystals by Zeitschrift f u r Kristallographie in 1931 he also derived the 18 symmetrically different possible states for liquid crystals, which could exist between three-dimensional crystals and isotropic liquids [loo]. His theorem from 1934 states [lo11 that if there is a rotation axis C, (of order n), then every tensor of rank r c n is isotropic in a plane perpendicular to C,, as shown in Fig. 28. For cubic crystals, this means that second rank tensors like the thermal expansion coefficient a+ the electrical conductivity ow or the dielectric constant E ~will , be isotropic perpendicular to all four space diagonals that have threefold symme-
553
try. This requires all these properties to have spherical symmetry, as already mentioned above for the optical wave surface and for the thermal expansion. It also means that crystals belonging to the trigonal, tetragonal, or hexagonal systems are all optically uniaxial (most liquid crystal cases can be included in these categories). The indicatrix is thus an ellipsoid of revolution, as illustrated in Fig. 29, with the optic axis along the threefold, fourfold, or sixfold crystallographic axis, respectively. If we have a fourfold axis C,, then the piezocoefficients d,, will be isotropic perpendicular to C4. Finally, if we have a sixfold axis C6, the elastic constants Cijkl will be isotropic perpendicular to C,. Thus in a smectic B the layer can also be considered isotropic with respect to the elastic constants.
I cn Material
IC
ROPefiY
Figure 28. The crystal symmetry compared to the property symmetry around an n-fold rotation axis.
0.a.
m
Positive
Figure 29. Media with a threefold, fourfold, or sixfold crystallographic axis must be optically uniaxial. Thus crystals belonging to the trigonal, tetragonal, or hexagonal system, including smectic B, must be uniaxial. The picture shows the indicatrix with its optic axis in the case of positive as well as negative birefringence.
554
2
Ferroelectric Liquid Crystals
There are now three cubic classes that do not have a center of symmetry. We should therefore expect these three - 23 (T), 43m (Td), and 432 (0)- to be piezoelectric, but only the first two are. The latter has three fourfold rotation axes perpendicular to each other, making the piezoelectric tensor d,, isotropic in three dimensions. The piezoeffect would not then depend on the sign of the stress, which is only possible for all dqkE0.
It is clear that similar additional symmetries would occur frequently if we went to liquids, which are generally more symmetric than crystals.
2.3.7 The Importance of Additional Symmetries A property that may be admitted by noncentrosymmetry may very well be ruled out by one of the other symmetry operations of the medium. As an example we will finally consider whether some of the properties discussed so far would be allowed in the cholesteric liquid crystals, which lack a center of inversion. A cholesteric is simply a chiral version of a nematic, abbreviated N*, characterized by the same local order but with a helical superstructure, which automatically appears if the molecules are chiral or if a chiral dopant is added (see Fig. 30). Could such a cholesteric phase be spontaneously polarized? If there were a polarization P,it would have to be perpendicular ton, because of the condition of Eq. (6), and thus along the helical axis direction m. However, the helical N* phase has an infinity of twofold rotation axes perpendicular to rn and the symmetry operation represented by any of these would invert P.Hence P = 0. A weaker requirement would be to ask for piezoelectricity. (Due to the helical configuration, the liquid has in fact some small
(4
Helix axis (b)
(C)
Figure 30. The symmetry of the cholesteric phase (a. b) and the effect of a shear (c).
elasticity for compression along m.)Nevertheless, as illustrated in the same figure, a compression does not change the symmetry, and hence a polarization P f 0 cannot appear due to a compression. Finally, it is often stated that a medium that lacks a center of inversion can be used for second-harmonic generation (SHG). This is because the polarizability would have a different value in one direction compared with that in its antiparallel direction. Could this be the case for the cholesteric phase, i.e., could it have a nonlinear optical susceptibility $*’#O? The answer must be no, as it cannot be in the n-direction, and the rn-direction is again ruled out by the twofold axis (one of the infinitely many would suffice). For the unwound (non-helical) N”, the two-fold axis along m works in the same way. The cholesteric example shows that it is not sufficient for a medium to lack a center of inversion in order to have SHG properties. Questions like these can thus be answered by very simple symmetry arguments, when we check how additional symmetries may compensate for lack of inversion symmetry. In contrast to the cholesteric phase, the unwound smectic C* phase does have a direction along which a second harmonic can be generated. This is of course the C, axis direction in the SSFLC geometry. Even if initially small, the existence of
2.4 The Flexoelectric Polarization
this effect was soon confirmed [102, 1031 and studied in considerable detail by several groups [ 1041. The SSFLC structure is the only liquid (if it can be considered as such!) with SHG properties. No other examples they can only be looked for among anisotropic liquids - are known, the externally poled electret waxes left aside (materials out of thermal equilibrium in which the polar axis is not an intrinsic property). Walba et al. were the first to synthesize C* molecules with powerful donor and acceptor groups active perpendicular to the director (thus along the C, axis), which is a necessity in order to achieve Y2)-values of interest for practical applications [ 105, 1061. However, there is in fact really no point in having a surface-stabilized ferroelectric liquid crystals as an SHG material. A pyroelectric material would be much better, in which the polar axis is fixed in space and nonswitchable, but this cannot be achieved in the framework of liquids. The first such materials were recently presented [107], made by using an SSFLC as a starting material and crosslinking it to a nonliquid-crystalline polymer. It is thus a soft solid. As we have seen, most liquid crystals have too high a symmetry to be macroscopically polar if they obey the n -+ -n invariance (which all “civilized” liquid crystals do, that is, all liquid crystal phases that are currently studied and well understood). The highest symmetry allowed is C 2 (monoclinic), which may be achieved in materials which are “liquid-like’’ at most in two dimensions. Even then external surfaces are required. Generally speaking, a polar liquid crystal tends to use its liquid translational degrees of freedom so as to macroscopically cancel its external field, i.e., achieve some kind of antiferroelectric order. For more “liquid-like’’ liquids, piezo-, pyro-, ferro-, and antiferroelectricity are a fortiori ruled out as bulk properties. These phenomena
555
would, however, be possible in crosslinked polymers (soft solids). A simple example may illustrate this. If we shear the cholesteric structure shown in Fig. 30c, Curie’s principle tells us that a polarization is now permitted along the twofold axis shown in the figure. If the liquid crystal will not yield, this would constitute a piezoelectric effect. Hence liquid-crystalline polymers are expected to show a piezoelectric effect both in the N* phase, the A* phase, and the C* phase (as well as in chiral phases with lower symmetries). However, as already pointed out, these materials are not really liquidlike in any direction, thus not liquid crystals but soft solids (like rubber). It may finally be pointed out that the symmetry operation n -+ -n describes a bulk property of liquid crystals. At surfaces, no such symmetry is valid. Therefore SHG signals can be detected from nematic surface states and have, indeed, been used to probe the order and directionality of such surface states [108]. As a general rule, a surface is always more or less polar, which certainly contributes to the complexity of alignment conditions at the interface between a surface and a liquid crystal with the special polar properties of the materials treated in this chapter. In this case, therefore, we have in principle a surface state with a polar property along n as well as perpendicular to n.
2.4 The Flexoelectric Polarization 2.4.1 Deformations from the Ground State of a Nematic Let us consider a (nonchiral) nematic and define the ground state as one where the director n is pointing in the same direction
556
2
Ferroelectric Liquid Crystals
everywhere. Any kind of local deviation from this direction is a deformation that involves a certain amount of elastic energy I GdV, where G is the elastic energy density
V
and the integration is over the volume of the liquid crystal. As n ( r )varies in space, G depends on the details of the vector field n (r). Now, a vector field, with all its local variations, is known if we know its divergence, V . n , and curl, V x n , everywhere (in addition to how it behaves at the boundaries). It was an advance in the theoretical description of liquid crystals (the continuum theory) when in 1928 Oseen, who had introduced the unit vector n, which de Gennes later gave the name “director” [38], showed [ 1091that the elastic energy density G in the bulk (i.e., discarding surface effects) can be written in the diagonal form
Figure 31. The three elementary deformations splay, twist, and bend. None of them possesses a center of symmetry.
which led to a revival in the international interest in liquid crystals. The denominations splay, twist, and bend stem from Frank. The Oseen-Frank constants K , KZ2,and K33 are components of a fourth rank tensor, just like the ordinary (first order) elastic constants. The question we will ask and answer in this section is whether these deformations will polarize the nematic. The reason for 1 Kj 1 ( V . n)’ + 1 KzZ [n . ( V X ~ ) ] ~ such a conjecture is, of course, the analogy G =with piezoelectric phenomena: as we have 2 2 seen in Sec. 2.3.5 an elastic deformation 1 + 2 K33 [ n x (V x n)]’ may polarize a solid. Do we find the same phenomenon in the liquid crystal? This relation expresses the fact that the elasWe recall from the discussion in Sec. tic energy is a quadratic form in three cur2.3.5 that a necessary condition for the appearance of a polarization was that the mevature deformations or strains, now called splay, twist, and bend, which we can treat as dium lacks a center of symmetry. The reason for this was that since at equilibrium the independent. They are sketched in Fig. 3 1 . stress as well as the strain will be centroThe splay is described by a scalar (a pure disymmetric, the piece of matter cannot devergence), V - n ,the twist is described by a pseudoscalar (it changes sign on reflection velop charges of opposite sign at opposite ends of a line through its center if it has a in a plane parallel to the twist axis or when we go from a right-handed to a left-handed center of symmetry, in accordance with reference frame), which is the component of Curie’s principle. On the other hand, inspecV x n along the director, IVxnl,,,whereas tion of Fig. 3 1 immediately reveals that none the bend is described by a vector with the of the three strains splay, twist, and bend has a center of symmetry. Hence Curie’s princicomponent of V x n perpendicular to the diple allows a local polarization to appear as rector, 1 Vxnl,. Oseen was also the first to realize the ima result of such local deformations in the director field, even if the medium itself has a portance of the n +-n invariance [ 1lo], which he used to derive Eq. (96). This excenter of symmetry. We see from Fig. 31 pression was rederived thirty years later by that the splay deformation violates the Frank in a very influential paper [ l l l ] , n +-n invariance, whereas twist and bend ~
~
,,
2.4 The Flexoelectric Polarization
557
do not. Therefore a polarization may appear along n in the case of splay, but has to be perpendicular to n in the case of twist and bend. In fact, as a result of a general local deformation in a nematic, a local polarization density P will appear in the bulk, given by
P = e,n ( V .n) + eblt
X(
Vxn)
(97)
This polarization is called flexoelectric and the phenomenon itself the flexoelectric effect.
2.4.2 The Flexoelectric Coefficients Equation (97) consists of two parts, one of which is nonzero if we have a nonzero splay, the other of which is nonzero for a nonzero bend. The coefficients e, and e b for splay and bend are called flexoelectric coefficients and can take a plus or minus sign (a molecular property). In the case where e, and eb are positive, the polarization vector is geometrically related to the deformation in the way illustrated in Fig. 32. For a splay deformation, P is along the director and in the direction of splay. For a bend, P is perpendicular to the director and has the direction of the arrow if we draw a bow in the same shape as the bend deformation. An important feature of Eq. (97) is that it does not contain any twist term, although the Curie principle would allow a polarization caused by a twist. However, as P would have to be perpendicular to n,it should then lie along the twist axis. Now, it is easy to see (see Fig. 33) that there is always a twofold rotational symmetry axis along the director in the middle of a twist. Thus any P along the twist axis would be reversed by a symmetry operation and must therefore be zero. In other words, the symmetry of twist does not permit it to be related to a polar
e >O
eb>O
Figure 32. Geometrical relation between the local polarization density and the director deformation in the case of positive values for the flexoelectric coefficients. For negative values the direction of the induced dipole should be reversed. The size and sign of e , and eb (alternatively called e , and e,) are a molecular property.
x
Figure 33. The symmetry of twist. If we locally twist the adjacent directors in a nematic on either side of a reference point, there is always a twofold symmetry axis along the director of the reference point. Therefore a twist deformation cannot lead to the separation of charges. Thus a nematic has only two nonzero flexoelectric coefficients.
vector (see our earlier discussion of additional symmetries in Secs. 2.3.6 and 2.3.7). Hence a twist deformation cannot lead to a separation of charges. This property singles out the twist from the other deformations, not only in a topological sense, and explains why twisted states are so common. The well-known fact that a nematic which is noninvariant under inversion is unstable against twist and normally adopts a helical (cholesteric) structure, would not have been the same if the twist had been connected
558
2
Ferroelectric Liquid Crystals
with a nonzero polarization density in the medium. This also means that a “twisted nematic” as used in displays is not polarized by the twist.
2.4.3 The Molecular Picture Recognition of the flexoelectric effect is due to Meyer [18], who in 1969 derived an expression equivalent to Eq. (97). He also had a helpful molecular picture of the effect, as illustrated in Fig. 34a. To the left in this picture, the unstrained nematic structure is shown with a horizontal director in the case of wedge-shaped and crescent-shaped molecules. To the right the same molecules are shown adjusted in their distribution corresponding to a splay and a bend distortion, respectively. In either case the distortion is
Bend
Splay
Bend
Splay
coupled to the appearance of a nonzero polarization density. As we can see, this is a steric (packing) effect due to the asymmetry of the molecular shape. The inverse effect is shown in Fig. 34b. When an electric field is applied it induces a distortion. In this figure we have illustrated a hypothetical compound splay-bend deformation and also used a slightly more general shape for the model molecules. It is clear that the observable effects will depend on the molecular shape as well as the size and distribution of the dipoles in the molecules. The inverse flexoelectric effect simply offers another mechanism for polarizing the medium, since the distortion will imply a polarization parallel to E . It is therefore a special kind of dielectric mode involving orientational polarization. In this respect, the inverse effect bears a certain resemblance to the fieldinduced lining up of dipoles in a paraelectric material, as the dipoles are already present in the molecules in both cases (see Fig. 35). Flexoelectric polarization leads to a separate contribution to the general term G = - E . P in the free energy. With Eq. (97) this contribution takes the form (98) G f = -e,E . n ( V . n )- e,E . [n x ( V x n)]
Bend
Figure 34.(a) The flexoelectric effect. A polarization is coupled to a distortion (from [18]). (b) The inverse flexoelectric effect. An applied field induces a distortion (from [I 121). With our sign conventions, (a) corresponds to e,>O, eb
Figure 35. Orientational polarization in an applied field is generally coupled to a director distortion in the liquid-crystalline state. The drawn direction of the dipoles corresponds to the case eb< 0.
2.4 The Flexoelectric Polarization
2.4.4 Analogies and Contrasts to the Piezoelectric Effect The flexoelectric effect is the liquid crystal analogy to the piezoelectric effect in solids. To see this we only have to make the connection between the translational variable in solids and the angular variable in liquid crystals. For both effects there is a corresponding inverse effect. However, the differences are notable. The piezoeffect is related to an asymmetry of the medium (no inversion center). The flexoelectric effect is due to the asymmetry of the molecules, regardless of the symmetry of the medium. We have seen how the elementary deformations in the director field destroy the center of symmetry in the liquid crystal. Therefore the liquid may itself possess a center of symmetry. In other words, the situation is just the opposite to the one in solids! The fact that the flexoelectric effect is not related to the symmetry of the medium, in particular means that it is not related to chirality. It means that the effect is common to all liquid crystals. Therefore expressions like, for instance, a “flexoelectric nematic”, which are encountered now and then, are nonsensical.
(which are mostly not stated). This leads to great confusion and difficulties in extracting correct values from published data (see the discussion in [ 1121). We may write the flexoelectric polarization (Eq. 97) in the form
P = e,S
B = n x (VX n )
(99)
(100
in the bend polarization density, corre sponding to the most common form (101
in the Oseen-Frank expression for the bend elastic energy. Often this last expression is, however, written in the equivalent form Gb = y1 K33 [(n * V)nl2
(102)
or
1 K33 (n . vfl)2 Gb = 2
(102a)
for instance, found with Oseen [lo91 and Nehring and Saupe [113], which then corresponds to a change of sign in B ’
v)n
(103)
This is due to the equality 12
The flexoelectric effect is still a “submarine” phenomenon, which has so far mostly been of academic interest. One of the reasons is its complexity when we go beyond nematics, but another reason is that, even in nematics, the size and sign of the flexocoefficients are largely unknown. A condition contributing to this is that Eq. (97) can be written in a number of ways, not only in terms of the vector operators, but also corresponding to different sign conventions
ebB
As far as the director gradients are concerned we have chosen to use the form
B = -eb(n
2.4.5 The Importance of Rational Sign Conventions
559
x ( V x n ) =-(n. V ) n
( 104)
It should be noted that Eq. (104) is not a general equality for vectors, but is only valid for a unit vector. In that case we may use the expansion rule for a triple vector product
x V XII = V ( n . n) - (n . V ) n
~t
(105)
which is equal to -(n . V)n,since n - n = 1 . If we use Eq. (103), the expression for the flexoelectric polarization (Eq. 97) changes
5 60
2 Ferroelectric Liquid Crystals
to
P = e,n ( V . n ) - eb (n V ) n
(106)
+
On the other hand, the signs in the expression could also change due to a different geometric convention adopted for the direction of P relative to the deformation. Thus Meyer in his first paper uses the opposite convention (Fig. 34) to ours (Fig. 32) for the positive direction of the P arrow, which leads to the form
P = e , n ( V .n) + e,(Vx n) x n
In one of his early classic papers from 1969, Bouligand [ 1151 showed that if a cut is made in a cholesteric structure at an oblique angle to the helix axis, an arc pattern of the kind in Fig. 34b will be observed as the projection of the director field onto the cut plane, as illustrated in Fig. 36. We will call this oblique plane the Bouligand plane or the Bouligand cut. Evidently, if we turn the director around an axis perpendicular to the helix axis until it is aligned along the Bouligand plane, we will have exactly
(107)
or
P = e,n ( V . n ) - ebn x ( V x n )
(107a)
although in later work he changes this to conform with Fig. 32 as well as Eq. (97). This geometric convention for the direction of the P arrow was first proposed by Schmidt et al. [ 1141. The different sign conventions are discussed at length in [112]. It is important that a unique sign convention be universally adopted for the flexoelectric effect. Our proposal is to write P in the form given by Eq. (97), which corresponds to the commonly used form for bend in the elastic energy, combined with the geometric convention as expressed by Fig. 32, which is most natural and easy to remember. This will be applied in the following.
2.4.6 The Flexoelectrooptic Effect The periodic deformation in Fig. 34b cannot be observed in a nonchiral nematic because it does not allow for a space-filling splay-bend structure. Instead, such apattern would require a periodic defect structure. However, we can continually generate such a space-filling structure without defects in a cholesteric by rotating the director everywhere in a plane containing the helix axis.
Figure 36. (a) Oblique cut through a cholesteric structure showing the arc pattern produced by the director projection onto the cut plane (Bouligand plane). In (b) the same right-handed twist is seen looking perpendicular to the twist axis, and in (c) looking perpendicular to the cut plane. Here the splay - bend pattern becomes evident, even if the directors are not lying in this plane (after Bouligand [ 1161). If an electric field is applied along no, which corresponds to the n direction at the top and bottom in (b), the directors will swing out around no into a Bouligand plane corresponding to the value of the field.
2.4
the pattern of Fig. 36, and therefore a polarization along the plane. This consideration will facilitate the understanding of the flexoelectrooptic effect. This new linear dielectric mode was reported [ 1171 by Pate1 and Meyer in 1987. It consists of a tilt $I of the optic axis in a short-pitch cholesteric when an electric field is applied perpendicular to the helix axis, as illustrated in Fig. 37. The optic axis is perpendicular to the director and coincides with the helix axis in the field-free state. Under an applied field, in its polarized and distorted state, the cholesteric turns slightly biaxial. The physical reason for the field-induced tilt is that the director fluctuations, which in
I
k >O e>O
E
8
E=O
:p
Figure 37. An electric field E applied perpendicular to the helix axis of a cholesteric will turn the director an angle N E ) and thereby the optic axis by the same amount. The director tilt is coupled to the periodic splay -bend director pattern shown below, which is generated in all cuts perpendicular to the new optic axis. In this inverse flexoelectric effect, splay and bend will cooperate if e , and eb have the same sign. The relation between E and 4is shown for a positive helical wave vector k (right-handed helix) and a positive average flexoelectric coefficient e =
1
( e ,+ eb).
2 When the sign of E is reversed, the optic axis tilts in the opposite direction (@+-$). ~
The Flexoelectric Polarization
56 1
the field-free state are symmetrical relative to the plane perpendicular to the helix axis, become biased in the presence of a field, because for tilt in one sense, keeping E fixed, the appearing splay-bend-mediated polarization lowers the energy by - E . 6 P , whereas a tilt in the opposite sense raises the energy by +E . 6 P . The mechanism is clear from a comparison of Fig. 36b, c. If we assume that the twist between top and bottom is 180", the director at these planes is no, as indicated in Fig. 36b. Viewed perpendicular to the Bouligand plane, the cholesteric structure corresponds to "one arc" in the splaybend pattern, but the directors do not yet lie in this plane. However, if they all turn around no as the rotation axis, also indicated in Fig. 36a, they will eventually be in the Bouligand plane and the medium will thereby have acquired a polarization (see the lower part of Fig. 37) along no. Hence, if we apply a field along no, increasing its value continuously from zero, the optic axis will swing out continuously, as shown in Fig. 38, and the Bouligand plane (perpendicular to the axis) will be more and more inclined. At the same time, the polarization P increases according to Eq. (97) with the growing amplitude to the splay -bend distortion. The flexoelectrooptic effect is a fieldsensitive electrooptic effect (it follows the sign of the field), which is fast (typically 10- 100 ps response time) with two outstanding characteristics. First, the induced tilt (I has an extremely large region of linearity, i.e., up to 30" for materials with dielectric anisotropy A&=0. Second, the induced tilt is almost temperature-independent. This is illustrated in Fig. 39 for the Merck cholesteric mixture TI 827, which has a temperature-independent pitch but not designed or optimized for the flexoelectrooptic effect in other respects.
562
2 Ferroelectric Liquid Crystals
E>o
c3
Optic axis
E=a
E=o
Figure 38. Field-induced tilt (left) and corresponding splay- bend distortion when looking at the Bouligand plane along the field direction (right).The same director pattern will be found in any cut made perpendicular to the tilted optic axis, whereas the director is hornogeneous in any cut perpendicular to the nontilted axis.
Irnl
It can be shown 1117, 1181 that the induced tilt is linear in E according to
4 ) -eE Kk where 1 e = -(es +q,) 2
and 1
K = - (4 1 + K33) 2 and k is the cholesteric wave vector. The response time is given by
r=- Y
Kk2
(''I)
where y is the characteristic viscosity. We note, in advance of discussing the same feature in the electroclinic effect, cf. Sec. 2.5.8, that the response time does not depend on the value of the applied electric field. The temperature independence is seen immediately from Eq. (log), because both e and K should be proportional to S2, the square of the scalar nematic order parameter. Therefore a mixture with temperature-independent pitch (not too difficult to blend) will have a @ ( E )that is independent of temperature. Since the original work of Patel and Meyer [ 1171, the effect has been further investigated [119- 1221, in the last period [ 112, 118, 123- 1261 with a special empha-
2.4 The Flexoelectric Polarization TI 827
563
ferroelectrics. They all belong to the category of "in-plane switching" with a continuous grayscale and still have a great potential to be exploited in large scale applications.
@(E) T=2S°C @(E) T=44"C
2.4.7 Why Can a Cholesteric Phase not be Biaxial?
0 0 0 0
E = 5OV/pm 10
25
30
35 40 Temperature ("C)
1 45
Figure 39. The flexoelectrooptic effect measured on the Merck mixture TI 827. (a) Induced tilt as a function of E. (b) Induced tilt as a function of temperature.
sis on ruling out the normal dielectric coupling and increasing the linear range, which is now larger than for any other electrooptic effect in liquid crystals. With the available cholesteric materials, the applied field is quite high but can be estimated to get lowered by at least a factor of ten if dedicated synthetic efforts are made for molecules with convenient shapes and dipoles. The flexoelectrooptic effect belongs to a category of effects that are linear in the electric field, and which all have rather similar characteristics. These include the electroclinic effect, the deformed helical mode in the C* phase, and the linear effect in anti-
The nonchiral nematic is optically a positive uniaxial medium. A cholesteric is a nematic with twist. The local structure of a cholesteric is believed to be the same as that of the nematic except that it lacks reflection symmetry. This means that the director and therefore the local extraordinary optic axis is rotating around the helix axis making the cholesteric a negative uniaxial medium with the optic axis coinciding with the twist axis. The question has been asked as to why the nematic with twist could not be biaxial, and attempts have been made to measure a slight biaxiality of the cholesteric phase. In other words, why could the twist not be realized in such a way that the long molecular axis is inclined to the twist axis? Why does it have to be perpendicular? Section 2.4.6 sheds some light on this question. As we have seen, as soon as we make the phase biaxial by tilting the director the same angle out of the plane everywhere, we polarize the medium. Every fluctuation 6n out of the plane perpendicular to the helix axis is thus coupled to a fluctuation 6P raising the free energy, -(6P)2. The energy of the state is thus minimized for 4=0, which is the ground state. In other words, the N* state cannot be biaxial for energetic reasons, just as the N state cannot be polar for the same reason (see the discussion in Sec. 2.2.2). In other words, the cholesteric phase is uniaxial because this is the only nonpolar state.
564
2
Ferroelectric Liquid Crystals
2.4.8 Flexoelectric Effects in Smectic A Phases In smectics such deformations which do not violate the condition of constant layer thickness readily occur. In a smectic A (or A*) this means that V x n = 0 and the only deformation is thus pure splay, in the simplest approximation. We will restrict ourselves to this case, as illustrated in Fig. 40. Special forms are spherical or cylindrical domains, for instance, the cylindrical structure to the right in the figure, for which a biologically important example is the myelin sheath which is a kind of “coaxial cable” around a nerve fiber. Let us consider such a cylindria1 domain. The director field in the xy plane is conveniently described in polar coordinates p and 0 a s
n = (np, no) = (120)
(112)
from which we get the divergence
(1 13)
This gives us the flexoelectric polarization density
P = e, n ( V .n) = e, n
(1 14)
b) \
Figure 40. The easy director deformation in a smectic A is pure splay which preserves the layer spacing everywhere.
The polarization density thus falls off as Ilp. In the center of the domain we have a disclination of strength one. Because the disclination has a finite core we do not have to worry about P growing infinite. It is interesting to take the divergence of this polarization field. We get
v. P = l ~
a (pP,) = 0
-
P aP
Thus the polarization field is divergence free in this geometry, which makes it particularly simple, because a nonzero V - P would produce space charges and long range coulomb interactions. Hence, a myelin sheath only has charges on its surface from the flexoelectric effect. It is further a well-known experience when working with both smectic A and smectic C samples, under the condition that the director prefers to be parallel to the boundaries, and that cylindrical domains are quite abundant. In contrast, spherical domains do generate space charge because, as is easily checked, v . P is nonzero, falling off as - ~ r * .
2.4.9 Flexoelectric Effects in Smectic C Phases Flexoelectric phenomena in smectic C phases are considerably more complicated than in smectic A phases, even in the case of preserved layer thickness. Thus under the assumption of incompressible layers, there are not less than nine independent flexoelectric contributions. This was first shown in [ 1271. If we add such deformations which do not preserve the layer spacing, there are a total of 14 flexocoefficients [128]. If we add chirality, as in smectic c*,we thus have, in principle, 15 different sources of polarization to take into account. In a smectic C , contrary to a smectic A, certain bends and twists are permitted in the
2.4 The Flexoelectric Polarization
director field without violating the condition of constant smectic layer spacing. Such deformations we will call “soft” in contrast to “hard” distortions which provoke a local change in layer thickness and therefore require much higher energy. As in the case of the N* phase, soft distortions may be spontaneous in the C* phase. Thus the chiral smectic helix contains both a twist and a bend (see Fig. 41) and must therefore be equal to a flexoelectric polarization, in contrast to the cholesteric helix which only contains a twist. This may even raise the question of whether the spontaneous polarization in a helical smectic C* is of flexoelectric origin. It is not. The difference is fundamental and could be illustrated by the following example: if starting with a homogeneously aligned smectic C you twist the layers mechanically (this could be done as if preparing a twisted nematic) so as to produce a helical director structure identical to that in a smectic C*, you can never produce a spontaneous polarization. What you do achieve is a flexoelectric polarization of a
Figure 41. Model of the director configuration in a helical smectic C*. To the left is shown a single layer. When such layers are successively added to each other, with the tilt direction shifted by the same amount every time, we obtain a space-filling twist - bend structure with a bend direction rotating continuously from layer to layer. This bend is coupled, by the flexoelectric effect, to an equally rotating dipole.
565
certain strength and sign, which is always perpendicular to the local tilt plane, just as the spontaneous C* polarization would be. However, the flexoelectric polarization is strictly fixed to the deformation itself and cannot, unlike the spontaneous one, be switched around by an external electric field. On the other hand, it is clear from the example that the two effects interfere: the flexoelectric contribution, which is independent of whether the medium is chiral or nonchiral, will partly cancel or reinforce the spontaneous polarization in a smectic C* in all situations where the director configuration is nonhomogeneous in space. This is then true in particular for all chiral smectic samples where the helix is not unwound, and this might influence the electrooptic switching behavior. The simplest way to get further insight into the flexoelectric polarization just described is to use the “nematic description” [46] of the C* phase. We then look, for a moment, at the smectic as if it were essentially a nematic. This means that we forget about the layers, after having noticed that the layers permit us to define a second vector (in addition to n), which we cannot do in a nematic. The second vector represents the layers and is the layer normal, z (or k ) , which differs from then direction by the tilt angle. The implicit understanding that z is constant in space represents the condition of undeformed smectic layers. We use the Oseen-Frank elastic energy expression [Eq. (96)] for a nematic medium as a starting point. Now, according to our assumption, the medium is chiral, and an ever so slight chiral addition to a nematic by symmetry transforms the twist term according to [ l l l ]
.)I2 + [n . ( V x n )+ qI2
[n . ( V X
(1 16)
The ground state now corresponds to a twisted structure with a nonzero value of
566
2
Ferroelectric Liquid Crystals
n . ( V x n ) given by a wave vector q, the sign of which indicates the handedness. Equation (1 16) is written for a right-handed twist for which n . ( V Xn ) =-q. Note that the reflection symmetry is lost but the invariance condition [Eq. (6)] is still obeyed. Chirality thus here introduces a new scalar quantity, a length characteristic of the medium. If the medium is also conjectured to be polar, it might be asked if it is possible, in a similar way, to introduce a true vector (n and z are not true vectors, since there is one symmetry operation that changes the sign of both). A look at the first term of Eq. (96) clearly shows that this would not allow such a thing. In fact, it is not possible to add or subtract any true scalar or vector in the splay term without violating the invariance of ( V . n ) 2 under the operation n + - a . Thus no ground state can exist with a spontaneous splay. Is there a way to introduce a vector in the bend term? There is. The bend transforms, obeying Eq. (6), as follows
[n x ( V x n ) I 2-+[ n x ( V x n ) - BIZ
(117)
where B is a vector. Only a vector B parallel to n x ( V x n ) can be introduced in the bend term. For undeformed smectic layers, n x ( V x n ) lies in he lzxnl direction, and B can be written
B=pzxn (1 18) where p is a scalar that must be zero in the nonchiral case. If p is nonzero, the medium is characterized by the local vector B and the reflection symmetry is lost. The form of the bend expression in the presence of a local polarization then corresponds to a constant spontaneous bend in the local frame of the director. The converse of this is the flexoelectric effect. Note that Eq. (117) conforms to Eq. (100). From the above reasoning we see two things: First, that this description permits the smectic C* to be polar and requires the
polarization vector to be perpendicular to the tilt plane, a result that we achieved before. Second, that the chiral and polar medium will be characterized by both a spontaneous twist and a spontaneous bend. The smectic C* is, in fact, such a medium where we have a space-filling director structure with uniform twist and bend. This nematic description has been very helpful in the past and permitted rapid solutions to a number of important problems [129, 1301. We will return to it in Sec. 7.1. If we insert the new twist term according to Eq. (1 16) into Eq. (96), the free energy attains its minimum value for n . V x n = -4 if splay and bend are absent (the cholesteric ground state). It means that we have a spontaneous twist in the ground state. This is connected to the fact that we now have a linear term in the free energy. For, if we expand the square in the twist term we could write the free energy as 1 q2 + K22 qn . ( V x n )(119) Gpp = (& + -K22 2
The last term is not reflection invariant and secures the lowest energy for right-handedness, which is therefore the lowest energy state. In the same way, if we expand the bend term (Eq. 117) we get the linear term -K33B [nx ( V Xn)] in the free energy. With both these linear terms present, the liquid crystal thus has both spontaneous twist and spontaneous bend. The general problem of tracing the deformations coupled to polarization in smectic C phases is complex, as has already been stated. We refer to [127] for the derivation in the incompressible case and to the discussion in [ 1281 for the general case. In the following we only want to illustrate the results in the simplest terms possible. This is done in Fig. 42, where we describe the deformations with regard to the reference system, k ,
2.4 The Flexoelectric Polarization
(3)
567
(4)
.
& (c.Vk.c)c (c.Vk.c)k
Figure 42. The six soft and the three hard deformations in a smectic C; these are coupled to the appearance of local polarization. Below each deformation is stated the covariant form of the independent vector field corresponding to the deformation. Five of the distortions (1,2,4,7,8) create a dipole density along the c (tilt) direction as well as along the k direction. The four other distortions (3,5,6,9) create a dipole density along thep direction, which corresponds to the direction of spontaneous polarization in the case of a chiral medium (C*). By the inverse flexoelectric effect, the distortions will be provoked by electric fields along certain directions. In more detail they can be described as follows: (1) is a layer bend (splay ink) with the bending axis alongp, ( 2 ) is the corresponding layer bend with bending axis along c. Both deformations will be provoked by any electric field in the tilt plane (c, k). (3) is a saddle-splay deformation of the layers, with the two bending axes making 45 ' angles to c and p . This deformation will be caused by a field component along p . (4) is a splay in the c director (corresponding to a bend in the P field if the smectic is chiral). It is generated by any field component in the tilt plane. ( 5 ) is a bend in the c director (in the chiral case coupled to a splay in P ) generated by ap-component in the field. (6) is a twist in the c director. It generates a dipole in the p direction (and is itself thus generated by a field in this direction). As this distortion is the spontaneous distortion in the helicoidal smectic C*, it means that we have a flexoelectric polarization along the same direction as the spontaneous polarization in such a material. Whereas these six deformations do not involve compression, the last three are connected with changes in the interlayer distance, described by the variable y=dulaz, where u is the layer displacement along the layer normal (z). Thus (7) is a layer compression or dilatation which varies along k and thereby induces a bend in the n director, connected with a dipole density, in the tilt plane. (8) is a layer splay inducing a splay-bend deformation in the n field, and thereby a dipole density, in the tilt plane. (7) and (8) are thus generated by field components in that plane. Finally, (9) is a layer splay perpendicular to the tilt plane, which induces a twist-bend in the n field alongp. The bend component then means a dipole alongp. Distortions (l), (2), and (4) are coupled among themselves as are (3), (3,and (6). The latter three, and in principle also (9), occur spontaneously in chiral materials.
c , p , where k is the local layer normal (along the direction of the wave vector for a helical smectic C * ) ,c is the local tilt direction, i.e., n tilts out in this direction (hence k, c is the tilt plane), and p is the direction of k xc (corresponding to the direction along which the spontaneous polarization has to
be in the chiral case). It should be stressed that k , c , andp are all considered unit vectors in this scheme, thus c does not give any indication of the magnitude of the tilt, only its direction. All in all there are 14 independent flexoelectric coefficients, 10 of which describe
568
2 Ferroelectric Liquid Crystals
five distinct deformations generating dipolar densities in the tilt plane. By the converse effect, these deformations are generated by electric field components lying in the tilt plane. A field component perpendicular to the tilt plane will generate the other four deformations (3, 5, 6, 9). which, consequently, themselves generate dipole densities along thep direction. In the figure, the deformations have been divided into three categories: those with gradients in k (1, 2, 3), those with gradients in c (4, 5, 6), and
au
those with gradients in y- -, i.e., gradients
aZ
in layer spacing (7,8,9) hard deformations. However, it is illuminating to make other distinctions. Thus deformations (l),(2), (4), (7), and (8) give quadratic terms in the free energy and are not influenced by whether the medium is chiral or not. As we have repeatedly stated, the flexoelectric effect is not related to chirality. However, a certain deformation which gives rise to a flexoelectric polarization, whether the material is chiral or not, may turn out to be spontaneous in the chiral case, like the C* helix. Thus the four deformations (3), (9,(6) and (9) turn out to give linear terms (like Eq. 119) in the free energy in the chiral case. Therefore we may expect them, at least in principle, to occur spontaneously. They all give contributions to the flexoelectric polarization in the direction alongp. At the incompressible limit, deformation (9) may be omitted. The remaining three deformations (3), ( S ) , and (6) are coupled to each other and have to be considered as intrinsic in the smectic C* state. Of these, the only space-filling structure is (6) (the same as illustrated in Fig. 41) and will therefore give rise to the dominating flexoelectric effect. Of the other two, deformation (3) in the chiral case means an inherent spontaneous tendency to twist the flat layers. This deformation actually only preserves a constant layer
thickness very locally, but not in a macroscopic sample, and will therefore be suppressed. In cyclindrical domains it will tend to align the c director 45 O off the cylinder axis [ 1271.Finally, deformation ( 5 )amounts to a spontaneous bend in the c director (corresponding to a splay in P).This means that P has the tendency to point inwards or outwards at the edges of the smectic layers. It means, on the other hand, that the effects are transformed to a surface integral so that the term does not contribute to the volume energy. Thus the general contributions to the flexoelectric effect are exceedingly complex and, at the present state of knowledge, hard to evaluate in their relative importance, except that the dominating contribution by far is the twisted (helicoidal) deformation. The consequences of the inverse flexoelectric effect are even harder to predict, especially in the dynamic case, without any quantitative knowledge of the flexocoefficients. When strong electric fields are applied to a smectic C (or C*) any of the nine deformations of Fig. 12 will in principle be generated, if not prohibited by strong boundary conditions. This consideration applies equally well to antiferroelectric liquid crystals as to ferroelectric liquid crystals. The fact that sophisticated displays work well in both cases seems to indicate that the threshold fields for these detrimental deformations are sufficiently high.
2.5 The SmA* - SmC* Transition and the Helical C* State 2.5.1 The Smectic C Order Parameter By changing the temperature in a system we may provoke a phase transition. The ther-
569
2.5 The SmA*-SmC* Transition and the Helical C* State
modynamic phase that is stable below the transition generally has a different symmetry (normally lower) than the phase that is stable above. The exceptions to this are rare, for instance, the liquid-gas transition where both phases have the same symmetry. In a number of cases of transitions between different modifications in solids there is no rational relation between the two symmetries. In such cases it may be difficult to construct an order parameter. In the majority of cases, however, the transition implies the loss of certain symmetry elements, which are thus not present any longer in the low temperature (condensed or ordered) phase. The symmetry group of the ordered phase is then a subgroup of the symmetry group of the disordered phase. In such cases we can always construct an order parameter, and in this sense we may say, in a somewhat simplifying manner, that for every phase transition there is an order parameter. Thus, in liquid crystals, the transitions isotropic ++ nematic ++ smectic A ++ smectic C f~smectic F, etc. are all described by their different specific order parameters. (There may be secondary order parameters, in addition.) The order parameter thus characterizes the transition, and the Landau free energy expansion in this order parameter, and in eventual secondary order parameters coupled to the first, has to be invariant under the symmetry operations of the disordered phase, at the same time as the order parameter itself should describe the order in the condensed phase as closely as possible. In addition to having a magnitude (zero for T > T,, nonzero for T< T J , it should have the same symmetry as that phase. Further requirements of a good order parameter are that it should correctly predict the order of the transition, and that it should be as simple as possible. As an example, the tensoria1 property of the nematic order parameter
correctly predicts that the isotropic - nematic transition is first order. Very often, however, only its scalar part S is used as a reduced order parameter, in order to facilitate discussions. In the case of the smectic A-smectic C transition, the tilt 8 is such a reduced order parameter. The symmetry is such that positive or negative tilt describes identical states in the C phase (see Fig. 43), hence the free energy can only depend on even powers in 8 and we may write, in analogy with the discussion in Sec. 2.2.5
For the time being, this simple expansion will be sufficient to assist in our discussion. A first-order SmA- SmC transition occurs if b 0 and T - T, = 0, 8 will be small and the aG = 0 then e6term can be dropped. Putting gives
a ( T - T,)B + be3 = 0
ae
(122)
with two solutions
e=o
(123)
which corresponds to the SmA phase (a check shows that here G attains a maximum value for T
Figure 43. Simple diagram of the SmA-SmC transition. Positive and negative tilt describe identical states.
570
2
Ferroelectric Liquid Crystals G
T > T,), and
\ // corresponding to the SmC phase (the extremal value of G is a minimum for T < T,). The transition is second order and the simple parabolic function of AT= T, - T at least qualitatively describes the temperature behavior of the tilt for materials having an SmA - SmC transition. However, the director has one more degree of freedom and we have to specify the tilt direction. In Fig. 43 we have chosen the director to tilt in the plane of the paper. By symmetry, infinitely many such planes can be chosen in the same way, and evidently we have a case of continuous infinite degeneracy in the sense that if all the molecules tilt in the same direction, given by the azimuthal angle cp, the chosen value will not affect the free energy. The complete order parameter thus has to have two components, reflecting both the magnitude of the tilt Band its direction cpin space, and can conveniently be written in complex form
y = Oe'q
(125)
With a complex scalar order parameter, the SmA-SmC transition is expected [131] to belong to the 3D XY universality class, which does not have the critical exponent p equal to 1/2. Nevertheless, experiments show [132] that it is surprisingly well described by mean field theory, although with an unusually large sixth order term. As all tilt directions are equivalent, the free energy can only depend on the absolute value squared of the order parameter. Actually, the first intuitive argument would say that there could be a linear term in the absolute value. However, physical descriptions avoid linear terms in absolute values, since these mean that the derivatives (with
tl
Figure 44. Functions of the kind G - 1 ~ 1 ,i.e., linear dependence in an absolute value, are with few exceptions not allowed in physics, because they imply discontinuities in the first derivative, which are mostly incompatible with the physical requirements.
physical significance) would have to be discountinous (see Fig. 44). Therefore, we assume that the free energy can only depend on
1yl2=Y * Y = Be-@x Be@= e2
(126)
The Landau expansion then has to be in powers of IY'I2= Y*Y and we see that the free energy is independent of cp, as it has to be. This is just equivalent to our first expansion. Generally speaking, G is invariant under any transformation Y - + Ye'W
(127)
This is an example of gauge invariance and the azimuthal angle is a gauge variable. The complex order parameter Y is shown schematically in Fig. 45 illustrating the conical degeneracy characteristic of the SmC
fluctuationsin 3!
Figure 45. Illustrations of the two-component order parameter Y = Qetqdescribingthe SmA-SniC transition. The thermodynamic variable Qandthe gauge variable qare completely different in their fluctuation behavior. The fluctuations in qmay attain very large values and, being controlled by an elastic constant scaling as Q 2 , may actually become larger than 27t at a small but finite value of 8.
2.5 The SmA*-SmC* Transition and the Helical C* State
phase. The gauge variable cp is fundamentally different in character from 8.The latter is a “hard” variable with relatively small fluctuations around its thermodynamically determined value (its changes are connected to compression or dilation of the smectic layer, thus requiring a considerable elastic energy), whereas the phase cp has no thermodynamically predetermined value at all. Only gradients Vcp in this variable have relevance in the energy. The result is that we find large thermal fluctuations in q around the cone, of long wavelengths relative to the molecular scale, involving large volumes and giving rise to strong light scattering, just as in a nematic. The thermally excited cone motion, sometimes called the spin mode (this is very similar to the spin wave motion in ferromagnets), or the Goldstone mode, is characteristic of the nonchiral SmC phase as well as the chiral SmC* phase, but is of special interest in the latter because in the chiral case it couples to an external electric field and can therefore be excited in a controlled way. This Goldstone mode is of course the one that is used for the switching mechanism in surface-stabilized ferroelectric liquid crystal devices. The tilt mode, often, especially in the SmA phase, called the soft mode (although “hard” to excite in comparison with the cone mode, it may soften at a transition), is very different in character, and it is convenient to separate the two motions as essentially independent of each other. Again, this mode is present in the nonchiral SmA phase but cannot be detected there by dielectric methods, because a coupling to an electric field requires the phase to be chiral. In the SmA* phase this mode appears as the electroclinic effect.
57 1
2.5.2 The SmA* - SmC* Transition If the medium is chiral the tilt can actually be induced in the orthogonal phase by the application of an electric field in a direction perpendicular to the optic axis, as shown in Fig. 46. The tilt is around an axis that is in the direction of the electric field. This is the electroclinic effect, presented in 1977 by Garoff and Meyer [21]. Soft mode fluctuations occur in the SmA phase just as in the SmA* phase, but only in the SmA* phase can we excite the tilt by an electric field. This is because a tilt fluctuation in the medium with chiral symmetry is coupled to a local polarization fluctuation, resulting from the transverse dipoles being ever so slightly lined up when the tilt disturbs the cylindrical symmetry of the molecular rotation. Superficially, it might be tempting to think that chiral and nonchiral smectic A (SmA* and SmA) would be very similar or even have the same symmetry, because they are both orthogonal smectics with the same organization of the molecules in the layers and with the same cylindrical symmetry around the layer normal. Nothing could be more wrong. As we have seen (in one striking example - several more could be given),
Figure 46. If an electric field E is applied perpendicular to the optic axis in a smectic A* (or any chiral orthogonal smectic), the optic axis will swing out in a plane perpendicular to the plane E , n defined by the optic axis and the field (electroclinic or soft-mode effect).
572
2
Ferroelectric Liquid Crystals
their physics is very different, due to the fact that they have different symmetry. Reflection is not a symmetry operation in the SmA* phase, and the electroclinic effect does not exist in the SmA phase just because the SmA phase has this symmetry operation. We may also apply the Curie principle to this phenomenon. The SmA phase has D,, (or -lm) symmetry, with one C, axis along the director (optic axis), infinitely many C2 axes perpendicular to this axis, and in addition one horizontal and infinitely many vertical mirror planes. The mirror planes are absent in the SmA* phase (D, or 0322). If we apply an electric field E (of symmetry C,) perpendicular to the C, axis, the only common symmetry element left is one C2 axis along E , which permits a tilt around C2. In Fig. 46 we also see that, in particular, the plane ( E , n) is a mirror plane in the nonchiral SmA phase, and consequently neither of the two tilting directors shown in the figure are allowed. In the SmA* phase ( E ,n ) is not a mirror plane, hence one of these tilt directions will be preferred. (Which one cannot be predicted as this is a material property.) An interesting aspect of this phenomenon is that it means that an electric field acting on the chiral medium actually exerts a torque on the medium. This is further discussed in Sec. 2.5.8. The torque is of course inherent in the chirality. The axial symmetry character is provided by the medium. The electroclinic effect is a new form of dielectric response in a liquid crystal. If we increase the electric field E, the induced polarization P will increase according to the first curve of Fig. 5. With a small field, P is proportional to E, and then P saturates. As the coupling between tilt and polarization is also linear at small values of tilt, we get a linear relationship between 8 and E. With 8 = e*E, the proportionality factor e* is called the electroclinic coefficient. It has an intrinsic chiral quality. (We have used an
asterisk here to emphasize this and also to clearly distinguish it from the flexoelectric e-coefficients.) In nonchiral systems, e * is identically zero. With present materials, 8is quite small (115 ”), but this may change with new dedicated materials. The electroclinic effect is also appropriately called the soft-mode effect, because the tilt deformation is a soft mode in the SmA phase, the restoring torque of which softens when we approach the SmA*SmC* transition, at which the deformation starts to “freeze in” to a spontaneous tilt. When we have such a spontaneous tilt as we have in the SmC* phase, we will also have a spontaneous polarization because of the rotational bias. It is important to note that the molecular rotation is biased in the nonchiral SmC phase as well as in the SmC* phase, but in a different manner. We may start with the “unit cell” of cylindrical symmetry of the SmA (or SmA*) phase and the corresponding cell of monoclinic symmetry of the SmC (or SmC*) phase, as in Fig. 47. We put a molecule in each one and ask whether the molecular motion (which, like the shape of the molecule, is much more complicated than here indicated) is directionally biased in its rotation around the optic axis (only roughly represented by the core part of the molecule). One simple way of representing this bias is to draw the surface segments corresponding to some interval in the rotation angle. Let us imagine that the molecule has a dipole perpendicular to its average rotation axis. We then find that the probability of finding the dipole in any particular angular segment is same in all directions in the SmA (SmA*) phase, as it has to be, because the optic axis is a C, axis. In the nonchiral C phase, the rotation cannot have this circular symmetry, but it must be symmetrical with respect to the tilt plane, as this is a mirror plane. This means that the rotational bias has a quadrupolar symmetry,
2.5 The SmA*-SmC* Transition and the Helical C* State
573
=t
9
A phase
Y
J
chiral molecule in A or A* matrix
phase is uniaxial
non-chiral molecule in C matrix
phase is biaxial and has quadrupolar order
chiral molecule in C or C* matrix
phase is biaxial and has polar order
Figure 48. Origin of the spontaneous polarization in a smectic C* phase. The illustration shows the directional bias for a lateral dipole in the rigid rod model of a molecule, with the directionality diagram for the short axis when the molecule is rotating about its long axis (from Blinov and Beresnev [45]).
I
I
tilt plane
Figure 47. The origin of the spontaneous polarization. The probability for a lateral dipole (averaged in time and space) to be in a unit angular segment is compared for the orthogonal, nonchiral tilted and chiral tilted phases. The common statement that the origin of polarization is a “hindered rotation” is quite misleading because, hindered or not, a rotation will only result in nonzero polarization for a specific (polar) directional bias.
which we can describe by a quadrupolar order parameter. If we now drop the mirror plane by making the phase chiral we will, in addition to this quadrupolar dissymmetry, have a polar bias giving a different probability for the dipole to be directed at one side out of the tilt plane rather than in the opposite direction. This will give a nonzero polarization density in a direction perpendicular to the tilt plane (see also the illustration in Fig. 48).Which direction cannot be predicted a priori but it is a molecular property. It is fairly obvious that the bias will increase as we increase the tilt angle, and
hence the polarization will grow when we lower the temperature below the SmA* SmC* transition. This transition occurs when the tilt 8 becomes spontaneous and is only weakly influenced by whether the phase is chiral or not. However, chirality couples 8 to P (which is a dramatic effect in a different sense) and brings P in as a secondary order parameter. There might also be a coupling between P and the quadrupolar order parameter, which will, however, be ignored at this moment.
2.5.3 The Smectic C* Order Parameters If we keep the tilt angle 8 in Fig. 48 fixed (just by keeping the temperature constant), we can move the molecule around the tilt cone, and we see that the rotational bias stays sterically fixed to the molecule and the tilt plane. The direction of the resulting P lies in the direction z x n . If we change the azimuthal angle by 180”, this corresponds to a tilt -8 (along the -x direction), and results in a change of P direction from y to -y. This means that we could tentatively write the relation between the secondary and pri-
574
2
Ferroelectric Liquid Crystals
mary order parameters as
P-0
(128)
or more generally that P is an odd function of 0 P = aO+ b e
+ ...
