Film processing

50 mm Tubular Film Machine

Mini 19 mm Tubular Film Machine

Figure 3.1.45 Wide-angle X-ray diffraction patterns of films obtained by 50 mm blown film machine and 19 mm blown film machine; matched pairs based on scaleup conditions

Film Impact Strength

Film Width

Film Thickness

Q : Out put rate V : Take up rate L : Film width H 0 : Die lip clearance H 2 : Film thickness F : Film impact strength (F 1 >F 2 ,F 3 >F 4 )

Figure 3.1.46 Film impact strength as a function of film thickness and film width

3.1.12

Processability

The problem of bubble stability was first described in an article by Han and Park [24] and later expanded upon by Han [25]. They present detailed descriptions of the instability, contrasting it to the so-called "draw resonance" phenomenon observed in film casting from slit dies [26, 27]. No examinations of the influence of drawdown or blowup ratio are contained in their work. The tubular film process operates in a stable condition for only a limited series of operating conditions. Typical unstable bubble shapes are shown in Fig. 3.1.47. At the various operating conditions one may have stable, unstable, or metastable conditions, the latter representing the existence of two stable states with ready passage between them. A theoretical stability analysis of instabilities due to axisymmetric disturbances in an isothermal Newtonian fluid has been given by Yeow [28]. It is not possible to make a detailed comparison of this theory with our experimental results because we are concerned with nonisothermal behavior of viscoelastic polymer melts. Yeow's results, presented in terms of dynamic and kinematic variables specifically for each input disturbance frequency, show that the instability occurs at a corresponding value of: T = M k

A =

nQ

n%AP nQ

x•

* Ra

(3L37)

or H*=§ M0

B*=^

XF=^ K0

(3.1.38)

K0

where R0 is the annular die radius. Yeow presents neutral stability curves on plots of T versus A or H* versus B for specific X¥. We present plots of the latter type in Fig. 3.1.48(a) and 3.1.48(b). In Fig. 3.1.48(a) we compare the stability of LDPE, LLDPE, and HDPE at X¥ = 12/0.75 = 16, while in Fig. 3.1.48(b) we contrast the LLDPE results forXF equal to 4, 8, 12, and 16. In comparison to Yeow's calculations we find our bubbles tend to be unstable.

Figure 3.1.47 behavior

Typical bubble instability

It would seem reasonable to discuss the differing bubble stabilities of LDPE, LLDPE, and HDPE in terms of elongational flow behavior. This does mark the relative sensitivity of melts to disturbances. Deformation-rate hardening should be stabilizing. Figure 3.1.5 thus suggests that stability should occur along the lines LDPE > LLDPE > HDPE. Figure 3.1.48(a) implies that LDPE is most stable and LLDPE unstable. As frost line height is decreased, HDPE becomes more unstable than LLDPE. Minoshima [29] reported that the polymer showing strain hardening has a more positive effect on bubble stability. LDPE > HDPE > LLDPE Ide and White [30] reported that strain rate hardening prevents disturbance of the diameter during the melt spinning. If the idea of strain rate hardening is extended for nonisothermal case, namely we express "deformation hardening" as the viscosity increases with increasing deformation, the larger the viscosity dependence on temperature the better the stability that will be observed. LDPE > LLDPE > HDPE

LDPE HDPE L-LDPE Unstable

H

Stable

Figure

H = HJH0 B

3.1.48(a)

Plot

of

versus B = RJR0

showing regions of stable and unstable behavior for LDPE, LLDPE, and HDPE, X{ = 16

H

Stable

Unstable

Figure 3.1.48(b) Plot of H = HL/H0 versus B = RL/R0 showing regions of stable and unstable behavior for LLDPE, Xf = 4, 8, 12, 16

B

The above orders give different results for HDPE and LLDPE, but LLDPE has better stability than HDPE under strong cooling or low frost line height conditions. In contrast HDPE has better stability than LLDPE at low cooling rate conditions. Stability is better at the lower frost line height than at the higher one, which is closely related to cooling rate: High zF < Low zF The dependence of stability on frost line height is: LDPE > LLDPE > HDPE In general, a polymer having large melt tension shows good stability. Large melt tension at the same MI means strain rate hardening and large activation energy. As the tubular film of high molecular weight HDPE is produced at high drawdown ratio, high blowup ratio, and high frost line height, bubble stabilizing equipment is needed to stabilize these bubbles.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30.

Alfrey, T., SPE Trans. (1965) 5, p. 68 Pearson, J.R.A., Mechanical Principles of Polymer Melt Processing (1966) Pergamon, Oxford Pearson, J.R.A., Petrie, C.J.S., J. Fluid Mech. (1970) 40, p. 1 Pearson, J.R.A., Petrie, C.J.S., J. Fluid Mech. (1970) 42, p. 609 Pearson, J.R.A., Petrie, C.J.S., Plastics Polym. (1970) 38, p. 85 Petrie, C.J.S., Rheol Acta (1970) 12, p. 92 Han, CD., Park, J.Y., J. Appl. Polym. ScL (1975) 19, p. 3277 Petrie, C.J.S., AIChEJ. (1975) 21, p. 275 Wagner, M.H., Rheol. Acta (1976) 15, p. 40 Wagner, M.H., Dr.-Ing.-Dissertation, University of Stuttgart (1978) Kanai, T., White, J.L., Polym. Eng. ScI (1984) 24, p. 1185 Kanai, T., White, XL., J. Polym. Eng. (1985) 5, p. 135 Alaie, S.M., Pananostasiou, T.C., Int. Polym. Process. (1993) 8, p. 51 Campbell, G.A., Cao, B., AIChE J. (1990) 36, p. 420 Ashok, B.K., Campbell, G.A., Int. Polym. Process. (1992) 7, p. 240 Kanai, T., Kimura, M., Asano, Y., J. Plastic Film Sheet. (1986) 2, p. 224 Simpson, D.M., Harrison, LR., Adv. Space Res. (1993) 13, p. 227 Sukhadia, A.M., SPEANTEC '94 (1994) 40, p. 202 Minoshima, W, White, J.L., Spruiell, XE., Polym. Eng. Sci. (1980) 20, p. 1166 Ide, Y., White, XL., J. Appl. Polym. Sci. (1978) 22, p. 1061 Yamane, H., White, XL., Polym. Eng. Rev. (1983) 2, p. 167 Oda, K., White, XL., Clark, E.S., Polym. Eng. Sci. (1978) 18, p. 25 Menges, G., Predohl, W, Plastverarbeiter (1972/3) 23, p. 338 Han, CD., Park, XY, J. Appl. Polym. Sci. (1975) 19, p. 3291 Han, CD., Shettey, R., IEC Fundam. (1977) 16, p. 49 Bergonzoni, A., DiCresci, AJ., Polym. Eng. Sci. (1966) 6, p. 45 Kase, S., J. Appl. Polym. Sci. (1974) 18, p. 3279 Yeow, XL., J. Fluid Mech. (1976) 75, p. 577 Minoshima, W, Ph.D. Dissertation, University of Tennessee (1983) Ide, Y, White, XL., J. Appl. Polym. Sci. (1978) 22, p. 1061

3.2

Kinematics, Dynamics, and Physical Properties of Blown Film Gregory A. Campbell, Bangshu Cao, and Ashok K. Babel

3.2.1 Introduction 3.2.1.1 Kinematics 3.2.2 Single-Phase Model Dynamics 3.2.2.1 Viscous Models 3.2.2.2 Viscoelastic Models 3.2.2.3 Maxwell Model above the Freeze Line 3.2.2.4 Other Literature Models 3.2.2.5 Aerodynamics 3.2.3 Fluid-Solid Models 3.2.3.1 Viscoplastic Model 3.2.3.2 Visco-Plastic-Elastic Model 3.2.3.3 Two-Phase Liquid Models 3.2.3.4 Two-Phase Crystalline Model 3.2.3.5 Constitutive Relationships 3.2.3.6 Energy Balance Equation 3.2.3.7 The Two-Phase Relationships 3.2.3.8 Liquid Phase Thickness Reduction 3.2.3.9 Deformation of the Crystallized Phase 3.2.3.10 Numerical Scheme 3.2.4 Property Development in Blown Film 3.2.4.1 Introduction 3.2.4.2 Theoretical 3.2.4.3 Experimental 3.2.4.3.1 Blown Film Design 3.2.4.3.2 Data Acquisition and Analysis 3.2.4.3.3 Film Properties 3.2.4.4 Results 3.2.5 Summary

114 115 117 117 118 119 120 121 122 122 122 123 124 125 126 127 127 128 128 130 130 130 131 131 131 132 133 138

3.2.1

Introduction

The theory for the blown film process (Fig. 3.2.1) was established by Pearson and Petrie in 1970 [1 to 3]. The literature during the following 20 years can be characterized as an evaluation of the incorporation of different rheological models into Pearson and Petrie's kinematic and dynamic analysis. Different rheological models, which demonstrate the relationship between material stress and strain, predict different behaviors of the polymer in the blown film process. Using the kinematics in the blow film process we relate the deformation rate tensor to the measurable quantities of the process, such as the bubble radius, film thickness, and film velocity. The most convenient coordinate system for analyzing the blown film process is probably the surface coordinate system used by Pearson and Petrie (Fig. 3.2.2). Almost all of the previous literature terminated the analysis at the freeze line, with the implicit assumption that the material would be solidlike above that point. Gupta [4] showed that the freeze line for polystyrene was about 1600C or about 60 to 70° above the reported glass transition temperature. Thus, we have to consider the transition at the freeze line to involve a rheological change that may not correspond to a true solidlike transition, as would be expected at the glass transition. We describe our attempts to extend the analysis of the

Final Film

Nip-rolls

Inflation Air

Film Freeze Section Tube-forming Area

Air-ring Inflation Air Melt From Extruder to the Die Figure 3.2.1

Blown film process

Figure 3.2.2 by [1 to 3]

Blown film coordiante system as developed

process through the freeze line and into the cylindrical portion of the bubble using a number of rheological equations. Our goal in this analysis is to describe the thermal-rheological changes in the polymer from the die through the bubble expansion and into the constant radius cylindrical portion of the bubble. This extension of the simulation above the freeze line is necessary if the changes in the polymer are to be understood as it cools from 60° above its Tg to room temperature, or from the melting point to room temperature. All previous simulations were truncated at the freeze line, which is well below the nip rolls. Attempts to extend the literature models above the freeze line were not successful. The failures of these models to predict realistic results beyond the freeze line are analyzed. To overcome these shortfalls, a new visco-plastic-elastic model for amorphous polymers is developed and presented in the latter section of this work. We then develop and discuss a two-phase model applicable to semicrystalline polymers. Finally, we propose a technique that appears to correlate the film properties to measurable kinematic parameters for the blown film process.

3.2.1.1

Kinematics

The components of the rate of deformation tensor, D, were derived in terms of measurable variables by Pearson and Petrie [1,2] using an orthogonal surface cartesian coordinate system shown in Figs. 3.2.2 and Fig. 3.2.3. The traditional assumptions [3] reduce the equation of continuity and motion to a simple macroscopic mass balance and a balance of forces in both machine and transverse directions. The rate of deformation tensor is thus written as:

(\dv --

V UZ

D = VCOsO 0 \

0

0

0

-— hdz 0

0

\ (3.2.1)

\dr - rdz/

where v is the bubble translation velocity, r is the bubble radius, and h is the film thickness. 9 is given by the relation 6 = arctan/^l

\dz)

(3.2.2)

(a) Top View

(b) Front View

Figure 3.2.3

Coordinate system

Gravity force due to the weight of the melt is neglected: 27TrAa11 cos 9 + nAp(rj -^)=F2

(3.2.3)

Neglecting surface tension, the force equilibrium equation in the normal direction is approximated by the thin membrane equation:

T + T = Ap

(3 2 4)

"-

In this analysis, Ap is the bubble pressure, F2 is the takeup force, and ?y is the final bubble radius. RL and R N are radii of curvature in machine and radial directions and given by

Rn = r SQC 9

(3.2.6)

The quantities PL and PH are the force per unit length in machine and radial directions respectively. The mass flow rate, q, of melt is related to the continuity equation by: Inrhvp - q

(3.2.7)

3.2.2

Single-Phase Model Dynamics

3.2.2.1

Viscous Models

The most simple viscous model is the Newtonian model which was first applied to the analysis of the blown film process by Pearson and Petrie in 1970. Other models that have been applied to blown film are the power-law fluid model by Han and Park (1975) [5], and for the crystallization model by Kanai and White (1985) [6]. The expression of viscosity, rj, varies with the individual models; the Newtonian model by Petrie [7] is a typical generalized Newtonian model:

rj = rioQxp(-b(T-To))

(3.2.8)

where f]0 is the zero shear viscosity at a reference temperature T0; b is a constant determined from the activation energy En. These generalized Newtonian viscous models can be cast in a similar form in the system equations of Pearson and Petrie: 2?2(A + B?2y = 6r' ^- + r(l + ?'2){A - 3B?2) W_ J--2?

r>

(l+72)(A+B?2)ri0 4~n

(3.2.9)

(3 2 10)

- '

where r and h are the dimensionless bubble radius and thickness, respectively. The prime and double prime represent the first- and the second-order derivative with respect to the distance from the die. The dimensionless inflation pressure, B, and dimensionless axial force, A9 are defined as B=^

(3.2.11)

A^-B(rA2 (3.2.12) Qno VoJ where Q is the polymer volumetric flow rate, r0 is the die radius, and ry is the bubble radius at the freeze line. If we extend the simulations using these generalized Newtonian models above the freeze line, unrealistic bubble radii and velocity profile are predicted above the freeze line as reported by Cao and Campbell [8]. It was found that above the freeze line, the generalized Newtonian models predict a sharp decrease of the bubble radius and rapid increase of the film velocity (Fig. 3.2.4). This is not consistent with reported data on the blown film process. Moreover, Campbell and Cao [9] demonstrated that the predicted force balance at the freeze line:

Fz<4nrJAp did not correlate with the data for polystyrene.

(3.2.13)

Bubble Radius

Newtonian model Power—law model Kanai-Wnite model

Distance from Die Figure 3.2.4 Response of Generalized Newtonian Models

3.2.2.2

Viscoelastic Models

Many investigators suggest that the simulation of the blown film process must reflect the elasticity of the polymer. Several viscoelastic models in the literature were employed in the simulations, such as the Maxwell model by Petrie (1975) [6], the Leonov model by Luo and Tanner [10], and the Marrucci model by Cain and Denn [H]. The simulations were truncated at the freeze line without exception. The conventional Maxwell model is cast as follows: AT(1) + T = 2*/£>

(3.2.14)

where X is the relaxation time conventionally defined as a ratio of the viscosity to the modulus, X = rj/G, and D is the deformation rate. The subscript (1) represents the convected derivative, in the notation of Bird et al. [12]:

9T.V

+

9T,V

tik dvi

dv-

^=^ ^wk- trt^

(3 2A5)

-

Restriction to one-dimensional heat transfer analysis at steady state leads to stress independents in the normal direction, the circumferential direction, and time:

O2

0C3

at

Moreover, since xtj = 0 and Dtj = 0 if/ ^j9 in shear-flow, Eq. (3.2.14) then is expanded into Eq. (3.2.17): 4 v ^ - 2 T 1 1 A i ) + T 11 = If]Dn x ( v ^ - 2T22D22^j + T22 = InD22

A

(

V

^"

2 T 3 3 J D 3 3

)

+ T 3 3 = 2

^

(3.2.17)

3 3

This rheological equation can now be related to the force balance developed by Pearson and Petrie [1 to 3]. For a detailed description of the derivation and method used to obtain the results reported here see Cao and Campbell [8, 12]. Numerical results for the Maxwell model in isothermal and nonisothermal conditions were reported previously by Petrie [6], Wagner [13], Luo and Tanner [10], and Cain and Denn [H]. These simulations appear to be fine below the freeze line. However, it has been found that if the Maxwell model is extended beyond the freeze line, similar unrealistic bubble radius and velocity profiles as found for the Newtonian model are predicted [8,12]. The predicted bubble radius rapidly decreases and the velocity appears to be unbounded (Fig. 3.2.5).

3.2.2.3

Maxwell Model above the Freeze Line

The assumption of no deformation above the freeze line leads to incorrect predictions for the Maxwell model. In the case of D = 0, when this model is integrated it leads to: A

+ T =0

(no sum)

(3.2.18)

at

T^T^expf-f

jdA

(no sum)

20

Bubble Radius

Gupta's data of PS, Run Maxwell Model

Distance from Die Figure 3.2.5 Response of Maxwell model when extended above the freeze line

(3.2.19)

By this prediction, the stress components would decay exponentially in the three principle directions. If there is no deformation above the freeze line, both the film thickness and the bubble radius would be constant, leading to a constant cross-sectional area. If the takeup force is a constant, the stress in the machine direction should be a constant. Also, if the internal pressure of the bubble is a constant, the hoop stress should be a constant. These process observations are not consistent with the predicted exponential decay above the freeze line (Eq. 3.2.19). Thus, it appears that the Maxwell model also cannot be extended beyond the freeze line.

3.2.2.4

Other Literature Models

Campbell and Cao [9] have also tested several other models that have been documented in the literature but have not been used in the simulation of the blow film process. Concepts not predicted by the Maxwell model such as anisotropy, nonaffine motion, thermodynamic irreversibility, and reptation are addressed by these models. These models were tested for blown film simulation using Gupta's polystyrene data as a reference amorphous polymer. Giesekus [14] proposed an anisotrophic model from a molecular argument to handle the anistropic property of the polymer melts or concentrated polymer solutions due to the interaction among the oriented polymer chains (dumbbells). AT(1) + T + (XT • T = 2rjD

(3.2.20)

where a is a parameter. The maximum and minimum anisotropy correspond to a = 1 and a = 0. Phan and Tanner [15] developed a network model that incorporates nonaffine motion of the polymer chains. Physically, nonaffine motion means that the relaxation of the polymer chains may be faster than the macroscopic deformation; the polymer chains retract immediately after the entire piece of the polymer is deformed. The PTT model incorporates nonaffine motion by using the Gordon-Schowalter operator. The PTT model leads to the constitutive equation: AT(1)+T + ^(tTT)T = 2l/£>

(3.2.21)

where a is an empirical parameter and G is the modulus. The model reduces to the Maxwell model if a — 0. Mathematically, for thermodynamically reversible models, the convected derivative, which contains the deformation rate tensor, has to approach zero at very rapid deformation rates, because otherwise the change caused from including the deformation rate tensor cannot be balanced by other terms in the constitutive equation. To describe the irreversible motion of the polymers, for example, a double step strain, White and Metzner [16] proposed a modified Maxwell model:

where

(3.2.22)

where the subscript WM represents the White-Metzner model. The relaxation time 1WM is a function of the second invariant of the deformation rate tensor, where a is an empirical parameter. Another thermodynamically irreversible model, which was proposed by Larson [17], was examined. Larson's irreversible model was developed from his reversible model, which was considered to be a differential approximation of the Doi-Edwards reptation model. Instead of using the Gordon-Schowalter expression, a modified Doi-Edwards [18] expression was employed to incorporate nonafflne motion. Larson's irreversible model is expressed as:

^( T ( 1 )

+

^

{ T

+ GS)l(T

+ G3):

Z)]

+)'/+T =

2rfD

(3 2 23)

' -

where oc is an empirical parameter within the range of zero to unity. The term in the brackets, [... ] + , is taken to be the value of the enclosed quantity if it is positive; if the enclosed quantity is negative, the term is set to zero. Recently Alaie and Papanastasiou [19] modeled the nonisothermal blown film process using integral models of the K-BKZ type. In all of these cases, if the models are extended above the freeze line, the radius tends to zero and the viscosity becomes unbounded. It is thus a judgment call as to when to stop the simulation and as to what is solidlike behavior. One way around this problem is to use rheological models that naturally shift from "liquid" like to "solid" like behavior.

3.2.2.5

Aerodynamics

The effect of the air from the air ring was first evaluated by Cao [21] and reported by Campbell et al. [20]. In this evaluation, a momentum balance was undertaken on the wall jet that is emitted from the air ring more or less parallel to the bubble. A simultaneous macroscopic mass and energy balance produced a function that, when the jet entrainment was included, produced very good predictions of the jet velocity as a function of distance from the air ring. An additional AP term, the normal pressure on surface of the bubble, was discovered that should be vectorially added to the bubble pressure:

AP = -£ cos(0) ^Rs dz

(3.2.24)

Here C is related to the initial momentum of the air as it exists the air ring and Rs is the local radius of the bubble. It was found that when this function was included in the force balance that the major effect is to change the shape of the bubble below the frost line. This, of course, changes the strain rate and strain history of the polymer as it is being stretched.

3.2.3

Fluid-Solid Models

3.2.3.1

Viscoplastic Model

The simulations using viscous or viscoelastic models have been found to be lacking when they are extended beyond the freeze line. A very simple viscoplastic model used by Cao [21], the Bingham model [22], introduced the concept of yield stress into blow film analysis. When the imposed stress (or its second invariant) is larger than the yield stress, material will flow, and if the stress is less than the yield stress, fluid will not deform. The concept of yield in polymers is different from that in metal and has been somewhat controversial for the past years. Although most polymers do not display a precise yield point, the yielding beahviour does appear to exist for amorphous polymers, reported by Beatty and Weaver [23] and Chow [24]. It appears that as an "engineering tool," the yield stress may provide a reasonable explanation for the observation that the bubble radius remains constant above the freeze line. The Bingham viscoplastic model is consistent with the assumption of no deformation above the freeze line. Although the Bingham model produced more qualitatively correct simulations, there were some flaws. This might be an expected result, as the Bingham model can be cast as a generalized Newtonian model [21].

3.2.3.2

Visco-Plastic-Elastic Model

Bubble Radius

The lack of success in the simulations using viscous, viscoelastic, and viscoplastic models led to the creation of a new rheological model, a visco-plastic-elastic model. The model is a phenomenological modification of the Maxwell model. The details of its development can be found in Cao and Campbell [8, 12]. Using this model the process is rheologically divided at the plastic-elastic transition (PET). The PET is defined as the position above the die where the deformation changes from a fluid dominated viscoplastic deformation to a solidlike elastic

Current model No yield stress No strain hardening

Distance from Die Figure 3.2.6 Response of visco-plastic-elastic model to parameter changes

deformation. In this model the change in flow mechanism is related to a yield stress criterion. The model can be cast as follows: f 4fft(i) + T = 2riefrD if y n ; > r eff /V3

I

2

T = 2GeffE iff T ^ ; < W V 3 * = 1/1-Z2IT-

^ C 4L^^ X P (-^P)^' >w = n G8S = G(H-O

(3.2.26)

"*= t _ ^/V3 where the subscript (eff) indicates an effective quantity, i/f is a measure of polymer strain hardening, Ix and I2 are the first and second invariants of the finger tensor, and £ is a structure memory function. As with all models to date the modulus had to be adjusted to fit the data. For viscosity, we used the expression given by Gupta. The equilibrium yield stress and its temperature dependence were not reported in Gupta's study. They have been treated as two parameters in the simulation. This of course adds to the adjustable parameters. The yield was defined as: Y= 10" 15 Qxp(AEy/RT)

where the activation energy of yield is assumed to be similar to that of viscosity. It should be pointed out that these parameters were not adjusted for each run number and, in fact, the simulation result is not very sensitive to the value of the equilibrium yield stress. Varying the yield stress over a range of 50% may cause the predicted PET to move up or down with respect to the die without much change in bubble shape if other parameters are slightly adjusted. The hardening constant, Q1, defined in Eq. (3.2.26), is another parameter. We have assigned a value of 0.06 to it in the simulation of Gupta's data, and find that it produces a fit. The hardening constant is also not adjusted with the run number. The parameters that we adjusted in the simulation with the sample number are initial angle of the film contour, initial hoop stress, and a factor to modify modulus, CG. The results of this model are shown in Fig. 3.2.6. We see that by setting the appropriate constants to zero the model reduces to the Maxwell or Newtonian model. For more complete discussions of this model the reader is referred to [8, 9, 12,21].

3.2.3.3

Two-Phase Liquid Models

Modeling the mechanics of film blowing using two phases was introduced by Campbell and Cao [25], who proposed that the film, in the tube-forming area, is composed of two layers.

This work was followed by research of Yoon and Park [26] in which the same technique of Campbell and Cao was extended to Newtonian and Maxwell rheological layers. The surface temperature of the film differs from the bulk average temperature (through thickness) by as much as 15 to 20 0 C in the tube-forming area [27]. This supported the concept that the film has a cooler crystalline layer near the surface and a hotter fluid layer in the interior. Extending the concept of [8,12] yield stress as a criterion for cessation of radial deformation beyond the freeze line leading to plastic-elastic transition (PET), the two-phase analysis of the film blowing process incorporates both viscoelasticity of the melt and yield stress [28] in the solidlike phase as a criterion for the demarcation between predominantly plastic to elastic deformations. This essentially plastic to elastic behavior in the solidlike phase provides a rheological constraint to define the point where the film remains parallel to the tube center line and replaces the traditional kinematically defined freeze line [29].

3.2.3.4

Two-Phase Crystalline Model

Analysis of heat transfer in the film blowing process is essential because the thermal state of the material defines the rheological state of the polymer during the course of the process. Polymer rheological properties are temperature dependent and thus the thermal state of the polymer dictates the polymer's response to an external force. Polymers can be treated Theologically as a combination of a viscous liquids or as elastic solids. All combinations of these effects can be important depending on their temperature. The highly nonisothermal environment in the film blowing process leads to very distinct behavior of the polymer melt at different stages of the process. In film blowing, the heat is transferred from the film to the surroundings predominantly from the outer surface of the bubble by convective and radiative means. In steady-state operations the energy transmission to the trapped air inside the bubble is treated as insignificant. As a result of the temperature gradient across the film, for a bubble of finite thickness, the surface temperature of the bubble reaches the crystalline melting point of the polymer well below the freeze line. Because of the finite thermal conductivity of the polymer melts and limiting heat transfer rates, we cannot assume an instant crystallization of melt throughout the film thickness. So it is believed here that after the inception of the crystallized phase on the film surface, its thickness grows as the film moves toward the nip rolls and more heat is transferred from the film to the surroundings. An idealistic separation of the two phases is shown in Fig. 3.2.7. The rheological behavior of the two phases is believed to be drastically different and hence we use appropriate rheological equations of state for both phases in this investigation. Cessation of the deformation in the radial direction is attributed to the small applied force in that direction instead an infinite viscosity [29]. The Levy-Mises yield criterion is used to define the plastic and elastic deformations of the crystallized phase. This defines the beginning of the reversible stretching on a rheological basis. An upper convected Maxwell viscoelastic equation of state is used to describe the rheology in the liquid region. Before the crystallized phase stops yielding, it is modeled as a perfectly plastic material. For numerical purposes, the modeling area of interest is divided into four distinct regions (Fig. 3.2.7). Region 1 starts at the die and consists only of the liquid phase of the melt. Region 2 begins when the surface temperature of the film reaches the crystallizing temperature of the melt.

This temperature need not necessarily be the crystallization temperature of the polymer under quiescent conditions (supercooling can be taken into consideratioin). It ends when the yield stress of the crystallized phase exceeds the effective applied stress. This plastic to elastic transition replaces the classic freeze line. Deformations in the third and fourth regions are elastic and are negligible owing to the high modulus of the crystallized phase. The third region allows crystallization to continue over the entire thickness of the melt after the transition has been achieved. The kinematic analysis follows Eqs. (3.2.1) to (3.2.7).

3.2.3.5

Constitutive Relationships

In this section we discuss again some of the rheology previously mentioned because it is used in a different context. The total stress tensor components are the sum of the deviatoric stress and a hydrostatic component: °V = -p8v + tv

(3-2.27)

Reg 3 Region 1

Region 4

Region 2

To nip-rolls Solid-like phase

Bubble Radius

Liquid-like phase

Boundaries: 1-2 Crystallization

begins

2-3 Solid phase stops yielding 3-4 Liquid phase disappears

Axial distance Figure 3.2.7 Two-phase concept

The liquid phase is modeled by the Maxwell equation of state given by: y|/r(1) + T = 2rjD

(3.2.28)

where the term T ( 1 ) denotes the upper convective Oldroyd derivative of the stress tensor components, and given by the expression: 3TJ7

3TI7

BK-

+v

T

W-

^=-i ^- <-< KT) = ^ z Lr(I)

(32 29)

'

(3.2.30)

The relaxation time X is a function of the local temperature. The crystallized phase is modelled as a perfect plastic material which behaves according to the constitutive relation in Eq. (3.2.31):

T = ^=D

if^>7/V3

V 7 ^D T = 2GE

(3.2.31) iff JWx < 7 / V 3

The elastic strain tensor, E, is defined in Eq. (3.2.32):

/In^

0

0 \

v

c

E=

0

V

0

In^

K

0

0

(3.2.32)

In-

rj

Here the subscript c refers to the reference value of the variable used to evaluate the strain. The second invariant of a diagonal tensor is the sum of the squares of the diagonal components. The constant k is related to yield stress in elongation by Eq. (3.2.33):

* =^

3.2.3.6

(3.2.33)

Energy Balance Equation

We approximate the heat transfer in the bubble as if it were a one-dimensional problem. Using the conservation of energy principle on a differential section of the bubble and assuming that the heat transfer to the air bubble is small compared to heat transfer to the surroundings, the air ring wall jet is: PCphvcos9—

= -U(T - Ta)

(3.2.34)

where C p is the heat capacity of polymer, U is the convective heat transfer coefficient to the wall jet, T and Ta are film and ambient temperature respectively, and p is the density of polymer melt. Heat generation due to the frictional forces and radiative cooling of the film are considered to be small and are neglected in the above expression.

3.2.3.7

The Two-Phase Relationships

At some point on the bubble the exterior of the film reaches a temperature where a "solid" phase begins to form. The deformation equations change to reflect the constitutive relation for this new phase. Here, we have assumed that the deformation rate in the machine and the transverse directions are the same for both phases. This defines the deformation rate in the thickness direction to be the same in both phases also. These assumptions of a single-phase system are thus carried over to this multiphase system. This is in part a consequence of the necessity of using the shell-membrane approximation. The deformation of the liquid phase is still governed by the single-phase system of equations with quantities referring to that of the liquid phase. The deformation of the crystallized phase is described by Eq. (3.2.32). The superscript s refers to the quantities pertaining to crystallized phase and 1 to the liquid phase in the remainder of this analysis. The forces per unit thickness of the film in the radial and machine directions are then respectively: P1 = ZzVn +AV 11 PH

=

(3.2.35)

hlaf33 +hsa\3

(3.2.36)

The new unknowns, relative to the one-phase problem discussed previously, are the stress components for the crystallized phase and its thickness. The added equations are the equation of state for the crystallized phase and the energy balance during crystallization. It is to be remembered that the two phases are in thermal equilibrium and the numerical implementation of the model would require a step change of normal stress components at the interface which is one of the major weaknesses of this model.

3.2.3.8

Liquid Phase Thickness Reduction

The rate of mass transfer from the liquid to the crystallized phase is controlled by the heat transfer rate and the heat of crystallization of the polymer melt, and basically determines the length of the two-phase region. The energy balance during crystallization then follows:

AH^cosO^- = -2nrU(Tc - TJ

(3.2.37)

The important assumption in this relation is instantaneous crystallization of the melt, locally, to the ultimate crystallinity of the polymer, denoted by
(3.2.38)

It is assumed that the mass densities of the two phases are the same. We use this assumption because it has been demonstrated that introduction of two densities does not substantially affect the simulation results [25]. Using these two equations one can now determine the liquid phase thickness reduction:

* dz

' v cos 6

tffV) \v

r)

,3.2.39,

where J =^ % ^

(3.2.40)

AHf(p p

The solid-phase thickness can be obtained using a macroscopic mass balance differentially throughout the film.

3.2.3.9

Deformation of the Crystallized Phase

The purely plastic deformation of the crystallized phase before the freeze line is represented by the Levy-Mises plastic flow equation. The model can be treated as the Newtonian model with the effective viscosity related to the yield stress. The deformation rates in the crystallized phase are obtained from liquid-phase calculations. The crystallized phase reverts to the elastic model after PET is reached. This is justified because a differential drop in the temperature of the crystallized phase would increase its yield stress so that it no longer satisfies the yield condition and deformation in the film can only be elastic and reversible.

3.2.3.10 Numerical Scheme The equations governing the flow in each region are derived separately and were solved using the shooting method. The boundary conditions available are found in Eq. (3.2.42). Because we are short of three boundary conditions, we asssumed 6 to be zero at the die and used the radial stress and pressure at the die as parameters to givQ reasonable results. A similar procedure was followed by other investigators. The governing system of equations r

die — r 0

^die = K T^ = T0 ldie

(3.2.41) 2nh0r0 cos O0

was changed from a single liquid phase to two phases when the crystallization temperature was reached. The starting values of the variables at the beginning of region 2 were taken to be the last values from the first region caculations. The temperature of the melt in this region remains constant at the crystallization temperature while the two phase exist. After the PET, the temperature remains constant only until all the melt from the liquid phase is transformed into the crystallized phase. The temperature begins to fall in region 4. For details of the simulation, including the working equations, see [29]. We tested this model using the data of Kanai and White for high-density polyethylene in the blown film process. The theory and the data for radius (Fig. 3.2.8) velocity (Fig. 3.2.9), and temperature (Fig. 3.2.10) are in reasonable good agreement. The largest deviation was in temperature above the PET and this suggests that the literature heat transfer coefficients in the zone are not very accurate.

Bubble radius cm.

Theoretical Experimental

Figure 3.2.8 Comparison of theoretical and experimental radius profiles

Axial velocity cm./sec.

Dimensional distance from die cm.

Figure 3.2.9 Comparison of theoretical and experimental velocity profiles

Dimensional distance from die cm.

Bubble Temperature in K Figure 3.2.10 Comparison of theoretical and experimental temperature profiles

Theoretical Experimental

Experimental Theoretical

Dimensional Distance from Die cm.

3.2.4

Property Development in Blown Film

3.2.4.1

Introduction

The blown film process leads to biaxially oriented thin polymeric films. Stretching the polymer in two directions provides an opportunity, not present in the cast film equipment, to impart a predetermined amount of molecular orientation in both directions to yield films of tailored response. Despite the advances made toward the better understanding of the process fluid dynamics and associated physical phenomena, theoretical prediction has not replaced art in developing process/property cause and effect. Trial and error, and experience still dominate the methods of troubleshooting and scaleup on blown film equipment. A number of techniques have been used to characterize the morphology produced by the flown film process. They include birefringence, wide-angle X-ray diffraction, and scanning and transmission electron microscopy [30 to 33]. Studies employing one or more of these methods of film characterization often use the blowup ratio and the drawratio as variables representing the processing conditions. Use of more visible processing conditions such as melt temperature, cooling air flow rate, and frost line height have only obscured the correlation between the film properties and processing conditions [34 to 38]. A more basic approach to analyze the correlation between film properties and processing had its beginning as early as 1970. Pearson and Petrie in their discussion mentioned that the freeze line neighbourhood was the most important area in the development of ultimate film properties [39]. For a given set of processing conditions on blown film equipment, polymer rheological properties also significantly affect the film properties [40]. This approach has been modified by several researchers to use strain or stress history to correlate film properties [41 to 47]. Understanding of these complex relationships will require using realistic models to relate the measurable film variables such as birefringence, crystal orientation, and recoverable strain to the process dynamics that caused these historical characteristics in the film product. We have developed a two-phase model for the film blowing of crystalline materials [29], and a main thrust of this model is the introduction of the plastic deformation of the melt in the neighborhood of plastic-elastic transition. The experimental results presented in the following section related to the plastic strain in the neighborhood of freeze line, will show that it plays a significant role in defining the film's ultimate physical properties. The importance of strain rate during the crystallization is also introduced. The so-called plastic strain is an analogy used in illustration of the rheological behavior of a perfectly plastic-elastic material [28]. To familiarize the reader with the methods used to obtain these data from experiments, we develop and discuss the analysis techniques used in this investigation in the next sections.

3.2.4.2

Theoretical

The kinematics of blow film extensional flow for a volume preserving melt as previously defined is represented by the deformation rate tensor:

(3.2.42)

Integration of principle strain rates with respect to time results in the strains given by:

e ln

(3243)

»= i>

--

S 33 =In^g

(3.2.44)

where direction 1 denotes machines directions, 3 denotes the cross or transverse direction, and ^0 is the time above the die where the relaxation time of the structure is long compared to the process time. We use these theoretically based definitions to evaluate the experimental data developed in the following section.

3.2.4.3

Experimental

3.2.43J

Blown Film Design

All films were 31.8 urn (1.25 mil) low-density polyethylene films produced on an instrumented experimental scale film line (5.1 cm) (2-in) diameter 760 urn (30 mil) die gap die 76 cm (30-in) layflat capacity, 3.8 cm (1.5-in) Killion extruder) using the resins whose characteristics are shown in Table 3.2.1. The processing variables, as shown in Table 3.2.2 for one of the resins, include the blowup and drawdown ratios. The other conditions varied in the study are melt temperature at the die, mass flow rate of the melt, and the cooling air flow rate. We refrain from tabulating all the information about the processing conditions for both materials but Tables 3.2.2. and 3.2.3 provide details for both LJA-402 and F5681-1. A thickness reduction of 24 (760 um to 31.8 urn) (30 mil to 1.25) was achieved with varying combinations of blow-up ratio (BUR) and drawdown ration (DR). 3.2.4.3.2

Data Acquisition and Analysis

Online measurement of surface and bulk temperature of the film was achieved by the use of a 3.43 um infrared sensor (Venzetti) and a 1.8 to 3.0 um IRCON sensor. The Venzetti signal processor directly gives the surface temperature whereas the use of a 1.8 to 3.0 um IR sensor

Table 3.2.1 Physical and Molecular Characteristics of the Resins Used in the Study LJA-4021

F5681-12

Density, (g/cc) l|, g/lOmin MP4, 0 C MW5 MW/MN 6 Mz7 Mz+18

0.9218 1.12 108.6 86448 10.21 291765 568287

0.9172 0.77 122.6 104175 4.24 284241 543967

1

Weight average molecular weight Polydispersity index 7 z average molecular weight 8 z + 1 average molecular weight

Resin

High pressure polyethylene Low pressure polyethylene 3 Melt flow index 4 Melting point 2

5

6

Table 3.2.2

Processing Variable Used to Produce 1.25 mil Film for LJA-402 LDPE

Run ID1

BUR2

MFR3

CA4

MT5

DR6

73093 730932 8393 83932 8483 8593 8693

3.023 2.569 2.037 2.037 2.6443 2.6578 2.610

4.002 4.002 4.224 4.224 6.243 6.276 10.308

3.22 3.22 3.19 6.06 6.06 5.56 9.67

232 232 232 232 232 204 204

7.948 9.34 11.7926 11.7926 9.076 9.028 8.914

1

4

Run identification number Blow-up ratio 3 Mass flow rate in kg/hr

Cooling air velocity in meter/sec. MeIt temperature in 0C 6 Draw ratio

2

Table 3.2.3

5

Processing Variable Used to Produce 1.25 mil Film for F5681-1 LLDPE

1

BUR2

MFR3

CA4

MT5

DR6

61693 61793 617932 61993 62093

2.102 2.452 1.754 2.130 2.063

2.76 2.76 2.76 2.76 1.896

3.01 3.01 3.01 2.34 2.34

234 237 237 237 238

11.69 10.16 14.09 11.63 11.89

Run ID

Run identification number Blow-up ratio 3 Mass flow rate in kg/hr

Cooling air velocity in meter/sec. MeIt temperature in 0C 6 Draw ratio

2

5

and a black body to obtain a bulk film temperature is described in detail in a published paper [27]. The video technique to obtain the film velocity and bubble radius is also described in the article by Haung and Campbell [44]. To smooth the data so obtained, we used highly nonlinear functions with seven parameters of the forms: r = (X1 - ((X2 + (x3x + (X4X2 + (X5JrV6*"7 V = P1-(P2+

p3X + ^4X2 + £ 5 xV 0 *' 7

(3.2.45 (3.2.46)

where r and v are the dimensionless bubble radius and film velocity; x = z/r0, where z is the vertical distance from the die. Once the velocity and radius function parameters are calculated, strain rates and strain can be evaluated with the use of Eqs. (3.2.43) and (3.2.44). 3.2.4.3.3 Film Properties Important physical properties of thin polymeric films include tear strength, impact strength, and tensile strength. Both tear and tensile strength of the film are typically measured in the two major directions of orientation, machine and transverse. Poor properties in one direction of the film usually result in poor impact strength. Standard ASTM methods were employed on an Elmendorf tear tester, a Spenser Impact tester, and an Instron tensile frame (for tensile

properties: ASTM D882-88). A crosshead speed of lOOmm/min was used for both lowdensity polyethylene (LDPE) and linear low-density polyethylene (LLDPE) films for the Instron tests. Ten samples were tested for each case to arrive at a representative measured value.

3.2.4.4

Results

Bubble Radius and Velocity, Dimensionless

To illustrate the procedure followed to arrive at the results, the bubble shape and velocity profiles for run 73093 are shown in Fig. 3.2.11. The points represent the data and the lines are the best fit for Eqs. (3.2.45) and (3.2.46). The strain rate profiles (Fig. 3.2.12) for the same run are obtained using the seven-parameter regression analysis after differentiating Eqs. (3.2.45) and (3.2.46) with respect to the dimensionless distance. The temperature profile is shown in Fig. 3.2.13 for the same run. Strains are calculated using Eqs. (3.2.43) and (3.2.44) in both machine and cross directions, starting at the dimensionless distance where the "constant temperature plateau" begins, which corresponds to t0, and terminating at the point where the strain rate goes to zero. The appropriate velocities and radii are calculated using Eqs. (3.2.45) and (3.2.46). Historically, we have correlated properties of blown film with machine direction of transverse direction process characteristics; usually drawndown ratio and blowup ratiio are the correlation parameters. Tas [43] recently demonstrated that film modulus could be correlated to calculated directional stress in the film. We have demonstrated [45] that both the machine direction and transverse direction film properties could be correlated to the plastic strain calculated as described previously. The problem with both the stress and the strain analysis was that there was a substantial amount of scatter, although both seemed to produce proper qualitative trends.

Bubble Radius (Exp.) Bubble Velocity (Exp.) Fitted Radius Fitted Velocity

Dimensionless Axial Distance Figure 3.2.11

Typical film velocity and radius profiles

Strain-rates, 1 /sec.

Machine Direction Cross Direction

Dimensionless Axial Distance Figure 3.2.12

Typical film strain rate profiles

Surface Temperature, Celcius

The rationale for developing the two-phase model was to develop a better physical model of the polymer dynamics during solidification of the semicrystalline polymer. Conceptually, the polymer is stretched in both the machine and transverse directions as a composite of an amorphous matrix filled with the developing crystallites. Correlation with blowup ratio and drawndown ratio assumes that the solid polymer "remembers" all deformation from the time it leaves the die. We propose that the strains and strain rate in the vicinity of the melting point plateau are more reflective of the structure in the film than blowup and drawdown ratios. The rationale is based on an anticipated much longer relaxation time at this point in the process

Dimensionless Axial Distance Figure 3.2.13

Typical film temperature profiles

lensWe Strength, MPa

owing to the temperature and the presence of the crystallites. It is important to emphasize here that the properties in both principle directions were correlated on the same axis. The crystallites, which are expected to incorporate some of the amorphous chain ends, also can be considered to be a source of physical crosslinks that will impede the ability of the amorphous molecules to return to their statistical equilibrium configuration. A potential measure of the state of nonequilibrium structure in the amorphous phase would be the stress that for any rheological fluid should be proportional to the strain rate. This is equivalent to the proposal of Tas, who found a correlation between calculated stress and modulus. We suggest that this nonequilibrium configuration may be trapped by the physical crosslinks during crystallization. Thus, the strain rate during the constant temperature stretching of the film might be a correlating parameter related to the residual stress. We use the strain rate at the onset of the crystallization plateau as our normalizing parameter. This provides an estimate of the stress-strain rate/viscosity relatioinship for about 25 urn thick film of partially crystallized polymer that has an average temperature of the crystallization plateau. Fruitwala and Shirodkar [37] have pointed out that the crystallite orientation can be used to correlate film properties; again there was substantial scatter. This orientation could be a result of the plastic strain that we have demonstrated [45] relates to the film properties. The strain in the solid phase might tend to orient the crystallites. We test this hypothesis in the paragraphs that follow. Both machine and transverse film properties are combined and are plotted against the strain rate and plastic strain in Figs. 3.2.14 to 3.2.19 except for impact strength which has only a single value for each sample. The normalized strains are calculated as the difference in the plastic strain in two major directions over the total plastic strain. A similar method was employed to calculate normalized strain rate. A surface plot of the LDPE film's tensile strength (Fig. 3.2.14) versus plastic strain and strain rate for resin LJA-402 demonstrates that almost all of the scatter previously found that has been dramatically reduced. The use of both plastic strain and strain rate as correlating variables, the result of the extension of the observations of Tas and Fruitwala and Shirodkar

Figure 3.2.14

Tensile strength of LJA-402

\mpac\S\T№g\Y\,MPa Figure 3.2.15

Impact strength of LJA-402

r\e\dS\teng\Y\,MPa

and our previous findings seem to be applicable. Figure 3.2.15 shows the Spencer impact strength variation with the normalized plastic strain and strain rate. There is only one datum point for each experimental condition because impact strength is a composite test. Figure 3.2.16 depicts the yield strengths of the LDPE film versus the plastic strain and strain rate. The drop lines on the datum point indicate the deviation of the experimental value from the regression value, represented by the surface grid. Further resin properties are found in plots (Figs. 3.2.17, 3.2.18, and 3.2.19) for the resin F5681-1, an LLDPE resin. The tear strength of the films (Fig. 3.2.18) has the most scatter about the correlating surface and it is suspected

Figure 3.2.16

Yield strength of LJA-402

TensUe SttengVa, MPa Figure 3.2.17

Tensile strength of F5681 -1

Tear Strength, Gms.

that we will need one more physically important parameter to collapse all of the data onto the surface, perhaps the time at constant temperature. The correlations in our previous work included only plastic strain and we felt that they resulted in excessive scatter. Here we utilize both the amount of plastic strain and the stress, in the form of the strain rate evaluated early in the temperature plateau region. We propose that these two kinematic effects may contribute to both amorphous and crystalline orientation. The tensile strength of the high-pressure polyethylene (LJA-402) (see Fig. 3.2.14) shows a greater sensitivity to plastic strain than that of the low-pressure low-density polyethylene (F5681-1) (Fig. 3.2.17). The presence of a higher number of long-chain branches on the

Figure 3.2.18

Tear strength of F5681-1

\mpac\ Sttentfh, MPa Figure 3.2.19

Impact strength of F5681-1

LDPE molecule may cause them to form a structure while the film freezes because the branches may interact with the growing crystallites and decrease the relaxation of the induced strain. If these structures can be frozen into the strained state, they will contribute to the enhancement of the film's physical properties. A lower slope of the best fit surface with respect to both strain and strain rate for the linear low-polyethylene resin films may be due to the absence of a large number of these strained structures on this resin. The impact strength of the films of both resins decreases with increasing normalized plastic strain (Figs. 3.2.15 to 3.2.19), but the resin type produces a different response with respect to strain rate. In Fig. 3.2.16, the yield strength increases both with an increase in plastic strain and the stress/strain rate. Tensile and impact strengths of F5681-1, two of the widely used properties to characterize films in the industry, show more convincing trends with respect to the drop lines from the surface plots; short drop lines indicate less scatter from the statistical model.

3.2.5

Summary

Starting with the original shell theory analysis of Pearson and Petrie, we have presented a historical development of the kinematics and dynamics that have been described over the past 20 years for the blown film process. We found that it is convenient to use rheological equations that provide a smooth transition from liquidlike to solidlike behavior at the platicelastic transition (PET). The aerodynamics of the air from the air ring adds a pressure term to the force balance that affects the strain and strain rate below the frost line. This change is important in film property development. A two-phase model was presented that attempts to address the physical reality that the temperature distribution through the film will result in the crystallization initiating near the surfaces of the film and migrating into the bulk as the heat is removed be radiation and convection to the cooling air. The two-phase model led to the

proposition that plastic strain could be a correlating function for film properties. It was found that this was a reasonable first step, and for the first time both machine direction and transverse direction properties could be related to a common dynamic parameter. However, there was a substantial degree of scatter when this one-way correlation was developed. Recognizing that stress/strain rate during crystallization was also a potentially important contributor to the film properties, a new two-way correlation of film properties was presented in which the property is related to a surface function with plastic strain and strain rate at the onset of the constant temperature plateau as the independent variables. This analysis works very well for most of the film properties. Tear strength had the greatest deviation from the best fit surface. Further work is now necessary to relate the process kinematics and dynamics to the polymer structure and the morphology of the product films. There is a remaining challenge of quantifying the relationship of polymer molecular properties, process kinematics, and dynamics with the ultimate morphology and physical properties.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27.

Pearson J.R.A., Petrie, C.J.S.J., Fluid Mech. (1970) 40, p. 1 Pearson, J.R.A., Petrie, C.J.S.J., J. Fluid Mech. (1970) 42, 609 Pearson, J.R.A., Petrie, CIS., Plast. Polym. (1970) 38, p. 85 Gupta, R.K., Ph.D. Dissertation, University of Delaware (1981) Han, CD., Park, XY, J. Appl. Polym. Sci. (1975) 19, p. 3257 Kanai, T., White, XL., J. Polym. Eng. (1985) 5, p. 135 Petrie, CXS., AIChE X (1975) 21, p. 275. Cao, B., Campbell, G.A., AIChe J. (1990) 36, p. 420 Campbell, G.A., Cao, B., In Polymer Rheology and Processing. Collyer, A.A., Utracki, L.A. (Eds.) (1990) Elsevier Applied Science, New York, Chapter 11 Luo, X.L., Tanner, R.I., Polym. Eng. Sci. (1985) 25, p. 620. Cain, XX, Denn, M.M., Polym. Eng. Sci. (1988) 28, p. 1527 Bird, R.B., Armstrong, R.C, Hassanger, O., Dynamics of Polymeric Liquids (1977) John Wiley & Sons, New York, p. 419 Wagner, M.H., Ph.D. Dissertation, University of Stuttgart (1978) Giesekus, H., J. Non-Newtonian Fluid Mech. (1982) 11, 29 Phan, N.T., Tanner, R.I.J., Non-Newtonian Fluid Mech. (1977) 2, 353 White, XL., Metzner, A . B , J. Appl. Polym. Sci. (1963) 8, p. 1367 Larson, R.G., Constitutive Equations for Polymer Melts and Solutions (1988) Butterworths, Boston, p. 146, 151, 197 Doi, M., Edwards, A.F., The Theory of Polymer Dynamics (1986) Clarendon Press, Oxford, p. 197-247 Alaie, S.M., Papanastasiou, T C , Int. Polym. Proc. (1993) VIII, p. 51 Campbell, G.A., Obot, N.T., Cao, B., Polym. Eng. Sci. (1992) 32, p. 751 Cao, B., Ph.D. Dissertation, Clarkson University (1990) Bird, R.B., Armstrong, R.C, Hassager, O., Dynamics of Polymeric Liquids, (1977) John Wiley & Sons, New York, p. 419 Beatty, CL., Weaver, XL., Polym. Eng. Sci. (1978) 18, p. 1109 Chow, T.S.X, Polym. Sci. (B) Polym. Phys. (1987) 25, p. 137 Campbell, G.A., Cao, B., J. Plast. Film Sheet. (1987) 3, p. 158-170 Yoon, K.S., Park, C W , Polym. Eng. Sci. (1992) 32, p. 1771-1777 Cao, B., Sweeney, P., Campbell, G.A., J. Plast. Film Sheet. (1990) 6, p. 117

28. Malvern, L.E., Introduction to the Mechanics of a Continuous Medium (1969) Prentice-Hall, Englewood Cliffs, NJ 29. Ashok, B.K., Campbell, G.A., Int. Polym. Proccess. (1992) 8, p. 240 30. Butler, T.I., Pirtle, S.E., SPEANTEC Tech. Papers (1992) p. 1833 31. Choi, K.J., White, J.L., Spruiell, XE., J. Appl. Polym. ScL (1980) 25, p. 2777 32. Kwack, T.H., Han, CD., J. Appl. Polym. ScL (1988) 35, p. 363 33. Patel, R.M., Butler, T.I., Walton, K.L., Knight, G.W, Paper presented at the Polymer Processing Society Annual Meeting, Akron, OH, April (1994) 34. Dealy, J.M., Faber, R., (1974) 14, p. 435 35. Simpson, D.M., Harrison, LR., SPEANTEC Tech. Papers (1991) p. 203 36. Butler, T.I., Lai, S., Patel, R.P., Spuria, J.E., SPEANTEC Tech. Papers (1994) p. 15 37. Fruitwala, H., Shirodkar, P.P., SPEANTEC Tech. Papers (1994) p. 2252 38. Shukhakia, A.M., SPEANTEC Tech. Papers (1994) p. 202 39. Pearson, J.R.A., Petrie, C.J.S., Plast. Polym. (1970) 38, p. 85 40. Bibee, D.V, Dohrer, K.K., Convert. Packag. (1988) March, p. 199 41. Babel, A.K., Campbell, G.A., J. Plast. Film Sheet. (1993) 9, p. 246 42. Shirodkar, P.P., Fridaus, V, Fruitwala, H., SPEANTEC (1994) p. 211 43. Tas, P.P., Paper presented at the International Polymer Processing Society Annual Meeting, Akron, OH April (1994) 44. Campbell, G.A., Haung, T.A., Adv. Polym. Technol. (1985) 5, p. 181 45. Babel, A.K., Campbell, G.A., SPEANTEC (1994) p. 224 46. Walton, K.L., Patel, R.M., SPEANTEC (1994), p. 1430 47. Babel, A.K., Nagarajan, G., Campbell, G.A. Paper presented at the International Polymer Processing Society Annual Meeting, Akron, OH April (1994)

3.3

Bubble Instability: Experimental Evaluation Gregory A. Campbell and Paul A. Sweeney

3.3.1 Introduction

142

3.3.2 Theory

144

3.3.3 Qualitative Experimental Analysis

144

3.3.4 Quantitative Stability Analysis 3.3.4.1 Equipment 3.3.4.2 Bubble Stability Diameter Analysis 3.3.4.3 ANOVA of Material and Process Sensitivity 3.3.4.4 Graphical Analysis 3.3.4.5 Fourier Transform Analysis

145 145 148 150 152 154

3.3.5 Summary

155

3.3.1

Introduction

The blown film process (Fig. 3.3.1) is used extensively to produce biaxially oriented film for many commercial products. This process produces a wide range of products including garbage bags, atmospheric balloons, irrigation pond liners, and waste land fill liners. In this process an annulus of polymer is extruded through a die and the polymer is biaxially oriented by an enclosed column of air and the nip rolls. The polymer annulus is simultaneously cooled into the proper shape by radiative and convective heat transfer. The convective cooling is provided by air from the air ring. The two dimensions that are of most importance to the film producer are the "layflat width,' the width of the flattened tube and the film thickness, or "gauge." As in all commercial processes, it is desirable to operate at a production rate that maximizes profits while maintaining key properties. This is usually the highest throughput rate possible. When the process reaches its stability limit, either or both of the desired dimensions vary "randomly" beyong acceptable limits. Examples of typical bubble shapes encountered when the bubble becomes unstable are diagrammed in Fig. 3.3.2. We note that the different types of instability, draw resonance, bubble instability, helical instability, and metastability have characteristic structure with regard to the relative position of sides of the bubble as a function of the distance from the die and thus as a function of time at a fixed distance from the die. Laboratory data from Fleissner [1] (Fig. 3.3.3) depict typical changes in layflat width and thickness for metastable instability.

Nip Rolls

Collapsing Frame Film Cooling Air

Takeup Reel

Air Ring Molten Polymer

Cooling Air Supply Spiral Mandrel Die Inflation Air Supply

Figure 3.3.1

Blown film process

Metastability

Bubble Instability

Draw Resonance

weight per 21 cm length

Types of instabilities

thickness

layflat width

Figure 3.3.2

Helical Instability

time Figure 3.3.3

Blown film dimension variation [1]

When the film dimensions vary with time, the local biaxial extension also varies and one expects a change in important physical properties such as impact strength and tear strength.

3.3.2

Theory

Recognition that process instability causes substantial loss of blown film properties has led to several literature reports about the cause and control of these instabilities. Although blown flim has been a commercial reality since the 1940s, the first theory was not published until 1970 when Pearson and Petrie [2, 3] applied membrane shell theory to the blown film process. The earliest theoretical treatment of blown film instability was published by Yeow [4] in 1976. Yeow published a linear stability analysis of the blown film process assuming an isothermal, Newtonian fluid. He calculated neutral stability curves for the operating space of inflation pressure, takeup force, and freeze line height. However, because of the simple model and potentially the limitations of linear stability analysis, the predicted results did not agree quantitatively with experimental results reported later. Cain and Denn [5] used Newman's method to solve the steady-state model equations for the blown film process. This method allows takeup force and inflation pressure to be treated as variables. Cain and Denn produced operating curves for the Newtonian and Maxwell rheological fluids. The results show the maximum amplification rate of the disturbance and its frequency for various operating parameters. They demonstrated that the predicted instabilities depend on which operating parameters are specified. Thus, their results suggest that blown film stability depends on the process variables used to control the process. As an example, Cain and Denn predict that the current control method of manual manipulation of the amount of air in the bubble will result in more stable operation than an advance automatic control scheme that controls internal bubble pressure. To date, these are the only extensive literature reports on blown film stability theory.

3.3.3

Qualitative Experimental Analysis

Essentially all of the early experimental work on blown film stability involved "subjective" analysis of the process and thus judgments as to the limits of the process stability. Early work on experimental evaluation of blown film stability was undertaken by Han and Park [6] and Han and Sherry [7], using high-speed motion pictures. In their investigations, they determined magnitudes of step changes in bubble pressure or nip speed necessary to perturb the system such that it would not return to a stable state. The authors concluded that higher polymer shear thinning characterises led to more rapid cooling, which increased the viscosity and stabilized the bubble. The group at Akron University—Kanai and White [8], Minoshima and White [9], White and Yamane [10], Kang et al. [11]—concentrated on determining a stable operating space of a laboratory blown film line. They developed three-dimensional correlations that related blown

film bubble stability to blowup ratio, drawdown ratio, and frost line height. They found that a blowup ratio of 1 tended to produce bubble draw resonance characteristics. They also found that high blow-up ratios and low drawdown ratios tended to produce helical instability. The authors concluded from their observations that deformation hardening during processing should enhance the system's stability because the viscosity will increase during processing. The conclusions in the two previous paragraphs led to opposite suggestions as to which rheology resin should exhibit to obtain maximum stability; White and co-workers propose deformation rate hardening and Han and co-workers propose shear thinning. More recently Fleissner [1] addressed this issue in an extensive experimental analysis and discussion regarding the interaction of polymer rheology and heat transfer on blown film stability. Fleissner determined that deformation hardening is more likely to produce stable blown film bubbles. If heat transfer is allowed to dominate, then deformation thinning materials will cool more rapidly and thus enhance stability because of the increase in viscosity as the temperature decreases. Fleissner concludes that although the rheological deformation characteristics are potentially important to film stability, it is probably better to rely on the system heat transfer to stabilize the bubble by lowering the temperature and thus raising the viscosity.

3.3.4

Quantitative Stability Analysis

The main limitation of the experimental research described in the previous section is that stability is assessed in a qualitative, pass/fail manner. Because almost all commercial blown film production lines exhibit some type and degree of instability, it is desirable to quantify the extent of the instability and relate it to the film properties and the process parameters. Such a system was reported by Sweeney et al. [12]. In this study, a real time video system was developed and used to evaluate the addition of low-density polyethylene (LDPE) to linear low-density polyethylene (LLDPE) to reduce process instability. This real time device and its application are described in detail in the remainder of the chapter. Most of the data and the analysis described in the following sections could be accomplished using commercial frame grabber boards, if an offline or restricted time frame is adequate for the experimental needs. The real time device provides instant analysis and thus makes process parameter evaluation rapid, and it can also potentially be used for online process control.

3.3.4.1

Equipment

The goal of a real time quantitative system is to capture data noninvasively and develop an analysis in a time frame shorter than the characteristic time of the process. The noncontact part of this system is a video camera (Fig. 3.3.4). Assuming an accuracy of 1000 pixels per line and that a commercial frame grabber collects about 500 lines per frame, a real time system has to process about 15,000,000 sixteen-bit words of data per second to completely find bubble edges. Even if one could use one line, all the data would still be transferred into the computer memory. This type of processing load is generally beyond even the fastest 80-

486 personal computer systems today. Thus, the authors developed a real time analog filter [13], or edge detector, which conditions the analog signal from the video camera so that only the bubble edges are recorded as digital words. This reduces the data from 15,000,000 to 31,000 points per second. A 8 MHz 80-286 personal computer can handle this data rate. The complete hardware system for stability analysis of the blown film process is diagrammed in Fig. 3.3.4. The blown film bubble is monitored continuously using a conventional video or CCD camera. The camera is gen-locked using a syncronous pulse from the edge detector. The video signal is received and conditioned by the edge detector. The digital locations of the edges are transferred to the personal computer through a Direct Memory Access (DMA) adapter. The video signal can also be optionally forwarded to a VCR and monitor to maintain a permanent record of the experiment and a real time picture of the experiment. The edge modifies the video signal so that detected edges are highlighted on the recorder and monitor. This allows the experimenter to determine if the sensitivity of the edge detection is sufficient to find the desired edges for a given experimental setup. A complete description of the device can be found in [14]. As with all video or photographic systems, one must develop standards of length and time. The time standard is built into the video system and we thus have either 1/30 or 1/60 of a second information by utilizing the whole or half frame information because of the interlacing nature of the standard video system. In this work, we generally use the whole

VIDEO CAMERA

VIDEO SIGNAL

SYNC LINE VCR

EDGE DETECTOR

MONITOR VIDEO SIGNAL

VIDEO SIGNAL

PERSONAL COMPUTER FOR DATA ANALYSIS AND RECORDING Figure 3.3.4

Stability analysis system

frame, 1/30 of a second time base. We use a clock rate in the analog filter that gives 909 pixels per video scan line. Thus, if the camera detects an area 909 mm (35.8 in) wide, the system resolution would be 1 mm (0.039 in). To maximize the system accuracy the camera should be focused so that the desired event will just fit into the cameras field of vision. One places a standard, an object of known size, into the video path at the distance where the bubble is to be monitored and the standard is used to produce a quantitative relationship between the video line number and a vertical distance as well as the number of pixels per horizontal length. It is also desirable to position the camera so that its center line corresponds to the center line of the blown film process. Regarding the blown film process, the data that we desire for a stability analysis can be related to Fig. 3.3.5. The reference plane corresponds to the left most edge of the camera's field of view, and has a pixel number of 0. We see from Fig. 3.3.5 that the diameter at any point can be related to the right edge count minus the left edge count. The left and right side radii can be evaluated from the two data and the center line count that was determined during the setup. The left edge is the first edge detected by the analog filter and its location is the first word recorded in the analog filter. The right edge detected next and is the second word recorded in the analog filter. These data are transferred to the computer for each scan line during each frame, every 1/30 of a second. This produces a near real time buffer of the whole

Bubble Position Measurements Center Line Distance to Left Edge

Distance to Right Edge

Reference Plane Figure 3.3.5

Blown film stability data reference

Air Ring

frame's bubble edges. One can then analyze all or part of the information depending on what is the desired experimental response. In one of the examples that follows only one scan line above the bubble frost line was recorded permanently by moving the only data for that scan line to an analysis buffer. All of the remaining data were discarded per frame. In another example, 19 lines were extracted from just above the air ring to above the frost line, and the stability at each line was evaluated to determine the dynamics of the instability as a function of position.