(129)
I
I$
' t e
8
Figure 49. Under the action of the twofold symmetry axis in the smectic C* state the tilt changes from 8 to 8+n.
As sin0 is an odd function, an expression that has this form is
P = Poz x rz = (PosinO)8
(130)
where we have introduced Po(with its sign, see Fig. 23 in Sec. 2.3.4), the magnitude of spontaneous polarization per radian of tilt. With 0 r z x n we may write &hetilt as a vector 0 = 8 8 to compare its symmetry with that of P. 0 is then an axial vector, while P is a polar. As we have no inversion symmetry in the chiral phase, this difference does not cause any problem, and if P and 0 transform in the same way we may make a Landau expansion according to the improper ferroelectric scheme of Sec. 2.2.6. If we take the scalar part of Eq. (130), it takes the form
P = Po sin0
(131)
This expression is often used but does not have the correct symmetry because it is not invariant under the C2 symmetry operation. For, if we change 8 to 8 + x, sin 0 changes to -sin 0 although P cannot change, because this is the same state (see Fig. 49). Therefore Eq. (131) should be replaced by 1 P=-&sin20 2
(132)
which is a C 2 invariant expression. In practice the expressions do not differ very much; P just increases somewhat slower at large tilts according to Eq. (132). For small values of tilt the expressions do of course give the same results, i.e., P=Po8. Experimentally, this simple linear relation between P and 0 often holds quite well, as shown in
Figure 50. (a) Schematic temperature dependence of the tilt angle 8 and polarization P at a second-order SmA* - SmC* transition. (b) Tilt angle versus temperature for DOBAMBC below the SmA*-SmC* transition at 95 "C (from Dumrongrattana and Huang [ 1331).
Fig. 50. However, there are exceptions, for instance, cases where P is a linear function of temperature rather than parabolic. Although the tilt angle has certain limitations, we will continue to use 0 as the order parameter for the time being. Finally, however, we will construct a different order parameter (Sec. 2.5. l l ) to describe the tilting transition.
2.5.4 The Helical Smectic C* State We did not change anything in the nonchiral order parameter (Eq. 125) when we pro-
2.5 The SmA*-SmC* Transition and the Helical C* State
ceeded to the chiral case, except that in addition we introduced a secondary order parameter P which does not exist in the nonchiral case. Now the normal state of the smectic C* is the helical C* state, i.e., one in which the tilt has a twist from layer to layer. At constant 6, q~is therefore a function of z (see Fig. Sl), with @z)=qz, q being the wave vector of the helix
575
z
(133) where the helix is right-handed for q > 0 and Z is the helical periodicity. For this case there is an obvious generalization of the nonchiral order parameter (Eq. 125) to y = eeiln(r) q
with
4 a= qz
(134)
(C)
Figure 51. (a) In the helical smectic C* state the constant tilt Bchanges its azimuthal direction cp such that cpis a linear function in the coordinate z along the layer normal. (b) The c director is a two component vector (cx, c,,) of magnitude sin 0, which is the projection of n on the smectic layer plane. (c) P makes a right angle with the tilt direction. The P direction here corresponds to a material with Po > 0.
where we have introduced a new length q-’ as an effect of chirality. Yqis now chiral by construction but does not make any change in the Landau expansion since Yq*Yqis still equal to 82, and we will still have the SmA* -SmC* transition as second order. We can also write Yqas
As the polarization vector is phase-shifted by 90” relative to the tilt vector Yq,we see from Eq. (136) that it can be written (see Fig. 5 1c) as
Yq= B(cosqz + i sinqz)
P = (-P sinqz, Pcosqz, 0)
(135)
It is interesting to form the divergence of this vector. We find
and as a vector Yq= (Qcosqz, esinqz, 0)
(1 37)
(136)
or
Yq= ec
(136a)
where we have introduced the “c director”, the projection of the director n on the smectic layer plane (see Fig. 51b). Note that the c director in this description (which is the common one) is not a unit vector, as it is in the movable reference frame k , c , p used, in contrast to the space-fixed reference frame x, y, z, in Sec. 2.4.9 to describe the flexoelectric deformations.
This is an important result as it means that the helicoidal C* state is a divergence-free vector structure P(r) in space. Hence we have no appearance of space charges anywhere. Thus not only does the helix cancel the macroscopic polarization and thereby any external coulomb fields, although we have a local polarization P everywhere, but the fact that V -P = 0 also secures that there are no long range coulomb interactions in
576
2
Ferroelectric Liquid Crystals
the material due to space charge. The helical state is therefore “low cost” and “natural” from several points of view. A homogeneous state of the director, as can ideally be realized by surface stabilization, of course also has V . P = O , although it has an external coulomb field and therefore is not stable by itself. However, as we will see later, the condition V . P = O cannot be maintained everywhere if we have a local layer structure of chevron shape (see Sec. 2.8.3). For the sake of completeness, but also for distinction, let us finally make a comment on an entirely different kind of chiral order parameter. Let us imagine that the substance we are dealing with is a mixture of two enantiomers (R) and (S). We can then define a scalar quantity R-S K=-----R+S
(139)
where R and S stand for the relative concentration of (R) and (S) enantiomers. This quantity can in a sense be regarded as an order parameter. K = 1 for “all R’, -1 for “all S”, and zero for a racemic mixture. Thus in general, 0 I I K I 5 1. This quantity is nothing less than what organic chemists introduced long ago, but in a completely different context. It is sometimes called “optical purity”, but is today rather called enantiomeric excess. It is an extremely useful quantity in its right place, but it is not relevant as an order parameter because it does not depend on the temperature T, only on the concentration, which is trivial in our context. It does not help us in introducing chirality and we will not have use for it.
2.5.5 The Flexoelectric Contribution in the Helical State We note from Fig. 5 1 that the projection of the director on the smectic layer plane is
n sin 6= sin 6. If we write the components of n in the x,y,z system, we therefore have n, = sin6 cosq n,, = sin0 sinq n, = cos6 If we insert v>(z) = qz for the helical state this gives,
n, = sin6 cosqz n,, = sin6 sinqz n, = cos6 This is a twist-bend structure, as we have repeatedly stated, and is therefore connected to a flexoelectric polarization of size (see Eq. 97) P, = ebn x ( vx n )
(142)
We will now calculate this contribution. Forming the curl as (143)
Y = - q sin 6 sin 6 cos qz sin &in qz cos 6
‘ i
X .
cos qz
sin qz
o i
I
2.5
The SmA*-SmC* Transition and the Helical C* State
Therefore we can write the flexoelectric polarization due to the helical deformation as
1 Pf =-eb.-qsin28 2
(147)
Note that this polarization grows with the tilt according to the same function as the spontaneous polarization P, in Eq. (132). We may then write the total polarization density P = P, + Pfas
P=-(Po 1 -ebq)sin28 2
(148)
or, for small angles P = (Po - e,q) 8
(148 a)
If Po and eb have different signs, the two contributions will cooperate, otherwise they tend to cancel. (This is not changed if we go from a certain chiral molecule to its enantiomer, as q and Po will change sign simultaneously.) In the absence of a smectic helix, q = 0, and the flexoelectric contribution will vanish. The sign of Po has been determined for a large number of compounds, but sign (and size) determinations of flexoelectric coefficients are almost entirely lacking. Such measurements are highly important and should be encouraged as much as possible. However, recent measurements by Hoffmann and Kuczyn'ski [134] show that the flexoelectric polarization is of the same magnitude as the spontaneous one. Equation (148) may also be a starting point for a new question. In the absence of chirality, thus with Po=O, could the flexoelectric effect lead to a helical smectic state in a nonchiral medium? This will be the topic of our next section.
577
2.5.6 Nonchiral Helielectrics and Antiferroelectrics As we have repeatedly stressed, flexoelectricity is a phenomenon that is a priori independent of chirality. But we have also seen that some flexoelectric deformations do have a tendency to occur spontaneously in a chiral medium. All except the helical C* state are, however, suppressed, because they are not space-filling. A flexoelectric deformation may of course also occur spontaneously in the nonchiral case, namely, under exactly the same conditions where the deformation is space-filling and does not give rise to defect structures. In other words, in creating the twist-bend structure which is characteristic of a helielectric. Imagine, for instance, that we have mesogens which have a pronounced bow shape and, in addition, some lateral dipole. Sterically they would prefer a helicoidal structure, as depicted in Fig. 52, which would minimize the elastic
Figure 52. Space-filling twist -bend structure of strongly bow-shaped achiral molecules equally split into right-handed and left-handed helical domains. (Here a right-handed domain is indicated.) A bowshaped molecule of this kind is illustrated in Fig. 53. The kind of domain depicted in this figure would correspond to the normal helical antiferroelectric organization in a smectic C*. As a result of the two-dimensional fluidity of these smectics, the cancellation can, however, be expected to occur on the smallest possible space scale.
578
2 Ferroelectric Liquid Crystals
energy, because the spontaneous bend B would cancel the bend term (Eq. 117) in the Oseen-Frank expression. The resulting local polarization from Eq. (148) with Po= 0 may still not be too costly because the external field is cancelled and V. P = 0. This would have an interesting result: because the starting material is nonchiral, we would observe a spontaneous breaking of the nonchiral symmetry leading to equal regions with left-handed and right-handed chirality. It would correspond to the well-known examples of SiO, and NaC10, discussed in Sec. 2.3.4. It seems that finally this kind of phenomenon may have been observed in liquid crystals [135]. However, in contrast to the cases of SiO, and NaClO,, the helical structures are probably possible on a molecular level as well as on a supermolecular level. Thus we may expect domains of nonchiral molecules in different conformations, right and left-handed, which behave as if they belong to different enantiomeric forms. The possibility that a space-filling flexoelectric deformation will be spontaneous for certain molecular shapes and thereby create a chiral structure out of nonchiral molecules will be much enhanced if the deformation can take place in the layer rather than in the interlayer twist -bend structure of Fig. 52, and may then lead to antiferroelectric (rather than helielectric) order similar to that in antiferroelectric liquid crystals made of chiral compounds. The polarization may very
QrN ‘gH17
Figure 53. Bow-shaped nonchiral molecule which may create chiral C* domains (from [135]).
well be switchable, because it is not connected to a supramolecular director deformation. In other words, the deformation represented to the lower right of Fig. 32 now applies to the single molecule and this can be flipped around by the electric field. Further investigations of these new materials are important and will shed light on a number of problems related to polarity and chirality. Whether we will find mechanisms for complete spatial separation reminiscent of the classic discovery by Pasteur, who could separate crystallites of tartaric acid into right-handed and left-handed pieces, is too early to speculate about, but the possibilities, as always in liquid crystalline systems, are quite rich.
2.5.7 Simple Landau Expansions In order to sharpen the observance for inconsistencies in a theory, it is sometimes instructive to present one which does not work. For instance, let us see if we can describe the transition to a polar nematic phase by a Landau expansion. It might also be thought of as describing the transition isotropic-polar smectic A or nematic-polar smectic A. (In either interpretation it will suffer from serious deficiencies.) We write the free energy as
G=-aS 1 2+-bP 1 2 -cSP2 2 2 where S is the (reduced) nematic order parameter and P the polarization. The same abbreviation a =a (T- To) and sign conventions are used as before. The form of the coupling term is motivated by the fact that S and P have different symmetries, quadrupolar and polar, respectively. (It is also easy to persuade oneself that a term -SP would lead to absurdities.) G now has to be minimized with respect to both order parame-
2.5
The SmA* -SmC* Transition and the Helical C* State
ters: putting aG/aP and aG/aS equal to zero gives b P - 2~ S P = 0
(150)
a S- cp2= 0
(151)
from which we deduce
(153) Whether it is already not clear physically how a non-zero S-value would couple to a non-zero polarization, we see that Eq. (153) describes a P(7‘) increasing below the transition point only if b < 0, at the same time as S is essentially independent of temperature. In order to give S > 0, we have then to require that c
579
xoq,
where is the dielectric susceptibility, by definition. For the chiral smectic phase we now write the free energy with the tilt 8 as the primary order parameter G = -1a 8 2 +-be 1 4 +- 1 p 2 2 4 2x0 Eo -c*P8-PE
(157)
where the 8- P coupling coefficient is written c* to emphasize that it is chiral in its nature, while all other coefficients are non-chiral. We have disregarded any coupling with the nematic order parameter S. This is totally justified. Although it is true that Sincreases to some extent when 8 increases, this is certainly of no significance around the A* -C* transition. At this stage we also neglect the complications of an eventual helical structure. This is admissible because the helix is not a necessary condition for a chiral tilted smectic. We are first interested in the spontaneous polarization, i.e. the case E=O. The variable P means just “polarization”, i.e. the total polarization, even if a number of sources may contribute - we cannot have different P variables for different “sorts” of polarization. We may however ask: what is the origin of the P2 term and what does it signify? Answer: take the coupling away, i.e. put the coupling coefficient c*=O. Then minimizing G with respect to P just gives
(154) Why we have chosen to write the coefficient in front of the P2 term in this form will be evident in a moment. aG/aP = 0 gives
L P - E = O
xo Eo
or
(155)
i.e.
P=O
(159)
In other words, the third term in the expansion counteracts polar order. It secures that P vanishes, unless there is a coupling between 8 and P. Its origin is entropic and has nothing to do with dielectric effects. The third term is just not “electric” and therefore
580
2
Ferroelectric Liquid Crystals
xois often referred to as a “generalized” susceptibility. What this P2term means is that other factors being equal, polar order increases the order, hence decreases the entropy and increases the free energy: a non-zero polarization is always connected with an entropic cost in energy - whence the plus sign in Eq. (157) -and therefore will not occur spontaneously if there is no other contribution that diminishes the energy even more for PzO. We might therefore expect that the result depends on the strength of the chiral coupling constant c*. With c* #O Eq. (157) gives in the field-free case (E= 0)
or
P = xoQc*e
(161)
gives
Hence
P = x o ~ c * +e X ~ G E
( 164)
Now we see that the total polarization has two origins. On one hand a polarization is induced by an external field, the proportionality factor being the susceptibility and on the other, there is a tilt induced polarization q,c* 8 independent of any external field E. if we would have applied the external field along just any direction, the E in Eq. (164) would correspond to the component perpendicular to the tilt plane. Therefore we could also write Eq. (164) as
xok,
xo
P = xIG(c*e
+ E>
(165)
Perhaps to our surprise, this means that however weak the coupling, any non-zero coupling constant c* actually leads to a nonzero value of spontaneous polarization P. This polarization, at least for small values of 6, is proportional to 8
expressing the two contributions to P and emphasizing that the susceptibility is the one perpendicular to the tilt plane. Without changing anything else, we can make c* = 0 by replacing the chiral substance by its racemate. Eq. (165) then reduces to
p-e
p = XL%E
(162)
i.e. the polarization increases with increasing tilt, and the proportionality factor xoq,c* only vanishes for c* strictly equal to zero. This means that however weak the coupling, it dominates the counteracting entropy factor. This is also consistent with our discussion in Sec. 2.3.2 of this Chapter: the coupling is via chirality which brings the decisive change in symmetry. We could symbolize the strength c* of the coupling constant by the concentration of chiral dopant which we add to a non-chiral smectic C host. Any non-zero concentration, however small, is sufficient to change the symmetry. if we now allow a non-zero external field along P, Eq. (157) in the same manner
(166)
xL%,
Hence our or xoq,,is the suceptibility of the racemate perpendicular to the tilt plane. Let us now continue with the case E=O, that is with the spontaneous polarization below T,. introducing the structure coefficient s* we can write the relation Eq. (161) as P = s*e
(167)
The structure coefficient
s* = xoq,c*
(168)
is the dielectric susceptibility of the racemate multiplied by the chiral coupling coefficient and thus another related chiral parameter, which we can expect to be essen-
2.5 The SmA*-SmC* Transition and the Helical C* State
tially temperature independent. We can expect it to grow very slowly towards lower temperatures, like -l/kT, originating in the entropic character of the P2 term (xi' kT) in Eq. (157). The linear relation Eq. (167) and the temperature independence of s* for reasonable temperature ranges have been experimentally confirmed in dielectric measurements, especially by Bahr and Heppke [188]. The quotient PI8= s* is free of divergences and a characteristic for each molecular species. Its meaning is the dipole moment per unit volume for unit tilt angle. In rare cases of strong conformational changes in the molecule it may behave anomalously and even change sign. It can be looked upon as a kind of susceptibility like and we will understand all these and similar susceptibilities more strictly as response functions in the limit of small tilts or small applied fields, = (aP/aE),=,. for instance The relation Eq. (167) may look trivial but hides something fundamental that we should just not let go unnoticed. The polar order expressed by P is a result of a rotational bias expressed by 8. It is counteracted by thermal disorder, represented by the 1 term - ( x o q J 1 P 2 in the Landau expansion 2 which is proportional to kT. Thus in Eq. (167) s* - 1IT. But this is nothing else than the old Langevin balance, just the same in principle as between a magnetic field H wanting to align magnetic dipoles and thermal motion wanting to destroy the alignment, leading to a magnetization
-
x
xO%
M - -H T or between an electric field E wanting to align electric dipoles and thermal motion, leading to a polarization P--E T
58 1
We already discussed this in Sec. 2.2 of this Chapter (cf. Eqs. 4 and 5). Now, with l/kT we can write Eq. (167) in the form
xo-
P--e T The tilt here acts like a (biasing) field corresponding to H and E in Eq. (169) and ( 1 70). This is thus nothing else than the Curie law, only unusual in the sense that the field variable is a tilt. As we already noticed in Sec. 2 of this Chapter, this law indicates that the local dipoles are non-interacting. The collective behavior in the medium is in 8, not in P. So far, except for discussing the physical character of the terms in the Landau expansion, we have mainly derived a very simple relation (Eqs. 167 and 168) between P and 8 in the case that both appear spontaneously, that is, in the C* phase. But what is their relation if P is a polarization induced by an electric field? When we consider the A* phase, i.e. T> T,, P and 8can be nonzero only if E#O, thus the -PE term is now important. And now we have a situation which in a sense is opposite to the one below T,: in the C* phase we have a non-zero tilt which gives rise to a non-zero polarization; here we have a non-zero polarization causing a non-zero tilt. How do we get the equilibrium value of 8for a certain constant value of E ? We here recall the expression Eq. (157). 1 4 +- l P 2 G = -1a 8 2 +-be 2 4 2x0 EO -C * P 8 - PE
(157)
and want to proceed by forming aG/a8 and putting it equal to zero. But the sensitive reader might react to this: we cannot vary 8 while keeping both E and P constant. In (aGla8),, we can keep E constant but we cannot vary 8 while keeping P constant. A variation of 6 involves a variation of P , or does it not? The answer to this question re-
582
2
Ferroelectric Liquid Crystals
veals the very special character of the Landau expansion. This is an expansion around equilibrium. The variables 0 and P appearing in the expression are pre-thermodynamic variables in the sense that only the minimization of G will give the relation between those variables in equilibrium. It is quite possible to imagine that we tilt the director without changing P , but then we disturb the statistics which costs energy. Conversely we may imagine that the rotational bias changes in such a way that P increases (we decrease the rotational entropy) without changing 0, but then we are not in equilibrium. In order to go back to equilibrium without changing 0 we would have to apply an electric field counteracting the 0 change (which costs energy), and so on. Hence, the variables in the Landau expansion have to be considered independent, and only when we have determined the equilibrium values by asap = 0, a a a o = 0, we may look upon them as dependent, interrelated variables. We will now take that step and see which physical results can be derived from the expansion. Putting the two derivatives equal to zero gives, respectively,
--
xo EO
with
T,=G+ xo Eo c *2 a Thereby Eq. (134) is reshaped into
a ( T - T,) + be2 = 0
(179)
giving the wellknown parabolic increase of 0 below T,. The reader will now remember from Sec. 2.5.1 that in the Landau expansion Eq. (157) the coefficient a( 7') is equal to a(T-T,) where To is the temperature at which the tilt goes to zero in the nonchiral system (the racemate). Therefore we see from Eq. (178) that the phase transition temperature has been raised to a slightly higher value than the transition temperature To for the racemate, cf. Fig. 54. This increase in transition temperature AT corresponds to the additional energy needed to break the coupling between polarization and tilt in the chiral case. Conversely, a spontaneous tilt
c*O-E=O
and aO+bO,-c*P=O
(173)
Writing the first one (as previously Eq. 164) P = xo&o~*O+ X~GE
(174)
and inserting P in the second, we find aO+ b@ - x o ~ ~ * 2 0 - x O ~ 0 ~ * (175) E= For E = 0 the first solution 0 = 0 corresponds to the A* phase. In the second solution a-xo&,,c*2
+ b82 = 0
(176)
we rewrite the first two terms according to
C-A
C*-A*
\\\\\\\\\\\\\\\\\\\\\\ \ I \\\\\\\\\\\\\\\\\\\\\\\ I
II I I I I
\\\\\\\\\\\\\\\\\\\\\\\ I 1 /1 /1 1
Figure 54. The chiral coupling between Band P shifts the tilting transition to a higher temperature than the C + A transition. The shift is proportional to the coupling constant squared. Doping a non-chiral SmC host we should therefore expect a shift ATproportiona1 to the square of the concentration of the dopant.
583
2.5 The SmA*-SmC*Transition and the Helical C* State
appears earlier on cooling a chiral material than the corresponding nonchiral material. We note that the offset in the transition point
AT =
xo Eo c *2 a
is proportional to the chiral coupling coefficient squared and inversely proportional to the nonchiral thermodynamic coefficient a, the latter fact being reasonable because a i s proportional to the restoring torque density (-&) trying to establish the 8 = O value of the orthogonal A* state, thereby diminishing the rotational bias. We have, so far, considered the non-helical C* case. With the helix present we would have found the transition C* +A* pushed even slightly further upwards in temperature because now, in addition, we have to bring up energy to unwind the helix at the transition. We would then have found another contribution to AT being proportional to q2, where q is the value of the helical smectic C* wave vector at the transition. In any case, AT still turns out to be quite small (like all chiral perturbations), in practice often less than a degree. With the same reshaping of a-XoGc*2 to a ( T - T o ) , which we just used in Eq. (179), our previous Eq. (175) will look like
a(T-T,)O+ b 8 3 - x o ~ ~ * E
(181)
With this we now specifically turn to the case T > T,. As the tilt induced in the A* phase by an external electric field is quite small we first discard the O3 term and get
a(T-TC)8=~o~c*E
(182)
This gives the induced tilt angle
It is thus linear in the electric field in this approximation, but strongly temperature
dependent, diverging as we approach T, from above. In the A* phase the relation between 8 and E is almost as simple as that between P and 8 in the C* phase, while the relation between P and 8 is not as simple. Equation ( 183) describes the electroclinic effect. We may write it 8 = e*(T)E
(1 84)
where e* is the electroclinic coefficient
showing the close relationship between the chiral material parameters e*, c* and s*. Specifically we see that the structure coefficient s* is the non-diverging part of e*.
2.5.8
The Electroclinic Effect
If we assume (which is not quite true, but empirically fairly well justified) that the same simple relation P = s* 8 is valid also for T > T,, the combination
p=s*e, 8=e*E
(186)
is equivalent to P=s*e*E With e* taken from Eq. (185) we see that
i.e., that part of the polarization which corresponds to the induced tilt, diverges in the same way as the primary order parameter. (There is of course also a non-diverging part of P). While 8 - s * in Eq. (184), P-s**, which has to be the case as P , unlike 8, cannot depend on the sign of s*. We note, furthermore, that as e* and s* only differ in the temperature factor they always have the same sign. This means that the electroclin-
584
2
Ferroelectric Liquid Crystals
ically induced tilt or polarization will never counteract a spontaneous tilt or polarization, except in the sense that in a switching process - because the electroclinic effect is so fast - the electroclinic contribution may temporarily get out of phase from the ferroelectric contribution. In order to get the correct relation between P and 8 for T > T, we have to start from the generally valid Eq. (174) which we write as
sponding to Eq. (1 88). The first is the “background” part corresponding to s* = 0, ie.e to a racemic or non-chiral substance. The electroclinic effect is linear only if we do not approach too closely to T,. At the transition, T = T,, the first term in Eq. (1 8 1) vanishes and the relation between 8 and E becomes
If we assume the linear relationship 8 = e* E to hold - which is not true near T, - then
This nonlinear behavior with saturation is well known experimentally. It means that the electroclinic coefficient becomes fielddependent and falls off rather strongly (-E-2’3) at high fields. It also means the same for the electroclinically induced polarization which acquires relatively high values at low applied fields but then shows saturation. It explains the shape of the measured P ( T ) curves near T, as illustrated in Fig. 18 (dashed line). For T# T, but near T, we have to keep all the terms in Eq. (18 1). We may write this expression in the form
P=s*8+s*8 c*e* and inserting e* from Eq. (185)
The first term slowly decreases with in- 1/T) whereas the creasing temperature second slowly increases. This explains the empirically found result that P / 8 is essentially the same (=s*) in the C* phase as well as in the A* phase. The ratio is thus practically the same whether P and 8 are spontaneous or induced. Within the approximation of small tilt, Eq. (182), we now insert the value for Bfrom Eq. (183) in the expression Eq. (189) for P. This gives
(xo
be3 = S* E
( 1 94)
or
A 8 + Be3 = E
( 196)
with
a ( T - T,) A =< S
(197)
and B=- b S”
or (193) The second part is the electroclinic contribution to the dielectric susceptibility corre-
Generally it can be said that Eq. (196) very well describes the experimental results. A particularly careful study has been made by Kimura, Sako and Hayakawa, confirming both the linear relationship Eq. (197) and the fact that B, and therefore b as well as s*, are independent of temperature [ 1891.
2.5
The SmA*-SmC*Transition and the Helical C* State
The electroclinic effect is intrinsically very fast. The torque acting on the director, and giving rise to a change in tilt, is obtained by taking the functional derivative of the free energy with respect to the tilt, (199)
Equation (157) combined with Eq. (164) then gives
585
axis relaxes back to its state along the layer normal from a beginning state of nonzero tilt. Equation (202) in this case simply reads
which is directly integrated to
with the characteristic time constant
-re=a0 + b02 - c*P = a ( T - T,)O+ b03 - s*E
(200)
= a0- x O q c * 2 0+ be3 - x O q c *E
As evident from the middle one of these equations, we confirm, by Eq. (194) that this torque vanishes when we approach T = T,, where 0 shows a diverging tendency and we can expect a critical slowing down in the response. The viscous torque r" counteracting any change in 0 is, by definition,
If instead a constant field Eo is applied at t= 0, the growth of 8 will be given by
which is integrated to
with the saturation value of 0 equal to
ao ru= -yQ at where '/e is the electroclinic or soft mode viscosity. In dynamic equilibrium the total torque r=re+T v is zero. This gives
This equation describes the dynamics of the electroclinic effect in a material where we have a lower-lying phase (T< T,) characterized by a spontaneous tilt of the optic axis. If we divide all terms by s*, it can be written
A 8 + B03 +($)b = E This is the dynamic equation corresponding to Eq. (196). For small induced tilts, however, we skip the O3 term in Eq. (202). If we further put E=O, we will see how the optic
which of course also corresponds to Eq. (183). If we finally apply a square wave, where we reverse the polarity from -EO to +Eo at t=O, the optic axis will change direction by an amount 20, according to
corresponding to the initial and final values
e(o) = -eO,o ( ~= )+oo.
We note that the response time given by Eq. (206) is independent of the applied electric field. In comparison, therefore, the response time due to dielectric, ferroelectric and electroclinic torque is characterized by different powers of E, as
586
2
Ferroelectric Liquid Crystals
The reason for this apparent peculiarity in the electroclinic effect is of course that if the field E is increased by a certain factor, the saturation value of the tilt is increased by the same factor. The angular velocity in the switching is doubled if we double the field, but the angle for the full swing is also doubled. Thus, electrooptically speaking, the speed of a certain transmission change in a modulator certainly does increase with increased field. But one mystery remains to be solved. How come, that the characteristic time zin Eq. (205) describing the relaxation back to equilibrium, is the same as the “response time” z in Eq. (208) describing the change of 8 under the influence of the electric field? Should not the relaxation back be much slower? This is what we are used to in liquid crystals: if a field is applied to a nematic, the director responds very quickly, but it relaxes back slowly when we take the field off. The answer is: the electric field exerts no torque at all on the director in the electroclinic action. Its effect is to shift the equilibrium direction in space of the optic axis. If the field is high the offset is large and the angular velocity in the director motion towards the new equilibrium state will be high. Equation (207) describes this motion and tells that the rate of change of t9is proportional to the angular difference between the initial and final director state. In fact Eqs. (204) and (207) are the same equation and can be written
The difference is only that the final state 0, in Eq. (204) is zero, whereas in Eq. (207) 80 is the value given by the electric field according to Eq. (209). Note that in Eq. (214) the electric field does not appear at all. The electric field E does, however, exert a torque on the whole medium during the electroclinic action. This torque, by conservation of an-
gular momentum, is opposite in sense to the torque exerted by the “thermodynamic force” on the director. As already mentioned in Sec. 1 of this Chapter, the electroclinic effect was first announced as a ‘‘piezoelectric’’effect [20], but shortly thereafter renamed. The similarities are interesting but the differences sufficient to characterize the electroclinic effect as a new dielectric effect. The variable 8 in which the “distortion” takes place is here an angular variable, cf. Fig. 55. If E is reversed, P and 8 are reversed. But there is no converse effect. (One cannot choose 26 in the distortion variable to induce a P of a given sign.) The electroclinic tilt is connected with a mechanical distortion, a shrinking of the smectic layer thickness d. In the simplest model, assuming tilting rigid rods instead of molecules, thus exaggerating the effect, the thickness change is
6d = d ( i -case) - e2
(2 15)
-
hence 6d E2, not -E and we have an electrostrictive, not a piezoelectric distortion. This is also consistent with the fact that no
t
1
t
I
Figure 55. Analogy between the piezoelectric and the electroclinic effect. A translational distortion in the former corresponds to an angular distortion in the latter. If the sign of the applied field E is reversed, the sign of P and 8 is also reversed. But there is no converse effect in the electroclinic case. The mechanical deformation is electrostrictive, i.e. proportional to E’. In the smectic C* case there is also a component proportional to E.
2.5
587
The SmA*-SmC* Transition and the Helical C* State
dilatation is possible in the A* phase, thus the effect is inherently unsymmetric. (Note that this is not so in the C* phase; with a finite 0 dilatation as well as compression is allowed.) The electrostriction may be a problem in the practical use of the electroclinic effect, because the field-induced layer shrinking, at least sometimes, leads to the appearance of layer kink defects, which may be observed as striations in the texture [ 1901. However, very little is known today of how the electrostrictive properties vary between different materials. The electroclinic effect is the fastest of the useful electro-optic effects so far in liquid crystals, with a speed allowing MHz switching rates in repetitive operation. Its electro-optical performance is discussed and compared with other modes in the review of reference [191]. A number of device applications are discussed in reference [140]. The effect appears in all chiral orthogonal smectics but has been studied in a very restricted class of materials. It suffers so far, except from the fairly strong temperature sensitivity, in particular from a limitation in the value of induced tilt angle (12 to 15 degrees). This means that only a very small part of the typical V-shaped transmission curve can be utilized for a modulator using this kind of material, cf Fig. 56. In this respect short pitch C* or N* materials are much better (exploiting the deformed helical and flexoelectro-optic mode, respectively) with a sweep in either direction of more than 22 degrees in the first and more than 30 degrees in the second case. However, new A* materials may very soon change the scene. The ideal material for the electroclinic effect would be a so-called de Vries compound [191a] in which the molecules have a large but unbiased tilt in the A phase (adding up just as in the short pitch C* or antiferroelectric case, to an optic axis along the layer normal) but a biased tilt in the C* phase.
-450
-22.5"
00
22.5"
45"
Figure 56. Modulation of the transmitted light intensity I for all electro-optic effects describing a tilt of the optic axis in the plane parallel to the cell plates (in-plane switching), for the case that the initial axis direction is along one of the two crossed polarizer directions. The curve is drawn for a cell thickness corresponding to A/2 plate condition, for which a tilt sweep of 45 degrees gives full modulation (from zero to 100 percent transmitted light). If this condition is not met, the degree of modulation will be reduced.
WewillreturntosuchmaterialsinSec. 2.8.10 because they are also of eminent interest for high resolution displays. Up to now they have been somewhat hypothetical but seem recently to have been confirmed [ 1921. Such de Vries materials would be ideal even if they have to be somewhat slower (the torque counteracting tilt fluctuations would not be so strong for such compounds) because first of all the electroclinically induced tilt would be very large, namely up to the full value of unbiased individual tilt, and this for an applied field that can be expected to be very low. Furthermore the tilt biasing does not involve any electrostrictive effect or, at least this would be minimal. Finally the temperature sensitivity can be expected to be very low as it is in the absence of collective behavior, essentially T-' instead of (T - T J ' .
2.5.9 The Deformed Helix Mode in Short Pitch Materials An interesting electro-optic effect utilizing the helical SmC* state of a short pitch ma-
588
2 Ferroelectric Liquid Crystals
terial was presented in 1980 by Ostrovskij, Rabinovich and Chigrinov [193]. In this case the twisting power was so high that the pitch came below the wavelength of light. In such a densely twisted medium the light wave averages out the twist to feel an optic axis directed along the helical axis, i.e. in the direction of the layer normal z (Fig. 57). When an electric field is applied perpendicular to this axis it starts to partly untwist the helix and in this way perturb the spatial direction of the average. The result is a linear
E-0
E>O
E
Figure 57. Partial untwisting of the helical axis in short-pitch materials (pitch in the range of 0.1 pm to 0.5 pm) has the effect of turning the averaged optic axis away from the layer normal as shown by the direction of the space averaged indicatrix. The twist also has the effect of averaging out part of the inherent large birefringence n,-no to a much smaller value (ne)- (n,) (averaged over a length > pitch) (from Beresnev et al. [194]).
effect very similar to that of the electroclinic effect and the flexoelectro-optic effect: the angular deviation (8)of the effective optic axis is proportional to the applied field. Like the other two mentioned effects this deformed-helix mode (DHM) has no memory but a continuous grey scale. Though not as rapid as the electroclinic effect it has at least two distinctive advantages. First, (0) can attain much higher values than the soft-mode tilt. Second, the apparent birefringence (An) is quite low, allowing a larger cell thickness to be used and still matching the ;1/2 condition. The short-pitch materials have shown another highly interesting property. When they are used in the SSFLC mode, i.e. when a field sufficient for complete unwinding is applied and then reversed, in order to actuate the switching between the two extreme cone positions, a new mode of surface-stabilization is found, in the limit Z+d, where 2 is the pitch or helical periodicity and d is the cell gap thickness. It may at first seem surprising that surface stabilization can be achieved not only for d IZ but also for d Z, in fact the smaller the value of 2 the better. In the limit Z 4 d it is a pinning phenomenon which makes it distinctly different from the first case of surface-stabilization. In other words, whereas for Z> d the non-helical state is the equilibrium state, for 2 6 d it is a metastable state. The helix thus tends to rewind but, for topological reasons (the back-transition is defect-mediated) it may stay for a considerable time. This means that short-pitch materials are very interesting alternatives to pitch-compensated materials for display applications. Their demonstrated inconvenience so far has been the difficulty to align then well, generally giving somewhat scattering textures. One further advantage of this effect is that the response time is only weakly temperature dependent. A general discussion of this and other fea-
+
2.5
The SmA*-SmC*Transition and the Helical C* State
tures is found in chapter VI of reference [41]. The DHM has been developed further by the Roche and Philips groups and applied in active matrix displays with grey scale, cf references [195] and [196].
2.5.10 The Landau Expansion for the Helical C* State As we repeatedly pointed out, the Landau expansion Eq. (157) used so far
1 2 +-be 1 4 +- l P 2 G=-aO 2 4 2x0 EO -c* P O - PE
(157)
refers to the non-helical C* state. Even if the non-helical state is somewhat special - the general case is one with a helix - and if it is true that for many purposes we may even regard the presence of the helix as a relatively small perturbation, it is now time to take the helix into account. The first thing we have to do then is to add a so-called Lifshitz invariant. This invariant is a scalar
589
Inserting this in Eq. (216) we find that the Lifshitz invariant (which has a composition rule slightly reminiscent of angular momentum, cf. L,=xp,-yp,) in the cholesteric case has the value equal to q, the wave vector. In fact we can gain some familiarity with this invariant by starting from an expression we know quite well, the Oseen-Frank expression for the elastic free energy Eq. (96). Because of its symmetry, this expression cannot describe the cholesteric state of a nematic which lacks reflection symmetry and where the twisted state represents the lowest energy. Now, if there is a constant twist with wave vector q, the value of n . V x n in the K2, term equals -4. The expression Eq. (96) therefore has to be "renormalized" to
G=1 Kl I (V.n)2 + 1 K22 (n . v x n + q)2 2 2 + -21 K33 ( n x v x n)2 (2 18) which, if there is no splay and bend present, becomes zero for n V x n = -4. If we expand the square in the K22term we can write the energy in the form GN* = GN + K22 q n . V X12 + 1 K22 q2 (219) 2
permitted by the local C2 symmetry which describes the fact that the structure is modulated in space along the z-direction. If in Fig. 49 we let the x direction be along the C, axis, we see that the C2 symmetry operation involves y +-y, z +-z, ny +-ny and nz+-n,, of which the first and last do not interfere and the middle two leave Eq. (216) invariant. We remember from Fig. 29 that the cholesteric structure has infinitely many C, axes perpendicular to the helix axis. The expression Eq. (2 16) is therefore also an invariant for the N* phase. If q is the cholesteric wave vector, we write the director as
n = (cos$, sin$) = (cosqz, sinqz)
(217)
where G, corresponds to the energy expression Eq. (96) for a non-chiral nematic. Two new terms have appeared in the energy as a result of dropping the reflection symmetry. The first is a linear term which is the Lifshitz term, the second is an energy term quadratic in the wave vector. In fact, a simple check shows that
590
2
Ferroelectric Liquid Crystals
We could therefore alternatively write
GN*=GN -K22q
n x z - n ya nx x ) + 1K22Y(221) 2
(
any
or use L=-n.Vxn
(222)
instead of Eq. (216). We may finally note that if we go from a right-handed to a lefthanded reference frame then the Lifshitz invariant (like angular momentum) changes sign because Vxn does. We can also see this in Eq. (216) because in addition to the C, operation the inversion involves that x +-x and n, +-nx. In the helical smectic C* case, again with q(z) = qz, the director components were stated in Eq. (141) n, = sin0 cos@ ny = sin0 sin$ n, = cos0
Inserting this in Eq. (216) we find that the Lifshitz invariant equals
L = q sin20
(223)
which is also often written
aq . 0 L=-sin
aZ
for the more general case that the twist is not homogeneous. We may also note, that in the smectic C* case we can equally well write Eq. (216) in the form
seen in Sec. 2.5.5, with a helical deformation we also have a flexoelectric contribution to P. This is opposite in sign to P, for e,>O, cf. Eq. (148), and proportional to the wave vector q. These two contributions must now be separated in the Landau expansion because we have to regard q as a new independent variable. In that case we not only have a coupling term -c*PBbut also one corresponding to the flexoelectric contribution which we could write eqP0. With this convention, Eq. (157) would be extended, for the helical C* case, to G = - 1a 0 2 + - 1b e 4 +- 1 p 2 2 4 2x0 Eo
where the -PE term has been skipped since we are here only interested in the field-free case. For the Lifshitz invariant we have used Eq. (223) in the limit of small 0, but chosen the minus sign, corresponding to A* > O in Eq. (219). In accordance with Eq. (219) we have also added a term proportional to q2. The origin of the last term, proportional to q202 is the fact that the smectic helix is a combined twist-bend deformation and that its energy therefore has to depend on the tilt angle as well as on q. By symmetry this dependence has to be -0’ (or, actually proportional to the square of sin 20). But it is illustrative to examine these last terms in a less ad hoc way. Thus, if we go back to our “nematic” description, introduced in Sec. 2.4.9, we can write Gc.
i.e. using the two-dimensional c director, as the n, component does not appear in L. Before we add the Lifshitz invariant to our Landau expansion Eq. (157) another consequence of the helix may be pointed out. It is the fact that, as we have already
=z1 K 2 2 ( n . V x n + q ) 2
(227)
+ 21 K33(n x V x n - B ) 2 ~
= Gc
+ 21 K22q2 + 21 K33 B2 -
~
+ K 2 2 q n .V x n - K33B . n x V x n
2.5
The SmA*-SmC* Transition and the Helical C* State
where Gc corresponds to the expression (96) without splay term. As the spontaneous 1 bend B is equal to - q sin 2 8 = q e for small 2 tilts, cf. Eq. (147), the third term on the right side is equal to the last term in Eq. (226). From Eq. (145) we further know that n x V x n =-qsinecose z x n for the helical C* case, hence the last term in Eq. (227) can be written K3,Bqe for small tilts. With P= ebB for the flexoelectric contribution we write this term eqPB, with the abbreviation K33/eb=e. This term was already included in Eq. (226). Before continuing with the Landau expansion we note that with n V x n =-q and n x V x n = B inserted in Eq. (227), the free energy in the helical C* state can be written in the form 1
G p = G,
- (K22
+ K33e2)q2
(228)
(K33q - Xo%e2q)e2+ K22q = (a* - xo%c*) e2
59 1
(234)
or K f q 2 0 2+ K22q= A*,@
(235)
We have here introduced the renormalized coefficients Kf = K33 - xo%e2 ,
a*-- a* - Xo%ec* (236) f
which contain the flexoelectric contributions. The wave vector is then obtained as
g e2 '=
KZZ+Kfe2
(237)
For a non-chiral material, Af* = 0 (both A* and c* are chiral coefficients in Eq. (236), and hence q = O . The pitch of the smectic helix Z equals 27c/q, thus
With the new terms in Eq. (226), minimizing with respect to P, 8 and q gives
z=K22 + Kf O2 n;-* e2
a'ae = a 0 + b e 3 - c* P + eq P - 2 a * q e + K33e q 2 = 0
indicating that the pitch should diverge at the transition C* +A*, cf Fig. 58. Experimentally, the situation is still not very clear regarding Z(T). While some measurements do indicate that a pure divergence exists if the layers are parallel to the cell plates, the majority of measurements give a result that the pitch goes through a maximum value
(230)
The first of these yields
ZPP) J
I I
Comparing this with Eq. (148) which, for small tilts we can write P=(Po-qeb)8
(233)
we find that Po corresponds to ~ o & o c * , equal to s* in Eq. (167), and that t?b corresponds to Xo%e, where e is the coefficient Tc in the Landau expansion' we now inFigure 58. The measured helical pitch Z at the transert p from Eq. (232) into Eq. (231) which sition C*-tA*. The pitch should diverge according gives to Eq. (238).
592
2
Ferroelectric Liquid Crystals
slightly below the transition and attains a finite value at T= T,. If we write the pitch dependence
z=z,+CC2
(239)
there should be a saturation value Z, = ~ ~ K ~ at I Alow; temperatures. Z, as well as C= 2 7 ~ K ~ ~ shows l A ; the balance between the non-chiral elastic coefficients ( K ) wanting to increase the pitch and the chiral coefficients (A*)wanting to twist the medium harder. When we finally insert the value of P from Eq. (232) into Eq. (230) we get
xosoc * 8~ + 2 x o E~ ec* q e - xosoe2 q28 a e + be3 -
- 2 a * q e + ~ ~ ~ e q ~ = o (240) After skipping the solution 8= 0, we are left with -
xosoc * -~2 (A* - xosoec*) q
(241)
+ ( K - xo s g e 2 )q2 + b e 2 a -xo so c * -~2 g q + Kf q2 + b e 2 = 0 Together with Eq. (237) this leads to a complicated expression for 8( T ) ,which we will not pursue further here. However, in the approximation that we take the low temperature limit for the wave vector a*
4 40 = Kf (corresponding to 2,) we see that Eq. (241) simplifies to a - x , ~ c *- Kfqi ~ + b82
(243)
which is reshaped in the usual way to
a ( T - T,)
+ b82
(244)
with a phase transition shift T, - Toequal to (245)
While AT is still expected to be generally small, it is certainly true that the contribution from unwinding the helix may raise the transition temperature more than the contribution from the chiral coupling, at least in the case of hardtwisted media like shortpitch smectics C* where the pitch is smaller than the wavelength of light.
2.5.11 The Pikin-Indenbom Order Parameter A group theoretical symmetry analysis by Indenbom and his collaborators in Moscow [197,198] led, around 1977, to the introduction of a very attractive order parameter for the A*-C* transition which usually is referred to as the Pikin-Indenbom order parameter. It is attractive because it presents, in the simplest form possible, the correct symmetry and a very lucid connection to the secondary order parameter P.It was adopted by the Ljubljana group around Blinc for the description of both static and dynamic properties of the C* phase [199-2041. The basic formalism has been described in particular detail by Pikin [40] and by Pikin and Osipov [41]. In the smectic C* phase, the layer normal z and the director n represent the only two natural directions which we can define. That is, z and n are the only natural vectors in the medium. Using these we now want to construct an order parameter which is a vector, is chiral, has C2 symmetry, leads to a second order A* - C* transition and is proportional to 8for small values of 8.We can do this by combining their scalar and vector products, multiplying one with the other,
N = (n . z ) (n x z)
(246)
We then obtain a vector in which the first factor is invariant, while the second changes sign on inversion. N thus has the two first
593
2.5 The SmA*-SmC*Transition and the Helical C* State Y
properties. Performing the multiplication we find
N = nz(ny,-n,, 0)
(247)
which only has two components, hence is written
N = (nzny,-nznx)
(248)
The n,ny and nznx combinations do not change on inversion but the x and y directions do, thus we see that N changes sign on inversion. The angle between n and z is 8. Therefore, taking the absolute value in Eq. (246) 1 N =cos8sin8=-sin28 2
(249)
We then recognize that this order parameter automatically reflects the C2 symmetry, cf. the discussions around Eqs. (131), (132) and Figure 49, where we had to introduce this symmetry in an ad hoc way. Clearly N = 8 is valid for small tilts according to Eq. (249). Finally, we can check that N and -N describe the same state from Eq. (248), by virtue of the fact that n and -n describe the same state. Thus, if we make a Landau expansion in N , only even powers can appear and the transition will be one of second order. Before going on to this expansion we should, however, make the connection to the secondary order parameter P . Looking onto the smectic layer plane in Figure 59 we have (for a positive material, Po > 0) a relation between the P direction and the tilt direction such that P advances in phase by 90 degrees in the positive cp direction. If we express P as a complex quantity P, + iP,, we can relate P directly to the C director expressed in complex form, c = c, +icy, by P,
+ iPy - -i(cx + icy)
Figure 59. The tilt vector n,c lags P in phase by 90 degrees (for Po> 0), corresponding to a multiplication by -i in the complex plane.
(250)
Let us now introduce the tilt vector 6 as the complex quantity nzc= (n,c,+inzcy) =
(n,n,
+ in,ny) and rewrite Eq. (250) as
P, + iPy - -i(n,n,
+ in,ny) = (n,ny - in,n,)
(251)
,
In vector notation the tilt vector is 6 = ( 5 , { 2 ) = ( n 2 n x , n p Y ) and Eq. (251) in vector form reads (PX?py>- ( 5 2 , -51)
(252)
This is the relation between the secondary order parameter P = (P,, Py)and the primary order parameter N = (nzny,-nznx),when the latter is expressed in the tilt vector 6 = ( 52).
We may now proceed to ask what invariants we may form in N and P , and their combinations, to include in the Landau expan1 1 sion. N 2 and N4 give -a({:+ 5;) and -b 2 4 corresponding to our earlier 8' and O4 terms, P 2 gives in the same way the
(ct+{;)2
(P,'+ Py")term. But because P and N 2x0 EO transform in the same way (cf. Eq. (252) under the symmetry operations, their scalar product P . N will also be an invariant,
P . N = PXt2- Py5,
(253)
594
2
Ferroelectric Liquid Crystals
t2,
This corresponds to our previous PO and gives a term -c* (P,52-Py51) in the Landau expansion. In contrast to PO the form Py5,directly shows the chiral character. Thus, this invariant changes sign when we change from a right- to a left-handed reference frame, which means that the optical antipode of a certain C* compound will have a polarization of opposite sign. Further, we have the Lifshitz invariant
P, and P,. convenient expressions for C,, This can be done in several ways if we only correctly express the spatial relationship of 6 and P . For a positive material (P,>O), P is always 90 degrees ahead. If the director tilts out in the x direction, this will cause a polarization along y, symbolically expressed by
a5 51 a 5 2 - 52 A aZ
and similarly, with tilt along y
P,t2-
(254)
corresponding to Eq. (225) and, because both 5 and P behave like the c director, also one in P ,
5 = (0, o), P = (0, PI
(257)
5 = (0, el, P = (-P, 01
(258)
Generally, with cp = qz, and small tilts, = n,n, = cose sine coscp = 8 cosqz
t2= n,ny = cose sine sincp
(255)
corresponds to
Both have the same chiral character as the form in Eq. (253). Only one of these can be chosen, because they are linearly dependent, according to Eq. (252). This results in a Landau expansion
P, = -P sinqz P, = P cosqz
=:
8 sinqz (259)
Inserting these in Eq. (256) immediately gives G = -1a e 2 + -1b e 2 4
4
+ - L P 2 2x0 Eo
+ 1(P,’ + Py?)+ c* (P, 5 2 - Py 51) 2X
This is the same as Eq. (226) except that 1 K2,q2 is lacking. While minhere the term 2 imizing with respect to P gives the same equilibrium value as before, aG/aq = 0 gives
a*e2+ K33qe2= o (262) Since P - 6, all terms will be proportional to eP8-
In this expansion the last two terms describe the flexoelectric (previously eq PO) energy and the elastic energy due to the helix. The wave vector q in these terms is hidden in the deriatives ag,/az and a52/az. The expression Eq. (256) is the “classical” Landau expansion in the formulation of Pikin and Indenbom. We now have to insert
O2 and the @dependencesimply cancels out. This means that the wave vector, according to this model, will simply be q = A;/K,, equal to the low temperature value of Eq. (242). Thus the pitch Zis temperature independent, equal to Z,. This is of course in serious disagreement with experiment and the reason
2.5 The SmA*-SmC* Transition and the Helical C* State
for this deficiency is the failure to recognize the twist component of the helix. We can learn from this that a good order parameter will not by itself take care of all the physics. But our previous Landau expansion is likewise far from perfect, even if it gives a more reasonable behavior for the pitch. We should therefore stop for a moment to contemplate how capable the theory is, so far, to reproduce the experimental facts. As we already discussed, the pitch has a diverging behavior as we approach T, (this is a priori natural, as no helix is allowed in the A* phase) but seems to change its behavior (within about 1 K from the transition) to decrease to a finite value at the transition. Another important fact is that the ratio PI0 = s* experimentally is constant, as predicted by theory, up to about 1 K from the transition after which it decreases to a lower value [ 1331. A third fact, which we had no space to develop, is that the dielectric response, according to the Landau expansion used so far, should exhibit a cusp at the transition, which does not correspond to experimental facts. What is then the deficiency in the theory? Did we make an unjustified simplification when taking sin 8 = 8 in Eq. (259)? Probably not since, as the problem seems to lie in the very vicinity of T,, where 8 is small, it would not do any good to go to the more accurate expressions valid for large values of 19.Then how do we go further? Should we extend our expansion to include O6 beyond e4,or P4beyond P2? No, rather the solution ought to come from physical reasoning instead of formal procedures. This step was taken by iekS in 1984 [201]. The argument is as follows. Our Landau expansion so far has failed to take into account a quite important non-chiral contribution. At the tilting transition rotational bias appears, whether the material is chiral or not, which is quadrupolar in character, cf.
595
Fig. 47. But if there is a strong quadrupolar order it will certainly contribute to increasing the polar order, once we remove the reflection symmetry. This leads to a coupling term in P and 8 which is biquadratic, -P202. If we now only consider those terms in the free energy which contain P and q, we can write
1 17p4- a * q e 2 1 e2 +2 4 1 +-2 K33q282-v*qe4
--a p 2
(263)
1 The biquadratic coupling term is - 5L.2 (P,
t2
- Py<,)2
using the Pikin-Indenbom order parameter. The v* q04 term is the higher in-
variant -v*({:+
(;)
gives a coupling between tilt and twist. The P4 term has been added to stabilize the system. dG/aP= 0 gives (264) P - c * 8 + e q e - ape2+ 17P3= 0
x o Eo
For small 8 we can skip 82 and P3 and get the same result as before, P=xo&oc*8or P/8= s*. For large P we get
P3 --PO2=0 Q
17 or
K
p=e
-
Thus the larger constant value of P/O is which drops to s* near T, where the rotational bias is not so efficient, as we expect for small tilts. Finally, aG/aq gives
m,
epe-
m2+ K3,q82 - v*e4 = o
(267)
596
2
Ferroelectric Liquid Crystals
from which follows
If 8 is not too small, P / 8 in the second term is constant and q increases with increasing 8, i.e. 2 decreases on lowering the temperature. Near T,, q increases again with increasing T since P/8 decreases. An interesting feature is that the flexoelectric coefficient e has to be positive in order to yield a maximum in the Z ( T )curve. It is therefore conceivable that certain materials show a divergence, while others do not. In general the coupled equations have to be solved numerically but give, at least qualitatively, the correct temperature dependence for the different parameters. We would like to close this section with some remarks, in particular concerning the different order parameters. First of all we note a surprising thing about the very smart Pikin-Indenbom order parameter. It has been very important in the basic symmetry discussion, but it has never really been used as such in practice. Perhaps because it is too sophisticated in its simplicity. Everybody instead uses the tilt vector 5 as order parameter. But g=(t,, t2)is non-chiral, hence does not have the correct symmetry, whereas N = ( t 2 , is chiral by construction. Thus the tilt vector l j should not be confused with the chiral vector ( n z n y , -n,n,). Having said this, however, it is clear that l j is easiest to handle, if we only combine it with (-P2, Pi).Note further that l j is not the projection of the director on the smectic plane, lj#c=(c,, c,>=(n,,n,). Althoughljandcare parallel they are not identical: g=nzc. The 8 dependence of l j and c is different but for small tilts the difference between the vectors is not big. After having defined 5, the first thing we did in using it in Eq. (256) was in fact to go to the small tilt limit. Thus in practice we have not used anything else than
the c director as order parameter. Which means that we have in essence, all the time, in different shapes, used the two component complex order parameter from the beginning of Sec. 2.5, cf. Eq. (125) Y = 8eiq = 8eiqz= Bcosqz + isinqz (269)
As primary and secondary order parameters we have thus used two two-component vectors lying in the smectic plane, perpendicular to the layer normal. The number of degrees of freedom, i.e. the number of components, is evidently more important than subtle differences in symmetry, if the order parameters are used with sound physical arguments.
2.6 Electrooptics in the Surface-Stabilized State 2.6.1 The Linear Electrooptic Effect The basic geometry of a surface-stabilized ferroelectric liquid crystal is illustrated in Fig. 60. The director n (local average of the
-cl)
Figure 60. Local symmetry of the srnectic C* phase. The direction of P is shown for a positive material (P>O); by definition, one in which z, n, and P make a right-handed system. If electrodes are applied as shown, P will follow the direction of the electric field generated between them.
2.6 Electrooptics in the Surface-Stabilized State
molecular axes) may be identified with the optic axis (we disregard the small biaxiality) and is tilted at the angle 8 away from the layer normal (z). In the figure the director is momentarily tilted in the xz plane with a tilt angle 8,which is fixed for a fixed temperature. Its only freedom of motion is therefore described by the azimuthal variable cp indicated in the xy plane. If the phase is chiral, no reflections are symmetry operations and therefore a local polarization P is permitted in the (positive or negative) y direction. If electroded glass plates are mounted as in the figure, such that the layer normal z runs between them in the middle, we see that this most peculiar geometry with P perpendicular to the optic axis is ideal for a display: by applying the electric field across the thin slice, we can move the optic axis back and forth between two positions in the plane of the slice. This so-called in-plane switching cannot be achieved in a solid ferroelectric (nor in a nematic) without the use of a much more complicated electrode configuration. A typical cell structure is shown in Fig. 61. It illustrates the fact that we have two equivalent stable states; this is the reason for the symmetric bistability. The coupling is linear in the electric field and described by a torque
T=PxE
(270)
driving n (which is sterically coupled to P) both ways on reversal of the field direction and, as we will see below, leading to a microsecond response speed according to
dominating over any quadratic (dielectric) terms at low fields. In Fig. 62 this linear electrooptic effect is compared with the quadratic effect controlling the state of a twisted nematic device.
597
Figure 61. Originally assumed FLC cell structure. The field E is applied between the electroded glass plates e. The smectic layers are perpendicular to these glass plates and have a layer thickness d(T) of the order of 5 nm, which is temperature-dependent. The thickness of the smectic slab is 1-2 pm and equal to L, the distance between the plates. The shaded area illustrates the achievable switching angle of the optic axis. The symbols below illustrate that the polarization vector can be actively switched in both directions (1 -2). Strangely enough, this simple geometry, which corresponds to the original concepts of [93 -951, has only been realized in recent times, thanks to a devoted synthetic effort by chemists over the last 15 years. Before these materials are coming into use (not yet commercial) the layer structure is much more complicated. These problems are discussed in Sec. 2.8.
With a torque -E2 the latter effect is insensitive to the direction of E and is driven electrically only in the direction from twisted to untwisted state, whereas it has to relax back elastically in the reverse direction. The difference is also striking optically. The important feature of the in-plane switching is that there is very little azimuthal variation in brightness and color, because the optic axis is always reasonably parallel to the cell plane. If the optic axis pointed out of this plane (see Fig. 63), which it often does in the field-on state of a twisted nematic, a considerable variation with viewing angle will occur, including reversal of contrast when the display is viewed along angular direc-
598
2 Ferroelectric Liquid Crystals
TRANSMITTING STATE
NoN-TRANSMITIWGSTATE
ANALYZER
GLASS
TWISTED NEMATIC
1
GLASS
POLARIZER
ANALyzwl
GLASS
FLC
GLASS
tions nearly coinciding with the optic axis. The basic FLC optical effect is also illustrated in Fig. 64. In-plane switching has another advantage than the superior viewing angle, which may be equally important but has so far passed fairly unnoticed. This lies in its color neutrality. In the top part of Fig. 62, it is seen that when intermediate values of the electric field are applied to a twisted nematic in order to continuously vary the transmission, the tilt of the optic axis and thus the birefringence are changed at the same time. Thus the hue is influenced at the same time as the grey level in a twisted nematic, which makes the color rendition less perfect in a display where the colors are generated either by red - green -blue filter triads or by sequential color illumination. In-plane switching, on the other hand, in principle allows perfect separation of color and grey shades.
Figure 62. Comparison between twisted nematic and FLC switching geometry.
p"
'tl .-
Figure 63. The presentation of the first Canon monochrome A4 size panel in 1988 not only demonstrated the high resolution capability based on speed and bistability, it was also a definite breakthrough in LCD optics, demonstrating the essentially hemispherical viewing angle connected with in-plane switching.
Figure 64. The basic FLC optic effect is illustrated by the 1988 Canon monochrome prototype in which the front polarizer sheet has been removed; this also makes the drivers along the bottom visible. The optical contrast between the two polarization states is given by the small hand-held polarizer to the lower left.
2.6 Electrooptics in the Surface-Stabilized State
2.6.2 The Quadratic Torque When we apply an electric field across an FLC cell there will always be a dielectric torque acting on the director, in addition to the ferroelectric torque. This is of course the same torque as is present in all liquid crystals and in particular in nematics, but its effect will be slightly different here than it is in a nematic. This is because in the smectic C phase the tilt angle 8 is a “hard” variable, as earlier pointed out. It is rigid in the sense that it is hardly affected at all by an electric field. This is certainly true for a nonchiral smectic C and also for the chiral C*, except in the immediate vicinity of TC***,where we may not neglect the electroclinic effect. Hence we will consider the tilt angle 8 uninfluenced by the electric field, and this then only controls the phase variable cp of Fig. 60. In order to appreciate the difference, it is illustrative to start with the effect in a nematic. We will thus study the torque on the director due to an electric field E that is not collinear with n, as illustrated in Fig. 65. If we introduce the dielectric anisotropy
AE =
- EL
(272)
we may write the dielectric displacement D = ~0 EEcaused by the field in the form of the two contributions
(273) Subtracting E ~ Efrom ~ E the~first ~ and adding it to the second term gives
D = % A E E+ ~ ~~ E L E = % A E ( .~E ) n + EOELE
(274)
Figure 65.The dielectric torque will diminish the angle a between the director n and the electric field for A&>O.
599
This gives a contribution to the free energy (which is to be minimized for the case of a fixed applied voltage)
f,
- - E~ A & ( n .E )2 - 1 cO.cLE2 L
L
We discard the second term as it does not depend on the orientation of n and write the relevant free energy contribution (276) 1 1 G = - - EO A E ( .~E)2= - -- EO AE E2cos2a 2 2 where a i s the angle between n and E. With positive dielectric anisotropy, A&>0, we see that this energy is minimized when n is parallel toE. If AE 0. The dieelectric torque T Eis obtained by taking the functional derivative of G with respect to a
(277) which yields
r E= - - 1E ~ A E E ~sin2a 2
(278)
The viscous torque is always counteracting the motion, and can be written
(279) where yl is the so-called twist viscosity counteracting changes in a. In dynamic equilibrium the total torque is zero. From this we finally obtain the dynamic equation for the local director reorientation in an ex-
600
2
Ferroelectric Liquid Crystals
ternally applied field E -1- ~ ~ A ~ E ~ s i y1 n 2-d= aO + 2 dt
In the nematic case we would have, with
n . E = E cos a and n x E = - E sina (280)
Equation (280) describes the dielectric response to an electric field. It is easily integrated, especially if we look at the case of very small deviations of the director from the field direction (a),for which we have sin2a= 2 a and
In this case, a will approach zero simply as
rE= -A&%E~ sina cosa
(286)
where a i s the angle between n and E , which is equivalent to Eq. (278). In the smectic case the rigidity of the tilt angle 19prevents any other change than in the phase variable cp. Consequently, we have to take the z component of the torque working on cpand causing the conical motion of the director. From Fig. 51 and Eq. (140) we find, with the external field E applied in the y direction, i.e., E = (0, E, 0)
n . E = E sine sincp
(287)
and where a, is the initial angular deviation in Fig. 65 and zis given by
n x E = E(n,, 0, -n,)
z=-
from which Eq. (285) takes the shape
Yl
A E E ~E2
= E(cose,O, -sine coscp)
(288)
I"=A&q,E2(sinecos8,0, The characteristic response time is thus inversely proportional to the square of the applied field. What we have derived so far is valid for a nematic, where there are no particular restrictions to the molecular motion. In smectic media there will be such restrictions, and therefore Eqs. (278) and (280) will be modified in a decisive way. In any liquid crystal the induced polarization Pi caused by an applied electric field P, is obtained from D = E ~ E E = ~ , E +as P , = D - q , E or, from Eq. (274)
Pi = q,A&(n.E ) n + ~ , E -~q ,EE = ( E ~ -I ) q , E + %AE(IZ. E ) n
.E ) ( n x E )
(289)
The z component of this torque is thus
r,"= -A&%E~ sin2e sincp cosq
(290)
Compared to the nematic case we get a formally similar expression, except for the appearance of the sin28 factor, but the involved angle q has a completely different meaning than a. The azimuthal angle q is not the angle between the director and the field, but in the SmC* case the angle between the spontaneous polarization and the field, as seen when we imagine the director to move out in direction cp in Fig. 60.
(284)
The first term represents a component parallel to the electric field and does not therefore give any contribution to the torque P x E . From the second we get
r"= Pi x E = AEq,(n
-sin20 sincp coscp)
(285)
2.6.3 Switching Dynamics We are now able to write down the equation of motion for the director moving on the smectic cone and being subjected to
60 1
2.6 Electrooptics in the Surface-Stabilized State
ferroelectric and dielectric torques, as well as the elastically transmitted torques KV2q, which tend to make n spatially uniform. Disregarding the inertial term J@ (of negligible importance) and the elastic torques from the surfaces (a far more serious omission), we can write the dynamic director equation
’ud,
x
Figure 66. If the xz plane is parallel to the electrodes and the electric field is applied in the positive y direction, the ferroelectric torque will turn the tilt plane (given by cp) in the negative cp direction.
y -=-PEsinq acp at -AEEOE 2 sin2 8 sinq cosq+ K V2cp (291) 9
write Eq. (293) as
acp = -sinq z-
For E = 0 this reduces to
at
1 --sin20sinqcosq+{2V2q
(294)
X which has the form of the equation for heat conduction or diffusion and means that spatial gradients in q will damp out smoothly with a rate determining quantity Kly, corresponding to the heat conductivity or diffusion coefficient, respectively. With regard to the signs, we note that (see Fig. 60) q is the angle between the tilt plane (or c director) and x, and therefore also between P and E . The torque P x E = - P E sinq is consequently in the negative z direction for q > O (see Fig. 66). Equation (291) describes the overdamped approach towards equilibrium given by the field E, together with the material parameters P, 0, y, K , and AE. Let us divide all terms by PE
.sin2Qsinqcosq+-V K PE
z q (293)
yq Introducing a characteristic time ZE -, PE
a characteristic length 5 = mensionless quantity
x = EOAEE’ we can -~
Evidently we can write Eq. (294) in an invariant form using the variables t’ = tlz and l a i a r‘=r/{. For, with - = 7 and - = - _
a
at
at
a ax 6 ax”
etc., Eq. 294 takes the dimensionless shape
. coscp(r’, t’)
+ V2q(r’, t’)
(295)
The new variables are scaled with
&,r‘-.-PE
(296
and 7xY 2-
PE
(297
which set the basic length and time scales for the space-time behavior of cp(r, t). In addition, the behavior is governed by the dimensionless parameter
X=-
P EO AEE
The characteristic time z determines the dynamic response towards the equilibrium state when we apply an electric field. If we put in the reasonable values
602
2
Ferroelectric Liquid Crystals
y,=50 CP (=0.05 Ns/m2) (see Fig. 67), P = 10 nC/cm2, and E = 10 V/pm, we get a z value of about 5 ys. The characteristic length Sexpresses the balance between elastic and electric torques. An external field will align P along the field direction except in a thin layer of the order of 5, where a de-
J
viating boundary condition will be able to resist the torque of the field. As this layer thickness falls off according to 5 - E-"2, it will be much smaller than the sample thickness d for sufficiently high fields. In fact, it also has to be much smaller than the wavelength of light in order for the sample to be optically homogeneous. Only then will Eq. (297) also apply for the optical response time. It is easy to check that this is the case. With the P and E values already used and with K = 5 x N, we find from Eq. (296) that 5 is less than a nanometer. Finally, the parameter ( expresses the balance between the ferroelectric and the dielectric torque. As it appears in the dielectric term of Eq. (295) in the combination s i n 2 0 / ~ which , is = 0 . 1 5 / ~for 0=22", would have to be less than about 0.5 in order for us to have to keep this term. With the same P and E values as before, this requires a (A&(value as high as 22.5. We will therefore skip this term for the moment, but return to this question later.
x
2
2.6.4 The Scaling Law for the Cone Mode Viscosity
1o ~ / T ( K )
Figure 67. (a, b) An external electric field E perpendicular to the smectic layer normal is rotating the local polarization P as indicated in (a), forcing P to end up parallel to E . The corresponding reorientation of the optic axis takes place through the variable qaround a conical surface, i.e., the tilt cone, with no change in tilt 8. In contrast to a pure emotion (corresponding to viscosity y& or the equivalent twist viscosity y, in the nematic case), the q reorientation has a significant component around the long molecular axis, which leads to low effective viscosity. (c) Arrhenius plot of the viscosity y, in the nematic phase, as well as soft mode and Goldstone mode viscosities yo and y, in the smectic C* phase of a two-component mixture (from Pozhidayev et al. [148]).
Figure 67 gives an indication that, for the motion on the cone, the effective viscosity ought to depend on the tilt angle. Evidently, for small values of tilt it approaches the limiting case, where all the motion is around the long inertial axis, which must have the lowest possible viscosity. We also note from the experimental data of that figure that the cone mode viscosity, y, is even lower than the nematic viscosity at a higher temperature, which at first may seem puzzling. We will look at the viscosity in a more general way in Sec. 2.6.9, but here only try to illuminate this question. We will treat the viscosity in the simplest way possible, regarding it for a moment as a scalar.
603
2.6 Electrooptics in the Surface-Stabilized State
To a first approximation, any electric torque will excite a motion around the 8-preserving cone, i.e., around the z axis of Fig. 60. The essential component of the viscous torque will therefore be r,, which is related to dpldt (-@).We can thus write for the cone motion
2.6.5 Simple Solutions of the Director Equation of Motion
-rz = Y,@
y -+PEsinq=O a9
(299)
For a general rotational motion of the director n , the relation between the viscous torque and the viscosity has the form -r=ynxn
(300)
If we discregard both the dielectric and elastic terms in Eq. (291), the dynamics is described by the simple equation (305)
q at
For small deviations from the equilibrium state, s i n p z p and Eq. (305) is integrated directly to
p = pee-'"
(306)
Taking the z component we get
-r, = yln x lil, = yIc x C l
(30 1)
expressed by the two-dimensional c-director, which is the projection of n onto the plane of the smectic layer. Their relation means that c=n sin8 = sin8 (see Fig. 51). However Ic x i.1 = c2@
(302)
Hence
-rz= ysin28@
(303)
Comparing Eqs. (299) and (303) we obtain the important scaling law with respect to the tilt angle for the viscosity y, describing the motion around the cone (Goldstone mode)
y, = ysin 2 8
(304)
The index prefers to the p variable, and the index-free y corresponds to the nematic twist viscosity. Equation (304) means that the cone mode viscosity is lower than the standard nematic viscosity ( y,< It also seems to indicate that the viscosity y, tends (8-0). to zero at the transition T-T,, This, of course, cannot be strictly true, but we will wait till Sec. 2.6.9 to see what actually happens.
where z= YV and cpo is the angle between PE E and P at time t= 0. The response time z is inversely proportional to the field, instead of being inversely proportional to the square of the field, as in the dielectric case. Generally speaking, this means that the FLC electrooptic effect will be faster than normal dielectric effects at low voltages, and also that these dielectric effects, at least in principle, will ultimately become faster when we go to very high applied fields. The unique advantage of FLC switching is, however, that it is not only very fast at moderate fields, but that it switches equally fast in both directions; a feature that cannot be achieved if the coupling to the field is quadratic. If 9 is not small in Eq. (305), we change the variable to half the angle (sin9 = 2 sin 9 cos -) 9 and easily find the analytical 2 2 solution ~
n).
(307) with the same z=
yq ~
PE ly be expressed as
. This can alternative-
604
2
Ferroelectric Liquid Crystals
2.6.6 Electrooptic Measurements
is directly obtained as
Equations (307) and (308) are a solution to Eq. (305) if the electric field is constant with time. The expression is therefore also useful when the field is a square wave. Such a field is commonly used for polarization reversal measurements when switching between +P, and -P, states. In order to switch from -Ps to + P , we have to supply the charge 2 P, to every unit area, i.e., 2 P,A over the sample, if its area is A. The reversal of the vector P, thus gives rise to an electric current pulse i(t)= dQ through the curcuit in dt which the sample cell is connected. This current is given by the time derivative of the charge due to P,on the electrodes of area A. When P, makes an angle cp with E , the polarization charge on the electrodes is Q = P,A cos cp. The electric current contribution due to the reversal of P, is thus given by (309)
When cp passes 90 O during the polarization reversal, i(t) in Eq. (310) goes through a maximum. The shape of the function i(t) is that of a peak. This is shown in Fig. 68 where Eqs. (308) and (3 10) have been plotted for the case cpo= 179 '. By measuring the area under the polarization reversal peak, we obtain the total charge transferred and can thus determine the value of the spontaneous polarization P,. The time for the appearance of the current peak then allows a determination of the viscosity y,. The curves in Fig. 68 have been traced for the case where P makes an angle of 1 O relative to the surface layer normal, corresponding to the same pretilt of the director out of the surface. This pretilt also has to be included as a parameter determining the electrooptic properties. On the other hand, the integration of Eq. (305) giving the current peak of Fig. 68 can only give a crude estimation of the electrooptic parameters, because the equation does not contain any term describing the surface elastic torques. The value of the method lies therefore in the
~
i(t)= P,A-[coscp(t)] d = -P,A-sincp(t) dcp dt dt Substituting the time derivative of cp from Eq. (305), the polarization reversal current
-1.0 - 0.8
> -
1°.6 - 0.4 50-
i0.2 I
0
2
4
6
tl
8
10
,
,
,
0.0
12
Figure 68. The polarization reversal q(r) according to Eq. (304) for a half-period of an applied square wave and the resulting current pulse i(t). The current peak appears roughly at t=5zand the reversal is complete after twice that time. The latter part of the cp curve corresponds to the simple exponential decay of Eq. (32). The optical transmission is directly related to Ht). If the state at t=O is one of extinction, the transmission will increase to its maximum value, but in a steeper way than ( d q l d t l (from Hermann 11361).
2.6
Electrooptics in the Surface-Stabilized State
fact that it is simple and rapid. The same can be said about the alternative formalism of [ 1371, which has proven useful for routine estimations of electrooptic parameters, at least for comparative purposes. In [137] a hypothetical ad hoc surface torque of the form Kcoscp has been added to the ferroelectric torque in Eq. (305). With only these two torques present, the equation can still be easily integrated in a closed form. However, the chosen form of the elastic torque means that it cannot describe the properties of a bistable cell. Numerous other approaches have been proposed in order to describe the switching dynamics, for instance by neglecting the surface elastic torques, but including the dielectric torque using the correct representation of the dielectric tensor [138]. Common to most of them is the fact that they describe the shape of the polarization reversal current and the electrooptic transmission curve reasonably well. They are therefore easy to fit to experimental data, but may give values to the electrooptic parameters that may deviate within an order of magnitude. (An important exception to this is the polarization value P,, which is essentially insensitive to the model used because it is achieved by integration of the current peak.) Hence no model put forward so far accounts generally for the switching dynamics, and there is a high degree of arbitrariness in the assumptions behind all of them. Experiments in which the parameters in the equation of motion are measured may be carried out with an electrooptic experimental setup, usually based on a polarizing microscope. In the setup, the sample is placed between crossed polarizers and an electric field E(t) is applied across the cell. The optical and electric responses of the sample to the field are then measured. The light intensities Z ( t ) through the crossed polarizers and the sample are mea-
605
sured by a photodiode after the analyzer. The electric current i(t)through the sample is obtained by measuring the voltage u ( t ) across a resistance R connected in series with the liquid crystal cell (see Fig. 69). All three signals E ( t ) , Z ( t ) , and i ( t ) are fed into an oscilloscope so that the switching dynamics of the liquid crystal cell can be monitored. The oscilloscope is connected to a computer so that the waveforms can be stored and analyzed in detail. From the optical transmission, the tilt angle and the optical response time can be measured. From the electric response the spontaneous (and induced) polarization can be measured, as well as the response time, as discussed earlier. If we also include the SmA* phase (the electroclinic effect), the coefficients of the Landau expansion of the free energy density may be derived. Estimations of the viscosities for the cp- and &motions may also be obtained from the electrooptic measurements. In Fig. 69 we see how the quasi-bookshelf (QBS) smectic constitutes a retarder with a switchable optic axis. In the smectic A* phase this axis can be switched continously, but with small amplitude. The same setup is also used to study the DHM effect in short pitch chiral smectics and the flexoelectrooptic effect in the cholesteric phase, in both of which we achieve much higher tilts. Inserted between crossed polarizers, the retarder transmits the intensity
z = z0 sin2 2~
sin
TcdAn
2 ~
A
where Y is the angle between the polarizer direction and the projection of the optic axis in the sample plane, An is the birefringence, ilis the wavelength of light in a vacuum, and d is the thickness of the sample. The function Z ( Y ) is shown in Fig. 70. A very important case is the lambda-half condition given by d A n = 112. A cell with this
606
2
Ferroelectric Liquid Crystals OPTICAL
DETECTOR I
i c ! -- - - - Optimum optical setting: p22.5'
i(t)=u(t)/li
Figure 69. (a) The experimental setup for electrooptic measurements. The sample is placed between crossed polarizers. (b) The RC-circuit used in the switching experiments. The current response from the sample is measured across the resistor R (from Hermann [ 1361).
1.0
0.4 CI W
0.2
0.0 0
22,5
45 (deg)
67,5
90
Figure 70. Transmitted light intensity I ( Y )for a linear optical retarder with switchable optic axis placed between crossed polarizers. Y is the angle between the polarizer direction and the switchable optic axis, and maximum transmitted light intensity is achieved for Y=45" combined with a sample thickness fulfilling the A12 condition. A smectic C* in QBS geometry and tilt angle 8=22.5 could ideally be switched from Y=O to Y=45 O in a discontinuous way. DHM and flexoelectrooptic materials could be switched in a continuous way. Z(Y)is proportional to Y in a region around Y =22.5 ', which is the linear regime (from Rudquist [ 1391).
value of d A n will permit maximum transmission and flip the plane of polarization by an angle 2 Y. Since the position of the optic axis, i.e., the angle Y', may be altered by means of the electric field, we have electrooptic modulation. As seen from Eq. (311) and from Fig. 70, the minimum and maxi-
mum transmission is achieved for Y=O and Y'=45 O , respectively. If we adjust the polarizer to correspond to the first state for one sign of E across an SSFLC sample, reversal of sign would switch the polarization to give the second state, if 28=45". For natural grey-scale materials (electroclinic, DHM,
2.6
Electrooptics in the Surface-Stabilized State
flexoelectrooptic, antiferroelectric), the electrooptic response to a field-controlled optic axis cell between crossed polarizers is modelled in Fig. 71. Here Y= Yo+@ ( E ) , where Yois the position of the optic axis for E=O and @ ( E ) is the field-induced tilt of the optic axis. The tilt angle in the SmC* phase can be measured by the application of a square wave of very low frequency (0.2- 1 Hz), so that the switching can be observed directly in the microscope. By turning the angular turntable of the microscope, the sample is set in such an angular position that one of the extreme tilt angle positions, say -$, coincides with the polarizer (or analyzer), giving Z=O. When the liquid crystal is then
607
switched to +Oo, I becomes #O. The sample is now rotated so as to make I= 0 again, corresponding to +Oo coinciding with the polarizer (or analyzer). It follows that the sample has been rotated through 2 Oo, whence the tilt angle is immediately obt ained . The induced tilt angle in the SmA* phase is usually small, and the above method becomes difficult to implement. Instead, the tilt can be obtained [ 1401 by measuring the peak-to-peak value AZpp in the optical response, from the relation 1 arc sin MPP Oind = ~
4
10
which is valid for small tilt angles.
Electrooptic signal / Transmitted light intensity
k
III
I
/ I
'
I
1
LA-! '
I I
I
I
vt
Applied voltage / Input signal, giving
II
Y = Yo+ @ ( E )
m
i I
Figure 71. Electrooptic modulation due to the field-controlled position of the optic axis between crossed polarizers. I) The optic axis is swinging around Yo=Ogiving an optical signal with double frequency compared to the input signal. 11) The linear regime. When the optic axis is swinging around Y0=22.5 the variation of the transmitted intensity is proportional to @. For a liquid crystal A / 2 cell with quasi-bookshelf (QBS) structure, it follows from Eq. (311) that the intensity I varies linearly with @ if b, is small (1/1,=1/2+2@(E)), which, for instance, is the case if the electroclinic effect in the SmA* phase is exploited. As electroclinic tilt angles are still quite small, certain other materials, though slower, have to be used for high modulation depths. 111) Characteristic response for @ ( E )exceeding 222.5 ". (from Rudquist [139]). O,
608
2
Ferroelectric Liquid Crystals
On applying a square wave electric field in the SmC* phase the electric response has the shape of an exponential decay, on which the current peak i(t) (see Fig. 68) is superposed. The exponential decay comes from the capacitive discharge of the liquid crystall cell itself, since it constitutes a parallelplate capacitor with a dielectric medium in between. The electrooptic response i(t) on application of a triangular wave electric field to a bookshelf-oriented liquid crystal sample in the SmC* and SmA* phases is shown as it appears on the oscilloscope screen in Fig. 72, for the case of crossed polarizers and the angular setting 'Yo= 22.5". Applying such a triangular wave in the SmC* phase gives aresponse with the shape of a square wave on which the polarization reversal current peak is superposed. The square wave background is due to the liquid crystal cell being a capacitor; an RC-circuit as shown in Fig. 69b delivers the time derivative of the input. The time derivative of a triangular wave is a square wave, since a triangular wave consists of a constant slope which periodically changes sign. The optical response Z ( t ) also almost exhibits a square wave shape when applying a triangular wave, due to the threshold of the two stable states of up and down polarization corresponding to the two extreme angular positions -8 and +8 of the optic axis (the
director) in the plane of the cell. The change in the optical transmission coincides in time with the polarization reversal current peak, which occurs just after the electric field changes sign. In the SmC* phase, the optical transmission change in the course of the switching is influenced by the fact that the molecules move out of the plane of the glass plates, since they move on a cone. They thus make some angle C(t) with the plane of the glass plates at time t. The refractive index seen by the extraordinary ray n , ( n depends on this angle. The birefringence thus changes during switching according to A n [ C(t)]= n, [ [ ( t ) ]-no. After completion of the switching, the molecules are again in the plane of the glass plates and {=O, so that the birefringence is the same for the two extreme positions -8 and +8 of the director. When raising the temperature to that of the SmA* phase, the polarization reversal current peak gradually diminishes. In the SmA* phase near the transition to SmC*, a current peak can still be observed, originating from the induced polarization due to the electroclinic effect. On application of a triangular wave, the change of the optical response can most clearly be observed: it changes from a squarewave-like curve to a triangular curve, which is in phase with the applied electric field. This very clearly illustrates the change from the nonlinear cone switching of the SmC* phase to the linear switching of,the SmA* phase due to the electroclinic effect.
2.6.7 Optical Anisotropy and Biaxiality (a)
SmC* phase
(b) SmA* phase
Figure 72. The electrooptic response when applying a triangular wave over the cell in the SmC* and the SmA* phases. The ohmic contribution due to ionic conduction has been disregarded.
The smectic A phase is optically positive uniaxial. The director and the optic axis are in the direction of highest refractive index, n11-n21=An>0. At the tilting transition
2.6 Electrooptics in the Surface-Stabilized State
SmA +SmC, the phase becomes positive biaxial, with rill -+n3 and nl splitting in two, i.e., nl+nl, n,. The E ellipsoid is prolate and n3 > n2 > a1
(313)
or A n > 0 , dn>O
(3 14)
where we use, with some hesitation, the abbreviations An = n3 - n1
(315)
an = n2 - n1
(316)
The hesitation is due to the fact that the refractive index is not a tensor property and is only used for the (very important) representation of the index ellipsoid called the optical indicatrix, which is related to the dielectric tensor by the connections E,
= n 2l ,
2 2 = n2, E~ = n3
(3 17)
between the principal axis values of the refractive index and the principal components of the dielectric tensor. For orthorhombic, monoclinic, and triclinic symmetry the indicatrix is a triaxial ellipsoid. The orthorhombic system has three orthogonal twofold rotation axes. This means that the indicatrix, representing the optical properties, must have the same symmetry axes (Neumann principle). Therefore the three principal axes of the indicatrix coincide with the three crystallographic axes and are fixed in space, whatever the wavelength. This is not so for the monoclinic symmetry represented by the smectic C . Because the symmetry element of the structure must always be present in the property (again the Neumann principle), the crystallographic C, axis perpendicular to the tilt plane is now the twofold axis of the indicatrix and the E tensor, but no other axes are fixed. This means that there is ambiguity in
609
the direction of along the director, (which means ambiguity in the director as a concept) as well as in the direction E, perpen) the tilt dicular to both the “director” ( E ~ and axis (E,). Only the latter is fixed in space, and therefore only &2 can be regarded as fundamental in our choice of the principal ax. es of the dielectric tensor ( E ~ &,, E ~ ) Now, it is well known that the triaxial character, i.e., the difference between and (or n2 and n l ) ,&=E,-E,, is very small at optical frequencies. The quantity &is now universally called the biaxiality, although this name would have been more appropriate for the degree of splitting of the two optic axes as a result of the tilt. Thus optically speaking we may still roughly consider the smectic C phase as uniaxial, with an optic axis (director) tilting out a certain angle 8from the layer normal. However, as has recently been pointed out by Giesselmann et al. [141], due to the ambiguity of the .cl and E~ directions, the optical tilt angle must be expected to be a function of the wavelength of the probing light. As they were able to measure, the blue follows the tilt of the core, whereas the red has a mixture of core and tail contributions. The optical tilt is thus higher for blue than for red light, and the extinction position depends on the color. While this phenomenon of dispersion in the optic axis is not large enough to create problems in display applications, it is highly interesting in itself and may be complemented by the following general observation regarding dispersion. At low frequencies, for instance, lo5 Hz, the dielectric anisotropy A&= E~ - is often negative, corresponding to a negatively biaxial material. As it is positively biaxial at optical frequencies (- 1015Hz), the optical indicatrix must change shape from prolate to oblate in the frequency region in between, which means, in particular, that at some frequency the E tensor must become isotropic.
610
2
Ferroelectric Liquid Crystals
2.6.8 The Effects of Dielectric Biaxiality At lower frequencies we can no longer treat the smectic C phase as uniaxial. Therefore our treatment of dielectric effects in Sec. 2.6.2 was an oversimplification, valid only at low values of tilt. In general, we now have to distinguish between the anisotropy, A&= E~ - E, , as well as the biaxiality, = E* - E , , both of which can attain important nonzero values typically down to -2 for A& and up to +3 or even higher for The latter parameter has acquired special importance in recent years, due to a special addressing method for FLC displays, which combines the effects of ferroelectric and dielectric torques. As for the background, it was successively discovered in a series of investigations by the Boulder group between 1984 and 1987 that the smectic layers are generally tilted and, moreover, form a so-called chevron structure, according to Fig. 73, rather than a bookshelf structure. The reason for the chevron formation is the effort made by the smectic to fill up the space given by the cell, in spite of the layer thickness shrinking as the temperature is lowered through the SmA - SmC transition and further down into the SmC phase. The chevron geometry (to which we will return at length in Sec. 2.8) reduces the effective switching angle, which no longer corresponds to the optimum of 28= 45 O , thereby reducing the brightness-contrast ratio (we have in the figure assumed that the memorized states have zero pretilt, i.e., that they are lying in the surface). This can, to some extent, be remedied by a different surface coating requiring a high pretilt. Another way of ameliorating the optical properties is to take advantage not only of the ferroelectric torque (-E) exerted on the molecules, but also of the dielectric torque (-E2). This torque always tries to turn the
a&.
highest value of the permittivity along the direction of the electric field. The tilted smectic has the three principal E values in the directions shown in the figure, E , along the chosen tilt direction, .s2along the local polarization, and &3 along the director. If is large and positive, it is seen that the dielectric torque exerted by the field will actually lift up the director away from the surface-stabilized state along the cone surface to an optically more favorable state, thus increasing the effective switching angle. The necessary electric field for this action can be provided by the data pulses acting continuously as AC signals on the columns. This addressing method thus uses the ferroelectric torque in the switching pulse to force the director from one side to the other between the surface-stabilized states (this could not be done by the dielectric torque, because it is insensitive to the sign of E ) , after which high frequency AC pulses will keep the director dynamically in the corresponding extreme cone state. This AC enhanced contrast mode can ameliorate the achievable contrast in cases where the memorized director positions give an insufficient switching angle, which is the case in the socalled C2 chevron structures (see Sec. 8.8). It requires specially engineered materials with a high value of Its main drawback is the requirement of a relatively high voltage (to increase the dielectric torque relative to the ferroelectric torque), which also increases the power consumption of the device. The AC contrast enhancement is often called “AC stabilization” or “HF (high frequency) stabilization”. A possible inconvenience of this usage is that it may lead to a misunderstanding and confusion with surface-stabilization, which it does not replace. The dielectric contrast enhancement works on a surface-stabilized structure. There is no conflict in the concepts; the mechanisms rather work together.
a&.
2.6 Electrooptics in the Surface-Stabilized State
61 1
Figure 73.The simple bookshelf structure with essentially zero pretilt would lead to ideal optical conditions for materials with 2 0equal to 45". In reality the smectic layers adopt a much less favorable chevron structure. This decreases the effective switching angle and leads to memorized P states that are not in the direction of the field (a, b). A convenient multiplexing waveform scheme together with a properly chosen value of the material's biaxiality d~ may enhance the field-on contrast relative to the memorized (surface-stabilized) value (c), by utilizing the dielectric torque from the pulses continuously applied on the columns (after [142, 1431).
In Eq. (291) we derived an expression for the director equation of motion with dielectric and ferroelectric torques included. If the origin of the dielectric torque is in the dielectric biaxiality, the equation (with the elastic term skipped)will be the closely analogousone a9 2 y -=-PEsincp-&oa&E sinqcosq at (3 18)
In the present case, where the layers are tilted by the angle Grelative to E, as in Fig. 73a, the effective applied field along the layer will be Ecos 6, thus slightly modifying the equation to
y -=-PEcosGsinq acp 9 at
- E~
a&E2cos2 6 sin cp cos q (3 19)
612
2
Ferroelectric Liquid Crystals
In addition to the characteristic time rand length 5, we had earlier introduced the dimensionless parameter describing the balance between ferroelectric and dielectric torques. Its character appears even more clearly than in Eq. (298) if we write it as
x
nc rc
= &g a&E2
If we again replace E by E cos 6, our new will be
x
P = &o a&Ecos6
FromX and z=
yq we can form a charPE cos 6
acteristic time
x
and from and Ed (cos 6 factors canceling in Ed), a characteristic voltage
The values of the parameters z, and V, are decisive in situations where the ferroelectric and dielectric torques are of the same order of magnitude, and they play an important role in the electrooptics of FLC displays addressed in a family of modes having the characteristics that there is a minimum in the switching time at a certain voltage (see Fig. 74a), because the ferroelectric and dielectric torques are nearly balancing. This means that the switching stops both on reducing the voltage (due to insufficient ferroelectric torque) and on increasing it (due to the rapidly increasing dielectric torque, which blocks the motion, i.e., it increases the delay time for the switching to take off). The existence of a minimum in the switching time when dielectric torques become important was discovered by Xue et al. [138] in 1987, but seems to have appeared in novel addressing schemes some years later in the British national FLC collaboration within the JOERS/Alvey program. It turns out [ 1451 that the minimum switching time
log v Vmin
.
.
lot
10
1
20
30
40
i .
. :
50
60
70 80 90 100
Pulse voltage, V, / V
Figure 74. (a) Typical pulse switching characteristic for a material with parameters giving ferroelectric and dielectric torques of comparable size; (b) Possible routes for engineering materials to minimize both zmi, and Vmin(from [144]).
2.6 Electrooptics in the Surface-Stabilized State
613
a&,
depends on y,, and P according to Eq. (322), and that this minimum occurs for a voltage that depends on and P according to Eq. (323). At present, considerable effort is given to reduce both zo and V,. Figure 74b indicates how this could be done: either (1) by lowering the viscosity y, whilst or (2) by inincreasing the biaxiality creasing both & and P by a relatively large amount.
a&
a&,
2.6.9 The Viscosity of the Rotational Modes in the Smectic C Phase In Sec. 2.6.4 we derived the scaling law for the cone mode viscosity with respect to the tilt angle 8. In this section we want to penetrate a little deeper into the understanding of the viscosities relevant to the electrooptic switching dynamics. Let us therefore first review the previous result from a new perspective. With 8 = const, an electric torque will induce a cone motion around the z axis (see Fig. 75a). We can describe this motion in different ways. If we choose to use the angular velocity ci, of the c director, that is, with respect to the z axis, then we have to relate it to the torque component
rl
-c= Y, ci,
(324)
In Fig. 75b (y, is denoted as q ) we have instead illustrated the general relation, according to the definition of viscosity, between the angular velocity & of the director n and the counteracting viscous torque rv
-rv = y&
(325)
As a is the coordinate describing the motion of the head of the n arrow (on a unit sphere), a = n x i , and the relation can be written
-r"=ynxli
(326)
Figure 75. (a) The variable cpdescribes the motion of the c director around the layer normal. (b) The relation between the rate of change of the director i ,the angular velocity CU, and the (always counteracting) viscous torque r.
We have used this before in Eq. (300). Several things should now be pointed out. The difference between y, and y is, in principle, one of pure geometry. Nevertheless, it is not an artifact and the scaling law of y, with respect to 8 has a real significance. In a nematic we cannot physically distinguish between the 8 motion and the cp motion on the unit sphere. Therefore yin Eq. (325) is the nematic viscosity. In a smectic C, on the other hand, we have to distinguish between these motions, because the director is moving under the constraint of constant 8. As is evident fromFig. 75b, however, this motion is not only counteracted by a torque Tz;instead r must have nonzero x and y components as well. We might also add that in general we have to distinguish between the 8 and cp motions as soon as we go to a smectic phase, either SmA or SmC. For instance, we have a soft mode viscosity y,in these phases, which has no counterpart in a nematic.
614
2
Ferroelectric Liquid Crystals
Let us now continue from Eq. (326). With sin 0 cos cp (327) we have
One of the drastic oversimplifications made so far has been in treating the viscosity as a scalar, whereas in reality it is a tensor of rank 4. In the hydrodynamics, the stresses oGare components of a second rank tensor, related to the velocity strains vk,/ 0.. = q-avk
- sin 0 sin cp@
z~
hence
(329) -sin0 cos2 cp -rv=y @ -sinOsincpcoscp sin2 0 cos2 cp + sin2 0 sin2 a,
I:
Therefore the z component is
-r; = y @sin20
1
(330)
A comparison of Eq. (330) with Eq. (324) then gives 2
y, = y sin 0
(331)
which is the same as Eq. (304) ( y is ' a nematic viscosity). We may note at this point that Eq. (331) is invariant under O + O+n, as it has to be (corresponding to n +-n). We have still made no progress beyond Eq. (304) in the sense that we have stuck with the unphysical result y, +0 for 0 +0. The nonzero torque components r, and ry in Eq. (329) mean that the cone motion cannot take place without torques exerting a tilting action on the director. With 0 constant, these have to be taken up by the layers and in turn counteracted by external torques to the sample. We also note that since O=const in Eq. (327), we could just as well have worked with the two-dimensional c director from the beginning c = (c,, cy)=
sin 0 cos cp sin 0 sin cp
to obtain the result of Eq. (329).
(332)
(333)
ax,
in which q is thus a tensor of rank 4 just like the elastic constants Cijkl for solid materials, for which Hooke's law is written (334)
o i.j . = c rjkl . . &kl
As is well known, however, the number 34= 8 1 of the possibly independent components is here reduced by symmetry, according to (335) giving only 36 independent components. They therefore permit a reduced representation using only two indices Cijkl
=cp,
0 p
= cp" &"
(336)
which has the advantage that we can write them down in a two-dimensional array on paper, but has the disadvantage that cpv no longer transforms like a tensor. The same is valid for the Oseen-Frank elastic constants and the flexoelectric coefficients in liquid crystals, which are also tensors of rank 4, but are always written in a reduced representation, Kq and e,, respectively, where K , and eijcannot be treated as tensors. The viscosity tensor in liquid crystals is a particular example of a fourth rank tensor. The viscous torque r i s supposed to be linear in the time derivative of the director and in the velocity gradients, with the viscosities as proportionality constants. This gives five independent viscosities in uniaxial ( 1 2 in biaxial) nematics, the same number in smectics A, but 20 independent components in the smectic C phase [146]. With nine inde-
2.6 Electrooptics in the Surface-Stabilized State
pendent elastic constants and as many flexoelectric coefficients, this phase is certainly extraordinary in its complexity. Nevertheless, the viscous torque can be divided in the rotational torque and the shearing torque due to macroscopic flow. When we study the electrooptic switching of SSFLC structures, we deal with pure rotations for which macroscopic flow is thus assumed to be absent. Even if this is only an approximation, because the cone motion leads to velocity gradients and backflow, it will give us an important and most valuable description because of the fact that the rotational viscosity has a uniquely simple tensor representation. If we go back to the Eq. (325) defining the viscosity, both the torque and the angular velocity are represented by axial vectors or pseudovectors. This is because they actually have no directional property at all (as polar vectors have), but are instead connected to a surface in space within which a rotation can only be related to a (perpendicular) direction by a mere convention like the direction for the advance of a screw, “righthand rule”, etc. In fact they are tensors of second rank which are antisymmetric, which means that
r.. V = -r.. J‘ and
&.IJ = -&..J‘
(337)
with the consequence that they have (in the case of three-dimensional space) only three independent components and therefore can be written as vectors. As yin Eq. (325) connects two second rank tensors, it is itself a fourth rank tensor like other viscosities, but due to the vector representation of T and a, the rotational viscosity can be given the very simple representation of a second rank tensor. Thus in cases where we exclude translational motions, we can write yas
(338)
615
Unfortunately, no similar simple representation exists for the tensor components related to macroscopic flow. We will now finally treat ynot as a scalar, but as a tensor in this most simple way. In Eq. (338) y is already written in the “molecular” frame of reference in which it is diagonalized, as illustrated in Fig. 76, with the principal axes 1,2, and 3. Because the C, axis perpendicular to the tilt plane has to appear in the property (Neumann principle - we use it here even for a dynamic parameter), this has to be the direction for y*. As for the other directions, there are no compelling arguments, but a natural choice for a second principal axis is along the director. We take this as the 3 direction. The remaining axis 1 is then in the tilt plane, perpendicular to n. The 3 axis is special because, along n,the rotation is supposed to be characterized by a very low viscosity. In other words, we assume that the eigenvalue y3 is very small, i.e., fi+y,, E. Starting from the lab frame x, y, z, y is diagonalized by a similarity transformation
f =T - ’ ~ T
(339)
where T is the rotation matrix
uj.,
cos8 0 -sin8 1 0 sin8 0 case
j
(340)
G Figure 76. The principal axes 1, 2 , and 3 of the viscosity tensor. In the right part of the figure is illustrated how the distribution function around the director by necessity becomes biaxial, as soon as we have a nonzero tilt 8.
616
2
Ferroelectric Liquid Crystals
whereas for 8= z/2 we would find (formally) that
corresponding to the clockwise tilt 8 (in the coordinate transformation the rotation angle 8 is therefore counted as negative) around the y (2) axis, and T-' is the inverse or reciprocal matrix to T; in this case (because rotation matrices are orthogonal) T is simply equal to its transpose matrix T (i.e., = TV).Hence we obtain the viscosity components in the lab frame as
Yq (">=y, 2
corresponding to the rotational motion in a two-dimensional nematic. There is another reason than Eq. (347) not be neglect E : as illustrated to the right of Fig. 76, a full swing of the director around the z axis in fact involves a simultaneous full rotation around
zj
y =TFT-~
(348)
(34 1)
which gives cos8 0 -sin8 y=[o 1 0 sin8 0 cos8
0 sin8
0
0
y3
-sin8
o case
1
y, cos2 8 + y3 sin2 8
o
(yl - y3)sinocos8
Y2
(yl -y3)sin8cos6
0
0 ylsin28+y3cos28
Assuming now the motion to be with fixed 8, the angular velocity a is
a= (O,O, ql)
(343)
and Eq. (325) takes the form
(344)
y1 sin$cosB@
- P = y[;]=[o
(yl sin2 8 + y3 cos28 ) @
the z component of which is
-r; = (nsin28 + Y,COS%)@
1
(345)
Comparison with Eq. (324) now gives y,(~) = yl sin28+ f i cOs%
(346)
This relation illustrates first of all that the cp motion is a rotation that occurs simultaneously around the 1 axis and the 3 axis, and it reflects how the rotational velocities add vectorially, such that when 8 gets smaller and smaller the effective rotation takes place increasingly around the long axis of the molecule. For 8=0 we have Y,(O) = 73
(347)
(342)
the 3 axis. Hence these motions are actually intrinsically coupled, and conceptually belong together. If, on the other hand, we had neglected the small f i in Eq. (342), the viscosity tensor would have taken the form
y1cos28
y=[o y1sinecose
o
y1sin8cosB
Y2
0 y1sin28
o
(349)
which would have given the same incomplete equation (304) for y, as before. The first experimental determination of the cone mode viscosity was made by Kuczyhski [147], based on a simple and elegant analysis of the director response to an AC field. Pyroelectric methods have been used by the Russian school [136, 1481, for instance, in the measurements illustrated in Fig. 67. Later measurements were normally performed [ 1491 by standard electrooptic methods, as outlined earlier in this chap-
2.7
Dielectric Spectroscopy: To Find the ?and ETensor Components
ter. The methodology is well described by Escher et al. [l50], who also, like Carlsson and kekS [ 1511, give a valuable contribution to the discussion about the nature of the viscosity. The measured viscosities are not the principal components yl, y2, y3 in the molecular frame, but y, and y2, which we can refer to the lab frame, as well as y3, for which we discuss the measurement methodin Sec. 2.7. As y2 refers to a motion described by the tilt angle 8, we will from now on denote it y , and often call it the soft mode viscosity (sometimes therefore denoted It corresponds more or less, like yl, to a nematic viscosity (see Fig. 67 for experimental support of this fact). The cone mode viscosity y,, which is the smallest viscosity for any electrooptically active mode, will correspondingly often be called the Goldstone mode viscosity (sometimes denoted yG).As yl and y, must be of the same order of magnitude, Eq. (304) makes us expect y," ye. The difference is often an order of magnitude. The value y3, finally, corresponding to the rotation about the long molecular axis, is normally orders of magnitude smaller than the other ones. The value should be expected to be essentially the same as in a nematic, where this viscosity is mostly denoted xl or yl. We will here prefer the latter, thus in the following we will write yl instead of y3.The value for twist motion in a nematic is mostly called yl but also % or, as opposed to xl, yL. As y, and y2 cannot be distinguished in the nematic, the twist viscosity corresponds both to yl and y2 (yo) in the smectic C. The meanings of yo and yl are illustrated in Fig. 77. If we symbolize the director by a solid object, as we have to the right of Fig. 76, we see that the coordinates 8, 9,and y,the latter describing the rotation around the long are three inaxis, thus corresponding to dependent angular coordinates which are re-
x).
x,
617
Figure 77.Rotations that correspond to viscosities yo and yl, as drawn for the uniaxial SmA (SmA*) phase.
quired for specifying the orientation of a rigid body. Except for the sign conventions (which are unimportant here), they thus correspond to the three Eulerian angles. More specifically, 9 is the precession angle, 8 the nutation angle, and y is the angle of eigenrotation. The three viscosities y,, yo, and y, determine the rotational dynamics of the liquid crystal. Only y, can easily be determined by a standard electrooptic measurement. All of them can, however, be determined by dielectric spectroscopy. We will turn to their measurement in Sec. 2.7.