3.3.4.2

Bubble Stability Diameter Analysis

As an example of the utility of this system for stability evaluation we examine the addition of LDPE resins to LLDPE resins to improve the process stability. More details of this evaluation can be found in [12]. In this case, we used the information from one line of data above the frost line on the bubble and we evaluated the diameter for a period of time. We calcualted a diameter at each frame, and then calculated a standard deviation from this table of diameters. The mean diameter, Z)mean, is the average diameter in the table, or the average of the different in the right and left position data. We then calculate the standard deviation of the bubble's right and left positions, Gx and G1. We used the following to calculate a diameter range, Dx, that will indicate the process stability: Anax = Anean + (^r + ™\) Anin = Anean ~ 0<7r + «*l) ^T

^max

^min

A small diameter range indicates a more stable process.

Time, sec

Bubble Edge Position vs Time

Edge Position, cm Figure 3.3.6

Base resin bubble edges

As an example of the utility of this analysis, we present an industrial trial where two LDPE resins, 2.00 and 0.25 MI were added to 1.0 MI LLDPE to improve its stability. The object was to determine the effect of the concentrations of the two LDPE resins on the process stability. The concentration of the LDPE was limited to 5% so as not to affect the film properties adversely. The evaluation was carried out on a commercial size, 78.6 mm extruder with a 15.24 cm die with a 0.254 cm die gap. The line had a Macro Corporation dual lip air ring and internal bubble cooling. The nominal processing conditions were: melt temperature 425 0 C, output 132 kg/h, lay flat 635 mm, blowup ratio-2, film gauge 0.0254 mm, cooling air temperature 54 0 C. The edge positions for the base resin are diagrammed in Fig. 3.3.6. The diameter range for the near LLDPE was 24.4 cm. When either LDPE resin was blended into the LLDPE, the stability improved (Figs. 3.3.7 and 3.3.8). We see that the 2.0 MI resin did not improve the stability when increased from 2.5 to 5wt% (Fig. 3.3.7). In contrast, the stability of the process continued to improve as the 0.25 MI resin was increased in concentration (Fig. 3.3.8).

Diameter Range, cm

The Effect of 2 MI LDPE Concentration

Weight Percent MI Resin Figure 3.3.7

Stability improvement

Diameter Range, cm

The Effect of 0.25 MI LDPE Concentration

Weight Percent of 0.25 MI Resin Figure 3.3.8

Stability improvement

The most likely explanation for these different responses for the two resins is in the differences in the long-chain branching characteristics in the two LDPE samples.

3.3.4.3

ANOVA of Material and Process Sensitivity

Because of the complexity and lack of a cause and effect model for blown film stability, a factorial design and an analysis of variance (ANOVA) was utilized to evaluate it. The complete discussion can be found elsewhere [14]. Here, we provide an overview of the findings. In the investigation, three resins were evaluated: a high pressure LDPE resin and two experimental LLDPE resins with 5 to 6% hexene co-monomer content. The major difference between the two LLDPE resins was the polydispersity, 4.25 versus 5.36. The experiments were run on a Killion KN-150,24-1 extruder with a 3:1 compression ratio screw. The die was a 2-inch spiral mandrel film die that was run with a 30 mil die gap. The cooling air was

supplied with a Sano single lip or a Western dual lip air rings. Air was supplied with a Spenser Vortex blower and passed through a heat exchanger for temperature control. Statistically designed experimental ANOVA analysis [15] is used to determine which factors have a significant effect on the process response, in this case the stability of the process. In an experimental design the factors that are expected to have an influence on the desired response are identified first. Then an experiment is designed in which each variable is evaluated at two or more levels. In this experimental design, each experiment was repeated six times to provide a statistically significant variance. Analysis of variance assumes the dependent variable is normally distributed; however, the variance of the data is not normally distributed unless a very large number of samples are taken. An alternative to taking large numbers of samples is to transform the data into a form that has a tendency to be normally distributed. We used the following transformation to improve the normality of the distribution: N = —101Og1 o (variance) This transformation is recommended by Phadke [16] when variance is the dependent variable in the model. We refer to N as the stability characteristic. The paragraphs below summarize this anlaysis for this experimental design. Using the data in Table 3.3.1, we see that for the laboratory line, the blowup ratio and air ring type have significant effects on the stability of the LDPE. We also observe that for these sets of conditions, the diameter or both the diameter and both sides of the bubble have significant effects. The velocity ratio did not have a statistically significant effect for these experiments. In Table 3.3.2, we see that the utility of this experimental technique, quantifying the response of both sides of the bubble independently as well as the diameter, is demonstrated by identifying that the response of the right and left sides of the bubble are different. This could lead the experimenter to examine further the process to determine which component is contributing to the nonsymmetrical response of the process stability. We also observe that the air ring did not have a significant effect in this phase of the analysis but it did have several significant two-way interactions. This is one indication that the stability of the blown film process is controlled by a complex interaction of resin characteristics and process dynamics. The results from the equivalent LLDPE ANOVA can be summarized as follows. Melt temperature, blowup ratio, air ring, resin/velocity ratio, and melt temperature/blowup ratio had no significant effects. Significant effects for the diameter model were resin, velocity ratio, resin/melt temperature, resin/blowup ratio, resin/air ring, melt temperature/velocity ratio, Table 3.3.1 ANOVA for LDPE with Constant Polymer and Air Flow Factor/interaction Melt temp Blowup ratio Velocity ratio Air ring Melt temp/blowup Melt temp/velocity ratio Melt temp/air ring Blowup ratio/velocity ratio Blowup ratio/air ring Velocity ratio/air ring

Diameter

Left

Right

Y

YY

Y Y

YY

Y Y Y

YY YY

Table 3.3.2 ANOVA for LDPE with Constant Melt Temperature, Blowup Ratio and Velocity Ratio Factor/interaction Air ring Polymer flow Air flow Air ring/polymer flow Air ring/air flow Polymer flow/air flow

Diameter

Left

Right

Y Y

Y Y

Y Y

Y Y

blowup ratio/air ring, and air ring/velocity ratio. The right side and left side models had significant effects from the following interactions: resin/blowup ratio, blowup ratio, velocity ratio, and blowup ratio/air ring. It is interesting to note that the two LLDPE resins had different stability characteristics even though their only major difference was polydispersity. It was found that the relatively small increase in polydispersity significantly increased the stability of LLDPE resin #1. It is also interesting to note that for these materials, the LDPE stability was sensitive to blowup ratio and the LLDPEs were not. Conversely, the LLDPEs were sensitive to velocity ratio, whereas the LDPE was not. It is interesting to note that for this limited experimental space, the melt temperature did not have a single factor significant effect for any of the resins, but it interacted with several other parameters including resin type. Caution should be exercised when extrapolating these results to other systems because of the size of the line that was used to collect the data. The results are presented as a guide as to quantitative stability analysis with this type of equipment and a statistically designed experiment. Moreover, the data can lead to identification of factors that give the greatest leverage in optimizing process stability for a given line and resin types.

3.3.4.4

Graphical Analysis

Once the important stability parameters of the resin type and process parameters have been identified, the dynamics of the development of the instability can be evaluated graphically. The graphical technique discussed in this section leads to more detailed understanding of the cause of the instability. As an illustrative example, we will discuss the stability of the LDPE resin described in Section 3.4.3.3 with respect to the effect of blowup ratio on bubble stability. In Fig. 3.3.9 the right and left sides of the mean radii are plotted along with the log (variance) for the diameter and the left and right radii. The three variances were our measures of stability, as a function of distance from the die. In these experiments 19 video lines were sampled and the variance was calculated for each line using left side data, right side data, and diameter data. The smaller the log (variance), the higher the level of instabilty. In Fig. 3.3.9 for a blowup ratio of 2.0, the bubble is quite stable except at two places, 5 and 9 inches above the die. At all other positions the log (variance) is about 40. When the blowup ratio is increased to 2.5 (Fig. 3.3.10), the same reversible excursion occurs at about 5 inches, but at about 7 inches, the bubble is very unstable and remains unstable through the frost line. This film would have

Resin = LJA-402 Blow Up Ratio = 2.0 Velocity Ratio = 7 Extrusion Temperature = 4000F Air Ring = Single Lip

Position, inches

-10 log(variance)

Left Right Diameter Right Side Position " Left Side Position

Distance above die, inches Figure 3.3.9 Graphical analysis for BUR — 2

Resin = IJA-402

Air Flow Rate =175 CFM Polymer Flow Rate = 0.3 lb/min Air Ring = Single Lip

Position, inches

-10 log(variance)

Left Right Diameter Right Side Position Left Side Position

Distance above die, inches Figure 3.3.10 Graphical analysis for BUR = 2.5

Resin = UA-402 Blow Up Ratio = 3.0 Velocity Ratio = 7 Extrusion Temperature = 4000F Air Ring = Single Lip

Position, inches

-10 log (variance)

Left Right Diameter Right Side Position Left Side Position

Distance above die, inches Figure 3.3.11

Graphical analysis for BUR = 3.0

very nonuniform properties. When the blowup ratio is increased to 3.0 (Fig. 3.3.11), the bubble shows some degree of instability below 5 inches and then returns to relatively good stability through the frost line. It would appear that this air ring does not produce a stable bubble at a blowup ratio of 2.5 for this LDPE. By using this graphical technique a more complete cause and effect relationship can be developed for process stability investigations. This information can then be used to make specific process improvements to minimize instabilities in this process.

3.3.4.5

Fourier Transform Analysis

Using the same data that were analyzed for the ANOVA we can use Fourier transform results to correlate the instability frequency to that of the fundamental frequencies of the process, such as the rotation speed of the screw, the blower, and the temperature controller cycles. When this anlaysis was applied to the above experimental data, the dominant frequencies were low, in the range of less than 2 Hz. The screw rotation speed was also in the less than 2 Hz range for this set of experiments so it is suspected that the screw rotation is a forcing function for the instabilities observed in these experiments.

3.3.5

Summary

The evaluation of stability and its theoretical understanding still require substantial work to be able to predict the stability of a blown film process of arbitrary combinations of materials and equipment. The evaluation of blown film process stability has evolved from a qualitative paradigm to one of quantitative measurement of the bubble edges as a function of time and position above the die. By using data from the real time measurement of the edges, several types of quantitative analysis can be used to quantify the type and magnitude of the stability. An understanding of the cause and effect relationships of process instability can then be used to optimize the process to maximize output while maintaining acceptable product properties.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.

Fleissner, M., Int. Polym. Process. (1988) 2, p. 229 Pearson, J.R.A., Petrie, C.J.S., J. Fluid Mech. (1970) 40, p.l Pearson, J.R.A., Petrie, C.J.S., J. Fluid Mech. (1970) 42, p. 609 Yeow, Y.L., J. Fluid Mech. (1976) 75, p. 577 Cain, J.J., Denn, M.M., Polym. Eng. Sci. (1988) 2, p. 1527 Han, CD., Park, J.Y, J. Appl. Polym. Sci. (1975) 19, p. 3291 Han, CD., Sherry, R., Indust. Eng. Chem. Fund. (1977) 16, p. 49 Kanai, T., White, J.L., Polym. Eng. Sci. (1984) 24, p. 1185 Minoshimam, W., White, J.L., J. Non-Newtonian Fluid Mech. (1986) 19, p. 275 White, J.L., Yamane, H., Pure Appl. Chem. (1987) 59, p. 193. Kang, H.J., White, J.L., Cakmak, M., Int. Polym. Process. (1990) 5, p. 62 Sweeney, RA., Campbell, GA., Feeney, F.A., J. Int. Polym. Process. (1992) VII, p. 229 Campbell, GA., Sweeney, PA., U.S. Patent 5,272,649 (1993) Sweeney, PA., Ph.D. Dissertation, Clarkson University (1994) Steel, R.G.D., Torrie, J.H., Principles and Procedures of Statistics (1960) McGraw-Hill, New York Phadke, M.S., Quality Engineering Using Robust Design (1989) Prentice-Hall, Englewood CHfTs, NJ

3.4

Optical Properties and Structural Characteristics of Tubular Film James L. White

3.4.1 Introduction

157

3.4.2 Background 3.4.2.1 Structural Characteristics 3.4.2.2 Electromagnetic Theory and Optical Characteristics 3.4.2.3 Theory of Dielectrics 3.4.2.4 Orientation 3.4.2.5 Interaction of Electromagnetic Waves with Surfaces

157 157 158 161 162 164

3.4.3 Measurement Methods 3.4.3.1 Measurement of Crystallinity 3.4.3.2 Measurement of Orientation in Films 3.4.3.3 Measurement of Haze

166 166 168 169

3.4.4 Orientation Development in Vitrifying Tubular Film

170

3.4.5 Structure Development in Crystalline Tubular Film

171

3.4.6 Mechanism of Haze

174

3.4.1

Introduction

Tubular film extrusion dates from technologies associated with producing cellulosic sausage casings [1—4]. Polystyrene was converted into film by tubular blowing processes by Norddeutsche Seekabelwerke AG in the early 1930s [5]. Polyethylene was developed by ICI in the 1930s and in about 1950 became the first important film forming polymer based on tubular film processes [6 to 9]. Most early patents focused on producing the film and not on its structural characteristics. However, concerns over structural anisotropy in sausage casings were described in the patent of Weingard and Muchlinski [4]. In the 1950s and early 1960s papers by Holmes et al. [10, 11] Huck and Clegg [12] and Kendall [13] of ICI, as well as Webber [14] of DuPoint, Pilard and Kremer [15] of US Industrial Chemical, and Wilchinsky [16] of Esso called attention to the problems associated with variations in film optical characteristics through processing. Holmes et al. [10, 11] described the first measurements of X-ray diffraction, birefringence, infrared absorption, and dichroism on polyethylene tubular film. Measurements of three-dimensional crystalline orientation in tubular film were first presented by Lindenmeyer and Lustig, of Visking [17] in 1965. Studies of the haze characteristics of polyethylene tubular film were initiated by Huck and Clegg [13] in 1961. It is our purpose in this chapter to discuss critically the structural characteristics of tubular film crystallinity, orientation, optical anisotropy, and haze. We treat this subject based on the electromagnetic theory of light [19-27].

3.4.2

Background

3.4.2.1

Structural Characteristics

Polymeric tubular film products in general have a complex structure, which exists on many different levels. Most important is structural order on the molecular level, which indicates whether the polymer exhibits crystalline order or a lesser level of order. Such crystalline order involves a three-dimensional lattice structural arrangement that may be characterized by wide-angle diffraction of X-rays (WAXS) and usually a high material density. This order is at a level of 5 Angstrom units. Crystalline polymers also exhibit order of level 100 Angstrom units associated with crystalline lamellae caused by the folding of polymer chains. This order is detectable through small-angle diffraction of X-rays (SAXS) and transmission electron microscopy. At a higher level of dimensions we have superstructure. In isotropic materials this is seen in the form of spherulites with dimensions of usually between 1000 and 100,000 Angstrom units dependent on the material and the crystallization conditions. In discussing structural characteristics of polymer films we must include the surfaces of the films, which can possess varying levels of roughness.

3.4.2.2

Electromagnetic Theory and Optical Characteristics

The optical characteristics of a material involve many features. The most fundamental of these is the refractive index (or indices) n of the material, which represents the velocity of light through the material v, as opposed to that in a vacuum c. For an isotropic material the refractive index is a scalar defined through: n=~

(3.4.1)

v

For an anisotropic material, one has, more generally, three refractive indices: associated with three basic directions. Thus: C H1=-

C n2= —

nl,n2,n3

C n

3

= -

(3.4.2)

To these quantites must be added the extents of scattering and absorption of light. The basis of the optical properties of polymers is found in Maxwell's electromagnetic theory [18-27]. Maxwell's equations for a dielectric (nonconducting) medium are: V-D = O

V-B = O

(3.4.3a,b)

VxE = - — VxH = — (3.4.3c, d) at at where E is the electrical field strength, D is Maxwell's displacement vector, B is the magnetic field strength, and H is the magnetic excitation. In Eq. (3.4.3a-d) we have neglected the presence of electrical charges and current densities. The magnetic excitation vector H in nonmagnetic materials is proportional to B through the magnetic permeability \L We may be eliminate the vectors B and H between Eqs. (3.4.3c) and (3.4.3d) by taking the curl (Vx product) of the former and the time derivative of the latter. Thus: -VxVxE =

^

(3.4.4a)

which is equivalent to: #D / ^ = [V 2 E-V(V-E)]

(3A4b)

The displacement vector D represents the flux lines due to electrical charge and the polarization of molecules. It may be expressed as the sum of a term proportional to the electrical field strength E and the polarization vector P which depends on the movements of electrons in the material, that is: D = 80E + P

(3.4.5)

For an isotopic material, P is in the direction of the electrical field vector, that is: P = S0NaE

(3.4.6)

where a is a term known as the molecular polarizability and Af is Avogadro's number. This leads to Eqs. (3.4.5) and (3.4.4a) being equivalent to: D = C 0 (I+ oc)E = eE

(3.4.7a)

/^=V 2 E

(3.4.7b)

It may be similarly shown that the magnetic excitation vector varies according to: O2TT

/ ^ - ^ = V2H

(3.4.7c)

Equations (3.4.7b) and (3.4.7c) are vector wave equations. If E and H vary only in the X1-direction, then: E = E(f - ^ )

H = n(t - ^ )

(3.4.8a)

where X1 is distance and v is the velocity wave given by:

v = -J=

(3.4.8b)

The refractive index n is from Eq. (3.4.1): C

n=

-=l^~J°.

(3.4.9)

where we have noted that \i and ^ 0 are usually very close in value. The vectors E and H may be shown to be perpendicular to the direction of propagation of the wave and in a polarized wave are perpendicular to each other. For an anisotropic material, electrons generally do not move in the same direction as the applied electric field. Thus the polarizability a must be considered a second-order tensor, a. In place of Eq. (3.4.6) we write: P = S0Ot-E

(3.4.10)

D = £0(E + a-E) = £-E

(3.4.11)

and in place of Eq. (3.4.7a):

where e is called the dielectric constant tensor. It is like a, a symmetric second-order tensor. Substitution of Eq. (3.4.11) in Eq. (3.4.4b) leads to: O2TJI

This is a much more complex expression than Eq. (3.4.7b) although it still represents a propagating wave. It can be shown that Eq. (3.4.12) leads to a velocity of light that varies with

direction in space: Specifically if k is a unit vector representing the direction of the propagating wave: /Ci

/C-)

!— + * - ±

/CT

—+

— =0

(3.4.13a)

V^-L ^__L

S1Ji

S2[I

s3n

where the coordinate axes (1,2, and 3) are fixed in the principal directions of the e tensor Eq. (2.2.13c) is known as Fresnel's law of wave normals. This may be rewritten: V

S1[I) y

S1Ii)

y

B1IiJy

s3[i)

y

e^jy

s2[ij (3.4.13b)

Equation (3.4.13b) is a quadratic equation in v2. It may be seen that, in general, there are two velocities in each direction. Thus for direction 1, there are two velocities: v[=~^

Ji=-F=

<3A14>

/I

(3.4.15)

with the corresponding two refractive indices: /I2=-

3

V1

=V2

Thus, in general, in an anisotropic dielectric there are two wave velocities associated with each direction. In the special case, where two of the dielectric constants, say e2 a n d £3 are the same, the material is referred to as a "uniaxial optical" crystal. This leads in the 1 direction to only one light velocity and refractrive index

<3Ai6>

Vi=-4==-4= Vw Vw

but in the 2 and 3 directions there are two velocities and two refractive indices. The discussion of the previous two paragraphs leads to the concept of the refractive index ellipsoid and with different refractive indices in different directions. As e is a symmetric second-order tensor, we may express it as a quadratic surface or ellipsoid through: EEW= 1 (3.4.17a) i

j

C1JCj + £2^2 + £3^3 = 1

(3.4.17b)

where X1 are the principal axes of the € tensor. If we define principal refractive indices ni,n2, n3 by: C C C W1=-= n2=—== n3=—== (3.4.18a)

CL

V £ ii"

LL

V£2i"

LL V ^

or

n1= IM.

H2=I^

U3=[^

(3.4.18b)

It follows that we may write Eq. (3.4.17b) as:

n2^ + 44 + nj4 = I

(3.4.19)

It is to be noted that there is an inverse tensor s~l defined by 8-8-l=I

(3.4.20)

where I is a unit tensor, e"1 also satisfies a quadratic of the form of Eq. (3.4.17). This leads to: X^

Xi

X^

-I + -I + -I=I n\

n\

(3.4.21)

n\

Equation (3.4.21) is called the index ellipsoid, the "reciprocal ellipsoid," or "Fletcher's ellipsoid". We may define birefringence as the difference in refractive indices in different directions. Thus if a material has principal axes 1, 2, 3, with refractive indices W1, w2, w3 w e m a v define birefringences Aw12, Aw13, and Aw23 through: An12 = W1 — w2

3.4.2.3

Aw13 = W1 — w3

Aw23 = W2 — w3

(3.4.22a,b,c)

Theory of Dielectrics

In the second half of the 19th century, relationships were developed between the dielectric constant s and the molecular polarizability a in isotropic materials. Equations (3.4.6) and (3.4.7) are formalistic. The electrical field experienced by a molecule is not just the external field E, but the sum of this field and the field exhibited by other polarized molecules. Formulations of this problem were given by H. A. Lorentz [21, 28] (see also [22-26]) among others. It was shown that the increase in dielectric constant due to polarizing molecules is: ^ =^ (3-4.23) v e + 2e0 3 ' where A^ is the number of molecules per unit volume. This is known as the Clausius-Mosotti formula. It should be noted that as s approaches e0, as would occur in a dilute gas, (s — S0) is proportional to TVa. If we introduce Maxwell's equation (3.4.9), we may rewrite Eq. (3.4.23) as:

U-Ni

Equation (3.4.24) is known as the Lorentz-Lorenz equation. This relates refractive index to the molecular polarizability and to the number of molecules per unit volume. It can be seen that refractive index increases with molecular polarizability. Thus films based on molecules with high polarizability such as those with aromatic rings and high atomic weight elements should have a high dielectric constant and high refractive index. Many researchers, beginning with Muller [29], have presumed that the Lorentz-Lorenz equation should also be valid for optically anisotropic systems, that is: w? - 1 Na

^

=T

P-4-25)

Lorentz [21, 28] in his writings makes the point that the derivation of Eq. (3.4.24) is strongly linked to isotropy. The generalization of the Lorentz-Lorentz equation to anisotropic and oriented systems has been considered by various investigators, notably R. S. Stein [30]. It is clear Eq. (3.4.23] is not generally valid.

3.4.2.4

Orientation

The anisotropic characteristics of polymeric films are associated with polymer chain orientation. The first efforts to represent orientation in fibers and films trace to the work of Preston [31], Morey [33-35], and Sisson [36-38] in the early 1930s. In 1939, Hermans and Platzek [39] defined a quantitative measure of uniaxial orientation that we know today as the Hermans orientation factor. In the same year Okajima and Koizumi [40] gave the first measurements and interpretations of biaxial orientation in films. In 1941, Muller [29] presented a new formulation of uniaxial orientation and derivation of the Hermans orientation factor that has come to be generally accepted. The Hermans orientation factor fn considers a series of anisotropic units with polarizabilities ay along their length and oc± perpendicular to them that are arranged with fiber symmetry around axis 1. Axes 2 and 3 are perpendicualr to axis 1. The Hermans orientation factor is expressed in terms of molecular polarizabilities aJJ, a^, and o^J, (following Muller [29]) as:

f* =

(3A26)

"f^r

If (j) is the angle the anisotropic units make with the fiber axis, fH is: /H =

wl-i

(3427)

If there is perfect orientation (J)1 = 0, then/fj is unity. If there is isotropy cos2 (J)1 is 1/3, a n d ^ is zero. If^1 is 90° and the anisotropic units are perpendicular to the axis of symmetry,^ is — 1/2. From the anisotropic Lorentz-Lorenz equation (Eq. 3.4.25) it follows that: a

ll

~ a 22

OLn — a ±

^

~

n

\ ~n2

«u — «j_

n

\ ~n2

= —T^— A

n

A

9 nx

(3.4.Z8;

The quantity A° is called the intrinsic birefringence. This represents the maximum possible birefringence. Thus: / H - ^

(3A29)

Equation (3.4.29) was originally given by Hermans and Platzek [39]. The first efforts to consider the implications of these definitions to partially crystalline polymers was given by PH. Hermans and his co-workers [41-43]. This was subsequently extended by Stein and Norris [44] and Stein [45]. It was realized that one could determine orientation by wide-angle X-ray diffraction, but this gave larger values than numbers obtained

by birefringence. Stein and Norris [44] proposed a two-phase model where one could write the birefringence as: An = XfRcA°c + (1 - X)fRamAlm

+ Anform

(3.4.30)

where Xis a crystalline fraction,^ and^ a m are Hermans orientation factors for crystalline and amorphous regions; A° and A°m are appropriate crystalline and amorphous intrinsic birefringences; and Aniorm is the form birefringence. Subsequently Stein [45] proposed introducing for crystalline polymers orientation factors representing the orientation of crystalline axes. Specifically, he wrote: 3 cos2
(3A31)

where j represents crystallographic axisy (j = a,b,c) and ^ 1 is the angle between they axis and the symmetry axis. Stein [46] was the first to seek to develop orientation factors representing a biaxial state of orientation. His work was subsequently extended by Nomura et al. [47^9]. Their biaxial orientation factors were developed on the basis of spherical coordinates and Euler's angles. Nomura et al's biaxial orientation factors were not symmetric with regard to machine and transverse directions in a film. Subsequently White and Spruiell [50-55] developed a set of biaxial orientation factors based on the angles between the polymer chain axis and the machine and transverse directions. These orientation factors were symmetric with regard to machine and transverse directions. They have the form: / f = 2COS2^1+ cos2 (J)2 - 1 B

2

2

/2 = 2 cos 2 + cos (f)x - 1

(3.4.32a) (3.4.32b)

Here (J)1 is the angle between the polymer chain and the 1 axis. (J)2 is the angle between the polymer chain and the transverse 2 axis./jB and ^26 may vary between +1 and —1. The state (/i B '^ B ) °f (0> 0) represents isotropy whereas (1, 0) and (0, 1) represent the two states of uniaxial orientation in machine and transverse orientation, respectively. The orientation state of (+1/2, H-1/2) represents equal biaxial planar orientation, whereas (—1/2, —1/2) represents orientation perpendicular to the surface of a film. White and Spruiell [50] have used an isosceles triangle (Fig. 3.4.1) to represent states of biaxial orientation. White and Spruiell [50] note that it is possible to generalize this development to express the state of orientation of crystallographic axes in a crystalline polymer by modifying Eq. (3.4.3.2a,b) to: ffj = 2 cos2 0 ly + cos2 02y - 1 B

2

2

f2 j = 2 c o s (J)2J + c o s (J)1J - 1

(3.4.33a) (3.4.33b)

where 0 ly and (j)2j represent the angles between directions 1 and 2 and they crystallographic axes.

PLANAR MACHINE DIRECTIONAND PERPENDICULAR TO THE SURFACE)

UNIAXIAL (MACHINE DIRECTION) PLANAR (FILM SURFACE) EQUAL BIAXIAL UNIAXIAL (TRANSVERSE DIRECTION)

ISOTROPIC

Figure 3.4.1 Orientation triangle of White and Spruiell indicating meanings of biaxial orientation [50]

3.4.2.5

Interaction of Electromagnetic Waves with Surfaces

When an electromagnetic wave moving through a vacuum or air strikes a plane surface, the wae is either transmitted through the surface or reflected. The relative amounts of reflection or refraction/transmission depend on the refractive index of the dielectric and the state of the polarization of the film. This is governed by Fresnel's laws which predate Maxwell's electromagnetic theory but are derivable from it. Three angles are discernible: the angle a between the incident beam and the normal to the film, the angle cd between the reflected beam and the normal, and the angle /? between the refracted beam and the normal. If the electric vector in the incident wave is normal to the plane of incidence, which is in the 1-2 plane, that is E is E3 e3, the incident and reflected waves E3 in medium A and the refracted E3 wave in medium B may be expressed as: g o _ ^ / £ 4 (x, sin a-x 2 cos a)

E 3 = A V ' ^ 1 sina '-* 2 coso ° gr _ g ^ f o sin/?-x2 cosjff)

(3.4.34a,b,c)

The boundary condition at x2 = 0, the plane of incidence, requires: J±eikAx\ si™' _j_ A'eikAxi

sin*' _ ^QeikB*\ *™P

(3.4.35)

It follows that: a' = a

(3.4.36)

sin/? = -^-sin a = — sin a

(3.4.37a)

sin£ = ^ s i n a

(3.4.37b)

sin£ = / ^ sin a

(3.4.37c)

The angle of reflection a' equals the angle of incidence a. The angle of refraction P is related to the angle of incidence a through Eq. (3.4.37) which is known as SnelPs law. The relationship between the initial and refracted wave may be expressed in terms of the wave velocities vA and vB or refractive indices nA and nB of the initial and second medium, or through Maxwell's theory in terms of the dielectric constant and magnetic permittivity. The ratios of the amplitudes A9 A' and B may be shown to be in accord with Fresnel's formula: A' _ sin(a - P) X ~ sin(a + P) (3.4.38a,b) B 2 cos oc sin P A ~ sin(a + #) when the magnetic permitivities of the two media are the same, which is a very good approximation. When the magnetic vector is normal to the plane of incidence another condition applies. A balance such as Eq. (3.4.35) can then be applied to the magnetic vector H3. This leads to in place of Eq. (3.4.38a,b), the second Fresnel formula: A' _

tan(a - p)

A =-Xm(OC

+P)

B_ 1 Ttan(a + p) A ~~ tan(a H- P) |_cos(a - P)

(3.4.39a,b) tan(a - p)l cos(a + /Oj

Let us now consider the question of the relative amplitudes of A7 and B relative to A, that is of the reflected and refracted waves versus the incident wave. As we approach normal incidence and a —> 0, we have from both Eqs. (3.4.38a) and (3.4.39a) that:

= ^TT

<3A40b)

where Snell's law is used in obtaining Eq. (3.4.40b). If we insert a value of n equal to 1.5, typical of glass, A'/A is 1/5 or 0.2. In terms of reflected intensity R or I'/T0, the ratio is:

V

/A\2

rUr 0 - 04

(3A41)

Consider an unpolarized wave to be imposed on a surface at an angle a. The amplitude of the reflected wave for the component of the light with the electric vector perpendicular to the surface is given by Eq. (3.4.38a) and the component with the vector parallel to the surface is given by Eq. (3.4.39a). Studying Eq. (3.4.38a) we can see that it changes sign when (a — /f) or (a + P) reaches a value of TT/2 (90°). When a -> 0:

*

(lz£)_ -(1-I)

(3 .4.42a,

which is negative and when a -> TT/2: A A

> +1

(3.4.42b)

tana = «

(3.4.43)

It may be shown that when

the value of (A!IA) goes to zero and the reflected ray is polarized. This is known as Brewster's angle. For glass with n = 3/2, Brewster's angle is 57°.

3.4.3

Measurement Methods

3.4.3.1

Measurement of Crystallinity

Polymers generally possess only limited levels of crystallinity. Unlike low molecular weight materials, they cannot crystallize completely. The reason for this is clearly the inability of polymer chains tofitinto crystallites. Generally crystallinity levels are below 70%. The primary methods of measurement of crystallinity are (1) density (2) heats of crystallization, (3) refractive index and (4) X-ray diffraction. We shall review these concisely. Density-based crystallinity measurements use a two-phase theory of polymers. Essentially it is presumed that all the polymer is either crystalline or amorphous and there are no states of intermediate levels of structure. The exception to this would be when more than one distinctly different crystalline phase is recognized (e.g., by wide angle X-ray diffraction). For a material with amorphous and crystalline regions, the specific volume v may be expressed:

v=Xvc + (\ -X)va

(3.4.44)

where X is the crystalline fraction, vc the specific volume of the crystalline phase, and va the specific volume of the amorphous phase. It may be shown from Eq. (3.4.44) that: X = _Va ~*

(3.4.45a)

In terms of density, this is: 1

1

X = -^—^Pa

(3.4.45b)

Pc

The crystalline and amorphous densities, pc and p a , of important polymers have been tabulated. The value of X is determined from measurement of p alone, together with the values of p a and pc. Usually density is measured using gradient density columns. However, other techniques exist. A second method of measurement of crystallinity involves the determination of heats of crystallization. In these measurements one again presumes a two-phase theory of materials. The specific enthalpy of a material H can be expressed as: H = XH°C + (1 - X)Hl

(3.4.46)

whre Hc is the specific enthalpy of 100% crystalline material and // a is the specific of amorphous polymer. The crystallinity X from Eq. (3.4.46) may be written: ~TT TTO X=_ _" (3.4.47) The value of// — //° is determined from a differential scanning calorimeter. It is necessary to know the value of Hc — Ha the heat of crystallization of a 100% crystalline polymer, to compute the fractional crystallinity in this manner. Crystallinity levels may also be determined from refractive index measurements. From the Lorentz-Lorenz equation [21], the refractive index n depends on the number density of molecules N. Density was first corrected with refractive index measurements by Schael [56, 57] in the mid-1960s. It was subsequently applied by DeVries [58, 59] to both polyolefins and to polyethylene terephthalate (PET). A later article by Cakmak et al. [60] applies this technique to PET. Correlations of this type are sometimes expressed directly in terms of the Lorentz-Lorenz equation as: ^i=Cp

(3.4.48)

where C is an experimentally determined constant. Cakmak et al. [60] cite two expressions for PET films which were obtained by regression analysis: -^-^

= CX+C2X (3.4.49a,b) C1 = n(X = 0)

Refractive index measurements of crystallinity are generally limited to films.

Measurements of the three principal refractive indices are obtained using methods dating to Okajima and Koizumi [6] in 1939. Generally these three refractive indices are different and the values of n used in Eqs. (3.4.48) and (3.4.49) is a mean value determined from: w~ii =

"i+^+"3

(3.4.50)

Okajima and Koizumi [61] proceeded by determining individual refractive indices using the Abbe refractometer [62] which is based on a total reflection technique. This method was subsequently used by Schael [56, 57], DeVries [58, 59], and Cakmak et al. [60]. Wide-angle X-ray diffraction is still another method of measuring crystallinity. It involves measuring the scattering intensity of the amorphous and crystalline regions of a polymer.

3.4.3.2

Measurement of Orientation in Films

Polymer chain orientation on films has primarily been measured by three different wide-angle X-ray diffraction techniques and birefringence, although it is possible to accomplish this by other techniques such as infrared dichroism. Measurements of refractive index and birefringence determine mean levels of orientation in the crystalline and amorphous regions. Generally two-phase models are used for a uniaxially filament. We may write after Stein and Norris [44]: An=XAnc + (\ -X)Ana + Anform

(3.4.51)

where Anc is the birefringence of the crystalline phase and Ana the birefringence of the amorphous phase, A«form is the "form birefringence" which arises whenever two materials of different mean refractive indices exist in an anisotropic configuration. The "form birefringence phenomenon" is discussed by Born and Wolf [23]. The birefringence Anc and A«a may be expressed in terms of the intrinsic birefringence A° and A° of the crystalline and amorphous phases/J and fa through: An0 =/ c A°

An3 =/aAa°

(3.4.52)

so that: An = XfcA° + (1 - X)f:Al

+ Anfom

(3.4.53)

This formulation may be directly generalized to biaxially oriented film. Here there are two birefringences An13 and An23 which may be expressed for an amorphous material as: An 13 =flBA°

An 23 =f2BA°

(3.4.54)

B

where / j and ff are biaxial orientation factors of Eq. (3.4.32). For biaxially oriented crystalline films, we have: An13 = X[J* A°cl +f^Kll

+ (1 - X)f?™A°a + A«form

(3.4.55a)

An23 = X[f»
(3.4.55b)

H e r e / ^ c , ^ c , y ^ c a n d ^ c are the biaxial crystalline orientation factors representing the a and c crystallographic axes, /i B a m and/f am are the biaxial orientation factors of the amorphous phase, Accb and Aacb are intrinsic birefringences representing differences in the c and b axes, and the a and b axes respectively in the crystalline phase and A° the value for the amorphous phase. There are two primary techniques for measuring birefringence. One involves measurement of the absolute refractive indices and then subtracting them. The second involves measurement of optical retardation. The measurements of refractive indices and their differences to obtain birefringences in films have been carried out by the method of Okajima and Koizumi [61] using the Abbe refractometer [62]; later measurements were made by Okajima et al. [63, 64], Samuels [65], and Cakmak et al. [60]. Stein [66] developed a technique for measuring the birefringences Aw13 and An23 using optical retardation. This involves an optical bench with a rotating stage. If the film is normal to the beam Aw12 is obtained. Rotation allows obtaining an out of plane value from which Aw13 may be obtained. A major method of measurement of orientation in films is wide-angle X-ray diffraction. Wide-angle X-ray diffraction measurements of films date to studies by Sisson [67, 68] on cellulose membranes in 1936-1940. Pole figure analysis of modern crystalline thermoplastic films was reintroduced by Wilchinsky [69] and by Heffelfinger and Burton [70]. In 1960, subsequent studies of pole figures of rolled and film products in the 1960s were presented by Wilchinsky [71, 72] Lindenmeyer and Lustig [17, 73] and Desper and Stein [74]. The crystalline orientation factors fy and/-^ of Eq. (3.4.33) may be determined from pole figures of appropriate crystallographic planes.

3.4.3.3

Measurement of Haze

The problem of optical clarity is an important aspect of films. Packaging films must be as clear as possible. Various measurements and terms have been used to describe these properties. A complete description of the clarity of a film/sheet is probably contained in a plot of transmittance versus angle over a 180° solid angle. Such information is difficult to obtain and integrated and approximate measures are generally used. These are often called "haze" or "loss of resolution" tests. An integrating sphere method was introduced by the American Society for Testing Materials as early as 1949 as ASTM D-1003 [75]. Haze is in this method is defined as that percentage of transmitted light that in passing through the specimen deviates from the incident beam by forward scattering more than 2.5° on the average. It was not intended for use when haze is greater than 30%. Webber [14] has noted that ASTM D-1003 does not really distinguish between "seethrough" and "haze" qualities. Films have scatter widely a large part of transmitted light, but interfere only slightly with the resolution of objects seen through it. He illustrated this by comparing two low-density polyethylene films each measuring approximately 15% haze which by this method exhibit very different resolutions. Webber describes a new instrument with a narrow beam and high angular resolution. He characterizes transparency through a zero angle transmittance relative to air. There have been later instruments for determination of

optical clarity in films using low-angle light scattering. These are contained in papers by Billmeyer [76] and Wilchinsky [16] among others. The interpretation of optical clarity experiments using instruments such as Webber's [14] has been discussed by Clampitt et al. [77]. The fraction of light that passes through the film undeviated from the original source is called the specular transmission. It is considered that this transmittance can be considered as the product of contributions from the bulk and from the two surfaces of the film, that is: y = T = TBTslTs2

(3.4.56)

where TB is transmittance from the bulk phase of the films and Tsl and Ts2 from the two surfaces. The contribution from the bulk of the film may be represented in terms of a turbidity T. If the film has a thickness w, then: TB = e~*h

(3.4.57)

It is possible to isolate TB from T by placing the film between glass slides and coating both surfaces of the film with liquids of refractive index equal to the film. If T is also known one may determine TsX Ts2 as well. This approach is found in the work of Keane and Stein [78], Clampitt et al. [77], and various later investigators.

3.4.4

Orientation Development in Vitrifying Tubular Film

It is possible to fabricate noncrystallizing thermoplastics such as polystyrene and polycarbonate into film. Indeed, polystyrene was one of the first synthetic polymers converted into a useful thermoplastic film. A study of tubular film extrusion of polystyrene was published by Choi et al. [82]. They determined "in-plane birefringence," Aw12, and "out-of-plane" birefringences Aw13 and An23 for tubular film. Here 1 represents the machine direction, 2, the film thickness direction, and 3 the transverse (circumferential) direction of birefringences Aw13, Aw23, and Aw12. Choi et al. have determined the influence of drawdown and blowup ratio on the film. The absolute value OfAw13 increases with drawdown ratio VL/V0, but there is little change in Aw23. Actually Aw13 and Aw12 become negative, but because the maximum intrinsic birefringence of polystyrene is negative, increasing negative birefringence corresponds to increasing molecular orientation. Choi et al. seek to correlate the variation in birefringence with differences in stressed determined at the freeze or frost line. These are after Pearson and Petrie [83-86]. Gn =

— (machine direction) ATLR j_h L

ff22=

ME "L

(T33=O

(hoop direct ion)

<3-4-58>

Birefringence [x103]; Any

Stress (MPa); Oj-Oj Figure 3.4.2

Frozen birefringence in polystyrene tubular film as a function of difference of stresses,

Here FL is the takeup tension, RL the bubble radius, hL the film thickness, and Ap the inflation pressure. Choi et al. found that the frozen in birefringence varies linearly with the appropriate differences in stresses. Specifically: An-IT1 =

13

C(CT 1 1 — <x 3 3 )

Jn

33

(3.4.59a,b)

This is shown in Fig. 3.4.2. Choi et al. [82] note that this birefhngence-frost-line stress correlation is the same as earlier found by Oda et al. [87] for melt spun polystyrene filaments and sheared samples and seems to be a result of great generality for the birefringence of melt processed vitrified glasses.

3.4.5

Structure Development in Crystallizing Tubular Film

Structural characteristics of tubular film were investigated from the 1950s. The earliest investigations were by Holmes et al. [11,12] on polyethylene film. In 1965, Lindenmeyer and Lustig [18] published a wide-angle X-ray pole figure study of polyethylene tubular film. This

was followed by more extensive studies by Desper [88], Nagasawa et al. [89], Rohn [90], Maddams and Preedy [91-93], Choi et al. [94], and Shimomura et al. [95] on various types of thermoplastics. Most of these authors used wide-angle X-ray diffraction to characterize orientation. Certain general observations run through this literature. Holmes and Palmer [12] clearly note that in all their polyethylene films, the b crystallographic axis is normal to the surface of the film. The a and c axes lie in the plane of the film. The relative directions of the a and c crystallographic axes vary with drawdown ratio and blowup ratio. Desper [88] concludes there are roughly equal amounts of a and c orientation in the machine direction, but under some conditions a axis orientation in the machine can exceed c axis orientation. The studies of Choi et al. [94] on polyethylene are unique in that the crystalline biaxial orientation factors of Eq. (3.4.33) and orientation triangles of Fig. 3.4.1 are used. Some remarks are pertinent. First, the levels of orientation are small. Second, for films which are approximately uniaxial as a result of the manner in which they are made, the authors find:

Jc? > 0 fii > 0 /M < 0

fl > 0 fl < 0 fl < 0

(3.4.60)

As drawdown increases/^ increases,^® becomes more negative;^ first increases then goes through a maximum, then decreases and becomes negative. For constant blowup ratio films, Choi et al. find:

I >g<0

I /»B2<0

(3.4.61)

ffx first increases and then decreases to zero with increasing drawdown ratio. For an almost equal biaxial film Choi et al. find: fix =/c! = +0-22 fix =fii = -0-2

(3.4.62)

JS=Zi = -0-2 Choi et al. [94] sought to correlate the development of orientation with the applied stress field as they had done with tubular film extrusion of polystyrene. The stress field at the freezeline was again taken as given by Eq. (3.4.58). The work of Choi et al. is strongly influenced by investigations of orientation development in crystalline polymers during melt spinning, notably by Kitao et al. [96], Abbot and White [97] Dees and Spruiell [99], White et al. [98], Spruiell and White [100], Oda et al. [87] and Nadella et al. [101] where uniaxial orientation factors are correlated with drawdown ratio and spinline stress. It seemed reasonable in tubular film that the biaxial state of orientation of films would depend upon the freeze-line stresses of Eq. (3.5.59). Choi at al. [94] proceeded by plotting differences in crystalline biaxial orientation factors Jj^ —f^ as a function of differences in principal stresses (i.e., (J11 — G12) as determined by Eq. (3.4.58), that is:

where O represents a functionality.

fHB

c-Axis a-Axis b-Axis fiber [Dees 4 Spruiel]

OJ1-CT22(MPa)

Figure 3.4.3 stresses

Biaxial orientation factors of polyethylene tubular film as a function of differences in principal

The result of such a plot from Choi et al. [94] is shown in Fig. 3.4.3. The^f — f^ biaxial orientation factor difference correlates well with the difference in principal stresses. The b axis orientation factor difference/^ ~f^ decreases rapidly with increase in stress and takes on a value near (—0.4). The c axis biaxial orientation factor difference increases monotonically with freeze-line principal stress difference. The a axis stress difference/^ —/& ^ rs ^ increases with stress difference, exhibits a maximum, and then decreases and becomes negative. Choi et al. [94] have contrasted their results with fiber spinline data of Dees and Spruiell [99], who plotted uniaxial orientation factors/,,/,, and/, as a function of spinline stress for melt spun polyethylene filaments. The data are found to overlap as seen in Fig. 3.4.3. These investigators also compared polyethylene tubular film birefringence Antj with difference in principal stresses au — o^-. This is shown in Fig. 3.4.4; a good correlation was obtained. Small-angle X-ray scattering studies of tubular film were first reported by Nagasawa and co-workers [89] and subsequently by Choi et al. [94]. These show patterns similar to those obtained in compression molded samples, extruded and melt spun filaments. There is a small angle repeat distance presumably representing a crystalline lamellae structure. The angular intensity of the scattering varies with the stress field. Uniaxial stresses give a two-point longitudinal pattern indicating lamellae perpendicular to the direction of stress. This suggests a "shish kebab" model (Fig. 3.4.5). Application of a biaxial stress field through inflation pressure as well as tensile stresses [see Eq. (3.4.58)] leads to a more uniform angular

Birefringence(xio3):An,.

An 1 2 An 2 3 An 1 3 Dees ASpruiel!

Stress(MPa):<7-Oj

Figure 3.4.4 Birefringences Antj as a function of ou — a^

distribution of scattering. This suggests lamellae with distributed orientations in the surface of the film as suggested by Fig. 3.4.4.

3.4.6

Mechanism of Haze

The mechanism of haze in tubular film has been considered in articles by Huck and Clegg [12], Stehling et al. [79], Ashizawa et al. [80], and White et al [81]. In a 1961 article, Huck and Clegg [12] of ICI suggested that haze in a low-density polyethylene (LDPE) film was due to two sources: bulk scattering and scattering by rough surfaces. In a 1981 articles, Stehling et al. [79] of Exxon noted that most investigators believed that surface roughness of LDPE films was due to surface roughness. Using scanning electron microscopy, Stehling et al. showed that hazy films generally have high levels of surface roughness. They associate the surface roughness with two mechanisms, rheological effects and crystallization. Generally narrow molecular weight distribution, less branched polymers gave lower haze. This conclusion was reinforced by a subsequent study of Pucci and Shroff [102]. Ashizawa et al. [80] studied a range of polyethylene films using the method of Clampitt et al. [78] to determine surface and bulk transmittances Ts and TB using Eq. (3.4.57). They

MO

TD

Figure 3.4.5

Morphological model for film with equal biaxial orientation

T1

PMMA. PC, PS

Figure 3.4.6 Correlations of surface transmissivity Ts of tubular film with surface roughness

N-6

LDPE-4 LDPE-3 LLDPE-3 LLOPE-2 HDPE -4 HOPE -5 PP PB

o

HOPE-S HOPE-4 PP PB LLOPE-2 LDPE-^ LDPE-3 LLDPE-1

dx 102

T T

Crystatlinity

Figure 3.4.7 Correlation of surface transmissivity of Ts of tubular film with crystallinity

also measured the mean surface roughness o1 with a surface profile. Measurements were made on LDPE and high-density polyethylene (HDPE) tubular films produced under a range of conditions. Ashizawa et al. found that the surface transmissitivities Ts of the HDPE films are much lower and the turbidity T of Eq. (3.4.57) is much higher than for the LDPE and LLDPE films. This suggested that higher crystallinity gives rise to rougher surfaces and more internal scattering and turbidity. Bheda and Spruiell [103] used similar methods to study haze and surface roughness of polypropylene films of varying molecular weight distribution as produced by viscracking. They find that narrowing molecular weight distribution reduces haze through decreasing Ts and surface roughness. This confirmed the observations of Stehling et al. [79] for a second thermoplastic. There would thus seem to be two mechanisms of surface haze, one associated with crystallization where roughness may correspond to "bunched" folded crystalline lamellae and a second associated with unstable melt flow induced by melt elasticity. White et al. [81] have studied the haze of a wide range of thermoplastic films including polycarbonate, polystyrene, poly(methyl)methacrylate, polyproplyene, polybutene-1, polyamide-6, and a range of polyethylenes. It was found that the glassy thermoplastics, polycarbonate, polystyrene, and poly(methyl)methacrylate had surface transmissitivites Ts of unity and no surface roughness. The turbidities of these polymers were zero. The polypropylene, polybutene-1, and the polyethylenes gave rise to lower Ts and nonzero turbidities. It was possible to correlate surface transmissivity Ts with surface roughness with all of the films as shown in Fig. 3.4.6. The various transmissivities and turbidities were correlated with the level of crystallinity in the various polymers as shown in Fig. 3.4.7.

A weaker correlation of surface roughness and transmissitivity was found with melt elasticity as measured by the steady-state compliance, JQ.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46.

Cohoe, W.P., U.S. Patent 1,163,740 (1915) Henderson, W.F., U.S. Patent 1,601,686 (1923) Henderson, WE, U.S. Patent 655,013 (1938) Weingard, R., Muchlinski, A., U.S. Patent 2,070,247 (1937) Studt, E., German Patent 655,013 (1938) Tornberg, H.T., U.S. Patnet 2,443,937 (1948) Fuller, E.D., U.S. Patent 2,461,975 (1949) Schenk, B.H., U.S. Patent 2,461,976 (1949) Haine, W.A., Land, W.M., Mod. Plastics (1952) Feb., p. 109 Homes, D.R., Miller, R.G., Palmer, R.P., Bunn, C.W., Nature (1953) 174, p. 1104 Holmes, D.R., Palmer, R.P. J. Polym. ScL (1.958) 31, p. 345 Huck, N.D., Clegg, PL., Trans. SPE (1961) 1, p. 121 Kendall, VG., Trans. Plastics Inst. (1963) 31, p. 49 Webber, A.C., J. Opt. Soc. Am. (1957) 47, p. 785 Pilard, J, Kremer, R., Mod. Plastics (1960) June, p. 115 Wilchinsky, Z.W., J. Appl. Polym. ScL (1961) 5, p. 48 Lindenmeyer, P.H., Lustig, S., J. Appl. Polym. ScL (1965) 9, p. 227 Maxwell, J.C., Philos Trans. R. S. (1864) 155, p. 459; ibid (1968) 158, p. 643 Maxwell, J. C , Electricity and Magnetism (1873) Constable, London Hertz, H., Wiedmanns Annalen (1890) 40, 577 Lorentz, H.A., Theory of Electrons (1909) reprinted by Dover NY (1952) Born, M., Optik (1950) Springer-Verlag, Berlin Bom, M., Wolf, E., Principles of Optics 4th ed. (1970) Pergamon, London Stratton, J.A., Electromagnetic Theory (1941) McGraw-Hill, New York Sommerfeld, A., Electrodynamics (1949) Academic Press, New York Sommerfeld, A., Optics (1949) Academic Press, New York Becker, R., Theorie der Elektrizitdt translated as Electromagnetic Fields and Interactions 17th ed (1964) Blaisdell, New York Lorentz, H.A., Wiedmanns Annalen (1880) 9, p. 641 Muller, F.H., Kolloid Z. (1941) 95, p. 138 Stein, R.S., J. Polym. ScL (1969) A-2 1, p. 102 Preston, J.M., J. Soc. Dyers Col. (1931) 47, p. 312 Trans. Faraday Soc. (1933) 29, p. 65 Morey, D.R., Textile Res. J. (1933) 3, p. 325 Morey, D.R., Textile Res. J. (1934) 4, p. 491 Morey, D.R., Textile Res. J. (1935) 5, p. 105 Morey, D.R., Textile Res. J. (1935) 5, p. 483 Sisson, WA., Clark, G.L., Ind. Eng. Chem. Awal. Ed. (1933) 5, p. 296 Sisson, WA., Clark, G.L., Ind. Eng. Chem. (1935) 27, p. 51 Sisson, WA., Clark, G.L., J. Phys. Chem. (1936) 40, p. 343 Hermans, PH., Platzek, P., Kolloid Z (1939) 87, ibid p. 296; (1939) 88, p. 68 Okajima S, Koizumi, Y , Kogyo Kagaku Zasshi (1939) 42, p. 810 Hermans, J.J., Hermans, PH., Vermaas, D., Weidinger, A., Rec. Trav. Chim. (1946) 65, p. 427 Hermans, PH., Hermans, J.J., Vermaas, D., Weidinger, A., J. Polym. ScL (1948) 3, p 1 Hermans, PH., Heikens, D., Rec. Trau. Chim. (1952) 71, p. 49 Stein, R.S., Norris, F.H., J. Polym. ScL (1956) 21, p. 381 Stein, R.S., J. Polym. ScL (1958) 31, p. 327 Stein, R.S., J. Polym. ScL (1958) 31, p. 335

47. Nomura, S., Kawai, H., Kimura, L, Kagiyama, M., J. Polym. ScL A2 (1967) 5, p. 479 48. Kawai, H., In Proceedings of the 5th International Congress on Rheology, Onogi, S. (Ed.) (1969) University of Tokyo Press, Tokyo 49. Nomura S., Kawai H., Kimura, L, Kagiyama, M., J. Polym. ScL A2 (1973) 8, p. 383 50. White, J.L., Spruiell, J.E., Polym. Eng. ScL (1981) 21, p. 859 51. White, J.L., Pure Appl. Chem. (1983) 55, p. 765 52. White, XL., Spruiell, XE., Polym. Eng. ScL (1983) 23, p. 247 53. Matsumoto, K., Fellers, XR, White, XL., J. Appl. Polym. ScL (1981) 26, p. 85 54. Choi, K.X, White, XL., Spruiell, XE., J. Appl. Polym. ScL (1980) 25, p. 2777 55. Choi, K.J., Spruiell, XE., White, XL., J. Polym. ScL Polym. Phys. (1982) 20, p. 27 56. Schael, G.W, J. Appl. Polym. ScL 8, p. 2717 57. Schael, G.W, J. Appl. Polym. ScL (1968) 12, p. 803 58. Devries, A.X, Bonnebat, C , Beautomrs, X, J. Polym. ScL Polym. Symp. (1977) 58, p. 109 59. Devries, A.X, Pure Appl. Chem. (1981) 58, p. 1011 60. Cakmak, M., White, XL., Spruiell, XE., Polym. Eng. ScL (1989) 29, p. 1534 61. Okajima, S., Koizumi, Y., Koggo Kogaku Zasshi (1939) 42, p. 810 62. Valasek, X, Elements of Optics (1932) McGraw-Hill, New York 63. Okajima, S., Kurihara, K., Homma, K., J. Appl. Polym. ScL (1967) 11, p. 1703 64. Okajima, S., Homma, K., J. Appl. Polym. ScL (1968) 12, p. 411 65. Samuels, R.X, J. Appl. Polym. ScL (1981) 26, p. 1382 66. Stein, R.S., J. Polym. ScL (1957) 24, p. 383 67. Sisson, WA., J. Phys. Chem. (1936) 40, p. 343 68. Sisson, WA., J. Phys. Chem. (1940) 44, p. 513 69. Wilchinsky, Z.W, J. Appl. Phys. (1960) 31, p. 1969 70. Heffelfmger, CX, Buron, R.L., J. Polym. ScL (1960) 47, p. 289 71. Wilchinsky, Z.W, In Advances in X-Ray Analysis, Vol. 6 (1962) Plenum Press, New York 72. Wilchinsky, Z.W, J. Appl Polym. ScL (1963) 7, p. 923 73. Lindenmeyer, PH., Personal Communication 74. Desper, CR., Stein, R.S., J. Appl. Phys. (1966) 37, p. 3990 75. ASTM D-1003, Haze and Luminous Transmittance of Transparent Plastics (1949) (revised 1977, 1979) 76. Billmeyer, F.W., J. Opt. Soc. Am. (1959) 49, p. 368 77. Clampitt, B.H., German, D.E., Anson, H.D., Anal. Chem. (1969) 41, p. 1306 78. Keane, XX, Stein, R.S. J. Polym. ScL (1956) 30, p. 327 79. Stehling, E C , Speed, C S . , Westerman, L., Macromolecules (1981) 14, p. 698 80. Ashizawa, H., Spruiell, XE., White, XL., Polym. Eng. ScL (1984) 24, p. 1035 81. White, XL., Matsukura, Y, Kang, H.X, Yamane, H., Int. Polym. Process (1987) 1, p. 83 82. Choi, K.J., White, XL., Spruiell, XE., J. Appl Polym. ScL (1980) 25, p. 2777 83. Pearson, XR. A., Mechanical Principles of Polymer Melt Processing (1966) Pergamon, London 84. Pearson, XR.A., Petrie, CXS., Plast. Polym. (1970) 38, p. 85 85. Pearson, XR.A., Petrie, CXS., J. Fluid Mech. (1970) 40, p. 1 86. Petrie, CXS., AlChE. J. (1970) 21, p. 275 87. Oda, K., White, XL., Clark, E.S., Polym. Eng. ScL (1978) 18, p. 53 88. Desper, CR., J. Appl. Polym. ScL (1969) 13, p. 167 89. Nagasawa, T, Matsumura, T., Hoshiwo, S., Kobayoshi, K., J. Appl Polym. ScL Appl Polym. Symp. (1973) 20, p. 275, 295 90. Rohn, CL., J. Polym. ScL C (1974) 46, p. 161 91. Maddams, W E , Preedy, XE., J. Appl. Polym. ScL (1978) 22, p. 2721 92. Maddams, WE, Preedy, XE. J. Appl. Polym. ScL (1978) 22, p. 2739 93. Maddams, WE, Preedy, XE., J. Appl Polym. ScL (1978) 22, p. 2751 94. Choi, K.X, White, XL., Spruiell, XE., J. Polym. ScL Polym. Phys. (1982) 20, p. 27 95. Shimomura, Y, Spruiell, XE., White, XL., J. Appl. Polym. ScL (1982) 27, p. 2663 96. Kitao, T, Ohya, S., Furukawa, X, Yamashita, S., J. Polym. ScL Polym. Phys. (1973) 11, p. 1091 97. Abbott, L.E., White, XL., J. Appl Polym. ScL Appl. Polym, Symp. (1973) 20, p. 247 98. White, XL., Dharud, K.C., Clark, E.S., J. Appl. Polym. ScL (1974) 18, p. 2539

99. 100. 101. 102. 103.

Dees, XR., Spruiell, XE., J. Appl. Polym. ScL (1975) 18, p. 1055 Spruiell, XE., White, XL., Polym. Eng. ScL (1975) 15, p. 660 Nadella, H.P., Henson, H.M., Spruiell, XE., White, XL., J. Appl. Polym. ScL (1977) 21, p. 3003 Pucci, M.S., Shroff, R.N., Polym. Eng. ScL (1986) 26, p. 569 Bheda, X, Spruiell, XE., Polym. Eng. ScL 1986) 26, p. 736

4.1

Theoretical Analysis of Film Deformation Behavior in Casting Toshiro Yamada

4.1.1

Introduction

181

4.1.2

Analysis of Film Deformation under Steady State 4.1.2.1 Vertical Casting Model 4.1.2.1.1 Mathematical Model 4.1.2.1.2 Simulated Results 4.1.2.2 Catenary Casting Model 4.1.2.2.1 Mathematical Model 4.1.2.2.2 Simulated Results

181 181 181 183 184 185 187

4.1.3 Analysis of Film Temperature 4.1.3.1 A Model for Cooling in Extruded Materials by Michaeli and Menges 4.1.3.1.1 Mathematical Model 4.1.3.1.2 Application for Flat Sheet Extrusion 4.1.3.2 A Model for the Cooling of Cast Film on a Chill Roll by Billon et al 4.1.3.2.1 Mathematical Model 4.1.3.2.2 Simulation Example

191 192 192 194 195 195 197

4.1.4

Analysis of Neck-In and Edge Bead Phenomena 4.1.4.1 Neck-In Phenomenon 4.1.4.2 Edge Bead Phenomenon 4.1.4.2.1 Theory for Formation Mechanisms of Edge Beads 4.1.4.2.1.1 Die Swell 4.1.4.2.1.2 Surface Tension 4.1.4.2.1.3 Edge Stress Effects 4.1.4.2.1.4 Experimental Characterization of Edge Beads 4.1.4.2.2 Conclusion

197 197 198 199 201 202 202 203 203

4.1.5

Influence of Processing Factors on Film Properties

205

4.1.6

Concluding Remarks

208

4.U

Introduction

The forming of thermoplastic film such as polypropylene, poly(ethylene) terephthalate, polyethylene, and nylon-6 can be classified roughly into a flat method such as T-die casting and an inflation tubular method such as circular die extruding. The T-die casting method, representative of flat film forming, gives higher productivity and greater uniformity of film thickness than does the blown film one. The T-die casting method is widely used in producing sheeting and as a step in manufacturing sheets for thermoforming or biaxially oriented film [I]. Many simulation models for blown film extrusion [2 to 10] have been proposed for the thinning behavior or instability of polymer melt as shown in Chapter 4.2. On the other hand, only a small number of reports have been published on film casting from a die onto a chill roll, which greatly affects the characteristics of the final products. Several attempts have been made in the simulation of film casting that present models in which molten polymer extruded from a die falls vertically onto the chill roll. See Kase et al. [11, 12], Yeow et al. [13, 14], Minoshima and White [15], Kanai et al. [16, 17], d'Halewyu and Agassant [18], Barq et al. [19], and Alaie and Papanastasiou [20]. From the practical point of view it is important to simulate the deformation behavior of polymer melt in the film casting process with the catenary profile of film such as the casting process of poly(ethylene) terephthalate film. Few papers, however, have been reported on the simulation model for the casting process of poly(ethylene) terephthalate film. Yamada et al. [21 to 27] have tried to predict the deformation behavior for the catenary profile of film casting with an electric pinning device under the assumptions of isothermal Newtonian viscosity and two-dimensional flow with analogies to melt spinning theory. Representative models for the casting process are introduced in the next section.

4.1.2

Analysis of Film Deformation under Steady State

4.1.2.1

Vertical Casting Model

4.1.2.1.1 Mathematical Model The polyolefin melt such as polyethylene and polypropylene is usually cast vertically from a die onto a chill roll. Kanai et al. [16] have derived the mathematical model for such vertical casting as shown in Fig. 4.1.1. In Fig. 4.1.1. £i, £2, and £3 are Cartesian coordinates at an arbitrary point P; the subscripts 1,2, and 3 denote the machine (flow), transverse (width), and thickness directions, respectively; w, h, and v are width, thickness, and velocity of film at P; z is the distance from a die to P.

T. die

Chill Roll

Figure 4.1.1 Vertical casting process of film

The strain rate tensor d at arbitrary point P is given by: dn ||
0 0 d22 0

d33

Q

=-¥-

-{l/w(dw/dz) + {l/h(dh/dz)} 0

0 {l/w(dw/dz)}

0

0

wn

0 0 {l/h(dh/dz)}

(4.1.1) where dx x + d22 + ^ 33 = 0 and Q — whv assuming an incompressible fluid. The stress tensor o acting on film can be obtained as follows:

IkIi=

Gn 0 o G22 0

0

0 (J33

20yo(n)/l dw | 2 ^ \ =S

0 0

Q

Q

2Qr10(H)(I dw 1 ^ \ w^ \w i/z h dz/ 0

Q

(4.1.2)

0

where rj0 is the shear viscosity given by rj0 = T]00(Tl/2){n~x)/1 Qxp[E/R(l/T - 1/T0)]; U is the second invariant of strain rate tensor d defined by VL = d\x H- d22 +d^E is the activation energy; R is the gas constant; n is the material constant of power law fluid; rj00 is the viscosity at n = 2 and T=T0. Considering the equilibrium of force at P9 we can obtain:

FL + ^whpgit = Guwh = -2Qno(n)^~

+y ^

(4.1.3)

where FL, p, and g are tension applied to film, melt density, and gravitational acceleration, respectively.

Then the balance of heat can be given as follows: JI~P

PQC?

Tz

=

-2WUV

~ ^ir) ~ ^MT4

~ Tf00J

(4.1.4)

where CP, U9 T, Tair, Troom, e, and X are specific heat of film, heat transfer coefficient obtained by Eq. (4.1.5), temperature of film, temperature of cooling air, room temperature, emissivity of film, and the Stefan-Boltzmann constant, respectively.

\ ^air /

\

^7air

/

\

A

air

/

where K2^, p air , L9 vave, and Cair are thermal conductivity of air, density of air, air gap shown in Fig. 4.1.1, mean velocity, and specific heat of air, respectively. To solve the above equations easily, we assume the neck-in phenomenon is negligible, that is, dw/dz = 0. 4.1.2.1.2 Simulated Results Figures 4.1.2 and 4.1.3 show the predicted results on the deformation behavior of polypropylene melt in casting it vertically from a die to a chill roll under a steady state, for the conditions of g = l k g / h , z;L = 3m/min, w= 155 mm, h0= 1.26 mm, L = 80 mm,

H (mm)

V

(m/min)

T

T ( 0 C)

V

H

Z (cm) Figure 4.1.2 Predicted velocity, sheet thickness, and temperature along the length of flat sheet for PP with g=lkg/h, VL = 3mJmm, W= 155mm, H0= 1.26mm, T0 = 2210C, air gap = 80mm

<7ii«1O"- (dyne/cm2j

du (sec-1)

d,i Cn

Z (cm) Figure 4.1.3 Predicted deformation rate dx i and takeup stress Cr11 along the length of a flat sheet for PP with g=lkg/h, F£ = 3m/min, W= 155mm, H0 = 1.26mm, T0 = 2210C, air gap = 80mm

T0 = 227°C, Tj00 = 3000 poise, E= 10.7kcal/mol, and n = 1; the subscript 0 denotes the die exit and the subscript L denotes the landing point onto a chill roll. As seen from Fig. 4.1.2, the film velocity v increases exponentially with increasing distance from the die exit z and as a result the film thickness h decreases rapidly. Then the film temperature decreases gradually because of the convection of air and radiation from molten film. Figure 4.1.3 shows the strain rate du and stress Gn in the machine direction. From this figure, it can be seen that the strain rate J 1 x increases with the distance from the die exit and its increment decreases gradually near the landing point, while the stress au increases exponentially because of the increase in the strain rate and viscosity. Figures 4.1.4 and 4.1.5 show the change in the film velocity v, strain rate dn, and stress CTn as a function of takeup speed vL. Each curve of the film velocity and strain rate similarly increases with increase in takeup speed. The curve of stress is similar to that of film velocity, but the change of stress with increase in takeup speed is greater than that of the film velocity.

4.1.2.2

Catenary Casting Model

It is widely noted that the polymer melt of such films as poly(ethylene) terephthalate and nylon-6 is cast in flat film, not vertically but with a catenary from a T-die onto a chill roll and that the landing point on the chill roll is fixed with an electric pinning device to increase the

V (m/min)

VL**4.5 m/min VL= 30 m/min VL=1.5m/mln

Z (cm) Figure 4.1.4 Predicted velocity profiles of flat sheet for different takeup velocities for PP (^0O = 30,000 poise, n = 1.0) with Q= lkg/h, W= 155mm, H0= 1.26mm, T0 = 227°C, air gap = 80mm

takeup speed and increase the width of film. Yamada et al. [21 to 27] have proposed a mathematical model for the casting process with an electric pinning device in which the polymer melt falls with a catenary. 4.1.2.2.1 Mathematical Model The following assumptions are made to analyze, theoretically, the deformation behavior of film in the casting process where the polymer melt in flat film shape, extruded from a die slit, lands on a chill roll following a catenary shape as shown in Fig. 4.1.6: (1) The flow is assumed isothermal between the die slit and the landing point because the temperature of polymer melt hardly changes between them as shown in Fig. 4.1.7. (2) Surface tension and aerodynamic drag are neglected. (3) The fluid is Newtonian. (4) The electrostatic force due to the pinning electrode is applied to the film by the analogy of Coulomb's law. (5) Only the flow of unit width along the film length is considered. (6) The velocity along the film width is uniform and the neck-in and edge beading phenomena are neglected. From the above assumptions, the

(dyne/cm2) CTM x 1O"6

d 1t (sec- 1 )

Z (cm) Figure 4.1.5 Predicted deformation rates J 11 and takeup stresses on for different takeup velocities or PP 0/0 = 30,000 poise, w = 1.0) with Q = lkg/h, W= 155mm, H0 = 1.26mm, r 0 = 227oC, air gap = 80mm

governing equations of film casting under the transient state can be given by the following equations: (dA/di) + {%Av)/dS} = 0 F = A(dv/dSp

P = P0 £*;

(dx/dS) = cos a = G)/(1 + ^ 2 ) 0 ' 5

(4.1.6) £o = A\JL

(4.1.7)

co = cot a

(4.1.8)

(dy/dS) = sin a = 1/(1 + co2)05 2 5

[9{F/(1 + (D f }/dS] = -Kfy-yM* [3{FQ>/(1

2

5

'^f

(4.1.9)

+ (V - ^ ) V ' 2

2

+ co )°- }/a^] = - p g ^ - AT(X - xe){(x - xe) + (y - J 6 ) F 2

5

(4.1-10)

15

(4.1.11)

where A is cross-sectional area of film (film thickness) (cm ); v is film velocity (cm/s); S is length along the film (cm); t is time (s); x, y = x, y coordinates (cm); F is tensile force (dyn); P9 P0 is elongational viscosity, p0 is A\i (dyn-s/cm2); /?* is a correction factor of P0 (-); /i is

Yd

L

Xe

X

DE

R+L

PN I NN IG ELECTRCX)B

y Ye

Chill roll

Figure 4.1.6

Catenary casting process of film with an electric pinning device

Newtonian viscosity (dyn-s/cm2); xe, ye are the x, y coordinates of electrode position (cm); Fe is the electrostatic force per unit length of film, Fe = K/L2e (dyne/cm); Le is distance between film and electrode (cm); K is power of electrode (dyn-cm); p is density of the polymer (g/cm3); OL is the tangential angle of film (rad or deg); g is gravitational acceleration (cm/s 2 ). When (d/dt) = 0 and /?* = 1, the governing equations under the steady state can be derived from Eqs. (4.1.6) to (4.1.11).

4.1.2.2.2 Simulated Results Figure 4.1.8 shows the simulated, steady-state results (that is, dA/dt = 0 in Eq. (4.1.6) for the conditions of A) 0 = 0.05 cm, ^ chill = 0.01cm, p = 1.2g/cm3, /?0 = 6000dyn-s/cm2, ^ 0 0 = 16.7 and 83.3cm/s, i? = 45cm, L = 4.8cm, ^ d = 0cm, xe = 5cm and j>e = 4.5cm using the electrostatic force K as a parameter, where the subscripts 00 and chill represent the die slit exit and the chill roll, respectively. In Fig. 4.1.9 are shown the simulated results for

Almost Isothermal landing point

TEHPEHATDHE

OF

FIUI

[tJ]

Die Exit

ELAPSED TIE [ s e c ] Figure 4.1.7

Simulated result of film temperature during the casing

the conditions of A00 = 0.05 and 0.1cm (that is, ^ooA4chiii = 5 and 10), ^chin = 0.01cm, p=\.2g/cm3, P0 = 6000dyn-s/cm2, Uo0 = 83.3cm/s, i? = 45cm, L = 4.8cm, j d = 0cm, xe = 5 cm, and ye = 4.5 cm using the electrostatic force K as a parameter. These figures suggest that higher electrostatic force ^brings the approach of the landing point to the top of the chill roll, shortens the length along the flow of film (that is, air gap S), and causes the rapid deformation of film and the higher peak of tensile force that exists near the pinning point. From Fig. 4.1.8, it can be seen that when the film velocity at the die exit is faster, the landing point of film recedes from the die, the air gap becomes longer, the tensile force becomes higher, the influence of electrostatic force on the deformation behavior of film because of the higher tensile force becomes less, the running time from the die exit to the chill roll becomes shorter, and the thinning speed becomes slower because of the longer air gap. As seen from Fig. 4.1.9, the higher elongational ratio (A00/Achm) creates higher tensile force and slower film velocity near the die exit because of the wider die slit but then the same

P :PINNING ELECTRODE / f - 0 [Pa] tf = 300 [Pa]

P PINNING ELECTRODE i [cm]

x [cm]

/C = O [Pa] K =300 [Pa]

SchiirS [mi]

y [cm]

(SN) [°]

y Icmj

ROLL

F [10%] v [an/sec] A [lOjti]

v [an/sec] A [10/ti]

CHILL

ROLL

[3K2-Oi] \

F [10%i] t [10"2sec] (90-a) [°]

Schiu"S [ran]

CHILL

Figure 4.1.8 Simulated results of deformation behavior, air gap (*SChM — S), angle (90 — a), elapsed time t, tensile force F, film thickness A, and film velocity v for V00= 16.7 and 83.3cm/s

velocity at the landing point. The elongational ratio hardly influences the deformation behavior of film such as the thinning speed, the length of air gap, and the landing point. Figure 4.1.10 shows the simulated and observed results of the deformation behavior of film. Figure 4.1.10 supports the validity of the mathematical model because the simulated results are similar to the observed ones.

P :PINNING ELECTRODE

K = O (Pa] tf=300 (Pa] x [cm]

x [cm]

P WINNING ELECTRODE tf = 0 (Pa] /f=300 (Pa] Aoo/AcHILL = 5

CHILL ROLL

F [10%!] t [10"2sec] (90-a) [°]

F [IPdyn] t [1(T2SeC] (9D-a) [°]

A [10/im]

v [an/sec] A [1Op]

CHILL ROLL

v [cm/sec]

Aoo/AcHia= 1 0

Figure 4.1.9 Simulated results of deformation behavior, air gap (SChiii — S), angle (90 — a), elapsed time t, tensile force F, film thickness A, and film velocity v for A00/Achm = 5 and 10

Figure 4.1.11 shows the simulated results under the conditions of A00 = 0.1 cm, p = 1.2g/cm3, i;Oo = 0.2cm/s, i;chill = 1 cm/s, R = 50 cm, L = 8 cm, >>d = 0cm, xe = 7cm, and je = 5 cm using the electrostatic force as a parameter. Figure 4.1.11 represents the variations of the flow profile of film, the tangential angle of film (a), and tensile force of film (F) from the die slit exit to the landing point on the chill roll under P0 = 6000 and 10,000dyns/cm 2 .

ore

SIMULATED

V = O [KV] V = I O LKV]

P

P

UNDING POINT

CHILL

.DIEJ

OBSERVED

/T=O [Pa] JC = 30 [ P a ]

UNDlNG POINT

ROLL

CHILL

ROLL

Figure 4.1.10 Comparison of simulated and observed results for deformation behavior

The findings from these figures are similar to those obtained from Figs. 4.1.8 and 4.1.9: (1) The stronger the electrostatic power (K), the shorter the length of film (S) is between the die slit (D) and the film landing point on the chill roll. (2) The higher the viscosity of molten polymer is, the nearer the flow profile draws to the electrode because of the higher tensile force. (3) Influenced by the electrostatic force, the flow profile suddenly changes around the electrode and the tensile force has its maximum value here. (4) The higher viscosity gives higher tensile force. This simulation model gives not only the above-mentioned information but also other information on the effects of die slit width, the air gap length and the chill roll diameter, the positions of the die slit and the pinning electrode, and the speeds of the polymer melt at the die slit and landing point on the chill roll.

4.1.3

Analysis of Film Temperature

It is important to predict the film temperature in casting, as it affects not only the characteristics of film but also its processability in the subsequent processing stages. Several articles on this subject have been published [28 to 30]. Michaeli and Menges [28] have reported work on the fundamental principles of the cooling analysis for extruded products by approximate use of the partial differential equations in the unsteady state of a fixed body for the run of film in the steady state. Their analysis of cooling in casting considers heat conduction across the cross-section of extruded film/sheet and boundary conditions with the surroundings. The variation of thermal properties with temperature is included but viscous dissipation is neglected. Their work also includes detailed calculations for the cooling of extruded polyethylene and polystyrene sheets as specific examples. On the other hand, Billon et al. [30] proposed that the modeling of the cooling of film on the chill roll during the cast film extrusion process, in consideration of the run of film, is expressed by the substantial derivative under the steady state. Here we introduce a summary of the analyses of Michaeli and Menges [28] and Billon et al. [30].

DIE P : PINNING ELECTRODE K-O K- 300 tf-500

P CHILL

y [cm]

/C-300

j3 0=10000 poise p

H

ROLL

CHILL ROLL y [cm]

V [cm/s]

V [cm/s]

SCHILL-S [cm]

SCHILL-S [cm]

A [/<m]

A [/'m]

FflO'dyn]

F[10Myn]

(90- a) [')

J

j3o=6000 poise

H

(so-a) n

J

K-O tf-500

[CONDITIONS FOR SIMULATION] p =1.2 g/cm3 ;Aoo = l mm;V0o=20 cm/sec ;VCHILL=100 cm/sec ;R=50 cm ;L=8 cm ;yd=O cm xe-7 cm ;y.=5 cm Figure 4.1.11 Simulated results of deformation behavior, angle (90 — a), tensile force F, film thickness A, air gap (Schm - S), and film velocity v for ^ 0 = 6000 and 10,000 poise

4.1.3.1

A Model for Cooling in Extruded Materials by Michaeli and Menges

4.1.3.1.1 Mathematical Model We now consider that the process is divided up into individual sections between the die and delivery/rolling up, as shown in Fig. 4.1.12, with different cooling conditions in each section. In compiling the theoretical cooling model the following main simplifications are assumed: (1) The width of the film/sheet remains constant throughout the process; (2) the film/sheet is not stretched during the process; (3) heat conduction in the direction of drawing is

disregarded; and (4) the increase in internal energy in the film/sheet caused by friction in the boss is disregarded (friction work is disregarded). To express the geometry of the flat film/sheet it is wise to choose Cartesian coordinates for sections in the extrusion unit where the sheet runs flat (Fig. 4.1.12), with cylindrical coordinates used in the roller sections. The fundamental heat conduction equation with temperature-dependent material values for Cartesian coordinates can be derived as follows:

i = - » - ( S + ? H * - [ © ' + ( D ] The equation for cylindrical coordinates can be derived accordingly:

^ • ( S ^ d r / £ H « - | W

+

( £ ) ]

' - "

where t is time, 6 is temperature, x, y are coordinates, a is thermal diffusivity; a =

A/pC?d = (l/pC?)(dl/d9). Convective heat transfer is expressed in mathematical terms using the Newtonian formula: q = a ( ^ - 0W) = - W9>0 surface

(4-1.14)

where a denotes the surface coefficient of heat transfer; the subscripts U and W denote surroundings and wall respectively, and n denotes the normal coordinate. AOW

roll 1

section 1

section 8 FUB)

section 2 FU2) roll

2

AV/23

roll 4

roll 3 AW % H

Figure 4.1.12

Sections of a flat film/sheet extrusion line; geometrical data

AW 3C V

sheet die

It is possible to describe the radiation exchange between a body and its surroundings (e.g., between rollers and the flat film/sheet) by means of the coefficient of radiation heat transfer arad, which is defined as follows: «rad = &ad/(A0^)

(4.1.15)

where Q is heat flow through radiation, AO is the temperature difference, A is surface area, and the subscript rad means radiation. According to the Stefan-Boltzmann law or radiation, however, the flow of heat from a surface area is: 2rad = e r a d ^[(r w /ioo) 4 - (Tyioo) 4 ]

(4.1.16)

where smd is emissivity of radiation and a is the Stefan-Boltzmann constant (unit conductance of black body). By use of Eqs. (4.1.12) through (4.1.16) and appropriate boundary conditions, the film temperature in cooling as shown in Fig. 4.1.12 can be calculated.

4.1.3.1.2 Application for Flat Sheet Extrusion

thickness 1Bm m

Figure 4.1.13 shows an example of the calculated cooling over the thickness and width of a polystyrene sheet (drawing velocity, v = 0.00362m/s) for unit sections shown in Fig. 4.1.12. The initial temperature profile in the sheet (t — 0 s) was constructed from the measured melt wall temperature in the lip and also from an assumed fictitious maximum temperature in the sheet core, illustrating a possible flow of heat from inner to outer areas. At stage tx an increase in sheet surface temperature, due to this heat flow, can clearly be seen. The different degrees of convective heat transfer on the topside and underside of the sheet are revealed at ^ through

to=Osec U = 1.6 sec Tnaterial: polystyrene environm. temp.: 80 0C Figure 4.1.13 Cooling of the sheet in section 1

measured point t2= 33.1 sec

different surface temperatures. Analysis of the effect of modified operating conditions and material reference on cooling behavior would appear to be of interest. From Fig. 4.1.14, a great deal of information may be obtained from the comparison of cooling behavior in a polystyrene and a polyethylene sheet. In section 3 the polyethylene sheet (with the same initial temperature profile as that shown in Fig. 4.1.13) clearly maintains its temperature, on account of the crystallization heat that is released at this point. Figure 4.1.15 shows the calculated start and end of crystallization for polyethylene over the sheet cross-section, assuming the initial temperature profile leads to asymmetrical crystallization behavior, with direct consequences on sheet deformation behavior. Cooling processes in extrusion unfortunately cannot be calculated with a sufficient degree of accuracy using simple means. Strictly speaking, the manner presented here is incorrect but it reveals the equipment required. It can rapidly become economic when applied for the purposes of (1) achieving a more reliable cooling path design, (2) optimizing extrusion units through describing the effect of individual process parameters on cooling, and (3) estimating the cooling performance of new processes and materials. Even though some difficulties still remain in the formulation of heat transfer laws for a number of extrusion processes, the calculation method presented here does open up the way for postulations on the influence that individual factors tend to have on cooling and for distinguishing between significant and insignificant influencing factors.

4.1.3.2

A Model for the Cooling of Cast Film on a Chill Roll by Billon et al.

4.1.3.2.1 Mathematical Model Billon et al. [30] proposed the model for the energy balance of polymer film during its run on the chill roll in a steady state. The outline is described below.

PE upper sheet surface PE material: polyethylene Ipolystyrene lower sheet surface PS sheet thickness: d=1.6 mm upper sheet surface PS sheet width: lower sheet surface b=BOO mm take-off speed: v = 0.00362 m/S temp, of cool.rotls: ^2 =100°C; ^3 * 7O°C

section 1sect/on 3section section 5

Figure 4.1.14

section 6

Cooling of a flat film/sheet; comparison of polyethylene and polystyrene

sheet thickness

sheet width

start of cristallization

time t[$ed

end of cr/stallizotion Figure 4.1.15

Start/end of crystallization in a polyethylene sheet

Consider a casting process where the flat film polymer extruded through a slit die is stretched on a short distance in air (viz. air gap) and then cooled on the metallic surface of a thermoregulated chill roll, using an electric pinning device or an air knife to achieve a good contact between the metal and the polymer. During its stretching in the air, the geometry of the film varies (its thickness and width decrease) but the temperature decrease is small (see Fig. 4.1.7). On the other hand, as soon as it is in contact with the roll, its geometry variations cease and the cooling becomes much more important. So, it can be assumed that the polymer is cooled on the chill roll only. In that case we will follow a section of the film during its run on the roll. We now consider a polymer film having a thermal conductivity and a specific heat dependent on temperature. Under the assumption that (1) the temperature changes in the width of the film, that is, in the ^-direction, can be neglected; (2) heat conduction in the flow direction can be neglected with respect to heat convection in that direction; and then (3) the flows in y- (width) and z(thickness) directions are negligibly small, the energy balance of cast film polymer can be expressed in the substantial (or Lagrangian) derivative (DTfDt) as follows:

Dt

~

K

)

dz*

PC¥(T)

BT

V9 V

C7(T)

dx

( A I )

In a steady state (dT/dt) = 0, and so the above equation can be written:

where 7 is the temperature of the film; t is time; x, y, z are coordinates; p is density of the film; Cp is the specific heat of the film at constant pressure; k^ is the thermal conductivity of the film; Ut is the linear velocity of roll; A//is the theoretical specific enthalpy of crystallization; oc is the transformed volume fraction (the volume fraction of the film overlapped by the spherulites); and a is the thermal diffusivity of the film; a(T) = Ic^(T)/pCF(T).

The lower surface of the film is cooled by heat conduction. Its temperature is calculated, as an interface temperature, by the following equation: T

_ ^roll * ^roll + ^pol(^pol) ' ^pol

,, , . Qx

^roll + ^poll^pol)

where Tsc is the temperature of the surface of the film in contact with the roll, bron, bpo\(Tpoi) are the thermal efrusivities of the metallic roll surface and of the polymer (b(T) = (kth(T) • p • Cp(r)) 1 / 2 ), TTO\\ is the temperature of the roll, and r pol is the mean temperature of the polymer at abscissa x. The upper surface of the film on the roll is cooled by air convection and radiation: - * * ( D § = HTn - T*) +
(4.1.20)

where r s a , T2^x, T2^00 are respectively the temperature of the surface of the film in contact with the air, of the air near the film, and of the air far from the film. spo\ and ^air are respectively the film and the air emissivities and a the Stefan-Boltzmann constant, h is the convection heat transfer coefficient, which is calculated locally as a function of the distance between the first point of contact film roll and the abscissa x [31, 32]: k Pr 1 / 3 h = 0.402 -^- (Rex)x ) 172 J7T-T7x + 0.45 x {l+(0.0336/Pr) 2/3 } 1/4

V(4.1.21)

where Pr is the Prandtl number; Pr = rjaiT/(pair, <2air), Rex is the Reynolds number; Rex = Pair' x ' Ut/riafr, rjair is the viscosity of air, pair is the density of air, and aair is the thermal difiusivity of air. 4.1.3.2.2 Simulation Example Figure 4.1.16 shows the crystallization that takes place at two different moments (x, abscissa) and also the temperature ranges for the two surfaces using the above theory with given values of physical parameters. This figure illustrates the very asymmetrical cooling of the film. It is clear that such cooling induces heterogeneous microstructures and properties within the film.

4.1.4

Analysis of Neck-In and Edge Bead Phenomena

4.1.4.1

Neck-In Phenomenon

In the T-die casting of film the viscoelastic behavior of the polymer melt causes problems of (1) a neck-in phenomenon, where the width of film becomes narrower and (2) the stretchability of film such that a surging or a breaking phenomenon occurs during the stretching in air (i.e., air gap). During the hot stretching of molten cast film in the air the film narrows and as a result the edges of the film get thicker as shown in Fig. 4 A.17. Neck-in is usually defined by the difference between the width of the die slit and that of the film. The larger the neck-in, the thicker the edges of the film (i.e., edge beads) are; therefore the yield of

Roll

z

m

A

m x

Air

•C 8

Tcmptrafurt

Figure 4.1.16 Cooling in cast film extrusion process: evolution of the positions during the run on the roll (A) and of the temperatures at which the crystallization begins, a = 0, and ends, a = 1 (B) versus z

a product diminishes according to the increase of the trimmings. It is known that neck-in is related to the surface tension and elastic modulus of the molten film and then is caused by contraction of the film. So, the higher the tensile force required in the taking up of film, the less the neck-in becomes. The degree of neck-in is related to the characteristics of a propylene polymer, such as its density and melt index (MI), and to its casting conditions, such as the temperature of molten film, the length of air gap, and the width of die slit. The degree of neck-in can be expressed as a function of its density and melt index for the characteristics of film as follows [33]: Degree of neck - in = c + 147.7 • d + 2.57 • log(MI)

(4.1.22)

where c is a constant and d is density. From Eq. (4.1.22), it can be seen that a higher density or a higher melt index gives a large neck-in under fixed casting condition. In addition, molten film having a high die swell ratio due to the Barus effect causes a decrease in neck-in. In regard to casting conditions, the longer the air gap, the wider the die slit, the higher the takeup speed, and the higher the temperature of molten film are, then the greater is the neckin. Figure 4.1.18 shows the influence of the air gap and the temperature of film. This figure suggests that both a longer air gap and a higher temperature give a larger neck-in and that the air gap has the greater effect. In general neck-in and stretchability show an approximately contrary tendency A molten film with large neck-in can be cast and thinned in higher takeup speed.

4.1.4.2

Edge Bead Phenomenon

Dobroth and Erwin [34, 35] tried to theoretically express the formation mechanism of edge beads and predict the method of their elimination by simulation. The summary of their analysis is introduced in the following section.

Die

Cast film

SURFACE OF CHILL ROLL NECK-IN

NECK-IN

CROSS SECTION OF FILM

EDGE BEAD

EDGE BEAD Schematic diagram of neck-in and edge beads

Neck-in (mm)

Figure 4.1.17

DIE W1DTH=700mm

POLYPROPYLENE Air gap (mm) Figure 4.1.18

4.1.4.2.1

Relationship between air gap and neck-in

Theory for Formation Mechanisms of Edge Beads

Cast polymer films are produced by melt extruding a polymer through a uniformly thin die slit onto a chill roll. Between the die and the chill roll, thick edges called edge beads form, which have to be trimmed from the film, and are either scrapped or recycled. Edge beads are usually

caused by three factors: surface tension, die swell, and an edge stress effect. Surface tension and die swell effects can be important in materials of low viscosity and in elastic materials respectively. The predominant cause of edge beads is an edge stress effect, which occurs when the film is stretched between the die and the roll. The edge elongates in uniaxial stress while the center material elongates in plane strain. The following assumptions are made in the modeling of edge bead formation: (1) Transients will be ignored. Because edge beads occur in steady flow, the analysis is limited to steady flows. (2) In steady flows, the boundaries and streamlines must not move. (3) Also, the flow rate of the fluid coming out of the die must equal the flow rate of the fluid that passes over the rolls. Because the streamlines are stationary, the volume flow rate between two streamlines at the die must equal the flow rate between the same two streamlines at the roll. The relationship between neck-in and edge beads can be shown by examining the streamlines and using conservation of mass principles. If the film is very wide, the streamlines in the center of the film will be straight. At the edge, the streamlines will be closer at the roll than at the die. The conservation of mass requirement between streamlines will show the relationship between edge beads and neck-in as illustrated in Fig. 4.1.19. If the average velocity is Fj, across one section of the die, AX, the volume flux at the die slit exit, vi5 is: Vx = V x - A X -h{

(4.1.23)

where hx is the thickness at the die slit exit. If the edges of AX, AX are followed downstream to the roll, the volume flux at the roll, Vf, is:

vf = VfAX'-hf

(4.1.24)

where Vf is the velocity at the roll, hf is the thickness at the roll, and the subscripts i and f denote die slit exit and chill roll, respectively. By mass conservation, the volume flow rate is constant, V1 = Vf. So, V1 • AX - h{ = Vf • AX' • hf

(4.1.25)

At the contact point, the fluid will reach the velocity of the roll, Vf. Dies are designed so that the volume flux and initial thickness will be constant across the width; so V1 = constant and h{ = constant. In Eq. (4.1.25) the only nonconstant variables are AXf and hx. For the thickness, hi, at the edge to be greater, the width of the film, AX', must be narrower. Near the center of the film, the streamline must be straight and even, so: AX = AX'

(4.1.26)

at the center, where the "center" refers to the entire region between the edge beads, not just the exact center of the film. Closer to the edge, edge beads will develop and the streamlines will curve inward: AX>AX'

(4.1.27)

at the edge. If AXand AX' are allowed to become dXand dX', Eq. (4.1.25) can be integrated to find the width of the film:

f

/2

fCo/2

VfadX =

VfhfdX' Jo

(4.1.28)

Edge Beads and Neck-in

W

Streamline AX

Contact line AX'

w

Figure 4.1.19

For steady flows the film width is a result of the edge bead thickness

where the origin is the center of the film, W is the width of the die, and at is the film. After the integration, Eq. (4.1.28) can be expressed by:

All of the terms in the integrand are constants except for hf. The term (W-Q), which means "neck-in," will become more positive with greater hf. Therefore edge beads and neck-in are the same problem. Three theories of edge bead formation due to die swell, surface tension, and edge stress effects are described in the following sections. 4.1.4.2.1.1 Die Swell Viscoelastic fluids swell to a larger thickness than the die Hp gap. Elastic stresses are accumulated from every wall in the die and the edge may accumulate additional swelling from the additional die wall. Swelling will occur everywhere across the width of the die. If the swelling is 2.1 at the center, the edge might be 2.5. The center-to-edge ratio would be 1.19. Because the edge bead size is the comparison of die swell effects from center to edge, the edge bead will probably be less than 2 at the worst. Where a die swell edge bead extends toward the center of the film it is not usually more than about five times as wide as the thickness of the film, independent of the width of the die

slit and the distance to the roll. For example, films are usually less than 1 mm thick, so it would be unusual to find an edge bead formed by die swell wider than 5 mm. As edge beads are commonly several centimeters wide, they do not appear to be the result of die swell. 4.1.4.2.1.2 Surface Tension Surface tension forces on the film must be balanced by the stress at the edge. This stress will push the edge material into the film, resulting in thicker edges. Assuming that (1) the strain rate, s, can be approximated by the final strain, s: s = s/t (2) the film is a Newtonian fluid; and (3) the surface tension forces are balanced by a transverse direction on the film, then the following equation can be derived.

«=?4

(4i-3°)

3 \m where S is the surface energy per unit area, h is the thickness of the film, / is the residence time of the film during the air gap, and /i is the viscosity of the film. The right side of Eq. (4.1.30) is two thirds the capillary number, which is the ratio of surface tension to viscous forces, and the capillary number must be of the same order as the strain. The capillary number is, at most, less than 1 for most cast polymer films; that is, surface tension is less than viscous forces. This means that in films made at low speeds from very low viscosity fluids, surface tension will contribute significantly, but it will not be important in most cast film applications. Therefore, surface tension will almost never apply in cast films but will be more important in extrusion coating. 4.1.4.2.1.3 Edge Stress Effects Surface tension forces on the film must be balanced by a stress at the edge. This stress will push the edge material into the film, resulting in a thicker edge. The stress and strain conditions near the edge differ from the middle. By comparing the center stress condition with the edge one, edge beads can be shown to be related to the size of edge stress. Near the middle, streamlines are straight and parallel. An element that travels between parallel streamlines has the same width when it reaches the roll. In the center, the strain and the strain rate in the transverse direction (x direction) equal zero: Sx = Sx = 0, and then the relationship between the machine direction stress, oy, and the transverse direction stress, Gx, can be given by Gx = Gy/2 for a Newtonian fluid because the stress in the thickness direction usually equals zero: GZ = 0. The size of edge beads resulting from edge stress effects can be found by comparing strains of elements between the roll and die. If ^ 1 is the ratio of final to initial dimensions of an element, the product of the three elongation ratios for an incompressible material equals 1: EJEyE1 = 1. The machine direction elongation ratio, Ey can be approximated as constant across the film. Because the die opening, hx, is constant, the exit velocity, vx, will be constant. At the roll, the fluid moves with the velocity of the roll, vf. The machine direction elongation ratio, Ey, is the ratio of the machine direction velocities, defined as the draw ratio, D: D = vf/v{=Ey

(4.1.31)

At the center the transverse direction elongation ratio Ex is 1 because of no change in the transverse dimension. BecauseExEyEz = \,EX = \, Ey = D, andE2 = hf/h{, we can obtain: [ V / S f = ^center

(4-1-32)

where /?f is the thickness near the center of the roll. At the edge there is no stress in the transverse direction or in the thickness direction; the elongation ratios in those directions are equal. The free edge conditions lead to the change in thickness between the center and the edge. Because the elongation ratios in the thickness and transverse directions are equal, Ex = E2, the final thickness at the edge is: [hjh, = VD]edge. gQ

If the die has a constant opening, tif (4.1.33) the following relationship:

(4.1.33)

QnteT

= hf

h?ge/h?nter=B

, we can finally obtain from Eqs. (4.1.32) and = VD

(4.1.34)

where B is the so-called bead ratio, defined as a ratio of edge to center final thickness. The analysis above has not used any assumptions about the material except for incompressibility and is true for any material. Solid and liquid materials behave according to Eq. (4.1.34). The width of the edge bead is closely related to the distance from the die to the roll. The dimension determining the width of edge beads due to edge stress effects is the distance from the die to the roll. Die roll distances are normally about 5 to 15 cm. Edge beads formed by the edge stress effect will have a characteristic width of the order of 5 cm. This simple analysis indicates that edge stress effects are the predominant cause of edge beads. 4.1.4.2.1.4 Experimental Characterization of Edge Beads An experiment to characterize the width and size of edge beads was performed for a low-density polyethylene cast film. Figure 4.1.20 shows the plot of bead ratio, B, against draw ratio, D. The draw ratio was calculated by measuring the center thickness and the die opening; the bead ratio was found by measuring the final edge thickness. The results strongly support the relationship of Eq. (4.1.34). The experiment can also demonstrate the conditions under which surface tension effects are important in films by extruding films with capillary numbers above and below unity. By plotting BfD against the capillary number, the effects of surface tension can be shown as illustrated in Fig. 4.1.21. The results show that edge beads do not occur for small capillary numbers. 4.1.4.2.2 Conclusion The predominant cause of edge beads is the edge stress effect. All polymer films and coatings that are drawn down in thickness have beads caused by this effect. Other factors such as surface tension and die swell affect the edge, but the size of the bead is much smaller and the width is on the same scale as the thickness of the film. The width of the bead due to edge stress effects is about as wide as the distance from the die to the roll. The edge stress effect occurs between the die and the roll. Edge beads due to surface tension and die swell occur only when the special conditions of low viscosities of elastic fluids are met.

BEAD RATIO

DRAW RATIO

BEAD RATIO/SQRT (DRAW RATIO)

Figure 4.1.20 Edge bead thickness as function of drawdown ratio. The theoretical predictions are shown as a solid line

CAPILLARY NUMBER Figure 4.1.21 Surface tension creates edge beads when the capillary number approaches 1

Table 4.1.1

Comparison of Causes of Edge Beads

When important Characteristic distance Normal dimensions Bead width Bead ratio

Surface tension

Die swell

Edge stress effects

Low viscosities Thickness 5 to 100 mils <5mm

Elastic fluids Thickness 5 to 100 mils <5mm <2

Always Die to roll distance = 6 in. = 6 in. 1.5 to 4

The comparison of edge beads caused by surface tension, die swell, and edge stress effects is tabulated in Table 4.1.1.

4.1.5

Influence of Processing Factors on Film Properties

Wibbens [36] previously reported the relationship between processing factors (polymer temperature, takeup speed, cooling temperature, die lip gap, and tension applied to film) and film properties (elongation, impact strength, transparency, modulus, fish eye, slipperiness, and thickness). In the report a higher polymer temperature creates much higher transparency but a much higher temperature causes negative effects on mechanical properties. When a film is quenched more rapidly, the transparency of film is improved and the mechanical properties become isotropic approximately, and moreover the impact strength increases, but the tensile strength and the elongation decrease somewhat. A takeup speed is related to the orientation of film. The higher speed leads to the difference in the degrees of in the machine and transverse directions and to the lower impact strength. These results are summarized in Table 4.1.2. Recently, Kanai [37] has examined the influence of processing factors on the properties of polypropylene film similar to the above work [36] and the results are tabulated in Table 4.1.3. Generally, it can be seen from Table 4.1.3 that compared to the processing factors in blown film operations, those in the T-die casting exert little influence on the mechanical properties of film, but they exert some influence on the heatsealing temperature of film, optical properties, and the coefficient of static fiction. In Fig. 4.1.22 the relationships between (a) the film thickness and the coefficient of static friction, (b) the polymer temperature and the haze and, (c) the chill roll temperature and the haze are shown. The higher cooling temperature of film causes the higher crystallinity. As a result, the heatsealing temperature becomes higher and the optical properties deteriorate. Then, the coefficient of static friction becomes lower because the surface becomes uneven because of crystallization and the modulus becomes higher because of the high crystallinity. The higher polymer temperature creates an improvement in the optical properties because it leads to the lower shear stress applied to polymer in the die and the higher relaxation of polymer out of the die slit. This, in turn, leads to higher impact strength but lower modulus because of the lower crystallinity.

Table 4.1.2

Processing Factors and Film Properties

Processing factor

Direction

Polymer temperature

MD TD

Takeup speed

MD TD

Cooling temperature

MD TD

Die lip gap

MD TD

Air gap

MD TD

Tensile strength

Elongation

Impact strength

Haze

Slipperiness

Fish eye

Table 4.1.3

Relationship Between Processing Conditions and Film Properties

Conditions

Direction Tensile modulus MD

Polymer temp. (180 to 2800C)

Output (10 to 80kg/h)

Roll temp. (20 to 800C)

Thickness (10 to 40 /mi)

Tensile strength (at yield point) TD

MD

TD

Tensile strength (at break) MD

TD

Heat-sealing temperature

Haze

Gloss

Impact strength

Slipperiness

Coefficient of Static Friction Iw[X]

Film Thickness Um]

haze [XJ

Polymer Temperature [0C]

Chill Roll Temperature [8C]

Figure 4.1.22 Influence of processing factors on film properties, (a) Film thickness and coefficient of static friction; (b) polymer temperature and haze; (c) chill roll temperature and haze

The film thickness affects the optical properties of film; the coefficient of static friction sharply decreases with a greater thickness.

4.1.6

Concluding Remarks

In this chapter the phenomena and problems encountered on casting were briefly introduced through theoretical analyses. It has been confirmed that two representative casting models, one a vertical casting model and another, a catenary casting model, were useful for process analysis. Recent approaches on the prediction of film temperature in casting were introduced. Representative problems in casting, neck-in and edge bead were discussed. The effects of processing parameters on film properties that are of practical significance were examined.

References 1. Yamada, T., In New Films and Membranes (1990) Kagaku Kogyou Nippousha, Tokyo, p. 232-274 (in Japanese) 2. Pearson, J.R.A., Petrie, C.J.S., J. Fluid Meek (1970) 40, p. 1 3. Pearson, J.R.A., Petrie, C I S . , J. Fluid Meek (1970) 42, p. 609 4. Han, CD., Park, J.Y., J. Appl. Polym. ScL (1975) 19, p. 3257 5. Han, CD., Park, J.Y., J. Appl. Polym. ScL (1975) 19, p. 3291 6. Kanai, T., et al., Sen-i Gakkaishi (1984) 40, p. T-465 7. Kanai, T., White, J.L., Polym. Eng. ScL (1984) 24, p. 1185 8. Sudou, M., Ichihara, S., Sen-i Gakkaishi (1985) 41, p. T-16 9. Cain, JJ., Denn, M.M., Polym. Eng. ScL (1988) 28, p. 1527 10. Cao, B., Campbell G.A., AIChE J. (1990) 36, p. 420 11. Kase, S., Matsuo T., J. Polym. ScL A (1965) 3, p. 2541 12. Kase, S., J. Appl. Polym. ScL (1974) 18, p. 3279 13. Yeow, YL., J. Fluid Meek (1974) 66, p. 613 14. Aird, G.R., Yeow, Y.L., Ind. Eng. Chem. Fundam. (1983) 22, p. 7 15. Minoshima, W, White, J.L., Polym. Eng. Rev. (1983) 2, p. 211 16. Kanai, T., Sen-i Gakkaishi (1985) 41, p. T-409 17. Kanai, T., Funai, A., Sen-i Gakkaishi (1986) 42, p. T-I 18. d'Halewyu, S., Agassant, J.F., Polym. Eng. ScL (1990) 30, p. 335 19. Barq, P., et al., Int. Polym. Process. V (1990) 4, p. 264 20. Alaie, S.M., Papanastasiou, T.C., Polym. Eng. ScL (1991) 31, p. 67 21. Yamada, T, et al., In Proceedings of the 5th Annual Meeting of PPS (1989) 06-13 22. Kase, S., et al., In Proceedings of the 5th Annual Meeting of PPS (1989) 06-14 23. Yamada, T, et al., In Proceedings of the 1st Polymer Processing Technology Symposium (1989) p. 59 24. Yamada, T, et al., Bull. Faculty Textile ScL Kyoto Inst. Technol. (1990) 14, p. 35 25. Yamada, T, Fujita, S., In Proceedings of the 24th Autumn Meeting of the Society of Chemical Engineers, Japan, ( 1 9 9 I ) L l I l 26. Yamada, T, et al., Int. Polym. Process. (1995) 10, p. 334 27. Yamada, T., Kemikaru Enjiniyaringu (Japanese) (1992) p. 798 28. Michaeli, W, Menges, G., Polym. Eng. Rev. (1982) 2, p. 99 29. Cotto, D., Haudin, J.M., Rev. Gen. Therm. Fr. (1985) 288, p. 879 30. Billon, N., Barq, P., Haudin J.M., Int. Polym. Process. N (1991) 4, p. 348 31. Churchill, S.W, Ozoe, H., J. Heat Transfer, Trans. ASME (1973) 950, p. 416 32. Dennis, S.R.C, Smith, N., J. Fluid Meek (1966) 24, p. 509 33. McDonald, W.F., Plast. Technol. (1958) 4, p. 10, 918 34. Dobroth, T., Polym. Eng. ScL (1986) 26, p. 462 35. Dobroth, T, Erwin, L., ANTEC'86 (1986) p. 893 36. Wibbens, R.L., Plast. Tech. (1961) 4, p. 35 37. Kanai, T, Plastic Age Japan (1986) Oct., p. 168

4.2

Analysis of Draw Resonance Instability in the Film Casting Process Hideaki Ishihara

4.2.1

Introduction

211

4.2.2

Relevance of the Problem in the Film Industry

212

4.2.3

Draw Resonance in Newtonian Fluids

212

4.2.4

Draw Resonance in Non-Newtonian Fluids 4.2.4.1 Power Law Fluids

216 216

4.2.4.2 Viscoelastic Fluids

218

4.2.5

Mechanism of Draw Resonance

222

4.2.6

Conclusion

224

4.2.1

Introduction

Draw resonance is an elongational flow instability characterized by a periodic variation of casting film thickness and spinline diameter in unstable melt processing of film and fiber respectively. There have been many studies on the mechanics and stability of melt processing of film casting and melt spinning. Draw resonance was first reported by Miller [1], Freeman and Coplan [2], and Bergonzoni and DiCresce [3, 4]. These reports suggest that the fiber spinning process may be highly sensitive to small periodic disturbances and, under certain circumstances, may even be completely unstable. Kase and co-workers [5] showed, in their theoretical analysis of draw resonance observed in the extrusion casting of plastic films, that the cooling of the extruded polymers played a predominant role in stabilizing the casting process and that in isothermal melt spinning it became unstable when the drawdown ratio was greater than 20. The same conclusions were obtained by Pearson and Matovich [6] and Gelder [7]. More detailed theoretical analyses of the stabilizing effect of cooling have been made by Shah and Pearson [8, 9] and Kase [10] using linear stability theory. In their reports, the stability of melt spinning was discussed with respect to the Stanton number. The above-mentioned previous works assumed Newtonian liquids. Pearson and Shah [11 to 13] have theoretically studied the draw resonance in the power law fluids using infinitesimal perturbations, giving the neutral stability curve which is dependent upon the power law exponent and the drawdown ratio. A nonlinear stability analysis for a viscoelastic fluid with a constant viscosity has been done by Zeichner [14] and Denn [15]. Zeichner showed that the range of stable operation was extended by fluid elasticity, and that a second stable region at very high drawdown ratio existed. The first publication on the nonlinear dynamics of the draw resonance in isothermal melt spinning may be that of Ishihara and Kase [16, 17]. The limit cycle solutions were obtained by solving the equations of continuity and momentum directly without recourse to perturbation. A similar study was made by Fisher and Denn [18] by means of a different approach. Concerning the draw resonance instability for film casting, on the other hand, several articles have been published [5, 19 to 23]. Yeow [19] studied the film flow stability for a Newtonian liquid using linear hydrodynamic stability theory. Solving the relevant eigenvalue problems, neutral stability curves were shown and discussed in comparison with the results of Pearson and Matovich [6] and Gelder [7] in the case of the two-dimensional disturbances stability analysis. Further, Aird and Yeow [20] extended the studies on draw resonance in film casting for the power law fluid model. It was shown that the critical extension ratio, which is related to the onset of instability, increases with the power law index (p). Different critical values of p exist for oscillations in the thickness direction and the width direction. In the case of p values less than 1.2, thickness oscillation occurs but remains uniform across its width. For p > 1.2, instability manifests itself as waves traveling across the width of the film. Barq and co-workers [21] investigated experimentally the draw resonance instability in the film casting process, showing the interesting coupling effects between thickness and width fluctuations. Clearcut understanding of the fluctuation mechanism might not be possible at this time owing to the complex two-dimensional stability problems with nonlinear coupling effects between the two directions. To reduce the draw resonance phenomenon in the film casting process, a draw resonance eliminator was reported to be set in the air gap position between extrusion die and chill roller

by Luccbesi and co-workers [22]. They applied their eliminator to the casting of linear lowdensity polyethylene (LLDPE). Also, Flanagan [23] introduced the method of stabilizing casting films in terms of air gap length and position by using a dual-chamber vacuum box near the air gap region.

4.2.2

Relevance of the Problem in the Film Industry

Film casting is a key process of drawing polymer melts extruded from a die into the films which are solidified on a cooling roll. It is important to study the mechanics of this process from the industrial point of view. The main theme has been concentrated on the stability of melt casting of films. Instabilities never develop in conventional casting, which is mostly utilized in the film industry. It does not follow, however, that casting is always stable. It does become unstable under certain conditions, resulting in clearly periodic and very large fluctuation in the thickness of casting films. This phenomenon has been called the draw resonance ever since Miller [1] used the term. It happens that conventional industrial film casting must be carried out under stable operating conditions. Draw resonance is a melt flow instability that is distinguished from the phenomenon of melt fracture, a distortion of the extrudate surface with severity ranging from simple roughness to helical indentations. The main cause of the occurrence of draw resonance is associated with the cooling effect of the extruded film between the die and the cooling roll. When the cooling is insufficient, the draw resonance occurs. Since the draw resonance phenomenon reduces productivity because it gives nonuniform film thickness, many researchers are directed to obtain information on stable processing regions and to determine more suitable casting conditions for industrial film casting processes. In this chapter, detailed results of the draw resonance analyses that were obtained, both theoretically and experimentally, for melt spinning by the author [16, 17, 24] are presented. Basically, draw resonance behaviors are essentially identical in both melt spinning and film casting with a few exceptions such as thickness/width coupling in the film case.

4.2.3

Draw Resonance in Newtonian Fluids

When the process of melt spinning becomes unstable, standing wave-type variations in the thickness of the filament taken up develop. Several researchers [2 to 9] made attempts to analyze draw resonance by means of perturbation studies of the equations of momentum, continuity, and energy set up for the conditions of melt spinning. Although these perturbation studies were successful in predicting the oscillation period and approximate conditions of neutral stability, they failed to predict the exact wave form of draw resonance, notably the amplitude due to loss of some information during linearizing the equations. To overcome this

drawback, the author intends to solve the equations of momentum and continuity for isothermal melt spinning directly without recourse to perturbation. The equations of melt spinning under isothermal conditions for Newtonian fluids take the form: SA/ST + S(Av)/Sx = 0 Sv/Sx = F/(AP) SF/Sx = 0

(4.2.1) (422) (4.2.3)

where x is time, x is the distance from spinneret, A is cross-sectional area, v is velocity in the x direction, F is spinning tension, and P is tensile viscosity assumed to be constant under isothermal conditions. Equations (4.2.1) and (4.2.2) are converted into nondimensional form by defining the following variables: £ = x/xw (nondimensional distance) T* = zvs/xw (nondimensional time) X = A/As (nondimensional cross — sectional area) (j) = v/vs (nondimensional velocity) Z=FxJ(AsvsP)

(4.2.4) (4.2.5) (4.2.6) (4.2.7) (4.2.8)

where the subscript s denotes the value at the spinneret point, and the subscript w denotes the value at the takeup point. Equations (4.2.1) and (4.2.2) now become: X - SQ/SC, = £ SX/ST* + • SX/SC = -£

(4.2.9) (4.2.10)

These are the nondimensionalized equations of isothermal melt spinning for Newtonian fluids. In a steady state, the derivative with respect to nondimensional time T* disappears from Eq. (4.2.10), which then yields the following equation: (j).SX/SC = -t

(4.2.11)

By using the relationship X-4> = 1, the steady-state solutions can be obtained in the following form: 0o = exp(£oQ 4, = exp(-f 0 O

(4.2.12) (4.2.13)

where the subscript 0 denotes the value in the steady state. When £ becomes equal to unity in Eq. (4.2.12), (J)0 means the value at the takeup point, which is identical with the drawdown ratio (pw. Then the Eq. (4.2.12) gives: f o =ln0w(=Z) where % is the natural logarithm of drawdown ratio.

(4-2-14)

For an easy visualization of solutions, the dependent variables 0 and X in Eqs. (4.2.12) and (4.2.13) are converted into ratios Kand Wto the respective steady-state values 0 O and A0: = V(J)0

(4.2.15)

A=JFA0

(4.2.16)

The dimensionless flowdown time £* is defined as: C* = [1 - exp(-xO]/Z (4.2.17) to simplify mathematical expression. By substituting Eqs. (4.2.15), (4.2.16) and (4.2.17) into Eqs. (4.2.9) and (4.2.10), the following equations can be obtained: SV/5(* + XVf(I - x£*) = Z/W • 1/(1 - ZC*) SW/ST* + S(VW)/d£* = 0

(4.2.18) (4.2.19)

Then, Eqs. (4.2.18) and (4.2.19) can be solved numerically under certain initial and boundary conditions using difference equations with the backward difference technique. Figure 4.2.1 shows the computed thread thickness at the takeup point as a function of time increments j , depending on / values. When the log drawdown ratio % exceeds 3.0, the solution starts to settle down to a sustained oscillation. This means that draw resonance (a); = 2.0

(b)z = 3.0

Ww


(dh = 4.0

J

Figure 4.2.1 Computed cross-sectional area for Newtonian fluid versus time increments j

instability occurs at ^ = 3.0 for Newtonian fluids. As the value of % increases beyond 3.0, the amplitude of the draw resonance wave increases rapidly. Draw resonance experiments were carried out using water-quenched melt spinning. The spinning process of water-quenched melt spinning is approximately isothermal when the air gap is small. In the case of film casting, the casting process is also isothermal when the distance between extrusion die and chill roller is short. The experimentally obtained draw resonance waves for polyethylene terephthalate (PET) polymer are shown in Fig. 4.2.2. The amplitude, maximum diameter of filament, and period of draw resonance waves increase with increase of log drawdown ratio, which is in good agreement with theory. The maximum and minimum cross-sectional areas denoted as WMAX and WMIN as a function of log drawdown ratio x are shown in Fig. 4.2.3. When x becomes greater than 3, that is, drawdown ratio 20, draw resonance instability occurs resulting in rapid changes in cross-sectional areas. The present theory tells little about the processability of the polymer, as the breakage of the casting film is not covered. The curve WMIN in the figure may indicate, however, that the draw resonance instability becomes an indirect cause of the breakage of the film.

DU)

log
D(M)

logi/>* = 3.81

D(M)

logt/>* = 3.65

Figure 4.2.2 Experimentally obtained wave form of draw resonance for PET

Length (cm)

Wmax

Wmin

Wmax

Wmin

log draw - down r a t i o

x

Figure 4.2.3 Computed maximum and minimum cross-sectional area versus log drawdown ratio %

4.2.4

Draw Resonance in Non-Newtonian Fluids

4.2.4.1

Power Law Fluids

The theoretically obtained draw resonance waves for Newtonian fluids agreed fairly well with experiment with respect to the oscillation period. Agreement, however, is poor for the amplitude, indicating that possibly the amplitude of draw resonance may be affected by deviation in the nature of polymer viscosity from Newtonian. Therefore, to simulate the experimentally observed wave form of draw resonance more exactly, analysis of the draw resonance for non-Newtonian fluids is required. In this section, the power law viscosity model is selected. Pearson and Shah [11 to 13] first reported the stability analyses of melt spinning for a power law viscosity by means of perturbation studies of the fundamental equations set up for the conditions of melt spinning. Their studies established the neutral stability of the draw resonance for the power law viscosity model. However, information on the amplitude and oscillation period of the draw resonance wave form is lacking because of the limitation of linear stability theory with respect to perturbation. For the analysis of nonlinear dynamics of the draw resonance in isothermal melt spinning for a power law viscosity model, the following viscosity equation is added to the fundamental equations (4.2.1 to 4.2.3) for the Newtonian case mentioned previously: P = PoWdxf-1

(4.2.20)

where fi is the tensile viscosity depending on the deformation rate, and /?o and p are material constants. When the power law index p is equal to unity, P becomes independent of the deformation rate, corresponding to the case in Newtonian liquids. Equation (4.2.20) is converted into nondimensional form by defining the following variable in place of Eq. (4.2.8) of the Newtonian case: (4.2.21)

^ = Ff(AJ0)-(XJv8Y Then, Eqs. (4.2.1) and (4.2.2) for power law fluids become: SA/ST* + S(X(I))/SC = 0

(4.2.22)

50/5C = ( W

(4.2.23)

where q=\lp. The dimensionless residence time C* is introduced as follows:

C* = (q ~ D • [№-" ~ I)C + If^-I]ZIq(K"1

- 1)}

(4-2.24)

Using this £*, Eqs. (4.2.1) and (4.2.2) are converted into the following forms: SW/ST* + S(VW)/SC* = 0 bV/b£* - V/{q(C* + co)} = (t/W)q • (o/(C* + to)

(4.2.25) (4.2.26)

where co = (q-l)/{q(^-l)}

(4.2.27)

Because no analytical solution is available for Eqs. (4.2.25) and (4.2.26), a numerical solution becomes mandatory. For this purpose, difference equations with a simple backward difference technique are used. Figure 4.2.4 shows the computed results of the draw resonance waves for power law fluids having power law indices greater than unity. The wave forms are demonstrated in terms of W versus j curves, where JF denotes the ratio of the cross-sectional area of draw resonance wave to the steady-state one, and j is the increment number in computation which corresponds to time. With increasing value of p, the amplitude of draw resonance waves decreases rapidly. When the p value exceeds 1.28 for the log drawdown ratio 4.095, the isothermal melt pinning becomes stable, that is, the draw resonance does not occur. Figure 4.2.5 shows the relationship between the peak value of draw resonance wave and p for log drawdown ratios of 4.095 and 3.595, respectively. The quantitative magnitude of amplitude for each p value can be understood from this figure. By summarizing the solutions for many conditions in terms of drawdown ratio and p value, the contours of constant Wmax, dimensionless maximum cross-sectional area, and TC , dimensionless oscillation period, on the/? versus log drawdown ratio plane can be obtained as shown in Fig. 4.2.6. The neutral stability curve which is approximately given by a straight line on the p versus log drawdown ratio plane, can be represented by the following equation: p = 0.286 log0 w + 0.144

(4.2.28)

In the region above the neutral stability line, melt processing is stable, whereas in the region below the line, it becomes unstable in association with the occurrence of draw resonance

W

P=L 28

W

P=I.25

W

P=I.20

W

P=LlO

W

P=LOO

Figure 4.2.4 Computed crosssectional area for a power law fluid having power law index p more than unity versus time increments j in the case of log drawdown ratio of 4.095

j

instability. The neutral stability line gives an important conclusion that shear thinning liquids (p < 1) reach neutral stability at a drawdown ratio less than the Newtonian value of 20.

4.2.4.2

Viscoelastic Fluids

Figure 4.2.7 shows the air gap dependence of the wave forms of draw resonance obtained experimentally for PET polymers. This experiment was done by water-quenched melt spinning, which might be similar to that for film casting using a chill roll. With decreasing air gap length, the draw resonance becomes suppressed, resulting in being stable for an air gap of less than 0.5 cm. To obtain a reasonable explanation for this phenomenon, an attempt was made to solve the transient nonlinear equations for viscoelastic fluids by direct numerical simulation. A convected Maxwell model with deformation-independent viscosity as the simplest viscoelastic fluid model was selected [14, 24, 25]. au =

_pgu+Tv 1

(4.2.29)

T? + Xx • A T V A * = 2rjd

iJ

(4.2.30)

W max

log0w = 4.095

Figure 4.2.5 Relationship between the peak value of draw resonance and power law index p

P

W max

Tt

P

Stable

Unstable

T* W max

0w Figure 4.2.6 Neutral stability of draw resonance for power law fluid including the contours of constant maximum cross-sectional area ^ m a x and oscillation period TC on the p versus log \j/w diagram

X w = 0.5 cm

1.0 cm

D(M)

2 . 0 cm

10.0 cm

Figure 4.2.7 Air gap dependence of the wave forms of draw resonance obtained experimentally for PET polymers

Length (cm)

where
(4.2.31) (4.2.32)

where JC denotes the direction along the spinline, and y is the direction across the spin line. The difference between Eqs. (4.2.31) and (4.2.32) is given as follows: f* _ Tyy + A1(Sx^fSt - SxWfSt) + A1V(Sx^fSx - Sx^/Sx) + XxSv/Sx(-2xxx - xW) = 3rjSv/Sxq (4.2.33) Assuming 3T*7(T*X

-xW) = e (constant)

(4.2.34)

and introducing the new nondimensional parameters in terms of tension and relaxation time as follows: ^ =xwF/(Asvs m = ^ilvs/xw

(4.2.35) (4.2.36)

^r1)

Equations (4.2.33) and (4.2.34) are converted into the following nondimensional forms: SV/SZ* + Z0V/{\M + m(l + S)Z0] = « + m • 8S/5
(4.2.37) (4.2.38)

where C* is the dimensionless fiowdown time. By using the parameters m and e, £* is defined as follows: C* = {1 + m(l + e)(l - (Aw))(I " l/
(4.2.39)

Under initial and boundary conditions similar to those in the cases of Newtonian and power law fluids, Eqs. (4.2.37) and (4.2.38) can be solved numerically using difference equations with the backward difference technique. Many numerical computations were done to construct the contours of constant Wmax, dimensionless cross-sectional area, and T*, dimensionless oscillation period, on the log m versus log \//w diagram. Shown in Figs. 4.2.8 and 4.2.9 are the contours Wmax and T* containing the neutral stability curve (Wmax= 1) and the attainable limit as follows: ^ w = 1 + \/m

(4.2.40)

Unstable Wmax =7 0-

0W

Unattainable Region

Neutral Stability

0w=l+l/m

Stable

m Figure 4.2.8 Neutral stability of draw resonance for viscoelastic fluid including constant maximum crosssectional area Wmax on the i^w versus m diagram

Unstable

1/>W

Unattainable Region

0w=l+l/n Stable

m Figure 4.2.9 Neutral stability of draw resonance for viscoelastic fluid including constant oscillation period T* on the \j/w versus m diagram

These figures give important information about the wave form of draw resonance and stability of isothermal melt processing for viscoelastic fluids. With increasing drawdown ratio \j/w under a given m value, the amplitude of the draw resonance wave becomes larger. Further increase of \j/w, however, yields the narrow second stable region. Such a second stable region cannot be observed in Newtonian and power law fluids. Under a given \j/w, on the other hand, melt processing becomes stable with an increase in the value of m. This means that both larger relaxation time and smaller air gap length are effective in depressing the draw resonance instability. The air gap dependence of draw resonance wave form shown in Fig. 4.2.7 can be explained by the m value for a viscoelastic fluid. In the case of an air gap of 10 cm, however, the processing system is not isothermal, due to the cooling effect, and becomes rather stable. The attainable limit expressed by Eq. (4.2.40) shows that for a given m there is a maximum attainable drawdown ratio beyond which the spinning tension is required to become infinite and processing is not possible. The attainable limit has also been reported by Zeichner [14] and Fisher and Denn [27].