2.7 Dielectric Spectroscopy: To Find the and 6 Tensor Components 2.7.1 Viscosities of Rotational Modes Using dielectric relaxation spectroscopy, it is possible to determine the values of the rotational viscosity tensor corresponding to the three Euler angles in the chiral smectic C and A phases. These viscosity coefficients (ye, y, yl) are active in the tilt fluctuations (the soft mode), the phase fluctuations (the Goldstone mode), and the molecular re-
618
2
Ferroelectric Liquid Crystals
orientation around the long axis of the molecules, respectively. It is found, as expected, that these coefficients obey the inequality ye> y,+ yl. While the temperature dependence of and y, in the SmC* phase can be described by a normal Arrhenius law as long as the tilt variation is small, the temperature dependence of yo in the SmA* phase can only be modeled by an empirical relation of the form ye=AeEJkT+ $(T-T,)-". At the smectic A* to SmC* transition, the soft mode viscosity in the smectic A* phase is found to be larger than the Goldstone mode viscosity in the SmC* phase by one order of magnitude. The corresponding activation energies can also be determined from the temperature dependence of the three viscosity coefficients in the smectic A* and SmC* phases. The viscosity coefficient connected with the molecular reorientation around the long axis of the molecules is not involved in electrooptic effects, but is of significant interest for our understanding of the delicate relation between the molecular structure and molecular dynamics.
2.7.2 The Viscosity of the Collective Modes Different modes in the dipolar fluctuations characterize the dielectric of chiral smectics. As the fluctuations in the primary order parameter, for instance represented by the tilt vector 1 2 1 sin 28 sin q
= n, n, = - sin28 cosq
t2= n, ny =
(350)
are coupled to P,some excitations will appear as collective modes. Dipolar fluctuations which do not couple to lj give rise to non-collective modes. From the tempera-
ture and frequency dependence of these contributions, we can calculate the viscosities related to different motions. In the standard description of the dielectric properties of the chiral tilted smectics worked out by Carlsson et al. [ 1521, four independent modes are predicted. In the smectic C* the collective excitations are the soft mode and the Goldstone mode. In the SmA* phase the only collective relaxation is the soft mode. Two high frequency modes are connected to noncollective fluctuations of the polarization predicted by the theory. These two modes become a single noncollective mode in the smectic A* phase. There is no consensus [153] as yet as to whether these polarization modes really exist. Investigations of the temperature dependence of the relaxation frequency for the rotation around the long axis show that it is a single Cole-Cole relaxation on both sides of the phase transition between smectic A* and smectic C* [ 1541. The distribution parameter a of the Cole-Cole function is temperature-dependent and increases linearly (a = aTT + bT) with temperature. The proportionality constant aT increases abruptly at the smectic A* to SmC* transition. This fact points to the complexity of the relaxations in the smectic C* phase. The dielectric contribution of each of these modes has been worked out using the extended Landau free energy expansion of Sec. 2.5.11. The static electric response of each mode is obtained by minimizing the free energy in the presence of an electric field. The relaxation frequency of the fluctuations in the order parameter is obtained by means of the Landau-Khalatnikov equations, which control the order parameter dynamics. The kinetic coefficients r, and r2of these equations have the dimensions of inverse viscosity. The soft mode and Goldstone mode are assumed to have the same kinetic coef-
2.7
Dielectric Spectroscopy: To Find the 7 and ETensor Components
ficient, r,,which, however, does not mean that they have the same measured value of viscosity. The viscosity of the soft mode in the smectic A* phase can be written, according to [152]
(351) where C* is the coupling coefficient between tilt and polarization, es is the dielectric contribution from the soft mode, andf, is the relaxation frequency of the soft mode in the smectic A* phase. In order to calculate the viscosity, a measure of the coefficient C* is needed. It can be extracted from the tilt angle dependence on the applied field, from Sec. 2.5.7
(352) The corresponding expression for the soft mode viscosity in the SmC* phase is not equally simple, and reads
(353) where b,lb, is the following combination of parameters from the expansion (263) C* - e q + 252P8 I ne3+37~2
($)-=xo -
(354)
Eo
This ratio can be obtained by fitting the experimentally measured values of E, versus temperature. In the frame of this Landau theory, the soft mode dielectric constant is
where the term wois a cut-off parameter.
619
Assuming the ratio b,lb, is independent of temperature, ye can be calculated in the smectic C* phase. This approximation is valid deeper in the smectic C* phase, where P , 8,and q have their equilibrium values. The Goldstone mode viscosity can be calculated [ 1521 according to the expression
(356) where P is the polarization, 8 is the tilt angle, and % andf, are the dielectric constant and relaxation frequency of the Goldstone mode. The polarization and the tilt angle need to be measured in order to calculate the viscosity. Figure 78 shows a plot of the soft mode and Goldstone mode rotational viscosities measured on either side of the phase transition between the smectic A* and SmC*. It can be seen that, except in the vicinity of the phase transition, the viscosity ye seems to connect fairly well between the two phases. The activation energies of these two processes are, however, different. This result may be compared to results obtained by Pozhidayev et al. [148], referred to in Fig. 67. They performed measurements of ye beginning in the chiral nematic phase of a liquid crystal mixture with corresponding measurements in the SmC* phase, and have shown the viscosity values on an Arrhenius plot for the N* and SmC* phases. Despite missing data of in the smectic A* phase they extrapolate the N* values of down to the smectic C* phase and get a reasonably smooth fit. Their measurements also show that yeis larger than y,, and this is universally the case.
620
2 Ferroelectric Liquid Crystals 10
Y (Nsec/m2)
1
Figure 78. The soft mode and Goldstone mode rotational viscosities as a function of temperature. The material is mixture KU-100 synthesized at Seoul University, Korea(courtessyofProf. Kim Yong Bai) (from Buivydas [lSS]).
0s 20
30
40 50 60 Temperature (“C)
2.7.3 The Viscosity of the Noncollective Modes
(357) where ft is the relaxation frequency of the molecular rotation around the short axis and 1 is the length of the molecule, as shown in Fig. 79. The viscosity related to the molecular rotation around the long axis has the corresponding expression
kT
80
by Nippon Mining Inc., which we may call LC1. It has the structural formula
The viscosity of the noncollective modes can be estimated, as shown by Gouda [ 1541 and Buivydas [155], using the original Debye theory of dielectric response. Assuming that the Stokes law is valid, the viscosity for the long axis rotation around the short axis scales as l r 3 , where 1 is the length of the long axis. For this transverse rotation we have
Yl =-87c2jid3
70
and the phase sequence I 105.0 SmA* 68.1 SmC* 8.0 Cr. The relaxation frequencies f i (of the order of 3 MHz) and f , (of the order of 110 MHz) are now measured as a function of temperature, the former in quasi-homeotropic alignment (layers parallel to the cell plates), the latter in QBS geometry. With a cross section d taken from a simple mothe correlecular model to be about 4.5 sponding function y l ( T ) is obtained from (358). Now, the length and width of a molecule used in Eqs. (357) and (358) are not self-ev-
w,
(358)
where fi is the relaxation frequency and d is the cross diameter of the molecule, cf. Fig. 79. The substance used in these measurements is a three-ring compound synthesized
L d J
~
Figure 79. The molecular dimensions d and 1 The depicted length/ width ratio corresponds to the substance LC1 (see later).
2.7
62 I
Dielectric Spectroscopy: To Find the ?and &TensorComponents
ident values. Therefore the Landau description may be used to calculate the viscosity related to the molecular rotation around the long axis. In the smectic C* phase, the viscosity is then expressed by
Landau method. In order to calculate yl ( T ) we also need a value for the molecular length 1. This can be obtained by the requirement that we can have only one single viscosity in the isotropic phase. Combining (357) and (358) gives
(359) In order to determine the same viscosity in the smectic A* phase, the normalization factor (He)*should be preserved, otherwise the viscosity will show a jump at T, [ 1541. Thus the corresponding equation will read
where (P/8), is the limiting value of the P/8 ratio measured at the transition. The viscosity '/I calculated by the Landau theory and the '/I evaluated by using the Debye formulas are shown for comparison in Fig. 80. We see that they agree fairly well in the limit of small tilt, thus particularly in the A* phase. The non-Arrhenius increase at higher tilts is here an artifact inherent in the
On putting %= we find
From this 1 is obtained as 15 A.When we check the molecular length by searching the lowest energy conformation of LCI in a simple computer program, we see that this value actually corresponds to the length of the core. We could of course also have slightly adjusted the input value of d such that the Debye and Landau viscosity values coincide exactly in the A* phase. This is found to occur for d = 4.7 A,corresponding to 1=16 The results from all viscosity measurements on the substrate LC1 are summarized in Fig. 8 1.
A.
lo2
Smectic C*
Smectic A*
10' ."
I
I
I
Y loo (Ns/mz) 10' 10-2
t 2,87
I 2,91
2,95
' 2,99
3,02
3,06
3,lO
1000/T (K-l)
Figure 80. Viscosities of noncollective motions evaluated by two different methods. The substance is LC1 (from Buivydas [155]).
2,62
2,70
2,79
2,87
2,95
3,04
1000/T (K-')
Figure 81. The three components of the viscosity tensor measured by dielectric relaxation spectroscopy. The substance is LC I (from Buivydas [ 1551).
622
2
Ferroelectric Liquid Crystals
The noncollective rotational viscosities are denoted by yl (longitudinal) and '/t (transverse). The collective motions have the corresponding designations (for soft mode) and yG (for Goldstone mode). Equivalently, yo and y, could also have been used. It is remarkable that the Goldstone mode viscosity is almost as low as the viscosity around the long axis of the molecule. As pointed out earlier, this is explained by the fact that a large component of the angular velocity is around this axis. The soft mode viscosity lies much higher and, as the results show, is essentially the same as the viscosity for the corresponding individual molecular rotation.
2.7.4 The Viscosity yq from Electrooptic Measurements In the smectic C* phase, the rotational viscosity y, can be estimated by observing the polarization reversal or the electrooptic properties of the cell, as described in Sec. 2.7.6. The estimation may, for instance, be based on the approximation mentioned there, using the elastic torque [ 1371
pS Esincp - K cosq + y, @ = 0
(363)
Solving this equation and fitting the observed polarization reversal process to the solution, the viscosity can be estimated and compared to the one measured by means of dielectric relaxation spectroscopy. This method is fast, but less accurate. The polarization reversal measurement is a large signal method requiring full switching of the liquid crystal, and therefore cannot be expected to coincide with the much more precise results from the low signal dielectric relaxation spectroscopy measurements. Basically, a &, value from the polarization reversal technique involves spurious contributions of elastic effects due to the
2,o .' ' ' ' '
1,s r In Y$
' ' '
0
1
I
s
- - . - .,
*
:
I
I
I
*
a
a
I
I _
O
I
1
-
a
: -
non'
-
a
I
-
/
4 5 2 measurements from dielectric a
I
-
4".
' (Nsec/mz) 0,s 1
-l,o
I
from polarization reversal
0
LO :
0,o
I
Smedic C*
"
1
a
W
*
L
T
*
* I*
I -
surfaces of the sample. However, the values from the polarization reversal method do not differ by more than typically a factor of two, and the difference tends to be smaller at higher temperatures (see Fig. 82).
2.7.5 The Dielectric Permittivity Tensor Phases having biaxial symmetry (tilted smectic phases) exhibit dielectric biaxiality in particular. At frequencies of 1 MHz and below, the biaxiality becomes important and critically influences the electrooptic switching behavior of the SmC* phase. It is therefore important to be able to measure the biaxiality at these frequencies. Being a symmetrical second rank tensor, the dielectric permittivity can always be diagonalized in a proper frame and described by three components along the principal directions. The three principal values can then be expressed by a single subscript and can be determined by three independent measurements performed at three different orientations of the director relative to the measuring electric field. In practice, this may not be that
2.7
Dielectric Spectroscopy: To Find the ?and &TensorComponents
straightforward, for instance, in the case of a thick sample (measured on a scale of the pitch) of a smectic C* when the helix is not quenched by the surfaces. In such a case the local frame of the E tensor is rotating helically through the sample. Y
2.7.6 The Case of Helical Smectic C* Compounds
(364)
0
E3
As for y in Sec. 2.6.9, we may consider 2 being brought to diagonal form (starting from the laboratory frame) by a similarity transformation
~(1,2,3)=T-'&(~,y,z)T
E ( 8 ) = TO 2 Tg'
(366)
with the rotation matrix TO cos8 0 0 1 sin8 0
(365)
where T is a rotation matrix and T-' is the inverse or reciprocal matrix to T, in this case identical to its transpose.
E(e) =
Figure 83. The definitions of the molecular axes and components of the dielectric tensor.
In Fig. 83 we may imagine a laboratory frame with the z axis along the layer normal (thus along ell in the figure), such that we have turned the director n a certain angle 8 around the y direction (along E~ in the figure). The x direction is along c. In this laboratory frame xyz, the permittivity tensor is then given by
In the molecular frame (Fig. 83) we write the tensor E as
0
EI
623
- sin8
(367) cos8
Performing the multiplication - the same as in Eq. (342) - we find
- E ~ sin0 ) coso c1cos2 o + E~ sin2 8 o 0 E2 0 ( ~ ~ - ~ ~ ) s i n o~ cE ]osin28+E3cos2e s ~
which can be written in the form
0 -A&sin8cosO E2 0 &(el = -A& sin8 cos8 0 Ell
1
(369)
by introducing the dielectric anisotropy A&= E~ -E' and the abbreviations cos28+ E ~ C O 2S8
(370)
E,, = I ,sin28+ c3cos2e
(371)
=
and If we now further turn the director by an angle cp around the z direction, the permittivity tensor will change to
624
2
Ferroelectric Liquid Crystals
~ ( 89) , = q,E(e)Tml
(372)
As this rotation is performed counterclock-wise (positive direction) in the xy plane, the rotation matrix is now instead
(373)
This gives
&(e,q) = T,T,~T,-~T,-~
(374)
or ) cosq -A&sin8 cos8 cosq cos2 q + E~ sin2 q -(el - E ~ sinq - ( ~ 1 - ~ ~ ) s i n q c o s q sin2 q + E~ cos2 q AEsin8 cos8 sinq AE sin 8 cos 8 sin q - A&sin q cos 8 cos q ElI
In the helical smectic C * , the tilt 8 is a constant while the phase angle q is a function of the position along the layer normal, q= q ( z ) . Averaging over one pitch, with (cos2 q) = (sin2 q) =
+
and (sinq) = (cosq) = (sinqcosq) = 0 E
simplifies to
0
(Ell)
with the new abbreviations 1 2
( E ~=) - (cl CO?
8 + E~ + E~ sin28)
and (E,,) =
sin28+ E ~ C O S ~ O
Equation (378) reveals that the helical state of the smectic C* is effectively uniaxial, if the pitch is sufficiently short to al-
1
(375)
low the averaging procedure. The shorter and more perfect the helix, the more completely the local biaxiality is averaged out (both dielectric and optical). This is consistent with the empirical evidence, showing almost perfect uniaxiality for helical samples of short pitch materials. Before we can use our derived relations to determine E ~ E~ , and E ~ we , have to perform one more refinement. The simple measurement geometry where smectic layers are parallel to the glass plates is easy to obtain in practice. On the other hand, it is very hard to turn them into being perfectly parallel to the plates; normally, the result is that they meet the surface with a slight inclination angle 6. To account for this case we have to see how the tensor ( ~ ( 0 )transforms )~ when we turn the layer normal by a certain angle 6 around the x axis. We perform the rotation clockwise (in this case the direction does not matter), corresponding to
2.7
625
Dielectric Spectroscopy: To Find the ?and CTensor Components
and giving 0
( ~ ( 86))q , = Ts ( ~ ( 8 T; )' ) ~ =
0 ( E ~cos2 ) 6 + ( ~ 1 1 ) sin26 (EL) - ( ~ ~ 1sin ) 6 cos 6 (EL) - (q) sin6 cos6 (eL)sin26 + ( ~ ~ , ) ( c6o) s ~
o
In the case where we assume a helix-free sample and fully addressed or memorized director states lying on extreme ends of the smectic cone, so that we might put cp equal to 0 or n in Eq. (375), would instead have given the tensor components cos2 8 + E~ sin2 8 A~sin8cos8sin6 - A&sin 8 cos 8 cos 6 E'
A&sin 8cos 8sin 6 ~2 cos2 6 + ( ~ 1 1 ) sin2 6 ( ~ -(elI))sin6cos6 2
-A& sin 8 cos 8sin 6 (12- (ell))sin 6 cos 6
(383) ~~sin~6+(~~~)cos~6
2.7.7 Three Sample Geometries
Eq. (378) or, by Eq. (379)
With the expressions derived in the last section, in the first version worked out by Hoffmann et al. [ 1561 and further developed by Gouda et al. [157], we can calculate E ~ E, ~ and E~ from three independent measurements, using three different sample geometries. Consider first that we have the smectic layers oriented perpendicular to the glass plates so that the applied field is perpendicular to the layer normal. In the Smectic A* phase we would call this planar alignment, and a dielectric measurement would immediately give the value in the SmA* phase. If we cool to the SmC* phase, the helix will appear in a direction parallel to the glass plates. By applying a bias field we unwind the helix and the signal field will now measure &nw, which is identical to ~2
&helix = -(el 1
Eunw
= EZ
(384)
the permittivity value along the direction of the polarization P . If we take away the bias field the helix will eventually relax. The value of the permittivity measured in the presence of a helix is denoted by &helix. It is equal to E~~ in the lab frame, i.e., to (el) in
2
,
cos28 + e2 + ~3 sin28 )
(385)
The third geometry normally requires a second sample aligned with the layers along the glass plates. We may call this geometry homeotropic and in the SmA* phase we measure the value &h = E,, along the layer normal. After cooling to the SmC* phase we may call the geometry quasi-homeotropic and denote the measured value &horn. The helix axis ( z ) is now parallel to the measuring field, which means that &horn is ,&, in the lab frame, which is (4,) in Eq. (378) or, by Eq. (380) =
&horn
sin28+ ~3 c0s28
(386)
From Eqs. (384) to (386) the three principal values of the dielectric tensor can thus be E ~ and , r,, calculated. After solving for the components of the diagonalized tensor can be expressed in the measured values as
1 1- 2sin2 8
&I = '
[(2&helix - &,nw ) Cos2 8 - &horn Sin281 (387)
&2 = ELinw
(388)
626
2
Ferroelectric Liquid Crystals
1 I - 2sin2 e
E3 =
be
. [(2&he1ix - E , , ~)sin 2 e - &horn cos2 e] (389) The three measurements require preparation of two samples. By using a field-induced layer reorientation, first investigated by Jakli and Saupe [158], Markscheffel [158a] was able to perform all three measurements on a single sample, starting in the quasi-homeotropic state, and then, by a sufficiently strong field, turning the layers over to the quasi-bookshelf structure. Generally, one would start with the quasibookshelf geometry and then warm up the sample to the smectic A* phase and strongly shear. The advantage of this technique is a very homogeneous, homeotropic orientation. The quality of homeotropic orientation may even improve (without degrading the quality of planar orientation) if the glass plates are coated by a weak solution oftenside.
= ( E , ) C O S+ ~~ (q,)sin26
(391)
while &horn stays unaffected, i.e., ( E ~ ~given ), by Eq. (386), because of the absence of the layer tilt in this geometry. The value of 6 is often known, growing roughly proportional to 6, and can in many cases be approximated as 6 ~ 0 . e. 8 The principal values of qj can then be extracted from Eqs. (386), (390), and (391). It turns out that the values are not very sensitive to small errors in 6. A special case of tilted layers is the chevron structure, for which the tilt makes a kink either symmetrically in the middle or unsymmetrically closer to one of the surfaces. The chevron structure means that two values +6 and -6 appear in the sample. As can be seen from Eqs. (389) and (390), the angle 6 only appears as a quadratic dependence, hence the relations are also valid in the chevron case. Solving for the principal values in the chevron or tilted layers case, we obtain 1
(392)
&'
=
~
1 (&nw - &horn sin' 6 ) cos2 6
(393) (394)
2.7.8 Tilted Smectic Layers When the layers make the inclination 6with the normal to the glass plates, we see from Eq. (383) that q,nw (= &yy) will be expressed by (E,,,
= &,cos26
whereas
+ (ql)sin26
390)
= E~~ in Eq. (382) turns out to
Typical measured variations of the permittivities &,, e2,and E ~as, we pass the phase boundaries from isotropic to tilted smectic phase, are shown in Fig. 84. The values of and ~2 have a similar temperature variation. Therefore their difference, the biaxiality 6&, has a weak but noticeable temperature dependence. The difference between the values and E~ is the dielectric anisotropy A&.This depends on temperature much
2.7
40
80 100 Temperature (“C)
60
627
Dielectric Spectroscopy: To Find the ?and 2.Tensor Components
120
Figure 84. The principal values of the dielectric permittivity tensor at 100-kHz measured by the short pitch method. The material is the mixture SCE12 by BDHlMerck (from Buivydas [155]).
scribed by Sambles et al. [159]. They found the profile to be uniform or nearly so within each surface-stabilized domain. However, other reports show that the surface-stabilized state is more accurately modeled by some triangular director profile [ 1601. When a uniform director profile is assumed, then the smectic director field n can be described by the three angles q, 6,and 6. These angles are uniform throughout the sample and the dielectric tensor component E~~ corresponds to the dielectric permittivity q,measured in the planar orientation. Under certain conditions this may be written Ep = &2 -8&
~
more strongly than the dielectric biaxiality. As a result of the fact that the relaxation frequency of E~ in the nematic phase lies below 100 kHz, the dielectric anisotropy is negative at that frequency. A negative value of A& is a common feature, which may greatly affect the electrooptic switching properties at room temperature. In contrast, the relaxation frequency of E~ lies much above 100 kHz, whence the positive biaxiality 8~(which may rather be considered as a low frequency value). This means that for information about A& we have to go to relatively low frequencies and inversely to high frequencies for corresponding information about 8 ~ .
sin2 6 sin28
(395)
where
8&= &2 - &I
(396)
is the dielectric biaxiality. When measuring in the quasi-homeotropic orientation, we will observe the component &h = E,, and, assuming the layer tilt 6 to be zero, &h takes the form gh = ~2
+A E C O S ~ ~
(397)
Again we have to look for an independent measurement of a third value, in order to cal-
2.7.9 Nonchiral Smectics C When the cell has another director profile than the uniform helix, averaging of the angle q over the pitch length cannot be performed in a straightforward way. It is necessary to know about the director profile through the cell before making simplifications. This profile is hard to get at but may be estimated by optical methods, as de-
SmC
30
40
SmA N
50 60 Temperature (“C)
70
Iso-
-
80
Figure 85. The dielectric biaxiality of the nonchiral smectic C mixture M4851 (Hoechst), measured by the long pitch method (from Buivydas [155]).
628
2
Ferroelectric Liquid Crystals
culate all three principal components of the dielectric permittivity tensor. At the second order transition SmA -+SmC, the average value of E is conserved, thus (398) With knowledge of the tilt angle 8 and the layer inclination 6, we then can calculate E ~ and , E~ from Eqs. (395), (397) and (398).
2.7.10 Limitations in the Measurement Methods
The reason for this failure is that for a 45" tilt angle 8 there is no difference in average dielectric anisotropy between the planar orientation and the quasi-homeotropic orientation, and thus the two equations in the system (Eqs. 385 and 386) are linearly dependent as far as that they give the same geometric relation between the direction of the measuring field and the direction of the principal axes and E~ (& is not involved in Equations (385) and (386) in this case give &helix
=
51 (El -tE 2 )
&2
(399)
and Each of the models serving as basis for the dielectric biaxiality measurements has been derived using certain assumptions. The method described by Gouda et al. [ 1571 assumes an undisturbed ferroelectric helix, and this assumption is best fulfilled in short pitch substances. Actually, the pitchhell thickness ratio is the important parameter. For measurement convenience, the cells cannot be made very thick, hence the method works well for materials with a helical pitch of up to about 5 pm. This includes practically all cases of single smectic C* substances. The method cannot be applied to nonchiral materials. The method described by Jones et al. [161] (long pitch method) was developed for materials with essentially infinite pitch. It may be used for long pitch materials in cells where the helical structure is unwound by the surface interactions and a uniform director profile is established. The weakness of the method is that it requires the director profile to be known. On the other hand, it works for the nonchiral smectic C. It also works for materials with 8=45" (typically materials with N 4 SmC transitions, lacking the SmA phase), which is a singular case where the short pitch method fails.
&horn =
z1
(El + E3)
(400)
respectively, whence it is not possible to , only measure their sum. split and E ~ but Using tilted layers (6#0) or knowing the average value E is not remedy for this, because only the combination &, + E~ appears in all equations. As a result of this the errors in the calculated values of and E~ increase and diverge when 8 approaches the value 45'. This is also evident from the denominator (1-2 sin28) in Eqs. (392) and (394). In Fig. 86 we show how the errors in and E~ grow with the tilt angle under the assumption that the value used in the calculation formula was measured with a 2% error and that the value of was assumed to be exact. The presence of this singularity limits the usability of the short pitch method to substances with tilt angle 8 up to about 35-37'. In practice, however, this is not too serious, as materials with a tilt approaching 40" are rare.
2.8 FLC Device Structures and Local-Layer Geometry 30
25 20 Error 15 (%)
10
5 0 0
10
20 30 Tilt angle 9 (deg)
40
50
Figure 86. The dependence of the errors in the tensor components E, and E~ calculated by the short pitch method when the smectic tilt angle @approaches45 ’. The input value is assumed to be measured with a 2% error (from Buivydas [ 1551).
2.8 FLC Device Structures and Local-Layer Geometry 2.8.1 The Application Potential of FLC Ten years of industrial development offerroelectric liquid crystal (FLC) devices have now passed. This may be compared with 25 years for active matrix displays. The potential of FLC was certainly recognized early enough following the demonstration of ferroelectric properties in 1980. In principle the FLC has the potential to do what no other liquid crystal technology could do: in addition to high-speed electrooptic shutters, spatial light modulators working in real time, and other similar hardware for optical processing and computing (all applications requiring very high intrinsic speed in repetitive operation), the FLC (and the closely related and similar AFLC) technology offers the possibility to make large-area, highresolution screens without the need for tran-
629
sistors or other active elements, i.e., in passive matrix structures using only the liquid crystal as the switching element. Several kinds of such structures (Canon, Matsushita, Displaytech) have now been demonstrated which give very high quality rendition of color images, and one polymer FLC technology has been developed (Idemitsu) capable of monochrome as well as multi-color panels. When the SSFLC structure was presented in 1980, some obvious difficulties were immediately pointed out: the liquid crystal had to be confined between two glass plates with only about 1.5 pm spacing or even less and, furthermore, in a rather awkward geometry (“bookshelf” structure), which meant that both the director alignment and the direction of smectic layers had to be carefully controlled. Luckily, a number of more serious problems were not recognized until much later. In addition, only a few molecular species had been synthesized at that time; in order to develop a viable FLC technology, a considerable effort in chemical synthesis would have had to be started and pursued for many years. (We may recall that the submicrosecond switching reported in the first paper had been observed on a single substance, HOBACPC, at an elevated temperature of 68 “C.) This chemical problem alone would have discouraged many laboratories from taking up the FLC track. Nevertheless, in 1983 excellent contrast and homogeneity in the optical properties were demonstrated on laboratory samples of DOBAMBC, one of the other single substances available (thus not on a room temperature mixture) and sufficiently well aligned for that purpose by a shearing technique [96]. Shortly afterwards, two Japanese companies, Canon Inc. and Seiko Instruments and Electronics, were engaged in R&D. By 1986 about twenty Japanese and five European companies were engaged in
630
2
Ferroelectric Liquid Crystals
FLC research, supported by about ten chemical companies worldwide. Common to almost all these ventures was the fact that the FLC teams were very small. When really troublesome obstacles began to show up, one company after the other left the scene, favoring STN or TFT technology. It was clear that the obstacles were not only in manufacturing technology, but there were tremendous scientific difficulties of a very basic nature as well. After having presented the first mature FLC prototypes in 1988 (black and white) and 1992 (color), Canon in Tokyo is now manufacturing the first 15 in. (37.5 cm) FLC panel with 1280x 1024 pixels, where each pixel, of size 230 ymx230 ym, can display 16 different colors because it is composed of four dots or subpixels. This screen (Fig. 87) has a remarkable performance and does not resemble anything else in its absolute freedom of flicker. At the other end of the scale, Displaytech Inc., U.S.A.,
is marketing FLC microdisplays, slightly larger than 5 mm by 5 mm in size with VGA resolution (640x480), where every dot is capable of 5 12 colors (see Fig. 88). Another remarkable display is Idemitsu Kosan’s fully plastic monochrome screen in reflection, of A4 size (15 in) with 640x400 dots (see Fig. 89). This is a passively multiplexed (1 :400) sheet of FLC polymer, thus entirely without glass plates and all in all 1 mm thick. Regarding these achievements, it may be time to look at the real SSFLC structures that are used in these devices.
2.8.2 Surface-Stabilized States It is important to point out that for a given material there is a variety of different realizations of surface-stabilized states (states with nonzero macroscopic polarization), on the one hand, and also a variety of other states. Among the former, those with a non-
Figure 87.Canon 15 in (37.5 cm) color screen which went into production 1995. High quality rendition of artwork is extremely sensitive to flicker. The FLC freedom of flicker therefore gives an unusual means of presenting art, here illustrated by the turn of the century artist Wyspianski (self-portrait) and Bonnard (Dining Room with Garden).
2.8 FLC Device Structures and Local-Layer Geometry
63 I
Figure 88. The first version of Displaytech’s miniature display (ChronoColor), which went into production in early 1997, in comparison with a conventional active matrix display. This microdisplay utilizes sequential color to produce full color on each pixel, resulting in a brighter, crisper image than that of an AMLCD, which uses a triad of red, green, and blue pixels to form a color. In the insets, the pixels of the ChronoColor display and AMLCD are magnified to show the difference in fill factors. The color is what makes the image that you see, and it occupies 75% of the display on the left, but only 35% of the corresponding active matrix display. (Courtesy of Displaytech, Inc.)
Figure 89. All-polymer FLC prototype presented by Idemitsu Kosan Co., Ltd., in 1995. This reflective monochrome display is 0.5 mm thick, has a 1:400 multiplex ratio, and a size of 20 cmx32 cm (400x640 pixels each 0.5 mmx0.5 mm), corresponding to a diagonal of 15 in (37.5 cm).
zero P along the applied field direction will have a strong nonlinear dielectric response in contrast to other states, which behave linearly until saturation effects dominate. Only the former may be bistable, i.e., show
a stable memory (P#O in the absence of an applied field E). We will give two examples to illustrate this. The first is a case with supposedly strong anchoring of the director along a specified azimuthal direction cp, cor-
632
2
Ferroelectric Liquid Crystals
responding to parallel rubbing at top and bottom plate of the cell 11271. This case is illustrated in Fig. 90, where successive n -P states are shown across the cell. Clearly we have two completely symmetrical arrangements, which have a certain effective polarization down and up, respectively, and which are, each of them, a stable state. They can be switched back and forth between each other by the application of convenient pulses, and have a symmetrical relationship similar to the two cases of Euler buckling of a bar in two dimensions under fixed boundary conditions. The cell is thus surface-stabilized and ferroelectric with a symmetrically bistable reponse. However, it is immediately clear that this configuration may not be the most desirable one, because we have a splayed P state with only a small part of P that can actually be switched by a short pulse, requiring a high voltage for a large optical effect. This is because the optical
contrast between the two memorized up and down states is very low. In order to enhance this contrast, we would have to apply a considerable AC holding voltage across the cell after application of the switching pulse, which seems to make this use of ferroelectric structure rather pointless. Clearly the structure is intrinsically inferior to the structure in Fig. 61 where the director profile is supposed to be homogeneous across the cell. However, it not only serves the purpose of illustrating that surface-stabilized structures can be of many kinds and that they might be characterized by their electrical (speed) as well as their optical efficiency, but also this structure actually turns out to be of high practical interest, as we will see in Sec. 2.8.6. The second example is what we call a twisted smectic [162], and is illustrated in Fig. 91. Ideally a smectic C* with 8=45" should be used as a twisted smectic. In Fig. 9 1 the anchoring is again assumed to be strong (although this is not a necessity for
@=-n
FIELD OFF
FULL FIELD ON
(TRANSMISSIVE)
(MINIMUMTRANShfIlTANCE) ,
polarizer glass
~
w
,
Nbbing direction
smectic layer rubbing direction glass
Figure 90. Surface-stabilized configuration with less than optimum efficiency, switchable between two symmetric states with low optical contrast. The surface pretilt angle has been chosen equal to the smectic tilt angle 8 i n this example. For a strong boundary condition with zero pretilt, a different extreme limiting condition with @approachingzero at the boundary is also conceivable, without any essential difference in the performance of the cell.
polarizer
Figure 91. The twisted smectic preferably uses a 45 O tilt material. It i s a fast-switching device giving an electrically controlled, continuous grayscale. This is a smectic C* working in a dielectric mode. It should not be mistaken for a ferroelectric device (after Pertuis and Pate1 [ 1621).
2.8
FLC Device Structures and Local-Layer Geometry
the working principle), and the alignment directions are at right angles (with zero pretilt at the surface) at top and bottom, introducing a 90” twist across the cell. This also results in zero macroscopic polarization along the direction in which the electric field is applied. With no field applied, the light will be guided in a way similar to that in a twisted nematic, and the cell will transmit between crossed polarizers. On application of an electric field, the twisted structure will unwind, until the whole structure except for one boundary layer has a homogeneous arrangement of the director, giving zero transmittance. The response is linear at low electric field and we have a fast switching device with a continuous grey scale. It has to be pointed out that this, of course, is not a ferroelectric mode. Thus a smectic C* liquid crystal does not have a ferroelectric response per se, but it can be used in many different ways. As already pointed out, bulk structures of smectic C* tend to have an antiferroelectric-like ordering in one way or another. The point about surface stabilization is that it transfers macroscopic polarization to the bulk, giving it ferroelectric properties in certain geometries. These properties are best recognized by the appearance of spontaneous domains of up and down polarization, and by the fact that the response to an electric field is now strongly nonlinear. Let us finally look back to Fig. 61 and consider the material parameters 6, P, and d, i.e., tilt angle, polarization, and smectic layer thickness. They all depend on temperature: B(T),P ( T ) , and d ( T ) . The temperature variations of 0 and P , if not desirable, at least turned out to be harmless. On the other hand, the much smaller temperature dependence of d ( T )turned out to be significantly harmful. If the liquid crystal molecules behaved like rigid rods, the layer thickness would diminish with decreasing temperature accord-
633
ing to d,cos 6, as the director begins to tilt at the SmA +SmC transition, i.e., we would have a layer shrinkage
A d ( T ) - 62
(401)
in the smectic C phase. In reality, the shrinkage is less (i.e., the molecules do not behave like rigid rods), but still a phenomenon that is almost universal, i.e., present in almost all materials. If, in Fig. 61, we consider the translational periodicity d to be imprinted in the surface at the nematic - smectic A transition, and if we further assume that there is no slip of the layers along the surface, the only way for the material to adjust to shrinking layers without generating dislocations is the creation of a folded structure in one direction or the other on entering the SmC phase, as illustrated in Fig. 92. As the layer thickness dc decreases with decreasing temperature, the chevron angle 6 increases according to
dc cos6 = dA
Figure 92. The shrinkage in smectic layer thickness due to the molecular tilt O(Q in the SmC* phase results in a folding instablity of the layer structure (“chevrons”). Even if the fold can be made to go everywhere in the same direction (in the figure to the right) to avoid invasive zigzag defect structures, the switching angle is now less than 2 0, which lowers brightness and contrast.
634
2
Ferroelectric Liquid Crystals
where 6 i s always smaller than 8. Often 6 and 8 have a similar dependence, such that 6= A@ with A= 0.85 -0.90 in typical cases. The resulting “chevron” structure constitutes one of the most severe obstacles towards a viable FLC technology, but its recognition in 1987 by Clark and his collaborators by careful X-ray scattering experiments [163, 1641 was one of the most important steps both in revealing the many possibilities of smectic local layer structures and in controlling the technical difficulties resulting from these structures.
2.8.3 FLC with Chevron Structures The extremely characteristic zigzag defects had been observed for many years before the
subtleties of the local layer structure were unveiled. Very often they appear as long “streets” or “lightning flashes” of thin zigzag lines, with the street going essentially along the smectic layers, whereas the lines themselves are at a small angle or almost perpendicular to the layers. In Fig. 93 the angle between the lines and the layer normal is roughly 5 ” . Often these thin lines are “short-circuited” by a broad wall, with a clear tendency to run parallel to the layers, as in Fig. 93a where it is almost straight and vertical, or slightly curved, as in Fig. 93b. It is evident that if the layers are not straight in the transverse section of the sample but folded, as in Fig. 92, then where we pass from an area with one fold direction to an area with the opposite direction there must be a defect region in between, and hence it is likely that the zigzags mediate such
(b)
Figure 93. Appearance of zigzag walls in a smectic C structure with smectic layers initially (in the SmA phase) standing perpendicular to the confining glass plates, running in a vertical direction on the micrographs (thin lines to the left, broad walls to the right). (Courtesy of Monique Brunet, University of Montpellier, France).
2.8 FLC Device Structures and Local-Layer Geometry
changes. The question is how. This may be illustrated starting from Fig. 94. In (a) we show the typical aspect of a zigzag tip with ybeing the small angle between the line and the layer normal (which is often the same as the rubbing direction). In (b) is shown the folded structure making chevrons of both directions, suggesting that at least two kinds of defect structure must be present. In the picture the fold is, as is most often the case, found in the middle of the sample - we will call this fold plane the chevron interface although its depth may vary, as in (c). We will mainly restrict ourselves to the symmetric case (b) in the following discussion of the general aspects. As we will see, the chevron interface actually acts as a third surface, in fact the one with the most demanding and restrictive conditions on the local director and polarizations fields. It is clear that the transition from one chevron to the other cannot take place abruptly in a layer as sketched in (d), as this would lead to a surface (2D) defect with no continuity of layer structure nor director field. Instead it is mediated by an unfolded part of width w (this region will be observed as a wall of thickness w ) in (e), looked at from the top as when observing the sample
through a microscope. The wall thickness \.t’ is of the order of the sample thickness L. A more adequate representation of the threedimensional structure is given in Fig. 95. The vertical part of the layer has the shape of a lozenge (in the general case, with unsymmetric chevrons it becomes a parallelogram). The sterically coupled fields n (r) and P ( r ) can now be mapped on this structure. Along the folds, n ( r )must simultaneously satisfy two cone conditions (i.e., to be on the cone belonging to a particular layer normal) indicated in the figure. This is always possible for 61 8 and gives a limiting value for the chevron angle 6. After the discovery of the chevron structures, a number of complexities in observed optical and electrooptical phenomena could be interpreted in these new terms. For a more thorough discussion in this matter, we refer to references [ 166- 1681. Our emphasis will be on the important consequences for the physics due to the presence of chevrons, but even this requires dealing with at least some structural details. First of all, the chevron fold forces the director n to be in the interface, i.e., to be parallel to the plane of the sample in this region, regardless of how n ( r ) may vary through the rest of the sample and independent of the surface conditions. Although the director n is continuous at the chevron interface, the local polarization field P cannot be, as shown in Fig. 96. It makes a jump in direction at the interface, nevertheless, in such a way that
V.P=O (c)
Irt)
(e)
Figure 94. Thin zigzag lines run almost perpendicular to the smectic layers making a small angle ywith the layer normal as shown in (a). In (b) we look at the chevron folds in the plane of the sample, in (e) perpendicular to the plane of the sample. Asymmetric chevrons (c) cannot preserve anchoring conditions at both surfaces and are therefore less frequent.
635
(403)
which means that the discontinuity is not connected with a build-up of local charge density. If we now apply an electric field between the electrodes, i.e., vertically as in (a), we see that there is an immediate torque because E and P are not collinear. Hence no nucleation is needed for switching from state 1 to state 2. Neither are fluctuations
636
2
Ferroelectric Liquid Crystals
Figure 95. Section of a thin wall mediating the change in chevron direction. The layers in the chevron structure make the angle 6 (the chevron angle) with the normal to the glass plates. Along a chevron fold where two surfaces meet, two cone conditions have to be satisfied simultaneously for n, which can be switched between two states. At the two points of the lozenge where three surfaces meet, three conditions have to be satisfied and n is then pinned, thus cannot be switched.
Ej
f r - r r l
(3
kK--Nk
@
4 ______________________________
Figure 96. (a) At the chevron interface the local polarization P is discontinuous, making a jump in direction. (b) When switching from the down to the up state, P rotates everywhere anticlockwise above and clockwise below the chevron interface (time axis to the right). The director is locked in the chevron plane and can move between n , and n2.
needed for this. In other words, the switching process is not fluctuation-controlled. On the other hand, the chevron region requires an elastic deformation of the local cone in order to switch: the local tilt 8 must dimin-
ish to a smaller value (midway between 1 and 2), which gives a contribution to the threshold for the process. Generally speaking, the bulk switching on either side of the chevron interface preceeds the switching in the interface. The latter contributes to the latching and thus to the bistability. As seen from Fig. 96b, the switching process is unambiguous as regards the motion of IZ and P (sterically bound to n): on the upper side of the chevron, P rotates counterclockwise, on the lower side it rotates clockwise when we switch from 1 to 2; everything turns around in the reverse switching direction. This explains why there are no twist and antitwist domains like the ones observed in twisted nematics prior to the time when chiral dopants were added in order to promote a certain twist sense. So far we have described the switching concentrating on the chevron interface, completely disregarding what could happen at the two bounding (electrode) surfaces. In fact, if the anchoring condition on the surfaces is very strong, switching between up and down states of polarization will only
2.8
FLC Device Structures and Local-Layer Geometry
take place at the chevron interface. At high voltage this will more or less simultaneously take place in the whole sample. At low voltage it will be possible to observe the appearance of down domains as “holes” created in an up background, or vice versa, in the shape of so-called boat domains (see Fig. 105) in the chevron interface (easily localized to this plane by optical microscopy). The walls between up and down domains have the configuration of strength one (or 27c) disclinations in the P field. It should be pointed out that the uniqueness of director rotation during the switching process is not a feature related to the chevron per se, but only to the fact that the chevron creates a certain P-tilt at the chevron interface. If the boundary conditions of the glass surfaces involved a similar P-tilt, this will have the same effect. A glance at Fig. 97 reveals another important consequence of the chevron structure. As P is not along E (applied field) there will always be a torque PxE tending to straighten up the chevron to an almost upright direction. Especially in antiferroelectric liquid crystals, which are used with very high P values, this torque is sufficiently strong for almost any applied field, for instance, normal addressing pulses, to raise and keep the structure in a so-called quasibookshelf structure (QBS) under driving conditions. In ferroelectric liquid crystals,
Figure 97. The fact that even after switching the polarization P is not entirely in the direction of the applied field will tend to raise the chevron structure into a more upright position, so decreasing the effective 6 but breaking up the layers in a perpendicular direction. This gives a characteristic striped texture from the newly created, locked-in defect network.
637
presently with considerably lower P values, the same effect was previously employed to ameliorate contrast and threshold properties, by conditioning the chevron FLC to QBS FLC by the application of AC fields 11691. The effect on the switching threshold can be extracted from Fig. 96. When the chevron structure is straightened up, 6 decreases and the two cones overlap more and more, leading to an increasing distance between 1 and 2, as well as further compression of the tilt angle 6 in order to go between 1 and 2. The threshold thus increases, in agreement with the findings of the Philips (Eindhoven) group. On the other hand, this straightening up to QBS violates the conservation of smectic layer thickness d,, which will lead to a breaking up of the layers in a direction perpendicular to the initial chevrons, thus causing a buckling out of the direction running perpendicular to the paper plane of Fig. 97.
2.8.4
Analog Grey Levels
As we just pointed out, in the chevron structure the polarization is no longer collinear with the external field. This can be used (for materials with a high value of P ) to straighten up the chevron into a so-called quasibookshelf structure, combining some of the advantages from both types of structure. For instance, it can combine a high contrast with a continuous gray scale. How to produce analog gray levels in an SSFLC display is perhaps not so evident, because the electrooptic effect offers two optical states, hence it is digital. Nevertheless, the shape of the hysteresis curve reveals that there must be small domains with a slightly varying threshold, in some analogy with the common ferromagnetic case. Normally, however, the flank of the curve is not sufficiently smeared out to be controlled and to
638
2
Ferroelectric Liquid Crystals
accommodate more than a few levels. Curve I of Fig. 98 shows the transmission -voltage characteristics for a typical SSFLC cell with the layers in the chevron configuration [ 1651. The threshold voltage is fairly low, as well as the achievable transmission in the bright state, leading to a low brightnesscontrast ratio. The position and sharpness of the threshold curve reflect the relatively large and constant chevron angle S, in the sample. If a low frequency AC voltage of low amplitude (6- 10 V) is applied, the smectic layers will be straightened up towards the vertical due to the P - E coupling, so that the local polarization vector increases its component along the direction of the field. This field action, which requires a sufficiently high value of P , breaks the layer ordering in the plane of the sample and introduces new defect structures, which are seen invading the sample. The result is that the chevron angle 6 is reduced, on average, and the threshold smeared out, as shown by curve 11. Lower 6 means a larger switching angle (and higher threshold), and thus higher transmission. Still higher transmission can be achieved by an additional treatment at a somewhat higher voltage (+25 V), giving threshold curve 111, corresponding to a new distribution around a lower &value and a microdomain texture on an even finer scale. The actual switching threshold is a complicated quantity, not fully understood (no successful calculation has been presented so far), and usually expressed as a voltagetime area threshold for the switching pulse. For a given pulse length it is, however, reasonable that the amplitude threshold increases according to Fig. 98 when the average value of 6 decreases. There are at least two reasons for this, as illustrated by Fig. 96. First, it is seen that the distance between the two positions n l and n2 in the chevron kink level (which acts as a third,
T
t
Figure 98. Amplitude-controlled gray scale in SSFLC. The chevron structure is transformed to a quasi-bookshelf (QBS) structure by external field treatment. In addition to giving gray shades, the QBS structure increases the brightness and the viewing angle. This method of producing gray levels was developed by the Philips (Eindhoven) group, who called it the “texture method”.
internal surface), as well as the corresponding positions at the outer surfaces and in between, increase when 6 decreases. It would therefore take a longer time to reach and pass the middle transitory state, after which the molecules would latch in their new position. In addition, it is seen that the local deformation of the cone i.e., a decrease of the tilt angle 6,which is necessary to actuate the transition from n , to n2, increases when Gdecreases. (A paradox feature of this deformation model is that it works as long as 6+0, whereas 6=0 gives no deformation at all -but also no chevron - at the chevron kink level.) . The smectic layer organization corresponding to curves I1 and I11 of Fig. 98 is generally characterized as a quasi-bookshelf (QBS) structure, denoting that the layers are essentially upright with only a small chevron angle. The QBS structure has a very large gray scale capacity. This might, however, possibly not be utilized to advantage in a passively driven display (as it can in the AFLC version). Its drawback in this
2.8 FLC Device Structures and Local-Layer Geometry
respect is that the shape of the threshold curve is temperature-dependent, which leads to the requirement of a very well-controlled and constant temperature over the whole area of a large display. Furthermore, the QBS structure is a metastable state. Finally, the microdomain control of gray shades requires an additional sophistication in the electronic addressing: in order to achieve the same transmission level for a given applied amplitude, the inherent memory in the microdomains has to be deleted, which is done by a special blanking pulse. Using this pulse, the display is reset to the same starting condition before the writing pulse arrives. As a result of these features, it is not clear whether the microdomain method will be successfully applied in future FLC displays. A combination FLCTFT might be required; if so it will be quite powerful.
2.8.5 Thin Walls and Thick Walls The micrographs of Fig. 93 indicate that the thin wall normally runs with a certain angle y to the smectic layer normal. What determines this angle 3: what determines the thickness of the wall, and what is the actual structure of it? To answer these questions w e have to develop the reasoning started for Figs. 94 and 95. This is done in Fig. 99 where we look at the layer kink (the lozengeshaped part in Fig. 95) from above. By only applying the condition of layer continuity, the following geometric relations are easily obtained, which describe the essential features of thin walls. Starting with Fig. 99a and remembering that the layer periodicity along the glass surface is dA, we obtain a relation between yand the layer kink angle p with the chevron angle 6 as a parameter. With dcld, = cos 6, this is writ-
639
ten (404) For small angles we can solve either for j3
or for y
This relation shows that y increases monotonously with p. Thus the larger the smectic layer kink, the more the wall will run obliquely to the layer normal. The fact that there is a physical upper limit for p (see below) explains why we never observe zigzag walls with a large inclination, y For ease in computation, when we make estimations Eq. (406) can more conveniently be written (407) Next we get the obvious relations between the width w of the wall and the width b of the lozenge or the length c of the cross section of the wall cut along the layer normal w = bcos(p- y) = csiny
(408)
as well as the width b of the lozenge from
c tan y = b cos6
(409)
But this width b is also related to the kink angle and the sample thickness L (see Fig. 99c, d and Fig. 94e). b sinp = Ltan6
(410)
We may now use Eqs. (408), (410), and (404) to obtain the relation between the wall thickness and the sample thickness
w = L cosy sin 6 sin P
640
2
Ferroelectric Liquid Crystals
y7:
L Y
Y (d)
(C)
Finally, we can express the angle o between the adjacent surfaces M and N in Fig. 40c by taking the scalar product of the corresponding layer normals u and v [marked in (a) and (d)]. This gives COSO
= cosp C OS S
(412)
Let us now extract the physical consequences contained in all these relations and start with the last one. As numerical examples we will use the data from Rieker and Clark [168] on the mixture W7-W82, for which the tilt angle 8 saturates at about 2 1O at low temperature, and the corresponding saturation value for the chevron angle Shas been measured as 18". To begin with we see that Eq. (412) sets an upper limit to the layer kink p, because of the requirement of uniqueness of the director n at each chevron interface. Figure 96a illustrates the fact
=
Figure 99. (a) Chevron structure like the one in Fig. 36, as seen from above. A thin wall of width w joins the region with a chevron bend in the negative z direction (left part of the figure) with another having the chevron bend in the positive z direction (right part of the figure). (b) Section through the wall cut along the z direction, (c) projection along the z direction, and (d) a cut parallel to the xz plane.
that where the two inclined layers meet they can share the director only to a maximum layer inclination of up to twice the tilt angle 8. At this point the two cones touch, and beyond it no uniqueness in the director field can be maintained. Thus o i n Eq. (412) has a maximum value equal to 2 6, which gives a maximum value, in practice only somewhat lower than 2 8, for the allowable layer kink p. This, .in turn, gives a limiting value for y. With the data for W7-W82 we get o=42", which gives (Eq. 412), p=39" and (Eq. 407) y= 15". The width of the wall in this case [Eq. (41 1)] is found to be roughly 0.5 L, i.e., half the sample thickness. This is thus the limiting case for an inclined zigzag in this material. Let us now assume that we observe another wall running at a 5" inclination to the layer normal. In this case Eq. (405) gives p=24" and Eq. (41 1) gives
2.8
FLC Device Structures and Local-Layer Geometry
15'1,'
J
r
i
I w = Wmax = L
w = 0.8 L. Finally, let us check a wall running exactly perpendicular to the layers (y= 0). In this case Eq. (404) shows /?to be equal to 6, hence p= 18", and w = L according to Eq. (411). This is the other limiting case with a wall of maximum width. Summarizing (see Fig. 100) we may say that a thin wall has its maximum width (equal to the sample thickness) when running perpendicular to the layers. The layer kink then has its minimum value, equal to 6, i.e., -- 8.Inclined walls are thinner, represent a higher energy density, and cease to exist when the layer kink approaches = 2 8,which sets the maximum value of obliqueness to about 15-20'.