4.2.5

Mechanism of Draw Resonance

The sustained oscillation of draw resonance is a limit cycle: standing waves of constant amplitude and period often encountered in the mechanics of nonlinear vibration [16]. The main cause for the occurrence of draw resonance is associated with the cooling effect of the

W

Period(%) * *>

AW-I

extruded molten polymers. When the cooling is insufficient or the spinning/casting process is isothermal, draw resonance occurs. The tensile viscosity rapidly increases with decreasing temperature of the molten polymer as a result of the cooling effect. This fact may be thought to lead to the smooth and sufficient feedback of the processing tension to every position on the extruded polymer, resulting in the stabilization of the melt processing system. Thus, it can be considered that the mechanism of draw resonance may be explained from the viewpoint that the melt processing involves a sort of feedback control system. Figure 4.2.10 shows the theoretically obtained side profiles of one oscillation period of draw resonance, where W denotes dimensionless cross-sectional area, and distances 0% and 100% are the positions of die slit and chill roll, respectively, in film casting. At the time denoted as 84.9% of the oscillation period, the cross-sectional area becomes maximum. Change of the dimensionless cross-sectional area along the casting line can be seen as if a wave propagates from the die slit to the chill roll with increasing time. It can be thought that such wave propagation may be related to the processing tension.

Figure 4.2.10 Theoretically obtained side profiles of one period of draw resonance for Newtonian fluids

Distance(%)

4.2.6

Conclusion

The theoretical and experimental work presented here provides a basis for quantitative prediction of the onset and growth of draw resonance in melt processing. The onset and growth of draw resonance were found to be dependent on the drawdown ratio and the melt flow properties of molten polymers. In the Newtonian case, draw resonance instability occurs when the log drawdown ratio exceeds 3. For the power law fluid model, however, critical drawdown ratio depends on the power law index. The extensional thickening liquids are more stable than the extensional thinning ones from the aspect of the critical drawdown ratio and of the magnitude of amplitude and oscillation period of the wave form of draw resonance. Another important point, which can be obtained from the nonlinear analysis of the draw resonance for viscoelastic fluids, is the fact that the fluid elasticity has a stabilizing effect on the melt processing. In film casting, it is necessary to understand the basic characteristics of the draw resonance phenomenon and to determine the operation conditions for film casting in consideration of the polymer rheology.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27.

Miller, IC. SPE Trans. (1963) 3, p. 134 Freeman, HX, Coplan, MJ., J. Appl. Polym. ScL (1963) 8, p. 2389 Bergonzoni, A., DiCresce, A.J., J. Polym. Eng. ScL, (1966) 6, p. 45 Bergonzoni, A., DiCresce, A.J., J. Polym. Eng. ScL (1966) 6, p. 50 Kase, S., Matsuo, T., Yoshimoto, Y., J Japan Tex. Mack Soc. (1969) 19, p. T63 Pearson, J.R.A., Matovich, MA., Ind. Eng. Chem. Fundam. (1969) 8, p. 605 Gelder, D., Ind. Eng. Chem. Fundam. (1971) 10, p. 534 Shah, Y.T., Pearson, J.R.A., Ind. Eng. Chem. Fundam. (1972) 11, p. 145 Shah, YT., Pearson, J.R.A., Ind. Eng. Chem. Fundam. (1972) 11, p. 150 Kase, S., J. Appl. Polym. ScL (1974) 18, p. 3279 Pearson, J.R.A., Shah, YT, Trans. Soc. Rheol. (1972) 16, p. 519 Shah, YT, Pearson, J.R.A., Polym. Eng. ScL (1972) 12, p. 219 Pearson, J.RA., Shah, YT, Ind. Eng. Chem. Fundam. (1974) 13, p. 134 Zeichner, G.R., Master of Chem. Eng. Thesis, University of Delaware (1973) Derm, M.M., Stability of Reaction and Transport Processes (1975) Prentice-Hall, Englewood Cliffs, NJ Ishihara, H., Kase, S., J. Appl. Polym. ScL (1975) 19, p. 557 Ishihara, H., Kase, S., J. Appl. Polym. ScL (1976) 20, p. 169 Fisher, R.J., Denn, M.M., Chem. Eng. ScL (1975) 30, p. 1129 Yeow, YL., J Fluid Meek (1974) 66, p. 613 Aird, G.R., Yeow, YL., Ind. Eng. Fundam. (1983) 22, p. 7 Barq, P., Haudin J.M., Agassant, J.F., Int. Polym. Process. V (1990) p. 264 Luccobesi, PJ., Roberts, E.H., Kurtz, SJ., Plastic Eng. (1985) May, p. 87 Flanagan, J., Modern Plastics (1993) Feb., p. 53 Ishihara, H. Ph.D. Dissertation, Kyoto University (1977) Denn, M.M., Marrucci, G. AIChEJ. (1971) 17, p. 101 Fredrickson, J.G., Principles and Applications of Rheology (1964) Prentice-Hall, Englewood Cliffs, NJ Fisher, RJ., Denn, M.M., Appl. Polym. Symp. (1975) 27, p. 103

5

Multilayer Films Charles R. Finch

5.1

Introduction

226

5.2

Monolayer Cast Film Extrusion

226

5.3

Monolayer Blown Film Extrusion

226

5.4

Coextrusion of Cast Film/Sheet

228

5.5

Coextrusion Feedblock and Multimanifold Dies

229

5.6

Coextrusion of Flexible Cast Film

234

5.7

Coextrusion of Blown Film

236

5.8

Coextrusion Equipment Considerations and Auxiliaries 5.8.1 Extruder Screws for Coextrusion 5.8.2 Mixers for Coextrusion 5.8.3 Gear Pumps for Coextrusion 5.8.4 Gauge Control of Coextruded Sheet and Film 5.8.5 Coextrusion Process Control

238 238 239 240 241 241

5.9

Coextrusion Coating with Lamination

242

5.10 Concluding Thought

242

5.1

Introduction

Multilayer films are made primarily by two major fabrication processes: film lamination and film coextrusion. In some cases, the two processes may be combined to make some of the more complex multilayer films. In other cases additional processes such as coating, printing, vacuum metallization, etc. may be part of the process to a final product. Thus, there exist a great variety of processes and combinations of processes for making the many multilayer films in the market. The emphasis in this chapter is on coextrusion because this is the newer and faster growing technology. In brief, the major advantages of coextrusion over lamination can include: no film manufacturing equipment costs, no film handling costs or problems, fewer problems with respect to appearance and adhesion, and use of polymers unavailable in film form (includes thinner layers). Coextrusion is certainly the preferred process on the basis of economics for those multilayer products in which the different layers of the structure have adequate compatibility for coextrusion and the volume requirements are large enough to justify a coextrusion line dedicated to that product. Of major importance to successful coextrusion is that the technology for the desired structure with regard to equipment, polymers, and operating conditions be completely developed so that efficient coextrusion of prime product is attainable.

5.2

Monolayer Cast Film Extrusion

A few comments on monolayer cast film and sheet are appropriate before discussing coextrusion. The distinction between sheet and film is rather arbitrary, but film is commonly defined as anything thinner than 250 /mi (10 mils). The extrusion equipment used for cast film and sheet is very similar. A frequent difference exists with the roll stack. Cast film systems most often utilize a vertical drop from the extrusion die to a casting roll and horizontal roll stack. This geometrical relationship avoids excessive sag between the die and the nip of the roll stack, which may occur if a horizontal die exit is used for film. Figure 5.1 is a depiction of a cast film line. Some companies have arranged extrusion systems in a manner to allow the vertical roll stack for sheet to be changed to a horizontal casting roll stack for film when appropriate.

5.3

Monolayer Blown Film Extrusion

Blown film extrusion systems can use the same extruders (designs and screws) as the flat die systems. The difference between the two starts with the die, which is circular for blown film. Dies of this style are available in sizes from 10cm to 200cm (4in to 80in+). Air enters through the die to fill the extruded tube and blow a bubble. The larger the diameter of the

Die Film winder

Chill roll

Cast roll

Air knife

Extruder

Figure 5.1 Typical cast film system layout. This type of system is usually the best for manufacturing monolayer structures less than 250 /mi (10mils) thick

bubble to the diameter of the die (called blowup ratio), the thinner the film becomes. The takeoff system (tower) collapses the bubble after an adequate cooling time. Trapping and pressurizing the air from the die inflates the bubble to a controlled size. Figure 5.2 depicts a blown film process.

Nip Rolls

-Collapsing Frame Film

Cooling Air

Takeup Reel Air Ring

Cooling Air Supply

Molten Polymer

Spiral Mandrel Die Inflation Air Supply Figure 5.2

Blown film process

5.4

Coextrusion of Cast Film/Sheet

There are two basic methods of coextrusion in use: the feedblock with a standard single manifold die and the multimanifold die method [I]. The older coextrusion process is the multimanifold method; this process is one way of making coextruded cast film and sheet. More important, the multimanifold die is virtually the only way of making coextruded blown film, blow molded bottles, pipe, and profiles. However, the production of coextruded flat sheet and film was relatively small volume until the advent of the feedblock coextrusion method. Today, 90% of the coextruded cast film and sheet production are by the feedblock method. The feedblock really made flat die coextrusion practical and economic, and on that basis it has grown. The feedblock system works with polymer melts because they are very viscous and flow in a very streamlined (laminar) and reproducible manner. This is the basis of the patent issued to Schrenk et al. and depicted in Fig. 5.3. The primary advantage of the feedblock is that it is much easier (more economic with respect to hardware) to stack multiple layers, uniformly, in a small width of 2.5 cm to 100cm (1 to 4 in) (typically) rather than the full width of a die. Moreover, it is very easy to rearrange and split (many times if desired) the layers in this small cross-section. From the feedblock, the layers flow in a deliberately streamlined conduit to and through the streamlined die. Figure 5.4 depicts this sequence of geometries. Total system design is critical to successful monolayer extrusion, but it is even more critical in coextrusion. This means scrutinizing the design of every component for capability (includes compatibility of polymers) of delivering adequate performance. The performance of each component must facilitate meeting the specifications of the multilayer structures to be made by that line. For example, the design of each of the extruders must be adequate for the resin and extrusion rates that it handles. Table 5.1 is a list of some of the major equipment

Exiting the Feedblock: Squeezing 1-3"

Spreading

Exiting the Die:

Figure 5.3 Basic feedblock patent, U.S. Patent 3,557,625, issued in 1971 to and licensed by The Dow Chemical Co. to some OEMs and flat die extruders. It teaches squeezing and spreading. A rectangular configuration is illustrated but the patent is broader than this. It was a method patent, not a design patent

Streamlined transition Feedports meter layers of two or more polymers Figure 5.4 Schematic of streamlined flow of a five-layer structure stacked in feedblock in 2.5 to 10cm (1 to 4 in) width and being squeezed and spread to die width. Film and sheet of widths over 3 m (10 ft) wide are being successfully made by this method

suppliers of coextrusion equipment: most of these original equipment manufacturers (OEMs) were originally coextrusion equipment licensees of The Dow Chemical Co.

5.5

Coextrusion Feedblock and Multimanifold Dies

The heart of the coextrusion system is the device that stacks the layers in the desired sequence with the needed uniformity for the application. This may be a feedblock, a multimanifold die, or a combination of the two. The feedblock is being used to make a large number of coextruded structures that are important for manufacturing film and semirigid structures. Most of the more complicated and challenging structures are for different applications in food packaging. Figures 5.5 and 5.6 Table 5.1 Sheet or Film Coextrusion Equipment Suppliers Black Clawson Company, Fulton, NY The Cloeren Company, Orange, TX Davis Standard Division, Pawcatuck, CT Dolci, Milanino, Italy Egan Machinery Co, Somerville, NJ ER-WE-PA GmbH, Erkrath, Germany Gloucester Engineering Co., Inc., Gloucester, MA HPM Corporation, Mt. Gilead, OH Killion Extruders Inc., Verona, NJ NRM Corporation, Columbiana, OH Reifenhauser GmbH, Troisdorf, Germany Welex Incorporated, Blue Bell, PA

depict some important structures used commercially for thermoforming applications that are made by the feedblock coextrusion method. The bottom three structures of Fig. 5.5 are applicable for shelf-stable containers. They can tolerate hot-filling and retorting because polypropylene (PP) is the bulk layer. The top two structures of Fig. 5.6 show coextruded sheets that are applicable to the growing form-fill-seal (FFS) applications area. This sheet is notable in that the bulk layer is high-impact polystyrene (HIPS). HIPS is the choice because it provides better container rigidity and thermoforming properties than any other low-priced polymer. This structure does not have adequate heat resistance for retort or hot-fill applications because of the limitations of the heat resistance of the HIPS. Table 5.2 is a list of the main advantages and disadvantages of feedblock coextrusion systems versus multimanifold die systems. It is obvious that the feedblock has more of the advantages. That is why the feedblock is being used in almost all the manufacturing processes for coextruded food packaging sheets for semirigid containers; however, the capability of the multimanifold die in handling polymers with widely different viscosities is a deciding advantage to its use for some applications. Recently, the multimanifold die is being used in more lines as an adjunct to the feedblock to more efficiently produce the more difficult to coextrude structures. Even though there are three main different types of feedblocks used in the United States, they all utilize the same principles of squeezing and spreading of the melt streams. Also, they all depend on the streamlined flow of viscous polymers to preserve the stacked structure and

Structures

Characteristics

HIPS Oxygen and moisture Tie Barrier barrier if barrier is PVDC excellent thermoformability Tie HIPS PP or HDPE Tie Barrier Tie

Retortable, high oxygen and moisture barrier

PP or HDPE

Scrap containing barrier structures: pp Tie Barrier Tie Scrap PP

Six layers with one scrap layer, called asymmetrical.

PP Scrap Tie Barrier Tie Scrap PP

Seven layers with two scrap layers, called symmetrical.

Figure 5.5 Structures and applicability of commercially manufactured semirigid barrier food packaging structures. Notable characteristics of each structure suggest appropriate applications. Probably the most popular barrier structure for shelf-stable applications is sheet with PP skin layers and EVOH as the gas barrier layer

PE Tie Barrier Tie HIPS

For FFS Applications

Two Barrier Layers with Scrap Recycle

PP PE Tie Barrier Tie HIPS HIPS

PP Tie Barrier Tie Scrap Tie Barrier PP

Heat sealable, oxygen and moisture barrier, low taste and odor, easy thermoforming

PP layer is strippable, revealing a sterile PE layer for the inner layer of an aseptic package. Structure is used in Erca and Connoffast systems. Probability of pinholes in the same area is low • Scrap is separated from food by a barrier layer. • Thinner PP layer next to food reduces flavor scalping by PP.

Figure 5.6 Structures of commercially important coextruded barrier structures. The top two are for the rapidly growing form-fill-seal (FFS) container applications produce a uniform layered product. The three basic types are: the Cloeren type (The Cloeren Co., Orange, TX), the Dow type (manufactured by various OEMs), and the Welex type (Welex Inc., Blue Bell, PA). However, between the principles and the practice there is the design process in which experience is required to obtain the right design for a given

Table 5.2 Comparison of Characteristics: Multimanifold and Feedblock Systems for Coextrusion Characteristic

Multimanifold die method

Feedblock method

Application to existing die Suitability for more than three layers Ability to increase number of layers Ability to change layer thicknesses Ability to change layer position Suitability for thin surface layer Suitability for very thin (25 (im. or 1 mil) adhesive or core layers Ability to coextrude wide viscosity differences (threefold differences)

Poor Poor Poor Poor Fair Good Fair

Good Excellent Excellent Good Excellent Good Excellent

Good

Suitability for heat-sensitive resins as core layers Ease of die adjustment

Poor Fair

Good if skin is lower viscosity Poor if skin is higher viscosity Excellent Excellent

application. Some of this experience is expensive; therefore, most detailed design information is proprietary. There is no universal feedblock. Feedblocks are useful for a range of polymers and rates, but there are limits. Changes in polymer type, operating rates, structure proportions, or operating conditions can each contribute to the need for a feedblock modification. Sometimes the required modification to change to a different product can be just the change of one or two plates or an insert (in a modular type feedblock). In other cases, a different feedblock is required. An example of the latter is that switching from ethylene vinyl alcohol (EVOH) as a barrier layer to polyvinylidene chloride (PVDC), which will require a feedblock designed specifically for PVDC. OEMs that supply feedblocks should point out that a feedblock designed to extrude PVDC will handle EVOH, but the reverse is not usually true because PVDC requires high-nickel alloys for contact with PVDC and EVOH does not. The down-time for module changes, so as to make significantly different structures, is being reduced as designs improve. For example, Er-We-Pa GmbH advertises feedblocks in which module changes are quick, made in a manner of minutes, through use of a screenchanger type mechanism. In the same vein, the layer sequencing plug in the Cloeren feedblock facilitates quick changes. The trend in barrier coextrusion for cast film or sheet is to use at least four extruders. Today, one extruder is, practically always, specified for regrind according to the OEMs. This does not mean that the regrind extruder is always running regrind; it can run virgin resin if regrind is not wanted or is unavailable. In a typical four-extruder system one extruder extrudes the barrier resin, another the two tie layers, another the regrind, and another the two skin layers. A five-extruder system is a more versatile design; this provides a separate extruder for each skin layer. Use of five extruders allows the skins to be different colors of the same resin or different polymers. The layout for a typical five-extruder line for sheet or cast film is illustrated in Fig. 5.7.

Sheet/film die Skin layer

SC/G

M

Feed Block

M

$C/G

Skin layer

Adhesive Scrap recycle

Barrier polymer

Figure 5.7 Typical layout for a five-extruder coextrusion line for sheet or cast film. The barrier polymer, which may be the most heat-sensitive polymer in the system, is given priority (shortest transfer line) to decrease polymer degradation or crosslinking. Abbreviations refer to frequent optional equipment items added for efficient coextrusion: M = stationary mixer; SC = screen changer; G = gear pump

Seven or eight extruders are being used for some barrier structures. One example is a structure containing seven different polymers: polyethylene (PE)/Tie-2/Regrind/Tie-l/ Barrier/Tie-1/HIPS/general purpose polystyrene (GPPS). Two different tie or adhesive layers were necessary for this structure, because one adhesive was not effective at all the interfaces between the dissimilar polymers. In structures of this type, there are limitations on the relative proportions of different polymers and the quantity of scrap recycled. One limitation is that the PE layer must constitute less than 15% of the total structure to allow regrind recycling while retaining adequate physical properties in that layer. More PE would make the regrind blend too brittle for most applications. Cloeren Co. advises that structures are becoming more complex because product requirements are becoming more stringent. Also, commercial lines are becoming bigger. A commercial barrier line may consist of five extruders, 5 to 11.5 cm (2 to 4.5 in). Experienced processors are asking for more elaborate controls of better product quality control and easier maintenance. For example, an equipment customer could have had transfer lines, feedblock, and die for $250,000, but the customer opted for upgrades that raised the price to $700,000. This sheet extruder's emphasis was on line uptime. The upgrade included gear pumps that were completely self-contained, that is, they are movable in or out of the coextrusion system within 20min. This is valuable when changing equipment because of polymer changes or equipment maintenance requirements. Also, the Cloeren feedblock was in two parts so that it was separable for cleaning. This design included a feedblock support consisting of two separate die carts that facilitated the splitting of the feedblock and the subsequent cleaning operations. Feedblocks are available to make coextruded structures with two barrier layers of the same polymer. Two barrier layers are thought to decrease the potential barrier loss caused by pinholes or flaws in one barrier layer. The rationale is that the probabilities of two adjacent holes in the separate barrier layers are negligible. With a split barrier layer, scrap can be recycled between the barrier layers. Some packages prefer this regrind location, because there is less chance of the food being affected by possible taste or aroma from recycled scrap. Typically, this type of structure will have nine layers, with the center layer being the designated scrap layer. Multimanifold dies are being used to supplement feedblocks for some applications. Typically, the feedblock feeds the central manifold of a three-manifold die as illustrated in Fig. 5.S. The outer manifolds handle polymer melts that, because of viscosity or high temperature, are incompatible with the polymer melts in the feedblock. The incompatibility problems avoidable by this procedure are layer nonuniformity and polymer degradation of a more heatsensitive polymer. The latter concern applies particularly to barrier-layer polymers for food packaging with PVDC or EVOH in the structure. When the desired structure has high melt temperature skin layer polymers, such as polycarbonate (PC) or polyethylene terephthalate (PET), the skin layers are brought through the outer manifolds of a three-layer multimanifold die. All the layers combine just before the total structure exits the die lips. This design minimizes the time-temperature exposure of the high-temperature polymer to the other polymers. To minimize this exposure further, thermal insulation can be built in between the manifolds. Processors sometimes seek the capability for extruding interchangeably EVOH and PVDC as barrier layers. A typical reason for wanting this capability is described in a report

I.

Problem: Extreme asymmetry causes interfacial instability in FB alone HIPS Tie

Barrier Tie PE II.

FB

MM Die

PP Scrap Barrier Tie

PP

III. Problem: extremely high temperature and/or viscosity of skin layers PC Tie PP Tie Barrier Tie PP Tie PC Figure 5.8 Some uses of one or more feedblocks and a multimanifold die. This combination can make possible the manufacture of structures with extreme asymmetry, high-viscosity skin layers, or high melt temperature skin layers

from Toyo Seikan [2]. Toyo Seikan was one of the pioneers in producing EVOH-containing barrier structures. This report recommends PVDC structures for retorted containers over those with EVOH; for other containers they continue to use EVOH. A single coextrusion line can be designed that is capable of coextruding both of these barrier polymers, plus nylon and others, if it is designed for the most critical material, PVDC. PVDC coextrusion requires the use of corrosion-resistant metals, streamlining the channels, and maintaining low melt temperatures and short residence times. HPM Corp. advertises that the same 20:1 length/ diameter (LID) extruder performs satisfactorily for both EVOH and PVDC polymers; however, it does require a screw change for best performance.

5.6

Coextrusion of Flexible Cast Film

There are both differences and overlaps in the resins used for the semirigid sheet structures discussed so far and the flexible film structures. Semirigid sheet makes most use of resins with high moduli such as HIPS, high-density polyethylene (HDPE), and PP for the bulk layers. Flexible film makes more use of low-moduli bulk layers such as low-density polyethylene (LDPE) and linear low-density polyethylene (LLDPE) and overlaps in using

PP. For barrier layers, EVOH and PVDC are used in both categories. For important reasons, greater use of nylon is made in flexible films. Aside from its gas barrier properties, nylon is valuable for its puncture, tear, and abrasion resistance properties and its thermoformability when required. A few examples of coextruded structures in the thin flexible film application area are given in Fig. 5.9. One example of an important film that is frequently coextruded is that for wiener packages. The compositions of these films do vary considerably. One common package design has a thermoformed half and a printed unformed half. The unformed half is frequently a laminate made using a reverse printed PET plus a sealing layer. The formed half may be coextruded and is commonly 50 to 75 jim (2 to 3 mils) thick. This formed half typically has nylon as an external surface to gain abrasion resistance and for its positive contribution to thermoformability, EVOH as a gas barrier, and ionomer as a heat seal layer. The structure also contains appropriate adhesive layers and LDPE or LLDPE for desirable properties and reduced raw material costs. Thus, there is much similarity between this multilayer structure

Example Coextruded Film Markets versus Typical Structures* Example structure

Application

2

• Trash bags: lawn & g a r d e n , ~_ _ ^1 c i \ 37.5um(1.5mls)

0

% HDTE

• Stretch cling: h a n d - w r a p , w * > ?0iinir0 8

m

20um (

.

U

i

8

l

m

^

i

l

8

0

s

)

L L D P E Green

60% Regrind black20% 5

%

1

0

EVA + 5% PB LLDPE

%

E V A +5 % p B

• Agriculture: g r e e n h o u s e , 3 3 % LLDPE+UV 1 5 0 u m ( 6 m i l s ) 3 4 % LDPE 33% LLDPE+AF (antifog)

• Meat packaging: p r o c e s s e d 1 0 % Nylon meat forming w e b , 1 2 % Tie 1 2 5 M m ( S m I l . ) ™ ™ 56% Ionomer • Cereal liner: barrier film, Z1 n -i \ 6 5 % H D P E An 4 7 . 5 u m ( 1 . 9 m i l s ) i O % T i e 10% Nylon 15% EVA _^m0^^-^m • Laminated

• Snack food: corn c 47.5jim (

1

.

h 9

m

i i

p

s

,

J

J

l

s

)

4

0

J EDPE chocoiatT"I % HDPE white 20% EVA+ionomer |

• Coextruded

* Information from Tom Butler of Dow Chemical, Frecport, TX Figure 5.9 A few examples of the diversity of coextruded flexible films that are less than 250/rni (lOmils) thick. The snack food example is made by a combination of the lamination of a reverse printed film to a three-layer coextruded structure. Most of these films can be made by either the coextruded cast or blown film processes

and those used for sheet. For temperature compatibility in the structure, the nylon used must have a low melting temperature, so nylon-6 or a nylon copolymer is the common choice. Figure 5.1 is a depiction of the layout of a monolayer cast film line. The essential add-ons for coextrusion are the feedblock or multimanifold die plus more extruders. With regard to feedblock or die design, the same principles apply as stated in the previous section on flat-die coextrusion for semirigid structures.

5.7

Coextrusion of Blown Film

A significant trend in the blown film area is the growing manufacturing of complex barrier films utilized in food packaging. Table 5.3 is a list of some of the blown film equipment suppliers. Figure 5.2 depicts the principal components of a monolayer blown film system, and it is also the basic layout for a coextrusion line when supplemented with few equipment adjuncts. The adjuncts are additional extruders and a blown film coextrusion die. Figure 5.10 is a representation of a coextrusion three-layer blown film die. Coextrusion has the ability to produce thinner layers than those available for lamination, which is particularly advantageous if thereby the required amount of an expensive barrier material is reduced. For example, if one-half mil of a barrier polymer is sufficient, coextrusion can produce such a layer, whereas this is too thin for lamination and very often too viscous for coating. Because blown film coextrusion uses annular dies (multimanifold), it can utilize

Die Lips

Extruder A Extruder C

Extruder B

Figure 5.10 Schematic of coextrusion blown film die for three layers. This drawing depicts the three layers being joined sequentially. Other designs have the layers joined together at a common plane. Blown film dies are a member of the multimanifold method of coextrusion. Dies with up to seven layer capability are used commercially

Table 5.3 Some Major Equipment Suppliers of Blown Film Dies Including Coextrusion Types Alpine American Corporation, Natick, MA, USA Battenfeld Gloucester Engineering Co., Gloucester, MA, USA Brampton Engineering Inc., Brampton, Ontario, Canada CA Windmoeller and Hoelscher Co., Lincoln, RI, USA Davis Standard Egan Film Systems, Somerville, NJ, USA Dolci, Milano, Italy Filmaster Inc., Parsippany, NJ, USA Macro Engineering and Technology Inc., Mississauga, Ontario, Canada Paul Kiefel GmbH, Worms am Rhein, Germany Reifenhauser-Van Dorn Co., Lawrence, MA, USA

polymers of widely different viscosities. This is in contrast to feedblock coextrusion, in which viscosities cannot be mismatched as widely. Many of the developments and trends previously covered under the flat sheet or film equipment topics apply equally well to blown film. An arrangement for up to three extruders around a blown film coextrusion die is fairly straightforward. When a fourth or fifth extruder is added the arrangement becomes substantially more cumbersome. Six or seven extruders become nearly impossible, unless extruders are "piggy backed" in compact systems such as the Flat-pak from Davis Standard or similar compact systems from Wilmington Plastics Machinery [3]. As the number of layers increases, the blown film die becomes more complex, bigger, and a challenge to assemble and disassemble for cleaning or maintenance. The number of layers that can be coextruded in blown film systems has more limitations than the number that can be coextruded in cast film coextrusion systems with a feedblock. Coextrusion of three layers is practical and straightforward. More than three layers is more difficult; however, blown film dies with seven-layer capability are commercially used. A complicating factor in blown film systems is that some means must be provided for helically distributing the 5 to 10% thickness variations inherent in the blown film process. Distributing the bands from the die is accomplished by rotating or oscillating the die by itself or with the extruders, or by oscillating the takeoff unit. Rotating the die to eliminate gauge bands for five layers is very difficult, and if done in coextrusion practically eliminates the ability to use internal bubble cooling (IBC). With five-layer coextrusions, some companies prefer to rotate or oscillate the primary nip; this randomizes both die bands and also cooling nonuniformities. Other companies favor mounting the extruders and die on an oscillating platform for these more complex structures. A relatively straightforward way to double the numbers of layers in a film structure is to collapse and seal the bubble, making this double thickness a single film [4]. This is being used to make films with two barrier layers which are claimed to have physical property and fabrication (improved thermoformability) advantages over single barrier layer structures. Tubular coextrusion dies for packaging are typically in the 10 to 150 cm (4 to 60 in) diameter range. The rate for a five-layer line with two 60mm and one 45 mm extruders, making 50 to 100/mi (2 to 4mil) film, with IBC, is about 200kg/h.

Bubble cooling ability normally limits blown film line rates. Cooling rates are being improved in newer systems by a variety of methods. IBC is fairly widely used, but is being applied more vigorously by one company that uses an external pressure equalizing air collar (PEAC) [5]. Another company achieves the same result with their patented method of cooling with a primary air ring, IBC, a secondary dual-lip ring, internal stalk guides, and microprocessor controls that balance these air pressures. With the latter integrated type cooling, production rates 40 to 60% greater than those achievable with single-orifice air rings are achievable. Long-stalk bubbles are achievable by cooling control [6]. This operating method has beneficial effects on the mechanical properties of some polymers, particularly, high molecular weight HDPE. The strong biaxial orientation gained with high molecular weight HDPE increases toughness and modulus properties of the resulting film. These property improvements allow down-gauging of film thickness in some cases. Down-gauging is doubly beneficial in that it reduces raw material costs and is a means of "source reduction" that is environmentally advantageous. Spiral dies are the standard for blown film. A five-layer die typically has five spirals nested on top of one another. The goal of new designs is to decrease polymer residence times, enable operation at lower pressures, minimize shear rates, optimize gauge control, and exhibit less sensitivity to changes in material rheology and rates. These types of improvements increase the versatility of a die with regard to polymers and production rates. They are being achieved by designs with longer spiral wraps, wider flow passages, and lip geometries that decrease shear stresses. They are also being achieved by dies with a more flat plate type design [7] as shown in Fig. 5.11. The most important die design considerations for multilayer blown film systems are pressure drop and residence time in long transfer lines (250 cm long is common). These are of critical importance for the more heat-sensitive polymers such as EVOH and some of the adhesive resins used. So far, PVDC is not being coextruded in blown film dies because of the difficulty of avoiding degradation problems because of long residence times in the blown film system. The transfer lines from the extruder to the die need to be short to achieve short enough residence time for some polymers.

5.8

Coextrusion Equipment Considerations and Auxiliaries

The next few sections contain comments on equipment that can be important to success in manufacturing multilayered films. These are optional equipment items that can prove very important to efficient coextrusion in many cases.

5.8.1

Extruder Screws for Coextrusion

Recycling scrap is important to reduce costs and waste problems for any extrusion operation. To successfully recycle coextruded scrap, adequate dispersion of the dissimilar polymers is most often of paramount importance. Only with adequate dispersion are satisfactory and

Nominal Dia.

•iayer E Layer D

Side fed inlet Layer C Layer B LayerA

Figure 5.11 Flat plate, modularly constructed blown film die. It is called a Slimline Coextrusion Die by Brampton Engineering

uniform physical properties achievable. In some cases, it is necessary to recycle at relatively low polymer melt temperatures. The latter is especially necessary when PVDC is in the scrap, because high temperatures, >210 0 C (415 0 F), will cause rapid degradation. For these reasons the scrap extruder screw design must be carefully selected. Two examples of specially designed screws that are candidates for this type application are the: • Double Wave™ screw offered by HPM Corp. [8] • HG extruder with BLB screw offered by Gloucester Engineering [9].

5.8.2

Mixers for Coextrusion

Stationary mixers are advantageous in coextrusion systems in which there are long transfer lines from the extruder to the feedblock because long transfer lines can introduce melt temperature nonuniformities. These nonuniformities develop from the parabolic velocity profiles in pipes and the mismatches of wall temperatures and melt temperatures that cause variations in incremental polymer residence times, variations in shears experienced, and nonuniform heating or cooling effects. A compensating practice by many OEMs is to put a stationary mixer that is a distributive mixing device at the end of the transfer line, just before

Table 5.4 Motionless Mixer Tradenames and Equipment Suppliers Thermoprofiler™ from Luwa Corp., Charlotte, NC Thermogenizer from Chemineer-Kenics, N. Andover, MA Koch from Koch Engineering Co., New York, NY ISG from Charles Ross & Son Co., Hauppage, NY Komax Equalizer from Komax Systems, Long Beach, CA the melt enters the feedblock, to rehomogenize the melt. Table 5.4 lists some suppliers of stationary mixers that are applicable to polymer blending. A higher shear stress dispersive mixing is frequently essential for the successful recycle of dissimilar polymers. If the polymers are compatible enough, high-shear mixing ensures uniform physical properties in these two or more phase mixtures. This is particularly true when difficult to disperse polymers are in the regrind such as the EVOH polymers. Special mixing screw designs are required with these types of regrinds.

5.8.3

Gear Pumps for Coextrusion

Gear pumps are economically justifiable, most often, as an add-on to the scrap extruder of a coextrusion system. Fifty percent or more total scrap is typical for extrusion forming lines used in making round containers. The bulk density of scrap regrind is relatively low and also varies; this results in more surging with a scrap fed extruder. Welex Inc. says that 100% of the coextrusion lines they supply have gear pumps on the scrap extruders. In contrast, Er-We-Pa GmbH recommends (when needed) a special process that agglomerates and densifies scrap by pressing the ground scrap through a perforated plate with a 3 to 5 LID auger machine [10]. This operation increases the bulk density of the scrap, making it a better and more uniform feed for an extruder. The resulting improved feed density and uniformity can eliminate the need for a gear pump. Extruders processing virgin polymers incorporate gear pumps less often. However, some relatively low melt viscosity polymers, such as PP and PET, extrude with less surging with a gear pump add-on. Gear pumps are not practical on PVDC extruders because of the degradation characteristics of this polymer. Gear pumps are being touted as means of ensuring that a barrier layer, such as EVOH, is present in a structure at the prescribed percentage. In this situation, the gear pump is essentially acting as a positive displacement metering pump. Microprocessor programs are available that allow control of individual layer thicknesses for Harrel, Inc., Welex Inc., and, undoubtedly, other OEMs for coextrusion systems that incorporate gear pumps on each layer. Control is straightforward because a gear pump's output is very close to being linear. Table 5.5 is a list of some of the major gear pump suppliers. Table 5.5

Major Gear Pump Equipment Suppliers

Harrell Inc., E. Norwalk, CT Luwa Corp., Charlotte, NC (agent for Maag Gear Wheel Co., Zurich, Switzerland) Nichols/Zenith, Waltham, MA Normag Corp., Hickory, NC

5.8.4

Gauge Control of Coextruded Sheet and Film

The mass or density of coextruded sheet can vary at a constant thickness if the ratios of different polymers with differing densities vary in the sheet. This means that the rather commonly used beta gauge (which measures mass using a radioactive source) is sometimes not the best choice for a coextruded sheet. In some cases, a preferable choice for total thickness is an air-type caliper. In a coextruded sheet there is, obviously, a real need for online thickness monitoring of individual layers, especially the barrier polymer layers which are critical to the maintenance of specified barrier properties. Infrared is the method being touted by most companies. However, there is a big difference between measuring layers in film of 250/mi (< lOmils), and sheet. Clear film is the easiest to measure and this is being practiced to a limited extent commercially. The general principle of measurement is exposure of the sample to multiple wavelengths, commonly generated by a rotating filter wheel. Measurements of selected absorption bands lead to individual layer thickness values and an online analysis of this information yields the thicknesses of the different layers. Measurement of three to five individual layers is the practical limit, if several corrections are necessary. The types of corrections that are necessary are for materials that affect infrared absorption, such as pigments, foil surfaces, etc. The barrier resin EVOH is rather easily measurable with near-infrared. PVDC is more difficult. For PVDC, some companies recommend a different method that utilizes low-energy X-rays capable of detecting the chlorine atom. Measurements of individual layers in sheet 1000/mi (40 mils) thick or more are not being considered because of the inability of infrared to penetrate such thicknesses. Pigment, when present, limits infrared further. Regrind recycle interferes with barrier layer measurements because the infrared will total-in the barrier polymer contents of the regrind layer. It is a fact that dispersed barrier polymer in regrind layers adds virtually nothing to barrier properties.

5.8.5

Coextrusion Process Control

Total computer integrated manufacturing (CIM) of an extrusion line is not totally achievable on monolayer extrusion lines. It is understandable that it has much further to go on coextrusion lines dedicated to producing complex coextruded structures. Gravimetric hopper weigh feeding systems are a growing method for multilayer control [H]. They are cost effective, in many cases, on the basis of raw material savings. Weigh feeding systems use a load cell on each extruder hopper to determine the feed rate of materials into each hopper. West German manufacturers of extrusion equipment, such as Keifel and Reifenhauser, recommend this approach. This approach controls within 1 to 2% the relative percentages of the different materials in a structure. However, the percentages do not show the uniformity of the layers. In other words, is a barrier layer uniform across the dimensions of the product? Therefore, other methods must be used to determine layer uniformity throughout the product such as microscopic examination of infrared layer measurements. Fortunately, typical operating experience is that once layer uniformity is achieved then the system is stable. Thus, barring any upsets, layer uniformities may be maintained with the gravimetric control system alone. A USA company, Process Control Corp. of Atlanta, says that their gravimetric control

system, called Gravitrol, for extrusion measures feeding weight continuously. This system makes rate calculations to 0.1 to 0.15 kg (0.2 to 0.31bs/h) every 20 s. Some of the European units make batch measurements.

5.9

Coextrusion Coating with Lamination

As previously indicated coextrusion can be used in various ways in combination with other processes. A layout for a process that combines lamination with coextrusion coating is depicted in Fig 5.12. For coextrusion coating, a feedblock designed on the basis of the same principles used for cast film or sheet, as previously described, is most often used. Equipment of the type shown in Fig. 5.12 can be used to manufacture premium cartons for perishable foods.

5.10

Concluding Thought

There are many different reasons why a multilayered product can be advantageous to a given market area, ranging from the need for a easy heat seal layer to needs for gas barrier properties. The structures can vary from two layers for heat seal improvement to five or more layers for gas barrier structures. Coextrusion is certainly the most economic method of making multilayered products when the application volume is large and when the development work to make the structure is complete. This is so true that this author believes that practically all films will be multilayered and made by coextrusion sometime in the future.

Optional

Coating Coextruder Feedblock Paperboard

Coated board

Figure 5.12 A combination process with coextrusion coating of paper board with film lamination. The film could be a reverse printed film

Abbreviations Used EVA EVOH HDPE HIPS LDPE LLDPE OPP PB PC PET PP PVDC

ethylene vinyl acetate ethylene vinyl alcohol, a polymer with high gas barrier properties high-density polyethylene high-impact polystyrene low-density polyethylene linear low-density polyethylene biaxially oriented polypropylene polybutylene polycarbonate polyethylene terephthalate polypropylene polyvinylidene chloride, a polymer with high gas barrier and moisture barrier properties

References 1. Schrenk, WJ., Alfrey, Jr., T. In Polymer Blends. S. Newman, D.R. Paul (Eds.) (1987) Academic Press, Orlando, FL, p. 129ff. 2. Yamada, M. In Proceedings ofEuropak '87: Ryder Conference, Diisseldorf, Germany, p. 127-140 3. Modern Plastics (1986) Dec, p. 58 4. Sorenson, L. "Recent Advances in Multilayered Flexible Films in Vacuum Packaging" In Proceedings of Barrier Pack '88: The Packaging Group, Inc., Chicago, IL 5. Modern Plastics (1987) Feb., p. 12 6. Modern Plastics (1987) March, p. 64 7. Perdikoulias, J. Petric, J., Coextrusion VI. SPE RETEC Proceedings, Chicago (1991), p. 156 8. Calland, W.N. Plastics Eng. (1990) April, p. 31 9. Plastics Technology (1990) May, p. 78 10. Djordjevic, D. In Proceedings of Coextrusion IV: SPE/RETEC, Arlington Heights, IL, p. 81 11. Plastics Technology (1987) Feb., p. 61

6.1

Biaxially Oriented Film K. Tobita, T. Miki, and N. Takeuchi

6.1.1

Introduction

245

6.1.2

Outline of the Tentering System Machine

245

6.1.3

Polymer Handling

249

6.1.4

The Extrusion Process 6.1.4.1 Performance Improvement on the Single-Screw Extruder

249 251

6.1.4.2 Capacity Increase by the Tandem Extruder

252

6.1.5

Filter and Die

256

6.1.6

The Casting Process

258

6.1.7

Stretching and Annealing Processes

265

6.1.8

Takeoff and Winding Processes

273

6.1.9

Process Control 6.1.9.1 Functions 6.1.9.2 Features 6.1.9.3 System Configuration 6.1.9.4 Automatic Film Thickness Profile Control System 6.1.10 Closing Comments

274 274 275 276 276 279

6.1.1

Introduction

In this chapter, the tentering process is described to develop an understanding of how it produces biaxially stretched films. In addition recent trends in biaxial stretching equipment are described. The use of plastic films as packaging and industrial materials keeps increasing at a remarkable rate. Thus it plays a major role in the growing use of thermoplastic polymers and extruders; with this expanding demand comes more complex product needs. Consequently, the function and the performance level required for thermoplastic extruders are becoming more and more stringent; machines having high levels of process control, labor-saving features, energy saving capacity, and preventive maintenance are in great demand. Such being the case, extruder manufacturers are making their utmost efforts to research and develop equipment to meet these demands. Also, in view of the function enhancement, diversity, and requirements of new plastic film products, research and development on various aspects of the essential technology is under way at numerous universities, laboratories, raw material manufacturers, and film manufacturers.

6.1.2

Outline of the Tentering System Machine

Overall there are two processes to produce biaxially oriented film: the tentering process and the double bubble tubular film process. The tentering process is divided further into the stepby-step stretching method (sequential stretching method) and the simultaneous stretching method. These two tentering methods are employed independently in accordance with the characteristics of resins, but production by the step-by-step biaxial stretching method is more common throughout the world. Table 6.1.1 shows that the step-by-step biaxial stretching method is adopted for biaxially oriented polypropylene (OPP), biaxially oriented polyethylene terephthalate (OPET), biaxially oriented polystyrene (OPS), and biaxially oriented polyamide (OPA); the simultaneous biaxial stretching method is used for OPA also. The biaxial stretching process was developed in Germany about 1935, and then put into practical use for the production of OPS film in the second half of the 1940s. But real development of biaxially oriented film began from 1952, when DuPont started to make and sell OPET film [I]. The sequentially biaxial stretching process basically consists of machine direction (MD) stretching and transverse direction (TD) stretching. Generally, OPP film is produced by MD and then TD stretching. For OPET film the following can be used: (1) MD ->TD; single-stretching method (2) MD -^TD -> MD; multistretching method (3) MD -^TD -> MD -> TD; multistretching method The multistretching method, as in (2) and (3), is adapted to the particular stretching machine [I].

Table 6.1.1

Manufacturing Methods of Biaxially Oriented Film and Features Thereof Tentering process

Features

>

I I

&

Tubular film process 1. Produciblefilmthickness range 2. Flexibility on the change of process conditions 3. Total productivity in conjunction with high speed and width broadening 4. Small lot production 5. Thickness accuracy 6. Isotropy in physical properties 7. Range of polymers that can be used

Corresponding film

A (Medium) A

Step by step

Simultaneous

© (Thin-thick) O

A

O (Thin-medium) A O

A

O

A O O

® A O

® ®

PP 5 PE Polyvinyl chloride (PVC) Polystyrene (PS)

PET, PP Polystyrene (PS) Polyvinyl chloride (PVC) Some grades of nylon (PA)

^ Nylon 6 <& Nylon 66 ^f Poly hexamethylene adipamide ^ Polyvinyl alcohol <& PMMA Copolymer i^ Nitrile film *PET Special polyester *PPS Polyarylate *Aromatic polyamide *Polyimide

©, very good; O, good; A, poor ^f, Step by step stretching technology is under study. *, Application of step by step stretching technology is under consideration.

RECEIVING HOPPER

VIRGIN CHIP

STORAGE HOPPER

EXTRUDER

CRYSTALLIZER AND CHIP DRYER

CUSHION HOPPER

FILTER

PELLETIZER

DIE

FLUFF TANK

CASTING UNIT

GRANULATOR

THICKNESS GAUGE MDSTRETCHER TDSTRETCHER THICKNESS GAUGE TRIMMING UNIT TREATER

PELLETIZER

MILL ROLL WINDER

FLUFF TANK

MILL ROLL STAND

GRANULATOR

SLITTER RESLITTER OPET(PRODUCT) Figure 6.1.1

Typical OPET process

Table 6.1.2

Comparison of PET Raw Material Drying Systems Final moisture content (ppm)

Mixing function

Installation space (m2 x mH)

Utility consumption rate

Drying method

Drying time ratio

Steam

Electricity

Ribbon type

Vacuum

1

®

Yes

60x25

1

1

Vacuum pump Feed hopper Control board

Hopper type and ventilation type

Hot air (Dehumidified)

1.4

O

No

50x20

5

1

Paddle type

Vacuum

®

No

150x 17 O

2.5

0.9

Paddle type

Hot air (Dehumidified)

0.6

No

12Ox 14 O

3

0.9

Drum type

Vacuum

2

No

200 x 20 A

4

0.5

Crystallization hopper Cooler Dehumidifier Feed hopper Control board Crystallizer Vacuum pump Dehumidifying refrigerator Feed hopper Control board Crystallizer Dehumidifying refrigerator Feed hopper Control board Crystallization hopper Vacuum pump Feed hopper Control board

Type

®

Remarks: 1. Installation space includes dryer, attachments, and spaces for operation and maintenance. 2. Utility consumption shows average value at time of continuous operation.

Attachments (Included in system)

As the MD =>• TD stretching process can lead to low cost film production, biaxially oriented film is mainly produced by this MD => TD process. The typical process of the sequentially biaxial stretching method for PET is shown in Fig. 6.1.1.

6.1.3

Polymer Handling

It is important to reduce water content in the starting raw materials to prevent degradation in the extrusion process of PET. Also, it is necessary to crystallize the pellets partially in the drying stage so that they will not block. Mixing of virgin material and reclaimed material, as well as master batch raw material, is also essential. As for raw material drying equipment, many types are available as shown in Table 6.1.2, and each has its own unique features. A ribbon type dryer in the table has particularly unique features: 1. Crystallization, drying, and mixing are carried out simultaneously. 2. Thermal efficiency is high because the ribbon blade shortens the drying time and less energy is consumed. 3. Processes from crystallization to extruding are treated under a vacuum condition, and thus prevent quality degradation. This drying system is shown in Fig. 6.1.2. Polypropylene (PP) is handled by adding the antistatic agent, the antiblocking agent, and the slip agent to the virgin pellets in master batch form as called for in the end product film. Also reclaimed pellets and trimmed edge films are fed back into the end product film. In addition, the drying process is added for any hygroscopic materials. The flow is shown in Fig. 6.1.3.

6.1.4

The Extrusion Process

Hitherto studies have been carried out to establish the essential conditions to satisfy the following requirements, not only for the biaxial stretching process alone but also for other film and sheet extrusion processes: 1. 2. 3. 4.

Variation in extrusion output shall be minimized. Mixing and melting shall be efficient and yet uniform extrusion shall be obtained. Low-temperature extrusion shall be possible so as not to degrade the resin. Bubbles should not be included. In addition, the extruder must be able to extrude at appropriate, high rates.

Material

Vacuum pump

Steam

Dryer Feed hopper

Steam

Control board Extruder

Figure 6.1.2 Example of PET drying system

1 ~ 5.

Raw material silo

6.

Storage silo and drying process

7.

Hopper

8.

Reclaim line trimmed edges

9.

OPP line

Figure 6.1.3 Example of raw materials flow for OPP

6.1.4.1

Performance Improvement on the Single-Screw Extruder

Inasmuch as there is a limitation resulting from the melting mechanism of the single extruder, major improvements cannot be expected by extending the conventional method. In the single screw, as represented by the Tadmor model [2] shown in Fig. 6.1.4, melting is carried out by shear heating at the thin melt film formed around the wall surface inside the barrel and by the heat transmitted from the barrel. When we designate the molten resin volume as Qm, the area of the melt film portion (the area where the solid contacts the melt film portion) as A, the circumferential speed of the screw as Vp and the density of resin as p, then Qm is expressed approximately by the following equation: Q1n = Q - V p - A . p

(6.1.1)

where Q is a constant dependent on the properties of the resin. Accordingly, it can be presumed that enlarging the melt film area A is necessary to increase the extrusion output rate per screw revolution speed. But it seems that increasing the output rate by enlarging the area A without changing the extruder dimension has already reached its limit. Under these circumstances, the following techniques have been developed recently to break through the obstacles. 1. Supplying as much energy as possible to the resin while it is in the solid state. This can be partially accomplished with a grooved feed barrel (Fig. 6.1.5). It has become known that friction energy between resin particles can be utilized effectively when the properly selected groove shape is provided. The energy thus generated is unexpectedly large compared with melting energy in the melt film. Therefore, the application has great advantages. 2. Feeding raw materials forceably beyond the melting capacity of the screw plasticizing zone. (The grooved feed barrel works effectively in this case also.) The pellets incompletely melted in the plasticizing zone are broken into as many fine particles as Melt film Barrel

Screw Solid bed Direction of screw rotation

Melt film

Figure 6.1.4 Model of melting with the melt surrounding the solid bed

Melt pool

A

A

Cross-sectional view A-A Figure 6.1.5

Grooved feed barrel

Homoge -nizing zone Figure 6.1.6

Metering zone

Mixing zone

Plasticizing zone

Feed zone

Special barrier screw

possible in the following mixing zone, leading to complete melting during flotation in the melt. Based on this concept a special barrier screw was developed as shown in Fig. 6.1.6 [3]. A comparison of performance between this type of screw and the conventional barrier screw is shown in Fig. 6.1.7. Extrusion performance improvement based on such a concept is seen in equipment built by many companies worldwide.

6.1.4.2

Capacity Increase by the Tandem Extruder

Since the first model of the tandem extruder for OPP film production was introduced in 1975 many extrusion systems have been installed around the world. Now there is a tendency to adopt the tandem extruder for high-capacity extrusion lines because it improves their performance. In response to this movement, many producers in the world are moving to make and sell similar model machines, with the following features:

Through - put Q (kg/hr)

Screw speed (rpm) Material used : Unstretched film grade PP (Ml = 9), pellet form Figure 6.1.7 Performance comparison between 90mm diameter special barrier screw and 90mm diameter conventional screw

1. Concept of the tandem extruder. On the conventional single-screw extruders, many functions such as solid conveying of raw materials, melting, mixing, metering, pumping, and the like are carried out by one screw, but on the tandem extruder, these features are divided functionally into two sections. In Fig. 6.1.8, the tandem extruder system is shown.

Primary extruder Heater Secondary extruder Connecting pipe Heater

Screw

Material Reduction gear unit Motor

Screw Pressure control unit Pressure gauge

Die

M oto R

Products Figure 6.1.8

Tandem extruder

Barrel cooling unit

Reduction gear unit

2.

The primary extruder, focused on the melting function, is a high-speed, small extruder with high melting efficiency. The secondary extruder, aimed at homogenizing, maintaining lower melt temperature, and metering, is a low-speed extruder with a larger screw diameter. By controlling the resin pressure at the inlet of the secondary extruder automatically, the machine can be operated as if both extruders were one. Characteristics of the tandem extruder: • High capacity extrusion is possible. • The melt temperature can be lowered.

3.

4.

In Fig. 6.1.9, the throughput and the melt temperature curves of the 200 mm diameter primary extruder are shown. In PP, the melt temperature can be controlled to less than 230 0 C in spite of the melting occurring at the tip of the primary extruder completely. The secondary extruder is a melt extruder and the screw speed is slow, so heat generation caused by shear is less. Thus the outlet melt temperature can be expected to be 20 to 30 0 C lower than that of the single-screw extruder. Quite stable extruding operation. As shown in Fig. 6.1.8, the screw speed of the primary extruder is controlled to keep the resin pressure constant, by measuring it in the connecting pipe between the primary extruder and the secondary one. By doing so, stable operation can be achieved because the inlet resin pressure at the secondary extruder is kept constant, even if raw material conditions such as bulk density etc. are varied. Shorter residence time of the resin in the extruder, which is advantageous for product quality.

Through -put

Melt temperature

melt temp.(°C)

Through - put Q (kg/hr)

PP GPPS

Screw speed (rpm) Figure 6.1.9 Capacity of 200mm diameter primary extruder

Table 6.1.3

Specifications of Tandem Extruder Series

Item

Extruder type

900/1150

1150/1500

1350/1750

Primary extruder

Screw L/D ratio Screw diameter (mm) Designed pressure (kg/cm2) Drive motor capacity (KW) Drive system

17 90 350 200

17 115 350 300

17 135 350 450

4 3

4 3

4 3

Screw L/D ratio Screw diameter (mm) Designed pressure (kg/cm2) Drive motor capacity (KW) Drive system

20 115 500 110

20 150 500 185

20 175 500 250

Temp, control zone Die gate temp, control zone PP (kg/h) PET (kg/h)

4 1 650 to 850 800 to 900

6 1 1100 to 1300 1300 to 1500

6 1 1500 to 1750 1600to 1800

Temp, control zone Connecting pipe control zone Secondary extruder

Out put

1500/2000 17 150 350 550 Direct drive 4 3 20 200 500 300 Direct drive 6 1 1900 to 2200 1900 to 2200

1750/2200

2000/2500

2200/2750

17 175 350 750

17 200 350 950

17 220 350 1200

4 3

4 3

4 3

20 220 500 400

20 250 500 500

20 275 500 600

7 7 1 1 2400 to 2700 2900 to 3300 2400 to 2700 2900 to 3300

7 1 3400 to 3800 3400 to 3800

5.

Because the extruder is compact, operability is excellent and energy saving and space saving advantages can be obtained.

The specifications of a tandem extruder are shown in Table 6.1.3. For OPET, the tandem extruder systems are already in use and this is expected to increase in the future. Not only for PP and PET but also for OPS, the tandem extruder is adopted for its low melt temperature advantage. As for the raw materials for OPP films, there is a trend toward making such films directly from raw material in bead form from the Spheripol process without going through the pelletizing process. Ito reported that a film making test was conducted at a test plant, and he developed a suitable tandem extruder designed for this type of material [3]. Spheripol PP will become an increasingly important starting material for OPP. A new extruder series with 1.5 times the output of the present series has been developed [4]. It has a hexagonal screw, a melt seal for higher pressure, and a special dulmage.

6.1.5

Filter and Die

The molten resin from the extruder is directed to the die through a connecting pipe. A filter is installed between the extruder and the die so as to separate foreign particles from the resin. Before and after the filter unit, pressure gauges are provided to measure the pressure differences caused by contamination of the filter. A wire mesh, sintered wire mesh, sintered metallic powder, and sintered metallic fiber are used for the filter medium. The filter types are classified into cylindrical type filter, candle filter, disc filter, and so forth. Depending on the application such as, for example, PET video tapes, and capacitors that demand high-quality performance, the filter elements range in size from several micrometers to 10 to 3O/mi and disc type filters, using sintered metallic fiber, are extensively used. The filter changes are sometimes regarded as an obstructive factor for the continuous operation of the film plant. Owing to the requirements for high production rates and quality, increased frequency of filter changes causes reduced productivity. Accordingly, a pair of long-life filters with a large filtering area is installed in the line with the aim of prolonging the filter changing intervals and reducing change overs [5]. The die must have an excellent adjusting function for the film thickness and be easy to disassemble, clean, regrind, and reassemble. The typical die construction is shown in Figs. 6.1.10 and 6.1.11. It consists of two bodies and a flexible lip, and the passage is of the coat hanger die type. The parallel plate flow of non-Newtonian fluid is expressed by the following equation:

Q =^ V ^

xW

• (V- x %YnxH^+l^

(6.1.2)

2(2n + 1) \2m dZJ where Q is the volumetric flow rate; His the die gap; W is the slit width; dp/dZ is the pressure gradient; n is the power law index: m = m0 x exp[—a(T — T0)]; melt viscosity m0 is m(T0), where T0 is a reference temperature; a is the temperature dependence coefficient; and T is temperature.

Neglecting the effects of die gap and resin viscosity on pressure gradient, assuming that the slit width is constant, and defining the die gap variation and resin temperature changes as AH and AT respectively, the rate of change of the flow rate is expressed by the following equation:

This equation indicates the effects of the die gap and the resin temperature changes on the film thickness. Let us take PP, PET, and PS, by way of example, to show the changes in flow rate (thickness) against the die gap and resin temperature changes in Fig. 6.1.12. As a result of these potential thickness variations, sheet thickness adjusting methods are used and divided into two different types. One is a die lip gap adjustment and the other is a viscosity adjusting method involving a lip heater [6]. Each method has merits and limits and they are summarized in Table 6.1.4. With regard to PP, there are two systems widely used, one in which the die gap is adjusted by an adjusting bolt rotated by a servomotor, and one in which the die gap is adjusted by the thermal displacement of the adjusting bolt whose temperature is changed by means of a heater. As for PET, it is desirable that the system can be adjusted statically without an external disturbance. As shown in Fig. 6.1.12, the sensitivity of the resin temperature is so high that the resin viscosity adjusting method is employed. Other systems are also being employed. Besides, as shown in Fig. 6.1.12, the flatness and finish of the die lip surface, and the

HEATER

HEAT BOLT Figure 6.1.10

Die for monolayer system (heat bolt type)

LIP HEATER

ADJUSTING BOLT

Figure 6.1.11

Die for three-layer system (robot and lip heater type)

uniformity of temperature in the direction of the die width are important items required for good die performance.

6.1.6

The Casting Process

A molten resin extruded from the die is formed by the casting machine into a base sheet. This process plays a very important role in the overall production process by establishing a base of good or bad quality upon which to build. In the casting process, the molten resin is solidified by quick cooling on the chill roll, ideally with the base sheet being cooled evenly on both sides. To achieve this, various methods have been proposed depending on the type of resin. In the case of PP, the typical casting methods are multirolls of small diameter as shown in Fig. 6.1.13, and a single roll having large diameter (with water bath). Recently, a large roll plus water spray having high cooling efficiency and a compact size has also been developed to cope with the high-speed operation (Fig. 6.1.14). In the case of PET, the casting method is adapted in such a way as to position the die just above the chill roll as is shown in Fig. 6.1.15, because of low viscosity. The important point of the quick quench for solidification is to pin molten resin to the chill roll rapidly. If the pinning is not effective, this not only lowers the cooling efficiency, but also entraps the air between the molten resin and the chill roll. These bubbles can remain on the base sheet and may result in problems called surface roughening or pinner-bubble.