Figure 101. Thin wall curving until it finally runs parallel to the smectic layers, then being a broad wall. The character changes from <<<>>> to >>><<< as soon as the wall reverses the inclination angle with the angle counted as positive if it is in the same direction as the layer kink fl; otherwise it is negative. That the sign of y relative to the layer normal is irrelevant for the character can be seen if we mirror the picture along a vertical line: the mirror image must have the same character in every part of the wall.
w = wmjn= 0.5L
64 1
Figure 100. Thin walls with limiting cases, y= 0 and y= ymax(in this case about 15 "). The width may vary by a factor of two, being of the order of the sample thickness L. The layer kink angle is at least equal to the chevron angle and at most slightly more than twice that value.
Let us now imagine that the thin wall of Fig. 99, if we follow it downwards in the positive z direction, will curve so that y changes sign, eventually to form a closed loop. Any cut along z will have the structure <<<>>> as long as y>O, whereas this configuration changes to >>><<< as soon as y< 0. This is illustrated in Fig. 101, where y finally approaches -90', which means that the wall runs parallel to the smectic layers. The thin wall has now turned to a thick wall, which thus mediates the transition >>><<<. With the nomenclature used so far, we can say that, while a thin wall in its course may change between <<<>>> and >>><<<, a thick wall can only have the structure >>> <<<. Figure 102 explains why. In (a) we have assumed, for the sake of argument, the opposite configuration. The translation period at the boundary is dA as before, and below it the layer can tilt in any direction to preserve this horizontal period while shrinking to layer thickness dc. However, when we reach the lozenge, layer continuity would demand the layers to expand not only to d>dc, but even to d>dA. This means that this whole area would stand under great tension. Note that this is entirely different from the seemingly similar configuration in Fig. 99 b. In that case the layers run obliquely to the cut, and hence the periodicity in this cut does not at all correspond to the layer thickness. In contrast, the layers in Fig. 102 run along the wall, and thus perpendicular to the cut. If we assume the >>><<< struc-
642
2
Ferroelectric Liquid Crystals
w
T
i Figure 102. A thick wall in its relaxed state has a width W much larger than the sample thickness L. It can only have the structure >>><<< as shown in (b), not the one in (a). While the chevron angle Gchanges with the smectic C layer thickness, the surface is assumed to maintain the pitch of the layers at the smectic A value, independent of the temperature.
ture, on the other hand, as in (b) we see that the thick wall can relax to an equilibrium configuration preserving the layer thickness everywhere. It is easy to see that this gives the equilibrium width W for the thick wall according to L = tan 6 W 2
-
(41 3)
or, for small values of 6
W = -2L
6
(414)
In a material with 6= 18" this would give an equilibrium thickness of 25 pm for a broad wall in a 4 pm thick sample. Thus a broad wall is much thicker than L, whereas a narrow wall is thinner than L. This certainly conforms very well with observation. Naturally, walls will also be observed that are not in equilibrium. If a thick wall is thicker than the equilibrium value, the smectic layers in the lozenge will be under tension, corresponding to a tilt 8 < Oeq. If it
is thinner, the layers will be under compression, corresponding to 8 > Oeq, and thus with a tilt that is larger than the equilibrium tilt angle. Because the layers are upright in the middle of a broad wall, the optical contrast between the two states is particularly high, and may be further enhanced if the width is smaller than the equilibrium value W corresponding to Eq. (413). As is evident from Fig. 102b, a broad wall is thicker the smaller the chevron angle 6. This is also most clearly expressed by Eq. (414). In contrast, the width of a thin wall is not very much affected by 6. However, it is useful to take a closer look at its behavior with varying '/. For this, let us go back to Fig. 101. We have already seen that the character of the wall changes from <<<>>> to >>><<<when ychanges from >O to O) as the wall curves in the other direction, until the layers are perfectly flat when the wall runs
a
2.8 FLC Device Structures and Local-Layer Geometry
parallel to the layers (y=-90”). It has been customary to denote a wall in this limiting state a “thick wall”, with the consequence that other walls, called “thin”, can sometimes have the configuration <<<>>> and sometimes >>><<< in the cross section along the layer normal on either side of the wall. However, it would make much more sense to use the fact that the character of the wall changes when ychanges sign. Thus we propose the designation “thin” for y> 0 and “thick” for y< 0. This means that, unambiguously, a thin wall has a <<<>>> configuration only, and hence that any wall of configuration >>><<< should be called a thick wall. As a consequence, w = L becomes the natural demarcation line between thick and thin walls: any wall with configuration <<<>>> has w>><<< has w > L. The proposed criterion should not, and does not, depend on the chevron angle 6, and thus not on temperature. For example, in the same material W7-W82 at a higher temperature, such that 6=5”, w still has the maximum width equal to L when y= 0 and attains its minimum width =L/2 when y=4” (ym,,). For y=-5” and -30”, w = 2.5 L and w = 12 L, respectively. This discussion may be briefly summarized by Figs. 103 and 104. In the first we have indicated a wall in the form of a closed loop, with the corresponding layer kinks and
643
the chevron configuration. In particular, we have marked out that the inclination of the wall relative to the layer normal does not determine the sign of y The thin walls ultimately merging into a fine tip thus have the same character. Figure 99 gives an idea of what happens at the tip: when the walls
Y> 0
Figure 103. Inside a closed loop the chevron has a unique direction: (a) downwards or, (b) seen from below, towards the reader. As the lozenges connect two opposite tips in the chevron folds (h), we likewise have a uniquely determined kink direction in the wall. It is relative to this direction that we decide whether y should be counted as positive (same sense) or negative (opposite sense). Thus note that y> 0 for both thin walls, even if they have geometrically opposite inclinations.
Figure 104. Zigzag wall making a closed loop. The smectic layers are assumed to be vertical in the picture. The chevron fold is always away from the zigzag inside and towards the thick wall. When the wall curves, the chevron character changes from <<<>>> for a thin wall ( w < L ) to >>><<< for a thick wall (w>L). The wall attains its maximum thickness (relaxed state) when it runs parallel to the layers.
644
2 Ferroelectric Liquid Crystals
merge, the kink becomes twice as large (2 p), which requires p to be less then 8. For 8 = 21”, this gives a maximum value for yof only 3” at the very tip. In fact, this narrowing of the tip angle can often be observed (see Fig. 93). In Fig. 104 finally, we have indicated how the character of the wall changes around a closed loop with zigzags when the wall curves in different directions. As for the chevron fold, inside the loop it can only be directed away from the zigzag and towards the thick wall.
2.8.6
C1 and C2 Chevrons
The presence of chevrons has numerous consequences for optics and electrooptics, above all for the transmission, contrast, bistability, and switching behavior. Some of these have already been hinted at earlier. The effects will be particularly drastic if we combine chevrons with polar boundary conditions that are very common, as most aligning materials favor one or the other direction f o r P (most often into and less frequently out of the liquid crystal). In contrast, the chevron interface represents a nonpolar boundary, by symmetry favoring neither the up nor the down state (see Fig. 96). These states are distinct and switchable as long as the chevron angle 6 i s less than the tilt angle 8 of the director. If the limiting case (6=6) is reached, the two states merge into one and the chevron no longer contributes to the bistability. In Fig. 103 we have indicated the P field distribution (one of many possible states) around two adjacent thin walls. The field is predominantly up in one of them and predominantly down in the other. Therefore alternate walls often serve as nucleation centers for domain switching taking place in the chevron plane, i.e., for the motion of walls between up and down domains. Such
domains often appear as boat-shaped “holes” of up state on a background of down state, or vice versa (see Fig. 105). On the other hand, the zigzags themselves do not normally move in an electric field, but are quite stationary. This is because zigzags normally separate regions with the same average P direction (up or down, as illustrated in Fig. 103b). Also, the optical state (transmission, color) is very often practically the same on both sides of a zigzag wall, as in Fig. 93b. Indeed, if the director lies parallel to the surface (pretilt a=O) at the outer boundaries, the chevron looks exactly the same whether the layers fold to the right or to the left. However, if the boundary condition demands a certain pretilt a#O, as in Fig. 105, the two chevron structures are no longer identical. The director distribution across the cell now depends on whether the director at the boundary tilts in the same direction relative to the surface as does the cone axis, or whether the tilt is in the opposite direction. In the first case we say that the chevron has a C 1 structure, in the second a C2 structure (see also Fig. 106). We may say that the C 1 structure is “natural” in the sense that if the rubbing direction (r)is the same at both surfaces, so that the pretilt a is symmetrically inwards, the smectic layer has a natural tendency (already in the SmA phase) to fold accordingly. However, if less evident at first sight, the C2 structure is certainly possible, as demonstrated in Figs. 105 and 106. The very important discovery of the two chevron structures and the subsequent analysis of them and their different substructures was made by the Canon team [170]. The presence of C1 and C2 as distinct structures has obvious consequences. Any wall now becomes a complete configuration consisting of one C1 and one C2 part. Its contrast changes with its running direction. A broad relaxed wall may be thick enough that its C 1
2.8
c1
FLC Device Structures and Local-Layer Geometry
645
c2
Figure 105. A zigzag street (lightning) running between two regions of opposite chevron fold for the case of nonzero pretilt 01. This gives a different structure to the left (C1) and to the right (C2). The two regions then have different properties, like transmission, color contrast, switchability, etc., which get more pronounced the higher a is. Only when a=O are the C1 and C2 structures the same thing. For a#O the director positions are different for C1 and C2, except in the chevron plane where n has to be horizontal. For the purpose of illustrating different possibilities, we have made a very small in the C1 case, whereas we have drawn the C2 case for medium a towards the upper, with high a towards the lower substrate. Thus the boundary conditions to the right and left to not correspond to the same surface treatment.
c 1 c2
DOWN
UP
c2
UP
UP
c1
UP
DOWN
Figure 106. Closed zigzag loop with thin and thick walls and a smaller loop inside. Inside any loop the chevron always points towards the broad wall. With a polymer coating on the inner side of the glass plates the rubbing direction is indicated by the unit vector r, giving the pretilt a to the inside. In the lower part of the figure, the C1 structure to the left and the C2 structure to the right of the thin wall are compared with their director and polarization fields in the case of switchable surfaces for C 1 and nonswitchable surfaces for C2. The figure is drawn for a material with P
646
2
Ferroelectric Liquid Crystals
and C2 parts, and even the small, almost pure bookshelf section in between, can be distinguished by different optical contrast. The regions representing opposite fold direction, separated by a wall, acquire different colors even if the chevron plane is in the middle, and so on. However, the optical differences are small for small pretilts of a. If we take a nonzero pretilt into consideration, leading to C 1 and C2 structures, thin and thick walls look as illustrated in Fig. 106. In the lower part of that figure we have also illustrated the quite important difference in the polarization and director fields across a C1 and across a C2 structure. It is hard to draw these figures to scale and yet demonstrate the characteristic features. In Fig. 106 the situation may roughly correspond to 8=30", 6=20", and a= lo", such that a + 6- 8. We may note that the C2 structure is none other than the chevroned version of the surface-stabilized configuration already discussed for Fig. 90. The same C2 configuration n - P would be found for any case with a + 6= 8, for instance, with a = 3", 6= 15", and 8 = 18", as long as 6< 8. We mentioned that V -P=O at the chevron interface, which means that even if P changes direction abruptly, P, (as well as any other component) is continuous across that surface (Fig. 96). As the boundary conditions at the substrates do not normally correspond to the director condition at the chevron, &',lax is nonzero between the chevron and the substrates, but is small enough to be ignored. That this is not true when we have polar boundary conditions, is shown in Fig. 107. Let us, for instance, assume that the polarization P prefers to be directed from the boundary into the liquid crystal. Whether we have a chevron or not, we will have a splay state P ( x ) corresponding to a splay-twist state in the director. With a chevron the splay is taking place in the upper or lower half of the cell when this is in its
Y
x
\
-
>
J
-
2 2
c
c
2
-
c
c
\
\
UP
DOWN
Figure 107. Polarization switching taking place in the chevron plane at fixed polar boundary conditions. In this case the condition is one of high pretilt a for n with the P vector pointing into the liquid crystal from the boundary.
up or down state, respectively. These halfsplayed states, which are most often just called twist states, occur in both C1 and C2 structures and are then abbreviated C 1T and C2T, in contrast to the uniform states C l U and C2U. The twist states are normally bluish and cannot be brought to extinction, hence they give very low contrast in the two switchable states. Moreover, due to the different sign of V . P , there will be an unsymmetric charge distribution between adjacent areas switched to the up and the down state, tending to burn in any already written static picture. For high P , materials, even the electrostatic energy has to be taken into account which, together with the elastic energy, may tend to shift the chevron plane to an unsymmetric state as illustrated to the right of Fig. 107, in order to relieve the high local energy density. Such a state is then completely unswitchable (monostable). It is evident that, whether we choose C1 or C2, a twisted state has to be avoided. In their first analysis of C1 and C2 structures, Kanbe et al. [ 1701 put forward the essential criteria for their stability. Both are allowed at low pretilt a. Whereas C1 can exist at high pretilts, the cone condition ( n must be on the cone) cannot be fulfilled for C2 if a i s larger than (6-S), as illustrated in
2.8
FLC Device Structures and Local-Layer Geometry
647
Figure 108. Stability conditions for chevrons of C 1 and C2 type (after [170])
Fig. 108. This means that for a#O it cannot be fulfilled at the phase transition point S m A j S m C when 8 and 6 are both zero. Hence the chevron that is first created when the sample is cooled down to the SmC phase is always C1. However, C1 is not stable when the tilt angle 8 increases. Therefore C2 appears together with C1 at lower temperatures and the sample is marred by zigzag defects. One of the reasons for this is that C 1 has a higher splay - twist elastic deformation energy, which increases with increasing 8. Another reason is that the director is more parallel to the rubbing direction in the C2 case; it has to split more to fulfill the cone condiditon for C1. This effect will favor C2 under strong anchoring conditions. Finally, as pointed out in the cited Canon paper [170], while a gradual transition C 1 - + C2 to an almost chevron-free state might be observed on cooling, the once such-created C2 state tends to be quite stable if the temperature is subsequently raised; it is almost necessary to go back to the SmA* phase in order to recreate C 1. Thus C2 is stable over a much broader range of temperature than C1. All this speaks for the C2 state, in spite of the considerably lower effective switching angle between its memorized states. Several FLC projects have also been based on C2 (JOERUAlvey, Thorn/CRL, Sharp). The fact that bistable switching only takes place through being latched by the chevron surface is compensated for by a number of advantages. First of all, the surface alignment is relatively simple, as the outer surfaces do not switch but only work togeth-
er with the chevron. It is also much simpler to avoid twist states for C2 than for C1. This is easily seen from Fig. 106. Here the structure has been sketched for a=(6-8) such that the director is exactly along the rubbing direction and strongly anchored. As already pointed out, the nonchevron version of this is shown in Fig. 90. In practice it is found [ 1711 that a medium pretilt a of about 5" is convenient for achieving this cone surface condition, whereas a values near zero give both C2U and C2T. For several materials, (8-6) is of the order of about 5"; however, observations have been made [ 1721of chevron-free C2U structures for a= 5", although (8-6) seems to be only about 1.5", thus violating the stability condition for C2. Whether this is due to a change of 6 under driving conditions (6 decreasing towards QBS case), is unclear. A further advantage with the C2 structure is that zigzags induced by (light) mechanical shock, which causes a local transition to C1, easily heal out by themselves in the C2 structure [170], whereas the opposite is not true. Fortunately, C2 also has a substantially higher threshold to so-called boat- wake defects, which appear on the application of a very high voltage. The main disadvantages with the C2 structure are obviously the low optical contrast in the true memorized state and the quite high voltages applied so far in the electronic addressing of the cell, when the socalled z - V ~addressing ~ ~ modes are used. This is also combined with a high power consumption. Thus the switching pulse is
648
2
010
~
Ferroelectric Liquid Crystals
-
1
5 10 15 AC voltage vd [v]
Figure 109. Effective switching angle in a C2 structure as a function of the amplitude V, of the applied data pulses for the so-called Malvern-3 scheme. The switching pulse amplitude is 30 V. V,= 0 corresponds to the memorized states as latched by the chevron Interface. The P, value of the material is 4.4 nC/cm2 (after 171).
used to accomplish latching in the chevron plane, whereas the bipolar AC data pulses are used to force the director as much as possible into the in-plane condition between the chevron surface and the outer surfaces (see the lower part of the right of Fig. 106). In this way the effective switching angle can be increased from a typical value of 14", corresponding to the memorized state, to the more significant value of 24" (Fig. 109), when data pulses of 10 V amplitude are applied [171]. This higher switching angle thus corresponds to what we might call "forced memorized states".
2.8.7 The FLC Technology Developed by Canon As indicated above, the first Canon prototype from 1988 had a=O giving a hemispherical viewing angle, which was a complete novelty at that time. However, the contrast (- 7:l) was only good enough for a monochrome display. Moreover, the C 1 structure could not be made sufficiently stable at low temperatures. To solve this problem the team decided not to abandon C1
in favor of C2, but instead to pursue the much more difficult road to go to a very high pretilt. The idea was to squeeze out C2 completely from the material because its cone condition a c ( 8 - 6 )can no longer be satisfied. Thus, by going to the rather extreme pretilt of 18" (a technological achievement in itself), Canon was able to produce zigzag-free structures, as the layers can only be folded to C1 chevrons. A considerable development of FLC materials also had to take place, among others, mixtures with (6-6) values between 3 and 5". In this way C2 could be successfully suppressed under static conditions, for instance, in a material with 8 = 15" and 6 = lo", which is not surprising, because a i s not only larger than (0-6) but is even larger than 8 alone. However, it turned out [173] that C2 would appear to some extent under dynamic, i.e., driving conditions. This obviously cannot be explained by assuming that 6 gets smaller under driving conditions. Thus, it seems that the stability criterion can hold at most under static conditions. This indicates that the underlying physics of the CUC2 structure problem is extremely complex. In order to avoid C2 at any temperature, several parameters had to be optimized, such that both 0 and Sshowed only a small variation as functions of temperature. The obvious advantage of working with C 1 is that the switching angle is high, at least potentially, between the memorized states. This is particularly true if the cell switches not only at the chevron surface, but also at both outer boundaries. However, surface switching does not normally occur at polymer surfaces with a low pretilt (although it does at SiO-coated surfaces). This is another advantage of going to high pretilt. The situation may be illustrated as in Fig. 110. At high pretilt the surface state not only switches, but the switching angle may be just as large as permitted by the cone angle of the
2.8
(a)
(b)
FLC Device Structures and Local-Layer Geometry
(C)
Figure 110. Switching angle under different conditions. (a) To the left QBS geometry is supposed. If the surface cannot be switched (for instance on polyimide), this will lead to a strongly twisted state. In the middle (b) a chevron geometry is assumed. If the surface is nonswitchable, it leads to a smaller twist than i n (a), if it is switchable, the switching angle is less than in a switchable version of (a). With high pretilt (c) a polymer surface normally switches and the switching angle may be optimized, similar to the situation in (a).
material used. This cone angle is limited by the possible appearance of C2 at low temperatures and also by the fact that the twisted state C1T would appear at higher 8. Thus 8 is limited, quite below the ideal performance value, in the C 1 state as well as in the C2 state. Whether the twisted state appears in the C1 case or not is, however, not so much determined by the tilt 6, but preeminently by the polar strength of the surface condition. It is therefore important to realize that this influence may be at least partly neutralized by a suitable cross-rubbing, i.e., obliquely to what is going to be the direction of the smectic layer normal. The idea is quite simple, but can give rise to a number of different interpretations, e.g., suppose that the lower surface demands the P vector to point into the liquid crystal. However, if n at this surface is tilted in a direction clockwise (seen from above) relative to the layer normal, then this n direction corresponds to the same direction of P (for P
649
tralized. Canon, in fact, uses this kind of cross-rubbing in order to increase the symmetric bistability and avoid the twisted state [ 173, 1751. The rubbing directions deviate f 10" from the layer normal, roughly corresponding to the switching angle. The basic geometry of rubbing, pretilt, etc., as applied to the actual Canon screen is illustrated in Fig. 11 1. While the contrast is far better in this version than in the 1988 version, the viewing angle - though still very good - has been compromised due to the fact that the local optic axis is pointing out of the flat surface by 18". The one hundred million chevrons across the screen all have the same direction, making a completely defect-free surface. Even so, Fig. 112 reminds us that on a local scale the order has to be disturbed everywhere where spacers are localized. As should be evident from this account, the development of FLC technology within the Canon group involved a lot of surprises. The group had to discover, and subsequently solve, a number of very complicated problems related to the polar nature of smectic C* materials. Among these problems were the appearance of ghost and shadow pictures (slow erasure of an already written image), and in addition to these was also the problem of mechanical fragility of the bookshelf or chevron layer configuration. The most complicated phenomenon, i.e., the strange electrodynamic flow (backflow net mass transport) that started to occur at high pretilt when electric fields were applied, could not even be superficially dealt with within the frame of this article. Already the materials problems were quite important. The hard to achieve high pretilt condition required several years of dedicated R&D in polymer materials. Finally, the group had to develop their own FLC materials and design manufacturing processes capable of handling large cells [48 in. (120 cm) diagonal]
650
2
Ferroelectric Liquid Crystals 0.a.
upper glasz plate
On
nk
5mectic 1 direction
Figure 111. Geometric features in the Canon screen of Fig. 87 showing rubbing directions, smectic layer direction, chevron direction, and director pretilt a,equal to the optic axis tilt out of the screen surface.
2.8.8 The Microdisplays of Displaytech Figure 112. Every spacer represents a distortion, which by necessity traps a thick wall. In this picture the chevron kink is to the left everywhere except in the local neighborhood of the spacer (after [176]).
at a cell gap of 1.1 pm. Considering all this, the development and manufacturing of the present FLCD is a real tour de force performed by Kanbe and his team.
This is an interesting contrasting case, not only because it is the question of an extremely small display with completely different application areas, but also because the small size permits a different approach in almost every respect. In this case, the FLC layer is placed on a reflective backplane, which is a CMOS VLSI chip providing k2.5 V across each picture element [ 1771.This is thus a case of active driving. Therefore the
2.8
FLC Device Structures and Local-Layer Geometry
question of the quality of the memorized states is unimportant, and we can safely use the C2 structure as the one with the simplest aligning technology avoiding any twisted state. (Displaytech uses rubbed nylon, which gives a low pretilt.) Because each pixel is fully driven and not multiplexed, we do not have the disadvantage of high voltage. We may recall the peculiarity of FLC switching in that the threshold is one of voltage - time area. Thus when the switching pulse time is replaced by the frame address time, which is now the relevant time for the applied voltage, the threshold in voltage becomes correspondingly low and well within the CMOS range. This is of course characteristic for all direct or “active” FLC driving. Furthermore, because each pixel is in its fully driven state, we have in-plane switching with its characteristic large viewing angle. A transistor can in principle be used for implementing microdomain grey levels by charge control (a method pioneered by the Philips Eindhoven group), but in the Displaytech case it is only used to write one of two states. The gray levels are instead produced by time modulation, which is quite natural for direct drive. Video color pictures are produced at a frame rate of 76 Hz. Each frame is, however, subdivided into three pictures, one for each color, so that the actual frame rate is 228 Hz, under the sequential illumination from red, green, and blue LEDs. (The LEDs are GaN for blue and green, and AlInGaP for red.) During each of the 4.38 ms long color sequences (corresponding to 228 Hz), a gray level is now defined for every pixel by rapidly repeating the scanning of the FLC matrix a number of times, with a pixel being on or off for the fraction of time corresponding to the desired level. For instance, if the VLSI matrix is scanned 25= 32 times during illumination of one color, then five bits of gray per color are
65 1
achieved. This requires a scanning time (basic frame rate) of little less than 150 ps for a matrix consisting of 1000 lines. Displaytech has presented several versions of this miniature screen, for instance, one 7.7 by 7.7 mm with 256 x 256 picture elements and an aperture ratio of 90%, and some with higher resolution of up to 1280x 1024. In the latter case the dimensions are 9.7 by 7.8 mm with individual pixel size of 7.5 x 7.5 pm. The display is viewed through a magnifying glass and may be headmounted. Obvious applications are virtual reality, high resolution viewers, but also projection displays which are good candidates for high definition television (HDTV) using FLC. The first version of this “Chronocolor” display had two bits per color giving 64 colors per pixel; the second has three bits giving 5 12 colors. The version now under development will give six bits per color corresponding to (26)3= 262 144 colors per pixel, i.e., essentially full color. The first version is the one illustrated in Fig. 88.
2.8.9 Idemitsu’s Polymer FLC In 1985, around the same time as Canon started their FLC development project, another Japanese company, Idemitsu Kosan, started to synthesize materials with the goal of making a polymer version of FLC. There is a conflict in a liquid crystal polymer in the sense that a long polymer chain wants to be as disordered as possible, while the liquid crystal monomers want to align parallel to a local director. Nevertheless, it is possible to make both nematic and smectic structures and, in particular, chiral materials having an SmA* - SmC* transition. In one of Idemitsu’s successful realizations, the main chain is a siloxane to which side group monomers (which would be normal FLC materials by themselves) are attached
652
2
Ferroelectric Liquid Crystals
via spacing groups. Whereas a nematic polymer reacts too slowly to electric fields to be of any electrooptic interest, the internal cone motion can be activated in the polymer SmC* phase, with its characteristic low viscosity y, giving a (relatively speaking) very fast switching. At high temperatures the switching time can go below a millisecond, i.e., the FLC polymer (FLCP) can be faster than a typical monomer nematic; however, the viscosity increases much more rapidly at low temperatures than in a nematic. The FLCPs have many similarities to the monomer materials. By measuring the polarization reversal current [ 1771 Idemitsu found that the P , value is about the same (typically a little larger) as in the corresponding monomer. As the layer spacing decreases with decreasing tilt angle in the SmC* phase, this also results in chevron structures. In thick samples the smectic helix is present. In thin QBS cells FLCPs show good bistability, and so on. The switching mechanism is in principle a little more complicated in the aspect that the main chain to some extent takes part in the switching. A simplifying aspect is that the polymerization may stabilize the SmC* phase, which may then have a very broad temperature interval (something that in the monomer case has to be made by a multicomponent mixture). The polymer state also seems to stabilize a major chevron direction such that zigzag defects are not so important. Nor has a QBS cell in the polymer version the mechanical fragility that is so characteristic of monomer FLCs. On the other hand, the differences are highly interesting. An FLCP display is flexible, light-weight, and only 0.5 mm thick. It is made by spreading the polymer onto an ITO-coated plastic substrate, which is then laminated in a continuous process to a second substrate (see Fig. 113) using rollers, one of which in its bending action shear-
-
polarizingfilm (180pm)
IT0 (0.05 pm)
Figure 113. (a) Cross-sectional view of the all-plastic 0.5 mm thick Idemitsu FLCP display showing the SmC* polymer (black) between the substrates. (b) This shows how in its preparation the display is first laminated and then shear-aligned (after [ 1781).
Figure 114. The FLCP display can be bent and shaped to a different curvature. The bottom picture also demonstrates the transmissive mode. (Courtesy of Idemitsu Kosan Co., Ltd.).
2.8
FLC Device Structures and Local-Layer Geometry
653
Figure 115. Two examples of simple color FLCP panels. The sizes are 20 cmx32 cm and 12 cmx60 cm, respectively. The color is produced by vertical color stripes giving eight colors per pixel. These 0.5 mm thin displays are mechanically durable and work at very low power thanks to the inherent memory. The picture can be changed twice a second. (Courtesy of Idemitsu Kosan Co., Ltd.).
aligns the smectic. The display thus needs neither spacers nor alignment layers, and can be made very large, in principle “by the meter”. Its flexibility is demonstrated in Fig. 114. Evident future applications for such panels that can be bent and are extremely lightweight are, for instance, in electrically controllable motorcycle or welding goggles. However, as already demonstrated in Fig. 89, a switching time of 1 ms at room temperature is also sufficient for fairly sophisticated static displays. Although the switching is between a hundred and a thousand times slower than in a monomer FLC, 1 ms is sufficient to give this display an update rate of 2 Hz. Two examples of simple large size color panels are given in Fig. 115.
2.8.10 Material Problems in FLC Technology FLC materials are complex and we are just at the beginning of exploring their physics and chemistry. As we have mentioned, they have nine independent elastic and 20 viscous coefficients, to which we may add that
there are 15 different independent sources of local polarization (10 if we assume incompressible layers). One of them is related to chirality, whereas all the others are flexoelectric coefficients (thus equally relevant to the nonchiral SmC phase) describing local polarization resulting from the different deformations in the director field. With a local polarization vector and with complicated smectic layer structures, it is evident that we will also have an extremely complicated hydrodynamic coupling to an external electric field E. These hints may suffice to indicate the completely new level of complexity in these materials. However, already the fact that they are not threedimensional liquids like nematics, but rather two-dimensional liquids with solid-like properties along one space dimension, makes them extremely fragile in their useful geometry - a pressure by the thumb is in practice sufficient to irreversible destroy the ordered bookshelf structure. On the other hand, the wealth of physical phenomena and the richness of potential effects to be exploited in future in these materials should be recognized.
654
2
Ferroelectric Liquid Crystals
the smectic layer thickness as a function of temperature. And here is the challenge: to synthesize and mix materials to form a smectic C that keeps its layer thickness constant in spite of an increasing tilt angle 8below the SmA-SmC transition. This would revolutionize the further development of FLC technology by avoiding all complica-
The molecular engineering of chiral tilted smectics is correspondingly complicated with a large number of parameters to optimize. In Table 1 we have listed the most important (so far recognized), in comparison with the standard nematic parameters. Beside phase sequence and sufficiently large phase range (not minor problems), we have to be able to control all the parameters with which we have already made acquaintance. The elastic constants can be taken as an example illustrating the relative progress on the way to full control of the materials in the nematic and in the smectic case. Whereas in nematics we can balance and adjust the three Kij values to suit any particular application, the relevant elastic constants have hardly been identified yet in smectics, and even less measured -there have been much more serious problems to take care of first, for instance, the matching temperature behavior of 8 and 6 (layer tilt) mentioned earlier in the description of the Canon C l technology. The most serious problem was initially recognized alongside the growing understanding of the relation between zigzag defects and chevrons and is connected with the parameter d(T) listed earlier, i.e.,
0
0 T << TAC
> TAC
Figure 116. Two possible mechanisms for having a tilted smectic phase with a temperature-independent smectic layer thickness below the SmA- SmC transition. In (a) the end chains are first disordered but get more straight as the temperature is lowered; in (b) each individual molecule keeps its tilt constant relative to the layer normal, but the azimuthal direction of the tilt is unbiased in the SmA phase. At the SmA- SmC transition the average direction of the molecules begins to get biased.
Table 1. Parameters for nematics and smectics C*. Material requirements Phase range
Preferred phase sequence Birefringence Dielectric anisotropy Dielectric biaxiality Twist viscosity Elastic constants Tilt angle Spontaneous polarization Smectic C* pitch Cholesteric pitch Smectic layer thickness
Nematics (Cr) -N
- (I)
An
A&
Smectics C* (Cr)- SmC - (SmA) (SmC) - SmA-(N) (SmA) - N - (I) N- SmA- SmC An A&
a&
Yl Kij
P Z @)
P d(T)
2.8 FLC Device Structures and Local-Layer Geometry
tions with chevrons and finally achieving the initially conceived structure of Fig. 61, with superior brightness, contrast, and viewing angle. That such materials could even be imaginated to exist is illustrated in Fig. 116. In this very simplistic picture (which may or may not be realistic), let us assume that (a), as the central aromatic part (essentially representing the optic axis of the molecule, and therefore 6)tilts more and more away from the layer normal on lowering the temperature, the aliphatic end chains get less disordered and stiffen, making them effectively longer. Various degrees of interdigitation (decreasing with higher tilt) of molecules in the layer could also be imagined for materials in which the layer corresponds to more than the length of one
molecule. A different mechanism (b) goes back to early ideas of the late crystallographer de Vries at Kent State University, who proposed that the molecules could already be tilted in the smectic A phase, but in an unbiased rotation making the phase uniaxial [191a]. At the SmA-SmC transition, a rotational bias appears, growing stronger on lowering the temperature, which is equivalent to a tilt of the optic axis. This tilt would then appear without being accompanied by a decrease of the layer thickness. Today we know that the majority of liquid crystals undergoing an SmA - SmC transition do not behave according to the de Vries model. This would seem to require a very low degree of interaction between the constituents from layer to layer, or even within layers, i.e., a high degree of randomness, yet connected with smectic order.
655
However, now and then, evidence has been reported indicating that some materials may behave like this. They would not only be of eminent interest for FLC applications, but just as much for use as electroclinic materials.
2.8.11 Nonchevron Structures At the Japan Display 1989 Conference in Kyoto, two contributions independently reported on new materials which seemed to almost automatically give a defect-free alignment, avoiding the zigzag defect. The first one, a collaboration between Fujitsu Laboratories, Mitsui Toatsu Chemicals, and Tokyo Institute of Technology [179] presented mixtures based of the naphthalene structure
with n=9 and 10 and m = 2 - 6 . The second contribution [ 1801 was from the central research laboratories of the company 3M in St. Paul, Minnesota, U. S. A., and showed the result of fluorination on a number of more conventional liquid crystal structures. The naphthalene compounds have since been used in research as well as in some Fujitsu FLC display prototypes. They are highly interesting, but suffer from a rather high viscosity. In the 3M research the starting point was 4’-alkyloxyphenyl4-alkyloxybenzoates
i
or corresponding thiocompounds L
a
o
656
2
Ferroelectric Liquid Crystals
which were partially fluorinated to structures like
This partial fluorination has a number of interesting and even surprising effects [lsl]. First, it almost always totally suppresses the nematic phase and strongly enhances the smectic phases, in general both smectic A and smectic C. Moreover, it lowers the birefringence of the liquid crystal: An may go from typically 0.20 to 0.07 or 0.10. It also makes the smectic C* phase less hardtwisted: the helical pitch may increase from about 2 pm to 5 - 10 pm. Another important effect is that it makes the smectic C phase occur at a shorter chain length than in the unfluorinated analogs. This means that fluorinated SmC* is faster used as FLC material; it has remarkably low viscosity. But first and foremost: these materials do not make chevrons. This means that the smectic C layer thickness must be essentially temperature-independent. Partial fluorination leads to large terminal dipole effects. The fluorocarbon tail is also stiffer than the hydrocarbon tail. It is therefore relatively easy to understand the suppression of the nematic phase and strengthening of layered phases. However, it is less clear, as also in the naphthalene case, how to explain why the layer spacing should be temperature-independent. In both materials there seems to be a tendency for molecular interdigitation, and thus the smectic layer is thicker than the molecular
length. This may be important, but we still have no precise molecular interpretation of the resulting effect. The 3M synthetic research in SmC* materials began in 1983 and has been pursued with a high degree of purposefulness. (It is thus not true that only Japanese companies invest in long-term research goals.) A number of pure compounds have been developed that exhibit almost continuous layer expansion on lowering the temperature in the smectic C phase, as well as in the smectic A phase. By mixing with other compounds, a practically temperature-independent spacing can be achieved. In addition to phenyl benzoate cores, 3M has largely used phenylpyrimidine cores, of which a general structure can be exemplified as [ 1821
As an example of how different materials behave, we compare their smectic layer spacing as a function of temperature in Fig. 117. For the Chisso-1013 mixture the
36
3
3M-A
34-
.* 2
32-
8
3
300
28
Chisso CS-1013
26( 0
I
,
20
I
I
40
60
80
,
,
100
,
0
TK l
Figure 117. Smectic layer spacing for a number of different FLC materials as a function of temperature. The SmA-SmC transition is indicated by a vertical bar. ChissoCS-1013 is amixture showingconventiona1 behavior, FA-006 is a Fujitsu naphthalene-based mixture, 3M-C is the pure pyrimidine compound with formula, whereas 3M-A is a mixture (after [183]).
2.8 FLC Device Structures and Local-Layer Geometry
decrease in the layer thickness is pronounced as soon as we enter the smectic C phase. The naphthalene mixture FA-006 has a behavior that is qualitatively similar, though much less dramatic. The fluorinated compound 3M-C, of formula
shows the opposite behavior, with a small, but characteristic negative layer expansion coefficient, and the mixture 3M-A is qualitatively the same with a weaker temperature dependence. Although the 3M materials lack a nematic phase and thus have the phase sequence I - SmA - SmC, they align fairly well on nylon 6/6 to a bookshelf structure with a small pretilt at the surface. They switch symmetrically according to Fig. 51 and it has been confirmed that the switching angle corresponds to the full cone angle. In principle, therefore, with a 8 optimized to about 22" they should have memorized states corresponding to the ideal switching angle of 45" (in comparison see Fig. 109, illustrating the "forced" C2 switching states). Although it must be a particularly hard task to develop such materials with all other parameters optimized, it seems that they are now very close to being used in FLC panels. Figure 118 shows a Canon prototype (not yet commercialized) which evidently is the first attempt to put chevron-free materials into a display. The lower birefringence of these materials has permitted the enlargement of the cell gap from 1.1 pm to 2.0 pm, which is an important advantage in manufacturing. The display has an XGA resolution (1024x768) where every pixel is 300 pm x 300 pm and consists of three RGB stripes, each of which is subdivided into four dots. This gives 16 different states per color and 4096 different color shades per pixel. This
657
"digital full color" display is interesting because it demonstrates that a binary technology (based on just two states, i.e., without any gray shade whatsoever) is capable of quite satisfactory rendition of full color pictures. It is only a question of resolution, as in newspapers and magazines. The materials development is far from finished in the case of chiral smectic materials. The observation of highest importance for smectic C materials now relates to the property of a negative layer expansion coefficient 6., In order to significantly increase the useful temperature range for high performance FLC displays, especially the lower end (for shipping by air a SmC* phase stable down to -40 "C is desirable) we have to increase the available pool of molecular structures with this property of negative yd. This is an important task for synthetic chemists. With the most critical problems now being understood or even solved, several groups are attacking the problem of sufficient depth in the rendition of gray levels. At least this could relatively soon be approached by going to a higher resolution, of which FLC is eminently capable. Another approach is active matrix driving, which uses charge control, and then can suppress the use of a high resolution color filter by use of color sequential backlighting. Other methods have been proposed which use amplitude control in the same kind of symmetric driving as known from antiferroelectric displays [ 1841, eventually in combination with color sequential backlighting of high P, QBS structures [ 1851. Finally, special addressing methods are being worked out using a number of different physical principles (for instance, resistance electrodes). Some of the most interesting of these are certainly of the kind represented by the so-called binary group addressing method [ 186, 1871, combining a time-dith-
658
2
Ferroelectric Liquid Crystals
Figure 118. Canon’s 1997 “digital full color” prototype is important in its demonstration that color pictures can be produced utilizing only two electrooptic states. The screen is here shown with two successive close-ups, the last of which with sufficient magnification to show the individual pixels. (Courtesy of B. Stebler.) The SSFLC structure in this panel is nonchevron and corresponds to Fig. 61.
ered gray scale with a substantial extension of the illumination period to nearly over the entire frame. Once the FLC devices are on the market, we may expect a diversity Of techniques and arapid development into different directions.
2.9 1s There a Future for Smectic Materials? The driving force for academic research is not only the generation of new knowledge, but also the development of industrial applications, even if these applications may lie far in the future. In liquid crystals it is evi-
2.9
dent that the industrial aspects are dominated by displays. The fact that displays are the most severe bottleneck in the present-day information technology motivates the enormous investments in this industry. The liquid crystal display market is today entirely dominated by nematic materials, mainly in form of twisted nematics for simple displays, supertwisted nematics, and, in particular, twisted nematics in combination with thin film transistor arrays for very sophisticated panels. During the last two decades, where practically everything has happened in the development of smectic display technologies, the nematic key technologies have constantly become better, and huge industrial investments have now been made which lock the development into a fixed direction for a very long time. Especially for those who extrapolate present trends, it is therefore doubtful whether there is any future for smectic materials at all, in spite of the enormous potential in the form of much higher speed, brightness, color neutrality, ideal viewing angle, memory, and so on, which these materials have already demonstrated at the same time as they have shown to be very difficult to handle. The situation has some similarity to the one in the semiconductor industry where gallium arsenide and similar materials, in spite of their much higher speed (in particular), have a hard time entering a marked completely dominated by classic and much simpler silicon technology, which by huge industrial investments is constantly becoming better and, in fact, always seems to be good enough for the present demands. As always in history, the few pioneers, especially in Japan, have found a number of unexpected problems and difficulties in smectic materials that set back the development and which just have to be solved in order for the development to proceed. Regarding the serious nature and complexity of
Is There a Future for Smectic Materials?
659
these problems, it is indeed remarkable what has been achieved, and the advent of the first FLC panels and also of AFLC prototypes in the last few years were important events. Moreover, the all-polymer FLC displays simply have no counterparts in the nematic domain. At the same time, it is clear that the chemistry that has been so instrumental for the perfection of the nematic technology has not yet, by far, reached the corresponding level of refinement for smectic materials. First of all this has to do with the simple fact that the materials development started much later for smectics, at the same time as it was much less intense. However, the task is also more complicated by the very rich polymorphism found in smectics, and it is harder to implement the requirements set by industry. For instance, it is generally harder to phase-stabilize any smectic such that it meets the requirements of storage and transport (-40 "C to 90 "C) and not only for the operation temperature interval, and this is still, to some extent, a limiting factor. On the other hand, there are yet many exciting discoveries to be made by synthetic chemists working with smectic materials, considering the richness in interactions when we go to the more complicated molecules that organize in smectic layers. There is no doubt that, in particular, Japanese industrial chemists have been very successful in this more speculative chemistry in the last decade, and their innovative activity will be very important for the future use of smectic materials. Smectic materials have already demonstrated their potential use in very large [15-24 in. (37.5-60 cm)] flat panels with very high resolution, a potential that nematic materials do not have if not used in combination with thin film transistors. All smectic materials essentially use the same inplane switching mechanisms, the cone mode or soft mode, based on the very fragile bookshelf geometry. This has long been
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considered a serious obstacle, but today well-known methods exist in spacer technology for making such displays mechanically rigid. With this and some similar problems eliminated, what we are probably going to see is not only powerful smectic displays working in passive matrix mode, but also a merging of the TFT technology and the smectic technology in panels of yet unachieved quality and sophistication.
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Handbook of Liquid Crystals Edited by D. Demus, J. Goodby, G. W. Gray, H.-W. Spiess, V. Vill Copyright 0 WILEY-VCH Verlag GmbH. 1998
3 Antiferroelectric Liquid Crystals Kouichi Miyachi and Atsuo Fukuda
3.1 Introduction Chandani et al. [ 11 confirmed the existence of antiferroelectricity in liquid crystals by observing the electric-field-induced transition between the antiferroelectric smectic C i (SmCi) phase and the ferroelectric smectic C* (SmC*) phase. Since then, a large number of investigations have been performed and several review articles have been published [2-71. In ordinary circumstances, it would not be easy for us to write another review. Fortunately, however, the last year or so has been full of excitement in the field of antiferroelectric liquid crystals (AFLCs). In the following sections we describe three unexpected findings: the origin of antiferroelectricity in liquid crystals, thresholdless antiferroelectricity (TLAF) and V-shaped switching, and AFLC materials with unusual chemical structures 181.
3.2 Origin of Antiferroelectricity in Liquid Crystals 3.2.1 Biased or Hindered Rotational Motion in SmC* Phases Meyer and coworkers [9,10] have described the mechanism for the emergence of ferroelectricity in liquid crystals. We begin with its review. In most of the ordinary liquidcrystalline phases (nematic, smectic A (SmA) and smectic C (SmC)), which appear successively on lowering the temperature from the isotropic phase, the symmetry is so high that free rotation about the molecular long axis and head-tail equivalence prevent the occurrence of ferroelectricity. In the chiral smectic C (SmC*) phase, however, the symmetry is low enough to allow the existence of chirality-induced improper ferroelectricity, which does not result from the Coulomb interaction between permanent dipoles. The molecules rotate thermally about their long axes, but this rotation is now biased or hindered so that a spontaneous polarization given by
666
3
Antiferroelectric Liquid Crystals
emerges. Here 2 is a unit vector parallel to the smectic layer normal and 6 is the director; the sense of i is chosen in such a way that i coincides with 6 when the tilt angle 6 becomes zero. The reversal of the tilting sense naturally results in a reversal of the polarization sense. In this way, biased or hindered rotational motion about the molecular long axis plays an essential role in the emergence of the spontaneous polarization. However, only a few experiments have been aimed at the quantitative, microscopic examination of this motion [11,12]. Quite recently, Kim et al. [13] studied a prototype AFLC, MHPOBC, the structure of which is shown
in Figure 1, together with different aspects of the molecule and its dimensions. Using polarized infrared (IR) spectroscopy, they obtained microscopic proof, at least in its static aspect, of the biased or hindered rotational motion of the carbonyl (C=O) groups about the molecular long axis in the ferroelectric SmC* phase. A slightly unexpected conclusion derived by Kim et al. was that the most probable orientation of each individual C=O group may not be perpendicular to the tilt plane along the C2 axis of the SmC* phase (the Yaxis), although the spontaneous polarization appears perpendicular to the tilting plane along the two-fold axis because of the head-tail equivalence.
-2.
-0.5
1 Figure 1. (a) Structural formula of MHPOBC and its minimumenergy molecular shape projected on (b) the y z plane, ( c ) the zx plane, and (d) the x y plane. The x,y and z axes are the eigen axes of the moment of inertia.
3.2
Origin of Antiferroelectricity in Liquid Crystals
Figure 2 gives a schematic illustration of the measuring geometry used by Kim et al. Figure 3 gives the absorbance as a function of polarizer rotation angle A (w)for the three representative peaks listed in Table 1, which were measured at 105 "C in the SmCz phase of a homogeneously aligned MHPOBC cell under the application of a d.c. electric field. In helicoidal SmC; at zero electric field (Figure 3 b), the w,,, values of the phenyl
Figure2. Measuring geometry of the abFdJance versus the polarizer rotation angle. When homogeneously aligned cells are used, IR radiation is incident along the Yaxis and w = O is the smectic layer normal. When homeotropically aligned cells or free-standing films are used, IR radiation is incident along the Z axis and w=O is the tilt-plane normal. Here the laboratory and molecular frames are ( X , Y ,Z)and (x,y , z ) , respectively. The remaining three equivalent molecular frames are obtained by nrotations about the Y and Z axes. (a)+5.7 V / p m
667
Table 1. The three absorption peaks considered in the text. Observed peak (cm-') 1739 1720 1604
Assignment a Core C=O stretching Chiral C=O stretching Phenyl ring symmetric stretching
Two carbonyl groups, the one in the chiral part (abbreviated as chiral C = O ) and the other in the core part (abbreviated as core C=O) give well separated absorption peaks, while the three phenyl rings give absorption peaks at the same wavenumber. a
and C=O peaks, at which the maximum absorbances are obtained, appear parallel or perpendicular to the smectic layer normal. By applying an electric field stronger than the threshold, the om,,of the phenyl peak rotates by the tilt angle +8 in SmC*, i.e. by about 22" at 105 "C in MHPOBC, as shown in Figure 3 (a and c). The tilt angle, determined from 2um,, obtained in the correspending b m a n experiment, coincides quite well with that determined by using polarizing optical microscopy (Figure 4) [ 141. This change in om,, implies a field-induced phase transition from helicoidal SmCz to unwound, uniform SmC*. The reorientation of the molecules aligned helicoidally
(b) 0 V / pm
(c) -5.7 V / pm
Figure 3. Absorbance versus polarizer rotation angle for the three peaks listed in Table 1 measured at 105 "C in a 2-5 pm thick, homogeneously aligned, MHPOBC cell under the application of a d.c. electric field: (a) unwound SmC* at -5.7 V pm-I; (b) helicoidal SmCi at 0 V pm-'; (c) unwound SmC* at +5.7 V Km-' (core C=O: 0,chiral C=O: and phenyl rings: 7 ) .
668
3 Antiferroelectric Liquid Crystals
30
x
0 Tilt angle (Optics)
0
0 Tilt angle (Raman)
50
70
90
O110
I 130
Ternperature("C)
Figure 4. Comparison for MHPOBC between the tilt angle determined from 2w,,,,, obtained in the corresponding Raman experiment and the same angle determined by means of polarizing optical microscopy.
in SmCi to a direction parallel to the substrate surface brings about an absorbance inand an absorbance decrease crease at omax at cornin,recovering almost the same values as those in SmA. The angular dependence of the phenyl ring stretching peak indicates that the average stretching direction of the phenyl rings is parallel to the molecular long axis, and its orientational order is fairly high. A characteristic feature in SmC* is that the polarization dependence of the C=O peaks shown in Figure 3 (a and c) is not symmetrical with respect to the director, i.e. the values of the pheline connecting the w, nyl peak through the origin. Upon application of a sufficiently strong electric field, the w, of the chiral C=O peak rotates by an angle much less than the tilt angle, and the urnax of the core C=O peak scarcely rotates at all. It is impossible to understand this C=O peak polarization dependence by assuming free rotation of the C=O groups. If the molecules are ther-mally rotating freely about their long axes, the angular dependence of the C=O peaks should be symmetrical with respect to the director. In order to describe the biased or hindered rotational motion, we must take account of the fact that
there are four molecular configurations with the chiral C=O group at the top or bottom and tilted to the right or left (Figure 2); ty is defined as the angle between the tilt-plane normal ( Y axis) and the projection of the C=O group onto a plane perpendicular to the molecular long axis. Even in the SmC* phase, the most probable orientation is not y=O, but y = w O + O ; i.e. there are two equivalent configurations. Miyachi et al. [15] showed that, to a first approximation, the biased or hindered rotational motion may be described by
1
f+( w )= If,+ (w)-I-fbf (v/>l
(2)
where
h+(w>= fbf (w) =
1
11 -k a cos(v - YO )I (3) in the molecular frame shown in Figure 2. Here a is the degree of biasing or hindrance, yo is the biased or hindered direction, and the subscripts t(b) and +(-) refer to top (bottom) and left (right), respectively. In the laboratory frame, the four distribution functions given by Eq. (3) have four corresponding, different biased or hindered directions. By neglecting the fluctuation of the molecular long axis, and by assuming the angle between the C=O stretching direction and the molecular long axis p (Figure 5 ) is approximately 60°, we can simulate the absorbance versus polarization rotation angle A ( o ) for the geometry where
Figure 5. Definition of the angle between the C=O stretching direction and the molecular long axis.