Change in flow rate (thickness) (%)

PP

PET

Change in flow rate (thickness) (%)

Change in die gap

PS

(%)

PET PP

Change in resin temperature Figure 6.1.12

PS

(0C)

Relationship between change in resin temperature, die gap, and change in flow rate

As for the pinning methods that stick a molten resin to the chill roll, there are many, such as the "air knife," "press roll," "liquid application," and "electrostatic" methods. The air knife and the electrostatic methods are generally applied for PP and PET respectively. The air entrapment phenomenon between the chill roll and the molten resin can be modeled as shown in Fig. 6.1.16, and the entrapped air layer thickness (between the molten

Table 6.1.4 Types of Automatic Film Thickness Profile Controllers and Their Advantages Characteristics Classification

Method

Advantages

Disadvantages

Lip gap adjustment

Servo motor

• Wide adjusting range • Quick response time • All bolts act at the same time. • Precise adjustment • All bolts act at the same time. • Precise adjustment • Quick response time

• One by one adjustment • External force acts • Narrow adjusting range

Thermal bolt

Piezo translator

Viscosity adjustment

Heater

• All heaters act at the same time. • Not mechanical (constant lip gap) • Precise adjustment

• Long response time • Heat resistance • Narrow adjusting range

• Confined to specific resin (temperature dependence of viscosity is large) • Narrow adjusting range

resin and the chill roll) can be expressed by the following equation:

where u is (V\ 4- F2)/2; h is the thickness of the entrapped air layer; K is a constant; R is the radius of the roll; fi is the viscosity of air; V\ is the takeup velocity of the molten resin on the

T-Die Air knife

Casting roll

Figure 6.1.13

Typical casting method (three-roll casting machine)

T-Die Air knife

Water bath Chill roll Figure 6.1.14

Water spray

Casting machine (single chill roll with spray cooling system)

chill roll; V2 is the circumferential velocity of the chill roll; P is the pressure of entrapped air; and Fp is the pinning force. In Eq. (6.1.4), [R9P] on the right hand side is balanced with the elongational force [F] of the molten resin film. F = RxP

(6.1.5)

This can be obtained by using the elongational strain rate, which was derived from the elongational flow of the Newtonian flow. The elongational force acting on the molten resin Normal position

Nip roll

Electrostatic pinning wire

Take-off roll

Dancer roll Strip roll

Figure 6.1.15

Casting machine (casting for low-viscosity resin)

Chill roll

PINNING FORCE et. AIR KNIFE PINNING ELECTROSTATIC PINNING

MOLTEN RESIN FILM ELONGATIONAL FORCE

CHILL ROLL ENTRAPPED AIR PRESSURE OF ENTRAPPED AIR Figure 6.1.16

Air entrapping phenomenon between the chill roll and the molten resin film

film is expressed by the following equation: F = Xx — xe

(6.1.6)

where

F is the elongational force of the molten resin film; X is the elongational viscosity; Q is the volumetric flow rate of the molten resin film; F0 is the velocity of the molten resin at the die exit; V\ is the takeup velocity of the molten resin on the chill roll; e is the elongational strain rate; L is the distance between the die exit and the chill roll. UNIT : 70 m/sec 100 m/sec

300 mm Aq (a) VELOCITY DISTRIBUTION Figure 6.1.17

Result of air knife air flow analysis (poor)

- 20 mm Aq

(b) PRESSURE DISTRIBUTION

In the case of PP, as the molten resin can be pinned on the chill roll by the use of air knife in general, this air knife shape and its attaching point are essential for the stable forming of the base sheet. For this reason, the design of the air knife is optimized by the practical application of the computer simulation analysis of the air flow. Figure 6.1.17 shows the distributions of air velocity and pressure in the case where the optimization is not considered. It can be observed that in the air velocity distribution figure, the vortex flow exists in the air current; following this a negative pressure is generated on the upper part of the base sheet shown in the pressure distribution figure. In such a case, the shape and location of the air knife that eliminates the negative pressure can be determined by the use of simulation analysis. The example of optimization is shown in Fig. 6.1.18. The relationship between the pinning force and the thickness of entrapped air at each resin forming speed in the optimized air knife shape can be obtained by using Eq. (6.1.4). An example of the result is shown in Fig. 6.1.19. For a lower viscosity molten film, such as PET, one employs the electrostatic pinning method. In this case the molten resin makes full contact with the chill roll by adding an electrostatic charge to the molten resin. Because such a low-viscosity resin generates vibration in the presence of a slight air current this makes the air knife unusable. The pinning force against the chill roll is determined by factors such as electrode voltages, distance between electrode and chill roll, electrode diameter, and electrical conductivity of the molten resin. The behavior of the electric charge in the case of electrostatic pinning has been considered as shown in Fig. 6.1.20 [7]. With increase of the forming speed, the electric charge density becomes lower and the pinning force decreases, leading to entrapment of air between the molten resin and the chill roll. However, when the electrode voltage is boosted to increase the electric charge density, an arc discharge occurs. The relationship between the line speed and marginal pinning voltage that does not result in entrapment is shown in Fig. 6.1.21 [8]. Various proposals for the improvement of the electrostatic pinning method were reported by Sakamoto et al. [7] and are shown in Fig. 6.1.22. Study and examination have been made of various methods such as modifications on the equipment side and polymer modifications, such as controlling the volume resistivity, etc. Recently, the combination of electrostatic pinning and water coating on the chill roll has been proposed [9]. This method has the following merits. The growth of oligomer on the chill roll greatly decreases, so the cleaning cycle of the roll is more than three times as long as that for the existing method, and frequency of film breaks in the stretching process decreases, leading to improved production efficiency. The molten films pinned to the chill roll are gradually cooled to solidification. The heat balance for the process in which the molten resin films are cooled to soldification can be analyzed by using the equation for non-steady-state heat conduction. However, in the case of a crystalline polymer such as PP, it is necessary to give full consideration to the enthalpy of crystallization. The equation of non-steady-state heat conduction, in which the heat of crystallization is taken into consideration, is expressed as:

pxCx

^

=KW)+^xAH^Xx{-3i)

(6 L7)

-

UNIT : 70m/sec 100m/sec

324 mm Aq

(b) PRESSURE DISTRIBUTION

(a) VELOCITY DISTRIBUTION Figure 6.1.18

Result of air knife air flow analysis (excellent)

Thickness of entrapped air /<m

CHILL ROLL DIA.

:

0.24m

LINE SPEED (m/min)

Pinning force Figure 6.1.19

35 mm Aq

Mpa

Relationship between the pinning force and the thickness of entrapped air

h

I = Ii + I 2

Extruding die

I2 V

I : Total current h : Leakage current I2 : Current provided to web Figure 6.1.20 The stream of charge during electrostatic pinning

where p is density; C is specific heat; T is temperature; t is time; K is heat transfer coefficient; y is thickness direction of the molten resin films; pc is density of a complete crystal; AHC is latent heat of crystallization; X is percent crystallinity.

6.1.7

Stretching and Annealing Processes

Voltage

KV

In the MD stretching process, the mechanical properties in the MD are improved by heating the base sheet and then stretching longitudinally between the rolls with different peripheral speeds, thus giving molecular orientation.

Line speed m/min Figure 6.1.21 Relationship between line speed and voltage

Polymer - p u control Polarity Power supply AC overlapping Material, Shape Improved methods Diameter Electrode

Plural Cover Preventing vibration

Machines Atmosphere

Lower pressure Various kinds of gas Covered with insulator

Casting drum

Rough surface Microcrack

Figure 6.1.22

Improvements of electrostatic pinning method

Consideration for stretching the sheet while suppressing neck-in is necessary to (1) absorb the thermal expansion of the sheet, (2) prevent looseness and slipping in the preheating zone, and (3) maintain widthwise uniformity in the physical properties and thickness in the stretching zone. There are two methods for the roll stretching process: cross-stretching and flat stretching (Fig. 6.1.23) [10, H]. Stretching Point Stretching Point

(a) Cross Figure 6.1.23

Stretching method

(b) Flat

The merit of the cross-stretching method is a smaller stretching gap. This method is used for PP etc., which shows large necking. This method then is preferable as the smaller stretching gap and reduced neck-in lead to more stable stretching and better gauge control. On the other hand, as flat stretching cannot set the stretching gap smaller than the diameter of the stretching roll, the stretching gap is larger than the stretching gap of the cross-stretching. The flat stretching is used for OPS, OPET, and others. Process auxiliary heating by electric heaters at the gap space prevents the film from sticking to the roll. It can increase stretching stability as the gap between the last heater and the high-speed side stretching roll is short. The TD stretching process is composed of the following steps: 1. Preheat the film uniformly by blowing heated air onto both the upper and lower sides while holding the film edges with clips after MD stretching. 2. Stretch widthwise to the required stretching ratio along the clip guide rail set for desired pattern. 3. Cool after annealing. As for the guide mechanism for the tenter clips, two types are available, the sliding type and the roller bearing type. The roller bearing type is preferred for industrial use films that require cleanliness to achieve quality. For the roller bearing type clip, the special roller bearing which is sealed by thermal proof grease is used. This is suitable for high running speeds as there is almost no concern that the film will be contaminated due to scattering of lubrication oil. But in this case, preventive maintenance checks, such as periodic bearing replacements, are necessary. For the heating chamber, the important point is to construct it to ensure uniform heating to the film surface by heated air and to keep different segments of the chamber separate. Thermal control is likewise important because the energy consumption is considerable. 1. Stretching of PET As described previously, generally the step-by-step stretching method is adopted. Stretching in the MD and then TD is carried out in sequence. The MD stretching temperature for PET is 90 to 1100 C, but preferably an infrared heater or nonsticking type roll is used in the stretching zone because there is a tendency to stick on a chromium plated roll in the stretching temperature range. The multistage stretching method also may be used to achieve higher line speeds. The performance requirements for the preheat roll of the MD stretching machine are nonsticking, nonstaining of the roll, durability, stable holding capacity for film, etc. As for the nonsticking property, there are many proposals for roll materials. Using a basic chromiumplated roll, the rolls with a ceramic coating (surface roughness: 1/xm; thickness, 0.1 to 0.5 mm) have been employed for PET at a temperature of 80 to 1250C [12]. Although the satin finish roll has the effect of increasing adhesion temperature, a scratch or abrasion may occur. The Teflon coating has good nonsticking properties; however, it has the problem of durability. Recently, the use of the ceramic roll, despite the high price paid for the nonsticking property, is generally increasing. The method of fixing the stretching point involves the following: • Contacting the film fast to the roll by using static electricity [13] • Concentrating heat energy by using a condensing heater [14]

A

V0

1

V^V1 d A u

V

Drawing rate = V0(A2-1)/2d

B

d

pddds iu 11j

V1

(e-Oix) uv a3ue6uj4ejig

A

Film speed Distance between A and B roll Draw ratio

draw ratio A =3.0 A =4.0 drawing rate u = 1 328% sec

V0 Position

Figure 6.1.24

Experimental behavior in super drawing

Film temperature (0C)

A

B ^B (draw ratio)

^A (draw ratio)

Figure 6.1.25

Schematic representation of apparatus for roll drawing

• Increasing close adhesion to eliminate the air between the film and the roll by installing a nip roll on the stretching roll [10, 11, 14 to 16, 18] • Fixing the separation point by installing a nip roll at the point where the film is separated from the roll [11, 14 to 18]. Super drawing is reported by T. Miki [19]. The experimental behavior of super drawing, which is a relationship between the MD stretching factor and the birefringence An9 is shown

Birefringence An (x10- 3 )

TA=HO0C

Theory

TA= 13O0C

TA : drawing temperature at A

Stretch ratio A( = AAXAB) Figure 6.1.26 Characteristic behavior of super drawing

in Fig. 6.1.24. The birefringence decreases with increasing stretching film temperature, and above 120 0C the drawing rate stops contributing to molecular orientation. In the OPET MD stretching test data, An with a temperature of 1300C at point A is less than An with a temperature of 110 0 C at point A. The MD stretching with a temperature of 130 0 C does not contribute to the molecular orientation at point A and also hardly contributes to the molecular orientation at point B (Fig. 6.1.25 and 6.1.26). This result suggests that the stretching process, which combines the conventional stretching method with the super drawing method, could realize higher stretching and low molecular orientation at the same time. It is thought that each OPET film producer operates with this modification to obtain high MD stretching. 2. Stretching of PP PP is generally heated to a specified stretching temperature (125 to 1400C) by preheating rolls. Because PP suddenly thins down substantially in some regions and stretches endlessly, causing so-called neck stretching, it must be stretched over a small distance between a pair of small diameter rolls. In the case where lower heat seal temperatures skins are involved, the MD stretching equipment and base sheet temperature control program, shown in Fig. 6.1.27, are proposed to protect the surface layer of the base sheet from sticking on the roll surface [20]. The use of Teflon coated rolls for the latter section of the preheating rolls is increasing because the film is apt to stick on the rolls. Recently, for the purpose of improving the physical properties along with the trend toward a high stretching ratio, the adoption of the so-called two-step stretching process, that is, stretching by two stages, is becoming popular. Figure 6.1.28 shows an example of the roll arrangement for a OPP MD stretching machine. In the case of TD stretching of PP for packaging, the sliding clip type is used. Although this technology has generally been limited to slower lines it has recently been applied on highspeed lines of more than 300m/min. The sliding clip type is advantageous from the standpoint of cost and maintenance. The construction of ovens has improved and the heat exchangers and blowers were symmetrically arranged at both sides of each room in the wide zone after the stretching unit. Uniformity of hot air flow was accomplished by constructing the oven in such a way that the air flow is symmetrical around the oven's horizontal center line and vertical center line respectively. For the purpose of realizating energy savings using a smaller oven, it is important to set the position of the air blower holes and their distance to the film so that the heat transfer coefficient to the film is maximized. In addition, as the ratio of exhaust heat to oven heat loss reaches approximately 0.7, an exhaust heat reclaimer contributes effectively to energy saving. 3. Bowing The stretching-annealing processes are most important in influencing the quality of the film products. In particular, the annealing process is conducted with the aim of relaxing the stress from the preceding process so as to improve the dimensional stability. However, in the stretching-annealing processes, a bowing phenomenon often occurs. The manner in which the bowing phenomenon occurs is shown in Fig. 6.1.29 and is indicated by the curvature of the line across the film which was initially perpendicular to the stretching direction.

V1 Furnace

Pre-heat

V2

Stretching gap CHiJI roll

Stretching roll

Stretching roll ©

To Simplified temp, program TK = Seal temp. TKW

Tv

TRW

Surface

Surface

After pre-heat TF : TkW:

Film temp. Chill roll temp.

Figure 6.1.27

TK :

After furnace Seal temp.

TRW :

After chill roll Tv :

Stretching roll temp. TR :

After stretching roll

Theoretical optimized temp, profile after stretching roll (D

Pre-heat temp.

T0 :

Stretching temp.

d :

Longitudinal stretching machine for coextruded multilayer films

Furnace temp, (over heat) Film thickness

Figure 6.1.28 Longitudinal stretching machine for OPP

Annealing zone

Stretching zone

Bowing ratio (%)

Figure 6.1.29 Bowing phenomenon

Preheating zone

Stretching zone

Thermosetting zone

Dimensionless length (—) Figure 6.1.30 Relationship between tenter length and bowing ratio

Cooling zone

Bowing ratio (%) Figure 6.1.31 Relationship between thermosetting temperature and bowing ratio

Thermosetting temperature (0C)

Observation of the bowing behavior shows that the straight line is deformed into a convex line in the initial region of the stretching process and then is returned to the straight line immediately before the end of the stretching process. Then the line is deformed into a concave line at the completion of the stretching process. Furthermore, the concave line reaches the maximum point at the beginning of the annealing process as shown in Fig. 6.1.30 [21]. (In Fig. 6.1.30, the annealing process occurs in the thermosetting zone.) In addition, the relationship between the bowing ratio and the annealing temperature, as illustrated in Fig. 6.1.31 [22], shows that the bowing ratio increases with increasing annealing temperature. In Fig. 6.1.31, the annealing temperature corresponds to the thermosetting temperature. The bowing phenomenon produces defects in the final products. For example, the film that undergoes bowing produces optical anisotropy in the TD owing to molecular orientation, and therefore research and development into its prevention has been conducted especially in the field of OPET films for floppy disk applications. On this basis various methods for optimizing the annealing conditions have been devised and proposed. They involve modifications to the methods of annealing of film: (1) the stretched film is kept first below the glass transition point to recover strength and then the film is subjected to annealing [22], and (2) the rate of heating the film for the annealing after the film has been kept below the glass transition point is controlled [23].

6.1.8

Takeoff and Winding Processes

The film coming out from the annealing process of the transverse stretching machine is taken off, the edges are trimmed, and the film is wound as a mill roll. In the takeoff part, a surface treatment is given to the film so as to activate the film surface with the aim of improving properties such as ink adhesion. The surface treatments are conducted to improve the surface by means of oxidation because of the inertness of the film surfaces. There have been many techniques for

improvement, and a "corona" treatment or a "flame" treatment are used, for the most part in industrial practice. The corona treatment is implemented in such a way that the film is passed through a corona discharge field in which the corona discharge is induced by imposing high voltages across the insulated electrode and the grounded dielectric substance. The main components of the corona treatment machine are discharge electrodes, dielectric coating rolls, and a corona power generator. The shapes of the electrode are based on three types: knifeedge, bar, and shoe, and the multiknife electrode [24] has been developed to obtain soft and uniform discharges. For the dielectric roll, a metallic roll is covered with a dielectric substance to produce the uniform corona discharge. For the dielectric substance, excellent materials are used such as silicone rubber, chlorosulfonated polyethylene, ethylene propylene rubber, etc. with high dielectric constant as well as ozone- and heat-resistant characteristics. Despite the high price, ceramic materials and fiberglass-reinforced plastic (FRP) are sometimes used. The electric power sources are usually solid state. The extent of difficulty of surface treatment varies depending on the chemical structure of the polymer and the kinds of additives used. OPP requires more energy to raise the surface tension to the desired level than OPET. The treatment energy consumed for OPET and OPP are lOWmin/m and 40Wmin/m respectively [24]. The flame treatment is reputed to be a method that does not generate ozone as does corona treatment while operating effectively. However, higher processes are restricted owing to the performances of the burners. Owing to the improvement of the burners and the gas controller, flame treating has improved in recent years. The quality of the winder has become very important with increased winding speed (250 to 350m/min), film width (6 to 8m) [25] and decreased film gauges. As the film speed increases, wrinkles and hence waste increase. To solve these problems, the following items can be adopted. 1. Improvement of wound-up design: The hardness of mill rolls is controlled to the optimum level by programmed control of the winding tension and pressure of the lay-on roll as a function of roll diameter. Wrinkles on winding have been much decreased by the use of spreader rolls. 2. Reduction of winder losses: For roll changes there has been developed a new mechanism that starts the roll by evenly sticking the film over the new core without use of any adhesive tape. Therefore, the folding of the film, wrinkles caused by the adhesive tape, scratches of film by the new core, and other defects have been decreased considerably [3]. Automatic roll unloading and automatic core loading are also gradually being adapted to save labor.

6.1.9

Process Control

6.1.9.1

Functions

With increased production levels and rates, computerized process control systems for the entire film production line are being utilized with the object of upgrading product quality,

increasing productivity, automating production, and saving labor (see Fig. 6.1.32). The functions of the process control system are broadly divided into three categories: 1. automatic setting of the operating conditions 2. centralized supervision and data acquisition 3. automatic film profile control.

6.1.9.2

Features

The technical features of the process control system are: 1. The high quality level of product can be maintained in a stable manner. In particular, product having the guaranteed minimum thickness can be obtained and can result in material saving. 2. The product changeover time can be reduced and can result in material and time savings. 3. The improvements of the production technology lead to reliable accumulation of process information and thereby higher quality levels.

ALARM MEMORY PRN I TER MAIN ALARM COMPUTER

PRN I TER

MOTOR CONTROL

EXTRUDER

FILM THC I KNESS CONTROL

TEMPERATURE CONTROL /S-RAY DIE

0-RAY

CASTN IG LSM TSM

Figure 6.1.32

Computerized process control system

TAKE-OFF

WN I DER

4. Normal operating staff can easily operate the machine. Moreover, the trouble caused by individual differences of operators will be eliminated, and labor savings become possible. Furthermore operators are released from operations such as die bolt adjustment under difficult conditions.

6.1.9.3

System Configuration

Several installations involve distributive type systems in which an overall supervisory system is installed in the center. As a subordinate part of the above system, the control system for line speed, temperature, and film thickness profile is connected with the central system. In addition, these systems are connected with a host computer and this enables total control of the entire film making plant.

6.1.9.4

Automatic Film Thickness Profile Control System

The characteristics of the films produced vary according to the required properties. However, the accuracy of the film thickness profile is common to them all and is very important. Therefore, to improve the film profile accuracy and to shorten the time to attain it, various concepts and devices have been proposed for the die body, the thickness adjustment equipment, and the control system. Thickness variations are classified into three categories: 1. thickness variations with a short period in the MD 2. thickness variations with a long period in the MD 3. thickness variations in the TD. The thickness variations having a short period in the MD are caused mainly by mechanical factors, that is, the extruder performance, variations of circumferential speed of rolls etc., and consistent reduction in these variations becomes impractical in principle, without improvement of the performance of the equipment. The thickness variations having a long period in the MD are caused by contamination of the melt filter, changes in materials or environmental conditions, etc.; adjustment of the average film thickness can be made by using feedback control in such a way that the time average thickness in the MD is measured so as to control the screw speed of the extruder according to the thickness information. The thickness variations in the TD are due to nonuniformity of molten resin, temperature inequality of die, and/or irregularity of die lip gap. To reduce these thickness variations is the main object of an automatic profile control system. An example of an automatic film thickness profile control system is shown in Fig. 6.1.33. To set up such a system, it is necessary to understand the forming process to establish the control method. Knowledge of the following items is essential for the control operation: 1. correspondence of the location in the TD of the measured film thickness profile to the location of the adjusting bolts on the die 2. mutual interference effects of the required die lip gap adjustment on the adjacent bolts

CONTROL DS PANEL IPLAY FL IM THC I KNESS CONTROL PANEL

MAIN CONTROL UNT I SCREW SPEED CONTROL SG I MAL C ( OMPUTER) HEAT CONTROL SG l NAl /?-ray HEAT T H C I K N E S S G A U G E CONTROL UNT I CONTROL PANEL THC I KNESS SG I NAL

/3-ray THC I KNESS GAUGE CONTROL PANEL THC I KNESS SG I NAL

M FILM FLOWDIRECTION TAKE-OFF MACHN IE AND WN I DER

EXTRUDER DE I ADJUSTN I G DEVC IE CASTN I G MACHN IE Figure 6.1.33

3.

/3-ray THC I KNESS GAUGE

LONGT IUDN I AL STRETCHN IG MACHN IE

TRANSVERSE STRETCHN IG MACHN IE

/?-ray THC I KNESS GAUGE

Automatic film thickness profile control system

the amount of the die lip gap adjustment needed to correct the deviation. As to item (1), there are many methods to be considered: • Method 1. After marks are put on the molten resin at the die exit, the positions of the marks are measured on the cast film base sheet, the longitudinally stretched film, and the biaxially stretched film. • Method 2. After the die lip adjusting bolts have been operated in consecutive order at a fixed rate, the profile changes are measured. • Method 3. By carrying out statistical analysis of the control data of the production operation, the appropriate position of the bolt can be determined [26].

As to item (2), the methods are: By using the experimental equation approximating the profile change when one adjusting bolt is operated, the control demand is computed. This is on the assumption that when several adjacent bolts are operated simultaneously, the profiles are regarded as the superposition of individual profile caused by individual bolt operation [27] (Fig. 6.1.33). As to item (3), there are methods that are obtained from Eqs. (6.1.2) and (6.1.3) and from observation of equipment responses. For a newly advanced control system, Mapleston has reported that their "randomization" software program corrects the film thickness having a thick or thin tendency caused by the die, and the thickness accuracy of ± 2 % of set value can be kept on 8 m webs. This stops the buildup of gauge bands or ribs on the mill rolls [28]. Akasaka et al. have reported a fundamental control system designed by using a state predictive servo theory. This fundamental control system controls by predicting the effects of the past control on the present and future output. This system is capable of reducing startup

Thickness set value

Thickness

Integrator State-transition calculation

Regulator gain

Profile process

Dead time

Memory State - prediction calculation

Vector quantity quantity

Thickness gauge Observer Figure 6.1.34

Block diagram of a fundamental control system (block diagram showing control-demand calculation for a fundamental control system) [29]

time and improving thickness accuracy. The average variance at a steady state was 200 (1.4% average thickness error) (Fig. 6.1.34) [29].

6.1.10

Closing Comments

In this chapter, the introduction of the finite tentering process was described at every step from supply of raw materials to winding. The processes are not actually independent but are mutually related, and the process conditions closely relate to the final product and film properties. The biaxially oriented film manufacturing machine must have high speed, wide width, and stable performance. So it is important to carry out fundamental studies on each process and the relationships among the processes.

Abbreviations Used FRP fiberglass reinforced plastic MD machine direction OPP biaxially oriented polypropylene OPET biaxially oriented polyethylene terephthalate OPS biaxially oriented polystyrene OPA biaxially oriented polyamide PP polypropylene PET polyethylene terephthalate PS polystyrene TD transverse direction

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.

Murauchi, K., Polymer Digest (1990) 2, p. 42-45 Tadmer, Z., Polymer Eng. ScL (July 1966) 6, p. 187 Ito, T., Japan Plast. Indust. Ann. (1990) 33, p. 80-88 Mod. Plast. Int. (March 1992) p. 67 Hensen, E, Siemetzki, H., Kunststoffe (1980) 11, p. 753-758 Ecchu, M., JP-A-51-109955 (1976) Sakamoto, K., Takizawa, T., Kato, K., Mitsubishi Kasei R&D Rev. (1988) 2, p. 120-125 Tsukamoto, H., Tsutsui, Y., Suzuki, T., Tobita, K., Mitsubishi Heavy Industries Techn. Rev. (1986) 2, p. 186-190 Aoki, S., Tsunashima, K., Ikegami, T, JP-A-3-23913 (1991) Nagasawa, T., Shuto T., JP-A-60-262624 (1985) Kimura, E, JP-A-1-237118 (1989) Sato, K. et al, JP-4844666 (1973) Sugawara, M., Uchida, H., JP-59-8343 (1984) Sudo, K., Shimura, K., Furuya, Y., JP-A-51 130479 (1976) Ichii, T., Matsunaga, S., Nakahira, T., JP-A-63-134222 (1988)

16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29.

Tobita, K., Hasegawa, H., Hino M., JP-A-62-147519 (1987) Hagiwara, 0., Sato, K., Okabe, K., JP-A-62-199427 (1987) Sato, K., Okabe, K., Ishitsuka, L, JP-A-62-158026 (1987) Miki, T., Kanesaki, T., Utsumi, S., Mitsubishi Kasei R&D Rev. (1990) 2, p. 109-115 Wellenhofer, P., Plastic Age (June 1980), p. 101-107 Nonomura, C, Yamada, T., Matsuo, T., Seikei Kako (1992) 4, p. 312 Kimura, M., Nanbu, K., Hirotomi, N., JP-A-51-80372 (1976) Shimura, K., Kouno, M., JP-A-61-8324 (1986) Philip, B., In Polymers Laminations and Coating Conference, (1989), p. 169-194 Plastics Age Encyclopedia (1986), p. 113 Iguchi, K., Nitta, S., JP-5-76412 (1993) Ootomi, Y., Kawasaki, K., JP-A-58-39050 (1983) Mapleston, P., Mod. Plast. Int. (June 1990), p. 38-^1 Akasaka,N., Narita, Y., Akiyama, N., Suzuki, T., Tsutsui Y., Mitsubishi Heavy Industries Techn. Rev. (Oct. 1989) 3, p. 1-7

6.2

Influence of Processing Conditions on Structure and Physical Properties of Biaxially Stretched Engineering Thermoplastics M. Cakmak

6.2.1

Chemistry of Polyesters and Its Importance in Processing

282

6.2.2

Solid State Phase Behavior of PET

282

6.2.3

PET Film Technology

284

6.2.4

Stress-Induced Crystallization

285

6.2.5

Development of Structure with Deformation 6.2.5.1 Stretching of PET below Tg 6.2.5.2 Stretching of PET above Tg 6.2.5.3 Deformation Behavior of PET in the Rubbery Region and Its Relationship to Thickness Uniformity 6.2.5.4 Structure and Morphology Developed by Biaxial Stretching of PET 6.2.5.5 Annealing Effects on PET 6.2.5.6 Crystallinity and Thermal Properties 6.2.5.7 Conformational Changes Due to Drawing and Annealing 6.2.5.8 Small-Angle X-Ray Studies (SAXS) on Stretched and Annealed PET

285 286 286 286 288 296 298 299 302

6.2.6

Dynamic and Static Mechanical Properties 6.2.6.1 Dynamic Mechanical Properties 6.2.6.2 Static Mechanical Properties 6.2.6.3 Uniaxial (Constant Width) Stretched Films 6.2.6.4 One-Step (Simultaneous) Biaxially Stretched Film 6.2.6.5 Two-Step Biaxially Stretched Films 6.2.6.6 Long-Term Creep Behavior

303 303 307 308 310 310 312

6.2.7

Other Properties of Interest 6.2.7.1 Gas Permeability Characteristics and Morphology

313 313

6.2.1

Chemistry of Polyesters and Its Importance in Processing

Polyethylene terephthalate (PET) synthesis is generally accomplished by direct esterification of terephthalic acid with ethylene glycol with water as byproduct. This water byproduct in the condensation process is a limiting factor in achieving high molecular weights because its presence in the structure hinders the chain extension reaction. This led to development of other polymerization techniques in which removal of the water molecules was accomplished in the solid state at elevated temperatures. Typical molecular weights as represented by intrinsic viscosity 0.5 to 1.2dl/g are regularly achieved, with the most commonly used range being 0.6 to 0.8 dl/g. Heffelfmger [64] indicates that below a critical degree of polymerization of about 25, PET is friable and brittle and beyond a higher critical value of DP of about 60 further increases in molecular weight are not economically justified and most commercial grades are made slightly above the latter higher critical value. In processing of polyesters, exclusion of moisture is of paramount importance so as not to lose the molecular weight developed during the polymerization process. The presence of moisture in the molten phase causes hydrolysis of ester linkages. Even with the best prevention methods (closed hopper systems, inert gas purging, etc.) this reduction is generally unavoidable and the reduction in molecular weight after a melt processing generally increases with the increase of molecular weight of the initial material.

6.2.2

Solid State Phase Behavior of PET

PET, having relatively rigid chain architecture due to the presence of the para-linked phenyl group, can easily be quenched into the amorphous form from the melt. Single crystals of PET were grown by Yamashita [I]. The polymer chains in parallelogram shaped single crystals are inclined at about 30 0 C to the normal to its basal plane. When crystallized from the melt near its melting temperature this polymer forms double-banded spherulites [2]. It can have positive as well as negative spherulites depending on molecular weight. The crystal structure of this polymer was determined first by Daubeny et al. [3]. The unit cell is triclinic and contains one chemical repeat unit as shown in Fig. 6.2.1. The unit cell parameters are: a = 4.56 A, b = 5.54 A, c= 10.75 A and a = 98.5°, 0=118°, y=112°. The molecules were found to be roughly planar with the aromatic rings nearly parallel to (100) planes. The density of crystals with the above parameters is 1.455g/cm3. For completely amorphous PET, Daubeny et al. [3] reported a density of 1.335 g/cm. More recent studies on PET by Fakirov et al. [4] resulted in the following unit cell parameters: a = 4.48 A, b = 5.85 A, c = 10.75 A and a = 99.5°, 0=118.4°, and y= 111.2°. These parameters give a crystal density of 1.515 g/cm3. There have been other reports on the crystal density of PET, that is, 1.501 g/cm3 by Zahn et al. [5] and 1.495 g/cm3 by Kilian et al. [6]. The glass transition temperature ranges between 67 and 75 °C. When heated, the amorphous PET crystallizes in the range ^ 95 to 145 °C. In general, the higher the chain orientation in the amorphous state, the lower the crystallization temperature is during a

Figure 6.2.1

Unit cell of polyethylene terephthalate

heating experiment. The melting peak of PET occurs at about 250 0 C. When the PET is annealed at temperatures between the melting and cold crystallization temperatures additional endothermic peaks are observed as a result of melting and recrystallization of preexisting imperfect crystals to higher perfection and/or larger sized crystals. This peak typically is observed about 10 to 20 0 C above that of annealing.

6.2.3

PET Film Technology

Various processes have been developed to produce uni- and biaxially stretched PET films [7 to 27]. A typical process involves the following stages: 1. 2. 3. 4.

extrusion of PET through a coat-hanger die; quenching stage; deformation stage(s); post-treatment stage(s).

In early processes the quenching of extruded molten sheets was carried out by immersing the sheet into a water bath. However, the films so produced left surface defects caused by local boiling of water. The water was then replaced by a 80% glycerol and 20% water mixture which resulted in good quality films. Later generation processes used chilled rollers (15 to 180C surface temperature) for quenching. In a process by Chren and Hofrichter [12] an additional localized stream or jet of inert gas is directed on the top surface of molten film at each side edge where the film first contacts the surface of the quenching drum. After the quenching stage, the films with negligible crystallinities are heated above Tg using blower heaters or, in later generations, using quartz heaters. In this stage the thermal operation window is 80 to 1200C and usually the temperature is kept between 80 and 1000C. The sheet that was softened is then stretched uniaxially, sequentially biaxially, or simultaneously biaxially, depending on the end use applications. Knox's [17] design provided simple uniaxial stretching of PET films with various roll systems. The later patent by Alles [8] also describes a uniaxial stretching system with roller assembly that includes slow rollers, idler rollers, and fast rollers. Grabenstein [28] describes a process to produce heat shrinkable PET films. These types of films are extensively used for wrapping articles of various shapes by enclosing an article within a heat shrinkable film, sealing the article, and subjecting the package to elevated temperatures. In the process for producing heat shrinkable sheets, the stretching of the film to 2X at temperatures ranging from 800C to 135°C occurs, permitting the film to cool to room temperature under tension. The film produced this way shrinks ~ 35% in TD and ~ 15% in MD above 80 0 C. Films for magnetic recording are produced by stretching in one direction from about 1.5X to 2X at temperatures of 180 to 200 0 C and heat setting at 190 to 200 0 C under tension such that no shrinkage is permitted [11, 29]. One of the earliest patents that describes sequential stretching is by Alles [7]. The softened sheets are either stretched widthwise and in later stages lengthwise or in the reverse procedure. He suggests that the temperature in the second stage should be at least the same as that used in the first stage or it can be 5 to 30 0 C higher but it should not exceed 1200C, at which thermally activated crystallization becomes appreciable. In a PET film processing for photographic applications [10, 19], first widthwise stretching occurs then lengthwise stretching takes place. After heat setting at about 190 to 200 0 C the film is coated with a colloid solution, that is, vinylidene chloride. The first mention of continuous simultaneously biaxial stretching of PET films was made by Alles [7] and later by Koppehele [18]. The apparatus is a tentering frame and edges of the extruded film were thicker than the rest of the film so that they could be gripped securely by

the tentering frame. Jones [16] described a process for preparing oriented PET film with a deglossed, writable surface. In this process, initially an amorphous film is stretched at 1120C for 4 x 4 . This produces a glossed surface. The same result could be obtained by stretching the film to 2 x 2, cooling it down to room temperature, and reheating and restretching to obtain gloss.

6.2.4

Stress-Induced Crystallization

Crystallization in polymers can take place in various ways. One is thermal induced crystallization in which a polymer is crystallized between the glass transition temperature and melting temperature, either by heating from the initially amorphous state or cooling from the melt. In the second, the polymer chains are subjected to stress fields to produce crystallization at conditions under which the thermal crystallization rate is not appreciable. The term "strain-induced crystallization" is often used in the literature to describe the phenomenon. However, it has been pointed out by Thompson [30] and Spruiell et al. [31] that at low stresses simple flow of structure without appreciable crystallization is observed; however, above a critical stress, crystallization occurs. So the key parameter in the study of flow-induced crystallization in bulk polymers appears to be the magnitude of the effective stresses acting upon the molecules. Therefore, the term "stress-induced crystallization" is more appropriate to represent the phenomenon, particularly in those polymers in which no crosslinks exist. Various theories have been developed to describe the stress-induced crystallization of deformed polymers. A thermodynamic approach was first described by Flory [32] followed by a number of other researchers [33 to 38]. In these studies the observed changes in melting point and crystallization rate were correlated to the orientation functions and applied stress. General conclusions from the studies of the above authors are that stress enhances the rates of crystallization and stress-induced crystallization shows wide deviations from Avrami kinetics [39] which had been successfully applied to many polymer systems that are crystallized under quiescent conditions [40 to 42].

6.2.5

Development of Structure with Deformation

Deformation causes changes throughout the hierarchy of the structure in polymers. The type and extent of changes that occur depends on a variety of properties and process conditions. Some of these are molecular weight, initial state of the polymer, deformation temperature, mode (uniaxial, biaxial, simultaneous, sequential) and rate and extent of deformation. As a result of these changes a variety of properties are influenced, including orientation distribution, crystallinity, thermal properties, optical properties, gas diffusion characteristics, and mechanical properties and their anisotropy. In the following paragraphs, we examine some of these effects.

6.2.5.1

Stretching of PET below Tg

The stretching of initially amorphous PET below its glass transition temperature results in poorly ordered what may be called highly paracrystalline structure [31]. It was postulated both by Heffelfinger and Burton [43] and Spruiell et al. [31] that stretching induces rather imperfect extended chain crystals that can later serve as a site for further thermal crystallization that likely occurs in chain-folded morphology. Under these deformation conditions there have been observations of poorly ordered spherulitelike structure under cross polarizers in films stretched uniaxially at 25 0 C by Desai and Wilkes [44], This was attributed to the local heating effects as a result of plastic deformation in the neck regions. It was experimentally observed that the temperature at the neck regions increases substantially during deformation [45]. This spherulitelike structure was also substantiated by small-angle light scattering which showed a four leaf clover pattern. As has been observed in many other polymers, stretching PET below Tg also gives rise to void formations in the structure [46]. When the extent of these void formations becomes significant and their sizes reach a size range comparable to the wavelength of visible light, the appearance of the PET films turns "pearly" as a result of scattering effects. This is a common observation in the processing of PET, particularly in the stretch blow molded bottles where too low a stretching temperature easily causes such appearance.

6.2.5.2

Stretching of PET above Tg

Above r g , the molecules have higher mobility and if the stretch rates are low, they relax as fast as they are oriented, resulting in little internal stress and thus orientation and crystallization. Above r g and below temperatures at which the thermal crystallization rate is low (i.e., < 1000C), the temperature effect and stretch effect are counter-competing factors at a given temperature [31]. If the rate of stretch is high, molecular orientation and as a result crystallization can take place as compared to low strain rates at which relaxation causes disorientation and inhibits crystallization. Dumbleton [52] studied the stretching of amorphous spun PET fibers. He suggested the following mechanism. As the amorphous fiber is stretched, the orientation of amorphous regions increases to a point at which crystallization starts to occur ( = 2.5X). Thereafter, the orientation of the amorphous regions remains constant because any material that orients past the threshold will crystallize. The orientations of crystalline regions were found to be not much greater than that of the amorphous regions.

6.2.5.3

Deformation Behavior of PET in the Rubbery Region and Its Relationship to Thickness Uniformity

The requirements for surface roughness in manufactured films vary depending on the applications. Films for magnetic recording media or capacitors need to have surface roughness in certain ranges [53 to 58] whereas polymer paper [59] or films for adhesion need to have quite rough surfaces. In the case of dish membrane solar collectors [60 to 63]

STRESS

smooth surfaces and better thickness uniformity are needed to improve the optical performance of the films. As indicated earlier, in the film processing the cast amorphous PET is brought to temperatures between its glass transition (67 to 75 0C) and cold crystallization temperatures (135 to 1450C). This processing temperature is typically in the mid range (85 to 1000C) between the latter two temperatures. In this range, the stress-strain behavior of the PET resembles that of a crosslinked rubber. That is, the stress-strain curve shows a rise in stress and reaches a steady plastic deformation at intermediate deformations. Above a critical value called the onset of stress hardening (sometimes called strain hardening), stress rapidly rises and when a critical stress is passed, fracture occurs [64]. Below the glass transition temperature, the initial deformation is accompanied by a highly localized yielding that manifests as a highly localized neck or a series of necks (see Fig. 6.2.2). The critical strain at the onset of strain hardening depends on several factors. These are molecular weight, processing temperature, and rate of stretching. It decreases with increase of molecular weight, decrease of deformation temperature, and increase of stretching speed. As indicated earlier the stress-strain behavior of amorphous PET resembles that of a crosslinked rubber. There are, however, mechanistic differences. In the case of crosslinked rubber this deformation takes place affinely, that is, the whole body of the part being stretched "feels" the same level of deformation all the way to its smallest molecule, whereas in the case of PET microscopic deformation is slightly different. This is illustrated in Fig. 6.2.3. As demonstrated schematically in Fig. 6.2.3, initial cast films possess certain levels of thickness nonuniformities (Case 1) coming from the casting process. As the stress is applied at the edge(s) of the film for uniaxial and biaxial deformation stress concentrations occur in the thin regions and only those regions experience stress hardening and related crystallization at the intermediate "macro" strain values (Case II). In this condition other regions remain thicker and in fact the thickness uniformity as measured by the standard deviation of thickness profile worsens. Because the thinned and stress crystallized regions (regions A in Case II) can sustain heavier loads, the deformation is transferred to other regions (regions B in Case II) and this continues until the whole film experiences the strain hardening and resulting "self leveling" effect. Once the strain hardening has progressed sufficiently the thickness uniformity begins to improve and eventually surpasses that of the initial film as schematically

T
Figure 6.2.2 Stress-strain curves for PET stretched at different temperatures

STRAIN

STRESS HARDENING

BAD

STRESS

Tg
III.

I.

THICKNESS UNIFORMITY

A II. B

A B

B STRKS HARDENING

PLASTIC DEFORMATION

GOOD

STRAIN Figure 6.2.3

Chemical structures of various high-temperature polymers

shown in Fig. 6.2.3. This has been observed in uniaxial, equal biaxial, and unequal biaxial stretching experiments in PET [65] and polyetheretherketone (PEEK) [66].

6.2.5.4

Structure and Morphology Developed by Biaxial Stretching of PET

Most other engineering thermoplastics such as polybutylene terephthalate, polyethylene naphthalate, poly /?-phenylene sulfide (PPS) and polyaryl ether ketone contain para-linked highly planar aromatic groups such as phenyl and naphthyl groups. Most of these groups (with the exception of PPS and PEEK) are linked together with highly flexible groups such that these molecules resemble flat circular boards connected with flexible strings (see Fig. 6.2.4). This unique characteristic gives rise to subsequent orientation behavior during deformation. When the stretching occurs the initially randomly oriented chains orient along the stretching direction. This is particularly true for PET and polyethylene naphthalate (PEN). While the chain axes orient along the stretching direction the platelike phenyl (PET) [69] groups or naphthyl (PEN) [67] groups were observed to become parallel to the broad surfaces of the films. This orientation behavior is manifested in optical properties as well. Yoshihara et al. [68] determined intrinsic refractive indices along the chain axis, normal to phenyl planes and in a direction normal to the latter two directions to be 1.8054, 1.3688, and 1.7728, respectively. In a PET chain in a crystalline state, the lowest refractive index is in the direction normal to the phenyl planes. As shown in Fig. 6.2.5, the refractive indices of the biaxially stretched films decrease in the normal direction (ND) regardless of stretching mode and it depends mostly on areal expansion ratio (product of the stretch ratios in the MD and TD). This can also be viewed as the inverse of the normal direction stretch ratio. Clearly the increase of TD stretch ratio causes an increase of TD refractive index and decrease of MD refractive index while the ND refractive index decreases [69]. This gives us the ability to evaluate the overall orientation behavior of the chain axes as well as the axes of plane normals of the phenyl groups from the principal refractive indices [see Figs. 6.2.5(a) and 6.2.5(b)].

n

POLYETHYLENE TEREPHTHALATE

POLY ETHYLENE NAPHTHALATE

n

S n

POLY P-PHENYLENE SULFIDE

O C

O n

m

POLY ARYL ( N-ETHER, M-KETONE) Figure 6.2.4

Chemical structures of various high-temperature polymers

These results are also confirmed by the WAXS pole figure analysis of the stretched and annealed films as shown in Figs. 6.2.6 and 6.2.7 [70] for simultaneously stretched films. Later Gohil [71] found similar results on sequentially stretched PET films. (100) planes which are roughly parallel to the phenyl planes rapidly orient parallel to the surface of the films and this registry improves with annealing. As indicated by the pole distribution of the (— 105) planes (these planes are roughly normal to the chain axis of the PET) the polymer chains are oriented along the direction along which the largest deformation has taken place. When the transverse stretch ratio increases, the chain axes are reoriented in the film plane towards the TD. When the equal biaxial condition is attained, the chain axes are oriented in the plane of the film but rather randomly. This is characteristic of the PET even in sequential biaxial conditions. PEN, on the other hand, behaves somewhat differently. The calculated intrinsic refractive indices for the PEN are nc= 1.808 (chain axis), Wn= 1.369 (normal to naphthalene plane), and nt = 1.908 (normal to latter two axes) [72]. The orientation of naphthalene planes occurs quite rapidly on stretching. This generally results in formation of multiple necks throughout the sample [73].

N

800C N TD ANNEALED N MD

NND

A M *A T Figure 6.2.5(a) Principal refractive indices as a function of areal expansion ratio (IMD stretched at 80 0 C and annealed at 150 0 C for lOmin

X

^TD)- Films

The behavior described above resembles very much isotropic to nematiclike ordering that takes place as a result of deformation. The preferential orientation of flexibly linked flat molecules parallel to one another occurs to reduce the interchain frictional resistance. In the case of polyethylene naphthalate this occurs so abruptly that it manifests itself as a highly localized neck even at temperatures as high as 30 0 C above the glass transition temperature.

N

NMD NTD N

8 0 ^ UNANNEALED

ND

AM* AT Figure 6.2.5(b) Principal refractive indices as a function of areal expansion ratio (AMD X >^TD)- Unannealed films stretched at 8O0C

Other polymers such as PEEK, in which the phenyl groups are more rigidly connected to one another and their planes make about 38° with one another along the chain, also behave similarly showing their broad faces to the surface of the films when stretched biaxially [74]. In the case of PEEK, this direction happens to coincide with the a-axis in the unit cell. This preferential orientation of the phenyl groups is reflected in the optical properties. As discussed earlier the normal direction refractive indices rapidly decrease with areal expansion ratio as a result of the phenyl group preferential alignment in the plane of the film. The mean square cosine of the phenyl plane was correlated with the normalized parameter

n\-\ Ji2 + 2 n\ + 2 ' n1 - 1 This is shown in Fig. 6.2.8.

CONTOOR VALUES

2 x1

CONTOUR VALUES

2 x2 CONTOUR VALUES

3x1

CONTOUR VALUES

3x2

CCNTOUR VALUES

3x3

CONTOUR VALUES

3.5 x 1 Figure 6.2.6(a)

CONTOUR V A L U E S

3.5 x 2

WAXS polefigureson (100) planes of PETfilmsbiaxially stretched at 800C and annealed at 1500C

CONTOUR VALUES

CONTOUR VALUES

2X1

2x2 CONTOUR VALUES

CONTOUR VALUES

3x 1

3x3

CONTOUR V A L U E S

CONTOUR V A L U E S

3.5 X 1

3.5X2 (10 O) plane, Annealed, 800C

Figure 6.2.6(b)

WAXS polefigureson (- 105) planes of PETfilmsbiaxially stretched at 8O 0 C and annealed at 15O0C

hvi D

^•MD

C-axis Benzene Ring

fTD

Figure 6.2.7(a) White-Spruiell biaxial orientation factors of oaxes and axes normal to the benzene ring on films stretched at 800C

Matsumoto et al. [75] found that by progressive stretching of PET film in a second stretching direction [MD(2)], the degree of planar orientation of (100) planes increases whereas oaxis orientation along MD(I) decreases and this oaxis orientation passes through the state of random orientation in the film plane and then increases along MD(2) to approach uniplanar axial orientation.

6.2.5.5

Annealing Effects on PET

The subjects of interest in crystallization of oriented polymers are the mechanisms of transition from oriented amorphous to oriented crystalline state, the consequent morphological changes, and structure-property relationships.

'MD ^•MD

C-axis Benzene Ring

fro

Figure 6.2.7(b) White-Spruiell biaxial orientation factors of c-axes and axes normal to the benzene ring on films stretched at 8O0C and annealed at 150deg;C for lOmin

The crystallites created by SIC act as nuclei for additional thermal crystallization in subsequent stage(s) of film production [31]. This nucleating effect and resulting orientation after annealing both decrease with strain rate imparted on samples during SIC. It appears that crystallization of a stretched amorphous network is a selective process in which crystals are nucleated by more highly oriented amorphous chains [38]. The increase of orientation of the amorphous phase promotes substantial increases in the subsequent thermal crystallization rate (during heat setting) [76]. This effect, in turn, depends on the crystallization temperature. The higher the temperature, the stronger the effect of orientation. The nucleation and initial growth of crystals is a very fast process in oriented PET, occurring at times as much as a decade faster than in those which are unoriented [39]. Furthermore, the crystallization rate depends on whether the sample is free annealed or fixed annealed. The rates of crystallization in constrained annealed samples were found to be much greater than those that are free annealed [31] presumably as a result of maintaining high levels of chain orientation with close registry with one another.

"W"3

/ ±L

2+2

/

IT2-,

80°C UNANNEALED 80°C ANNEALED 100°C UNANNEALEC 10O0CANNEALED

Y= 1.0954 - 0.3449X Regr: 0.95

COS^ of the normals of the benzene planes on films with a variety of thermal-deformation histories

6.2.5.6

Crystallinity and Thermal Properties

When the polymer chains are oriented, they come in close registry with one another, leading to the formation of a crystalline lattice. However, this behavior was found to depend on the mode of deformation as illustrated in Fig. 6.2.9. If the film is stretched uniaxially, density increases in accordance with increase of crystallinity. However, the situation becomes more complex in the biaxial mode. As shown in Fig. 6.2.9(a,b), (AMD > ATD) the density decreases apparently as a result of reduction in packing efficiency of the chains in the crystalline lattice. This disruptive effect is reversed with an increase of ATD until the equal biaxial condition is achieved. When the processing temperature is increased, the latter effect of reduction in crystallinity with the TD stretch lessens and moves to the curves with higher MD stretch ratios. One consequence of these orientation effects can be observed in the thermal behavior of the stretched films (Fig. 6.2.10). As a result of increased crystallinity, the area under the cold crystallization peak in the differential scanning calorimeter decreases and this peak moves to lower temperatures as the oriented chains require less energy to crystallize because of the reduction in their entropy. The phenomena described above give a clear indication of the formation of structure as a result of orientation of chains in preferential directions. The temperatures at which this structural densification (crystallization) occurs are not conducive to the practical thermally activated crystallization. In the 80 to 1000C range, PET exhibits half-times for thermally activated crystallization in hundreds of seconds. So a distinction must be made as to the effects of deformation. These structural changes accompanying orientation are called stressinduced crystallization. Let us examine the particulars of the SIC.

Density (g/cm3)

Crystallinity (%)

Figure 6.2.9(a) Density as a function of biaxial deformation history on simultaneous biaxially stretched PET (processing temperature 8O0C)

6.2.5.7

Conformational Changes Due to Drawing and Annealing

The ethylene glycol linkage in PET chains exists in two rotational isomeric forms: a trans or extended form and a gauche or relaxed form. The trans conformation can be produced by a partial rotation about the carbon-carbon bonds [77]. In unoriented amorphous regions 13% of all ethylene glycol segments were found to be in a trans conformation. The gauche [78] form in the amorphous regions changes into the trans form upon crystallization and the trans form is the only form that exists in crystalline regions. However, the trans form also coexists with the gauche form in the amorphous regions [79]. When the film is stretched at 80 0 C, the trans concentration linearly increased with draw ratio up to 3.5X (which is beyond the onset of strain hardening), and above this value it levels off [80]. Huchinson et al. [81] suggested the following mechanisms. Up to the yield point the elastic strains are concentrated in the glycol linkage, leading to frequency shifts in the bands associated with trans and gauche

Density (g/cm3)

Crystallinity (%)

Figure 6.2.9(b) Density as a function of biaxial deformation history on simultaneous biaxially stretched PET (processing temperature 100 0 C)

conformers and orientation of these parts of the chains. Above the yield point, both stress and this local orientation decrease because the conformational changes can take place to allow the overall network structure to rearrange. After this, networks achieve higher orientation. On stretching the semicrystalline PET, the first region to be stressed is located between the crystalline regions [82]. Then the stresses are transmitted to crystalline regions. Although the conformational changes occur in response to external stresses, the number of taut tie molecules also increases while the amount of folded chains decreases. An increase of deformation temperature causes a slight decrease in the number of these taut tie molecules [83, 84]. Koenig and Cornell [85] studied the effects of drawing and molecular weight on the structure of biaxially stretched films. They also found the stretching causes the same amount of gauche to trans transformation in both low and high molecular weight samples. This

ENDO>

100C, Unannealed Scan rate, 20.00 deg/min

Temperature (K) Figure 6.2.10 DSC scans on PET films stretched at 1000C under a variety of biaxial stretching conditions

indicated that the amorphous regions in low molecular weight samples contain more trans ethylene glycol linkages because crystallinity is higher in high molecular weight samples and all linkages are in trans form in crystalline regions. In sequentially stretched films the amorphous trans content increases as a result of second stretch [50]. This gauche-trans transformation was also observed in the homologues of PET, namely polybutylene terephthalate. Jakeway et al. and Yokouchi et al. found that the conformation of glycol lineage in polybutylene terephthalate chains changes from gauche-trans-gauche sequence in the unstressed state to &\\-trans sequence under stress [86 to 88].

6.2.5.8

Small-Angle X-Ray Studies (SAXS) on Stretched and Annealed PET

SAXS studies have been performed on unoriented, crystallized [89], and uniaxially and biaxially stretched films [90 to 93]. Qualitatively the PET fibers and films show two-point [90] and four-point [90, 91, 94] patterns and equatorial streaks, depending on the deformation levels, annealing conditions, and relative orientation of the incident X-ray beam with respect to the sample. Bonart [94] interpreted the structure of uniaxially drawn and annealed PET as a chessboard array of crystalline/amorphous regions to account for quadrant scattering. Heffelfinger and Lipport's [90] studies indicated the four-point SAXS pattern transforms the two-point pattern with strain relaxation of uniaxially deformed films. Increase of strain was shown to reverse this transformation. Yeh and Geil [95] suggest that the four-point pattern is related to staggered arrangements of spherically shaped paracrystalline domains that were originally present in the unoriented amorphous PET. Statton and Goddard [91] also suggested a model structure for uniaxially deformed PET films. Their model consists of parallel platelets stacked one upon another. They also suggest that within each sheet the individual crystallites are oriented in a chessboard array in an amorphous matrix. Fakirov and Fischer's [4] experiments demonstrated that the appearance of a structure responsible for four-point diagrams is correlated with the macroscopic shape of the sample. They concluded that the four-point pattern is caused by staggering of the molecules along the (100) planes. In a sample with rectangular cross-section, a preferred orientation of these planes parallel to the broader surface takes place during stretching. In samples with circular cross-section (fibers), however, a random orientation about the fiber axis is observed and no largely extended crystalline layer with staggered conformation can be developed. PET films stretched uniaxially or biaxially show center streak scattering when viewed through the transverse direction or through the end (along the machine direction). It was found that this scattering develops at relatively early stages of deformation and is independent of the amount of crystallinity and type of orientation, but dependent on the temperature/tension history of the sample. Statton and Goddard [91] attributed this streak scattering to the presence of microvoids or regions of low electron density in the samples. Heffelfinger and Lippert's results suggest that the shape of center streak scattering is related to differing electron densities of large platelet shaped domains oriented essentially parallel to the surface of the film. This structural interpretation seems to be common among researchers [91, 94, 96]. The platelet formation may be the precursor of the appearance of pearlescence which was observed in low-temperature blown

stretch blow-molded bottles [97]. The low pearlescence in bottles was attributed to void formation. One of the few quantitative SAXS studies performed on PET was carried out on fibers by Fischer and Fakirov [92]. Their results showed that effective densities in amorphous and crystalline regions are no longer material constants but change as a function of thermal and deformation history of the samples. They suggested that the difference between effective density pc and "X-ray density" pc, of the crystalline layers in caused by the lattice vacancies in the boundaries of mosaic blocks. Eisner et al. [93] studied the change of SAXS patterns during the crystallization of preoriented PET fibers using synchrotron radiation with a vidicon camera. Their results indicate a decrease of azimuthal half-width of SAXS peaks and long periods with crystallization time. Fischer and Fakirov [92] and others [95, 98] observed an increase of long spacing of drawn and annealed PET with annealing temperature. It was determined that an increase in regular chain folding as well as decrease in strength occurs when oriented films are annealed. It was then speculated that loss in strength resulted from an increased number of folds [99, 100]. SAXS pole figures on uni- and biaxially stretched and subsequently fixed annealed PET films were done by Cakmak et al. [101], who showed that the shapes of the intensity contours in SAXS patterns taken in identical directions in unannealed and annealed films with the same deformation histories are similar. This suggests that the fixed annealing does not cause a major reorganization of the structure, but it merely perfects the structures developed primarily by stress-induced crystallization. The four-point pattern developed in the SAXS patterns (Fig. 6.2.1 la,b) together with the WAXS analysis suggested that the reason for the formation of the four-point pattern is the formation of staggered crystallite formation in the solid state because the phenyl planes become parallel to the surface of the films with deformation. The angle a remains essentially constant and this is related to the apex angle of the unit cell of the PET as shown in the models in Fig. 6.2.12a-c.

6.2.6

Dynamic and Static Mechanical Properties

The films deformed in two mutually perpendicular directions exhibit orthorhombic symmetry. This implies that the macro properties such as modulus, elongation to break, tensile strength, etc., are expected to show anisotropic behavior in the film plane. Thus, the researchers who study the orientation and mechanical behavior of films generally report these properties obtained in several directions in the film plane. Some of these experiments employed are creep [102], dynamic mechanical (low frequency) [52, 103, 104], ultrasonic (high frequency) [105, 106], and static tensile tests [107 to 115].

6.2.6.1

Dynamic Mechanical Properties

Illers and Breuer [116] studied the dynamic mechanical properties of unoriented PET films of different crystallinities. It was found that the position of the fi relaxation peak that is

MD

TD

,MD 1MD

TD

ND

UNANNEALED

Figure 6.2.1 l(a) SAXS patterns of PET films stretched to various stretch ratios: First column shows pattern taken with the beam along ND; third column shows pattern taken with the beam along TD; fourth column shows the pattern taken with beam along MD

MD

TD

MD ND

TD

ND

ANNEALED

Figure 6.2.11 (b) SAXS patterns of PET films stretched to various stretch ratios and annealed at 15O0C; first column shows pattern taken with the beam along ND; third column shows pattern taken with the beam along TD; fourth column show the pattern taken with beam along MD

UNIAXIAL FREE WIDTH

MD

TD Low Stretch Ratio

MD

TD High Stretch Ratio STRUCTURE Figure 6.2.12(a) samples

SAXS PATTERN

Structural models developed based on the SAXS and WAXS patterns: Uniaxial free width

associated with the glass transition moved to higher temperatures for crystallinities up to 30%; at higher crystallinities the transition moved to lower temperatures. Illers and Breuer attributed this behavior to the effect of crystal size on amorphous regions. At low crystallinities, there would be many small crystallites that would act like crosslinks and inhibit the motion of segments in the amorphous regions whereas at higher crystallinities, the crystallites would be larger and fewer in number and consequently would allow the segments in the amorphous regions more freedom. Dumbleton et al. [52] have shown that drawn crystalline fibers exhibit a shift in the position of transition to lower temperatures. Relaxation moduli of uniaxially [104] and biaxially stretched films [117 to 120] have been measured as a function of stress, time, and temperature. In uniaxially stretched films Murayama et al. [104] found that at constant crystallinity the effect of orientation is to increase the magnitude of modulus without changing its time dependence and to decrease the temperature dependence of the modulus. Fakirov and Stahl [121] reported that the dynamic modulus for drawn PET decreases with increase of annealing temperature. Studies on stress relaxation of biaxially stretched films [117 to 120] suggest that increased uniplanar orientation causes a reduction of both the magnitude and rate of stress relaxation. Time- and temperature-dependent relaxation of

UNIAXIAL CONSTANT WIDTH

MD TD Through Thickness

ND MD Edge View Figure 6.2.12(b) width samples

Structural models developed based on the SAXS and WAXS patterns: Uniaxial constant

ordered noncrystalline regions in PET films has been considered to be the major cause of shrinkage of films [122]. Linear thermal expansion coefficients of biaxially stretched films were also determined by Blumentritt [122]. He found that a minimum coefficient of thermal expansion was observed along the principal orientation direction and a maximum was found perpendicular to the latter direction.

6.2.6.2

Static Mechanical Properties

In undrawn amorphous films, self-oscillation of necking (serration) was observed during testing [121]. This gives rise to serrated stress-strain curves. These serrations occur alternately with opaque bands accompanied by voids and transparent bands in necking during cold drawing. They observed that faster rates resulted in smaller transparent band fractions. This behaviour was attributed to heat dissipation during necking corresponding to local temperature jumps and periodic strong variation of modulus of elasticity due to poor heat conductivity of the polymer. In a recent article, Tant and Wilkes [123] showed that physical aging of PET significantly affects the mechanical behavior of PET. They found that the extent of localized necking and associated strain-induced crystallization was greater for samples aged for longer periods of time. The studies of Biangardi and Zachman [115] showed

MD

TD

MD

ND

Figure 6.2.12(c) samples

Structural models developed based on the SAXS and WAXS patterns: Unequal biaxial

MD

TD

Figure 6.2.12(d) samples

Structural models developed based on the SAXS and WAXS patterns: Equal biaxial

that improvement of mechanical properties with stretching is caused not only by the increasing orientation of molecules but also increasing amount of taut tie molecules.

6.2.6.3

Uniaxial (Constant Width) Stretched Films

The studies of Matsumoto et al. [125] on PET indicate that the anisotropy of mechanical properties of the films uniaxially unconstrained stretched is greater than that of films stretched under constant width at the same stretch ratio in the machine direction. Some for the in-plane anisotropy data on the uniaxially constant width stretched films are shown in Fig. 6.2.13 a,b,c [124].

MODULUS MD GPa Undrawn

80°C

TD

Figure 6.2.13(a)

In-plane modulus anisotropy in uniaxial constant width stretched PET

As expected from the chain orientation behavior, the largest increases of modulus is observed in the machine direction and in the transverse direction it remains roughly the same as that of the original film. Tensile strength data also show similar behavior, although some losses as a result of deformation are observed in the transverse direction. The most interesting behavior is observed in the elongation to break data. With deformation, the largest decrease of this value is observed in the machine direction while in the transverse direction it actually increases to a value larger than that of the original unstretched film. At high deformation ratios is also decreases.

ELONGATION TO BREAK Undrawn MD 800C

TD

Figure 6.2.13(b)

6.2.6.4

In-plane elongation to break anisotropy in uniaxial constant width stretched PET

One-Step (Simultaneous) Biaxially Stretched Film

For PET, it was found [124, 125] that irrespective of stretch ratio, the mechanical properties are equal to both AMD(1) a n d ^MD(2) indicating a planar isotropy in these films. This behavior is shown in Fig. 6.2.14a,b,c [124].

6.2.6.5

Two-Step Biaxially Stretched Films

The extent of the anisotropy of mechanical properties for the sequential biaxial PET [125] films is larger in the first stretching direction than in the second stretching direction before the balanced point (/IMD(1) X >^MD(2)) of mechanical properties is obtained. Then the anisotropy is

TENSILE

STRENGTH MD XIO7Pa

80°C

TD

Figure 6.2.13(c)

In-plane tensile strength anisotropy in uniaxial constant width stretched PET

reversed after the balance point (AMD(I) X ^MD(2))- However, it was observed that the balance points for modulus, tensile strength and elongation to break do not occur at the point where the two stretch ratios in MD(I) first machine direction equal that of the second machine direction , MD(2). This occurs at points where AMD(2) is a little less than AMD(I> Thus, Matsumoto et al. [125] noted that it is hard to obtain films with "all" the mechanical properties in a balanced state by two step biaxial deformation.

MODULUS

SB

Undrawn MD

XiO9Pa

80°C

MD

Figure 6.2.14(a)

6.2.6.6

In-plane modulus anisotropy in equal biaxially stretched PET

Long-Term Creep Behavior

The key structural parameters, crystallinity and the level and type of orientation distribution imposed by the stretching process, have significant influence on the tensile creep behavior and its anisotropy in PET films at temperatures below the glass transition temperature. Increase of crystallinity and increase of chain orientation in a given testing direction invariably cause a rapid reduction in creep strain values. These are demonstrated in Fig. 6.2.15 [126]. The unoriented films with different crystallinities subjected to long-term creep show minimal difference at short testing times and films with higher crystallinity exhibit lower creep strains. The main influence of crystallinity on the creep behavior becomes apparent at high creep times. The samples with higher crystallinities exhibit lower creep strains at all times. The effect of biaxial orientation on the creep strains is demonstrated in Fig. 6.2.16. Biaxial orientation significantly reduces the slope of the long-term creep behavior. This is as a result of a combination of increase of crystallinity which densities the film structure

ELONGATION TO BREAK MD Undrawn

SB

80°C

MD

Figure 6.2.14(b)

In-plane elongation to break anisotropy in equal biaxially stretched PET

and the preferential orientation of the polymer chains, thereby reducing the slower creep process even below the glass transition temperature also.

6.2.7

Other Properties of Interest

6.2.7.1

Gas Permeability Characteristics and Morphology

The preferential orientation of the phenyl planes was found to correlate with the oxygen barrier behavior of biaxially stretched films. Gohil [127] used an orientation index called

MDxIO8Pa

800C

MD

Figure 6.2.14(c)

In-plane tensile strength anisotropy in equal biaxially stretched PET

PROF that was determined from principal refractive indices to describe the orientation behavior of phenyl planes and found a good correlation between this parameter and oxygen permeability as shown in Fig. 6.2.17. In addition he found that in sequential biaxial stretching the oxygen permeability decreases rapidly upon first stretching and on stretching in the second stretching permeability was found to increase slightly, indicating that a structural "opening-up" occurs and with a further increase of stretch ratios, the permeability values decrease (Fig. 6.2.18). Perkins [128] found that annealing decreases the oxygen permeability and annealing the PET films at 1800C produces the least permeability. At this temperature PET shows the fastest crystallization. Annealing above this temperature always causes melting and recrystallization which presumably reduces the orientation gained in stretching. On the other hand, annealing below this temperature causes crystallization which follows a certain amount of orientation relaxation as was found by Venkatesvaran and Cakmak [129] with an online twocolor laser measurement system. At the fastest crystallization temperature, the oriented structure is better preserved, leading to a more tortuous structure in the films which prevents the passage of the small gas molecules.

CREEP STRAIN

CREEP TEST: 5OC, 13.78 MPa UNANNEALED( 7.7%) ANN. 1 MIN.(20%) ANN. 2 MIN.(30%) ANN. 12 HRS.(37%)

TIME(sec) Figure 6.2.15 parentheses)

Long-term creep behavior of unoriented PET samples with varying crystallinities (shown in

CREEP STRAIN

CREEP TEST: 4OC, 13.78 MPa PET 1x1 PET 2X2(STRETCHING: 80 C) PET 3x3

TIME(sec) Figure 6.2.16

Long-term creep behavior of biaxially oriented PET samples (unannealed)

PERMEABILITY(cc-mil/100in2.24h-atm)

UNORIENTED CRYSTALLINE UNIAXIAL SIM. UNANNEALED SEQ. ANNEALED AT 170C SEQ.ANNEALED AT 200C SEQ. UNANNEALED

PROF(%) Figure 6.2.17 Permeability versus PROF(%) parameter on PET films of varying thermal-deformation histories (From ref. [127]) UNANNEALED

PERMEABILITY(cc-mil/100in2.24h-atm)

UNNEALED AT 200C ANNELAED AT 170 C

DRAW RATIO IN TRANSVERSE DIRECTION Figure 6.2.18

Permeability versus transverse stretch ratio in PET films (From ref. [126])

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53.

Yamashita, Y, J. Polym. ScL (1965) A3, p. 81 Geil RH., Polymer Single Crystals (1973) Krieger, Huntington, New York p. 289 Daubeny, R. de P., Bunn, C.W., Brown, CJ. Proc. R. Soc. (1955) A226, p. 531 Fakirov, S., Fischer, E.W., Schmidt, G.F, Die Makromol. Chem. (1975) 176, p. 2459 Zahn, H., Krzikalla, R., Die Makromol. Chem. (1957) 23, p. 31 Kilian, H.G., Halboth, H., Jenkel, E., Kolloid Z. Z. Polym. (1960) 172, p. 166 Alles, F.P., U.S. Patent 2,627,088 (Feb. 3, 1953) Alles, FR, U.S. Patent 2,728,941 (Jan. 3, 1956) Alles, FR, U.S. Patent 2,767,435 (Oct. 23, 1956) Alles, FR, U.S. Patent 2,779,684 (May 5, 1959) Alles, FR, U.S. Patent 2,884,663 (May 5, 1959) Chren, W.A., Hofrichter, C.H., U.S. Patent 2,736,066 (Feb. 28, 1956) Crooks, C.H., U.S. Patent 2,728,944 (Jan. 3, 1956) Heffelfinger, C.J., U.S. Patent 3,257,489 (June 21, 1966) Heffelfinger, C.J., U.S. Patent 3,432, 551 (Mar. 11, 1969) Jones, J.W., U.S. Patent 3,088,173 (May 7, 1963) Knox, K.L., U.S. Patent 2,718,666 (Sept. 27, 1955) Koppehele, H.R, U.S. Patent 3,055,048 (Sept. 25, 1962) Long, C.W., U.S. Patent 2,968,067 (Jan. 17, 1961) Miller, D.F, U.S. Patent 2,755,533 (July 24, 1956) Miller, M., U.S. Patent 2,920,352 (Jan. 12, 1960) O'Hanlon, A.F., Witherington, X, U.S. Patent 2,728,951 (Jan. 3, 1956) Peterson, A.K., U.S. Patent 2,759,217 (Aug. 21, 1956) Ryan, W.H., U.S. Patent 2,854,697 (Oct. 7, 1958) Tooke, W.R., Lodge, E.G., U.S. Patent 2,923,966 Winter, FR., U.S. Patent 2,995,779 (Aug. 15, 1961) Witherington, J., Crooks, C.H., U.S. Patent 3,107,139 (Oct. 15, 1963) Grabenstein, T.A., U.S. Patent 2,784,456 (Mar. 12, 1957) Heffelfinger, C.J., U.S. Patent 3,627,579 (Dec. 14, 1971) Thompson, A.B., J. Polym. Sci. (1959) 34, p. 741 Spruiell, J.E., McCord, D.E., Beuerlein, R.A., Trans. J. Rheol. (1972) 16, p. 535 Flory, RJ., J. Chem. Phys. (1947) 15, p. 397 Flory, P.J., J. Chem. Phys. (1947) 15, p. 397 Gent, A.N., J. Polym. ScL (1965) A3, p. 3787 Gent. A.N., J. Polym. ScL (1966) A2, p. 447 Kobayashi, K., Nagasawa, T., J. Macromol. ScL Phys. (1970) B4, p. 331 Ziabicki, A., Kolloid Z. Z. Polym. (1974) 252, p. 207 Krigbaum, W.R., Roe, R.J., J. Polym. ScL (1964) A2, p. 4391 Smith, FS., Steward, R.D., Polymer (1974) 15, p. 283 Avrami, M., J. Chem. Phys. (1939) 7, p. 1103 Avrami, M., J. Chem. Phys. (1940) 8, p. 212 Burns, T.R., Turnbull, D., J. Appl. Phys. (1966) 37, p. 4021 HerTelfinger, CX, Burton, R.L., J. Polym. ScL (1960) 47, p. 289 Desai, A.B., Wilkes, G.L., J. Polym. Sc. Lett. (1975) 13, p. 303 Miyake, A., J. Polym. ScL (1959) 38, p. 479 Yeh, G.S.Y., Geil, RH., J. Macromol. ScL Phys. (1967) B l , p. 251 Qian, R., Shen, X, Zhu, L., Macromol. Chem. Rapid Commun. (1981) 2, p. 499 Fischer, E.W., Z Naturforsch. (1957) 120, p. 753 Caddel, R.M., Raghava, R.S., Atkins, A.G., J. Mater. ScL (1973) 8, p. 1641 Heffelfinger, CX, Schmidt, RG., J. Appl. Polym. ScL (1965) 9, p. 2661 Heffelfinger, CX, U.S. Patent 3,627,579 (Dec. 14, 1971) Dumbleton, XH., Murayama, T., Bell, XR, Kolloid Z. Z. Polym. (1968) 228, p. 54 Kagiyama, T, Oguri, Y, Kunugihara, K., et al., European Patent 0 257 611 A2 (1987)

54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 100. 101. 102. 103. 104. 105. 106.

Kagiyama, T., Oguri, Y., Kunugihara, K., et al., European Patent 0 257 611 A2 (1987) Sakamoto, S., Sato, Y., European Patent 0 229 255 A2 (1986) Fujiyama, M., Kawamura, Y, Wakino, T., Okamoto, T., J. Appl. Polym. ScL (1988) 36, p. 985 Hobbs, S.Y., Pratt, C E , Polym. Eng. ScL (1982) 22, p. 594 Nakatani, M., Kakita, H., Nakatsui, H., Sato, H., Rep. Prog. Polym. Phys. Jpn. (1980) 23, p. 185 Tanaka, A., Nagano, H., Onogi, S., Rep. Prog. Polym. Phys. Jpn. (1982) 25, p. 365 Wilkins, E, Energy (1987) 12, p. 179 Gupta, B.P., Energy (1987) 12, p. 187 Schissel, P., Neidlinger, H.H., Czanderna, A.W., Energy (1987) 12 p. 197 Benson, B.A., Energy (1987) 12, p. 203 Heffelfinger, CJ., Polym. Eng. ScL (1978) 18, p. 1163 Iwakura, K., Wang, YD., Cakmak, M., Int. Polym. Process. (1992) 7, p. 327 Cakmak, M., Simhambhatla, M., Polym. Eng. Sd. (1995) 35, p. 1562 Cakmak, M., Wang, YD., Simhambhatla, M., Polym. Eng. ScL (1990) 30, p. 721 Yoshihara, N., Fukushima, A., Watanabe, Y, Nakai, A., Nomura, S., Kawai, H., Sen-i Gakkaishi (1981) 37, p. 10, T-387 Cakmak, M., White, J.L., Spruiell, J.E., Polym. Eng. ScL (1989) 29, p. 1534 Cakmak, M., White, XL., Spruiell, XE., J Polym. Eng. (1986) 6, p. 291 Gohil, R., J. Appl. Polym. ScL (1993) 48, p. 1649 Venkatesvaran, R.H., unpublished research Cakmak, M., Lee, S.W., Polymer (1995) 36, p. 4039 Cakmak, M., Simhambhatla, M., J. Appl. Polym. ScL (to be submitted) Matsumoto, K., Izumi, U., Imamura, R., Sen-i Gakkaishi (1972) 28, p. 179 Alfonso, G.C., Verndona, M.D., Wasaik, A., Polymer (1978) 19, p. 711 Schmidt, P.G., J. Polym. ScL (1963) 41, p. 1271 Miyake, A., J. Polym. ScL (1959) 38, p. 479 Farrow, G., Mclntosh, X, Ward, I.M., Makromol. Chem. (1960) 38, p. 147 Cunningham, A., Ward, LM., Willis, H.A., Zichy, V, Polymer (1974) 15, p. 749 Hutchinson, LX, Ward, I.M., Willis, H.A., Zichy, V, Polymer (1980) 21, p. 55 Sikka, S.S., Kausch. H.H., Coll. Polym. ScL (1979) 257, p. 1060 Zachman, H.G., Polym. Eng. ScL (1979) 19, p. 966 Prevorsek, D.C., Sibilia, XR, J. Macromol. ScL Phys. (1971) B5, p. 617 Koenig, XL., Cornell, S.W., J Macromol. ScL Phys. (1967) B l , p. 279 Jakeways, R., Ward, I.M., Wilding, M.A., Hall, I.H., Desborough, LX, Pass, M.G., J. Polym. ScL Polym. Phys. (1975) 13, p. 799 Jakeways, R., Smith, T., Ward, I.M., Wilding, M.A., J. Polym. ScL Polym. Lett. (1976) 14, p. 41 Yokouchi, M., Mori, X, Kobayashi, Y, J Appl Polym. ScL (1981) 26, p. 3435 Groeninckx, G., Raynears, H., Bergmans, H., Smets, G., J Polym. ScL Phys. (1980) 18, p. 1311 Heffelfinger, CX, Lippert, E.L., J Appl. Polym. ScL (1971) 15, p. 2655 Statton, WO., Goddard, C , J Appl. Phys. (1957) 28, p. 1111 Fischer, E.W., Fakirov, S., J. Mater. ScL (1976) 11, p. 1041 Eisner, G., Zachman, H.G., Milch, XR., Macromol. Chem. Rapid Commun. (1981) 182, p. 657 Bonart, R., Kolloid Z. Z. Polymer (1964) 199, p. 136 Yeh, G.S.Y, Geil, PH., J. Macromol. ScL Phys. (1967) B l , p. 251 Baker, W P , J. Polym. ScL (1962) 57, p. 993 Miller, B.H., SPEANTEC Tech. Papers (1980) p. 540 Statton, WO., J. Polym. ScL (1972) A2, p. 1587 Koenig, XL., Harmon, M.X, J. Polym. ScL (1969) A2, p. 667 Prevorsek, D.C., Sibilia, XP, J. Macromol. ScL Phys. (1971) B5, p. 617 Cakmak, M., Spruiell, XE., White. XL., Polym. Eng. ScL (1987) 27, p. 893 Buckley, C P , Gray, R.W, McCrum, N.G., J Polym. ScL Polym. Lett. (1970) 8, p. 341 Seferis, XC, McClough, R.L., Samuels, R.X, Polym. Eng. ScL (1976) 16, p. 334 Murayama, T., Dumbleton, XH., Williams, M.L., J. Polym. ScL (1968) A2, p. 787 Price, H.L., SPEJ. (1968) 24, p. 54 Rider, XG., Watkinson, K.M., Polymer (1978) 19, p. 645

107. 108. 109. 110. 111. 112. 113. 114. 115. 116. 117. 118. 119. 120. 121. 122. 123. 124. 125. 126. 127. 128. 129.

Marshall, L, Thompson, A.B., Proc. R. Soc. (Lond.) (1954) A211, p. 541 Matsumoto, K., Ishii, K., Kimura, W., Imamura, R., Sen-i Gakkaishi (1971) 27, p. 49 Uejo, H., Hoshino, S., J. Appl. Polym. ScL (1970) 14, p. 317 Matsumoto, K., Sato, K., Ishii, K., Imamura, R., Sen-i Gakkaishi (1970) 26, p. 537 Matsumoto, K., Izumi, Y., Imamura, R., Sen-i Gakkaishi (1972) 28, p. 179 Vadimsky, R.G., Keith, H.P., Padden, Jr., FJ., J. Polym. ScL (1969) A2, p. 1367 Ishai, O., Weller, T., Singer, J., J. Mater. ScL (1968) 3, p. 337 Sacher, E., Mod. Plast. (1976) 53, p. 58 Biangardi, HJ., Zachman, H.G., J. Polym. ScL Polym. Symp. (1977) 58, p. 169 Illers, K.H., Breuer, H., J. Coll. ScL (1963 )18, p. 1 Hawthorne, J.M., J. Appl. Polym. ScL (1981) 26, p. 3317 Ward, I.M., Polymer (1967) 5, p. 59 Pinnock, P.R., Ward, I.M., Polymer (1966) 7, p. 255 Takayanagi, M., Mem. Fac. Eng. (1963) 23, p. 41 Fakirov, S., Stahl, D., Die Ang. Macromol. Chem. (1982) 102, p. 117 Blumentritt, B.F., J. Appl. Polym. ScL (1979) 23, p. 3205 Tant, M.N., Wilkes, G.L., J. Appl. Polym. ScL (1981) 26, p. 2813 Cakmak, M., (unpublished data) Matsumoto, K., Izumi, Y., Imamura, R., Sen-i Gakkaishi (1972) 28, p. 179 Cakmak, M., Wang, YD., J. Appl. Polym. ScL (1990) 41, p. 1867 Gohil, R.M., J. Appl. Polym. ScL (1993) 48, p. 1649 Perkins, W, Polym. Bull. (1988) 19, p. 397 Venkatesvaran, H., Cakmak, M., SPEANTEC Tech. Papers (1993) 39, p. 257

6.3

Stretching Conditions, Orientation, and Physical Properties of Biaxially Oriented Film Kenji Tsunashima, Katsuya Toyoda, and Toshiya Yoshii

6.3.1 Introduction

321

6.3.2 Outline of the Film Making Process

322

6.3.3 Sequential (LD -> TD) Stretching 6.3.3.1 Casting 6.3.3.2 Longitudinal Stretching 6.3.3.3 Transverse Stretching 6.3.3.4 Heat Setting

324 324 324 327 327

6.3.4 General Properties of PET Film 6.3.4.1 Mechanical Properties 6.3.4.2 Thermal Properties 6.3.4.3 Optical Properties 6.3.4.4 Barrier Properties 6.3.4.5 Chemical Resistance 6.3.4.6 Electrical Properties

328 328 330 332 334 334 335

6.3.5 Quality Improvement of PET Films 6.3.5.1 Bowing 6.3.5.1.1 Mechanism of Bowing 6.3.5.1.2 Reduction of Bowing 6.3.5.2 Thermal Stability 6.3.5.3 Gauge Uniformity 6.3.5.4 Tensilized Film 6.3.5.5 To Make the Film Thinner 6.3.5.5.1 History of PET Film Thinning 6.3.5.5.2 Thinning Technology 6.3.5.5.3 Limit of Thinning

339 339 339 340 342 343 344 348 348 349 350

6.3.1

Introduction

Polyethylene terephthalate (PET) is manufactured by the polymerization of terephthalic acid and ethylene glycol, and has the following chemical structure: HO-CH 2 -CH 2 - [ 0 - O C H Q ^ CO-O-CH 2 -CH 2 ]^-OH To obtain good physical properties, PET should have long molecular chains. Molecular chains that are too long, however, are undesirable, because many entanglements of molecular chains disturb the film formability. The number of repeating units, n, is usually about 100 for film grade PET. PET was discovered in 1941 by Winfield and Dickson at ICI, who then promoted the production of PET and established the worldwide patent rights, except in the United States, where DuPont started production by the use of a patent license from ICL PET was first used in the fiber industries. PET fibers went into the market under the brand names Terylene from ICI and Dacron from DuPont. Several years later, PET film was commercialized in the 1950s under the brand name of Mylar of DuPont, followed by Melinex of ICI. DuPont gave the manufacturing license for PET film to Eastman Kodak, and ICI to Kalle (Germany), Le Cellophane (France), Toray (Japan), Teijin (Japan), and other companies. Now, 20 different companies manufacture PET film throughout the world. PET film is characterized by a combination of favorable qualities and fairly low cost. It has good properties such as mechanical strength, optical transparency, electrical insulation, dimensional stability, thermal stability, resistance to chemicals, and hygienic safety. The markets for PET film were electrical insulation, metallized and slit yarns, and stamping foils in the early stage. The market spread to photographic films, capacitors, and tracing papers and further in the 1970s to magnetic tapes such as audio, computer, and video tapes, resulting in a rapid increase in production. In the 1980s, paralleling the development of the electronics and information industries, PET film found increased usage in electronics parts, graphic products, and other new applications for office automation and factory automation. Because of the large growth of the market for PET film, the amount of PET film consumption increased dramatically, and is now around 1.1 million metric tons per year throughout the world. The first step in making PET film is to melt the PET pellets in the extruder, then to form a sheet through a slit type die, and to quench the sheet on the casting drum. The resulting sheet is nonoriented and amorphous, so that the physical properties are not very good. The amorphous sheet is heated and biaxially stretched in both the longitudinal and transverse directions. Biaxial orientation of polymeric molecular chains takes place with this stretching, resulting in the improvement of physical properties. This stretched film, however, has a serious defect, that is, high shrinkage at high temperature. To remove this defect, the stretched film is heat set under tension to promote the crystallization and to remove the stress caused by the stretching. The key characteristic of the PET film manufacturing process is biaxial stretching, which is not usually used in the manufacture of conventional polyethylene and polyvinyl chloride films. Biaxial stretching technology has grown with developments in the PET film industry. Thereafter, this technology has been applied for the manufacture of other films made from polypropylene and polyamide.

The manufacturing method and properties of PET film are explained in detail in the following sections.

6.3.2

Outline of the Film Making Process

Because the cast PET film is brittle, most PET film is biaxially stretched. Biaxial stretching processes are classified as shown below (LD, longitudinal direction; TD, transverse direction): Simultaneous Biaxial Stretching by the Tenter Process Two processes are available: the pantograph process and the pitch screw process. These processes, however, are not very popular for the following reasons: Simultaneous biaxial stretching

Tenter process (A) Tubular process (B)

Biaxial stretching Sequential biaxial stretching

LD —• TD stretching (C) TD - * LD stretching (D)

• • •

complicated structure of tenter, and, therefore, difficult maintenance unsuitable for high-speed processing difficulty in changing the LD stretching ratio.

But recently DuPont has invented the newly simultaneous biaxial stretching technology patented by USP4853602, USP5753172, USP5771547 et al., so-called LISIM (linear motor simultaneous) technology, and Bruckner has commercially developed this process. With this novel LISIM- technology, the advantages of the current simultaneous stretching methods can be maximized and the disadvantages avoided. • •

Good processability (less break, ultra thin possible, high speed, high efficiency, changing of stretching parameters within minutes, low maintenance) simultaneous relaxation (low shrinkage also for tensilized).

Simultaneous Biaxial Stretching by the Tubular Process Tubular cast film, made through circular die, is heated and inflated with the aid of air pressure to form a biaxially oriented film. This process has the following advantages and disadvantages.

Advantages: • •

inexpensive investment cost high production efficiency (as a result of no edge trim, which is necessary in the tenter process). Disadvantages:

• • •

poor gauge uniformity and film flatness, because of instability of the blown film process unsuitable for high-speed processing unsuitable for manufacturing thick film.

The use of the PET film made by this tubular process is limited mainly to shrink film applications such as shrink wrapping of food and electric wires. Sequential Biaxial Stretching (LD —> TD Stretching) As mentioned previously, simultaneous biaxial stretching is less suitable for PET film manufacturing. Most PET film is produced by the sequential biaxial stretching process. Sequential biaxial stretching consists of stretching the cast sheet in one direction; then stretching the uniaxially stretched film in the other direction; and then heat setting the film. Two processes are available for sequential biaxial stretching. One is LD —> TD stretching (the film is stretched first in LD and then in TD), the other TD —> LD stretching (the film is stretched first in TD and then in LD). LD stretching is usually carried out between two pairs of rotating rolls. The stretching ratio is determined by the difference between the rotating speeds of the rolls. TD stretching is done in the clip running tenter. The TD stretching ratio is determined by the ratio of film width of the inlet and outlet of the tenter. Worldwide, LD —> TD stretching is the principal PET film manufacturing process. Sequential Biaxial Stretching (TD -> LD Stretching) This process has some advantages, for example: • • •

easy manufacture of LD-tensilized film low level of "bowing" (mentioned later) easy process for high-speed manufacture (because manufacturing speed is not limited by the tenter speed).

A serious problem with this process, however, is the difficulty in stretching the wide film uniformly in the longitudinal direction, as wide rolls easily bend and wide nip rolls usually give uneven nip pressure. As mentioned previously, the principal process for PET film production throughout the world is the sequential biaxial (LD -> TD) method, which is detailed in the following sections.

6.3.3

Sequential (LD -> TD) Stretching

6.3.3.1

Casting

The role of the casting process is to quench the molten sheet coming from the die slit forming the nonoriented sheet. Because PET has a melting point of about 270 0C and a glass transition temperature of about 70 0 C, the molten sheet, having a temperature higher than 270 0 C, should be quenched down to a temperature lower than 70 0 C. In this process, quick quenching is important. A slow rate of quenching usually causes crystallization in the nonoriented sheet, which has a negative influence on the subsequent stretching. The usual casting method is to use the rotating quenching drum, around which the molten sheet is wound. The molten sheet solidifies to form a nonoriented sheet. This casting method is effective in yielding a sheet with good gauge uniformity, because the drum works as a support for the molten polymer with fairly low viscosity. In the casting process, it is very important to quench the molten sheet as quickly as possible. To attain the quick quenching, two techniques are used. 1. To keep the drum temperature as low as possible. This method, however, is quite limited, because low temperature often causes the formation of dew on the drum surface. To avoid dew trouble, the drum temperature is usually kept at around 20 0 C. 2.

To obtain good contact between drum surface and molten sheet. To improve the contact, several techniques are available:

(a) (b) (c) (d)

pinning by static electricity [1] press roll casting [2] coating the drum surface with some liquid [3] air knife casting

Of these techniques, the electropinning method is usually preferred from the viewpoint of good contact, good gauge uniformity, and defect-free surface.

6.3.3.2

Longitudinal Stretching

This process involves heating and stretching the cast nonoriented sheet in the longitudinal direction, aligning the molecular chains in the stretched direction. Longitudinal stretching is usually carried out in equipment with some preheating rolls and a pair of stretching rolls, each of which is driven at different rotating speeds. The longitudinal stretching ratio is defined as the ratio of speed of these rolls. Figure 6.3.1 [4] shows three basic systems of roll arrangement for longitudinal stretching. Stretching with Long Free Path The sheet is stretched between a pair of nip rolls rotating in the same direction. Radiation energy is supplied to the sheet during stretching. This system usually has a long free path,

Heater

v

x

v.t>vx

v

i

a) Stretching with long free-path Figure 6.3.1

V

x

Vi

vz > Vx

b) Stretching with short free-path

V1

vz>v{

v

x

c) Stretching between densely arranged rolls with small diameter

Roll arrangements of various drawing processes and typical film cross-section

which causes substantial "neck down" (reduction of width during stretching). A large amount of "neck down" is not preferred because of thick edge formation. Stretching with Short Free Path The sheet is stretched between counter-rotating rolls. Because of short free path, this system works well from the viewpoint of avoiding "neck down." This system, however, is vulnerable to the formation of surface defects such as sticking and scratches. Stretching between Multirolls The sheet is gradually stretched between a sequence of many small rolls. This system shows tolerable "neck down." However, sticking and scratches result because of the existence of many rolls. The longitudinal stretching system actually used is the combination of these basic systems. Probably the system differs from company to company. The materials used for the surface of rolls are: • • • •

plated hard chrome sintered ceramics fluorine-containing polymer silicone rubber.

Each material has a different stick-start temperature, above which the nonoriented sheet sticks to the roll surface. Usually, hard chrome is used below 80 0 C, ceramics below 100 0 C, and fluorine and silicone polymer below 120 0 C. Figure 6.3.2 [5] shows differential scanning calorimetry (DSC) chart of amorphous PET. Three peaks are found. The first peak is around 70 0 C because of the change of specific heat, the second endothermic peak around 1400C because of crystallization, and the third exothermic peak around 270 0 C because of melting of crystals. This DSC curve shows the mobility of polymer chains with varying temperature:

EXO ENDO

Annealed at 2000C

Figure 6.3.2 DSC Thermograph of annealed PET

Temperature(°C)

1. At room temperature, polymer chains are frozen, that is, in the glassy state. This condition lasts up to the glass transition temperature (Tg). 2. At temperatures above Tg, the polymer is in a "supercooling" state, which extends to the crystallization temperature (Tc). 3. At the temperature approaching Tc, the polymer molecules begin to crystallize, which is called "heat-induced crystallization." To give the sheet good molecular alignment, stretching should be carried out in the temperature range between Tg and r c , that is, in the supercooled condition. Actually, a suitable temperature range is from 80 0 C to 1200C for the longitudinal stretching. Figure 6.3.3 [6] shows stress-strain curves in the uniaxial stretching of cast PET sheet. Stretching at the temperature below 70 0 C, the curves have clear yield points, which means that the temperature is not sufficient for the good stretching. Such stretching is called "stretching with necking," which does not give the sheet good molecular alignment and usually has poor gauge uniformity. At temperatures above 80 0 C, the stress-strain curves

Stress(Kg/mm2)

Stretching Temp.

Stretching Figure 6.3.3

Stress-strain curve of amorphous PET

Ratio

become smooth, showing that the condition is suitable for stretching. At temperatures above 100 0 C, the stress does not rise much with increasing strain. Such stretching is called "superdraw," which is a "flow" process rather than "stretch." In "super-draw," little molecular alignment takes place with the reduction of thickness and width. By combining this "superdraw" with normal stretching, high stretching ratio is obtained as a result of raising the filmforming speed. This idea originated in PET fiber technology and was later transferred to film. Some patent literature [7 to 9] shows the process of high longitudinal stretching ratios, ranging from 4 to 9 times. In the case of longitudinal stretching, consideration must be given to its influence on successive transverse stretching. Too high a longitudinal stretching ratio causes poor stretchability in the transverse direction, because of excessive strain crystallization taking place. To keep good stretchability in the transverse direction, the longitudinally stretched film should have limited physical properties, for example, density below 1.355 g/cm 3 (density of amorphous PET is 1.335 g/cm3) and the value of birefringence smaller than 0.100. To get such a longitudinally stretched film, the stretching temperature should range from 90 to 1000C and the stretching ratio from 3.5 to 4.0 times its original length.

6.3.3.3

Transverse Stretching

Transverse stretching is generally carried out by the use of tenter, after which a heat set stage follows. Both edges of the longitudinally stretched film are gripped by the tenter clips, which lead the film into the tenter oven, where the film is preheated and transversely stretched to 3.0 to 4.5 times its original width at temperatures ranging from 90 to 120 0 C. In the tenter oven, the film is heated by the hot air blowing from above and below nozzles, and is stretched with diverging clip chains. The important point in the transverse stretching is how to control the "heat-induced crystallization" in the preheating zone. Preheating at high temperature and/or for a long time usually promotes this crystallization, which leads to poor stretchability, for example, and bad gauge uniformity. A good parameter that relates to the level of heat-induced crystallization is the "crystalline initiation temperature." The lower this temperature is, the easier heat-induced crystallization takes place. As a reference, for amorphous cast film this temperature is about 140 0 C, whereas for longitudinally stretched film it is about 110 0 C. To improve the gauge uniformity in the transverse direction, the idea of "stretching during cooling" was proposed [10], the point of which is the combination of high preheating temperature with rather lower stretching temperature.

6.3.3.4

Heat Setting

Biaxially stretched PET film has a lot of built-in stress induced by the stretching, so that the film shrinks when exposed to high temperature and even at room temperature, the film slowly shrinks with time. Hence, the film is usually heat set at the temperature from 180 to 235 0 C. Heat setting increases the crystal size and degrees of crystallization, and permits relaxation in the strained amorphous region which contributes to the improvement of thermal dimensional

Density (g/cc)

Biaxally (3.0x3.5) stretching PET film

Annealing temperature (0C) Figure 6.3.4

Change of film density by annealing for 100 s under fixed lengths

stability. Heat set temperature below 1800C contributes little to the improvement of thermostability, whereas temperatures above 235 0 C degrade the crystal structure induced by the stretching, with serious deterioration of mechanical properties. Figure 6.3.4 [11] shows the relationship between heat set temperature and degree of crystallinity (density). This relationship is useful for estimating the heat set temperature of the sample film by the measurement of the density. Figure 6.3.5 [11] shows the relationship between heat set time and heat shrinkage of the film. Several seconds are required to finish the heat set. Figure 6.3.6 [11] shows the relationship between relaxation rate and heat shrinkage. Relaxation during heat set is effective to improve the thermal stability. However, a large ratio of relaxation usually causes a poor flatness of the film, so that the preferable relaxation rate is below 10% as the original width.

6.3.4

General Properties of PET Film

Some properties of the PET film obtained by the process mentioned previously are discussed below.

6.3.4.1

Mechanical Properties

Tensile Properties Figure 6.3.7 [12] shows the stress-strain curves of stretched PET film. From these stressstrain curves, tensile strength, elongation, elastic modulus, and F-5 value (stress at 5% strain)

Heat shrinkage (%) Figure 6.3.5 Annealing time versus heat shrinkage. (Heat shrinkage was measured at 150 0 C, lmin)

Heat shrinkage (%)

Annealing time (sec)

Figure 6.3.6 Heat shrinkage versus transverse relaxation of annealing zone. (LD, longitudinal direction; TD, transverse direction)

Relaxation ratio (%)

Transverse Direction

1. Uniaxially stretched under free width( 4x1') 2. tMaxially stretched under constant width( 4x1) 3.4.5. Two-way successively biaxially stretched and heat-set (4x3, 4x3.5, 4x4; respectively) 6. Simultaneously biaxially stretched and heat-set ( 4x4)

Stess(Kg/mm2)

Machine Direction

Stain(%) Figure 6.3.7

Strain(%)

Typical stress-strain curves for stretched PET films

are obtained, which are tabulated in Table 6.3.1 [12]. As shown in this figure and table, tensile properties of PET film vary considerably with different preparation conditions. Common biaxially stretched PET film in the market has tensile strength approx. 25 kg/mm 2 , tensile elongation approx. 120%, elastic modulus approx. 400 kg/mm 2 , and F-5 value approx. 11 kg/mm 2 . Viscoelastic Properties Figure 6.3.8 [13] shows the viscoelastic properties of the biaxially stretched PET film. Two peaks exist in the tan 3 curve, one at approx. — 50 0 C and the other approx. 120 0 C. The — 50 0 C peak is called a "/^-transition" caused by the movement of side chains of the molecules. The 1200C peak is called "a-transition" caused by the movement of main chains, which corresponds to glass transition temperature (Tg). Tg of biaxially stretched PET film is much higher than that of amorphous PET (approx. 70 0 C), as a result of the orientation of molecules. Propagating Tear Strength Propagating tear strength of various films is shown in Table 6.3.2 [14]. This strength decreases with biaxial stretching. Impact Strength Table 6.3.2 [14] shows impact strength of various films. Biaxial stretching usually raises the impact strength.

6.3.4.2

Thermal Properties

Reversible Deformation When the PET film is heated and cooled at low temperatures, deformation with heat returns it to the original dimension. This deformation is called reversible deformation. The rate of this

Table 6.3.1

Mechanical Properties of Stretched Polyethylene Terephthalate Films

Methods of stretching

Ratio of stretching

Tensile strength (kg/cm2)

(LD x TD)i

LD

TD

Elongation at break (%)

Young's modulus (kg/mm2)

F 5 value (kg/mm2)

LD

TD

LD

TD

LD

TD

Unstretched, no heat set

1.0 x 1.0

5.8

6.7

410

435

200

235

3.7

3.9

Unstretched, heat set

1.0 x 1.0

6.0

5.0

640

580

180

170

3.8

3.7

Uniaxially stretched under free width, no heat set

1.5 x Y 2.0 x Y 2.5 x Y 3.0x1' 3.5x1' 4.0x1'

7.2 11.9 19.3 23.5 24.6 27.5

3.4 3.5 4.2 4.5 3.1 3.0

380 350 270 140 71 62

430 480 450 600 830 910

150 160 300 320 470 490

150 150 160 170 150 100

4.7 5.2 8.7 9.1 11.3 15.6

3.7 3.6 3.0 2.8 3.3 3.0

6.0 11.1 20.0 22.2 24.5 25.6

5.8 4.8 5.6 5.8 5.9 5.7

530 370 140 96 73 50

610 480 480 490 470 500

180 180 410 480 600 660

160 160 170 190 210 240

3.9 4.5 8.9 12.0 14.2 16.9

3.6 3.5 4.0 4.2 4.3 6.9

4.0x2.5 4.0x3.0 4.0x3.5 4.0 x 4.0

24.7 23.0 22.0 20.5 19.6 16.5

8.1 11.6 15.8 18.3 19.2 18.4

46 43 34 44 47 39

380 130 140 88 62 32

700 600 520 490 430 360

230 310 300 380 410 470

21.3 16.8 15.0 13.2 13.3 12.2

8.1 10.3 10.5 12.3 12.5 16.0

1.5x1.5 2.0 x 2.0 2.5x2.5 3.0x3.0 3.5x3.5 4.0 x 4.0

5.2 10.5 18.4 18.7 22.2 24.0

5.0 10.8 18.2 20.3 22.0 24.1

420 330 110 66 61 41

410 340 100 70 62 36

190 220 360 380 400 390

180 230 330 380 390 400

3.7 6.4 10.5 11.8 13.0 13.6

3.7 6.3 10.4 11.8 12.0 12.9

Uniaxially stretched under 1.5x1.0 constant width, no heat set 2.Ox 1.0

2.5x1.0 3.0x1.0 3.5x1.0 4.Ox 1.0 4.Ox 1.5 Two-way successively biaxially stretched, heat set 4.0 x 2.0

Simultaneously biaxially stretched, heat set

Material, polyethylene terephthalate films prepared by the T-die process; medium of stretching and heat setting, hot dry air.

heat deformation is called "heat expansion coefficient," usually measured between 20 and 40 0 C in the 65% RH (relative humidity). Table 6.3.3 [15] shows the heat expansion coefficients of various PET films. The value of the heat expansion coefficient is closely related to molecular orientation and thermal movement of molecular chains. Usually, the value of the heat expansion coefficient decreases with increasing molecular orientation.

tan 8

Dynamic modulus (dyn/cm2)

LD TD

tana

Teraperature(°C) Figure 6.3.8

Temperature dependence of dynamic modulus of balanced PET film

Irreversible Deformation When the film is heated to high temperature, heat shrinkage takes place, and the film does not return to the original dimension. This is called irreversible deformation. The value of heat shrinkage is controlled by heat set temperature and ratio of relaxation. Figure 6.3.9 [15] shows the relationship between temperature and heat shrinkage for two kinds of PET films. Generally, the higher the molecular orientation is, the higher is the heat shrinkage.

6.3.4.3

Optical Properties

Figure 6.3.10 [16] indicates the variation of three direction refractive indices when the PET film is uniaxially stretched. The value of refractive index increases in the stretched direction and decreases in the thickness direction with increasing stretching ratio, whereas the value in the direction perpendicular to the stretched direction decreases at initial stage and thereafter increases with increasing stretching ratio. This variation is due to the degrees of planar orientation. Figure 6.3.11 [16] shows the variation of refractive indices with elongation of biaxially stretched PET film.

Table 6.3.2

Properties of Nonaxial and Biaxially Oriented Plastics Films

Properties

Units

Branched polyethylene

Polypropylene

NO

BO

NO

1 to 3 50

8 to 10 3 to 5 50 60 to 90 10 to 15 50to 500 1 to 2 18

Tensile strength Tensile modulus

kg/mm2 kg/mm2

Propagating tear strength Impact strength

g/mil

100 to 350 kg • cm/mil 2

Haze

%/mil

6 to 10 1 to 3

Heat shrinkage % 20 to 60 1000C, min Service temperature 0 C -50to -50to range 80 110 g • 0.1 mm Water vapor day • m2 permeability 4.4 0 40 C, 90% RH cc.0.1 mm Oxygen 750 0 day • m2 permeability 25 C, 1300 1 atm

Unplasticized polyvinyl chloride BO

Polyethylene terephthalate

Nylon-6

NO

BO

NO

Vinylon*

BO

NO

13 to 30 200to 300 4 to 15

5 to 8 10 to 15 140to 300to 200 240 350 10 to 100 3 to 10

16 to 25 400to 500 10 to 20

6 to 10 20 to 25 45 to 140to 60 220 50 20 to 28

17

2

15

25

35

25

2 to 4 1 to 2

2 to 3

1

4 to 7

2

0

Oto 8

0

30 to 50

0 to 120

-50to 130

70

-60 to 70

80

6

17

3 to 4 1.5

0

0

-70to 150

130

5.5 10

600

O t o 1 1 to 5

240

* Data of vinyl on BO are those of Emblar, OV coated with PVDC on both sides. NO, nonoriented; BO, biaxially oriented

8 19

90

15

BO

NO

BO

5 to 6 25 70to 480 80 12 1

2 0.5

-60to 130 40

^100

6

^0.5

^0.3

Table 6.3.3

Thermal Expansion Coefficients of PET Film Thermal expansion coefficient, at (/ 0 C)

Film type

70 x22~ 6

Nonoriented film Balanced film

(LD) (TD) (LD) Tensilized film (TD) Uniaxially oriented film ( x 4.8) (LD) (TD)

6.3.4.4

16.5 x 15.9 x 4.5 x 22.0 x 18.7 x 124 x

1(T 6 1(T 6 1(T 6 1(T 6 10~ 6 10~ 6

Barrier Properties

Table 6.3.4 [17] shows the barrier properties of various films against some gases and liquids. Figure 6.3.12 [18] shows the variation of gas permeability with increasing temperature. Generally, gas barrier properties decrease with increasing temperature. Figure 6.3.13 [18] shows the water vapor permeability of biaxially stretched PET film.

6.3.4.5

Chemical Resistance

Heat shrinkage (%)

Table 6.3.5 [19] shows the resistance of PET film against chemicals. PET film is slightly weak against alkalis but strong against acids. PET film is insoluble in the general organization solvents.

Tensilized film

Normal film

Temperature ( 0 C) Figure 6.3.9

Temperature dependence of heat shrinkage

Refractive index n

Draw direction

Perpendicular diijection

Thickness direction

Draw ratio Figure 6.3.10

6.3.4.6

Refractive index versus draw ratio of longitudinal direction

Electrical Properties

Refractive index n

Dielectric properties of PET film are shown Table 6.3.6 [20] compared with those of other films.

LD stretching ratio

TD stretching ratio

Figure 6.3.11

Refractive index of biaxially oriented PET film caused by TD stretching ratio

Table 6.3.4

Permeability of Polymers

Polymer

Gas permeability at 25 0 C, 50%RH / cc • /mi \ 4 2 V10 cm • day • arm/

Liquid permeability at 25 0 C

O2

H2O

SO2

14

0.6

15

0.8

50 24 120 80 140 520

2.0 4.0 6.0 4.6 10.0 28.2

6.0

<2.0

<2.0

<2.0

<2.0

< 2.0

<0.4 <2.0 19 -20 3.0 ^ 2.0 2.4 <2.0 18 <2.0 14 -20

< 2.0 <2.0 < 2.0 <2.0 < 2.0 <2.0

<2.0 <2.0 1.7 2OxIO 3 48 —

89

Temperature(°C) Figure 6.3.12

Permeability of biaxially oriented PET film

C2H5OH C7H16 CH3COOC2H5 <2.0

Permeability (ml/m2*day*MPa)

Acrylonitrile-styrene 4.4 copolymer Acrylonitrile-acrylate 4.4 copolymer + butadiene graft Polychlorotrifluoroethylene 12 Nylon-6 12 PET 28 Polyvinyl chloride 32 Polyacetal 48 Polymethyl 160 methacrylate + butadiene graft

CO2

/ g • jum \ 1 ( ) 4 c m 2 da \ ' Y/

(g/m2*day) Water vapor transmission rate

Film thickness (micron meter) Figure 6.3.13 Water vapor transmission rate of biaxially oriented PET film Table 6.3.5

Chemical Resistance 1000C, 5 hours

0

20 C, 20 Days Glacial acetic acid Cone. 35% hydrochloric acid 18% Hydrochloric acid Cone. 60% nitric acid 35% Nitric acid 80% Sulfuric acid 70% 60% 10% 10%

Sulfuric acid Sulfuric acid Potassium hydroxide Sodium hydroxide

10% Sodium carbonate 28% Ammonia 12% Ammonia Acetone Ethyl acetate Benzene Xylene Tetrachloromethane Tetrachloroethane Chloroform Freon

B C B E (Strength lowering to 0 for 5 days) C E (Strength lowering to 0 for 5 days) B A D E (Strength lowering by half over 10 days) A E (Strength lowering to 0 for 5 days) E (Strength lowering by half over 10 days) A A A A A A B A

Glacial acetic acid 20% Hydrochloric acid 30% Nitric acid 20% Nitric acid

A A E A

10% Nitric acid 70% Sulfuric acid

A E

60% Sulfuric acid 40% Sulfuric acid 20&Sulfuric acid 10% Potassium hydroxide

A A A E

10% Sodium hydroxide 10% Sodium carbonate

E C

12% Ammonia

E

Acetone Ethyl acetate Benzene Xylene Tetrachloroethane Ethanol

B A A A C A

A, Excellent; B, strength lowering less than 10%; C, strength lowering less than 20%; D, strength lowering more than 20%; E, strength lowering to 0

Table 6.3.6

Dielectric Properties of Films

Properties Measurement frequency (cps)

Dielectric constant 60

10

10

60

10

10

Volume resistivity (Q • cm)

PET Polycarbonate Polystyrene Polyethylene Polyvinyl chloride (unplasticized) Polyvinyl chloride (plasticized) Cellulose triacetate Tetrafluoroethylene

3.2 3.17 2.4 to 2.7 2.25 to 2.35 3.2 to 3.6

3.1 3.1 2.4 to 2.7 2.25 to 2.35 3.0 to 3.3

3.0 3.0 2.4 to 2.7 2.25 to 2.35 2.8 to 3.1

0.003 0.0009 0.0001 to 0.0003 < 0.0005 0.007 to 0.02

0.003 to 0.004 0.0011 0.0001 to 0.0003 < 0.0005 0.009 to 0.017

0.016 to 0.017 0.010 0.0001 to 0.0004 < 0.0005 0.006 to 0.019

>10 16 >10 13 >10 16 >10 16 >10 15

5.0 to 8.0

4.0 to 7.0

3.5 to 6.5

0.10 to 0.15

0.09 to 0.16

0.09 to 0.10

1012-13

3.5 to 6.5 2.0 to 2.1

3.2 to 4.5 2.0 to 2.1

3.2 to 4.4 2.0 to 2.1

0.01 to 0.06 0.002 to 0.003

0.01 to 0.06 0.0002 to 0.0003

0.01 to 0.10 0.0002 to 0.0003

1012-13

3

Dielectric loss 6

3

6

>10 16

6.3.5

Quality Improvement of PET Films

Some recent topics are introduced in the following paragraphs, concerning quality improvement or value-adding of PET films.

6.3.5.1

Bowing

The phenomenon of bowing is illustrated in Fig. 6.3.14 [21]. A straight line, drawn transversely on the film at the inlet of the tenter, curves, like a bow, at the outlet of the tenter. Bowing causes property differences in the transverse direction. For example, Fig. 6.3.15 [22] shows the difference of expansion rates between those of center and edge parts of the PET film. In the center part, the film has the same values of expansion rates at any measurement directions, whereas in the edge part, expansion rates differ from measurement direction to direction. The center part is called "isotropic," whereas the edge part is "anisotropic." This anisotropy in the edge part of the film is caused by the bowing. In some serious applications, this anisotropy can cause major problems. 6.3.5.1.1 Mechanism of Bowing Nonomura et al. conducted an experiment to examine the mechanism of bowing occurring in the tenter oven. A straight line marked film was placed into the tenter oven, then preheated, stretched, thermoset, cooled, and at this point the process was stopped. The stretched film, with marked lines, was spread from inlet to outlet in the tenter oven. The result of this experiment is shown in Fig. 6.3.16 [23], where the bowing distortion is shown along the tenter oven length. The straight line (bowing distortion is 0%) in the inlet of tenter first curves during the beginning of stretching into an "outlet side-bowed line" (bowing distortion is Bowing Line (line is deformed as a bow) Straight Line (marking)

Film in (uniaxially oriented film)

Film out ideal line

Preheating

Figure 6.3.14

Bowing phenomenon

Transverse drawing

Annealing

Slowly cooling

LD

LD

TD

TD

Center part of the film

Edge part of the film

•— Hydroscopic expansion coefficient • Thermal expansion coefficient Figure 6.3.15 Hydroscopic and thermal expansion coefficient minus %), then at the end of this stretching returns to the straight line. Then, in the thermosetting zone it becomes an "inlet side-bowed line" (bowing distortion is plus %). The bowed line in the thermosetting zone shows no change in the cooling zone or after exiting the tenter oven. This bowing presumably takes place by a mechanism such that the necking stress in the stretching zone pulls the film in the thermosetting zone, where the rigidity of the film is rather low because of the high temperature. Sakamoto measured the change of refractive ellipsoids in each part of the process, which is shown in Fig. 6.3.17 [24]. A cast film has no orientation so that the refractive ellipsoid is a "sphere," which changes to an "American football" in the longitudinal stretching zone. Then in the transverse stretching zone the direction of the main orientation axis gradually turns to the transverse direction as a result of transverse stretching stress. The shape of ellipsoids and direction of the main axis vary along the transverse direction. In the thermosetting zone, the shape of the ellipsoid varies at each point of transverse direction, because of shear stress which is 0 at the center of tenter and increases with increasing width. Sakamoto concluded that isotropic film cannot be made, in principle, in the normal tenter process.

6.3.5.1.2 Reduction of Bowing Some techniques are proposed to reduce the degree of bowing in the patent literature, as follows.

Bowing distortion (%)

Pre-heating zone Stretching zone

Cooling zone Thermo-setting zone

Zones of tenter (arbitrary unit) Figure 6.3.16

Distribution of bowing in the tenter oven

1. To prevent stress propagation Because the necking stress in the transverse stretching zone is presumed to be a main reason for bowing, it has been proposed that this bowing can be reduced by reducing the stress propagation between the stretching and thermosetting zones. One idea [25, 26] is to cool the

Y

Biaxially oriented film

Longitudinal direction

C

B

X

A

Longitudinal drawing

As cast film Figure 6.3.17

Changes of refractive ellipsoids in each unit process

stretched film before it goes into thermosetting zone. Temperature reduction of the film results in increase of the rigidity, which prevents stress propagation to some extent. Another idea [27] is that edge grip be released just after the end of transverse stretching, and then the film is regripped as it enters the thermosetting zone. Still another idea [28] is to put a nip roll between stretching and thermosetting zones. The role of the nip roll is to prevent stress propagation. 2.

Thermosetting at multiple stages [29]

1. The transversely stretched film is cooled down below glass transition temperature. 2. Then it is heat set at a temperature T1 ranging from 200 to 240 0 C. 3. Then heat set again at a temperature T2 (T2 is a temperature between Tx and T3) while the film is transversely stretched at a ratio of 1 to 20% during heat setting, 4. The film is then heat set again at a temperature T3 ranging from 100 to 200 0 C. 3.

Temperature difference in the transverse direction

One idea [30] is that the biaxially stretched film is slightly relaxed, that is, in the longitudinal tension below 10 kg/m, and the center of the film is heated up to a temperature above 150 0 C, while the edge is heated up to 100C or more higher than that of the center. Heating is by infrared radiation heater. The other idea [31] is to heat the edges to a temperature between the glass transition and heat setting temperature, in the middle zone located between stretching and heat setting zones. Another idea [32] is to create a temperature gradient from the hightemperature edges to the low-temperature center. 4.

The others

Many ideas are presented in the patent literature. For example, a woundup film is again placed into a heat setting tenter oven, where the bowing is corrected by running the film in the reverse direction [33]. This method, however, detracts from production efficiency. As mentioned previously, many techniques are presented to improve bowing. However, an effective method is not available, particularly from the industrial viewpoint. In fact, at present PET film generally has more or less bowing.

6.3.5.2

Thermal Stability

Two kinds of thermal stability are required. One is thermal stability below 100 0 C, and the other is concerned with temperatures above 150 0 C. The former is required in, for example, magnetic tape industries, whereas the latter is important in general industrial applications. Thermal stability at high temperature is easily attained by heat setting under relaxation. Transverse heat setting is easy in the tenter oven, for the clip chain is easily diverged and converged. Longitudinal relaxation, however, is difficult in the tenter process. Hence, longitudinal thermal stability is sometimes insufficient for some severe applications. To improve this, PET film is heat set again under longitudinal relaxation in an oven with a temperature of 180 to 200 0 C. This "offline" heat setting is effective to reduce longitudinal heat shrinkage. However, this method is costly because of the additional heat setting

procedure. To reduce the longitudinal heat shrinkage in a film-forming line, the following remedial techniques may be used: 1. Longitudinal relaxation is achieved by reducing the clip pitches in the tenter heat setting zone [35]. The key feature of this method is the special mechanical structure of the clip and chains of the tenter. 2. Longitudinal relaxation can be gained between two hot rolls of a roll heat setter placed after the tenter oven [36]. 3. Longitudinal relaxation can also be obtained through a speed difference between tenter clip chain and vacuum-suctioned roll located after the exit of the tenter oven [37]. This method is said to be effective in improving thermal stability at lower temperatures. 4. Heat set film is again heat set in the floating condition [38]. Because the film is floating, relaxation in both directions is easily attained in this method. Thermal stability of the film is fundamentally improved by relaxation heat setting. The purpose of these methods is to achieve considerable relaxation while retaining film flatness.

6.3.5.3

Gauge Uniformity

Of film qualities, gauge uniformity is one of the most important because of the considerable influences on film flatness and roll formation and hence suitability in various fabricating processes. There are two key points to improve the gauge uniformity: (1) how to get the cast sheet with good gauge uniformity, and (2) how to avoid worsening of gauge uniformity during stretching. Some efforts to improve gauge uniformity are discussed in the following paragraphs. Cast Sheet with Good Gauge Uniformity An effective method is to use a die with automatic gauge control system, in which the thickness is automatically adjusted by the signals from the thickness measurement gauge located at the exit of the casting roll and/or tenter oven. Four methods are available to adjust the thickness variation: 1. The die gap is adjusted by die bolts that expand or shrink with heat energy controlled by signals from the thickness profile. 2. Die bolts are controlled by piezoelectric elements. 3. Die bolts are controlled by a servomotor that operates in the transverse direction. 4. Die lip temperature is controlled by the thickness gauge. Temperature difference causes viscosity changes in the molten polymer, resulting in changes in thickness. To improve small thickness variations or surface defects, some ideas [39 to 41] have been proposed involving use of special types of metals, for example, chrome, for the inner surface of the die lip. To improve the electropinning property in the casting zone, use of additives to raise the dielectric constant of the molten polymer has been proposed [42, 43].

Gauge Uniformity During Stretching 1. Electropinning during longitudinal stretching is effective in fixing the stretching point in a good position [44, 45]. 2. Surface-controlled ceramic rolls are useful in longitudinal stretching to reduce the surface defects [46, 47]. 3. Low-temperature stretching is said to be effective to improve gauge uniformity (longitudinal stretching, 55 to 80 0 C; transverse stretching, 50 to 1000C) [48].

6.3.5.4

Tensilized Film

Normal PET film has an F-5 value of 10 to 13 kg/mm 2 both in longitudinal and transverse directions. This film, however, is not sufficient for the base film of long play or smaller size magnetic tapes. For these magnetic tapes, more rigid film is required. As the effective rigidity of the film is proportional to the product of (film thickness)3 x (film modulus), the film should have high modulus even in the case of thin film. Higher film modulus is obtained by increasing the molecular orientation of the film. Because longitudinal modulus correlates with tape runnability and transverse modulus with head touch property, high modulus is required in both directions. (Tape runnability is usually evaluated by such factors as tape elongation, tape edge damage, and tape folding.) Some classes of tensilized film are listed below. 1. 2. 3. 4. 5.

Semitensilized film (F-5 value in LD: 13 to 15 kg/mm 2 ) Normal-tensilized film (F-5 value in LD: 15 to 18 kg/mm 2 ) Supertensilized film (F-5 value in LD: 18 to 22 kg/mm 2 ) Ultra-supertensilized film (F-5 value in LD: 22 to 26 kg/mm 2 ) Both sides tensilized film (e.g., F-5 value in LD, 15 kg/mm 2 : F-5 in TD, 14 kg/mm 2 )

Some physical properties are shown in Table 6.3.7 [49]. As the molecular orientation is very high in the case of tensilized film, physical properties are different from those of normal PET film. For example, heat shrinkage increases with increasing tensilizing, as shown in Fig. 6.3.18 [50]. This variation of heat shrinkage is irreversible. Thermal expansion coefficients are shown in Table 6.3.3 [15] and humidity expansion coefficient in Table 6.3.8 [15]. Both coefficients decrease with increasing tensilizing. These variations are reversible. Figure 6.3.19 [51] illustrates the relationship between stretching ratio and modulus. Modulus increases with increasing stretching ratio. This modulus increase is, of course, caused by molecular orientation, especially molecular orientation in the amorphous region (Fig. 6.3.20) [51]. The general process to make tensilized film is as follows: 1. 2. 3. 4. 5.

Stretching in LD Stretching in TD Restretching in LD Restretching in TD, if required Heat setting.

Restretching in LD is rather difficult, for the film is so thin and wide that film width reduction and film breakage frequently occurs. Some techniques to facilitate restretching are:

Table 6.3.7

Properties of Tensilized PET Film Type

Properties

^^^^ ^

Thickness (jum) Strength (kg/mm2) Elongation (%) F-5 value (kg/mm2) Heat shrinkage (%) 1000C x 3 0

LD TD LD TD LD TD LD TD LD TD

80 0 C x 3 0

Semi-T

T

ST

UST

WST

11 38 26 80 140 14 11

5 to 12 42 23 68 160 17 11 1.1

7 to 10 45 23 60 155 20 11 1.0

10 48 25 50 150 23 11 2.0

11 35 35 80 80 15 14 1.3

^

0.8 0.5

0.4 0.25 0.1

0.3

1.2 0.40 0.2

1.1 0.2 0

F-5 value (kg/mm2)

Sample: Toray Lumirror Semi-T, Semi-tensilized; T, normal-tensilized; ST, super-tensilized; UST, ultra-super-tensilized; WST, both sides tensilized

Heat shrinkage(%) at 1000C for 30 min Figure 6.3.18 Heat shrinkage versus F-5 value of polyester film Table 6.3.8

Hydroscopic Expansion Coefficient of PET Film

Film type

Hydroscopic expansion coefficient, ah (/%RH)

Nonoriented film Balanced film (LD) (LD) Tensilized film Uniaxially oriented film ( x 4.8) (LD) (TD)

22 x l O ~ 6 12x10"6 8 x 10" 6 7 x 10" 6 29x10"6

Modulus (GPa)

Uniaxially oriented PET film

Draw ratio

Modulus (GPa)

Figure 6.3.19 Modulus versus draw ratio

Degree of orientation in amorphous region measured by fluororescence method Figure 6.3.20 Modulus versus degree of orientation in amorphous region

1. Both edges should be formed rather thick to prevent width reduction. 2. Preheating and stretching rolls should have as small deflection as possible. 3. Stretching temperature should be raised as the film progresses through the machine. As such a restretching process is usually costly, another process has been proposed to reduce the manufacturing cost. This new process [52] is characterized by that first LD stretching being carried out in two stages. Typical conditions are shown below. 1. Cast film is first stretched in LD at a temperature of 120 to 150 0 C. Stretching ratio is controlled such that the birefringence value of stretched film ranges from 0.005 to 0.025. 2. Then secondary LD stretching is done at a temperature of 60 to 1000C. 3. Uniaxially stretched film thus obtained is stretched in TD at a stretching ratio higher than 4.3. 4. Biaxially stretched film thus obtained is then heat set. According to this process, manufacturing cost of tensilized film is lower, because the restretching process is unnecessary. Various methods to make supertensilized film are proposed, some of which are illustrated below: 1. Biaxially oriented film is again simultaneously biaxially stretched [53]. The stretching ratio for the second simultaneous stretching is 1.05 to 1.90 in LD and 1.0 to 1.9 in TD. Stretching temperature of simultaneous stretching is between (Tg + 10) and (Tm — 40) 0C (Tg, glass transition temperature; r m , melting temperature). 2. Combination of LD stretching in multistages with restretching [54]. Cast film is stretched in LD in multistages to obtain uniaxially oriented film with a birefringence value of 0.02 to 0.10. Then the film is stretched in TD at a stretching ratio of 2.5 to 4.5, and restretched in LD at a ratio of 1.5 to 2.5. The product of LD, TD, and LD stretching ratio can be higher than 25. 3. Combination of LD stretching in multistages with simultaneous biaxial stretching [55]. Cast film is stretched in LD in multistages to obtain uniaxially oriented film with a birefringence value of 0.02 to 0.10. Then the film is stretched in TD at a stretching ratio higher than 2.5, followed by simultaneous biaxial stretching in which the stretching ratio ranges from 1.4 to 2.5 in both directions. The product of total stretching ratio should be higher than 27. 4. Zone stretching followed by zone annealing. Zone stretching and annealing involve stretching and annealing the film under tension with pinpoint heating. The aim of zone stretching is to obtain high molecular orientation while preventing crystallization, which is attained by neck-in stretching the film at a temperature of approx. Tg. The aim of zone annealing is to obtain chain-extended crystals by means of annealing the stretched film under high tension at a temperature between Tc and Tm. Figure 6.3.21 [56] shows the results of zone annealing the conventional biaxially oriented PET film. The LD modulus of zone annealed film is nearly double the modulus of the original film, although the TD modulus drops.

Dynamic modulus E'(GPa)

Zone annealed PET fi}m(LD)

Normal PET film

Zone annealed PET film (TD)

Temperature ( 0 C) Figure 6.3.21

6.3.5.5

Temperature dependence of dynamic modulus E' of zone-annealed PET film

To Make the Film Thinner

The thinnest PET film available is now approaching 0.5 /mi, which is much thinner than other films, for example, 3 /mi for biaxially oriented polypropylene film, 2 /mi polycarbonate film, and 8 /mi polyethylene film. The process suitable for making thinner film is either a biaxial stretching process or solution casting process. The former is suitable for PET and PP films, and the latter for polycarbonate film. The conventional blown film inflation process and the Tcast die process are not suitable for making very thin film. Generally, it is quite difficult to make very thin film, for example, thinner than 10 /mi, through a die gap. Some literature suggests that a plasma polymerization method is a good process to make a very thin film. This process is characterized by a glow discharge in monomer gas. The thin film made by this process, however, is an academic product at the present time.

6.3.5.5.1 History of PET Film Thinning The thickness of PET film that is easy to manufacture seems to be around 25 /mi. Toray started the production of PET film approximately 30 years ago. At that time the main thickness was 25 /mi. During the intervening 30 years, PET film thinning and thickening have succeeded with the result that the thinnest film is 0.8 /mi and the thickest 500 /mi. Both films are commercially available with the brand name Lumirror produced by Toray. Figure 6.3.22 shows the thinnest gauge of Toray PET film over the years. The thinnest gauge commercially available is 0.8 /mi, which is much thinner than the diameter of human hair (approx. 70 /mi) and common bacteria (approx. 1 to 2/mi). The trend toward such "thinning" is the result of the requirements of the capacitor industry.