3.2 Origin of Antiferroelectricity in Liquid Crystals
IR radiation is incident along the Y axis in Figure 2:
+I
2n
f t + ( w )(sin w' sin p sin w + cos o' cos p)2d y + [a corresponding term withfb+ (w)] (4)
A (0') =
0
Here o'=o-8 is used for convenience. Some of the calculated results are shown in Figure 6. The absorbance shows maxima at o = a,,, and w',,, + 180", and its polarizer-rotation angle dependence is symmetrical with respect to the line connecting the maxima through the origin. When the biased or hindered direction (the most probable orientation) in the molecular frame vois I
'
sn
669
zero, we obtain wI,,,= 90", irrespective of the value of a, the degree of biasing or hindrance, so long as a is small. As wo increases, a',,,rotates clockwise, as shown in Figure 6(a). Since the core C=O is distant from the chiral centre, mirror symmetry must exist and, in the present approximation, yo=90"; i.e. the core C=O appears to lie on the tilt plane. Experimentally (Figure 3), ~ ' , , ~ = 6 8 "for the core C=O, and hence we obtain a = 0.3 or slightly smaller. Similarly (Figure 3) o',,, = 83" for the chiral C=O, and hence we obtain yo=15" for the (R)enantiomer and 165" for the (S) enantiomer if the chiral C=O has the same degree of biasing or hindrance as the core C=O. Here, we have also used the fact that the ( S ) enantiomer of MHPOBC has a positive spontaneous polarization.
3.2.2 Biased or Hindered Rotational Motion in SmC; Phases
270
t
1
-3
70
a=0.3
60 0
30
60
90
vo(deg.)
Figure 6. Calculated results in SmC* for the IR radiation incident along the tilt-plane normal by using the distribution function given in equation ( 2 ) . (a) Normalized absorbance versus polarizer rotation angle; a = 0.2, w' = w- 0, and w = 0 is the layer normal. (b) Rotation angle at which A(w') becomes a maximum versus biased or hindered direction, mkax(y&for several values of a.
Let us consider the biased or hindered rotational motion of the core C=O in SmCi. It is well established that the molecular orientation in SmCi in its unwound state is a herringbone structure. In each smectic layer, the director tilt with respect to the layer normal is uniform; in adjacent layers, the tilt is equal in magnitude, but opposite in sign (the azimuthal angles specifying the tilt directions differing from each other by 180") [ 16, 171. Because of this herringbone structure, the measuring geometry with the homogeneously aligned cells used for SmC* cannot be used to study the biased or hindered rotational motion of the chiral C=O in SmCi. Instead, the measuring geometry obtained with free-standing films or homeotropically aligned cells, where IR radiation is incident along the 2 axis in Figure 2, is used. If we average the two possible SmC* states, one tilted to the left and the other to the right,
670
3 Antiferroelectric Liquid Crystals
molecules are apparently configured equally for both SmC* and SmCi; nevertheless, the results obtained experimentally offer a remarkable contrast. Figure 7 summarizes the dependence of absorbance on the polarizer rotation angle in the SmC* and SmCiphases [13,15]. Partial racemization not only simplifies the phase sequence, but also elongates the pitch of the helicoidal structure in SmCi so that its unwinding occurs at a relatively low electric field. However, a strong applied electric field was still needed because the anisotropy which causes unwinding is not very large. Although systematic investigations have not yet been performed and the data so far available are far from satisfactory, it is safe to conclude that the angular (a)
1.4 1.2
5 1.0
5
[r
0.8 0.6
$ 0.4 Q
0.2 0.0' -90
(b)
'
' 0
I
' . 90 180 ANGLE (degree) .
270
1 .o
1
f ( w >= 4[h+(w) f b + (w> + h- (w) + f b - (w)]
A(w)= 4
2
0. 0.01 -90
j h+(w> 0
0.6
O.
2n
. [sin cc) (- cos p sin 8 + sin p sin w cos 0)
+ cosw(sinp C O S ~d) v] ~
a
8
(5)
where ft+(y),etc., are the same as in Eq. (3). In SmC*, either of the distribution functions describing the two possible states, one tilted to the left and the other to the right, given in Equation (2) results in the same normalized absorbance dependence on the polarizer rotation angle. Thus, for both SmCi and SmC* we obtain 1
0.8
8f
dependence of the chiral C = O peak in SmCi is quite different from that in SmC*. The dependence in SmCz is very characteristic and conspicuously in phase with that of the phenyl peak, while it is out of phase in SmC*. The biased or hindered rotational motion of the chiral C = O in SmCi appears to be substantially different from that in SmC*. In SmCg, four equivalent configurations exist because the X and Y axes are the twofold symmetry axes; the chiral C=O rotational motion is biased or hindered not in a unique direction, but in four directions. To a first approximation, the hindered rotational motion is described by
+ [three corresponding terms] '
'
0
.
'
"
go
180
.
I
270
ANGLE (degree)
Figure 7. Absorbance versus the polarizer rotation angle in MHPOBC. (a) A (a)in unwound SmC* ohtained at 120°C, with a 75 V mm-' electric field, and using an approximately 8 pm thick, homeotropically aligned cell of (S)-MHPOBC. (b) A (a)in unwound S m C i obtained at 85"C, with an 800 Hz, +1400 V mm-' electric field, and using a 10 pm thick, homeotropically aligned cell of partially racemized ((R)-MHPOBC/(S)-MHPOBC = 84116) MHPOBC.
(6)
where m'= 0 'is the tilt plane normal [ 151. Figure 8 (a) illustrates some of the simulated results, which naturally depend on the degree of biasing or hindrance a , and the biased or hindered direction yo.Figure 8 (b) summarizes the degree of polarization versus the most probable orientation D ( w 0 ;a )
-
2 [&=(lo
(YO; a> - Am=9Oo(YO;a>] (YO;a ) + Am=90° (v0;a>
(7)
3.2 Origin of Antiferroelectricity in Liquid Crystals (a)
0.39
0.38 0 0)
m
$ 0.37 In 2 0.36
0.35' 0
'
"
90
'
.
'
180
.
'
'
270
'
'
360
67 1
from that in SmC*, provided that a does not change during the field-induced phase transition from SmCi to SmC*. Using the experimentally obtained degree of polarization, D ( y o )= -0.03, and assuming that the degree of biasing or hindrance is a =: 0.3, we determine that yo= 135" (45") for the partially racemized ( S ) ( ( R ) )enantiomer in the SmCi phase. If a = 0.2, then yo=100" (80"). In the SmC* phase of (S)-MHPOBC at 120°C however, the experimentally obtained value is D (yo)= 0.05, and hence we obtained yo= 175" (5") for a =: 0.3 and yo= 165" (15") for a = 0.1.
0
3.2.3 Spontaneous Polarization Parallel to the Tilt Plane
-0.05
-0.10 0
30
60
90
vo(deg.)
Figure 8. (a) Normalized absorbance versus the polarizer rotation angle calculated for SmC* and SmC; for radiation incident along the smectic layer normal by using the distribution function given in equations (3) and ( 5 ) . The molecular tilt angle and the degree of hindrance are assumed to be 8=25" and n = 0.2, respectively, and w = 0 is the tilt-plane normal. (b) Degree of polarization versus the most probable orientation for several values of a .
for various values of a. Note that positive and negative signs of D ( y o ;a) correspond, respectively, to the out-of-phase and inphase cases with respect to the phenyl peak. As the molecules are tilting from the smectic layer normal along which the IR radiation is incident, the C=O peak shows the out-of-phase angular dependence even when the rotational motion is free. Nevertheless, the conspicuous out-of-phase and in-phase angular dependencies in SmC* and SmCi, respectively, given in Figure 7, clearly indicate that yo in SmCi differs
We can conclude, therefore, that the chiral C=O has a tendency to lie on the tilt plane in SmCi, while it assumes a fairly upright position in SmC*. For several years antiferroelectricity has been modelled as arising from the pairing of transverse dipole moments at the smectic layer boundaries [17, 181. Although the chiral C=O in question is not at the end of the molecule, the unexpected bent shape of MHPOBC in its crystal phase just below SmCi, as revealed by X-ray crystallographic studies, has been considered to support the pairing model [ 18, 191. The model based on the pairing of transverse dipole moments is physically (or, rather, chemically) intuitive in relation to an understanding of the stabilizaton of antiferroelectric SmC;. However, because yois as large as 45" or more, as concluded above, it is not reasonable to ascribe an essential role to the pairing alone, and we must look for other causes for the stabilization of SmCi ~151. The symmetry arguments that Meyer used to develop his speculation about ferroelectric SmC* may help us to clarify anti-
672
3 Antiferroelectric Liquid Crystals
ferroelectric SmCi. There are two types of two-fold axis: one at the layer boundary is parallel to the X axes in the tilt plane (C2X,b), and the other is located in the centre of the layer, perpendicularly ( C , , ,) (Figure 9). In the pairing model, the C2y,caxis is the only one taken into consideration explicitly; the spontaneous polarization along C,,, , P,, alternates in sign from layer to layer [ 16- 18,20,21].However, Cladis andBrand [22, 231 insisted on the importance of the C,,,, axis in the tilt plane, and the above
Z
c2y, b
(b)
(a) Figure9. The two types of symmetry axes in unwound SmC; and SmC*. (a) Unwound SmC; has two-fold axes, C 2 , b and C2y,c,at the smectic layer boundary and at the smectic layer centre, respectively. (b) Unwound SmC* has two-fold axes, c , , and C2Y,c,at the smectic layer boundary and at the smectic layer centre, respectively.
(a)
Smc'
SmC;
conclusion about biased or hindered rotational motion of the chiral C=O supports their indication. The chiral C=O in question, although not in the core, is not at the end of the molecule either. Nevertheless, it is natural to consider that the in-plane spontaneous polarizations exist at smectic layer boundaries; they are parallel to the tilt plane along &X,b in SmCi, but are perpendicular to the tilt plane along C,,,b in SmC*. Their magnitude in SmCi may not be equal to that in SmC*. Note that C 2 y , b exists, as well as C2y,c,even in SmC*, as illustrated in Figure 10. An unanswered question is whether or not the Coulomb interaction among the permanent dipoles plays an important role. If the interaction is considered to result in in-plane spontaneous polarizations parallel to the tilt plane Px,we can designate this viewpoint as the Px model. For the stabilization offerroelectric SmC*, the Coulomb interaction among the permanent dipoles has not been considered essential, as insisted upon initially by Meyer [lo]. It is also possible that this interaction does not play any essential role in the stabilization of SmCi [24]. A SmC'
Figure 10. In-plane spontaneous polarizations in SmC; and SmC*. (a) Previous dipole pairing model. Only C2y,c,and hence the in-plane spontaneous polarization along the tilt-plane normal P,, are taken into consideration. (b) The present P, model. Both C2,,, and C2y.b are considered; hence in-plane spontaneous polarizations are considered to exist at the smectic layer boundaries, P, in SmCi and P , in SmC*.
3.2
Origin of Antiferroelectricity in Liquid Crystals
tempting feature of the P, model is, however, the possibility of explaining the herringbone structure, where the tilt planes in adjacent smectic layers are parallel to each other; we could not devise any other simple explanation for the structure. When permanent dipoles of equal magnitude are distributed on a plane, they may align in the same direction in order to minimize the Coulomb interaction energy, resulting in the in-plane spontaneous polarization parallel to the tilt plane Px. The sign of Px alternates from boundary to boundary; this fact also contributes, through fluctuation forces, to minimizing the Coulomb interaction energy between P , planes 125,261. Let us consider three dipoles which are located at the apices of a regular triangle with one side d, and oriented in the same direction and sense as illustrated in Figure 11. When another dipole approaches along a line perpendicular to the triangle and passing through its centre, it will align parallel to the three dipoles if zdl&, in order to minimize the Coulomb interaction energy. Although, in the pairing model, we have to invoke rather ad hoc assumptions (i.e. the local spontaneous optical resolution and the conformational chirality), the present P, model can naturally explain the existence of SmC,; the in-plane spontaneous polar-
Z
k
Figure 11. Illustration of three dipoles at the apices of a regular triangle with one side d and another dipole approaching on the Z axis (see the text for details).
673
ization parallel to the tilt plane P, is independent of chirality [22, 23, 271 and emerges even in racemates and non-chiral swallow-tailed compounds with two terminal chains of equal length [24].
3.2.4 Obliquely Projecting Chiral Alkyl Chains in SmA Phases The above discussion shows that it is most probable that in-plane spontaneous polarizations emerge at smectic layer boundaries and stabilize antiferroelectricity in the SmCi phase. In fact, Jin et al. [28] have quite recently shown unambiguously that the chiral chain projects obliquely from the core, even in SmA* and hence is considered as precessing around the core long axis; the angle between the chiral chain and core axes is more than the magic angle 54.7'. Such a bent molecular structure may allow the permanent dipoles in adjacent layers to interact adequately through Coulombic forces. By deuterating the chiral and achiral alkyl chains separately, Jin et al. observed the IR absorbance as a function of polarizer rotation angle for the CH, and phenyl ring stretching peaks in the SmA* phase of MHPOBC in a homogeneously aligned cell. Their results are summarized in Figure 12. Because of the selective deuteration, Jin et al. were able to obtain information about the achiral and chiral chains independently. The angular dependence of the CH, stretching peaks, both asymmetric (2931 cm-') and symmetric (2865 cm-'), shows a marked contrast between the achiral and chiral chains. In the achiral chain it is out of phase with that of the phenyl ring stretching peak, while in the chiral chain it is in phase. Moreover, the degree of polarization is very small. Jin et al. calculated the normalized absorbance by assuming an average transition di-
674
3
Antiferroelectric Liquid Crystals
x 0.4
pole moment of the CH, stretching vibrations, which is perpendicular to the average chain axis and is rotating freely about it, and by neglecting the sample anisotropy. Several necessary angles are defined as depicted in Figure 13: a is the angle between the chain and core axes; is the azimuthal angle of the chain axis around the core axis; I+Y is the angle of rotation of the transition dipole moment about the chain axis; and 13 is the tilt angle in SmC* which is zero in SmA*. The relationship between the absorbance and the polarizer rotation angle is given by
x
0.2
b
0'01'80
' -90' ' ' ' $0 ' ' lA0 Polarizer rotation angle,w (deg)
0
1.5
0
2x 2x
A ( w ' ; a ) =1G J
J f(x>
0 0
. (sin o' cos x sin I,Y - sin o'cos a sin I+Y (8) - cosw' sin a cos I+Y),d x d t,u
-180
-90 0 90 180 Polarizer rotation angle,w (deg)
Figure 12. Absorbance versus the polarizer rotation angle in SmA* measured at 130°C using a homogeneously aligned cell. (a) 4.0 pm thick cell, (R)-MHPOBC-d,, (enantiomeric excess 30%); (b) 9.6 pm thick cell, racemic MHPOBC-d,, . (0)Phenyl ring stretching; (A) CH, asymmetric stretching; ( 0 )CH, symmetric stretching.
Here the distribution function in SmA* is f ( x )= 1 4 2 ~ )the ; chain axis rotates freely about the core axis because of the uniaxial SmA* symmetry. Figure 14 shows the calculated normalized absorbance in SmA*. At the magic angle a = c0s-l ( U 6 ) = 54.7", the absorbance does not depend on the polarizer rotation angle A (o; a) = 1 / 6 . The aforementioned inphase and out-of-phase relationships corre-
0.6 a, t
2 0.4 P
n u N ._ 1 0.2 E
b
2
0.0
Figure 13. A model of the transition dipole moment for the CH, stretching vibrations, situated on the alkyl chain and freely rotating about the chain axis. The chain itself makes an angle a with the core axis, and precesses around it.
-180
-90 0 90 180 Polarizer rotation angle,w'(deg)
Figure 14. Normalized absorbance versus the polarizer rotation angle in SmA*, calculated for various values of a.
3.3 Thresholdless Antiferroelectricity and V-Shaped Switching
spond to a> 54.7" and a < 54.7", respectively. In this way, as shown unambiguously in Figure 12(b), the chiral chain in the SmA* phase projects obliquely, precessing around the core axis; the angle between the chain and core axes is more than 54.7", but is probably close to the magic angle because of the fairly small observed degree of polarization. Figure 12 (a) also clearly shows that, in this case, the other terminal chain in SmA* makes an angle of a < 54.7" with the core axis. By taking into account of the fact that not only the average transition moment, but also the average chain axis itself, is actually fluctuating, the appreciable degree of polarization observed may indicate that the angle is greatly different from the magic angle and rather close to zero. Jin et al. also analysed how the chiral chain precession becomes biased or hindered in SmC*, and suggested that the biasing or hindering may occur to the tilt plane normal = 0'). Although no experimental study of the biased or hindered precession in SmCi has yet been made, it is tempting to speculate that the biasing or hindrance may occur to the tilt plane (xo= 90"). As described in Sec. 3.2.1 and 3.2.2, the biased or hindered direction of the C = O group near to the chiral carbon atom in SmC* is quite different from that in SmCi. Anyway, we can safely conclude that in a prototype AFLC, MHPOBC, the molecules have a bent structure so that the C=O groups near the chiral carbon atoms, i.e. the permanent dipoles, in adjacent smectic layers can adequately interact through Coulombic forces to stabilize the antifen-oelectric SmCi (SmCA), and that in-plane spontaneous polarizations are produced at layer boundaries along the two-fold C2X,baxes which are parallel to the molecular tilt plane. Figure 15 presents an illustrative Px model based on bent shaped molecules.
(xo
675
n
Figure 15. An illustrative Px model based on bent shaped molecules.
3.3 Thresholdless Antiferroelectricity and V-Shaped Switching 3.3.1 Tristable Switching and the Pretransitional Effect Ordinary antiferroelectricity in liquid crystals results in tristable switching, which is the electric-field-induced transition between antiferroelectric SmCi and ferroelectric SmC* and has the characteristic d.c. threshold and hysteresis shown in Figure 16 [29-351. When a weak electric field is applied perpendicularly to the page, the dielectric anisotropy unwinds the helicoidal structure of SmCi and the tilt plane of the unwound SmCi becomes perpendicular to the page; all in-plane spontaneous polarizations, p b , have the same magnitude, but point upwards and downwards alternately. After the phase transition into SmC*, the molecules are parallel to the page, tilting uniformly either to the right or to the left; all p b have the Same magnitude and point uniformly either downwards or upwards. During the pretransitional effect, the Pbstay
676
3
Antiferroelectric Liquid Crystals
Electric field
m
-
I
i Electric field H -Bh
F
L -€th
L Bh
H
Bh
Pretransitional AF Pretransitional F
Figure 16. Ordinary tristable switching; (a) apparent tilt angle versus applied electric field; (b) optical transmittance versus applied electric field; (c) molecular tilt directions during the pretransitional effect and in the antiferroelectric (AF) and ferroelectric (F) states.
perpendicular to the page, but their magnitude and sense may change alternately from boundary to boundary, so that a slight net spontaneous polarization, either downward or upward, may emerge. The molecular tilting changes slightly from the unwound SmCi directions towards either of the unwound SmC* directions, and the tilt planes in neighbouring layers are no longer parallel to each other; Pbat a boundary is neither par-
allel nor perpendicular to the tilt plane in either of the neighbouring smectic layers. The unwinding process and the pretransitional effect may be virtually indistinguishable if the helicoidal pitch is short and the threshold field is low, or if the applied field changes very quickly. Because of the antiferroelectric unwound herringbone structure, however, the unwinding process in SmCi alone does not induce any apparent tilt angle; the small induced apparent tilt angle in SmCi clearly results from the pretransitional effect and increases almost linearly with the applied field from zero up to the threshold. The pretransitional effect causes a parabolic response in the optical transmittance versus applied electric field in a homogeneously aligned (smectic layer perpendicular to substrate) cell between crossed polarizers, one of which is set parallel to the smectic layer normal. In order to see more clearly the temporal behaviour of electric-field-induced phase transitions between SmCi and SmC*, it is useful to observe the optical transmittance when the applied field is changed stepwise across the threshold, &,h or &$the results for which are summarized in Figure 17 [36]. The antiferroelectric to ferroelectric (AF+F) switching (Figures 17(a) and 17(c)) critically depends on E h , but not on E l ; it contains two components, fast and slow. The fast component increases at the expense of the slow component as E h becomes higher. The slow component is seriously affected by E h and the response time representing the transmittance change from 10% to 90% is approximately proportional to ( E h - &,h)4. The reverse switching (F+AF) (Figure 17b and d) critically depends on E,, but not on E,; it consists of the slow component only. The response time is approximately proportional to (Eth,l-E1)7.A hump is observed when E, becomes sufficiently negative, i.e. when E1S-1.6 V . pm-l.
3.3 Thresholdless Antiferroelectricity and V-Shaped Switching
0
200
0
100
LOO 600 Time ( ~ s )
800
P m C c
'E 2
e
I-
200
300
LOO
Time (us1
0
200
LOO 600 Time ( ~ s l
800
: g
2 . L ,
The observed ratio of the fast component to the total change in transmittance was confirmed to be almost consistent with the estimated ratio from the maximum induced apparent tilt angle during the pretransitiona1 effect and the tilt angle after the transition to SmC*. Therefore, the fast component represents the pretransitional effect, which involves no macroscopic domain formation; when observing the effect through a microscope, the viewing field changes uniformly. The slow component represents a change due to the SmCi-SmC* (AF-+F) phase transition. Stroboscopic microscope observation has revealed that the transition always accompanies the movement of the domain (phase) boundaries of characteristic shape, as shown in Figure 18 [36, 371. The hump observed in Figure 17(d) originates from the F + F switching (process) which occurs temporarily. Since the domain boundary propagates rather slowly, so that the middle part of the cell stays ferroelectric for a while (Figure 18), the director in this part may not switch directly from F to AF, but tends to rotate on the cone from F (+) to F(-), or vice versa, and then to return to AF, if E, is negative. Therefore, the apparent tilt angle overshoots into the opposite side, crossing x=O".The overshoot can actually be seen in the stroboscopic photomicrographs shown in Figure 18 (b and c), which were obtained by choosing the crossed polarizer directions in such a way that F(+) becomes dark. The bright (green) area in the middle is F(-) and the intermediate (blue) area appearing at the electrode edges (the right and left sides of the photomicrographs) is AF. The boundary of characteristic shape between the AF and F(-) regions moves towards the middle. The dark (black) area observed in Figure 18 (b and c) clearly indicates that the F(-) +F(+) process really does occur; although not shown in Figure 18, the F(+)+AF process follows
x
P
I-
0
LO
80 120 Time (PSI
160
Figure 17. Optical transmittance change with crossed polarizers as a function of time after changing the electric field stepwise. Measurements were made using a 2.5 pm thick, homogeneously aligned cell of (R)-TFMNPOBC at 80°C by setting the polarizer in such directions that the antiferroelectric state becomes dark. The stepwise changes are (a) EFX= 0 V pm-' -+ Eh = 11.2- 15.2 V pm-'; (b) Eh=11.2-15.2Vpm-' -+ Ef'"=OVpm-I; (c) E l = -3.2-0.8 V pm-' + E F = 12 V pm-'; (d) E z X= 12 V pm-' + El=-3.2-0.8 V pm-I. U refers to uniform ferroelectric and 3rd to helicoidal antiferroelectric.
677
678
3
Antiferroelectric Liquid Crystals
Figure 18. Stroboscopic photomicrographs recorded at (a) 0.145 V (253 ms), (b) 0.290 V (256 ms) and (c) 0.339 V (257 ms) by linearly changing the voltage from -48.4 V (0 ms) to 48.4 V (500 ms) in a 4.6 pm thick, homogeneous cell of (S)-MHPOBC at 80°C. One of the ferroelectric states is chosen to be dark, overshooting to which is actually observed as clearly seen in (b) and (c). UI and Ur refer to ferroelectric states tilted uniformly to the left F(-) and to the right F(+), respectively, and 3rd refers to helicoidal antiferroelectric state (A).
afterwards, and the whole area becomes blue. These switching processes are also identified in the polarization reversal current measured by applying the triangular electric field (Figure 19). If the temporal rate of change of an applied electric field dEldt is not large, two bell-shaped peaks may typically appear, which correspond to the two processes F(-)+AF and AF+F(+). As dEldt increases, the F(-) +AF bell-shaped
J
0
200
LOO Time (ms)
600
Figure 19. Polarization reversal current in a 4.6 pm thick cell of (S)-MHPOBC at 80°C by applying a 548.4 V triangular wave voltage of 1 Hz. Overshooting to the other ferroelectric state is observed as a conspicuous sharp peak near 0 V followed by a backward current peak.
peak shows a cusp; with further increase in dEldt, the cusp becomes a conspicuous sharp peak, indicating the F(-) + F(+) process, and even the negative polarization reversal current, which results from the backward process F(+) + AF, is observed (Figure 19). Note that the small cusp was observed in the initial measurement made by Chandani et al. [29], although its significance was not realized at that time. In this way, it becomes clear that, phenomenologically, the pretransitional effect, as well as the phase transition between SmCz (AF) and SmC* (F), can be described by the rotation of the azimuthal angle 4 ; tilted molecules in alternate smectic layers rotate in the same direction, but those in the neighbouring smectic layers rotate in the opposite direction [38,39]. Let us consider what happens during biased or hindered rotational motion about the molecular long axis. In Sec. 3.2.3 we concluded that the biased or hindered direction yoin S m C i (I,$") is substantially different from that in SmC* (vz); more generally speaking, tytFand yc may be regarded as representing the rotational states about the molecular long axes in S m C i and SmC*, respectively. From this
3.3 Thresholdless Antiferroelectricity and V-Shaped Switching
point of view, the pretransitional effect is considered as a slight change in yofrom ytF towards .:yt Note the essential point that, not only the magnitude and direction of Pb at a boundary, but also the molecular tilt directions (azimuthal angle) in the neighbouring smectic layers of the boundary, are determined by the molecular rotational states. We have tried to observe this change in yo directly by means of polarized fourier transform IR (FTIR) spectroscopy, but have so far been unsuccessful. In the rotation of the azimuthal angle @ during the F(-) -+ F(+) process, or vice versa, the molecular rotational states have been observed to some extent by means of polarized dispersive IR spectroscopy in the submicrosecond regime [40].
3.3.2 Pretransitional Effect in Antiferroelectric Liquid Crystal Displays Antiferroelectric liquid crystal displays (AFLCDs) have been relevant to flat panel displays since the discovery of AFLCs. Their characteristic features can be summarized as follows: In the SmCi phase stable at zero electric field, the optical axis is almost parallel to the rubbing direction. This favours the ease and stability of alignment of the molecules. Nakagawa et al. [41] have shown that the smectic layer normal in SmA* does not coincide exactly with the rubbing direction, deviating clockwise by several degrees for (S)-MHPOBC relative to the substrate. There is no permanent spontaneous polarization, but polarization emerges when needed. Hence the switching may not be hampered by the so-called ‘ghost effect’ or the unnecessarily strong, difficult to erase, memory effect.
679
The switching is characterized by the distinctive d.c. threshold and hysteresis, which allow matrix addressing of large capacity displays, if use is made of a positive or negative bias field. The use of a symmetrical bias field, positive in one frame and negative in the next, also ensures an ideal viewing angle, much wider than that in SSFLDs, although the pretransitional effect that induces a small increase in the apparent tilt angle in SmCi may slightly decrease the contrast ratio. The quasi-bookshelf smectic layer structure is realized and the twisted state of the director alignment is inherently avoided. Hence the relatively high contrast ratio of 20-30 is easily obtained. The switching response time may become as short as 50 ps or better under acceptable driving conditions by optimizing the materials used. Stripe domains parallel to the smectic layer appear from the electrode edges quite regularly during switching, and the speed of movement of their boundaries depends critically on the field applied. This fact is utilized in controlling the grey scale, in combination with the distinctive d.c. threshold and hysteresis. Self-recovery from alignment damage caused by mechanical and thermal shocks is observed during operation. This results from the reversible layer switching between the bookshelf and the quasibookshelf structures, which occurs in the network of characteristic stripe defects parallel to the layer normal. Because of these attractive characteristics, much attention has been paid to AFLCDs, and two prototype AFLCDs with passive matrix (PM) addressing have been developed and exhibited. One is a 6-inch, video rate, full-colour display by Nippondenso
680
3 Antiferroelectric Liquid Crystals
Co., Ltd. [42], and the other is a 5.5-inch, VGA monochrome display by Citizen Watch Co., Ltd. [43], both of which have an extremely wide viewing angle with a relatively high contrast ratio of 30. What prevents AFLCDs from achieving much higher contrast ratios is the pretransitional effect, which manifests itself as a slight increase in the transmittance below the threshold (see Sec. 3.3.1). Ironically, during attempts to develop materials that can suppress the pretransitional effect, we have encountered materials which show a large pretransitional effect and, at the same time, a remarkable decrease in the threshold field strength. Hence we came to consider that enhancement of the pretransitional effect, in combination with the use of active matrix
(AM) addressing, is another way of endowing liquid crystals with attractive display characteristics [34,35]. Taking some compounds and their mixtures as examples, let us show in a concrete way how the threshold becomes lower as the pretransitional effect is enhanced. Table 2 [44,45] shows that, in a series of compounds with the general molecular structure, an ether linkage and its position in the chiral end chain influence the threshold field Eth,h in a subtle way. When the ether linkage is located at the chain terminus, &h,h becomes higher than that of the reference substance of equal chain length but having no ether linkage. As the linkage moves towards the core, E t h , h becomes lower and, finally, SmC* (F) appears instead of SmCi (AF).
Table 2. The effect of an ether linkage position on the threshold field strength.
3.4
15.7 6.5
Table 3. The effect on the contrast ratio of substituting the phenyl rings in 1 (1 = 1, m = 4, n = 1, la) with fluorine.
c,1H23o&CO1&
la
CO2-C*H(CF3)C,H@CH, y2
Contrast ratio a 36
27 12 31 28 10 a Measured at 20°C below the SmC* (SmA*)-SmCi phase transition temperature by using a 1.7 pm thick cell and applying a 0.1 Hz, k 4 0 V triangular wave voltage.
3.3 Thresholdless Antiferroelectricity and V-Shaped Switching
Blending further reduces E t h , h as illustrated in Figure 20 [35].Furthermore, the pretransitional effect can be enhanced by suitably substituting phenyl rings with fluorine [35]. In order to evaluate the pretransitional effect we measured the contrast ratio TF/TAF just below E t h , h ; the smaller the contrast ratio, the larger the pretransitional effect. Table 3 summarizes the results, indicating that substitution at Yl decreases the contrast ratio and hence enhances the pretransitional effect most remarkably. 100
I SmA
!
I-
'/020 4 0
L
0
20
40 60 80 Mixing ratio(%)
100
In this way we can enhance the pretransitional effect and reduce the threshold Eth,h.An unanswered question is that of whether or not we can prepare a system where the threshold becomes zero, so that the pretransitional effect prevails and the AF-F phase transition occurs continuously. Surprisingly, it was not difficult to realize this property in a three-component mixture; the field-induced F-AF-F phase transition looks like a V-shaped switching (Figure 21) [34, 351. Hereafter we will call this property 'thresholdless antiferroelectricity'. Although no detailed investigations have yet been made, the response of the system to an applied stepwise field is rather fast, as illustrated in Figure 22. When we observed the switching by means of polarizing optical microscopy, the visual field varied uniformly and continuously without showing any irregularities, indicating the boundary movement characteristic of tristable switching or the disclination lines caused by the helicoidal unwinding of a ferroelectric liquid crystal. The V-shaped switching is totally different from tristable switching and helicoidal unwinding.' We still need to optimize the V-shaped switching characteristics by further developing suitable materials, but the results obtained with the materials available so far appear to indicate the possibility of realizing:
F C , H I ~ OW
C
0
2
G CO2- & W C & O C , H s
3
Figure 20. The phase diagram of a binary mixture of 2 and 3 and the threshold field versus mixing ratio. The phase boundary between the AF and F regions is parallel to the temperature axis and hence the stability of the AF phase becomes equal to that of the F phase in the binary mixture at this particular boundary mixing ratio. As the mixing ratio approaches the boundary, decreases, although it could not be confirmed that it diminished to zero.
68 1
0
0
a tilt angle of more than 35"; a field of less than 2 V ym-' to complete the AF-F switching; light transmission that is almost linear with respect to the applied field, and free from hysteresis; a AF-F switching time of less than 50 ps; a contrast ratio as high as 90; and an extremely wide viewing angle of more than 60".
682
3 Antiferroelectric Liquid Crystals
1.o
0.8
-
0.6
c .-
0.4
! +
0.2 0.0 -6
-4
0
-2
2
4
6
Electric field (V/pm)
Figure 21. The V-shaped switching observed at 25°C by applying a 0.179 Hz, +7 Vpp triangular wave in a 1.4 pm thick, homogeneous cell of a mixture of 4, 5 and 6 in the mixing ratio 40 : 40 : 20 (wt%), which has a tilt angle 0 of 35.7'.
3.3.3 Langevin-type Alignment in SmCg Phases
1
Transmittance-.
\
Time Figure 22. Temporal behaviour observed at 25 "C by applying a +4 V rectangular wave to the same cell as that in Figure 21: (a) 2 msldivision; (b) 50 psldivision.
A small cell, although very primitive, has actually been made, and demonstrates these attractive display characteristics.
We will begin with speculation about thresholdless antiferroelectricity in terms of the molecular rotational motion which plays an essential role in the emergence of inplane spontaneous polarizations in liquid crystals. We concluded in Sec. 3.2.3 that the biased or hindered direction yo in SmCi (ykF)is substantially different from that in SmC* (y:); more generally, ytF and y: may be regarded as representing the rotational states around the molecular long axes in SmCz and SmC*. We also concluded in Sec. 3.3.1 that the pretransitional effect is considered as a slight change in yo from ykF towards y:. Based on these conclusions, we speculate as follows. In the phase showing thresholdless antiferroelectricity, the biased or hindered rotational motions (more generally, the molecular rotational states in SmC; and SmC*) characterized by ytF and y: have nearly the same energies and, furthermore, the barrier between them diminishes, so that the states characterized by any yobetween yeFand are equally thermally excited at zero electric field.
683
3.3 Thresholdless Antiferroelectricity and V-Shaped Switching
As noted in the previous section, this arbitrariness in tyo makes the molecular tilting direction uncorrelated between adjacent layers. Figure 23 illustrates a simplified model of the phase SmCg that shows thresholdless antiferroelectricity. The director tilting is uniform and has constant polar and azimuthal angles in a smectic layer, but its azimuthal angle varies randomly from layer to layer. In-plane spontaneous polarizations exist at the smectic layer boundaries, their orientation being random and their magnitude varying from boundary to boundary. Random tilting of the smectic layers ensures the disappearance of the net spontaneous polarization, but an applied electric field induces it according to a Langevintype equation [46]. The difference from the ordinary Langevin equation is that we are dealing with very large effective dipole moments of variable magnitude because many molecules interact cooperatively and produce in-plane spontaneous polarizations, and their rotation is restricted in the twodimensional space.
The light transmittance was obtained by assuming that the effective dipole moments have the same magnitude peffand follow the same distribution as the c director. The two-dimensional and three-dimensional Langevin alignments are given by 7l
exp (x cos 4) cos @ d@
(9)
(cos@)=O exp(x cos@>d# 0
and
respectively, where x = peffE / ( k T ) ( k is the Boltzmann constant and T is temperature) [46]. Figure 24 shows the numerically calculated results; the two-dimensional case aligns more steeply than the three-dimensional one. In a rough approximation, it is convenient to use an apparent tilt angle (cos #) = cos oaap
(1 1)
We will further assume that the index of the ellipsoid is uniaxial with its eigen values, nl, and n,, independent of the applied field.
1.o
_______*----
0.8 c
$ 0.6
2-dimensional 3-dimensional
E
01
0.4 -E
E=O
+E 0.2
0 Langevin-type alignment
Random from boundary to boundary
Langevin-type alignment
Figure23. A simplified model of the phase that shows thresholdless antiferroelectricity.
'
0.0
0
I
5
10
15
20
X
Figure 24. The two- and three-dimensional Langevin alignments.
684
3 Antiferroelectric Liquid Crystals
$
;::m
+
0.2
X
X
; (m 0.6 ._
Figure 25. Calculated switching behaviour for cell thickness d = 1.55 pm,n,= 1.5, wavelength of incident light L=500 nm: (a) rill= 1.65, And/L=0.45; (b) n i l =1.71, And/L=0.63; (c) rill= 1.75, And/L=0.75.
0.4
L
0.0 -10
-5
0
5
10
X
Some calculated results are shown in Figure 25. The switching behaviour in the final stage near the bright ferroelectric state naturally depends on a parameter A n . d/A, where d is the cell thickness and ilis the wavelength of the incident light. In this approximation, when An . d / A= 0.63, the behaviour becomes ideal.
3.4 Antiferroelectric Liquid Crystal Materials 3.4.1 Ordinary Antiferroelectric Liquid Crystal Compounds Because of their potential application in display devices, a large number of, probably almost 1000, AFLC and related compounds have been synthesized in Japan. Most of these have been reported in Japanese Patent Gazettes; some have been reported in scientific reports and papers, but many of these are written in Japanese, in particular, those
in the Abstracts of Japanese Liquid Crystal Conferences. As access to these publications may not be easy for non-Japanese scientists and engineers in the liquid crystal community, and as these sources contain valuable information, we will try to summarize those AFLC compounds that have been reported mainly in Japan. Note that the materials characterized by the V-shaped switching due to thresholdless antiferroelectricity, which form one of the main topics of this discussion, are reported in these publications. Almost all the related Gazettes and Abstracts so far publicized are listed in [47] and [48]. Fortunately, the Abstracts contain titles and authors together with institutions written in English and chemical structural formulae used in the Gazettes and the Abstracts are international. The phase sequence of a prototype AFLC, MHPOBC, has been known to be complex since the early stages of the investigation of antiferroelectricity in liquid crystals [ l , 6, 491. The origin and the structures of the subphases have been well documented [6, 501. However, it is not easy to identify the sub-
3.4 Antiferroelectric Liquid Crystal Materials with Unusual Chemical Structures
phases properly in newly synthesized compounds. Moreover, the existence of subphases as well as the structures may be critically influenced by the substrate interfaces. Both the subphases, SmC;, SmCT, etc.. and SmCz itself are quite similar to SmC*, and the differences in free energy between them must, therefore, be very small. As MHPOBC was first reported as a ferroelectric liquid crystal, the phase identifications given in the Gazettes and Abstracts are usually primitive and not always correct; they frequently disregard the details of the subphases, simply specifying them as ferroelectric or antiferroelectric. Therefore, when we refer to these publications, we must be aware of this ambiguity; nonetheless, these reference sources are very useful. Note that the most general subphase sequence currently known is [50-521:
-AF
- Ferri/anti
77G
-c=C-C-O-
685
(-CHZCHC02-)
-[SmC*I- SmC; - SmA*
The chemical structural formulae of MHPOBC and another prototype AFLC, TFMHPOBC, are given in Figures 1 and 26, respectively. Most AFLC compounds so far synthesized have similar molecular structures to those of MHPOBC and TFMHPOBC. The structure can be considered to consist of three sub-structures: the chiral chain, the central core, and the nonchiral chain (Figure 26). In the chiral chain, it may be convenient to differentiate between the connector to the central core and the remaining part of the chiral chain; here-
(d) Non-chiral chains ~
non-chiralchain
core
connecter chiral chain
Figure 26. Structural formula of TFMHPOBC, illustrating four substructures: non-chiral chain, central core, connector, and chiral chain.
R-
RO-
RC02-
ROCO-
R:C,H2"+1
Figure 27. Some typical sub-structures of AFLC compounds: (a) chiral chains; (b) connectors; (c) cores; (d) non-chiral chains.
686
3 Antiferroelectric Liquid Crystals
after we will designate these the 'connector' and the 'chiral chain', unless otherwise stated. The types of substructure so far studied (i.e. chiral chains, connectors, cores and non-chiral chains) are summarized in Figure 27. In this section, the chemical structural formulae are drawn in such a way that the chiral chains are located on the righthand side. Chiral chains play a critical role in determining the stability of the antiferroelectricity. The variety of chains is rather limited. The most common chiral chain is -*CH(CF,)C,H2,+1, which stabilizes the antiferroelectricity much more than does -*CH(CH3)C,H2,+1, as illustrated in Figure 28; the odd-even effect is clearly observed in -*CH(CH,)C,H2,+I, while only the SmCi phase occurs in - *CH(CF,)C,H,,+, . Trifluoromethylalkoxy alkyl chains, -*CH(CF3)C,H&OC,H2,+ give a low threshold field and fast response
(see Sec. 3.3.2). The pretransitional effect is very small in some compounds containing trifluoromethylcycloalkane chains, such as -*CH(CF,)-C,H, and -*CH(CF,)-CsH9 (see e.g. 7 and 8).
Monofluoro- and difluoromethylalkyl chains do not stabilize antiferroelectricity. Racemates do not exhibit antiferroelectricity, but they do frequently have the herringbone structure. Moreover, Nishiyama and coworkers [53, 541 have shown that chirality is not essential for the appearance of the herringbone structure; the swallow-tailed compounds (e.g. 9), C ~ H , , O ~ C ~ C - C O ~ ~ C O ~ 3-~ 7C) 2H ( C 9
which do not have an asymmetric carbon atom, have the herringbone structure, and
C l o H z l ~ C O z ~ ~ C 'H(CF3)C,H2,+l 0 2 C
10BIMFn 2
n-6 n=7 n=8 n-9 n.10
20
40
60
80
100
120
140
160
180
n-2 n=3 n-4 n-5
n-6 n-7
2
n-6 n=7 n-8
chiral end chains (Please note: In the figure the old nomenclature - S instead of Sm and Is0 instead of I - is used).
3.4 Antiferroelectric Liquid Crystal Materials with Unusual Chemical Structures
the addition of a small amount of chiral dopant induces tristable switching. Some connectors are listed in Figure 27(b). Almost all AFLC compounds have a carbonyloxy connector between the asymmetric carbon atom and the ring in the core, but some compounds [55] have a carbonyl or oxycarbonyl connector (Figure 29). Inui [56] studied the alkylcarbonyloxy connectors and found that -C2H,COO- exhibits antiferroelectricity but -CH,COO- does not; although -CH=CH- is better regarded as included in the core, cinnamates also show antiferroelectricity. A characteristic feature of core structures is that there are three or more rings, at least two of which are not directly connected but are separated by a flexible group. Some examples are given in Figure 27(c). AFLC
687
compounds containing only two rings are quite exceptional. Four-ring compounds usually show antiferroelectricity at temperatures above 100°C. The flexible connecting groups known so far are -C(O)O-, -OC(O)-, -OCH,-, -CH,O-, C(0)S-and -C(O)NH-. Of these, -COO- is the most commonly used. An increase in the number of flexible connecting groups may stabilize the antiferroelectricity, but makes the compound viscous. Rings used in the core are benzene, cyclohexane, tetralin, naphthalene, 1,3-dioxane, piperidine, pyrimidine, etc. Of these the benzene ring is the most commonly used. Six-membered rings may be connected directly, forming biphenyl, phenylpyrimidine, pyrimidine phenyl, dioxane phenyl, phenylcyclohexane, piperidine phenyl, etc. Halogen-substituted rings are also used, as illustrated in Figure 29. In this way, a variety of core structures can be used to obtain AFLC compounds.
8
SCA SCA
sc
10 SCA
Figure 29. Some AFLC compounds containing a carbonyl, oxycarbonyl or alkylenecarbonyloxy connector.
Figure 30. Odd-even effect in compounds containing non-chiral and chiral end chains (Please note that the old nomenclature - S instead of Sm - is used).
688
3 Antiferroelectric Liquid Crystals
Some non-chiral chains are listed in Figure 27(d). Alkoxy chains, RO-, are the most common. The alkanoyloxy chain, RCOO-, increases both the stability and the viscosity, while alkoxycarbonyl chains, ROCO-, decrease them. Simple alkyl chains, R-, may slightly decrease the stability and viscosity at the same time. The odd-even effect is less clear in non-chiral chains than in chiral chains, as illustrated in Figure 30.
3.4.2 Antiferroelectric Liquid Crystal Compounds with Unusual Chemical Structures A homologous series of AFLC compounds, which have entirely different chemical
n
-_
Ps lnCicrn'1.b, 0 ideal b, -
Phase transition temperatures on cooling stepa)
104 129 129 147 159 194
50
40
60
70
80
90
100
'z
Cr SrncA* SmA I a) cooling rate = SKlmin. b) Tc-T = 5K.
structures from the ordinary ones characterized by having a carbonyl group in the connector, have been synthesized by Aoki and Nohira [57-591. The chemical structures and the corresponding phase sequences are summarized in Figure 3 1. They identified the phases by checking miscibility with a TFMHPOBC-like compound as shown in Figure 32. The ordinary tristable switching, as illustrated in Figure I6(b), was observed optically, and is characterized by a d.c. threshold and hysteresis. Tristable switching was also observed electrically by detecting two current peaks that correspond to the appearance and disappearance of the spontaneous polarization, Aoki and Nohira further confirmed that the racemates have the SmC, phase. According to the Px model de-
110
30 34 35 37 38 40
Figure 31. Structural formula of AFLC compounds synthesized by Aoki and Nohira [57-591 and their phase sequences and physical properties (Ps, spontaneous polarization; 0, tilt angle).
150
100
. ?
b
50
Figure 32. Miscibility test for 10 with n = 1 (see Figure 31) with a reference AFLC.
0 0
20 Weight 40 percent 60 of801 100
C,oH210 ~ C O , ~ C O & ( C F ~ ) C ~ H E 10 a
3.5
scribed in Secs. 3.2.3 and 3.2.4, the molecules are expected to be bent at the chiral carbon atom. It is an interesting problem for the future to study whether or not this is the case. A second class of materials are pyrimidine host mixtures containing pyranose guests, some examples of which are given in Figure 3 3 . Although the SmCi phase is not exhibited by the guest compounds themselves, Itoh et al. [60,61]* have clearly confirmed the appearance of the SmCi in the mixture, the composition of which is specified in Figure 33, by observing the typical tristable switching. This finding is very important, suggesting as it does the possibility of developing practical guest-host type mixtures of AFLC materials. Although detailed investigations have not yet been performed, some of the subphases associated with the SmCi phase seem to have been observed in the series of AFLC
Cry
71'C
Is0
Figure 33. Pyrimidine host mixtures containing pyranose guests.
References
689
compounds 11 synthesized by Wu et al.
[a.
* Note added in proof: Quite recently, Itoh et al. reported that the phase in these pyrimidine host mixtures is not antiferroelectric but ferroelectric and that the typical tristable switching results from an ultrashort pitch of about 50nm. (K. Itoh, Y. Takanishi, J. Yokoyama, K. Ishikawa, H. Takezoe and A. Fukuda, Jpn. J. Appl. Phys. 1997,36, L784).
3.5 References [ l ] A. D. L. Chandani, E. Gorecka, Y. Ouchi, H.Takezoe, A. Fukuda, Jpn. J. Appl. Phys. 1989,29, L1265. [2] J. W. Goodby, J. Muter. Chem. 1991, 1 , 307. [3] R. Blinc, CondensedMatferNews 1991, 1, 17. [4] P. E. Cladis, Liq. Cryst. Today 1992, 2, 7. [5] A. Fukuda (Ed.), The Future Liquid Crystal Display and its Materials, CMC, Tokyo, 1992 (in Japanese): A. Fukuda, J. Li, Chap. 1 , p. 1; Y. Yamada, Chap. 8, p. 102; K. Itoh, Chap. 13, p. 287; M. Johno, T. Yui, Chap. 14, p. 297; S. Inui, H. Iwane, Chap. 15, p. 308; and S . Nishiyama, Chap. 16, p. 318. [6] A. Fukuda, Y. Takanishi, T. Isozaki, K. Ishikawa, H. Takezoe,J. Muter. Chem. 1994,4,997. [7] I. Nishiyama, Adv. Muter. 1994, 6, 996. [8] K. Miyachi, Ph. D. Thesis, Tokyo Institute of Technology, 1996. [9] R. B. Meyer, L. Liebert, L. Strzelecki, P. Keller, J. Phys. (France) 1975, 36, L69. [ l o ] R. B . Meyer, Mol. Cryst. Liq. Cryst. 1977, 40, 33. [I 11 M. Luzar, V. Rutar, J. Seliger, R. Blinc, Ferroelectrics 1984,58, 115. [I21 A. Yoshizawa, H. Kikuzaki, M. Fukumasa, Liq. Cryst. 1995, 18, 351. [13] K. H. Kim, K. Ishikawa, H. Takezoe, A. Fukuda, Phys. Rev. E 1995,51,2166. (Erratum: Phys. Rev. E 1995, 52, 2120.) [14] K. H. Kim, K. Miyachi, K. Ishikawa, H. Takezoe, A. Fukuda, Jpn. J. Appl. Phys. 1994, 33, 5850. [I51 K. Miyachi, J. Matsushima, Y. Takanishi, K. Ishikawa, H. Takezoe, A. Fukuda, Phys. Rev. E 1995,52, R2153.
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3
Antiferroelectric Liquid Crystals
[16] A. D. L. Chandani, E. Gorecka, Y. Ouchi, H. Takezoe, A. Fukuda, Jpn. J. Appl. Phys. 1989, 28, L1265. [17] A. Fukuda, Y. Takanishi, T. Isozaki, K. Ishikawa, H. Takezoe, J. Muter. Chem. 1994,4,997. [l8] Y. Takanishi, H. Hiraoka, V. K. Agrawal, H. Takezoe, A. Fukuda, M. Matsushita, Jpn. J. Appl. Phys. 1991,30, 2023. [19] K. Hori, K. Endo, Bull. Chem. Soc. Jpn. 1993, 66,46. [20] L. A. Beresnev, L. M. Blinov, M. A. Osipov, S. A. Pikin, Mol. Cryst. Liq. Cryst. l988,158A, 1. [21] Y. Galerne, L. L. Liebert, Phys. Rev. Lett. 1991, 66, 2891. [22] P. E. Cladis, H. R. Brand, Liq. Cryst. 1993, 14, 1327. 1231 H. R. Brand, P. E. Cladis, H. Pleiner, Macromolecules 1992,25, 7223. [24] I. Nishiyama, J. W. Goodby, J. Muter. Chem. 1992, 2, 1015. [25] J. Prost, R. Bruinsma, Ferroelectrics 1993,148, 25. [26] R. Bruinsma, J. Prost, J. Phys. I1 (France) 1994, 4, 1209. [27] Y. Galerne, L. Liebert, Phys. Rev. Lett. 1990,64, 906. [28] B. Jin, Z. H. Ling, Y. Takanishi, K. Ishikawa, H. Takezoe, A. Fukuda, M. Kakimoto, T. Kitazume, Phys. Rev. E 1996,53, R4295. [29] A. D. L. Chandani, T. Hagiwara, Y. Suzuki, Y. Ouchi, H. Takezoe, A. Fukuda, Jpn. J. Appl. Phys. 1988,27, L729. [30] A. D. L. Chandani, E. Gorecka, Y. Ouchi, H. Takezoe, A. Fukuda, Jpn. J. Appl. Phys. 1989, 28, L 1265. [31] M. Johno, A. D. L. Chandani, J. Lee, Y. Ouchi, H. Takezoe, A. Fukuda, K. Itoh, T. Kitazume, Proc. SlD 1990,31, 129. [32] M. Yamawaki, Y. Yamada, N. Yamamoto, K. Mori, H. Hayashi, Y. Suzuki, Y. S. Negi, T. Hagiwara, I. Kawamura, H. Orihara, Y. Ishibashi in Proceedings of the 9th International Display Research Conference (Japan Display '89, Kyoto), 1989, p. 26. [33] K. Miyachi, J. Matsushima, Y. Takanishi, K. Ishikawa, H. Takezoe, A. Fukuda, Phys. Rev. E 1995,52, R2153. [34] A. Fukuda in Proceedings of the 15th International Display Research Conference (Asia Display '95, Hamamatsu), 1995, p. S6-1. [35] S. Inui, N. Iimura, T. Suzuki, H. Iwane, K. Miyachi, Y. Takanishi, A. Fukuda, J. Muter. Chem. 1996,6, 67 1 . [36] M. Johno, K. Itoh, J. Lee, Y. Ouchi, H. Takezoe, A. Fukuda, T. Kitazume, Jpn. J. Appl. Phys. 1990,29, L107. [37] X. Y. Wang, P. L. Taylor, Phys. Rev. Lett. 1996, 76, 640.
[38] T. Akahane, A. Obinata, Liq. Cryst. 1993, 15, 883. [39] H. Pauwels, A. de Meyere, J. Fornier, Mol. Cryst. Liq. Cryst. 1995,263, 469. [40] M. A. Czarnecki, N. Katayama, M. Satoh, T. Watanabe. Y. Ozaki, J. Phys. Chem. 1995.99, 14101. [41] K. Nakagawa, T. Shinomiya, M. Koden, K. Tsubota, T. Kuratate, Y. Ishii, F. Funada, M. Matsuura, K. Awane, Ferroelectrics 1988, 85, 39. [42] N. Yamamoto, N. Koshoubu, K. Mori, K. Nakamura, Y. Yamada, Ferroelectrics 1993, 149,295. (431 E. Tajima, S. Kondon, Y. Suzuki, FerroelecrricJ 1994,149,255. [44] S. Inui, T. Suzuki, N. Iimura, H. Iwane, H. Nohira, Ferroelectrics 1993, 148, 79. [45] M. Johno, T. Matsumoto, H. Mineta, T. Yui, Abstracts 11: Chemical Society of Japan 67th Spring Meeting, Chemical Society of Japan, Tokyo, 1994, Abstract 1 1B31 12. [46] G. M. Barrow, Physical Chemistry, 5th edn, McGraw-Hill, New York, 1988, p. 67 I . [47] Japanese Patent Gazettes: H 1-213390; H 13 16339; H1-3 16367; H1-316372; H2-28128: H2-40625; H2-78648; H2-131450; H2-153322; H2-160748; H2-173724; H2-176723; H2230117; H2-270862; H3-11041; H3-68686; H38395 1; H3- 121416; H3- 123759; H3- 141323; H3- 1675 18; H3-18 1445; H3-197444; H3197445; H3-2 18337; H3-223263; H3-291270; H3-292388; H4-29978; H4-46158; H4-46159; H4-55495; H4-96363; H4-82862; H4-89454; H4-103560; H4-108764; H4-117345; H4159254; H4-173779; H4-178353; H4-198155; H4-217942; H4-235950; H4-244047; H4261 162; H4-261163; H4-266853; H4-266855; H4-266876; H4-282344; H4-305554; H4305555; H4-312552; H4-3 16562; H4-327576; H4-338361; H4-338362; H4-342546; H4342547; H4-360850; H4-360854; H4-372929; H5-1041; H5-4945; H5-17407; H5-17408; H532675; H5-32973; H5-39246; H5-58959; H565484; H5-70392; H5-85988; H5-85989; H597821; H5-98258; H5-105644; H5-105877; H5132449; H5-140046; H5-140119; H5-155880; H5-163208; H5-163248; H5-186401; H5186402; H5-201929; H5-201983; H5-202028; H5-213881; H5-221928; H5-230032; H5230033; H5-230035; H5-247026; H5-255 193; H5-247026; H5-255193; H5-255196; H5311171; H5-320125; H5-331107; H6-25098; H6-25099; H6-25100; H6-32764; H6-32765; H6-32770; H6-65 154; H6- 108051; H6- 1 16208; H6-128236; H6-145111; H6-211749; H6228056; H6-247898; H6-247901; H6-247902; H6-271852. [48] Abstracts of Japanese Liquid Crystal Conferences: 1990,16,2K101,2K102,2K103,2K104, 2K105,2K106; 1991,17,2F302,2F315,3F313,
3.5 3F314, 3F316, 3F318, 3F321, 3F322, 3F324; 1992,18,2B408,2B409,2B410,2B411,2B412, 2B417, 3B416, 3B417, 3B419, 3B420, 3B421, 3B422,3B423,3B424,3B425; 1993,19, l A l l , 1A12, 1A14, 1B13, 2A03, 2A08, 2A10, 3D08; 1994,20, 1F603,1G303,2F610,2F614,2F617, 3G201, 36203,3G205,3G206,36208,3G213, 3G215, 3G216, 36218; 1995,21, 2C01, 2C04, 2C05, 2C09, 2C10, 2C12, 2C13, 2C14, 2C18, 3C07,3C08. [49] M. Fukui, H. Orihara, Y. Yamada, N. Yamamoto, Y. Ishibashi, Jpn. J. Appl. Phys. 1989, 28, L849. [50] K. Itoh, M. Kabe, K. Miyachi, Y. Takanishi, K. Ishikawa, H. Takezoe, A. Fukuda, J. Muter. Chem. 1996, 7,407. [51] H. Hatano, Y. Hanakai, H. Furue, H. Uehara, S. Saito, K. Muraoka, Jpn. J. Appl. Phys. 1994, 33, 5498. [52] T. Sako, Y. Kimura, R. Hayakawa, N. Okabe, Y. Suzuki, Jpn. J. Appl. Phys. 1996, 35, L114. 1531 I. Nishiyama, J. W. Goodby, J. Matel: Chem. 1992,2, 1015.
References
69 1
[54] Y. Ouchi, Y. Yoshioka, H. Ishii, K. Seki, M. Kitamura, R. Noyori, Y. Takanishi, I. Nishiyama, J. Muter. Chem. 1995,5,2297. 1551 K. Kondo in Extended Abstracts of 52nd Research Meeting, JSPS 142 Committee of Organic Materials for Information Science (Sub-Committee of Liquid Crystals) 1993, 1 . [56] S. Inui, Ph. D. Thesis, SaitamaUniversity, 1995, p. 1 (in Japanese). [57] Y. Aoki, H. Nohira, Liq. Cryst. 1995, 18, 197. [58] Y. Aoki, H. Nohira, Liq. Cryst. 1995, 19, 15. [59] Y. Aoki, H. Nohira, Ferroelectrics 1996, 178. 213. [60] K. Itoh, M. Takeda, M. Namekawa, S. Nayuki, Y. Murayama, T. Yamazaki, T. Kitazume, Chem. Lett. 1995, 641. [61] K. Itoh, M. Takeda, M. Namekawa, Y. Murayama, S. Watanabe, J. Muter. Sci. Lett. 1995, 14. 1002. [62] S.-L. Wu, D.-G. Chen, S.-J. Chen, C.-Y. Wang, J.-T. Shy, G. Hsiue, Mol. Cryst. Liq. Cryst. 1995, 264, 39.
Handbook of Liquid Crystals Edited by D. Demus, J. Goodby, G. W. Gray, H.-W. Spiess, V. Vill Copyright 0 WILEY-VCH Verlag GmbH. 1998
Chapter VII Synthesis and Structural Features Andrew N. Cammidge and Richard J. Bushby
1 General Structural Features The discovery of discotic liquid crystals is generally dated to the work of Chandrasekhar on the hexaesters of benzene [l], although the concept that liquid crystal phases should be formed by disk-like as well as rodlike molecules had already been recognized by DeGennes and others [2]. Structural similarities also exist with the carbonaceous phases, which have been known for some time [3]. The least ordered (usually highest temperature) mesophase formed by disk-like molecules is the nematic ( N D ) phase which is directly comparable to the nematic phase formed by calamitics. The molecules in such a phase have orientational order but no positional order. Examples of N D phases remain rather few, and more common are those phases in which the molecules stack into columns, the columns then being organized on a two-dimensional lattice. In some respects these columnar phases are analogous to the smectic mesophases of calamitic liquid crystals. However, whereas the smectic phases can be thought of as two-dimensional liquids (they have positional order in one dimension and are disordered in the other two), the columnar phases can be thought of as one-dimensional liquids (they have positional order in two dimensions and are disordered in the third). Columnar phases show rich polymesomorphism and they are normally classified at three levels; according to the symmetry of the two-dimensional array, the or-
ientation of the core with respect to the column axis, and (sometimes) the degree of order within the column. The latter criterion has been the subject of a variety of different interpretations. The main types [4] are illustrated in Figure 1 and they are discussed in more detail in Chapter 8 in this volume. Typically, if a compound forms both a D,' phase (rectangular columnar) and a D, phase (hexagonal columnar) the D, phases are found at lower temperatures. It should be noted, however, that exceptions exist. Determination of columnar mesophase structure can often be difficult, since the differences in the X-ray diffraction results can be quite subtle. The archetypal discogenic molecule has a rigid, planar aromatic core with three-, four- or six-fold rotational symmetry, and generally six or more flexible side chains, each more than five atoms. However, exceptions to all these 'rules' are now quite common. Systems are known with low symmetry, a non-planar, non-aromatic core, and with side chains as short as three atoms. We survey here the different classes of discotic mesogens, the methods by which they have been synthesized, and the phase behaviour claimed for each system. Interest in the development of new routes to discotic mesogens has provided a welcome stimulus to a somewhat unfashionable area of organic
'
In this contribution the nomenclature D for a columnar mesophase of disk-like molecules has been used, but the reader should appreciate that D,, D,, D, etc. are the same as Col,, Col,, Colt etc.
694
VII
Synthesis and Structural Features
2 Aromatic Hydrocarbon Cores
Nematic Phase ND
Disordered Columnar Hexagonal Phase Dhd
2.1 Benzene 2.1.1
Common variations in stacking within the columns
Ordered (0)
Disordered (d)
Tilted (t)
Common variations in stacking of the columns
Hexagonal (h)
Rectangular (r)
Oblique (ob)
Figure 1. Schematic diagram illustrating the basis for the classification and nomenclature of the discotic mesophases. For the columnar phases the subscripts are often used in combination with each other. Hence D,, refers to a (two dimensional) rectangular lattice of columns within which the discs are stacked in a disordered manner
synthesis, i.e. of polynuclear aromatic and heterocyclic systems. Quite a lot of what has been developed so far has exploited old, and in some cases very old, chemistry in which the polynuclear core is assembled through some ‘one-off’ condensation process. There is clearly a need to develop rational general synthetic strategies based on modern methods. Undoubtedly more of these will emerge in the next few years.
Esters and Amides
The hexasubstituted benzenes were the first discotic liquid crystals to be reported. Chandrasekhar and coworkers [ 1, 51 prepared a series of hexaesters of hexahydroxybenzene and found that the heptanoyl and octanoyl homologues were liquid crystalline. The synthetic route used, which has been adapted by others to prepare related derivatives, is shown in Scheme 1 . Hexahydroxybenzene [6] is prepared from glyoxal and treated with an acid chloride to give the esters. Yields of the hexaester are improved if an argon atmosphere and/or a partial vacuum is used. Typically, no solvent is used for these reactions. The mesophase behaviour of a range of hexaesters is summarized in Table 1. All derivatives that have been characterized so far form an hexagonal mesophase, but the stability (temperature range) of the mesophase is extremely sensitive to
HC-CHNaO
OH
HO
0
OH OH
ic ROCO$L:
ROC0 OCOR
Scheme 1. Synthesis of the hexaesters of benzene. Reagents: (a) Na,SO,/O,; (b) SnC1,IHCI; (c) RCOCl 14-87% [ 7 ] .
2
Table 1. Transition temperatures for hexaesters
695
Aromatic Hydrocarbon Cores
0
0
OH
(RCOO-) of benzene. R
Phase transitionsa
Refs.
Cr 81 Dh 86 I [I, 5, 81 Cr 82 Dh 84 I [ l , 5, 81 Liquid [71 0C6H I3 CH2OCSHl1 Cr 68 Dh 94 I [71 C2H40C4H9 Cr 30 D, 32 I [71 C3H60C3H7 Cr 43 Dh 44 I [71 [71 CSHIOOCH3 CI' 16 Dh 25 I CH2OC3H7 CrllODh1121 171 CH20C7HlS Cr 74 Dh 94 I [71 Cr 66 Dh 67 I (Cr 69 I) [7,9] CH2SCSHI I C2H4SC4H9 Cr 101 I PI C3H6SC3H7 ? 53 D 57 I [91 CsH,,SCH3 Cr 32 D 37 I [91 CH(Me)C6H13 Liquid 1101 CH,CH(Me)C,H, Cr 96 I [lo1 C,H4CH(Me)C4H, M 96 I I101 M 1021 I101 C3H6CH(Me)C,H, C4H8CH(Me)C,H, Cr 61 M 87 I [I01 [lo1 C,H,,CH(Me)CH, Cr 85 M 87 I C,H,CH(Et)C,H, Cr 60 MI 86 M, 87 I [lo] [lo1 CsH,,CH(Me)C,H, Cr 52 M 75 I C6H I 3 C7HlS
a
Scheme 2. Synthesis of the tetraesters of 1,4-benzoand I ,4-hydro-quinone. Reagents: (a) RCOCl/pyridine reflux 30-60% [lo]; (b) H+ 90-95% [ l 11.
Table 2. Transition temperatures for the tetraesters (RCOO-) of 1,4-benzo- and 1,4-hydroquinone.
Quinones Hydroquinones
H
O
G
o
M, mesophase. HO
/ NHz
heteroatoms in the side chain. The greatest stabilization is found for derivatives bearing a P-oxygen atom in the side chain. If the position of this atom is moved towards or away from the core, either the mesophase stability is drastically reduced or a mesophase is not observed at all [7]. Branched side chains stabilize the mesophase if the branch point is close to the middle, but destabilization is observed as it approaches the core [lo]. Some partially (2,3,5,6-) acylated derivatives of hexahydroxybenzene have also been found to exhibit discotic liquid crystal phases, as have the related tetraesters of 2,3,5,6-tetrahydroxy- 1,4-benzoquinone [ 1 I]. Their synthesis, shown in Scheme 2, is relatively straightforward. 2,3,5,6-Tetrahydroxy- 1,4-benzoquinone [ 121 is acylated with an excess of the acid chloride in refluxing pyridine. Neutral work-up yields the quinone, whereas the hydroquinone is iso-
:
a
R
Phase transitions
Refs
C,H,, C,H,, C6HI3 C7Hl,
Cr55D57I Cr68D70I
[Ill [Ill
Cr 80 D 85 I Cr79D82I
[13, 141 1141
RCOp@
NHCOR
RCOp
/
OCOR
NHCOR
1
Scheme 3. Synthesis of N,N'-dialkanoyl-2,3,5,6-tetrakis(alkanoy1oxy)-1,4-benzene diamines. Reagents: (a) RCOCUpyridine [ 131.
lated from an acidic work-up [ 131. Both sets of compounds, however, have very narrow mesophase ranges (Table 2). Another variation, employed by Matsunaga and coworkers, has been to replace some of the ester linkages of the benzene hexa-alkanoates with amide groups. The most heavily substituted members of this class of compounds, the N,N'-dialkanoyl2,3,5,6-tetrakis(alkanoyloxy)-1,4-benzene diamines (1) [15], are prepared by total acylation of 3,6-diamino-1,2,4,5-tetrahydroxybenzene [ 161 (Scheme 3). The mesophase behaviour of this series is summarized in Table 3. It is immediately apparent that the introduction of the two amide groups stabiliz-
696
VII
Synthesis and Structural Features
A
Table 3. Transition temperatures of N,N'-dialkanoyl2,3,5,6-tetrakis(alkanoyloxy)(1) (RCONH-/RCOO-). 1,4-benzene diamines
C4H9 CSHI I C6H 13
C7H IS C8H17 C9H19
CI,HZl CIIH23 1 3H27
ClSH3,
Cr 134 D, 208 I Cr 71 D, 209 I Cr 64 D, 208 I Cr 75 D, 205 1 Cr 77 D, 200 1 Cr 77 D, 199 1 Cr 81 D, 198 I Cr 89 D, 197 1 Cr 92 D, 189 I Cr 94 D, 190 I
a
"J2&NO2
-
NH2*
R
CHI
CH3
m
b
_c
N
H
CH3
i
CHI NHCOR
NHz
Scheme 5. Synthesis of 1,3,5-trimethylbenzene triamides [19]. Reagents: (a) HN03/H2S0,; (b) Sn/HCI; (c) RCOCUpyridine.
Table 5. Transition temperatures for 1,3,5-trimethylbenzene triamides (RCONH-) (see Scheme 5 for structure). R
Phase transitions [ 191
C3H7 C4H9 CSHI 1 C6H13
I
OH
I OCOR
Scheme 4. Synthesis of benzene 1,3-diamide-2,4diesters [18]. Reagents: (a) NaN02, -2°C [17]; (b) SnCI2/HCI. (c) RCOCl/pyridine.
C7H 15 C9H19
CIOHZI c l lH23
I 3H27
C15H31
Cr 380 D, 410 1 Cr 315 D, 380 1 Cr 300 D, 357 I Cr 257 D, 357 I Cr 239 D, 346 I Cr 200 D? 222 D, 340 I Cr 189 D? 206 Dh 342 1 Cr 185 D? 191 D, 338 I Cr 183 D? 189 D, 342 I Cr 118 D? 182 D, 338 I Cr 120 D? 175 D, 328 I
Table 4. Transition temperatures for benzene 1,3diamide-2,4-diesters (RCONH-/RCOO-) (see Scheme 4 for structure). R
Phase transitions 1181
C6H I3
C7HlS C9H19
CIOHZI C,lH23 13H27 C1SH31
Cr 89 D, 124 I Cr 87 D, 122 1 Cr 90 D, 121 I Cr 93 D, 122 I Cr 95 D, 120 I Cr97Dh1171 Cr 101 D, 114 I Cr 103 D, 114 I
NHCOR
& y y J J L ~ z f f o R
es the discotic mesophase substantially with respect to the parent hexaester. The melting points Of the two sets Of are very Similar for derivatives O f the Same chain length (e.g. for C,H,,CO-, hexaester m.p.
NO2
NO2 RCONH
NHCOR
C
Scheme 6. Synthesis of mixed ester and amide derivatives of benzene [21], Reagents: (a) Sn/HCI; (b) RCOCl/pyridine; (c) HN03 [20].
2
Aromatic Hydrocarbon Cores
697
Table 6. Transition temperatures for mixed ester and amide derivatives of benzene (RCONH-/RCOO-) (see Scheme 6 for structures). Phase transitions [21]
R
A
B
C
144 Dhd 222 I 133 D,, 225 I 129 Dh, 229 I 123 D,, 227 I 109 D,, 226 I 1 1 1 D,, 227 I Cr 107 D,, 225 I Cr 112 D,, 225 I Cr 113 Dh, 218 I
Cr 100 Dh, 241 1 Cr 55 Dh, 238 1 Cr 63 D,, 241 I Cr 49 D,, 242 I Cr 73 D,, 227 I Cr 65 D,, 225 I
Cr 113 D,, 196 I Cr 67 D,, 208 I Cr 88 Dh, 208 I Cr 77 Dh, 208 I Cr 93 Dh, 206 I Cr 92 Dh, 203 I Cr 96 D,, 202 I Cr 101 D,, 203 I Cr 103 Dhd 198 I Cr 103 Dhd 193 I
Cr Cr Cr Cr Cr Cr
C4H9 CSH, 1 C6H13 C7H I S C9H 19
C10H21 CI,H,, 1 3H2?
C15H31
COCl
ClCO
Cr 78 Dh, 224 I Cr 84 Dh, 224 1 Cr 66 D,, 225 I
Table 7. Transition temperatures for N,N',N"-1,3,5benzene tricarboxamides (RCONH -).
CONHR
COCl
RNHCO
CONHR
Scheme 7. Synthesis of N,N',Nf'-l,3,5-benzene tricarboxamides [22]. Reagents: (a) RNHJpyridine.
R
Phase transitionsa [22]
C5Hl I C6H 13
C7H1s C8Hl?
C9H 19
82 "C, bisamide m.p. 75 "C) and the mesophase extension results primarily from an elevation of the clearing points. The mesophase-stabilizing effect of the amide group allows discotic benzene derivatives to be prepared that carry fewer long chains. The syntheses of such materials are shown in Schemes 4-6, and their mesophase properties are given in Tables 4-6. The N,N',N"- 1,3,5-benzene tricarboxamides [22] also form mesophases, but it should be noted that their columnar structure has not been confirmed unambiguously. These compounds are simply synthesized from commercially available 1,3,5benzene tricarbonyl chloride and alkylamines by refluxing in pyridine (Scheme 7). Their thermal behaviour is shown in Table 7. It should be pointed out that other 1,3,5-trisubstituted benzenes have been synthesized and shown to form monotropic mesophases [23].
CIOH2, CI 1H23 c 12H2.5 C13H2? 14H29
CISH31 I 6H33 I 7H35 1 sH37
a
Cr119M206I Cr 99 M 205 I Cr116M208I Cr 102 M 204 I Cr 65 M 215 I Cr 49 M 208 I Cr 72 M 216 I Cr 88 M 212 I Cr 81 M 216 I Cr 61 M 209 1 Cr 88 M 214 I Cr 73 M 205 I Cr87M211I Cr 68 M 206 I
M, mesophase.
2.1.2 Multiynes A widely studied class of discotic benzene derivatives are the multiynes prepared by Praefcke and coworkers [24].Like the structurally similar naphthalenes, these materials are prepared by palladium-catalysed coupling of polybromobenzenes with acetylene derivatives (Scheme 8). Their mesophase behaviour is given in Table 8. The hexakisalkynylbenzenes themselves exhib-
698
VII
Synthesis and Structural Features
Table 8. Transition temperatures for benzene multiynes (see Scheme 8 for structures). X
R
Phase transitions
Refs.
Cr 170 N, 185 Idecomp Cr 124 N, 142 I Cr 98 N, 131 I Cr 80 ND 96 I Cr 109 N, 193 I Cr 170 D >240 Idecomp Cr 246 D >260 Idecomp Cr 171 D 230 N, 250 Idecomp Cr 106 D 285 Idecomp [I-16 D] [I-8 D]
-
%: R
R
I
+ RONa-
Br%Br
Br
Er
/
RO
OR
A Scheme 8. Synthesis of benzene multiynes. Reagents: (a) RC=CH/Pd[O].
Scheme 9. Synthesis of hexakis[(alkoxyphenoxy)methyllbenzenes [28].
it only monotropic mesophases [ 3 ] . Formation of ‘superdisk’ structures such as benzene hexakisphenylacetylenes [24, 251 gives rise to materials that exhibit relatively stable discotic nematic phases. Enlarging the core even further (biphenyl analogues) leads to columnar discotic mesophases [27].
Table 9. Transition temperatures for hexakis[(alkoxyphenoxy )methyl]benzenes (ROCH, -).
2.1.3 Hexakis(a1koxyphenoxymethyl) Derivatives One further class of discotic benzenes comprises the hexakis[(alkoxyphenoxy)methyl] derivatives [28]. These compounds are simply prepared from hexakis(bromomethy1)benzene and an excess of p-alkoxyphenoxide (Scheme 9). The thermal behaviour of these materials is given in Table 9 [28], but it should be noted that the authors were un-
R
Phase transitions [28]
Cr 68 D,, 97 I p-C5H110C6H4Cr 76 D,, 83 I p-C6H I 3°C6H4p - ~ 7 ~ 1 5 ~ ~ 6 ~ Cr 4 67 - D,, 71 I
able to confirm unambiguously the presence of a discotic mesophase and point out that the ‘mesophase’ might be a special type of crystal [28].
2.1.4 Hexakis(alkylsu1fone) Derivatives Finally, a class of benzene derivatives that also form discotic mesophases is the hexa-
2
-
clQ
a
CI
61
Cl
.'"@
Rs+
SR
RS
699
A
S02R
RS4
SR
Aromatic Hydrocarbon Cores
W2R
Scheme 10. Synthesis of hexakis(alkylsu1fone) derivatives of benzene [29]. Reagents: (a) RSNdHMPT 80-95%; (b) m-CPBAICHCI, 60-70%. Scheme 11. Synthesis of naphthalene multiynes. Reagents: (a) RC6H4C=CH/Pd[O]. Table 10. Transition temperatures for hexakis(alky1sulfone) derivatives of benzene (RS02-). R
Phase transitions
Table 11. Transition temperatures for naphthalene multiynes (see Scheme 11 for structures).
Refs.
R C6H 13
C7HE CXH17 C9H19
ClOH2, C11H23
CI2H2S C13H27
C14H29 C15H31
I hH33
I 164 Cr I 138 D, 120 Cr I 134 D, 108 Cr 1 130 D, 87 Cr I 125 D, 77 Cr I 115 D, 65 Cr I 103 D, 45 Cr I 9 0 D, 44 Cr 1 77 D, 42 Cr I 63 D, 49 Cr I 6 9 Cr
kis(alkylsu1fone) derivatives prepared by Praefcke and coworkers [29]. The synthesis (Scheme 10) is straightforward. Hexachlorobenzene is treated with an excess of sodium alkylthiolate, typically in HMPT, to give the hexakis(alky1thio)benzenes. Oxidation with rn-CPBA affords the sulfones. The compounds appear to form relatively disordered hexagonal mesophases [30-321 (Table lo), which show significant supercooling.
2.2 Naphthalene Two general series of naphthalene derivatives are known to give discotic liquid crystal phases, the multiynes [27, 331 and the p-alkoxyphenoxymethyl derivatives [28]. The multiynes are synthesized through
Phase transitions
Cr 121 D, 156 D, -260 Idecomp Cr 69 N, 98 D, 134 D, -245 Idecomp Cr 49 N, 95 D, 159 D, -230 Idecomp Cr 60 N, 112 D, 137 D,, -200 I C9H19 Cr68N,llOI CSHIIO Cr 144 N, -250 Idecomp HC6H4 Cr 240 D >260 dI CSH11C6H4 Cr 122 D >240 dI C8H17C6H4 Cr 75 D >240 dI C,HI,C,H, Cr 58 D -180 N, -230 Idecomp CSHll C~HI, CTHl, C,H,,
Refs. [33] [33] [33] [33] [33l ~331 ~271 ~271 1271 [27]
a palladium-catalysed coupling of hexabromonaphthalene with aryl acetylenes [33] (Scheme 11) and their mesophase behaviour is summarized in Table 11. The multiynes exhibit a rich polymesomorphism and tend to form the relatively rare nematic discotic phase, which may be due to the 'super-disk' structure of the molecules [27,33]. The most striking feature, however, is the reverse phase sequence for the lower homologues in the alkylphenylacetylene series. It should be noted that the related alkylacetylene derivatives do not give any liquid crystal phases. The p-(a1koxyphenoxy)methylnaphthalenes are easily synthesized by a nucleophilic substitution on bromomethylnaphthalenes (prepared by bromination of polymethylnaphthalenes [34]) with p-alkoxyphenoxides [28] (Scheme 12). Their mesophase behaviour is summarized in Table 12 and it can
700
VII
Synthesis and Structural Features
lb
OR
R
O
z
C
W
N
O
R
A
c
O
W
OR
CCOR
R02C
R' = H or CH20PhOR
6R
0
AcO
OAc
OCOR
0
OR
4
Scheme 12. Synthesis of (p-alkoxyphenoxymethyl) derivatives of naphthalene [28]. Reagents: (a) Br2/hv ;
4
(b) NaOC,H,OR/DMF 80°C, 2 h 20-63%.
Table 12. Transition temperatures for [(p-alkoxyphenoxy)methyl]naphthalenes (see Scheme 12 for structures). R C5H,, C,H,:, C7HI5 C,H,, C,H,, C6H13
C7H15
R'
Phase transitions [28]
C5H,,0PhOCH2 Cr 162 D, 164 I C6H130PhOCH, Cr 135 D, 167 I C,H,,OPhOCH, Cr 105 D, 167 I C,H,,OPhOCH, Cr 78 D, 167 I C,H,,0PhOCH2 Cr 62 Dh 165 I H Cr 65 D,, 147 D, 184 I H Cr 79 D,, 92 D:, 138 D, 182 I
be seen that the symmetrical (octa-substituted) derivatives give a single hexagonal mesophase. The unsymmetrical (hepta-substituted) materials, however, are polymesomorphic, with the higher homologue giving two distinct rectangular phases in addition to the high-temperature hexagonal phase.
2.3 Anthracene (Rufigallol) The rufigallol esters occupy an important place in the history of discotic liquid crystals, as they were one of the earliest systems
OAC
RO
0
RO
OR
0
OR
Scheme 13. Synthesis of Anthracene (Rufigallol) based discotic liquid crystals. Reagents: (a) 98% H,S0,/100 "C/2 h [36]; (b) Ac20/trace H,SO,/reflux12 h [36]; (c) pyridinehoil [36]; (d) Hf 1361; (e) RBr/Na,C03/DMF/160"C/16 h [38]; (f) RCOCI/ pyridine - acetonel40 "CI1 h [37].
reported to form a columnar mesophase but to have a nucleus with only C, symmetry [35]. Rufigallol (3) is made in low yield through the acid-catalysed self-condensation of gallic acid (2) [36] and it is normally purified through its hexa-acetate (4). The esters are prepared from the hexaphenol(3) [35, 371, but the ethers are better made directly from the acetate (4) [38]. The syntheses are shown in Scheme 13 and the mesophase behaviour of the products is summarized in Table 13. All the ethers C, to C,, [38] and esters C7 to CI41371 show enantiotropic behaviour, and the esters C, to C, [35, 371 also show monotropic behaviour, a more ordered mesophase being formed when the normal columnar phase is cooled to 108 "C in the case of the heptanoate [37], 99 "C in the case of the octanoate 1351 and 83 "C in the case of the nonanoate [37].
2
Table 13. Transition temperatures of anthracene (rufigallol) based discotic mesogens. Substituent
Phase transitions a
Cr 105 Dh 131 I 1381 Cr 83 D, 117 I [381 Cr 53 Dh 105 1 [381 C7HlS0 Cr 49 D, 102 I [381 C8H170 Cr 37 D, 96 I [381 C9H190 Cr 32 Dh 92 I [381 c IOH2lO Cr 48 D, 87 I [381 Cr 26 D, 84 I [381 CI I H2,O C12H250 Cr 37 Dh 79 1 [381 C13H270 Cr 62 D, 72 I 1381 C3H7CO2 Cr 216 I I371 C4H9C02 Cr 170 I [371 CSHl lc02 Cr 152 I [371 C6H I 3c02 Cr 112 M b 134 I [371 C,HlsC02 Cr 110 (108) M C133 (128) I [37 (35)] C8H17C02 Cr 81 M d 128 I [371 C9H 19c02 Cr 109 M 128 I [371 c lOH21CO2 Cr 92 126 I [371 c l 1H23C02 Cr 99 M 124 I 1371 I 2H25C02 Cr 96 M 120 I 1371 13H27C02 Cr 103 M 117 I [371 a
Me0 OMe
-
OMe
Refs.
C4H9O CSHIIO C6H I3O
M, mesophase. Gives a different mesophase on cooling to 108 "C. Gives a different mesophase on cooling to 99 "C. Gives a different mesophase on cooling to 83 "C.
M
e
0
8
H
OMe
MeO
d
HO
OH
(OH)
(OW
RCO,
O OMe Z
-
\
/=\
PCOR
RCO*p+&
)"
RC02
"(OCOR
Scheme 14. Synthesis of phenanthrene based discogens [39]. Reagents: (a) LiOMe/MeOH; (b) 12/hv; (c) BBr,; (d) DCCI/DMAP/RCOOH.
Table 14. Transition temperatures for phenanthrene based discotic mesogens (see Scheme 14 for structures). R
R'
Phase transitions (391
H H RC02RC02-
D51 I D 75 I Cr 76 I Cr -13 D 145 I
2.4 Phenanthrene Discotic phenanthrene derivatives have been prepared by Scherowsky and Chen [39]. Their synthesis is illustrated in Scheme 14. The phosphonium salt prepared by bromination of trimethoxybenzyl alcohol and reaction of the benzyl bromide with triphenyl phosphine was deprotonated and a Wittig reaction with 2,4-dimethoxyor 2,3,4-trimethoxybenzaldehydeproduced the stilbene. Photocyclization gives the phenanthrene, which can be demethylated with boron tribromide and acylated using the Steglich method. The mesophase behaviour of discotic phenanthrenes is given in Table 14. It was
70 I
Aromatic Hydrocarbon Cores
~~
C,H,,OCH*(CH3) C6H,3CH*(CH3)0CH,C7HI5OCH*(CH,)C6H13CH*(CH,)OCH,-
~
found that straight-chain esters of hexahydroxyphenanthrene gave only narrow, monotropic mesophases. Enantiotropic mesophases were formed for branchedchain penta- and hexaesters. A helical 'Dr' mesophase structure is proposed for these chiral derivatives, which show electrooptic switching.
702
Synthesis and Structural Features
VII
2.5 Triphenylene The hexasubstituted derivatives of triphenylene were among the first discotic mesogens to be discovered. The most commonly studied derivatives are the hexaethers and hexaesters of 2,3,6,7,10,1 l-hexahydroxytriphenylene, and their basic synthesis is illustrated in Scheme 15.1,2-Dimethoxybenzene (veratrole) is oxidatively trimerized using chloranil in concentrated sulfuric acid to give hexamethoxytriphenylene [40]. The reaction takes about a week. Demethylation with boron tribromide [41] or hydrobromic acid [42] yields the hexaphenol,
a
-
CH3O
Ib RC02 OCOR OCOR
OH
b(R=CH3)
o JR (
' OR
e,f
which is then alkylated or acylated to give the required mesogen. Alternatively, treatment of the hexamethoxy compound with trimethylsilyl iodide gives the hexatrimethylsilyloxy derivative, which can be alkylated or acylated directly [43]. Under the chloranil/concentrated sulfuric acid conditions, longer chain 1,2-dialkoxybenzene derivatives also undergo oxidative trimerization to give the required hexaethers directly, but the products are heavily contaminated with impurities [44] (mainly dealkylation products) which are difficult to remove so that, in general, the three-step procedure has been preferred. An improved synthesis of hexaalkoxytriphenylenes has been developed more recently in our laboratories [45], allowing dialkoxybenzenes to be converted directly to the corresponding triphenylene in a single high-yielding step using ferric chloride as the oxidizing agent. The reaction is typically carried out in dichloromethane solution, is complete in about an hour, and is worked up reductively with methanol. Alternative oxidizing agents used for the synthesis of related triphenylenes include ferric chloride/sulfuric acid [46] and electrosynthesis [47]. Indeed, it was in these electrochemical syntheses that the advantages of and the need for reductive work-up procedures was first recognized 1481.
2.5.1 Ethers, Thioethers and Selenoethers
''
Ro@R RO
OR
OR
Scheme 15. Synthesis of ethers and esters of triphenylene. Reagents: (a) chloranil/70% H, S04/73% [46]; (b) 48% HBr/HOAc/reflux/lS h [42]; (c) RBrlbase [49, 501; (d) RCOCl/base [49, 501; (e) FeCI,/CH,CI, [45]; (f) MeOH/86% (R=CH,) 73% (R=C6H1,)two steps [45].
The mesophase behaviour of simple symmetrical hexaether derivatives of triphenylene is summarized in Table 15. A11 derivatives with side-chains longer than propyloxy form a single hexagonal mesophase, with both the transition temperatures and the mesophase range decreasing as the length of the side chain is increased. The corresponding thioethers and selenoethers are made
2
703
Aromatic Hydrocarbon Cores
Table 15. Transition temperatures for ethers of triphenylene. Phase transitions
Refs.
/
Cr 177 I [44,45,50] Cr 89 Dh, 146 I [44,45, 501 Cr 69 Dh, 122 1 [44, 50, 5 11 Cr 68 Dh, 97 (100) 1 [43, 44, 50 (45)l [43, 44, 501 Cr 69 D,, 93 I [44, 45, 501 Cr 67 Dh, 86 I Cr 57 D,, 78 I [44, 45, 501 Cr 58 Dh, 69 I [44, 501 Cr 54 Dh, 66 1 [43,44, 501 Dh, 49 I ~44,501
Scheme 16. Synthesis of thioethers and selenoethers of triphenylene. Reagents: (a) FeCl, 1531; (b) hv/I,
from the reaction of hexabromotriphenylene [52] and the requisite nucleophile. As shown in Scheme 16, the hexabromide is readily obtained from triphenylene itself. Unfortunately, this is an expensive starting material and troublesome to make on any scale. Of the several routes available [57] perhaps the most convenient for a smallscale laboratory preparation is the ferric chloride oxidative cyclization of o-terphenyl [53], a relatively cheap starting material. Transition temperatures for the thioethers and selenoethers are summarized in Table 16. Interest in the ether derivatives arises from the fact that they are photoconductive and that, when doped with a few mol per cent of an oxidant such as aluminium trichloride, they become semiconductors [59]. Oriented samples of the D, phase can be produced, and it is found that the preferred direction of conduction is parallel to the director; the system behaves rather like a molecular wire, with the conducting stack of aromatic cores being surrounded by an insulating sheath of alkyl chains. The hexahexylthioether derivative gives a 'helical' ordered columnar phase at low temperatures 158, 601, which shows remarkably high charge-carrier mobility in experiments in
[54]; (c) Br2/Fe/C,H,N02/reflux/2 h, [ 5 2 ] ; (d) RSNa/DMEU/10O0C/1-2 h, 40-55% [55]; (e), (i) RSeNa/HMPA/2 h/80"C, (ii) RBr/15 h/60 "C, 38-55% [56].
Table 16. Transition temperatures for thioethers and selenoethers of triphenylene. Substituent
Phase transitions
Refs.
which the charge carriers are generated photochemically [61].
2.5.2 Esters The mesophase behaviour of the discotic triphenylenehexakisalkanoatesis summarized in Table 17. Simple, straight-chain derivatives tend to form a rectangular mesophase with the higher homologues also forming a hexagonal phase at higher temperatures. Melting and clearing temperatures do not alter significantly through the series. The effect of heteroatom substitution into the side
704
VII
Synthesis and Structural Features
chain depends on its nature [9] (oxygen or sulfur) and position [9, 641, and it is worth noting that mesophase behaviour is destroyed if a bromine atom is present in the side chain [65]. The hexabenzoate esters of triphenylene have received particular attention because they tend to form nematic phases. Their mesophase behaviour is summarized in Table 18. Increasing the chain length of the p-alkyl or p-alkoxy substituent in the benzene ring tends to reduce the transition temperatures slightly, but more pronounced effects are observed when lateral (ortho or meta) methyl substituents are introduced into the benzene rings. The number and position of these additional methyl groups influences both the transition temperatures and the phase sequence [68, 691. The corresponding cyclohexane carboxylates (in which the benzene ring is formally reduced
to a trans-l,4-disubstituted cyclohexane) show wider mesophase ranges and they exhibit mesophase behaviour with shorter alkyl chain substituents. This is illustrated in Table 19 [51, 701.
2.5.3 Multiynes As shown in Scheme 17, palladium catalysed cross-coupling of hexabromotriphenylene [52] and p-alkyl derivatives of phenylacetylene gives liquid crystalline hexaalkynyl derivatives of triphenylene [24]. These discogens, which have a core diameter of about 2.4 nm, give enantiotropic nematic phases only (7:R = C,H, Cr 157 N D 237 I; R=C7HI5,Cr 122 N D 176 I). Straightchain alkylacetylene derivatives (like 7,but without the benzene rings) are not liquid crystalline [24].
Table 17. Transition temperatures of esters of triphenylene Substituent
Phase transitions
Cr 146 I Cr I08 D, 120 I Cr 64 D, 130 I (Cr 66 D 126 I) Cr 62 (66) D, 125 (129) I Cr 75 (65) D, 126 I Cr 67 Dra 108 D, 122 I Cr 80 D? 93 D, 1 1 1 D, 122 I Cr 83 Drb 99 D, 118 I Cr 87 D, 96 D, 11 1 I Cr 59 D 65 D,97 I Cr 75 D 138 I Cr 86 D 198 I Cr 57 D 202 I D, 203 I Cr 98 I Cr 94 I Cr -14 Dh 227 1 Cr ? D 93 I Cr ? Dh 156 I a
Gives another columnar phase on cooling to 56 "C. Gives another columnar phase on cooling to 81 "C.
Refs.
2
705
Aromatic Hydrocarbon Cores
Table 18. Transition temperatures for benzoate esters of triphenylene of the general type 5.
C
X
5 X
A-D
Phase transitions
A-D=H A-D=H
Cr 210 I (Cr 130 D 210 I) Cr 208 N, 210 I (Cr 179 N, 192 I) [Cr 125 D, 179 D, 222 I] Cr 175 D, 183 N, 192 I Cr 185 D, 189 I Cr 257 N, 300 I Cr 224 N, 298 I Cr 186 D, 193 N, 274 I Cr 168 N, 2.53 I (Cr 142 N, 248 I) Cr 152 D, 168 N, 244 I Cr 154 D, 183 (180) N, 227 (222) I [Cr 147 D, 182 D2 230 I] Cr 142 D, 191 (155) N, 212 (177) I Cr 145 D, 179 N, 18.5 I Cr 146 D, 174 I <25 D 300 I Cr 109 ND 164 I ? 129 N, 170 I Cr 150 Dhd 210 N, 243 I Cr 170 Dhd 195 ND 215 1 Cr 157 Dhd 167 ND 182 I 143 N, 1.51 I Cr 125 Dh 156 ND 183 I Cr 170 N, 196 I Cr 155 N, 170 I Cr 108 ND134 I Cr 88 N, 99 I Cr 161 I
A-D=H A-D=H A-D=H A-D=H A-D=H A-D=H A-D=H A-D=H A-D=H A-D=H A-D=H A-D=F A=CH,; B - D = H A, B, D=H; C=CH3 A, D=H; B, C=CH3 A, D=H; B, C=CH3 A, D = H ; B, C=CH, A, D = H ; B, C=CH3 A, D = H ; B, C=CH, A, D=CH,; B, C = H A, D=CH3; B, C = H A, D=CH,; B, C = H A, D=CH,; B, C = H A, D=CH,; B, C = H
2.5.4 Unsymmetrically Substituted Derivatives Unsymmetrically substituted derivatives of triphenylene have been prepared both by
Refs.
‘statistical’ and ‘rational’ routes. An obvious ‘statistical’ approach to the problem is illustrated in Scheme 18. Oxidative trimerization of a mixture of two different 1,2-dialkoxy derivatives of benzene gives a mixture of all four possible triphenylene prod-
706
VII
Synthesis and Structural Features
Table 19. Transition temperatures for cyclohexanoate esters of triphenylene of the type 6 .
6
A
R C5HIl
C6H13 C7H1S
C,H,,,
Phase transitions Cr Cr Cr Cr 108 D,,
Refs.
158 D,, 300 1 [701 146 D,, 240 I ~701 150 D,, 255 I ~701 245 I (c25 D >345 I) [70 (51)1
ucts [45, 50, 711. If the two reactants are used in equal proportions the ratio of these products is almost exactly statistical, and often the mixture is very difficult to separate, although in the case of electro-oxidations it is possible to manipulate the product ratio to some extent by varying the reaction conditions [72]. In other cases it may be advantagous to use one reactant in excess, or favourable solubility properties may mean
that separation can be achieved fairly easily [45]. An alternative 'statistical' strategy that has been successfully exploited is that of partial alkylation of the hexa-acetate of triphenylene, as shown in Scheme 19 [41]. The reaction gives a mixture of hexa-alkoxy, penta-alkoxy, tetra-alkoxy, etc., derivatives, but the penta-alkoxy derivative can be isolated in low yield. Hydrolysis and acylation or alkylation of the product has led to a series of penta-alkoxymonoacyloxy and unsymmetrical hexa-alkoxy derivatives. The introduction of a single ester (particularly a branched ester) side chain increases the clearing temperatures, but more notably it surpresses crystallization such that these systems readily form glasses [41, 731. The simplest and most straightforward of the 'rational' syntheses is the oxidative coupling of a tetra-alkoxybiphenyl and a 1,2-dialkoxybenzene derivative (74 - 761 using the ferric chloride/methanol work up protocol shown in Scheme 20. The reaction is easy to perform, offers a good degree of regiocontrol, and has been adapted to yield products in which both the number and nature of the substituents have been varied. Through this reaction a variety of different ring substitution patterns has also been produced [75]. The biphenyl derivatives required for these phenylhiphenyl coupling
6 R
a
Br Br
R 7
Scheme 17. Synthesis of multiyne derivatives of triphenylene [24]. Reagents: (a) RC6H,C = CH/Pd(PPh,),Cl,/PPh,/Cu(l)/ 1OO0C/38h, 52-5770.
2
-
RO R
OAc
\
O\
‘
RO \ RO@
g
\ \
OR
707
Scheme 18. ‘Statistical’ route to unsymmetrically substituted derivatives of triphenylene. Reagents: (a) electrochemical, FeCl,, or chloranil oxidation.
OR2
OR2
Aromatic Hydrocarbon Cores
OR
OR
OR
Scheme 19. ‘Statistical’ synthesis
+ isomeric diacetates
OR OR
gR‘ -
OR‘
OR’
a,b
/ \
OR’
OR2
of unsymmetrically substituted derivatives of triphenylene [41]. Reagents: (a) RBr/K,CO,/ PhCOMe/l16”C/17 h, 26% monoacetate.
R
.
~ 3 \ 0
0
8
R2
\
\
OR2
OR‘
reactions can be prepared either through Ullman or Heck coupling reactions, and the only significant limitation on this strategy arises from a lack of regiospecificity in the coupling step itself, such that, if neither the phenyl nor the biphenyl component has C2 symmetry, a mixture of regioisomers will result. Longer and more elaborate strategies [77,78] have been developed that allow full regiocontrol. In these, ‘Heck’ chemistry is
Scheme 20. ‘Rational’ synthesis of unsymmetrically substituted derivatives of triphenylene [74-761. Reagents: (a) FeCI,/CH,Cl,; (b) MeOH
used to assemble a terphenyl, which is then subjected to oxidative cyclization to yield the triphenylene. One of these routes is illustrated in Scheme 21 [78]. A third, and even longer, route to unsymmetrically substituted triphenylenes was originally developed by Wenz in his synthesis of discotic liquid crystalline polymers [79- 821, but has since been adapted for the synthesis of low molar mass discogens [83]. Scheme 22 il-
708
VII
Synthesis and Structural Features
F O R 2 OR'
OR'
R
5
0
4 R3
b
R60
~50%
R60
'
OR'
\
Scheme 21. 'Rational' route to unsymmetrically substituted derivatives of triphenylene [78]. Reagents: (a) Pd,(dba),/Ph,P/THF/ \
0
OR'
OR'
~
2
reflux/4.5 h, 45%; (b) FeC1,/CH,Cl2/1 h, then MeOH (dba = dibenzylidine acetone, THF = tetrahydrofuran).
Scheme 22. 'Rational' synthesis OC5H11
C
~
C4Hg02C
H
~
Ol 1
~
___)
C
~
' 'I \
OC5H11 OC5H11
lustrates its use in the synthesis of the diester 8, which gives a columnar phase (Dhd) between room temperature and 167 "C and shows very interesting self-organizing behaviour at the phase-interfaces [83 1861. Transition data for unsymmetrically substituted systems are given in Table 21.
8
OCSH1 OC5H11
of unsymmetrically substituted derivatives of triphenylene [79, 831. Reagents: (a) CH,COCH,/'BuOK/EtOHI reflux/4 h; (b) TsOH/C6H,C1/C,H,O2CC = CC0&4H,; (c) 12lhv.
2.5.5 Modifications of the Number and Nature of Ring Substituents Reactions have now been developed that allow the properties of triphenylene hexaeth-
709
2 Aromatic Hydrocarbon Cores
Table 21. Transition temperatures for unsymetrically substituted derivatives of triphenylene of the type 9.
R20
'' '
OR^
OR^
9 R'
R2
R3
R4
Phase transitions
Refs.
Cr 72 Dh 101 1 Cr 55 D, 106 I Cr? D,, 161 1 Cr 44 D,, 177 I D,, 182 I D,, 182 I D,, 191 1 Cr 56 Dh127 I Cr 60 Dh 104 I Cr 51 D, 100 I Cr 32 D,, 55 1 Cr 67 Ia Cr 53 D 72 I Cr 50 D,, 117 I Cr 80 I Cr 54 D,, 74 1 Cr 61 D,, 63 I Cr 61 Cr 128 Dh 139 1 Cr 68 I b Cr 47 Dho 84 1 Cr 47 D, 84 I Cr 51 D 61 I Cr 53 D,, 71 I Cr 56 I Cr 87 D, 99 D, 118 I Cr 65 I' a
Gives D,, phase on cooling to 51 "C. Gives D, phase on cooling to 64 "C. Gives D phase on cooling to 55 "C.
er discogens to be modified either by introducing extra substituents into the aromatic nucleus through electrophilic aromatic substitution or by removing some of the alkoxy groups through selective reduction. The outcome of electrophilic substitution reactions on the unsubstituted hydrocarbon triphenylene seems to be determined by a conflict between electronic effects that favour a attack and steric factors (involving mainly the
interaction with the peri hydrogen atoms) that favour P attack, but normally P attack dominates. In those mesogens in which all the P-positions bear substituents steric crowding must be severe, but the systems can be readily nitrated, chlorinated and brominated [92 -941. The introduction of the nitro substituent is a particularly valuable step since, as shown in Scheme 23, it can be readily transformed into a wide range
710
VII
Synthesis and Structural Features
Table 26. Transition temperatures for hepta-substituted derivatives of triphenylene of the type 11. RO
C6H130@
L
OC6H 1 3 l3
OR
OR
%HI30 \
OC6H13 OC6H13 11
X
if
\ OR
OR
OR
Scheme 23. Modification of the substituents through electrophilic substitution. Reagents: (a) HNO,/Et,O/ AcOH/15 min, 73% 1921; (b) Sn/AcOH/reflux/4 h, 87% 1921; (c) NaNO,/AcOH [94]; (d) KN,, 58% [94]; (e) NaNO,/AcOH, 45%, [92]; (f) R'COCl/K,CO,/ CH,C1,/18 h, 95% (R=Me) 1921.
of other substituents and many of the products show enhanced mesophase properties as detailed in Table 26. Note also those compounds, shown in Scheme 24, that are not themselves mesomorphic but which give mesomorphic nitro derivatives ( e g 12-14, the second and third of which are readily available through variations on the 'biphenyl' route shown in Scheme 20) [93]. Hence 12 shows Cr 96 I, but its nitration product gives a columnar phase on cooling to 88 "C. Compound 13 shows Cr 83 I and its nitration product Cr 81 I, but gives a columnar phase on cooling to 64°C. Compound 14 shows Cr 70 I and gives a columnar phase on cooling to 60 "C, but its nitra-
NO, NH, N, NHCOCH, NHCOC,H, NHCOC3H7 NHCOC,H, NHCOCSH, 1 NHCOC,HI, NHCOC7HIs NHCOCSHI, NHCOC,H,, NHCOC 1 1 H,,
c1
CHZOH
Phase transitions
Refs.