Thickness (\i m) Figure 6.3.22 Trend of minimum thickness of PET film

6.3.5.5.2 Thinning Technology It is easy to make a "handkerchief" size thin film. It was likely even 30 years ago that 1 //m PET film was made of limited size. Such limited size, of course, is not applicable to industry. The film must be wound on a core with reasonable width and length (usually, several to tens of thousands of meters long). This wound film is called a "roll." Hence, the development of thinning technology can be expressed as "from handkerchief to roll." Much recent literature describes how to make very thin film [57]. Many techniques, of course, are used by each film manufacturer. The key criteria in producing thin film are gauge uniformity, slip property, reduction of film breakage, reduction of wrinkles, and uniform winding and slitting. Some of these are explained in the following paragraphs. 1. Stretching process "Stretching" is the key factor to make a thin film. Much patent literature [58] has been published concerning stretching methods and stretching conditions. 2.

Accuracy of the machine

A film making machine is comprised of many rolls and other mechanical components, which should have a high level of mechanical accuracy. 3.

Slip property

Good slip of the film is important for suitable machining and handling thin film. To obtain good slip, it usual to add some additives, for example, inorganic and/or organic fillers, into the film. Such additives, however, sometimes cause film breakages and, in the case of electrical applications, insulation failures. Clever compromises are usually necessary to overcome this dilemma. 4.

Elimination of foreign matter

Foreign matter such as dusts, carbonized polymers, and gels usually causes film breakages, pinholes, and physical failures. Hence, clean polymers and clean working environment are required together with good filtering systems.

5.

Stiffness of the film

Because the stiffness of the film depends on the third power of the thickness, wrinkles and sags easily occur in thin film manufacture. Therefore, it is desirable to use high-modulus polymers for making thin films. PET has comparatively high modulus, thus offering some advantages in thin film making. Reduction of stiffness also causes vulnerability to static electricity. Hence, it is important to prevent the accumulation of static charge and to remove static electricity. 6.

Thickness gauge

Usually, a /?-gauge with promethium-147 (Pm147) as the /?-ray generator is used to measure the thickness of very thin film. The accuracy of this gauge, however, is limited to a range of 0.1 /mi, which is not satisfactory for the measurement of the film thinner than 1 /mi. More accurate gauging techniques are now required. 6.3.5.5.3 Limit of Thinning PET film thinning is controlled by such factors as molecular structure of polymers, surface roughness, mechanical properties (ease of handling), dust and foreign matter, and applicability to end uses. By summarizing these factors, the actual lower limit of PET film thickness seems to be in the range of 0.3 to 0.5 /mi for the near future, and 0.025 to 0.05 /jm in the more distant future [58]. The active effort to achieve these lower thickness limits will continue well into the future, particularly in capacitor applications. At a recent electronics show, ultra-small size film capacitors were demonstrated by a capacitor manufacturer in which the capacitors consisted of 0.65 /im PET film made by Toray. The sizes of these film capacitors is expected to be competitive with that of tantalum electrolyzed capacitors and ceramic capacitors.

Abbreviations Used F-5 value LD TD Tg Tm PET

stress at 5% strain longitudinal direction transverse direction glass transition temperature melting temperature polyethylene terephthalate

References 1. Du Pont, JPN Kokoku Tokkyo Koho JP 37,006,142 2. USP 3,223,757 (1965) 3. Nat. Distillers, British Patent P934773 (1963)

4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56.

Toray, USP 5,076,976 (1991) Teijin, JPN Kokoku Tokkyo Koho JP 63,004,494 Satoyuki Minami, Sen-i Gakkaisi (1985) 41, p. 290 Lin, S.B., Koenig, JX., J Polym. Symp. (1984) 71, p. 121 Satoyuki Minami, Zairyou Kagaku (1985) 21, p. 6, 309 Toray, JPN Kokoku Tokkyo Koho JP 52,033,666 Toray, PCT Int. Appl. WO 96/06722 Toray, JPN Kokoku Tokkyo Koho JP 57,049,377 Toray, JPN Kokoku Tokkyo Koho JP 57,049,378 Du Pont, JPN Kokoku Tokkyo Koho JP 34,000,442 Toray, JPN Kokoku Tokkyo Koho JP 37,000,534 Matsumoto, K., Izumi, Y., Imamura, L., Sen-i Gakkaisi (1972) 28, p. 179 Toray, Technical Report Satoyuku Minami, Sen-i Gakkaisi (1985) 41, p. 290 Watanabe, H., Asai, T, Ouchi, L, Proceedings of 23rd Japan Congress on Materials Research (1980) p. 282 Heffelfinger, C.J., Burton, R.L., J Polym. ScL (1960) XLV, p. 289 Sweeting, O. J., The Science and Technology of Polymer Films, Vol. II (1970) John Wiley & Sons, New York, p. 278 Davis, G. W., Talbot, J.R., Encyclopedia of Polymer Science and Engineering, Vol. 12 (1970) Kozo Maeda, Polymer Digest (1988) 9, p. 39 Gisaku Takahasi, Plastic Film Nikkan Kogyo Shinbunsya, 1996, p. 92 Kazuo Yuki, Howa Polyester Jyusi Handbook Nikkan Kogyo Shinbunsya, 1989, p. 689 Hiroshi Noda, Netsu Sokutei (1987) 14, p. 70 Nonomura, S., Yamada, T, Matsuo, T, Seikei Kako (1992) 4, p. 312 Kunisuke Sakamoto, Kobunshi Ronbunsyu (1991) 48, p. 671 Toyobo, JPN Kokai Tokkyo Koho JP 03,130,127 Toyobo, JPN Kokai Tokkyo Koho JP 03,216,326 Toyobo, JPN Kokai Tokkyo Koho JP 03,158,225 Teijin, JPN Kokoku Tokkyo Koho JP 63,024,459 Teijin, JPN Kokoku Tokkyo Koho JP 62,043,856 Fuji Film, JPN Kokai Tokkyo Koho JP 61,233,523 Teijin, JPN Kokai Tokkyo Koho JP 62,183,327 Teijin, JPN Kokai Tokkyo Koho JP 62,183,328 Teijin, JPN Kokai Tokkyo Koho JP 59,114,028 Yukio Mitsuishi, PET Film, P140, Gijyutsu Jyohokai Toray, JPN Kokai Tokkyo Koho JP 62,158,016 Teijin, JPN Kokai Tokkyo Koho JP 61,019,923 Toray, JPN Kokai Tokkyo Koho JP 59,187,818 Teijin, JPN Kokai Tokkyo Koho JP 01,004,921 Toray, JPN Kokai Tokkyo Koho JP 63,288,730 Toray, JPN Kokai Tokkyo Koho JP 63,293,032 Toray, JPN Kokai Tokkyo Koho JP 63,302,016 Diafoil, JPN Kokoku Tokkyo Koho JP 61,043,173 Toray, JPN Kokai Tokkyo Koho JP 01,262,119 Diafoil, JPN Kokai Tokkyo Koho JP 55,027,270 Teijin, JPN Kokai Tokkyo Koho JP 60,189,422 Toray, JPN Kokai Tokkyo Koho JP 02,102,023 Toray, JPN Kokai Tokkyo Koho JP 02,111,525 Teijin, JPN Kokai Tokkyo Koho JP 50,132,077 Kazuo Yuki, Howa Polyester Jyusi Handbook. Nikkan Kogyo Shinbunsya, 1989, p. 734 Yukio Mitsuishi, PET Film, P135, Gijyutsu Jyohokai (1990) Bower, D.I., Korybut-Daszkiewicz, K.K.P., Ward, I.M., J Appl. Polym. Sci. (1983) 28, p. 1195 Teijin, JPN Kokoku Tokkyo Koho JP 04,000,455 Toray, JPN Kokai Tokkyo Koho JP 55,027,211

57. 58. 59. 60.

Toray, JPN Kokai Tokkyo Koho JP 58,118,220 Toray, JPN Kokai Tokkyo Koho JP 58,140,221 Plastic Film no Enshin Gijyutu to Hyoka. Gijyutu Jyohokai (1992), p. 38 ex. Toray, JPN Kokai Tokkyo Koho JP 58,045,421, JPN Kokoku Tokkyo Koho JP 37,004,638, JPN Kokoku Tokkyo Koho JP 52,010,909, Teijin, JPN Kokoku Tokkyo Koho JP 46,025,534 61. Kenji Tsunashima, Plastic Age (1987) 33, p. 143

6.4

Theoretical Analysis of the Tentering Process Toshiro Yamada, Chisato Nonomura, and Susumu Kase

6.4.1 Introduction

354

6.4.2 Mathematical Model for the Extension of Thin Uneven Rubber Film 6.4.2.1 Derivation of Governing Equations 6.4.2.2 Numerical Analysis of Rubber Film Extension

354 354 361

6.4.3 Numerical Analysis of Film Extension by the Finite Element Method (FEM) 6.4.3.1 Analytical Method for Two-Dimensional Plane Stress or Strain Problem 6.4.3.2 Observation of Deformation Behavior in a Tenter 6.4.3.3 Simulation of the Bowing Phenomenon in the Tenter Process 6.4.3.4 FEM Simulation of Tensile Testing

366 366 371 373 378

6.4.1

Introduction

It is common practice to stretch a film made of linear thermoplastic polymer such as polypropylene, poly(ethylene) terephthalate, polyethylene, nylon, polystyrene, and so on, to produce an orientation that will upgrade its performance. The stretching methods are classified generally into flat film stretching and tubular inflation. In stretching a flat film in the transverse direction, a tenter is usually used. Although many articles are available on the properties of uniaxially and biaxially stretched films, those discussing the technology of the industrial stretching of films are few in number. In particular, very few publications are available on film deformation behavior in the tenter process and the tenter has usually been dealt with as a "black box" defying analysis because of its high cost and the complexity of film behavior in it. In this section several theoretical analyses of film deformation behavior in the stretching process are presented.

6.4.2

Mathematical Model for the Extension of Thin Uneven Rubber Film

6.4.2.1

Derivation of Governing Equations

Kase et al. [1 to 3] analyzed theoretically, the extension of thin film that is uneven in thickness and that obeys the constitutive equation of rubberlike elasticity. Their analyses are described in the following paragraphs. Equations (6.4.1) to (6.4.3) of continuity and momentum governing the extension of thin film uneven in thickness and always lying on the (x, y) plane are derived under the following assumptions [4]: 1. The film is incompressible. 2. Forces due to inertia, gravitational pull, surface air drag, and surface tension are negligible. 3. Assuming the film to lie on the (x, y) plane the flow field of plane film extension is such that the velocities Vx and vy are independent of the coordinate z. 4. Within the thickness H of the film the velocity vz is in direct proportion to the coordinate z. This is equivalent to assuming the film is symmetrical with respect to the (x, y) plane with the half-thickness surface of the film always coinciding with the (x, y) plane. Continuity equation: SH + S(H^ dt dx

+

a(%) ay

=

0

Momentum equation in the x direction: ^

+^

ox Momentum equation in the y direction: ^

= 0

(6.4.2)

oy

W (6.4.3) = 0 dx dy In Eqs. (6.4.1) to (6.4.3) t is time (s): x andj are Eulerian (x, y, z) space coordinates (cm): H(x, y, t) is film thickness (cm): Vx and vy are velocities in the x and y directions (cm/s): and 2 <JXX(X, y, t), (Tyy(x, y, t), and (J^(X, y, t) are the total stress components (dyne/cm ); for example, oxy(x, y, i) is the total tensile stress component acting in the y direction upon a plane perpendicular to the x-axis and so on. Discussed below are the intuitive derivations of Eqs. (6.4.1) through (6.4.3) expressed in Eulerian coordinates. We consider a rectangular domain ABCD on the film as shown in Fig. 6.4.1, whose sides are the lengths Ax and Ay, respectively, and whose coordinates at the center are (x, y). When the density of the film is constant, we obtain the continuity equation according to the following procedures. In Fig. 6.4.1, the volume of rightward polymer flow per unit time through the AD face is: +

Similarly, the volume of polymer flow per unit time through the BC face is:

A>((^) + ^ . f ]

(6.4.5)

The volume of upward polymer flow per a unit time through the AB face is given by:

H w ~ * fl

(6A6)

The volume of polymer flow per unit time through the DC face likewise is: f

H

w + d(Hv )

(6A7)

AvI

* fl v

C

D

Vx

A Figure 6.4.1 Infinitesimal film element on (x, y) plane. Volume conservation

Y

(X,Y)

B

X

Vy

The sum of polymer flow per unit time into the domain ABCD is obtained by [(Eq. 6.4.4) - (Eq. 6.4.5) + (Eq. 6.4.6) - (Eq. 6.4.7)], resulting in:

The net inflow in a unit time expressed by Eq. (6.4.8) must equal the rate of the increase in fluid volume in the domain ABCD due to increasing film thickness given by AxAy(SH/dt\ thus giving the continuity equation (6.4.1). Next, we derive the momentum equations (6.4.2) and (6.4.3). First, the stress otj is defined as the stress acting in they direction on a surface normal to the / axis by a fluid element having larger / coordinate value. In this definition, atj has a positive value in extension and a negative value in compression. Considering the above, we first try to derive the momentum equation in the x direction. In Fig. 6.4.2, the force in the x direction exerted on the side AB is given by:

Similarly, the force in the x direction exerted on the side DC is given by: T

7 + d(Ha

vx)

AvI

+H ^ "* f]

(6A10)

The force in the x direction exerted on the side AD is given by:

Then the force in the x direction exerted on the side BC is given by: As the sum of the forces in the x direction expressed by Eqs. (6.4.9) to (6.4.12) is equal to zero from assumption (2) stating that inertia, gravitational pull, surface air drag, and surface tension are negligible, the momentum equation (6.4.2) in the x direction is readily obtained. The momentum equation (6.4.3) in the y direction is derived in a similar manner. a yy

D

tfyx

C tfxy Y

a

<7xx

(X,Y)

A

X

B

Figure 6.4.2 Infinitesimal film element on {x, y) plane. Force balance

Here, for the purpose of easier handling of the geometry of film extension, we try to transform Eqs. (6.4.1) to (6.4.3) into Lagrangian expressions. Now, in consideration of the assumption (3) the position (x, y) after the deformation of the particle initially located at (u, v) can be expressed as follows: JC=/(M, v, t)

(6.4.13)

y = g(u, v, t)

(6.4.14)

The total derivatives of Eqs. (6.4.13) and (6.4.14) are: Ax =fuAu +fvAv +ftM

(6.4.15) (6.4.16)

Ay = guAu + gvAv + gtAt Then the above equations can be solved for Aw and Av to obtain; Au = {gv(Ax -ftAt) -fv(Ay - gtAt)}/(fugv Av = [fu(Ay - gtAt) - gu(Ax -ftAt)}/(fugv

-fvgu) -fvgu)

(6.4.18)

where fu, for example, denotes the derivative ofZwith respect to u. The partial derivative (d/dx) appearing in Eqs. (6.4.1) to (6.4.3) can be expressed in the derivatives with respect to the Lagrangian space variables u and v as follows: (d/dx)yJ = (du/dx)yJ(d/du\t + (dv/dx\t(d/dv\t

(6.4.19)

where the subscripts indicate the variables held constant in the partial differentiation. As (du/dx) t means the (du/dx) at Ay = 0 and At = 0, the following equation can be derived from Eq. (6.4.17): (6.4.20)

(du/dx)yJ =gv/(fugv -fvgu) Similarly, (dv/dx) t also can be obtained from Eq. (6.4.9) as follows: (dv/dx)yJ = -gu/(fugv

(6.4.21)

-fvgu)

Substitution of Eqs. (6.4.20) and (6.4.21) into Eq. (6.4.19) gives the following derivative transformation formula for (d/dx)yt: (d/dx)yJ = {gv{d/du\t - gu(d/dv)UJ}/(fugv

-fvgu)

(6.4.22)

-fvgu)

(6.4.23)

Similarly, the formula for (d/dy)xt is obtained as follows: (d/dy)Xtt = {-№/du)v,

+fu(d/dv)UJ}/(fugv

In the same manner, the partial derivative (d/dt) can be expressed in the derivatives with respect to the Lagrangian space variables u and v as follows: {d/dt\y = {d/dt\v + (du/dt)Xfy(d/du)VJ + {dv/dt\y(d/dv\t

(6.4.24)

The (du/dt)xy and (dv/dt)xy in Eq. (6.4.24) can be obtained by equating Ax = Ay = 0 in Eqs. (6.4.17) and (6.4.18) to obtain: (3/St)x j = (d/8t)UtV + + gtifvWto\t

[ft{-gv(d/du)Vtt+gu(d/to)u,t} -Wl'to)u,t)V'ifugv

-fvgu)

(6.4.25)

From Eqs. (6.4.22) and (6.4.23) the relationships below follow: (Bf/Bx)yJ = 1; (Bf/By)XJ = 0; (Bg/Bx)yJ = 0; (Bg/By)x, = 1

(6.4.26)

where fU9 fV9 a n d / represent (Bf/Bu)9 (Bf/Bv), and (Bf/Bt)9 respectively; andg w , gv, andg^ represent (Bg/Bu), (Bg/Bv)9 and (Bg/Bt)9 respectively. Then, the velocity components in the x and y directions, Vx and vy9 are given as Eqs. (6.4.27) and (6.4.28) in Lagrangian expressions: Vx = (Bf/Bt)UtV =ft

(6.4.27)

vy = (9g/Bt)UtV=gt

(6.4.28)

As the expressions of Eqs. (6.4.1) to (6.4.3) in Lagrangian (u, v, w) coordinates is preferable to those in Eulerian (x, y, z) space coordinates for their convenience in handling the geometry of film stretching, all subsequent equations are done in Lagrangian (w, v, w) coordinates. Suppose the rubber thin film is relaxed and stress free before extension and the film element located at point (u, v) in the (x, y) plane at t — 0 moves to position (f g) after the extension. The continuity equation (6.4.1) can be then converted to the Lagrangian expression (6.4.29) by use of the transformation formulas (6.4.19) through (6.4.25) to obtain: 1 BH H Bt

Wdt)(fugv -fvgu)]u,v fugv -fvgu

Equation (6.4.29) can be integrated from t = 0 to t = t with respect to time t to obtain

x

=m^r^-f^

(6A30)

where H0(u, v) or H(u, v, t)is the film thickness before the extension (when t = 0) and after the extension (when t = t), respectively. The % is the film thin down ratio. In a similar manner we can obtain the Lagrangian expressions (6.4.31) and (6.4.32) of the momentum equations (6.4.2) and (6.4.3): {gv(B/du) - gu(BIBV)](HGX,) + {-fv(B/Bu) +fu(B/Bv))(Ho^) = 0

{gv(B/Bu) - Eu(BZBv)](H^) + {-fv(B/bu) +UBIBv)](Ho^) = 0

(6.4.31)

(6.4.32)

On the other hand, the constitutive equation for a material which shows rubber elasticity behavior is given by Eq. (6.4.33) for the incompressible large deformation: CT = G ( X - I ) - ^ - I

(6.4.33)

where a is the stress tensor expressed by Eq. (6.4.34), G is the elastic modulus of rubber,/? is the static pressure when the compressive stress is positive, 1 is the unit tensor defined by Eq.

(6.4.35), and \ is the strain tensor given by Eq. (6.4.36) expressed as the product of displacement tensor 7 and its transpose Y T : G

xx

G

xy

°xz

<*= °yx °yy °yz _Gzx

G

zy

(6.4.34)

°zz _

"1 0 0" 1 = 0 1 0 0 0 1_

(6.4.35)

\ = 7 •7T

(6.4.36)

Suppose a material particle constituting an elastic body is located at position (u, v, w) in the Eulerian (x, y, z) space initially in a relaxed state and subsequently moves to position (f, g, h) because of a deformation of the body. Then (u, v, w) constitute a set of body or Lagrangian coordinates with (f, g, K) serving as the dependent variables in a set of simultaneous partial differential equations governing the general three-dimensional deformation. It is known further that such a deformation can be described by the displacement tensor 7 defined as: y=

"Bf/Bu Bf/Bv Bf/BwI \fu fv fw~ dg/du dg/dv dg/dw = gu gv gw _dh/du

dh/dv

Bh/Bw]

\_hu

hv

(6.4.37)

hw _

In the extension of thin flat films the previous assumptions (1) through (4) hold to greatly simplify Eq. (6.4.37). From assumption (3) stating that/and g are independent of w, the following relationship holds: Zw=Sw = O

(6.4.38)

From assumption (4) stating that the velocity vz is always in direct proportion to the coordinate z, the following relationship holds: h(u, v, w) = w- h*(u, v)

(6.4.39)

where /2* is the initial thickness distribution. Differentiating h(u, v, w) with respect to w, we obtain: A11(K, v, w) = w- hu*(u, v)

(6.4.40)

As the average of the hu in Eq. (6.4.40) over the thickness H of the film is equal to zero as a result of the symmetry with respect to the half-thickness plane, we obtain: 1 tH/1

h (u v) tH/1 hu=-\ w- hu(u, v)-dw= MV ' } w-dw = 0 (6.4.41) H J -H/2 ti J-H/2 Similarly hv also is equal to zero. When the hu and hv in Eq. (6.4.37) are approximated by their respective averages hu and hv mentioned earlier (as the displacement in the direction of thickness is negligibly small in comparison to horizontal displacements), we obtain: hu=hv = 0

(6.4.42)

From assumption (1) of incompressibility, we obtain: ITI = (fugv -fvgJK

=i

(6.4.43)

or K = (fugv -fvgu)~l

(6-4.44)

Substituting Eqs. (6.4.38), (6.4.42), and (6.4.43) into Eq. (6.4.37), we have the following expression for the displacement tensor 7 that characterizes the extension of thin flat film uneven in thickness:

y=

"fu fv 0 gu gv 0 .0 0 (fugv-fvguyl

(6.4.45) _

The 7 in Eq. (6.4.45) is consistent with the continuity and momentum equations (6.4.1) to (6.4.3) in Eulerian expressions as these four equations are all based on assumptions (1) to (4). As the hw appearing in Eq. (6.4.37) is equal to H/H0 and to (fugv —fvgu)~l in view of the definition of hw and Eqs. (6.4.30) and (6.4.39), Eq. (6.4.30) is equivalent to Eq. (6.4.44), confirming that the continuity equation (6.4.1) in Eulerian form is consistent with the Lagrangian displacement tensor 7 in Eq. (6.4.45). The stress ozz acting perpendicularly on the free surface of the film is equal to zero when stresses are measured in gauge pressure because no external forces other than atmospheric pressure act on the two free surfaces of the film: azz = 0

(6.4.46)

Combining Eqs. (6.4.36) and (6.4.45), we find

*=

'fu+fv teu+fev .0

fugu+fvgv 0 Si+Si 0 0 (fugv-fvgur2_

(6.4.47)

Substitution of Eq. (6.4.47) into Eq. (6.4.33) considering Eq. (6.4.46) gives the final expressions of p and 0 as follows: P - Gifugu -fvguY2 - 1

<*=

°yx ayy ° 0 0 0 1

fu +fv - (fugv -fvgu) = fugu +fvgv _0

_2 fugu +fvgv gl+g2v-(fugv-fvguY2 0

(6.4.48)

-1 0 0 0_

(6.4.49)

Finally, the substitution of Eqs. (6.4.30) and (6.4.49) into Eqs. (6.4.31) and (6.4.32) gives the complete governing equations (6.4.50) and (6.4.51) below in Lagrangian form ready to be solved: r a \_g"du

r

a

a - i ^ c ^ Mfugv-fvguUu+J°

gu

Uu8v

2 J

hgu)

(6450)

a-i//.(,,••) V

JJ

O1

n/

X

(6.4.51)

Note that the continuity equation (6.4.30) is independent of the governing equations (6.4.50) and (6.4.51). Once Eqs. (6.4.50) and (6.4.51) are solved for/and g, Eq. (6.4.30) can be used separately to derive the film thickness H from the/and g values.

6.4.2.2

Numerical Analysis of Rubber Film Extension

To solve the governing equations (6.4.50) and (6.4.51) numerically for the general case, Eq. (6.4.50) is expanded to obtain Eqs. (6.4.52), consisting of the derivatives of/, g, and HQ with respect to u and v: (gvHou - guHoM +tf - (fug, -feu)-2] + H0gv[2(fJuu +f/uv) - (fu VJuuov ' Juouv

Juvou

Jvouu)\Ju&v

3

X (fuSv -fvguT ] - H0gu[2(fJuv +f/J x

Jv&u)

'

\JuuSv ' Juouv

+ft)

Juvou

Jvouu)

2

- (fu +fv )(fuvgv +fugvv -fvvgu -fvSuv)

X

(fuSv -fvSu)~ + 3(fuvgv +fugvv -fvvgu -fvSuvXfuSv -fvgu)~3] + (~fvH0u +fuH0v)

X UuSu +fvgv) - Hofv\fuugu +fuguu +fuvgv +fvguv - UuSu +fvSv)Uuu8v +fuguv Juvgu

Jvguu)\Jugv

Jvgu)

J ~r **QJuUuvgu 'Juguv "T"Jvvgv

\Jugu

* Jvgv)\Juvgv ~i~Jugvv Jvvgu

Jvguv)\Jugv

'Jvgvv

Jvgu)

J

^

(6.4.52) Similarly, Eq. (6.4.51) can be expanded to obtain the mirror image Eq. (6.4.52') of Eq. (6.4.52) derivable by exchanging/with g and u with v in Eq. (6.4.52). Finite difference approximation of the above expanded equations (6.4.52) and (6.4.52r) may be performed by replacing the derivatives such as fu, fv, fuu, and so forth with central differences defined as: fu = Us -/ 4 )/(2A),

fv = Ui ~/ 6 )/(2A), 2

fuv = (/9 ~fi - / 3 +/s)/(4A ),

fuu = Us ~ 2/1 +/ 4 )/A 2 ,

^

2

fvv = (J2 - Ifx +/ 6 )/A ,...

where A shows the common differencing increment in the u and v directions and /i> h-> - - •' /9 s n o w the/values in the nine-point differencing mesh shown in Fig. 6.4.3. By use of the relationships in Eq. (6.4.53), the expanded governing equations (6.4.52) and

(V)

i

(U)

Figure 6.4.3 Nine-point differencing mesh for numerical simulation of flat film stretching

v

u

Figure 6.4.4 Rubber string network as a model of a flat rubber film initially uniform in thickness

(6.4.52') can be transformed into two algebraic equations in the unknown/and g values at the (i, 7) mesh point and its eight neighboring mesh points shown in Fig. 6.4.3. To easily solve the governing equations (6.4.52) and (6.4.52'), an attempt was made to approximate the rubber film extension to the stretching of the "rubber string mesh" shown in Fig. 6.4.4. An individual string mesh consists of square and diagonal rubber strings initially unstressed and welded together at each mesh point denoted by the black dots in Fig. 6.4.4. The rubber strings were assumed to obey the two alternative elasticities shown by Eqs. (6.4.54) and (6.4.55): For the Hookean solid, Vi = T-I

(6.4.54)

For the rubberlike elastic body,

n=^P

(6A55)

where rj is the tensile force acting on an individual string and T is the elongational deformation defined as the present extended string length over the initial unstressed length. In the string mesh model shown in Fig. 6.4.4 the counterparts of the governing equations (6.4.52) and (6.4.52') are two equations stating the balance of x and y component forces, respectively, exerted by rubber strings to each welded mesh point.

Considering the mesh point (i, j) in Fig. 6.4.4 as point 1 and eight points from 2 to 9 neighboring point 1, the strain for the string connecting points 1 and k after stretching is given by

*

VOl-^H-te-^ AorV2A

where the denominator of Eq. (6.4.56) is the initial length between point 1 and point k before stretching; its value is A or -JlA depending on whether k is an even or an odd number. The sum (FF)11 of tensile forces in the u direction acting on point 1 is given by:

(FF\ = !>*(/* -/i)/|"\/(A-/i) 2 +fe-^) 2 1 fc=2 L -I

( 6A57 )

Similarly, the sum (FF)v of the tensile force in the v direction acting on point 1 is given by: (FF)V = J2ik(gk -gi)/\y/(fk -fif + (gk-gif 1 (6A58) where r\k can be obtained by substitution of the Tk in Eq. (6.4.56) into Eq. (6.4.54) or Eq. (6.4.55). The results of equations governing the extension of the string mesh shown in Fig. 6.4.7 are obtained by setting (FF)n = (FF)v = 0 in Eqs. (6.4.50) and (6.4.51). Equations (6.4.52) through (6.4.58) were solved numerically for three different film extension problems. In the first problem a rectangle-shaped rubber film, initially uniform in thickness having unity side lengths as shown in Fig. 6.4.5, is extended in such a manner as to form a trapezoidal outer boundary. As the film is extended point A remains stationary while point B moves to B! by a distance of C and in the direction of 45 ° northeast. Because of symmetry only the upper half of the film plus one extra row of mesh points below the center line are shown in Figs. 6.4.5 and 6.4.6. Each side of the initial square is divided into m (m = 16 as shown) equal differencing increments to form the square mesh as shown.

B'

Figure 6.4.5 Extension of initially square and even film into a trapezoidal shape. Square differencing mesh is Lagrangian (u, v) coordinates

A

B

D E

C F

C F1

B'

A

C

D E

F'

Figure 6.4.6 The (u, v) mesh after the extension described in Fig. 6.4.5. The three different curves of constant u are from left to right (1) solution of Eq. (6.4.52) and (6.4.52'); (2) string mesh approximation; rubberlike elasticity and (3) string mesh approximation, Hookean elasticity

Values of/(/, j) and g (/, j ) on the outer boundary E-A-B / -F / are known because they are forced to be uniformly extended to form the trapezoid. Moreover, owing to the center line symmetry the values of g(i, 2) on the center line are equal to zero and the/(z, 1) and g(i, 1) on they = 1 row are the mirror images of those in they = 3 row: /(i, 1) = / ( / , 3),

g(i, 1) = -g(i, 3),

g(/, 2) = 0

(6.4.59)

This leaves altogether: N = 2(m- l)(m/2 - 1) + (m - 1) = (m - I)2

(6.4.60)

Unknown values of/and g in the field of computation are shown in Fig. 6.4.5. On the other hand, governing equations (6.4.52) and (6.4.52') or (6.4.57) and (6.4.58) must hold at every inside mesh point. Accordingly, the number of equations required to be satisfied is N = (m — I) 2 , matching the number N of unknown variables given in Eq. (6.4.60). The value m = 16 (i.e., Af= 225) was used in the present problem as shown in Figs. 6.4.5 and 6.4.6. As Fig. 6.4.6 shows the above three different numerical solutions are discernible only in the curves of constant u; the rightmost u curves are due to the string mesh approximation with the Hookean elasticity in Eq. (6.4.54), the middle u curves are due to the string mesh approximation with the rubberlike elasticity in Eq. (6.4.55), and the leftmost u curves are the solution for the correct governing equations such as Eq. (6.4.52). The second example is that of a rectangle-shaped rubber film initially uniform in thickness and 1 x 3 in size, as shown in Fig. 6.4.7, extended in such a manner as to form the ABCDE shape outer boundary. The extension along the boundary ABCDE is assumed uniform. As in Fig. 6.4.6 the above three different numerical solutions are discernible only in the curves of constant u in Fig. 6.4.7; the rightmost u curves are due to the string mesh approximation with the Hookean elasticity in Eq. (6.4.54), the middle u curves are due to the string mesh approximation with the rubberlike elasticity in Eq. (6.4.55), and the leftmost u curves are the solution of the correct governing equations (6.4.52) and (6.4.52;).

C

A

D

B

Figure 6.4.7 The (u, v) mesh before and after stretching. The three different u curves are the same as in Fig. 6.4.6

E

The third example, shown in Fig. 6.4.8, is similar to the second problem shown in Fig. 6.4.7 except that the right film end is free. The numerical solution shown in Fig. 6.4.8 is for the string mesh approximation with Hookean and rubberlike elasticities. The solution of the correct governing equations (6.4.52) and (6.4.520 did not converge. In Fig. 6.4.8 the right u curves are due to the Hookean elasticity and the left ones are due to the rubberlike elasticity. It

C

A

B

Figure 6.4.8 The (u, v) mesh before and after stretching. The two different u curves are the (2) and (3) in Fig. 6.4.6

Figure 6.4.9

D

Experimental observation of rubber mesh stretching

E

is confirmed that these numerical predictions are similar to the experimental results shown in Fig. 6.4.9 [5]. When the rubber film is initially uniform in thickness, the string mesh approximation shown in Fig. 6.4.4 may be preferable to the rigorous numerical solution of the correct governing equations (6.4.52) and (6.4.52'). Because the former method produces solutions close enough to the rigorous solution, it is considerably easier for obtaining the convergence of numerical processes and is convenient in handling the unconstrained free edges of the film whenever they are present.

6A3

Numerical Analysis of Film Extension by the Finite Element Method (FEM)

6.4.3.1

Analytical Method for Two-Dimensional Plane Stress or Strain Problem

In the previous section theoretical analysis by the finite difference method (FDM) was introduced for rubber film extension, which is characterized by the finite difference approximation of the physically exact governing equations. In this section, examples of numerical analysis by the finite element method (FEM) are introduced for polymer film extension, which is characterized by replacement of approximate simultaneous linear equations by conceptual finite elements to the governing equation. The theory of a FEM about the plane problem is briefly outlined below. Please refer to a reference text on FEM such as [6] if further information is required. The general analytical procedure of the FEM is conceptually described as follows. 1. The continuum is separated by imaginary lines or surfaces into a number of "finite elements." 2. The elements are assumed to be interconnected at a discrete number of nodal points situated on their boundaries. The displacements of these nodal points are the basic unknown parameters of the problem. 3. A set of functions is chosen to define uniquely the state of displacement within each "finite element" in terms of its nodal displacements. 4. The displacement functions now define uniquely the state of strain within an element in terms of the nodal displacements. These strains, together with any initial strains and the constitutive properties of the material, define the state of stress throughout the element and, hence, also on its boundaries. 5. A system of forces concentrated at the nodes and equilibrating the boundary stresses and any distributed loads is determined, resulting in a stiffness relationship. Using the FEM mentioned previously, we can obtain approximate solutions to practical problems that are difficult to solve by other methods such as FDM, although the computation by FEM requires much computer time and its accuracy is often inferior to that obtained by a special analytical method suited for the particular problem. The above advantage of FEM can

y

m V 1 (V 1 )

Xj

i

U 1 (U 1 )

Yi

j

Figure 6.4.10 An element of two-dimensional continuum

x

be utilized to find a solution to the extremely difficult problems of tentering in film processing. Discussed below is the FEM for plane deformation. Now, we consider a typical triangular element as shown in Fig. 6.4.10, which is defined by nodes i,j, m numbered in a counterclockwise order with straight line boundaries. We first explain the displacement function. The corresponding displacement at of node /, having two components, is given by:

a, = { JJ }

(6.4.61)

All components (six components) for the three nodes of the elements are grouped in a vector ae h i a e =\aj [

(6.4.62)

where the superscript e denotes element. The displacements within an element are uniquely defined by these six values. The simplest expression is clearly given by two linear polynomials: u = (X1 + (X2X + (x3y;

v = a 4 + a 5 x + oc6y

(6.4.63)

The six constants a can readily be evaluated by solving the two sets of three simultaneous equations by substituting the nodal coordinates for (x, y). For example, three simultaneous equations for the u component of the nodal displacements are denoted by: U1 = Oc1 + (X2X1 + cc3y(;

uj = Oc1 + Oc2-Xy = a^-;

um = U1 + a2xm + cc3ym

(6,4.64)

We can easily solve Eq. (6.4.64) for oci, a2, and a3 in terms of the nodal displacements U1, Uj, um. Substituting the results obtained above into Eq. (6.4.63), we finally obtain the horizontal displacement u as follows: w = — {{at + bfc + c-yX + (a,- + bjX + Cjy)uj + (am + bmx + Cn^uJ

(6.4.65)

where «i = ^ym ~ xmyp

bt = yj -ym=

yjm;

ct =xm-

Xj = xmj

(6.4.66)

Similarly, other coefficients at ay, bj, Cj, . . . , cm can be obtained by a cyclic permutation of subscripts in the order i,j, m. Then, the A in Eq. (6.4.65) is given by: 2 A = det 1 Xj yj = 2 x (area of triangle ijm) 1 *m ym

(6.4.67)

The equation for the vertical displacement v is similarly V =

2A {(fl/

+ bfC + coi)Vi +

^

+

^

+ Cjy)Vj + ( m +

"

^*

+ Cmy)Vm]

(6.4.68)

From this point one can represent the above relationships, Eqs. (6.4.65) and (6.4.68), in the following standard form for horizontal and vertical movements of a point within the element:

u = { " } = Na* = [IN,, IN7, I N J . '

(6.4.69)

where the functions N will be called "shape functions," I is a two by two identity matrix, and N k = (ak + b k x + C ky)/ 2 A for k = i, j , m. The chosen displacement function [Eq. (6.4.63)] automatically guarantees continuity of displacements with adjacent elements because the displacements expressed by Eq. (6.4.63) vary linearly along any side of the triangle and, with identical displacement imposed at the nodes, the same displacement will clearly exist all along an interface. Second, we will explain the strain (total strain). With displacements known at all points within the element the strain at any point can be determined. The total strain at any point within the element written in matrix notation, s, can be defined by its three components which contribute to internal work as shown below:

I

ex 1 Vd/dx, sy 1 = O,

yxy\

L9/^'

O "I f , d/dy \ U I = Lu

(6.4.70)

9/9xJ m

where L is a suitable linear operator. Substituting Eq. (6.4.69) into Eq. (6.4.70), we have: h i E = Ba 6 ^[B 1 , Bj, BJJa 7 -

(6.4.71)

where a typical matrix Bt is given by B1=LINj=

"ajVf/ax, 0, \_3NJdy,

o I Vb1, o " dNt/dy = (1/2A) • 0, C1 BNf/dx] \_cf, bt _

(6.4.72)

It should be noted that in this case the B matrix is independent of the position within the element, and hence the strains are constant throughout the element. Third, we will explain the stresses. In general, the material within the element is subjected to initial strains owing to temperature change, shrinkage, crystal growth, and so on. If such initial strains are denoted by £ 0 , then the stresses will be caused by the difference between the present and initial strains. Although this initial strain vector, e0, defined by Eq. (6.4.73), in general, depends on the position within the element, it is usually represented by

average, constant values. This is consistent with the constant strain conditions imposed by the prescribed displacement function.

B0=I

h° 1 6 X)

(6A73)

Anisotropic materials present special problems, because the coefficients of thermal expansion may vary with direction. Letx' a n d / show the principal directions of the material. The initial strain due to thermal expansion becomes, with reference to these coordinates for plane stress:

Ko ) \«xee) «o = { Vo [ = { « / e

I V*/o J

(6-4-74)

l0J

where ocx and a are the expansion coefficients referred to the x' a n d / axes respectively, and 6e is the temperature rise. To obtain the strain components in the x, y system it is necessary to use an appropriate strain transformation matrix T giving 4 = TT£0

(6.4.75)

where superscript T means the transposed matrix. With /?, which is the angle of the x'—y7 coordinate system inclined against the x-y coordinate system, it is easily verified that: cos2 P sin2 P - 2 sin p cos ft 2 T = sin p COs2P 2 sin £ cosjS _ sin P cos P —sin P cos p cos2 P — sin2 P _

(6.4.76)

Thus, £0 can be simply evaluated. It will be noted that the shear component of strain is no longer equal to zero in the x-y coordinates. In addition it is convenient to assume that at the outset of this analysis the body is subjected to an initial residual stress cx0 that may be measured but the prediction of which, without the full knowledge of the material's history, is impossible. These stresses can simply be added onto the general definition. Thus, assuming general linear elastic behavior, the relationship between stresses and strains will be linear and of the form: h i a = I Gy \ = D(e - E0) + a0

(6.4.77)

where D is the elasticity matrix containing the appropriate material properties and s is given by s= \sy

I

Next, a 0 in Eq. (6.4.77) is excluded which is simply additive.

(6.4.78)

For plane stress in an isotropic material we have, by definition: Sx = (Tx/'E - vGy/E + ex0

(6.4.79)

sy = -VOx/E + Gy/E + Sy0

(6.4.80)

yxy

(6.4.81)

= 2(\ + v)TXy/E + yxyQ

where E is the elastic (Young's) modulus and v is the Poisson ratio. Solving the above for the stresses, we obtain the matrix D as

fl

F

v 0

D = —-^- v 1 0 {l v; |_0 0 (l-v)/2_

(6.4.82)

For plane strain in an isotropic material a normal stress oz exists in addition to the three other stress components. For the special case of isotropic thermal expansion we have: sx = Gx/E - VGy/E - VGJE + a6e

(6.4.83) e

Sy = -VGx/E + Gy/E - VGJE + oc6

(6.4.84)

yxy = 2(1 + v)xxy/E

(6.4.85)

but in addition sz = 0 = -VGx/E - VGy/E + GJE + a6e

(6.4.86)

On eliminating GZ and solving for the three remaining stresses and by comparison with Eq. (6.4.74) where G0 is excluded, the matrix D is

E(l-v)

^~v) °

P

D = , 1 ± \ n \ , v/(l-v) 1 (l + v)(l-2v) |^ 0 Q

0 (l-2v)/2(l-v)J

(6.4.87)

where 6e is the temperature rise and a is the coefficient of thermal expansion. For a completely anisotropic material, 21 independent elastic constants are necessary to define completely the three-dimensional stress-strain relationship. If two-dimensional analysis is to be applicable a symmetry of properties must exist, implying, at most, six independent constants in the D matrix. To describe the most general two-dimensional behavior, it can be given by: d

ll

D=

d

12

d22 (sym.)

d

13

Cl23 d33_

(6.4.88)

where the necessary symmetry of the D matrix follows from the general equivalent of the Maxwell-Berti reciprocal theorem and is a consequence of invariant energy irrespective of the path taken to reach a given strain state.

For instance, the D matrix for plane stress of a x-y anisotropic thin film (isotropic in the thickness direction) in two dimensions is given by: D=-

^ -

ri nv

d-nv? y )[ 0

nvxy 0 n 0 Q

(6.4.89)

m( i_nv2 y) J

where n = Ey/Ex, m = Gxy/Ex, Ex and Ey are the Young moduli in the x and y directions, respectively; G^ is the shear modulus; and vxy is the Poisson ratio, and then vyx can be obtained by vyx = nv^ from the relationship vyx/vxy = Ey/Ex = n from the Maxwell-Betti reciprocal theorem. When the direction of the anisotropic principal axis is inclined to the x axis considered now, to obtain the D matrix in the universal coordinates, a transformation is necessary. Taking D' as relating the stresses and strains in the inclined coordinate system (x1', / ) , the D matrix can be easily obtained as follows: D = TD'TT

(6.4.90)

where T is as given in Eq. (6.4.76). Then, the stiffness matrix Ky of the element ijm as shown in Fig. 6.4.10 is defined from the general relationship by coefficient Kg = BjDB^tdxdy

(6.4.91)

where t is the thickness of the element and the integration is taken over the area of the triangle. If the thickness of the element is assumed to be constant, a good assumption as size of elements decreases, then as neither of the matrices contains x or y we have, simply Kfj = BjDBj^A

(6.4.92)

where A is the area of the triangle defined by Eq. (6.4.67). This form is now sufficiently explicit for computation, with the actual matrix operations being left to the computer. Further expressions can be obtained in [7].

6.4.3.2

Observation of Deformation Behavior in a Tenter

Figure 6.4.11 shows a typical tenter process for successive biaxial stretching of PET films. In Fig. 6.4.11, the extruder (EXT) melts and extrudes the polymer. The extruded film is cast (CA) on a chill roll to form an amorphous sheet. The PET sheet subsequently is stretched in EXT TDJS MD

TM FW

CA Figure 6.4.11

Schematic of representative film production process

the machine direction (MD) to become the uniaxially oriented film. The film is then stretched in the transverse direction (TD) and thermoset (TS) to become the biaxially oriented film and finally trimmed (TM) and taken up on the film winder (FW). In the TD and TS sections of the tenter process films often develop the so-called "bowing" phenomenon. Bowing is a kind of uneven stretching in which a straight line drawn transversely on the film entering the tenter bends in a bow shape as the film goes through the TD and TS sections. As shown in Fig. 6.4.12 the distortion of bowing is expressed as the bow height b as percentage of film width W. When the film center lags behind the film edges the bow height b is considered positive. The bowing distortion b/ Wmeasured at different positions within the TD, TS sections consists of four zones: preheating, TD stretching, thermosetting, and cooling as indicated in Fig. 6.4.12. Shown in Fig. 6.4.13 are the changes in the distortion b/ Wof experimentally observed bowing as the film goes through the TD, TS sections. In Fig. 6.4.13 the position in the tenter is expressed as the dimensionless length L/ W which is the distance from the entrance of the Bowing line

W

Bowing line

Film Pre-heating zone

Stretching zone

Thermo-setting zone

Cooling zone TD

b

MD Four zones of tenter

Bowing distortion (%)

Figure 6.4.12

Pre-heating zone

Stretching zone

Thermo-setting zone

Cooling zone

Dimensionless length (-) Figure 6.4.13 Experimentally observed deformation behavior in tenter expressed in bowing distortion versus dimensionless length

Bowing distortion (%) Figure 6.4.14 Bowing distortion at tenter exit versus thermosetting temperature

Bowing distortion (%)

Thermo-setting temperature (°C)

Figure 6.4.15 Bowing distortion at tenter exit versus cooling temperature

Cooling temperature (0C)

tenter L divided by the film length W. We note in Fig. 6.4.13 that bowing remains insignificant in the preheating zone. As the film enters the transverse stretching zone, the film develops a negative bowing followed by a quick change into positive bowing. Bowing takes its maximum positive value in the first half of the thermosetting zone. Thereafter the bowing maintains a high positive level. The above results are somewhat different from the assumptions for the theory in the previous articles by Sakamoto [9, 10]. Figure 6.4.14 shows that higher thermosetting temperatures tend to increase the distortion of bowing, while changing the temperature of cooling does not affect bowing as Fig. 6.4.15 shows. It was found that allowing the film to shrink transversely in the thermosetting zone, that is, relaxing, tends to increase bowing as shown in Fig. 6.4.16. Negative relaxing, that is, restretching, in the thermosetting zone tends to suppress bowing.

6.4.3.3

Simulation of the Bowing Phenomenon in the Tenter Process

A FEM simulation of the phenomenon of bowing occurring in the (TD, TS) sections of the tenter process was carried out assuming the film to be a thin elastic body [H].

Bowing distortion (%)

Relaxation ratio in TD (%)

Figure 6.4.16 Bowing distortion at tenter exit versus relaxation ratio in TD within thermosetting zone

After stretching

After stretching

Figure 6.4.17

Two kinds of initial mesh

As shown in Table 6.4.1, four different materials were considered: homogeneous isotropic, homogeneous anisotropic, heterogeneous isotropic, and heterogeneous anisotropic. The shape of the film before stretching was assumed to be a rectangle (initial shape a) or a rectangle-plus-ramp shape (initial shape b) shown in Fig. 6A.17. The width of the initial rectangle was considered equal to the width of the film entering the TD section of the tenter. Initial division of the film shape into triangular elements is shown in Fig. 6.4.17. The film shapes in Fig. 6.4.17 are intended to cover the region extending from the entrance of the tenter to the point of maximum temperature located in the thermosetting zone. This choice was made because throughout the region between the maximum temperature point and the tenter exit the extent of bowing was known experimentally to remain unchanged. Figures 6.4.18 to 6.4.22 compare experimental observations of b/ W values with the results of the FEM simulation. Bowing is considered positive when the bow shape is concave toward the tenter exit, that is, when the film center lags behind film edges. Figure 6.4.18 compares experimental results with the FEM simulation assuming the film to be homogeneous isotropic and having initial shape a (rectangle). The simulation is not satisfactory. Figure 6.4.19 is the same as Fig. 6.4.18 except that in the FEM simulation the film material was assumed to be homogeneous anisotropic with four independent elastic constants: Ex, Ey, Gxy, and vxy.

Table 6.4.1

Simulation Conditions Material constants Pre-heating zone Start

Stretching zone End

Start

Case Mesh EL no. type (GPa)

ET (GPa)

(")

EL Ex (GPa) (GPa)

(")

1 2 3 4 5

4.000 1.000 4.500 1.125 1.125

0.36 0.36 0.36 0.34 0.34

4.000 4.000 4.500 4.500 4.500

0.36 4.000 0.36 4.000 0.34 4.000 0.34 4.000 0.34 4.000

a a a a b

4.000 4.000 4.500 4.500 4.500

4.000 1.000 4.500 1.125 1.125

EL Ex (GPa) (GPa) 4.000 1.000 4.000 1.000 1.000

Thermosetting zone Start

End

End

EL (GPa)

ET (GPa)

(")

EL (GPa)

Ex (GPa)

(")

EL (GPa)

(GPa)

0.36 4.000 0.36 4.000 0.36 4.000 0.36 4.000 0.36 4.000

4.000 1.000 4.000 4.000 4.000

0.36 4.000 0.36 4.000 0.36 0.500 0.36 0.500 0.36 4.000

4.000 1.000 0.500 0.500 4.000

0.36 4.000 0.36 4.000 0.42 0.500 0.42 0.500 0.36 0.500

4.000 1.000 0.500 0.500 0.500

^LT (")

0.36 0.36 0.42 0.42 0.42

Bowing distortion (%)

Casei Pre-heating zone

Stretching zone

Thermo-setting zone

Cooling

zone

Dimensionless length (-) Figure 6.4.18 Bowing, experiment and FEM simulation, Case 1 in Table 6.4.1. •, experimental; • , calculated

Bowing distortion (%)

Case 2 Thermo-setting zone

Stretching zone

Pre-heating zone

Cooling zone

Dimensionless length (-) Figure 6.4.19 Bowing, experiment and FEM simulation, Case 2 in Table 6.4.1. •, experimental; • , calculated

Figure 6.4.19 shows a comparison of the experimental results with the calculated results under the assumption that the film is a homogeneous anisotropic material with the initial film shape of a rectangle as shown in Fig. 6.4.17(a). With these constants G^ is given by the following equation:

G

xy

E

A5

\Ex

E

y

E

x J

where Ex and Ey are the Young moduli, G^ is the shear modulus (rigidity), v^ is the Poisson ratio, and E45 is the Young modulus in the direction at an angle of 45 ° to the machine (longitudinal) direction which is given by the average of Ex and Ey\ E45 = (Ex + Ey)/2. The subscripts x and y stand for longitudinal (machine) direction and transverse direction, respectively. In addition to the above the reciprocal theorem states that Vyx/v^ = Ey/Ex.

Bowing distortion (%)

Case 3

Pre-heating zone

Stretching zone

Thermo-setting zone

Cooling zone

Dimensioniess length (-) Figure 6.4.20 Bowing, experiment and FEM simulation, Case 3 in Table 6.4.1. •, experimental; • , calculated

Bowing distortion (%)

Case 4

Pre-heating zone

Stretching zone

Thermo-setting zone

Cooling zone

Dimensioniess length (-) Figure 6.4.21 Bowing, experiment and FEM simulation, Case 4 in Table 6.4.1. •, experimental; • , calculated

In the FEM computations fixed values were given to the above elastic constants at the entrance and exit of each zone and the values within the zone were assumed to be linear interpolations of values at the entrance and exit. Isotropic materials were assumed to have two independent elastic constants E and v, meaning that E = Ex = Ey — E45 and v — v^ = vyx. Evidently the simulation shown in Fig. 6.4.19 is not good enough. Figure 6.4.20 shows the comparison for the case of heterogeneous isotropic film with initial shape a (rectangle). Again the simulation is not entirely satisfactory. Figure 6.4.21 is for the case of the heterogeneous anisotropic film with initial shape a (rectangle). The FEM simulation in this case is worse than the one in Fig. 6.4.20.

Bowing distortion (%)

Case 5 Pre-heating zone

Stretching zone

Thermo-setting zone

Cooling zone

Dimensionless length (-) Figure 6.4.22 Bowing, experiment and FEM simulation, Case 5 in Table 6.4.1. •, experimental; • , calculated

Figure 6.4.22 is for the case of the heterogeneous anisotropic film b [rectangle-plusramp; see Fig. 6.4.17(b)]. This particular initial film shape b was conceived to take into consideration the 20% or more shrinkage of the bioriented film entering the thermosetting zone at 105 0 C near the transverse stretching temperature. In other words the ramp part of the initial film shape was intended to include in advance the plastic deformation measured as the shrinkage of the film just after the TD extension. The simulation shown in Fig. 6.4.22 is more satisfactory than any of the ones shown in Figs. 6.4.18 to 6.4.21. Agreement with experimental values is particularly good at and after the point where the bowing turns from negative to positive values.

6.4.3.4

FEM Simulation of Tensile Testing

Tokuda [12] carried out a series of FEM simulations for the tensile testing of polyethylene terephthalate (PET) films, assuming the film to be a two-dimensional elastic-plastic body. The simulation covered several different aspects of the tensile extension of PET films. First was the simulation of the large two-dimensional deformation of PET film specimens in tensile testing. The second was the numerical prediction of the effects of initial transverse thickness nonuniformity. The third simulation concerned the tensile testing of PET film specimens containing fine spherical particles. Local deformation in the vicinity of the particle was simulated with respect to the formation of a protrusion on the film surface and the formation of a void around the particle. For the FEM simulation the rheology of the PET film in the thermoplastic region was assumed to be represented by the dynamic model shown in Fig. 6.4.24 which in turn simulates the rheology of the amorphous (A) and crystalline (C) model structure shown in Fig. 6.4.23. The dynamic model expressed in the form of constitutive equations is: a = ox + (T2

(6.4.94)

dox/dt = -(Jx/T + G' dl/dt (72 = rj- dl/dt

(6.4.95) (6.4.96)

T = rj/G

(6.4.97)

where a, Oe1, and a2 are stresses applied to the film as shown in Fig. 6 A.24; t is time; G is shear modulus (rigidity); X is elongational deformation or stretch ratio; rj is coefficient of viscosity, and T is relaxation time. The C in Fig. 6.4.24 is the nonlinear elastic element and its shear modulus G (rigidity) is given by the formula: G = C1(T)(X"1 - rn) +

C2(X/K)P{T)

(6.4.98)

where Tis absolute temperature: Cx(T), C2, m, n, K, and P(T) are characteristic parameters of a polymer having constant values at a given temperature. The A in Fig. 6.4.24 is the nonlinear viscous element having a coefficient rj of viscosity given by: n =/(A) • n°° • (TT/2) ( "- 1)/2 • exp[t/(l/r - l/T0)/R\

(6.4.99) o

Force

tfi

G2

c A

I

C

A

Figure 6.4.23 Orientation structure model for PET film

A

Figure 6.4.24 Dynamic rheology model equivalent to the model shown in Fig. 6.4.23

where/(i,) is a characteristic parameter of the polymer and is a function only of elongational deformation, rf° is the coefficient of viscosity at infinite time, (/is apparent activation energy in the Andrade expression, R is the gas constant, n is a characteristic parameter, and T0 is the reference temperature. To test the adequacy of the above constitutive equations, three different tensile tests were carried out on PET film specimens. The results shown in Fig. 6.4.25 are (a) tensile testing of as-cast amorphous film, (b) continuous roller drawing of as-cast amorphous film, and (c) transverse stretching of uniaxially oriented film, all over a range of temperatures. Shown in Fig. 6.4.26 are stress (7-elongation curves X due to FEM simulation assuming PET and an elongational strain rate of 50%/s. The simulated curves in Fig. 6.4.26 are in qualitative agreement with the experimental curves in Fig. 6.4.25.

a (MPa) a (MPa)

X (-)

a (MPa)

A(-)

Figure 6.4.25 Experimental stress cr-elongation X curves of PET film. (a) Tensile testing of as-cast amorphous film; (b) continuous roller drawing of as-cast amorphous film; (c) transverse stretching of drawn oriented film on testing machine

a (MPa) Figure 6.4.26 Simulated stress cr-elongation X curves for PET film

A (-)

A

Figure 6.4.27 Experimentally observed deformation of PET film in tensile testing

I

Figure 6.4.28 FEM simulation of the tensile testing shown in Fig. 6.4.27

Pre-heating zone Figure 6.4.29 Transverse unevenness. The shaded part of the film is initially 2% thicker than the rest of the film

Stretching zone

Temperature (0C)

Q T s : Set temperature T: Film temperature Q : Unevenness of thickness T5 T

Unevenness of thickness (-)

Stretching zone

Pre-heating zone

Distance from Inlet of tenter (m)

Stretching zone

Temperature (
Q T s : Set temperature T : Film temperature Q : Unevenness of thickness Ts T

Unevenness of thickness (-)

Pre-heating zone

Distance from Inlet of tenter (m)

Figure 6.4.30 Magnification of the initial 2% unevenness, a FEM simulation. (a) Fine tuning of temperature by providing five zones; (b) just two temperature zones provided

2R

Initial mesh Displacement Particle

Higher temperature In stretching

After stretching Lower temperature Void In stretching Void Figure 6.4.31 Polymer deformation around a spherical particle contained in the film

After stretching

Angle (deg.)

Figure 6.4.27 shows the uniaxial stretching of a rectangular PET film. Square grids were drawn on the film before stretching. Shown in Fig. 6.4.28 is the FEM simulation of the experiment in Fig. 6.4.27. A fair agreement was obtained between the two. Next FEM modeling was made to predict the magnification Q of transverse variation of film thickness while in TD stretching. The shaded part of the film shown in Fig. 6.4.29 was assumed to be initially 2% thicker than the rest of the film. As the transverse (TD) extension proceeds the initial 2% nonuniformity was predicted to be magnified as shown in Fig. 6.4.30.

Figure 6.4.32 Angle of surface protrusion versus distance from film surface to particle, experimental. •, condition A (lower tensile stress); • , condition B (higher tensile stress)

Film surface

9 : Ange l

2R

1R 2R 3R

4R

6R

Distance from film surface to particle

8R

Two different cases were considered in the simulation. In case (b) the film is subjected to just two different temperatures, one in the preheating zone and another in the TD stretching zone. By contrast in case (a) a total of five temperature zones were provided to enable a finer tuning of environmental temperature. Note that the fine tuning results in a considerably lower magnification of the 2% initial thickness nonuniformity. Finally a FEM simulation was made to predict the deformation in the neighborhood of a fine spherical particle contained in the film being extended. Mixing of these particles into the film is for the purpose of creating a texture on the film surface and the deformation around the particles is known to greatly affect the texture. Figure 6.4.31 shows the simulation results for two different stretching conditions. The upper part of Fig. 6.4.31 is the initial mesh of film before stretching, the middle is the deformation behavior in higher temperature stretching, and the lower is the deformation behavior in lower temperature stretching. As a result the tensile stress is lower in higher temperature stretching than in lower temperature stretching. The protrusion or rise of film surface near the particle is predicted to be much more pronounced in higher temperature (lower tensile stress) stretching than in lower temperature (higher tensile stress) stretching. The formation of a large void on each end of the particle is predicted in lower temperature stretching. In contrast with higher temperature stretching no void is predicted to form. Shown in Figs. 6.4.32 and 6.4.33 are experimental results corresponding to the FEM predictions in Fig. 6.4.31. When a PET film containing fine glass beads was extended at a high temperature and a low extension ratio (condition A), which led to lower tensile stress, a pronounced steep peak formed around the glass bead. In contrast, condition B, having lower temperature and higher extension ratio which led to lower tensile stress, produced no outstanding peak. That is, condition A results in much more distinguished peak formation than condition B.

Figure 6.4.33

Photography of film surface showing ruptured void around embedded particles

Further, condition B brought about void formation around the glass beads as the scanning electron microscope (SEM) photograph in Fig. 6.4.33 shows. Evidently the FEM predictions shown in Fig. 6.4.31 are consistent with experimental results. Theoretical analysis of the deformation of polymer films in the tenter process still has a very short history. It is highly desirable to clarify the behavior of the film in the tenter which has been heretofore regarded as the "black box" of the film production process. We would be satisfied if our descriptions, even in a minor way, help elucidate film behavior in the tenter.