<25 D 136 I Cr 35 D 77 I C r 7 0 D 1181 Cr 99 D 162 I Cr 104 D 167 I Cr 98 D 176 I Cr 103 D 186 I Cr 96 D 186 I Cr 90 D 191 I Cr 90 D 191 I Cr 84 D 192 I Cr 78 D 190 I Cr 68 D 181 I Cr 37 D 98 I Cr 70 I
I921 I921 1931
tion product shows Cr 45 D 89 I. Another important development has been the introduction of the 'reductive removal of substituents' by the group of Ringsdorf [90, 951. An example of this route is shown in Scheme 25. After selective removal of the methoxy methyl group [96], tetrazenyl hydrogenolysis is used to remove the hydroxyl group [97]. The p-sites 'exposed' in this way also provide convenient entry points for the introduction of functionality into the triphenylene nucleus through electrophilic substitution reactions. In the example shown the sites are brominated, but there are other obvious possibilities. Whereas 15 is not mesomorphic (m.p. 86 "C), the bromide 16 is liquid crystalline (D, 19 Dh 165 I). In a similar manner it has proved possible to prepare a symmetrical triphenylene with three alkoxy chains (2,6,10-trispentyloxytriphenylene). This is also non-mesomor-
2 Aromatic Hydrocarbon Cores
711
12
13
k6H13
C6H130
14
OCeH13
Scheme 24. Nitration reactions leading to enhanced mesophase behaviour [93].
Scheme 25. Selective removal of methoxy substituents [95]. Reagents: (a) FeC13/CHzClz;(b) MeOH: (c) Ph,PLi/THF; (d) 5-chloro-l-phenyltetrazine/ KzC03/CH,COCH3/reflux/18 h; ( e ) Pd/C/H,/THFbenzene/40 W 2 4 h, 80% (two steps); (f) Br,/CH,CI2, 92-98%.
712
VII
Synthesis and Structural Features
phic (m.p. 95"C), but bromination gives 3,7,1 I-tribrom0-2,6,IO-trispentyloxytriphenylene which is mesogenic (Cr 189 D, 217 I) [95].Although these substitution and dealkoxylation routes have been developed (but perhaps not yet fully exploited) for triphenylene-based liquid crystals, they are also applicable to some of the other classes of mesogen described in this chapter.
produce hexamethoxydibenzopyrene- 1 3 quinone [98]as the key intermediate. Reduction followed by acylation affords the chiral octaester (18), the mesophase structure of which was deduced to be tilted columnar after demonstration of its ferroelectric switching in an applied electric field [63]. The basic synthesis has also been modified to produce a discotic octapentyl derivative, which forms an hexagonal mesophase ~71.
2.6 Dibenzopyrene Derivatives of 1,2,5,6,8,9,12,13-octahydroxydibenzo-[e, 11-pyrene (17) giving discotic mesophases were discovered by Bock and Helfrich [63] in their search for ferroelectrically switchable columnar mesogens. The synthesis (Scheme 26) involved modification of a known literature procedure to
2.7
Perylene
Discotic derivatives of perylene have been prepared by Mullen and coworkers [99]. The discotic mesophase behaviour of these highly fluorescent materials is quite unusual because the molecules have low symme-
OR
OR RO a
RO
OR
RO
OR
_c
-
COR'
a
RO
OR
OR
1
R = CH, or CsH,,
borc
OR
R = CsHtt g l w -35Dh98 I [an
CHI R' =CeH13 / I f c r w
0
D,124 ~[cq
Scheme 26. Synthesis of dibenzopyrene based discogens. Reagents: (a) chloranil/H,S0,1CH,C02H 6 0 T , 24 h, 51% [87]; (b) Na2S20, [98]; (c) Zn [87]; (d) BBr,; (e) R'COX; (f) C,H,,Br/KOH; (8) C,H, ,Br/K2C0,.
R
Scheme 27. Synthesis of perylene based discogens [99]. Reagents: (a) R'COCI; (b) NH,NH,. HCl/base; (c) Br,; (d) BuLi, -78°C; (e) B(0-'Pr),; (f) H,O; (g) Pd(O)/PPh,/K,CO,/toluene,reflux; (h) KIDME; (i) xylene, reflux.
2 Aromatic Hydrocarbon Cores
Table 30. Transition temperatures for perylene based discotic mesogens (see Scheme 27 for structures). R
R”
Phase transitions [99]
C18H37
C5H11
C18H37
C17H35
Ci2H’25
C11H35
CSHI 1
C17H35
1
1
C12H25
C17H35
C5Hl
Cr 69 D 261 I Cr 45 D,, 305 I Cr -20 D,, 373 I Cr 85 D 200 I Cr 27 D 319 I Cr 15 D,, 316 I
713
that contain perylene (R) and amide (R”) side chains of approximately equal lengths. When the molecular shape approximates to a disk the hexagonal (Dh) mesophase is produced, but deviations from this structure occur when there is a mismatch of sidechain lengths.
2.8 Truxene try. The synthesis is outlined in Scheme 27 with the key features being the efficient synthesis of 3,10-dialkylperylenes (19) [ 1001 and their smooth double Diels -Alder reaction with 4-alkyl-3,5-dioxotriazoles. The mesophase behaviour of the discotic perylenes is summarized in Table 30. It is apparent immediately that the columnar phase of these perylene derivatives is remarkably stable, with the largest temperature range being observed for the materials
The hexaesters of truxene 23 [101, 1021 show a fascinating variety of phases, including nematic N, phases, but unfortunately they are not very easy to synthesize. The synthesis used is based on the self-condensation of indanone brought about by treatment with ethyl polyphosphate [ 1031 (Scheme 28). When the reaction is applied to the dimethoxy analogue 20 it generates a mixture of the desired trimeric truxene 22
21
20
b
22
/ RCOp
OH
23
Scheme 28. Synthesis of derivatives of truxene [ 1051.Reagents: (a) PPEICHCl, -EtOH/reflux, 66%; (b) BBr, . Me2S/ C1CH2CH2Cl/reflux/72 h, 86%; (c) RCOCl/pyridine DMAP/48 h, 86% (Cid
714
VII
Synthesis and Structural Features
Table 31. Transition temperatures for derivatives of truxene. Substituent C6Hl 3c02
C7HlSC02
C8H17C02 C9H19C02
CIOH2 IC02 1 I H,3C02
c 12H25C02 C13H'27C02 C14H29C02
ClsH3 1 co2 c l lH230C6H4C02 12H2S0C6H,C02
a
g
Phase transitions
Refs.
Cr 112 D, (Drd)a 138 Dh (DhJ 280 I Cr 98 D, (D,d)' 140 (158) Dh (Dh,,) 280 1 Cr 88 DrC141 Dh (Dho)280 I Cr 68 N, 85 D, (Drd) 138 D, (Dho) 280 I Cr 62 N D 89 D, (Drd) 118 D, 250 (277) I Cr 64 N, 84 D, (Drd) 130 Dh 250 (253) 1 Cr 57 N D 84 ~ D, (Drd) 107 (1 12) D, (Dhd) 249 (246) I Cr 58 (61) NDe 83 Dh (Drd 112 Dho) 235 (241) 1 [Cr 61 ND 84 D,, 112 D,, 241 I] Cr 64 N D 82 ~ D,d 95 Dh, (Dhd) 241 (221) 1 Cr 69 NDg 84 D,, 95 Dhd210 I Cr 90 D,d 137 ND 171 (179) D,.d 284 ND 297 I Cr 90 N, 173 D,, 260 ND >297 I
[lo1 (104)l [lo1 (104)l [lo1 (104)l [lo1 (104)] [I01 (104)] [lo1 (104)l [I01 (104)l [lo1 (104)l [106, 1071 [I08 (104)] [104, 1081 [lo9 (105, 106)l [105, 1061
Gives N, on cooling to 96 "C. Gives N, on cooling to 85 "C. Gives N, on cooling to 87 "C. Gives Dhd on cooling to 53 OC. Gives D,, on cooling to 56 "C. Gives Dhd on cooling to 56 OC (58 OC). Gives Dhdon cooling to 62 "C. Gives D, on cooling to 79 "C.
and the dimeric indanylindanone 21. The original paper by Tinh et al. [ 1041 gives no clues as to how this rather intractable mixture should be treated. However, more recently, a detailed experimental procedure has been provided by Lee et al. [105]. The trimer is so insoluble that it cannot be purified by recrystallization or chromatography, but it can be freed of the dimer and most other impurities simply by washing with solvent. Lee et al. then recommend demethylation using boron tribromide - dimethyl sulfide complex and the use of 4-dimethylaminopyridine (DMAP) to catalyse the esterification. The shorter chain-length esters (C, to C,) give D, and D, phases and a monotropic N, phase is produced on cooling the D, phase. The longer chain-length esters give enantiotropic N,, Dh and, up to C1,, D, phases (Table 31). The alkoxybenzoate esters give re-entrant N, and D,, phases [l05, 1091, and a mixture of 13% dodecyloxybenzoate and 87% tetradecanoate shows a re-entrant isotropic phase
(Cr 67 N, 112 I 129 D,, 214 I) [106], although there has been some disagreement in the literature over the nature of the D,, phase [105].
2.9
Decacyclene
The decacyclene derivatives 24a and 24b are unusual in that they have only three side chains. They are readily synthesized by a direct Friedel - Crafts acylation of the parent hydrocarbon, a reaction claimed to proceed with very good regioselectivity (Scheme 29). Both compounds show a high tendency to aggregate, even in dilute solution, and both give two mesophases which are stable over a wide temperature range (24a, heating, Cr 92.8M1 115 M, 262 I; 24b, heating, Cr 98 M, 108.5 M, 240.5 I). Hysteresis is observed on cooling. Reduction of the keto groups to methylene groups gives non-mesomorphic products [ 1101.
2 Aromatic Hydrocarbon Cores
RCO
715
Scheme 29. Synthesis of derivatives of decacyclene. Reagents: (a) RCOCI/AlCI,/CICHzCHzCl/reflux, 38% (24).
CH30DCH20H b
CH3O
)$
CH3O H HO
O
T
OCH3 27
\ / HO
OH
1
f or g or i RO
RC02 OCOR
2.10 Tribenzocyclononatriene The tribenzocyclononatriene nucleus has three-fold symmetry and adopts a shallow cone-shaped conformation. Consequently,
OR
Scheme 30. Synthesis of tribenzocyclononatriene based discotic mesogens. Reagents: (a) AcOH/1% H,SO,/ 1OO0C/15min, 87% [114, 118, 1191; (b)70% HzSO,/O"C [118, 119, 1241; (c) CHzO/HCI [118, 119, 1241; (d) BBr3/CHCl3 or C,H,/reflux, 85% [ 1241; (e) pyridine hydrochloride [120]; (f) RCOC1/185 "C, 58% (Ci3) [ I 111; (g) RCOCVO "C/24 h, 67% (C15)[ I 111; (h) RBr/K,CO,/DMF/refluxl24 h [ l 1 11; (i) RCO,H/DCCI/ DMAP [120]; (j) RBrlK,CO,/i-BuCOCH,/reflux/6 days [114]; (k) 37% HCl/room temp. 3 h, 60 "C 5 h, 20% [120].
it has been suggested that the liquid crystalline materials based on this nucleus should be termed 'pyramidic' rather than discotic [ 1111. As a result of this particular conformation the molecule has a net dipole along its C3 axis, and this has the interesting consequence that the columnar phases in which
716
VII
Synthesis and Structural Features
Table 32. Transition temperatures for derivatives of tribenzocyclononatriene. Substituent CH,O C4H9O C5Hl10 C6H 13O
C7H150
CXHI7O C9H 190 ClOH21O c l IHZ3O
C12H250
C,H,C02 C7H I Sc02
CXH,
7c02
C9H19C02
ClOH2IC02 c 1 1H23CO2 IZH2SCo2
CI 3H27C02
c l,H29CO2 I 5H3 1c02
C7H1SC6H4C02 C8H17C6H4C02
C10H21C6H4C02 C10H210C6H4C02 C12H250C6H4C02 a
Phase transitions
Refs.
Cr 232 I Cr 136 Ia Cr 104 I b Cr 41 D, 92 I Cr 25 D, 80 I Cr 25 D, 72 I Cr 19 D, 66 I Cr 26 D, 63 I Cr 35 D2 44 D, 62 I Cr 48 DI 62 I Cr 197 I Cr 5 D,153 I (Cr 150 I) Cr 24 D4 153 I Cr 33 (50) D, 146 (145) I Cr 32 D5 39 D, 132 D, 141 I Cr 59 (55) D4 119 (116) D, 141 (138) I Cr 67 D, 100 D, 139 I Cr 73 D, 81 D3 136 I Cr 81 D, 135 I Cr 80 D, 129 I Cr 33 D, 57 D7 149 I Cr 12 D, 21 D7 I57 I D, 43 D7 I62 I Cr 51 D, 100 D7 190 I Cr <25 MI 75 M, 188 I
Gives D, on cooling to 127°C.
' Gives D, on cooling to 96 "C.
these molecules are stacked one on top of the other are potentially ferroelectric or antiferroelectric [ 112, 1131. However, the situation is complicated by the fact that the cone can be inverted quite easily. At the temperatures at which the mesophases are formed this inversion is rapid for isolated molecules in isotropic solution, but it is somewhat slower in the mesophase itself. This is presumably because of the need for cooperative behaviour in the latter case [ 113, 1141. The basic reaction through which this nucleus is made (Scheme 30), the acid catalysed condensation of veratrole and formaldehyde, has a long and complicated history. Working in the 1920s, Robinson identified the product as the dimer (a dihydroanthracene) [ 1151. Once this structure had been disproved, a hexameric structure was pro-
posed [116, 1171. This also proved to be false. Using more modern analytical techniques, Lindsey [ 118, 1 1 91 was able to show that the main product was the trimer (the tribenzocyclononatriene 27) and the minor product the tetramer (the tetrabenzocyclododecatetraene 26). He further claimed that, under his reaction conditions, the same approximately 5:l mixture of 27 and 26 was obtained from the acid-catalysed condensation of veratrole and formaldehyde, from the acid-catalysed oligomerization of 3,4-dimethoxybenzyl alcohol and, most surprisingly and most significantly, from an attempted chloromethylation of the diphenylmethane derivative 25! Of all these routes the veratrole/formaldehyde reaction is normally chosen. Complete separation of the mixture of 27 and 26 requires careful fraction-
2
CH3d
Aromatic Hydrocarbon Cores
717
bCH3
26
lg
If
lester) H
HO
H
RO
Scheme 31. Synthesis of derivatives of tetrabenzododecotetraene. Reagents: (a) TFA/CH2CI,/O"C/4 h, 55% [125, 1261; (b) BBr,/CHCI,IO"C, 78% [125, 1271; (c) RBrlK,CO,/EtOH-DMFlreflux, 56% (C,) [125]; (d) RBr/K,CO,/EtOH/reflux, 50% (C,) [125]; ( e ) NaBH,, 58-96% [125]; (f) TFA/CH,C12/4 h, 19% (Cig) [126]; (8) RCOCl [127].
RoDcH20H
RO
a1 crystallization. Repeated crystallization from benzene gives the pure trimer as a 1 : 1 benzene complex. Demethylation of 27 can be achieved using either boron tribromide [ 118 - 1201or pyridine hydrochloride [ 1201, and the hexahydroxy product alkylated or acylated. As well as simple ether [ 1111 and ester [ 111, 1201 derivatives, alkoxybenzoates [121] and acyloxybenzoates [118, 1191 have also been reported and simple methods have been described for deuteriation of the nucleus 11141. Table 32 gives the mesophase ranges for both esters and ethers [ l l l ] . Since this nucleus is also an important building block in the synthesis of host molecules such as cryptophanes, a number of other variations have been developed on the basic synthesis. It is now possible to make a multitude of analogous systems with substituents at both the methylene and the aryl ring positions [122]. Of particular rel-
evance to the future development of this area is the recently reported development of routes to derivatives bearing aryl amino substituents - derivatives for which further elaboration is clearly possible [ 1231.
2.11 Tetrabenzocyclododecatetraene The tetrabenzocyclododecatetraene nucleus, like the tribenzocyclononatriene nucleus, is non-planar. It is, however, much more flexible. It has, on average, four-fold symmetry, undergoing rapid interconversion between two symmetry-related 'sofa' conformations. Whereas it was believed that the reactions shown in Scheme 30 always gave the trimer as the major product and initial work on the tetramer relied on the isolation
71 8
VII
Synthesis and Structural Features
Table 33. Transition temperatures for derivatives of tetrabenzocyclododecatetraene. Substituent C4H9O CSHIIO C6H130
C7H150
C*Hl,O C9H190
C10H210 CI I H 2 4 C12H250 I ?H270
C14H290
C,SH310 ClfiH?30 c I IH23C02 C13H25C02
C14H29C02 Ci5H31C02
ClOH21~fiH4CO2 CH3OCHZCH20 CH,O(CH,CH,O), CH,O(CH,CH,0)3 a
Phase transitions a
Refs.
Cr 223 I Cr 182 (177) D, 190 (186) I Cr 162 (160) D, 172 (170) I Cr 139 (136) D, 162 (160) I Cr 137 (137) D, 154 (153) I Cr 114 (109) D, 148 (148) I Cr 113 (112) D, (137) D, 140 (142) I Cr 101 (98) D, (129) D2 137 (137) I Cr 97 (94) D, (122) D, 131 (133) I Cr 93 (92) D, (113) D2 127 (128) I Cr 97 (96) D, (106) D, 120 (123) I Cr 96 (93) D, (102) D, 118 (119) I Cr98D1 100D21151 Cr 82 D, 246 (246) I Cr 90 (90) D, 237 (236) I Cr 92 D, 230 I Cr 95 D, 223 I Cr 96 M 151 I Cr 82 M 211 I Cr 30 M 109 I Cr 22 M 63 I
~1251 [125 (129)] [125 (129)l [125 (129)l [125 (129)l [125 (129)l [125 (129)l [125 (129)] [I25 (129)l [125 (129)] [125 (129)] [125 (129)] [ 1291 [129 (127)] [ 129 (127)] ~ 9 1 ~1291 [ 1271 [1301 [ 1301 [ 1301
Figures in parenthesis are as in the reference also given in parenthesis.
of the minor product, Percec [125, 1261 has shown that, by varying the reaction conditions, the tetramer can be made the major product. The key observation was that the trimer could be obtained by chloromethylation of the diphenylmethane (25). Clearly, the reactions are all reversible. According to Percec's analysis, the trimer is the kinetic product of the oligomerization of 3,4dimethoxybenzyl alcohol and is formed in highest yield using very strong acids (e.g. HC104 or CF3S03H) and a poor or a nonsolvent, whereas the tetramer is the thermodynamic product and it becomes the major product if the reaction is carried out in dilute dichloromethane solution using an excess of trifluoroacetic acid as the catalyst [ 125, 1261 (up to a 6 :1 ratio of tetramer to trimer, Scheme 3 1). The octamethoxy compound 26 can be demethylated using boron tribromide, and alkylated or acylated in the normal way [ 127- 1291. Preparation of the octaether derivatives by alkylation of the re-
sultant octaphenol gives both higher yields and purer products than the alternative route shown in Scheme 31, in which the alkoxy substituents are introduced before the oligomerization step [ 1251. Initial reports suggested that these ethers gave a single enantiotropic mesophase [125, 1281, but it was later shown that, while the C, to C9 ethers give a single D, mesophase, the C,, to C,, ethers from both D, and Dh phases [129]. The transition between these two has not been detected by DSC, but is observed by polarizing microscopy. The ethyleneoxy derivatives (Table 33) show both thermotropic and lyotropic behaviour giving what is probably a D, phase [130]. Generally the tetramers give higher transition temperatures than do their trimeric counterparts, and show less tendency to polymorphism. Transition data are summarized in Table 33.
2
"@ 41:; +
Aromatic Hydrocarbon Cores
719
a OH
RCOp
RCOp
Scheme 32. Synthesis of metacyclophane based discotic mesogens. Reagents: (a) HCl/EtOH/O "C, 72%; (b) RCOCl/180"C.
28
2.12 Metacyclophane Metacyclophanes of the type 28 have a rigid cone-shaped or crown-shaped conformation in which the ring methyl substituents adopt an endo orientation. Like the tribenzocyclononatrienes they give potentially ferroelectric columnar phases. The key step of the synthesis shown in Scheme 32 is the acid-catalysed condensation of pyrogallol and 1,l -diethoxyethane [ 131- 1331. Although many dodeca-ether and dodecaester derivatives have been examined, only the C,, to CI8 esters with methyl substituents on the ring proved to be mesmorphic (Table 34) [ 1341. They give a D, phase. The
Table 34. Transition temperatures for metacyclophane based discotic mesogens [ 1341. Substitutent 1 2H25C02 13H27C02 c l 5H31C02
L7H&02
Phase transitions Cr 46 D,, Cr 30 D,, Cr 48 D,, Cr 58 D,,
66 I 67 I 61 I 68 I
properties of mesogens with a random, statistical mixture of ester chains [ 1311 and the synthesis of deuteriated derivatives [ 1351 have also been reported.
2.13 Phenylacetylene Macrocycles Discotic liquid crystals of phenylacetylene macrocycles 29 were first reported by Zhang and Moore in 1994 [ 1361. Their synthesis involves the stepwise build-up of phenylacetylene hexamers [ 1371 followed by a macrocyclization step [138]. The key reactions of the synthesis (Scheme 33) are the palladium-catalysed coupling of aryl iodides and acetylenes, and the selective 'deprotection' steps allowing the ends of the growing oligomer to be distinguished. The synthesis shown is just one of the many possible sequences that can be used to prepare the macrocycles. The mesophase behaviour of the discotic derivatives prepared to date is shown in Table 35 [136]. In some ways
720
VII
Synthesis and Structural Features
3 Heterocyclic Cores
N3Et2
H 3
3.1 Pyrillium
R
R
R C
R
R
n
R
R
Scheme 33. Synthesis of phenylacetylene macrocycles. Reagents: (a) K2C03/MeOH; (b) Pd(0); (c) MeV1 10°C.
Table 35. Transition temperatures for discotic phenylacetylene macrocycles (see Scheme 33 for structures). R
R’
Phase transitions [ 1361
0C7H15 0C7H15 I 192 ND 168 Cr OCOC7Hl, OCOC,H,, I241 ND 121 Cr [I 202 ND 130 D, 103 Cr]” COOC,H,, OC,H,, a
Monotropic phases.
these macrocycles can be compared with the ‘tubular’ azacrowns. They are, however, much more rigid and, unlike the azacrowns, tend to form nematic phases. This behaviour is similar to the ‘super-disk’ benzene, naphthalene and triphenylene multiynes, the core-sizes of which are of the same order.
The pyrillium salts 30 are relatively simply synthesized. As shown in Scheme 34, the key step is the acid-catalysed condensation reaction between a chalcone and an acetophenone derivative [139, 1401. The C, to C1, derivatives all give a D,, columnar phase [ 139- 1421.The dependence of phase behaviour on chain length is illustrated in Table 36. Unfortunately, these systems are not very thermally stable, so the actual transition temperatures are subject to considerable uncertainty. The really surprising aspect of the phase behaviour of these systems is that a mesophase is obtained for systems with side chains as short as C 2 and C, [ 1421. It is believed that, in these systems, the disordered nature of the BF, counterions is important in helping to bring about the disordered stacking of the pyrillium ring inherent to the columnar phase [ 1421. Analogous systems bearing aryl substituents at the 2 and 6 positions (only) of the pyrillium ring have also been synthesized. Despite the fact that they are very non-disk-like and bear only four side-chains there are some indications that these also give D, phases, but unfortunately thermal instability problems have, once again, prevented full characterization [141, 1431. Table 36. Transition temperatures for pyrillium based discotic mesogens. Substituent C2H50
C3H7O C4H9O C.5H110
C8H170 C12H250
Phase transitions Cr 194/200 D, 213/217 I Cr 167 Dh 240/247 I Cr 100/117 D, 277 I Cr <25 Dh 265/283 I Cr <25 D, 200/237 I Cr <25 Dh 231/288 I
3 Heterocyclic Cores
Scheme 34. Synthesis of pyrillium based discotic mesogens. Reagents: (a) RXlphase transfer conditionslcat. Aliquat 366 (Oc,NMe+CI-) [139, 1441; (b) MeCOCl/AICI,/CH,Cl, [139]; ( c ) RX/KzC0,/DMF180 "C [1391; (d) NaOH/EtOH/6O0C [139]; (e) HBF4/Acz0/100"C [139].
RO
30
pR a
72 1
0
R
/
0
C104
31
Charge-transfer Complex
fi
32a X = B F i
32b X = C I O i
Scheme 35. Synthesis of bispyran based discotic mesogens. Reagents: (a) HC(OEt),/ HCIO,; (b) PBu,/MeCN; ( c ) EtiPr,NlMeCN/reflux/2 h; (d) ZnlMeCN; (e) electro-oxidation/ R,NfX-; (f) TCNQ.
722
VII
Synthesis and Structural Features
2
b
Coruleoellagic acid
\4
te
34 RCOz RRCOzC
\
\ e
0
Table 37.Transition temperatures for bispyran based discotic mesogens. Substituent ~
Phase transitions [ 1451
~
C5Hl 1
C9H19
C,2H2s
Cr 228 I Cr 54 M 172 I Cr 96 M 147 I
3.2 Bispyran The bispyrans shown in Scheme 35 can be generated from the 1,6-biarylpyrillium salts either directly by reaction with zinc [145], or indirectly via the trialkyl phosphine complex [146, 1471. They show a marked tendency to aggregate in organic solvents, a property that is doubtless related to their ability for form columnar phases [148].
OC0R Z
R
Scheme 36. Synthesis of discotic mesogens based on condensed benzyprone nuclei (flavellagic acid and coruoellagic acid). Reagents: (a) K,S,O8/H2SO4/160 "C; (b) As,O,/ H,SO,; (c) RBr/ K2C0,/DMAA/90 "CI3 days or RBr/Aliquat 336 (Oc,NMe+CI-)/ KOH/13O0C/4 h; (d) RCOCI; (e) RBr/K2C0,170"C/ 4 days.
Their propensity to form columnar phases is not destroyed by the introduction of charge into the nucleus [ 1461. Hence, electro-oxidation produces mesogenic salts 32a and 32b, and treatment with tetracyanoquinodimethane (TCNQ) produces a mesogenic charge transfer complex. In the C12series the parent bispyran 31 has a mesophase range of 96- 147 "C, the radical cation tetrafluoroborate gives two discotic phases between 142°C and about 240"C, the perchlorate two phases between 144°C and about 261 "C, and the TCNQ charge-transfer salt also gives two phases between 11 "C and 242°C [146]. The dependence of the phase behaviour of the bispyrans on chain length is illustrated in Table 37 [ 1451.
3 Heterocyclic Cores
3.3 Condensed Benzpyrones (Flavellagic and Coruleoellagic Acid) The reaction of gallic acid 2 with potassium persulfate and concentrated sulfuric acid gives the condensed a-pyrone, flavellagic Table 38. Transition temperatures for discotic mesogens based on condensed benzopyrone nuclei. Substituent
Phase transitions [149]
Flavellagic acid (33) Cr 16 Dh, 198 I Cr 37 Dh, 186 I Cr 23 D,, 176 I Cr 45 D,, 166 I Cr 42 D,, 146 I C r4 5 D,, 141 I Cr 46 D,, 134 I Cr 55 D,, 125 I Cr 42 D,, 118 I Cr45Dho1161 Cr 53 Dh, 109 I Cr 181 I Cr 104 Dh 183 I Cr 79 D, 175 I Cr 90 D, 174 1 Cr 70 D, 171 I Cr 83 Dh 176 I Cr 88 D, 168 I Cr 97 D, 165 I Cr 93 Dh 164 I Cr 102 Dh 162 I
C6H130
C7HlS0 C8H170 C9HlY0
CIOH2lO IH23O CIZHZSO c1
I 3H270 C14H290 C15H310 Ci6H330 C7H1SC02 C8Hi7C02 C9H 1gC02
Cl"H2iCO2 cl
1H23C02
c 1 ZH2SCOZ C13H27C02
c I4H2YC02 lcoZ
C16H33C02 Couleoellagic acid (34) C3H7O C4HYO
CSHIIO C6H130
C7HlS0
C8H170 C9H190
c lOH21O C8H17C0Z C9HlYC0Z
c IOHZICOZ 1 1 H23C02
CI zHzsCO2 1 3HZ7C02
C14H29C0Z C15H3iC02 16H33C02
Cr Cr Cr Cr Cr Cr Cr
Cr 143 D, 160 I Cr 73 D, 170 I Cr 4 D, 170 I Cr -85 D, 159 I Cr -77 D, 152 I Cr -35 D, 138 I Cr 4 D,123 I Cr6Dh1171 Cr 159 D,, 217 I 154 D,, 200 D,, 211 I 146 Dhi 189 DhZ 209 I 145 Dhl 175 D,, 206 I 141 Dhl 167 D,, 202 I 140 DhI 157 D h Z 199 I 138 DhI 148 Dh2 195 I 137 Dhl 141 Dh2 190 I Cr 134 Dh2 187 1
123
acid 33, which can be oxidized to coruleoellagic acid 34 using As,O, in sulfuric acid (Scheme 36). Both the ester and the ether derivatives of 33 and 34 give D, phases. Their phase behaviour is summarized in Table 38 [149]. Esters of coruleoellagic acid may form two mesophases, the transition between which cannot be observed by DSC but is clear by polarizing microscopy, the lower temperature M, phase being much more birefringent. Both 'phases' are miscible with other D, phases, and both seem to be of the D, type. It is not clear that the transition between these two 'phases' is a true phase transition. If so, it must be second order or very weakly first order.
3.4 Benzotrisfuran Destrade and coworkers [ 1501 have prepared a series of benzotrisfuran derivatives that give discotic mesophases. The synthesis, outlined in Scheme 37, hinges on the condensation of phloroglucinol with p,p-dimethoxybenzoin to give hexakis(methoxypheny1)benzotrisfuran. This intermediate is demethylated with pyridinium hydrochloride, and the resultant hexaphenol is acylated by treatment with an acid chloride
b
::? f l 4 f 3 C J
Scheme 37. Synthesis of discotic mesogens based on benzotrisfuran [150]. Reagents: (a) H2SO4/159"C, 5 min, 35%; (b) pyridine . HC1/220"C, 7 h; (c) RCOClIMglbenzene, reflux.
724
VII
Synthesis and Structural Features
Table 39. Transition temperatures for discotic benzotrisfurans (RCOO-) (see Scheme 37 for structure). Substituent C,Hl
icoz
Phase transitions [I501 Cr 186 Dho 244 1 Cr 134 Dho 177 1 (1 100 Dho) (1 95 D d Cr 203 ND,decornD
C6H I 3c02 C7Hl ScoZ
C8H17C02
C8H170
and magnesium metal in refluxing benzene. The mesophase behaviour of the discotic derivatives is summarized in Table 39. Only two members of the series (pentyl and hexyl) show enantiotropic columnar mesophases. Longer chain homologues give monotropic (heptyl and octyl) or no (nonyl or longer) mesophases. The octyloxy derivative is an exception in that it gives a nematic phase (as determined by optical microscopy), but slow decomposition of the material at these high temperatures prevented any further analysis.
CH3O& /
CH.0
Scheme 39. Synthesis of derivatives of thiatruxene. Reagents: (a) NaNO,/HCl; (b) KSCSOEt; (c) KOH/ EtOH; (d) H+; (e) BrCH,CO,Et/base; (f) KOH/EtOH; (8) H+; (h) PPE; (i) pyridine.HC1; (j) RCOCl/pyridine.
Table 40. Transition temperatures for derivatives of oxatruxene. Substituent
Phase transitions
Refs.
~521 ~521 C9H19C02 1521 c IOHZIC02 [152] c I IH23C02 [I521 Cl,H25C02 [152] Cl,HZ7CO2 [151, I521 Ci5H31C02Cr 80 Dobdh84 Drd 138 Dh, 152 I [ 1521 C7H15C02
C8H17C02
a
w
Scheme 38. Synthesis of oxatruxene derivatives [ I 5 1, 1521. Reagents: (a) BrCH2C0,Et/K2C03/acetone/reflux/90 min; (b) KOH/EtOH/reflux/l50 min; total (a) and (b) 38%; (c) P2O5/H3PO,/llOoC/30min, 55%; (d) PPE/140 "C/25 min, 46%; (e) pyridine . HCI/ 140 "C/30 min; (f) RCOCl/pyridine/48 h, 40% (C14).
g
Cr 95 Drda 194 I Cr 90 Drdb197 I Cr 82 DrdC192 I Cr 76 Drdd 194 I Cr 78 Drde 184 I Cr 78 Drdf 172 Dh, 177 1 Cr 74 Drdg158 Dh, 166 I
Gives N, on cooling to 89 "C. Gives N, on cooling to 75 "C. Gives N, on cooling to 68 "C. Gives N, on cooling to 62 "C. Gives D on cooling to 64 "C and N, at 58 "C. Gives D on cooling to 64 "C and N, at 59 "C. Gives Do,, on cooling to 71 "C and N, at 58 "C. Gives N, on cooling to 60 "C.
3.5 Oxatruxene and Thiatruxene Like the truxenes themselves, esters of oxatruxene [ 151,1521 and thiatruxene [ 153,
3 Heterocyclic Cores
72.5
Table 41. Transition temperatures for derivatives of thiatruxene. ~
Substituent C6Hl TC02
C7H15C02 C8H17C02
CYHlYCO2
C10H21co2 C11H23C02
C12H2.5C02 1 ?H27C02 14H29C02 IOH250C6H4C02 C12H250C6H4C02 13H270C6H4C02 C16H330C6H4C02
Gives N, Gives N, ' Gives N, Gives N, a
~~
Phase transitions
Refs.
Cr 133 Drd(p211a)218 Dhd 241 I Cr 103 Drd(p21/a)a212 Dhd 236 I Cr 90 Drd(P21/a)h 173Drd(CZ/m) 191Dhd 229 I Cr 87 N, 93 Drd(p211a)185 D h d 210 I Cr 62 N, 98 Drd(p211a)155 (151)D h d 193 I Cr 78 (64)N D 93 Drd(P21/a) 146Drd(C2/m) 149 Dhd 180 I Cr 79 N, 87 Drd(p21/n)136 Dhd 191 I Cr 82 Drd(P21/a)c 132Drd(C2/m) 134 Dh 179I Cr 88 Drd(P21/a)d 121 Drd(C2/m) 125 Dhd 178I Cr 83 N, >300 I Cr 81 ND 295 I Cr 86 ND 280 I Cr 96 N, 241 I
[I531 [I531 [I531
[153,1541 [(153) 1541 [(153) 1541 [I531 [153,1541 [I531
[I531 [I531 [I531
[1531
on cooling to 92"C. on cooling to 82 "C. on cooling to 72 "C. on cooling to 8 1 "C.
1.541 show complex polymorphism. They are also made in a similar way, the only essential difference lying in the somewhat lengthy syntheses that need to be employed to generate the heteroatom analogues of the indanone precursors. These synthesis are summarized in Schemes 38 and 39, and the phase behaviour is given in Tables 40 and 41.
are 'banana-shaped' and the nucleus has only four side chains, they seem to give a Dh phase [143]. It has been suggested that some non-covalent dimer is the effective mesogen, but there seems to be no evidence to support this [ 1411. The phase behavior of these systems is summarized in Table 42.
Table 42. Transition temperatures for derivatives of dithiolium.
3.6 Dithiolium
Counterion
Phase transitions [ 1431
C,2H2,0
BF, BF, BF, BFi
C,H,,O CioH2iO C,2H25O
ClO, ClO, ClO,
Cr 160 I Cr 133 D, 141 I Cr 129 D, 154 I Cr 120 Dh 145 I Cr 144 Dh154 I Cr 144 Dh 163 I Cr 138 Dh 176 I
Substituent C5H1 l o
The dithiolium salts 35 are prepared by the reaction of the corresponding chalcone and phosphorus pentasulfide followed by an acid work-up as shown in Scheme 40 [141, 1431. Despite the fact that these molecules
R RO
o
w o "OR O H
R
a.b
CsH170 ClOH2lO
R O W :: RO
gS-S
x@
35
Scheme 40. Synthesis of dithiolium derivatives [143].Reagents: (a) P4Sl0/1~0"C; (b) HX or LiX/AcOH (X=BF4 or Clod), 3-47% overall.
726
3.7
VII
Synthesis and Structural Features
activity suggests that the risk involved in using these mesogens is small. However, until proven otherwise, they must all be treated as potential carcinogens. It has been suggested that the carcinogenic activity of tricycloquinazoline and its derivatives arises from their ability to intercalate into DNA, and that this may not be wholly unrelated to their ability to form stable 'stacked' columnar phases. Although the tricycloquinazoline nucleus can be assembled in a variety of ways, the published syntheses of the mesogens due to Keinan et al. [158, 1591 have both been based on the ammonium acetate/acetic acetate mediated trimerisation of an anthranil (Schemes 41 and 42). In general this is a poor-yielding process, and in our experience it has proved difficult to match even the moderate yields claimed for these steps in the literature. Both the hexa-alkoxy
Tricycloquinazoline
The tricycloquinazoline nucleus possesses C, symmetry and is attractive for a variety of reasons. Firstly, the parent hydrocarbon possesses remarkable thermal and chemical stability. Secondly, the electron-deficient nature of the nucleus renders liquid crystal derivatives susceptible to doping by reducing agents giving n-doped semiconductors [ 1551. Thirdly, these derivatives are coloured. Against these advantages must be weighed the fact that the parent heterocycle, tricycloquinazoline, is a potent carcinogen. The effect on the carcinogenicity of introducing substituents into the tricycloquinazoline nucleus seems to be difficult to predict [ 156,1571.The general observation that polysubstitution destroys the carcinogenic
d. e
RO
CH3O
OR
OCH3
RO
CH3O
+f
j y
Y
f
SR
yp,% RS
C CI & '% . \
CI
CI
\
RS
SR
Scheme 41. Synthesis of tricycloquinazoline hexaether derivatives [ 1581. Reagents: (a) HNO,, 90%; (b) Sn/AcOH, 54%; (c) NH40Ac/AcOHlsulfolane/reflux, 27%; (d) HCl/pyridine/230 "C. 50%; (e) RBr/KOH/DMSO, 20-30%.
Scheme 42. Synthesis of tricycloquinazoline hexathioether derivatives [ 1591. Reagents: (a) AcOH/H2S0,/HN0,/O-5 "C, 95%; (b) Ac,O/ H,SO,ICrO3IO-5"C, 28%; (c) EtOHl H,O/HCl/reflux, 58%; (d) AcOH/Sn; (e) NH,OAc/AcOH/sulfolane/l50" C ,40%; (f) RSKIN-methylpyrrolidone/lOO"C, 8 - 50%.
727
3 Heterocyclic Cores
Table 43. Transition temperatures for derivatives of tricycloquinazoline. Substituent
Phase transitions
0
Refs.
Cr 350 I Cr 315 I Cr 286 D,, 306 I Cr 240 Dh, 306 I Cr 188 Dho 301 I Cr 80 D,, 237 1 Cr 72 D,, 215 I Cr 67 D,, 166 I Cr 160 Dh 274 I Cr 156 Dh 241 I Cr 114 D, 223 I Cr 95 Dh 214 I Cr 81 D, 207 I Cr 54 D, 170 1 Cr 57 D, 152 I Cr 92 Dh 184 1
0
0
Me0-0Me +
a.b
H
'IfK 0 0
ic
HOpC GOpH
U
36
MeO$
C,OzMe
ROzC COzR
ROpC
X
ROpC COzR
[ 1581 and hexathioalkyl [1591 derivatives show good mesophase stability with a single D,, phase over a wide temperature range and over a wide range of chain lengths (Table 43). Whereas, in the alkoxy series, both the melting and the clearing transitions are reversible, in the thioalkyl series only the clearing point transition shows good reversibility. The corresponding derivatives with only three symmetrically disposed side chains (C, to C18)to not exhibit any liquid crystalline behaviour [ 1591.
Scheme 43. Synthesis of the esters of porphyrin octa-acetic acid [I611. Reagents: (a) isopentyl nitrite, HCl; (b) Zn, AcOH, 75°C; (c) T1(NO3),/MeOH/ HClO,; (d) Pb(OAc),; (e) 20% HCl, reflux; (f) 0,; (8) ROH, H2S04, 50°C; (h) Zn(OAc)2, CHCl,/ MeOH. reflux. Table 44. Transition temperatures for the esters of porphyrin octaacetic acid (see Scheme 43 for structures). R
M
Phase transitions [ 161]
C4H9 C4H9
HZ Zn H2 Zn H2 Zll
Cr 178 D 222 I Cr 184 D 273 I Cr 59 D 132 D, 220 I Cr 61 D 136 D, 232 I Cr 96 D 99 D, 166 I Cr 91 D 101 D, 208 I
C6H13
C&13
3.8 Porphyrin 3.8.1 Octa-Substituted Porphyrin Fox and coworkers [16] have synthesized two closely related series of porphyrin discogens. Esters of porphyrin octa-acetic acid were prepared according to Scheme 43, porphyrin octa-acetic acid being prepared following the procedure of Franck [160]. Consequently, a Knorr condensation be-
C8H17
GH,7
tween acetyl acetone and 3-aminodimethylpentandioate (generated in situ) gives the pyrrole 36. Treatment with thallium nitrate yields the triester, which is oxidized with lead tetraacetate to give compound 37. Boiling with 20% hydrochloride acid produces the macrocycle (and hydrolyses the esters), which is air oxidized to porphyrin octaacetic acid. Esterification proceeds smoothly, simply by warming the acid with the appro-
728
VII
Me0$
C,OzMe
Synthesis and Structural Features HOZF C,02H
H°CH2 I
Table 45. Transition temperatures for discotic porphyrin octaethers (ROCH2CH2-), (see Schemes 44 and 45 for structures).
CHzoH \
R
H2 Zn H, C6H13 C6H 11 Zn H2 C8H17 C8H17 Zn Cu C8H17 Pd C8H17 Cd Zn C8H17 Zn ClOH21 Hz CIOH21 Zn COC,H,, (41) Zn C4H9 C4H9
w
ROCH2 CHzOR
Scheme 44. Synthesis of porphyrin octaethers [162]. Reagents: (a) NaOMe/MeOH; (b) BH,/THF; (c) TsCl/pyridine; (d) ROHltoluene; (e) Pb(OAc),; (f) KOH/EtOH; (g) HBr/EtOH; (h) chloranil; (i) M(OAc),, CH2C12/MeOH,reflux. HOCYp CH ,O ,H
AcOCp CpOAc
H /c,d,e HOCHp CHpOH
M
HOCHp HOCHp HZOR
8 ROCHp CHpOR
CH2OH CHpOH HOCHz CHpOH 40
Scheme 45. Synthesis of porphyrin octaethers via porphyrin octaethanol. Reagents: (a) AcCl/NEt,; (b) Pb(OAc),; (c) KOH/EtOH; (d) HBrlEtOH; (e) 0,; (f) NaH/DMSO, RX; (8) M(OAc),, CH2C12/MeOH, reflux.
priate alcohol using concentrated sulfuric acid as catalyst [ 1611. Metallated derivatives are then synthesized by heating the metal-free compounds with zinc acetate. The mesophase behaviour of the porphyrin octaesters is summarized in Table 44 [ 1611. The most stable mesophase is formed from derivatives with intermediate side-
M
meso Phase transitions 11621
H H H H H H H H H CN NO, H H H
Cr 1541 Cr 159 D 164 I Cr 111 I Cr 114 D 181 I Cr 84 D 89 I Cr 107 D 162 I Cr 84 D 132 I Cr 89 D 123 I Cr 103 D 136 I Cr 85 D 140 I Cr93D118I Cr 69 I Cr 86 D 142 I Cr 169 I
chain lengths (hexyl), with a central zinc ion tending to raise the clearing temperature. The mesophases give fan-like textures, indicating a columnar architecture, but their precise nature has not been determined. The synthesis has been modified to produce a series of porphyrin octaethanol derivatives (ethers) [ 1621. Pyrrole trimethyl ester (37) is selectively hydrolysed with sodium methoxide in methanol to give the diacid monoester (38), which is reduced (BHJTHF) and tosylated. The ditosylate was heated with the appropriate alcohol to afford the diether (with concommital transesterification of the pyrrolic a-ester). Oxidation with lead tetra-acetate gave compound 39, which was converted to the metal-free porphyrin in one pot by treatment with potassium hydroxide to hydrolyse the ester, hydrobromic acid to decarboxylate and cyclize, and chloranil to oxidize the macrocycle to the porphyrin (Scheme 44). In a different, lower yielding method the derivatives were prepared from the common intermediate porphyrin octaethanol (40), the synthesis of which is outlined in Scheme 45. The octa-alcohol could also be esterified to produce structural isomers of the porphy-
729
3 Heterocyclic Cores
rin octaesters already described. Standard procedures were employed to synthesize the meso-nitro [ 1631 and cyano [164] substituted derivatives. The thermal behaviour of the octaethanol porphyrin derivatives is shown in Table 45. It is immediately apparent that the liquid crystal behaviour of these compounds is extremely sensitive to relatively small structural changes. The octaester 41 shows no liquid crystal phases at all, whereas its structural isomer (Table 44, R=C,H,,, M=Zn) gives two mesophases over a wide temperature range. Within the octaether series the most striking effect appears to be that of the central metal ion. The metal-free derivatives show little tendency to form mesophases, whereas the metallated compounds give stable mesophases, typically through raising the clearing points. meso-Substitution tends to lower both transition temperatures, with the nitro compound also having a reduced mesophase range.
3.8.2 meso-Tetra(p-alkylpheny1)-porphyrin Shimitzu et al. [165] have reported the mesophase behaviour of 5,10,15,20-tetrakis(4n-dodecylpheny1)porphyrin (Scheme 46) [ 1651. The material is easily synthesized from pyrrole and 4-n-dodecylbenzaldehyde by refluxing in propionic acid [ 1661. The DSC trace shows the presence of two distinct mesophases. X-ray analysis of the two mesophases indicated that their structure is very similar, and is defined as discotic lamellar (DJ.
6 C12H25
Cr 31 Dh52 D,,, 155 I
Scheme 46. Synthesis of 5,10,15,20-tetrakis(4-n-d0decylpheny1)porphyrin [ 1651.Reagents: (a) propionic acid, reflux.
NaCN
+
CS$+NC-C-SNa.DMFL II
RS
wSR
S
NC-C-SNa 1 I NC-C-SNa IC
I : : : M=
If
Scheme 47. Synthesis of tetra-azoporphyrin based discogens. Reagents: (a) DMF, 0°C; (b) H,O, 12 h; (c) RBr, MeOH; (d) Mg(OPr),/PrOH, 1OO"C, 12 h; (e) CF,CO,H; (f) M'Cl,.
(and their metal complexes) has been prepared and some members were found to be mesomorphic. The synthesis is shown in Scheme 47 [167]. Treatment of carbon disulfide with sodium cyanide in DMF yields the addition product. Addition of water couples the salt to give the ethylene dithiolate, which is alkylated with an alkyl bromide. Refluxing with magnesium propoxidel propanol yielded the magnesium porphyrin derivative, which could be demetallated with TFA. The metal-free compound was then metallated by treatment with the appro3.8.3 Tetraazaporphyrin priate metal chloride/acetate in warm dioxane. A series of 2,3,7,8,12,13,17,18-octakisThe transition data for these derivatives (alkylthio)-5,10,15,20-tetraazaporphyrins are given in Table 46 [ 168 - 1701. The most
730
VII
Synthesis and Structural Features
Table 46. Transition temperatures for discotic materials based on tetra-azoporphyrin (RS -) [ 1691 (see Scheme 47 for structures).
R
Phase transitions
C4H9 C,H,, C7H I5 C8H17 C9H19
C,"H2, I ZH25
H2
co
Ni
cu
Zn
Cr 113 D 122 I Cr 78 D 92 I Cr 75 I Cr 82 I Cr 79 I Cr81 I Cr 85 I
Cr 95 D 271 Idecomp Cr 45 D 243 I
Cr 117 D 184 I Cr 75 D 154 I Cr 68 D, 119 I Cr76D90I
Cr 112 D 223 I Cr 80 D 190 I Cr 70 Dh 170 1 Cr 68 D, 152 I Cr 62 D, 133 I C r 6 9 D 1221 Cr 83 D 102 I
Cr 54 D 208 I Cr 46 D 168 I
-
Cr 55 D, 208 I Cr 62 D 177 I Cr 73 D 153 I
striking feature of the data is the mesophase stabilizing effect of the central metal ions. I t can be seen that the only metal-free derivatives to give mesophases are the butyl and hexyl homologues, whereas all the metal complexes (up to dodecyl) show enantiotropic mesophases. The clearing temperatures decrease linearly with increasing side-chain length, and for a given homologue the stabilizing effect of the central metal ion (higher clearing temperature) is Co > Cu > Zn, Ni > H,. A non-hexagonal columnar structure is proposed for the metalfree derivatives, whereas a hexagonal columnar structure is most likely for the metal complexes.
-
-
Cr 41 D 49 D, 120 I -
Cr 54 D 87 I -
originally developed by Pawlowski and Hanack [172] (Scheme 48). o-Xylene is ring-brominated with bromine [ 1731 and a-brominated with NBS [ 174, 1751 to give tetrabromoxylene 42. Nucleophilic displacement with alkoxide yields bis(a1koxymethyl)dibromobenzene, which is converted to the phthalonitrile by treatment with copper(1) cyanide in DMF. Conversion of phthalonitriles to phthalocyanines has been achieved in a number of ways. Direct routes include treatment of the phthalonitrile with
Id 3.9 Phthalocyanine 3.9.1 Peripherally Substituted Octa(alkoxymethy1)phthalwyanine 2,3,9,10,16,17,23,24-0cta( dodecyloxymethy1)phthalocyanine was the first discotic phthalocyanine derivative to be reported [171]. Many more discotic variants have since been synthesized by changing the side chains and/or the central metal ion, but all the syntheses follow a similar route to that
Scheme 48. Synthesis of peripherally substituted octa(alkoxymethy1)phthalocyanines (X = 0)and related thio analogues ( X = S ) . Reagents: (a) Br,; (b) NBS; (c) RX-; (d) CuCN/DMF; (e) N,N-dimethylethanolamine, reflux; (f) CSHl,OLi/C,H, ,OH, reflux, (8) H+; (h) NH,/MeOH; (i) M' acetate.
3 Heterocyclic Cores
73 1
Table 47. Transition temperatures for octa(alkoxymethy1)phthalocyanines and related thio analogues (see Scheme 48 for structures). XR
M
Phase transitions
Refs.
OCXH I7 OCBH 17
Ni co Pb H2
Cr 68D Idecomp Cr 72D Idecomp Cr -45(53) D, 158 (1 15) I Cr 78 Dh 264 I Cr 53 Dh >300 I Cr 78 Dh >300 1 Cr 44 D,280 I Cr -12 Dh I25 I Cr 59 D, 114 I (Cr 46? 60 I) Cr <25 D, >300 I Cr 23 D, 66 D, 158 I Cr 29 D 191 I Cr 95 D 267 I Cr 108 D 304 I Cr 52 D 247 I Cr 70 D 255 I