References 1. Kase, S., Nishimura, T., Sonoda, Y., Kado, M., Takuma, K., Bull. Faculty Textile ScI Kyoto Inst. Technol (1988) 12, p. 33-50 2. Nishimura, T., Kase, S., Hino, K. Bull Faculty Textile ScL Kyoto Inst. Technol (1989) 13, p. 69-80 3. Kase, S., Nishimura, T., J Rheol (1990) 34, p. 251-273 4. Kase, S., Kono, N., Higuchi, T., Bull Faculty Textile ScL Kyoto Inst Technol (1987) 11, p. 303-350 5. Yamada, T. (unpublished work) 6. Zienkiewicz, O.C., The Finite Element Method, 3rd ed. (1977) McGraw-Hill, New York 7. Lekhnitskii, S.G., Theory of Elasticity of an Anisotropic Elastic Body (1963) Translation from Russian by R Fern. Holden Day, San Francisco 8. Nonomura, C , Yamada, T., Matsuo, T., J Japan Soc. Polym. Process. (Seikei-Kakou) (1992) 4, p. 312317 9. Sakamoto, K., J Japan Soc. Polym. Process. (Seikei-Kakou) (1991) 3, p. 496-502 10. Sakamoto, K., Koubunshi Ronbunshuu (1991) 48, p. 671-678 11. Yamada, T., Nonomura, C , J. Appl Polym. ScL (1993) 48, p. 1399-1408 12. Tokuda, T., Preprint in the 2nd Annual Meeting of the Japan Society of Polymer Processing (SeikeiKakou), (1990), p. 235-236

7.1

Double Bubble Tubular Film Process System and Theoretical Analysis of Stress Development and Scaleup Rule Masao Takashige and Toshitaka Kanai

7.1.1 Introduction

387

7.1.2 Technical Trends and Typical Applications

387

7.1.3 Experimental and Theoretical Background 7.1.3.1 Outline of the Double Bubble Tubular Film Process 7.1.3.2 Relationship Between Process Conditions and Film Stretching Stress 7.1.3.3 Scaleup Rule for the Double Bubble Tubular Film Process

388 388 389 390

7.1.4 Results and Discussion

391

7.1.4.1 Conclusion 7.1.5 On Adaptability to Noncrystalline Resin (PS)

397 400

7.1.6 The Film Stretching Process and Its Physical Properties (Simultaneous versus Multistage) 402 7.1.7 The Heat Set Technique (Production of Shrink Film)

404

7.1.8 Development of Peripheral Technology for the Double Bubble Tubular Biaxial Stretching Process 7.1.9 Prospective Directions of Double Bubble Tubular Biaxial Stretching

405 407

7.1.1

Introduction

In addition to the tenter frame process the double bubble tubular film process is one of the most important polymer processing operations to produce biaxially oriented film. Particularly for the case of oriented nylon-6 film, this process is widely used to produce biaxial stretched film, because the tenter frame process, which is usually a multistage process, has difficulty in producing a uniform film because of hydrogen bonding generated perpendicular to the machine direction in the first stage stretching. Thus it is important that we learn how to use the double bubble tubular process more effectively through the choice of resins and process conditions based on processability and film quality. Little research work has been reported, however. Kang et al. [1, 2] reported basic studies of polyethylene terephthalate (PET) double bubble tubular film that cover the influence of process conditions on the stability of bubble formation and structure development in the film. This double bubble tubular film process is closely related to the tubular film one, so we use the basic studies reported on the tubular film process. Studies on the tubular film process were investigated by various researchers. The earliest investigations were published by Alfrey [3] and also by Pearson [4], generally considering kinematics and stress analysis as applied to membranes. In a subsequent series of articles, Pearson and Petrie [5 to 7] elaborated on this analysis and made specific calculations for an isothermal Newtonian fluid model. An isothermal viscoelastic model was described by Petrie [8]. Analysis of temperature fields and their interaction with kinematics were first considered in articles by Han and Park [9] and Petrie [10] in 1975. These efforts were continued by Wagner [11, 12] in a later article. Kanai and White [13] considered local kinematics and heat transfer rates as well as bubble stability. These results were used as the basis for construction of a model of the dynamics, heat transfer and structure development in tubular film extrusion. A later report [14] represented an advance on earlier articles on modeling by inclusion of crystallization and more quantitative representations of local transfer rates. These studies apply the theoretical equations to the tubular film process using high molecular weight high-density polyethylene as an example [15] and dealt with scaleup [16]. The theory and practice of the single bubble tubular film process is dealt with in detail in Chapters 3.1, 3.2, 3.3, and 3.4 of this volume.

7.1.2

Technical Trends and Typical Applications

The double bubble tubular biaxial stretching process has been studied using various resins such as polyvinylidene chloride (PVDC), polypropylene (PP), PET, polystyrene (PS), nylon6 (Ny6), ethylene vinyl alcohol copolymer (EVOH), and polyphenylene sulfide (PPS) [17 to 36]. Among many other resins, PP, Ny6, and PS are being produced by both tenter and double bubble tubular processes, and the features of each of these processes are well suited to these

polymers. In OPP films, the tenter frame process plays a major role in terms of production, yet almost all types of shrink films are produced by the double bubble tubular process because of the high shrinkage and shrink balance the process develops. A specific way of using shrink film is as follows: To protect various forms of goods, such as instant noodles or cosmetics, the film is wrapped around the goods, external heating is applied, and the film shrinks tightly around the product. This use of shrink film protects goods from dust, prevents tampering, and is gaining in use. To enhance the value of goods, film with a high shrinkage percentage enhances the consumer's sense of close contact with the product. PP shrink film formed by the double bubble tubular biaxial stretching process responds to this need. Biaxially oriented Ny6 films are produced by five different Japanese companies using five different processes and they are competing with one another in the same market applications. The processes employed by these manufacturers are roughly divided into three: (1) a multistage biaxial stretching in a tenter frame, (2) a simultaneous biaxial stretching in a tenter frame process, and (3) a simultaneous biaxial stretching version of the double bubble tubular process. These processes have almost the same share of the market. O H

Il I In the case of Ny6 resin in particular, there is an amide linkage —C—N— in the molecular structure, and thus hydrogen bonding occurs readily between molecular chains. For this reason, multistage film forming difficulties are encountered in the biaxial stretching process such as film breaks and uneven stretching. If the molecules are oriented in the machine direction (MD) at first, hydrogen bonds always occur, this causes resistance to transverse direction (TD) orientation. On the other hand, the simultaneous biaxial stretching process can give an even force to the surface in both directions without forming these strong hydrogen bonds, this process is widely used for biaxial stretching of Ny6. Other resins that are characterized by this strong hydrogen bonding include EVOH and polyvinyl alcohol (PVA), and the resulting difficulties are being coped with by using the double bubble tubular biaxial stretching technique (simultaneous biaxial stretching process). In this section, mention is made of the technical development of the double bubble tubular biaxial stretching technique of Ny6 in view of its commercial success. At the outset, we explain the analysis of stretching stress and stretching deformation behavior and then touch upon the scaleup analysis. Furthermore, we state the impact of the simultaneous and multistage biaxial stretching processes and the influence of the heat set conditions upon film properties. Lastly, we forecast the technical trends of this double bubble tubular biaxial stretching process, including how to make the best use of it in the future.

7.1.3

Experimental and Theoretical Background

7.1.3.1

Outline of the Double Bubble Tubular Film Process

A schematic view of the double bubble tubular film process is shown in Fig. 7.1.1. At first a nylon film is produced with low orientation and crystallization by the tubular film process

T A K EU PR O L A R IN R G I H E A N T G I A PA R A T U S

N01 (TOP)

EXTRUDER

DIE

COOLING BATH

T A K EU PR O L N02 (BOTTOM)

A N N E N A G L I WINDING

TAKE UP ROLL

Figure 7.1.1

Schematic view of double bubble tubular film process

cooled by chilled water, which prevents crystallization. Then the tubular film is biaxially stretched between two pairs of top and bottom nip rolls. Biaxial stretching occurs in the heating apparatus controlled by the heater temperature and cooling air velocity. The stretching ratio in both machine direction (MD) and transverse direction (TD) is determined by inside bubble pressure and the difference in roll speeds between the top and bottom rolls.

7.1.3.2

Relationship Between Process Conditions and Film Stretching Stress

In this manner the second bubble is simultaneously stretched in both machine direction and transverse directions. Figure 7.1.2 shows the method of measuring the stretching stresses. Stretching stresses were calculated with the help of Eqs. (7.1.1) and (7.1.2):

* ™ = ^

^ = ^k

(7.U)

(7L2)

-

HEATING

AP

:

INSIDE BUBBLE PRESSURE

T

: TORQUE

R

: BUBBLE RADIUS

Hu

: FILM THICKNESS

APPARATUS

R AP HL

r Figure 7.1.2

T

Measurement method of stretching stress

where AP, 7, R, r, and HL are inside bubble pressure, torque, final bubble radius, radius of bottom nip rolls, and final film thickness respectively. The deformation rate Df is calculated as follows: D

, = § x l x ±

CMJ,

where D0, D, and t are thickness of the unstretched film, thickness of stretched film, and time of deformation. The bubble stability is closely related to the deformation pattern, but it is very difficult to measure the deformation pattern during the second bubble inflation, because the heating apparatus covers the bubble. To analyze the behavior of the deformation pattern, the extruder and takeup device were suddenly stopped and a bubble sample was collected. The bubble width pattern and film thickness at each position of the bubble sample were measured on the bubble sample. Stretching ratio at each position was calculated by using the bubble width and film thickness patterns. The birefringence was measured by using Olympus BH2 (type Olympus BH-2, Japan) at each point.

7.1.3.3

Scaleup Rule for the Double Bubble Tubular Film Process

A scaleup rule for the tubular film process is developed from theoretical principles [16]. The force balance on the double bubble tubular film is developed from membrane theory.

Membrane theory leads to a set offerees on the film between positions Z and takeup position L. This has the form: F1 = 2nRHaMD cos 6 + n(R2L - R2) - AP

(7.1.4)

The stresses aMD and aTD are related to the pressure AP through the expression: K2

A1

where FL is the bubble tension, RL is the final bubble radius, and R1 and R2 radii of curvature.

((1+dR/dZ)2?'2

*

1=

an

appropriate

R R2=

^RTdZ*

are

^i0

(7 L6)

-

are

The maximum stretching stresses GMD d ^TD closely related to the physical properties of the film. The maximum stress at the final stretching point is used to set up the scaleup rule. At the final stretching point, bubble diameter is equal to final bubble diameter: *- = 2 *

T

D

(7 L7)

^

-

= ^

(7.1.8)

where H1 is the final film thickness. By using dimensional analysis, the stresses <7MD and
B Qri0RL

Qr10 K0K1H1

Qn0R1,

°™ = n-W[=G2W[

Qr10 K0K1H1

(7 U0)

-

where Q is output rate; ^ 0 is viscosity; R0 is initial bubble radius; ZL is axial distance between beginning point and final point of bubble inflation; A and B are constants under the same conditions of RL/R0, VL/V0, ZL/R0; G1 and G2 are constants under the condition of constant stretching ratio in the machine direction and transverse direction. It is observed that the stretching stress was a function of film thickness and the square of bubble diameter.

7.1.4

Results and Discussion

The most important factor for the double bubble tubular film process is bubble stability. Many process conditions influence bubble stability, including stretching ratio, process temperature, deformation rate, film thickness, and the cooling conditions. Three of these factors—the stretching ratio, process temperature and deformation rate—were studied. Figure 7.1.3 shows the relationship between stretching stress and stretching ratio. The stretching stress increases

STRETCHING STRESS (Kg/cm 2 )

BUBBLE BREAK

MD TD

STRETCHING RATIO

Figure 7.1.3 Relationship between stretching ratio and stretching stress

with increasing stretching ratio. The bubble break occurs above a stress of about 1300 kg/cm 2 and bubble instability occurs below a stress of about 600 kg/cm 2 . The relationship between stretching stress and process temperature is shown in Fig. 7.1.4. The stretching stresses in both the MD and TD decrease with increasing process temperature in the same manner. The bubble break occurs over a stress of 1300 kg/cm 2 and bubble instability occurs below a stress of 600 kg/cm 2 similarly to what is seen in Fig. 7.1.3. Figure 7.1.5 shows the relationship between stretching stress and deformation rate. The stretching stress of the MD decreases with increasing deformation rate. The computed value of D0/D x if gives the value (%/S). When (%/s)= 1000 the deformation rate= 1.0 in Figure 7.1.5. On the other hand, the stretching stress in the TD increased with increasing deformation rate. The decrease of deformation rate can cause both bubble instability and bubble break within the experimental range. The cross point of stretching stress, which means crMD is equal to crTD, gives very good processability. Figure 7.1.6 shows a typical example of bubble shape during the second bubble inflation. It is found that the bubble shape is influenced by the deformation rate, which is controlled by heater temperature, cooling air speed, drawdown ratio, and blowup ratio. The differences between the MD and TD stretching ratios are calculated from Fig. 7.1.7 and plotted in Fig. 7.1.8 for two different deformation rates. Initially the MD stretching increases more rapidly than for the TD but they eventually return to relative balance. The birefringence at each position of the sample after it was stopped was measured. Figure 7.1.9 shows the relationship between birefringence and distance from air ring under the different deformation rates. The birefringence for the low deformation rate is clearly

MD

BUBBLE BREAK

STRETCHING STRESS (Kg/cm 2 )

TD

BUBBLE INSTABILITY

PROCESS TEMPERATURE

Figure 7.1.4

( 0C )

Relationship between stretching stress and process temperature

STRETCHING STRESS (Kg/cm2)

BUBBLE BREAK

CROSS POINT OF STRETCHING STRESS (
BUBBLE INSTABILITY

DEFORMATION RATE MEASUREMENTOF DEFORMATION RATE D0 = THICKNESS OF NON-STRETCHING FILM D = THICKNESS OF STRETCHING FILM t = TIME OF DEFORMATION DEFORMATION RATE = 2 l

x

J_ x

100

MD TD

(o/o/S)

1000(%/S)= 1.0 Figure 7.1.5

Relationship between stretching stress and deformation rate

=


MO)

DEFORMATION RATE 1.0

Figure 7.1.6

DEFORMATION RATE 0.6

Bubble shape during the second bubble inflation for different deformation rates, 1.0 and 0.6

higher than that for the higher deformation rate. These results correspond to the experimental values for stretching ratio difference shown in Fig. 7.1.7. Process conditions influence the behavior of the stretching stress pattern during the second bubble inflation process. As shown in Fig. 7.1.10 the strain rate in the MD is greater than in the TD. At low deformation rate the strain rate of TD increases slowly. Figure 7.1.11 shows the results through the polarizing plate of the bubble sample which is related to stress development during the second bubble inflation process. It suggests that the deformation range is broad under the low deformation rate. This observation is consistent with the stretching ratio pattern. In the evaluation of film thickness uniformity, Fig. 7.1.12 shows the uniformity of the stretched film thickness is worse than that of the unstretched film thickness and high temperature causes large deformations and makes the film thickness variation worse. To support the scaleup rule derived theoretically, stretching stresses under the different film thickness and different die diameters were measured. We calculated the cross point of deformation rate where the stretching stress in the MD is equal to the stretching stress in the TD. The stretching stress for the different starting film thicknesses, 90, 120, and 160/mi, using two die diameters, 50 and 75 mm^, were measured. For the case of converting bubble radius R and film thickness H into KR and LH, the output rate K2LQ is needed. Figure 7.1.13 shows the relationship between film thickness, extrudate, and stretching stress in the case of 75mm0 dies. Figure 7.1.14 shows the relationship between film thickness, extrudate, and stretching stress in the case of 50 mm^ dies.

1.0

STRETCHING R A T I O

DEFORMATO I N RATE

MD TD

DISTANCE FROM AIR RING (cm) DEFORMATO I N RATE

Figure 7.1.7 Stretching ratio pattern in each position

0.6

DISTANCE FROM AIR RING (cm)

The extrusion rate at the cross point increases with increasing film thickness. The cross point of stretching stress is shown in Fig. 7.1.15. The extrusion rate that corresponds to cross point is directly proportional to film thickness and is proportional to deformation rate. The slope of the straight line of the 75 mm die and 50 mm(/> die, and the ratio of the slope of the 75mm0 die to the slope of the 50mm(/> die were calculated. The ratio is 2.25. The square 2.25 of the ratio of the diameter of the 75 mm0 die to the 50 mm0 die is 2.25. This result suggests that the scaleup rule of the bubble diameter is applicable, namely the cross point of stretching stress is a function of QfR2H. The scaleup rule is applicable to predict the physical properties and bubble stability. As a result of the experimental evaluation, we found that the stretching stress and deformation pattern were very important factors to produce biaxially oriented Ny6 film by the double bubble tubular process.

( M D - T D)

DIFFERENCE OF STRETCHING RATIO

DEFORMATION RATE UO DEFORMATION RATE

0.6

D I S T A N C E FROM A I R R I N G ( c m )

Difference in stretching ratio, M D - T D

Birefringence ( M D - T D )

Figure 7.1.8

Distance from Air ring Figure 7.1.9

(CITI)

Birefringence pattern versus distance from air ring

DEFORMATION RATH

1. 0

DEFORMATION RATE

0. 6

DEFORMATION RATE

1.0

STRAIN RATE (SEC"')

MQ ID.

DISTANCE FROM AIR RING ( c m )

DEFORMATION RATE

Figure 7.1.10 Strain rate at different deformation rates

0.6

DISTANCE FROM AIR RING ( c m )

We can predict the bubble stability and film physical properties for a large scale double bubble tubular film process, if the double bubble tubular film extrusion is carried out using a small-scale machine and a small amount of resin.

7.1.4.1

Conclusion

The double bubble tubular film process of Ny6 was investigated. An optimum stretching stress range during the second bubble process exists. Bubble breakage occurs above a stress of 1300 kg/cm 2 and the bubble instability occurs below a stress of 600 kg/cm 2 . The cross point of stretching stresses (ffMD = erTD) which depends on deformation rate and bubble stability, is an optimum point.

DEFORMATION RATE 1.0

DEFORMATION RATE 0.6

(%)

Figure 7.1.11 Observation through a polarizing plate of the second bubble sample for different deformation rates, 1.0 and 0.6

THICKNESS U N I F O R M I T Y

STRETCHED FILM

NON-STRETCHED FILM

PROCESS TEMPERATURE ( I C )

Figure 7.1.12

Influence of process temperature on film thickness uniformity

Deformation rate is closely related to bubble stability. The higher deformation rate in both the MD and the TD leads to better bubble stability. The better bubble stability leads to better film thickness uniformity and film quality. The scaleup rule is applicable to predict the film physical properties and bubble stability. We can predict the bubble stability and film physical properties for a large scale double bubble tubular film process, once a trial extrusion is carried out using a small-scale machine and a small amount of resin.

75<> j Dies 120*i

160*i

Stretching Stress (Kg/cm2)

90*i

Extrudate (Hg/Hr) Figure 7.1.13

Relationship between extrudate and stretching stress in each film thickness

75(|> Dies 120*1

16OjLi

2

Stretching Stress (Kg/cm )

90 *i

Extrudate (Hg/Hr) Figure 7.1.14

Relationship between extrudate and stretching stress in each film thickness

75(|> Dies

Extrudate (Kg/Hr)

Y = 0.147X

Y = 0.65X 50<> | Dies

Film thickness (\i) Figure 7.1.15 Cross point of stresses as functions of extrusion rate and film thickness for different die diameters, 50 mm and 75 mm(/>

7.1.5

On Adaptability to Noncrystalline Resin (PS)

Studies have been conducted on a double bubble tubular biaxial stretching process using PS as a typical noncrystalline resin [37]. In this publication an effort was made to forecast not only the forming behavior and stress deformation but also to study the forming behavior on scaleup of the equipment by means of computer simulation which uses a numerical analysis method. As a result, there is a good agreement between theory and experiment for the correlation between the bubble inner pressure and the resulting bubble tension. Also a good correlation is seen between the shrinkage stress and the maximum stretching stress obtained from theory (Fig. 7.1.16). The literature states that theoretical predictions were gained concerning the deformation velocity of double bubble tubular stretching, bubble temperature, bubble form, stretching stress, and the like and that comparisons were made with a crystalline polymer. One of the most characteristic results in this analysis of PS is that because strain velocity in the MD direction decreases, the stretching effect in the TD direction is stronger than in the MD direction despite the stretching ratio of MD being larger than that of TD. This is an interesting point and the finding is significantly different from that for crystalline resin (Fig. 7.1.17). Because of its unique gas permeability, PS film is used in the packaging field to maintain freshness of vegetables such as lettuce. PS film itself is a very brittle base material, but it can be changed into reasonably strong film by orienting. GPPS closely resembles PS, and so a technique has been developed that produces modified PS by the addition of SBR (styrene butadiene rubber) to improve workability when stretching begins [38].

Film Shrinkage stress 0" (Kg/cm 2 ) Maximum Stretching stress
R/R o , V / V o

H/H 0

Strain Rate dfaec 1 )

Stretching Stress CTn%c22 (kg/cm1)

Figure 7.1.16 Relationship be-tween maximum stretching stress and shrinkage stress

2/Ro Figure 7.1.17 Predicted characteristics R(z)/R0, V(z)/V0, H(z)/H0, T(z)/T0

7.1.6

The Film Stretching Process and Its Physical Properties (Simultaneous versus Multistage)

The tenter frame process usually involves a multistage biaxial stretching process while the double bubble tubular process involves a simultaneous biaxial stretching. One can compare the performance of biaxially stretched nylon film (ONy film), a unique case in which the film is made commercially by both film forming processes described earlier. This comparison includes tensile characteristics, impact strength (temperature dependence), heating shrinkage characteristics, and high-dimensional structure. The two samples were made of Ny6 at a stretching ratio of MD/TD = 3.0/3.2 using different film forming processes. Their thickness is 15 /mi which is representative. The properties are shown in Table 7.1.1. It is seen that the film from the multistage biaxial stretching process is characterized by a greater imbalance in the MD and TD directions compared to that by the simultaneous process. As was expected, a TD stretching effect in the latter process had an effect on the film. The sample film made by the simultaneous biaxial stretching process is better in film impact value (impact strength), perhaps because of the difference in balance traits. In Fig. 7.1.18 which shows the temperature dependence of a film impact value, the film has better strength through the entire range of temperatures. Such balanced orientation has a significant influence on practical strength, which is important in film applications.

Table 7.1.1 General Properties of Biaxially Oriented Nylon Film (Simultaneous Biaxial Stretching Film versus Multistage Biaxial Stretching Film) Films

Simultaneous stretching film biaxial

Multistage biaxial stretching film

Testing method (23°C-50%RH)

MD TD MD TD MD TD MD TD

24,000 21,000 2,600 2,900 130 110 8 8 9,300

27,000 17,000 2,500 3,200 110 80 8 7 7,600

ASTM-D882

Properties Tensile modulus (kg/cm2) Tensile strength (kg/cm2) Elongation (%) Elemendorf tear strength (kg/cm2) Film impact (kg • cm/cm) Film impact (kg) Coefficient of static friction Haze (%) Gloss (%) Heat shrinkage (%)

0.7 in-in out-out 95 0 C 1200C

1.00 0.45 1.9 140 2.1/1.8 4.6/4.2

0.7 0.90 0.40 2.0 140 1.0/2.5 2.8/5.2

JIS-Z-1702 IPC Method, 1/2 in ball head JIS-IPC Method, Pyramidal head IPC Method ASTM-D1003 ASTM-D1003 IPC Method

Simultaneous biaxial stretching film

Film Impact (Kg - cm/cm)

Multistage biaxial stretching film

Temperature (0C)

Figure 7.1.18

Film impact strength (dependence on temperature)

Other characteristics that are strongly influenced by the balance in stretching are the shrinkage characteristics. These characteristics come into question where heating treatment, such as retort or boiling treatment, is applied to sterilize food contained in film bags. At this time, if the surface base material of films has an unbalanced value in shrinkage ratio, then the films become deformed and detract from their commercial value as bags. As shown in Fig. 7.1.19 the film formed by the simultaneous biaxial stretching process shows very well balanced shrinkage in each direction. However, the one formed by the multistage biaxial stretching process reveals unbalanced shrinkage owing to the memory of TD stretching in the process. The result of a structure appraisal of these films also shows that this behavior results from the difference in the stretching effect between MD and TD. Wide-angle X-ray diffraction (WAXS) shows that the film from the simultaneous biaxial stretching process is characterized by balance in shrinkage, and the film from the multistage biaxial stretching by imbalance (Fig. 7.1.20).

Simultaneous biaxial stretching film

Multistage biaxial stretching film

Shrinkage Condition (Hot Water) 1200C x 30min 95°C x 30 min

Figure 7.1.19

Heat shrinkage properties (shrinkage pattern)

(M.D.) (M.D.) (T.D.)

(T.D.)

2c|)/degree Simultaneous biaxial stretching film Figure 7.1.20

2(f>/degree Multistage biaxial stretching film

Wide-angle X-ray diffraction

This study emphasized biaxially stretched nylon film as a representative sample. PP shrink film, one of the typical goods made by the double bubble tubular process, also shows more balanced properties.

7,1.7

The Heat Set Technique (Production of Shrink Film)

It has been explained that a typical application of the double bubble tubular simultaneous biaxial stretching process includes shrink film and biaxially stretched nylon film. Here we outline heat set technology, a process following the forming process stated above, with a focus on the manufacturing conditions of biaxially stretched Nylon-6 film (ONy6 film) for general and shrink applications. General grade film must have heat resistance so as to be used in a wide variety of applications ranging from retort packaging to frozen foods. To this end, it is necessary to lower the shrinkage percentage by increasing the heat set temperature which increases the density. In the case of shrink film (shrink grade), conversely, it is necessary to keep the shrinkage percentage upon use as high as possible, and so the heat set temperature must be lowered as far as possible to keep the density low. Figure 7.1.21 shows a change in film density against heat set temperature, and Fig. 7.1.22 shows a change in film shrinkage percentage against heat set temperature. As shown in Figs. 7.1.21 and 7.1.22, as the heat set temperature increases, the film density increases and the film shrinkage percentage drops. The comparison of these conditions and performance enables us to set manufacturing conditions corresponding to the purpose and applications of the film.

Density (g/cm2)

Heatset Temperature (0C) Figure 7.1.21

Relationship between density and heat set temperature

To improve the performance of this shrink film (shrink grade) further and ensure the film has a greater shrinkage percentage, it is necessary not only to improve the stretching conditions and heat set, but also to reformulate the resin. To take one example, by changing conventional Ny6 resin to Ny6-66 copolymer resin (NyG/66 = 85/15) it becomes possible to obtain film featuring lower crystallization, high shrinkage percentage, and good balance in shrinkage. As shown in Fig. 7.1.23, the copolymer film can be shrunk in hot water at 95 0 C yielding a shrinkage percentage 10% higher than Ny6 shrink type of film. This property is useful in the meat wrapping field [39, 40].

7.1.8

Development of Peripheral Technology for the Double Bubble Tubular Biaxial Stretching Process

In earlier articles it was stated that the double bubble tubular stretching process is lower in equipment cost but inferior in thickness uniformity to the tenter frame process. For this reason, mention is made of recent technical developments to improve this shortcoming.

Hot Water 1 2 0 "C X 3 0 m i n 35tx30min MD

Shrinkage (%)

TD

Heatset Temperature (0C) Figure 7.1.22

Relationship between heat set temperature and heat shrinkage

1. Thickness accuracy has reached a considerably higher level in terms of performance because of improvements in the technique of designing circular dies as well as in heating control [41]. In the future it will be necessary to realize that optimum design conditions must correspond to resin properties to make further progress. 2. As for stable processability in a stretching process, it is forecast that setting the optimum conditions for a particular resin will require a clear understanding of the proper stretching stresses [42, 43]. 3. Despite the nature of double bubble tubular stretching technology, the methods of heat set are so abundant that one can select as one pleases from among the many choices such as a double bubble tubular heat set method and the oven technique. As stated previously, in the case of shrink type film the double bubble tubular method is satisfactory because the heat set temperature can be lowered, but in the applications requiring heat resistance, for example, retorting, the heat set technique using an oven is favored to ensure dimensional stability (decreased shrinkage percentage). 4. In heat set; double bubble tubular process made film, one handles a collapsed tube which can be fusion blocked using heat unless care is taken with the temperature conditions. To solve such a problem, a system has been developed and put into practical

Ny 6-66 Co-polymer

Shrinkage (%)

Ny6

Water Temperature (0C) Figure 7.1.23

Relationship between water temperature and heat shrinkage

use. This system is restricted only slightly by the type of resin, and is used with a variety of resins [44]. 5. The bowing phenomenon, which is one of the important problems with the tenter frame process, also occurs with the double bubble tubular process as long as it uses an oven heating system. However, because the balanceability in the stretching stage is better for the double bubble tubular process than for the tenter, the degree of the bowing phenomenon is relatively small [45, 46]. In recent years a version of the double bubble tubular process has been developed in which the bowing ratio in the final heat set stage is decreased by reverse bowing occasioned by intentionally heat controlling the bubbles at the stretching stage. In any event the process continues to evolve and it is hoped that excellent technology will be further developed to meet industrial needs and properties will be obtained to meet the increasingly demanding requirements.

7.1.9

Prospective Directions of Double Bubble Tubular Biaxial Stretching

It is expected that significant progress will be made in the future in the field of applications for films made by the double bubble tubular biaxial stretching process. Specifically, it is foreseen that a multilayer stretching and blended stretching process will play an active role in the broadening of application. Reference is made to technical development in two processes.

7.1.9.1

The Multilayer Stretching Process

As long as a single resin is used, there is a limit to the performance of products made, however well the stretching technology performs. To achieve product differentiation, studies have been made into a method of satisfying targeted functions by combining several resins and improving the performance of film in total terms. This is being put into practical use. Total performance is improved by combining the characteristic resins in a multilayer structure, yet there are many problems remaining to be solved in stretching and forming consistently a combination of resins with different properties. The multilayer functions hoped for now include the following: • • •

improvement in gas barrier properties (low oxygen permeability) improvement in service strength improvement in surface bond strength.

The resins used can be changed depending on the specific purposes. As a recent example, I will explain very briefly a development involving improved gas barrier properties. If biaxially stretched nylon film (ONy film) required a high gas barrier property, its surface would be coated with a thin film made of vinylidene chloride resin (PVDC). In recent years, however, it has been hoped that PVDC, having chlorine in its molecular structure, can be eliminated because of heightened environmental concerns. So studies have been made on commercialization of the following structures using multilayer stretching (Fig. 7.1.24): • •

biaxially stretched film of Ny/EVOH/Ny biaxially stretched film of Ny/MXD6/Ny.

The technology that has been studied is the one whereby the resin having low gas permeability, such as EVOH and MXD6, is arranged in the middle layer, and high-strength Ny6 is arranged in both outside layers to apply simultaneous biaxial stretching by the double bubble tubular process [47 to 51]. MXD6 is the polyamide formed from adipic acid and mxylylene diamine. Like Ny6, EVOH and MXD6 are resins liable to undergo hydrogen bonding, and so the double bubble tubular process and simultaneous biaxial stretching technology are a suitable combination for them. EVOH is very good in its gas barrier property, but when it is blended with Ny6 gelation occurs quickly, and so there are technical problems remaining in recycling. MXD6 is not as good in its gas barrier traits as EVOH, but it has good compatibility with Ny6 and is free from any problems during recycling.

7.1.9.2

Blend Stretching Technology

Another method of modifying film performance includes a blending technique. Specifically, studies are being made into blending with other resins or inorganic substances (filler) depending on the purpose. The double bubble tubular stretching technique for the process using inorganic fillers is aimed at providing microporosity to the film [52]. As a function controlling technique of particular interest, studies are being made to stretch a blend of Ny6 and MXD6 resin.

Multi-layer Biaxial Stretching Film Ny 6

Ny 6

IiIIi Ny 6

Ny 6

Hg i h Gas barrier property Hg i h strength property EVOH MDX6 NYLON-6 Figure 7.1.24

Multilayer biaxially stretched film

This is an interesting process that is based on retaining strength by means of the double bubble tubular biaxial stretching technique and providing an oriented film with easy tearability in a straight line by controlling Ny6 and MXD6 in the form of special, phase separated structure [53, 54]. Generally speaking, this easy tear property is provided by a uniaxial stretching process (including roll stretching). However, the product with these traits has good breakability, but very poor service strength such as impact strength, and is not useful in most practical cases unless it is covered with another base material (including ONy film). Therefore, as a result of the double bubble tubular biaxial stretching technology which blends Ny6 and MXD6, it has become possible to combine good service strength and good breakability (easy to tear in a straight line). In structural terms, it can be said that MXD6 becomes phase-separated as small islands in a sea of Ny6 (Fig. 7.1.25). This phase separated state makes it possible to obtain this unique morphology through simultaneous biaxial stretching in vertical and transverse directions. Here, in connection with multilayer and blend stretching, it is likely that the double bubble tubular stretching technology will be applied and promoted in the future. As these examples have shown, there are advantages and disadvantages with the double bubble tubular process (simultaneous biaxial stretching process) as well as with tenter (multistage biaxial stretching process), and thus it is impossible to say one is better than the other. It is clear, however, that these processes will play an important role in enhancing the quality and function of goods made by them if they are matched properly to appropriate applications and used with a clear understanding of their capabilities.

Blend Biaxially Stretched Film in an Electron Microscope

MD

MD Observation

TD

TD Observation

White — MXD6 (20,000 Magnification)

Black — Ny6

<Stretched Film> MD Observation

TD Observation

(20,000 Magnification) Figure 7.1.25

Blended biaxially stretched film as seen in an electron microscope

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.

Kang, H., Cakmak, M., White, J.L., SPE ANTEC Tech. Papers (1988) 34, p. 187 Kang, H., Cakmak, M., White, J.L., Polym. Proc. Soc. Annual Meeting Preprints (1988) p. 4 Alfrey, T., SPE Trans. (1965) 5, p. 68 Pearson, J.R.A., Mechanical Principles of Polymer Melt Processing (1966) Pergamon, Oxford Pearson, J.R.A., Petrie, C.J.S., J. Fluid Mech. (1970) 40, p. 1 Pearson, J.R.A., Petrie, C.J.S., J. Fluid Mech. (1970) 42, p. 609 Pearson, J.R.A., Petrie, C.J.S., Plastics Polym. (1970) 38, p. 85 Petrie, C I S . , Rheol Ada (1973) 12, p. 82 Han, CD., Park, J.Y., J. Appl Polym. Sci. (1975) 19, p. 3277 Petrie, C.J.S., AIChJ. (1975) 21, p. 275 Wagner, M.H., Rheol. Ada (1976) 15, p. 40 Wagner, M.H., Dr.-Ing. Dissertation, University of Stuttgart (1978) Kanai, T., White, J.L., Polym. Eng. Sci. (1984) 24, p. 1185 Kanai, T., White, J.L., J. Polym. Eng. (1985) 5, p. 135 Kanai, T., Kimura, M., Asano, Y., J. Plastic Film Sheeting (1986) 2, p. 224 Kanai, T., Int. Polym. Proc. (1987) 1, p. 137 Dow Chemical, U.S. Patent 2,488,571

18. 19. 20. 21. •22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54.

ICI, JPN Kokoku Tokkyo Koho JP 38-18978 Dupont, JPN Kokoku Tokkyo Koho JP 46-16439 Mitubisiyuka, JPN Kokoku Tokkyo Koho JP 48-20231 Showadenko, JPN Kokoku Tokkyo Koho JP 50-18514 WRGRACE, JPN Kokoku Tokkyo Koho JP 51-44019 Okurakogyo, JPN Kokai Tokkyo Koho JP 56-15325 Kojin, JPN Kokoku Tokkyo Koho JP 45-27480 Okurakogyo, JPN Kokai Tokkyo Koho JP 59-215829 Kojin, JPN Kokoku Tokkyo Koho JP 51-48676 Mitubisireyon, JPN Kokoku Tokkyo Koho JP 49-11626 Kalle, JPN Kokoku Tokkyo Koho JP 44-15917 Okurakogyo, JPN Kokai Tokkyo Koho JP 57-25920 Idemitsu, JPN Kokoku Tokkyo Koho JP 04-056736 Kojin, JPN Kokoku Tokkyo Koho JP 52-23368 Kojin, JPN Kokoku Tokkyo Koho JP 55-43897 Idemitsu, U.S. Patent 4443399 Idemitsu, JPN Kokoku Tokkyo Koho JP H04-048088 M. Takashige, Kanai, T, Int. Polym. Process. (1990) 5, p. 4 HJ. Kang, White, XL., Int. Polym. Process (1992) 7, p. 38 T. Kanai, Takashige, M., Senigakkaisi (1984) 141 Asahikasei, JPN Kokoku Tokkyo Koho JP 57-20135 Yunitika, JPN Kokai Tokkyo Koho JP 57-170720 Idemitsu, JPN Kokai Tokkyo Koho JP H03-130129 Idemitsu, JPN Kokai Tokkyo Koho JP 01-301229 Idemitsu, U.S. Patent 4869863 Idemitsu, U.S. Patent 5094799 Idemitsu, U.S. Patent 4978484 Idemitsu, JPN Kokai Tokkyo Koho JP 03-106635 Idemitsu, U.S. Patent 5158637 Okurakogyo, JPN Kokai Tokkyo Koho JP 58-72422 Okurakogyo, JPN Kokai Tokkyo Koho JP 59-76256 Idemitsu, JPN Kokai Tokkyo Koho JP 03-158226 Toyobo, JPN Kokai Tokkyo Koho JP 57-51427 Idemitsu, JPN Kokai Tokkyo Koho JP 05-192995 Kojin, WO89-04244 Idemitsu, JPN Kokai Tokkyo Koho JP 05-192997 Idemitsu, U.S. Patent 967249

7.2

Biaxially Oriented Double Bubble Tubular Film: Process and Film Character James L. White

7.2.1 Introduction 7.2.2

Process Technologies and Structural Characteristics of Double Bubble Tubular Film . . 413 7.2.2.1 Polyvinylidene Chloride 413 7.2.2.2 Polyethylene Terephthalate 414 7.2.2.3 Poly/?-Phenylene Sulfide 419 7.2.2.4 Polypropylene 425 7.2.2.5 Polyamide-6 426 7.2.2.6 Polyethylene 426 7.2.2.7 Polyvinylidene Fluoride 426

7.2.3

Final Comments

427

7.2.1

Introduction

The double bubble tubular film process generally involves a first tubular film forming process followed by a second blowing and biaxially orienting step. The double bubble tubular film process seems to have been first proposed in a 1939 Sylvania Industrial Products patent by Reichel and Craven [I]. It was aimed at developing improved cellulosic sausage casing as compared to single bubble film through the development of biaxial orientation. This technology subsequently was applied to biaxially oriented melt processed thermoplastic film in patents filed from 1943 to 1951 by the Dow Chemical Company [2-6] for polyvinylidene chloride (PVCl2). According to the key patent in this series, by Stephenson [3], the purpose of the double process was to produce an amorphous film of the slowly crystallizing PVCl2 in the first bubble, and then to biaxially orient and crystallize it in the second bubble. In succeeding years, double bubble tubular film extrusion has been applied to a wide range of polymers by many different industrial firms around the world [ 7 ^ 5 a]. Among the polymers that this technology has been applied to include polyethylene terephthalate [7, 10, 17, 25, 31, 34, 46-48], polypropylene [10, 12-15, 20-22, 28, 29, 31, 36-38, 40], polyethylene [10, 11, 13, 23, 28, 29], polyvinyl chloride [10], polyamide-6 [45, 45 a], polyphenylene sulfide [49], and polyvinylidene fluoride [50]. Beyond Dow Chemical [2-6,16,33], the companies establishing patented double bubble technologies include ICI [7, 8, 12-14, 26, 30, 31, 38], W.R. Grace [9, 11, 15], DuPont [10], Union Carbide [17, 23], Kohjin [20-22, 32], Allied Chemical [24], Hoechst-Kalle [25, 34], Showa Denko [28, 29], Chisso [39-41], and Idemitsu Petrochemical [43, 45, 45a]. Although the patent technology literature on double bubble tubular film extrusion is extensive [2 to 44, 50] basic studies are few in number [eg. 46-49]. In this chapter we describe double bubble film technologies from the literature and describe what is known about how structure is developed during the film processing operation.

7.2.2

Process Technologies and Structural Characteristics of Double Bubble Tubular Film

7.2.2.1

Polyvinylidene Chloride

The first polymer extensively investigated in connection with the double bubble tubular film process was polyvinylidene chloride [2-6]. The double process used to produce PVCl2 film is shown in Fig. 7.2.1. The basic process is best described in the January 1947 patent application of Stephenson [3]. The PVCl2 extrudate is first quenched in a cold inert liquid bath such as water at a temperature between 0 ° and 20 0 C. The extruded tube is then passed out of the bath and through a set of two rolls under conditions of inflation. The tube is then passed through a warming zone in the region of 20-50 0 C. The tube now inflates radially. As the two sets of rolls operate at different speed, the tube is stretched both longitudinally and radially to form the biaxially oriented film.

Figure 7.2.1

Double bubble tubular film process to produce PVCl 2 film (After Stephenson [3])

The extruded supercooled tube in the first stage is seemingly vitrified, without orientation, and is largely glasslike. The film produced by the second state is semicrystalline and biaxially oriented. The film has roughly equal mechanical properties in the plane of the film. No structural characterization data are cited in the early Dow patents. In a December 1951 patent application, J. W. Mclntyre [6] of Dow Chemical described a triple bubble process shown in Fig. 7.2.2. The purpose of the third bubble is clearly to anneal the biaxially oriented film to stabilize and enhance (including heat setting) the structure produced in the second bubble.

7.2.2.2

Polyethylene Terephthalate

A double bubble process to produce biaxially oriented polyethylene terephthalate (PET) film was first described in December 1956 and August 1957 patent applications by Gerber [7, 8] of ICI. The author described a vertically downward double bubble process with only an air quench as shown in Fig. 7.2.3. The first bubble is referred to as an inflating bubble, the second bubble as a crystallizing bubble. However, no data are presented on material characteristics after either the first or the second bubble. A second double bubble tubular film process is described in a November 6, 1958 patent application by Goldman [10] of DuPont. The process used is shown in Fig. 7.2.4. The second bubble contains a volatile inert liquid that becomes pressurizing under the processing conditions established. The second bubble is operated at 85 0 C, at which the volatilized inert liquids exert a gauge pressure of more than one atmosphere. In the second bubble PET

> ^ y

F^.

2

JF^y.3

Figure 7.2.2 Triple bubble tubular film process to produce PVCl2 film (After Mclntyre [6])

film decreases in thickness by 90% and the mechanical properties are greatly enhanced. No structural data are given. A three bubble process for producing biaxially oriented PET film is described in an October 12,1964 patent application by Underwood et al. [17] of Union Carbide. The process is shown in Fig. 7.2.5. The first bubble shapes the film; the second bubble biaxially orients the film. The purpose of the third bubble is to complete the crystallization process and biaxially heat set the film. It is thus very much the same as Mclntyre's 1951 triple bubble patent application [6] on PVCl2. The Underwood et al. technology is unique in that a coextruded polyethylene is used as a "support" for the lower viscosity PET. The polyethylene is later peeled off. Underwood et al. indicate the PET from the first bubble is amorphous. The PET

Figure 7.2.3 Gerber, ICI, double bubble process for making PET film [7, 8]

Figure 7.2.4 Goldman, DuPont, double bubble process for making PET, polyvinyl chloride, and polypropylene film [9]

from the second bubble is biaxially oriented but heat shrinkable above the glass transition temperature. The third bubble completes the crystallization process and heat stabilizes the film. Seifried and Klenk [25] of Kalle AG present in a November 12, 1969 patent application another double bubble process to produce PET film (Fig. 7.2.6). The first bubble is quenched in air around a mandrel to form a glassy tube. The tube then moves through a pair of rolls into an air-heated conditioning stage with air above Tg (ca 90 0C). The second bubble contains air at higher pressure resulting in its inflation and crystallization to form a biaxially oriented structure. Again no structural data are given. Later patents by Davis et al. [31] of ICI and Stretzel et al. [34] of Hoechst AG describe alternate double bubble procedures to produce biaxially oriented PET film. No structural data are provided. In a series of studies published in 1988-1990 Kang and his co-workers [46-48] investigated double bubble tubular film extrusion of PET. The apparatus of these authors is shown in Fig. 7.2.7. The chamber around the second bubble was set at both 80 and 97 0 C with the better results obtained at the higher temperature. Regions of operating stability are described and the characteristics of unstable behavior are discussed. These authors determined crystallinity, crystalline orientation birefringence, and tensile mechanical properties of film from both the first and second bubbles. In Fig. 7.2.8, we show differential

Figure 7.2.5 film [17]

Underwood et al., Union Carbide, three bubble process to produce biaxially oriented PET

scanning calorimetry (DSC) scans for single bubble products. In this figure DDR is drawdown ratio of the film and DBUR is the blowup ratio. It can be seen that the films produced are largely amorphous. It was estimated that these films were 3-7% crystalline. DSC scans for the second bubble film are shown in Fig. 7.2.9. The levels of crystallinity arise with second draw ratio (SDR) as shown in Fig. 7.2.9(a). The variation of crystallinity with the second blowup ratio (SBUR) for PET film is shown in Fig. 7.2.10(b). Second bubble crystallinities are in the range of 5 ^ 5 % . Second bubble crystallinity increases with SDR at all SBUR. However, at fixed SDR, crystallinity at low SDR increases with SBUR, whereas at high SDR, crystallinity decreases with increasing SBUR. Kang et al. [47] consider the influence of subsequent annealing on crystallinity of the double bubble PET film. The result of annealing at 150 0C for lOmin is shown in Fig. 7.2.10. Annealing leads to a more perfected crystallinity in the range of 45-55%. This undoubtedly was the purpose of the above cited Underwood et al. patent which describes the use of three bubbles. Orientation in first and second bubble PET film has been investigated by Kang et al. using birefringence and X-ray diffraction pole figures. PET has a triclinic unit cell with the polymer chain axis corresponding to the ocrystallographic axis. The phenyl ring lies in the be plane. Figure 7.2.11 shows pole figures for the annealed second bubble (100) plane. This clearly shows that the a axis is normal to the surface of the film and the phenyl ring is in the

Figure 7.2.6 Seifried and Klenk, Kalle AG double process for producing biaxially oriented PET film

plane of the film. Crystalline orientation can be represented in terms of the biaxial orientation of White and Spruiell [51]. These have the form for crystalline axis y: f$ = 2 COS^i7- + Co^(J)2J - 1

(7.2.1a)

f$ = 2cos202/ + cos20ly - 1

(7.2.Ib)

where c/>ly is the angle between they axis and the 1 direction and (J)2J is the angle between they axis and the 2 direction. Biaxial crystalline orientation factors of the polymer chain axis ffc and f2c for biaxial films values of order (0.4, 0.4) were achieved, indicating high levels of biaxial orientation. Kang and White have also measured birefringence. These involve refractive index differences between the machine direction 1, the transverse direction 2, and the thickness direction 3. In Fig. 7.2.12, we show the birefringences Aw13 and An23 of the second bubble as a function of second drawdown ratio. The Aw13 increases with the second drawdown ratio,

Lay/Ut 2nd Nip Rolls

JdI.r Roll

Collapsing Fr a m *

2nd

Bubbl*

CAMERA

PYROMETER Hot

AiV Ring

1st .Nip Rolls

Collapsing P r i m * Wlndir Roll of Film

R u i n PtIIa(S 1st

Bubblt

too* A I r Ring Dl*

HOOP"

Figure 7.2.7 Double bubble apparatus of Kang et al. [46-49] for biaxially oriented PET film

Ertmdtr

IdUr Rol

while A«23 increases with second blowup ratio. For an equal biaxial film we would have Aw 13

=An23.

The mechanical properties of single and double film were measured. Generally, the Young modulus and tensile strength increase and "elongation to break" decrease as one moves from first bubble to second bubble to annealed film (Fig. 7.2.13). In double bubble films with unbalanced orientation, the direction of higher orientation has higher modulus and tensile strength and lower elongation to break (see Fig. 7.2.14).

7.2.2.3

Poly /7-Phenylene Sulfide

Double bubble tubular film extrusion of poly /?-phenylene sulfide (PPS) has been described by Kang and White in a 1990 publication [49]. This again uses the apparatus shown in Fig. 7.2.7 with the air blowing temperature around the second bubble at 105 0 C. These authors determined levels of crystallinity, birefringence, and tensile mechanical properties for both first and second bubbles. DSC scans for the first bubble film are shown in Fig. 7.2.15. It was found that the films are largely amorphous. It was estimated that there was 7-9% crystallinity in the first bubble. DSC scans for the second bubble are shown in Fig. 7.2.16. Crystallinities are in the range of 8-20%. WAXS pole figures and birefringences were measured. The general trends of crystallinity and orientation development with PPS are similar to that found with PET described in the previous section.

<EN0O

BUR-I. 75

Haul Flo. (V/g)

PET 7352

(EMOO

(*C3

Tomparaturo

(*C5

OrWO

Hoot Flow (VZ 3 )

?ST 73S2

Tamoaraturo

Figure 7.2.8 DSC scans of PET film produced from a single bubble process (a) The blowup ratio is set at 1.75 and the drawdown ratio has values 10, 20, 50, and 200 (b) The drawdown ratio is set at 40 and the blowup ratio has values 1.0, 1.25, and 1.75

SOR = 2.0

*°U ^H

ENOO

SOR = 3.0 SDR = 4.0 SDR = 5.0

Temperature

W/g S8UR=3.0

Heat flow

NOO

SBUR = 2.5 S8UR = 2.0 S8UR=1.5 S8UR = 1.0

Temperature

Figure 7.2.9 DSC scans of Kang et al.'s double bubble PET film (a) SBUR = 2.0, various second drawdown ratios (b) SDR = 3.0, various second blowup ratios

Annealing of the double bubble film at 150 0 C increases the crystallinity from 8-20 up to 30-35%. This would indicate that a three bubble process would be useful here. It also gives rise to substantial increases in birefringence and orientation. As with PET double bubble films, the modulus and tensile strength increase and the elongation to break decreases as one moves from first bubble to second bubble to annealed film.

Annealed (15O 0 C 10 mini S8UR

Second draw down raKo

Unannealed SOR

/4JUJiIe^sXJj

Xjiu!))e4.sXj3

Unannealed S8UR

Annealed (150 0 C 10min] SDR

Second blow up ratio

Figure 7.2.10 Effect of second bubble on PET crystallinity(a) Variation of crystallinity with SDR (SBUR is fixed) (b) Variation of crystallinity with SBUR (SDR is fixed)

KO.

Anneae l d second bubbe l (SORxSeUR) (100) Pa l ne

2x2 Contour values

NO

MO

TD

MQ

N.O.

T.0.

MD.

N.O. 4x2 Contour values

4*1 Contour values

M.0.

ID.

4*3 Contour values

MO.

•T.0,

N.O.

5x2 Contour values

M.0.

Figure 7.2.11

TO.

WAXS pole figures for the 100 plane in PET

An x 102

SBUR

Second draw down raho Figure 7.2.12 Birefringences An13 and A«23 of double bubble PET as a function of drawdown ratios for different blow ratios

3

Stress

b

c

Figure 7.2.13 Engineering stress-strain curves for first bubble (c), second bubble (b), and annealed PET films (a)

Sfrain

Elongation to break

First bubble (OR = 20, BUR = 1.25) Second bubble UnanneaUd ,Annealed S3UR

Angle

First" bubble (OR = 20, BUR =1.25) Second bubble Tensile strength

Unanneated Annealed SBUR

Angle Figure 7.2.14 Variation of elongation to break and tensile strength as a function of direction in double bubble PET film (a) elongation to break (b) tensile strength

<£N00

rrn SIHCLE VUSSLC BU*-2.O

T».y«-«lA^r-» CO Figure 7.2.15 DSC scans of Kang and White's PPS film after the first bubble [48]

7.2.2.4

Polypropylene

The first application of double bubble tubular film extrusion to isotactic polypropylene is attributable to Goldman [10] of DuPont and is described in his November 6, 1958 patent application. The patent examples include polypropylene (as well as PET and polyvinyl chloride). He indicates that the first bubble was quenched in water and that lateral stretching of the second bubble occurs at 110-150 0 C. Based on the work of Spruiell and White and their co-workers [52-55] it may be concluded that the film forms a "smectic" (i.e., a poorly formed) crystalline structure in the

(DiOO

SSUH-Z. O

lmmf>»r<,%.^'m

<*C>

Figure 7.2.16 DSC scans of Kang and White's [48] double bubble PPS film after the second bubble [49]

first bubble and a well-defined a phase polypropylene film in the second bubble. The biaxial stretching in the second bubble film during the transition of "smectic" to a produces biaxial orientation. Subsequent patents dealing with double bubble extrusion of polypropylene [12-15, 2022,28,29,31,36-38,40] are basically similar. BiId and Robinson [14] discuss running a tube from the die to the second bubble to control the inflation pressure. Tsuboshima et al. [20] describe the use of two air rings.

7.2.2.5

Polyamide-6

Double bubble tubular film extrusion has been applied to produce biaxially oriented polyamide-6 film in a March 9, 1990 patent application by Takashige and his coworkers [45, 45 a] of Idemitsu Petrochemical. More recently, bubble stability and structure development in double bubble tubular film has been investigated by Rhee and White [56].

7.2.2.6

Polyethylene

The first double bubble process for shrinkable polyethylene was by Baird et al. [9] of W.R. Grace in a February 1958. Single bubble polyethylene film is first produced at 150 0 C which then goes through a nuclear radiation chamber that crosslinks it [Fig. 7.2.17(top)]. This film is then passed into a second bubble where biaxial orientation occurs. The use of various irradiation procedures is claimed. A second double bubble tubular film process for producing a shrinkable polyethylene film is described in a January 31, 1962 patent application by Benning et al. [11] of W.R. Grace. Peroxides are mixed into the polyethylene in the screw extruder. The peroxide is specified as 2,5-dimethyl-2,5-di(te?t-butylperoxy) hexane and is present at a 0.75% loading. The first bubble is formed at 160 0 C, at which the peroxides do not react. The melt then passes through roller nips into a second bubble where there is a furnace at 290 0 C whose heat causes the peroxides to react and crosslink. The polyethylene bubble expansion in the second bubble produces biaxial orientation in the bubble (Fig. 7.2.17(bottom)]. These double bubble processes are also unique and different from the PVCI2, PET, and PPS technologies. A highly crystalline polyethylene film is formed in the first bubble. The second bubble provides a hardening step not through crystallization but rather through chemical crosslinking produced before (or during) the inflation.

7.2.2.7

Polyvinylidene Fluoride

White and Nie [50] in an October 25,1990 patent application describe a method of producing a biaxially oriented polyvinylidene fluoride (PVF2) film in a double bubble process by using a blending technique. They used the same apparatus as Kang et al. [46^9]. Polymethyl methacrylate (PMMA) is miscible with amorphous PVF2. Blends of PVF2 with PMMA crystallize more slowly and form products with lower crystallinity content. Generally single

Figure 7.2.17 Shrinkable polyethylene film process of Baird et al. [9] and Benning et al. [11] of W.R. Grace (top) nuclear radiation process (bottom) reactive process with peroxides

bubble PVF2 tubular film is crystalline. Introducing sufficient PMMA can produce a PVF2 blend tubular film that is glassy. This film may be biaxially stretched and crystallized in a second bubble in a heated chamber.

7.2.3

Final Comments

Double bubble tubular film extrusion is an industrial film manufacturing process with a half century history. The literature treating the process is almost entirely a patent literature [1-44, 45a, 50] and there has been little basic study. Only HJ. Kang, S.K. Rhee and the author

[46^19, 56] have published such studies. It is clear that the first bubble is used to form a film shape that is preferably glassy in character. The second bubble generally leads to straininduced crystallization and biaxial orientation. Third bubbles have often been proposed for the purpose of annealing and heat setting the film.

References 1. Reichel, RH., Craven, A.E. (to Sylvania Ind. Products) U.S. Patent (filed March 15, 1939) 2,176,925 (1939) 2. Wiley, R.M. (to Dow Chemical) U.S. Patent (filed Nov. 22, 1943) 2,409,521 (1946) 3. Stephenson, W.T. (to Dow Chemical) U.S. Patent (filed Jan. 13, 1947) 2,452,080 (1948) 4. Trull, R.R. (to Dow Chemical) U.S. Patent (filed Dec. 11, 1947) 2,488,571 (1949) 5. Irons, C R . (to Dow Chemical) U.S. Patent (filed Aug. 11, 1948) 2,541,064 (1951) 6. Mclntyre, J.W. (to Dow Chemical) U.S. Patent (filed Dec. 26, 1951) 2,688,773 (1954) 7. Gerber, K.G. (to ICI) U.S. Patent (filed May 18, 1956) 2,862,234 (1958) 8. Gerber, K.G. (to ICI) U.S. Patent (filed Aug. 23, 1957) 2,916,764 (1959) 9. Baird, W.G., Lindstrom, CA., Besse, A.L., d'Entremont, DJ. (to W.R. Grace) U.S. Patent (filed Feb. 27, 1958) 3,022,543 (1962) 10. Goldman, M. (to DuPont) U.S. Patent (filed Nov. 6, 1958) 2,979,777 (1961) and with M. Wallenfels U.S. Patent (filed August 24, 1960) 3,141,912 (1960) 11. Benning, CX, Gregorian, R., Werber, KX. (to W.R. Grace) U.S. Patent (filed Jan. 31, 1962) 3,201,503 (1965) 12. BiId, K, Robinson, W. (to ICI) U.S. Patent (filed Feb. 14, 1962) 3,166,616 (1965) 13. Last, A.G.M. (to ICI) U.S. Patent (filed April 12, 1962) 3,325,575 (1967) 14. BiId, R, Robinson, W (to ICI) U.S. Patent (filed Nov. 12, 1963) 3,300,555 (1967) 15. Lindstrom, CA., Baird, W.G., Bosse, A.L., d'Entremont, DJ. (to W.R. Grace) U.S. Patent (filed Oct. 29, 1964) 3,260,776 (1966) 16. Wiggins, G.C, Frohreich, R.A., Sweebe, C H . (to Dow Chemical) U.S. Patent (filed Dec. 18, 1969) 3,280,233 (1966) 17. Underwood, WF., Craver, J.W, Sacks, W. (to Union Carbide) U.S. Patent (filed October 12, 1964) 3,337,665 (1967) 18. Carlson, F.A., Zavits, WE. (to Celanese Corp.) U.S. Patent (filed Oct. 27, 1966) 3,466,356 (1959) 19. Ebert, A., Pirot, E., Holler, F., Steinhilber, G. (to Bemberg) U.S. Patent (filed Feb. 2, 1968) 3,544,667 (1970) 20. Tsuboshima, K., Matsuou, T., Kanoh, T., Nakamura, K. (to Kohjin) U.S. Patent (filed Feb. 10, 1968) 3,499,064 (1970) 21. Notomi, R., Kanoi, T., Matsuru, T. (to Kohjin) U.S. Patent (filed May 28, 1968) 3,576,658 (1971) 22. Tsuboshima, K., Kanoh, T. (to Kohjin) U.S. Patent (filed April 15, 1969) 3,510,549 (1970) 23. Pahlke, H.E. (to Union Carbide) U.S. Patent (filed Dec. 5, 1968—original application March 12, 1965) 3,555,604 (1971) 24. Vaghi, G. (to Allied Chemical) U.S. Patent (filed Dec. 26, 1968) 3,576,934 (1971) 25. Seifhed, W, Klenk, L. (to KaUe) U S . Patent (filed Nov. 18, 1969) 3,725,519 (1973) 26. Robinson, W, Davis, J.B., Skilling, D. (to ICI) U.S. Patent (filed March 1, 1971) 3,819,776 (1974) 27. Higashi, M. (to Polymer Processing Research Inst. Ltd., Tokyo) U S . Patent (filed August 22, 1972) 3,853,448 (1974) 28. Sato, W, Uemura, O. (to Showa Denko) U.S. Patent (filed May 3, 1973) 3,904,342 (1975) 29. Sato, W, Uemura, O. (to Showa Denko) U.S. Patent (filed July 13, 1973) 3,887,673 (1975) 30. Hasler, R. (to ICI) U.S. Patent (filed July 19, 1973) 3,950,466 (1976) 31. Davis, J.B., Skilling, D., Wakley, N.E. (to ICI) U.S. Patent (filed June 17, 1974) 3,993,723 (1976) 32. Notomi, R., Shigeyoshi, T, Sugiyama, M. (to Kohjin) U.S. Patent (filed Nov. 8, 1974) 3,985,849 (1976) 33. Bridge, WA. (to Dow Chemical) U.S. Patent (to Nov. 25, 1974) 3,989,785 (1976) 34. Stretzal, H., Gneuss, D., Klenk, L. (to Hoechst) U.S. Patent (filed March 18, 1975) 4,034,055 (1975)

35. Nohtomi, R., Sugiyama, M., Shigoyoshi, T. (to MMM) U.S. Patent (filed Oct. 6, 1975) 4,061,707 (1972) 36. Nash, J.L., Polich, S.J., Carrico, P.H. (to General Electric) U.S. Patent (filed May 5, 1977) 4,112,034 (1978) 37. Eustace, J.W., Hobos, S.Y., Carley, E.L. (to General Electric) U.S. Patent (filed March 15, 1979) 4,225,381 (1981) 38. Hendy, B.W. (to ICI) U.S. Patent (filed April 25, 1979) 4,263,252 (1981) 39. Hayashi, K., Morihara, K., Nakamura, K. (to Chisso) U.S. Patent (filed Dec. 19, 1979) 4,279,580 (1981) 40. Hayashi, K., Morihara, K., Nakamura, K. (to Chisso) U.S. Patent (filed Dec. 19, 1979) 4,341,279 (1982) 41. Hayashi, K., Morihara, K., Nakamura, K. (to Chisso) U.S. Patent (filed Jan. 24, 1980) 4,290,996 (1981) 42. Peterson-Hoj, P. (to Tetra Pak) U.S. Patent (filed Jan. 25, 1980) 4,370,293 (1983) 43. Takashike, M., Kaneda, K., Murakami, N. (to Idemitsu) U.S. Patent (filed April 21, 1982) 4,443,399 (1984) 44. Wang, J.C. (to General Binding) U.S. Patent (filed Sept. 7, 1983) 4,484,971 (1984) 45. Takashige, M., Kanai, T. Int. Polym. Process (1990) 5, p. 287 45a. Takashige, M., Y. Ohki, T. Hagashi and M. Fujimoto (to Idemitsu) US Patent (filed March 9, 1990) 5,094,799 (1992) 46. Kang, H.J., Pollack, M., Cakmak, M., White, J.L., SPEANTEC Tech. Papers (1988) 34, p. 187 47. Kang, H.J., White, XL., Cakmak, M., Int. Polym. Process (1990) 5, p. 62 48. Kang, H.J., White, XL., Int. Polym. Process. (1992) 7, p. 38 49. Kang, H.X, White, XL., Polym. Eng. ScL (1990) 30, p. 1228 50. White, XL., Nie, T. (to EPIC) U.S. Patent (filed Oct. 25, 1990) 5,082,616 (1992) 51. White, XL., Spruiell, XE., Polym. Eng. ScL (1981) 21, p. 859 52. Spruiell, XE., White, XL., Polym. Eng. Set (1975) 15, p. 550 53. Nadella, H.P., Henson, H.M., Spruiell, XE., White, XL., J. Appl. Polym. ScL (1977) 21, p. 3003 54. Nadella, H.P., Spruiell, XE., White, XL., J. Appl. Polym. ScL (1978) 22, p. 3121 55. Shimomura, Y., Spruiell, XE., White, XL., J. Appl. Polym. ScL (1982) 27, p. 2663 56. Rhee, S. and XL. White SPE ANTEC Tech Papers (1998) Polym. Eng. ScL 44, p. 155 (in press)

Index

Index terms

Links

A α-transition

330

Accurate model

47

Aerodynamics

121

Air cooling ring

68

flow

263

knife

263

Amide

388

Amorphous

137

Anisotropic

339

materials

369

Annealing

296

Annulus

417

40

Antiblocking

249

Antistatic

249

Automatic

68

B β relaxation

303

β-gauge

350

β-transition

330

Balanced orientation

402

Barrier coextrusion

232

films

236

layer

237 This page has been reformatted by Knovel to provide easier navigation.

431

432

Index terms

Links

Barrier (Continued) properties

334

screw

252

structure

230

Biaxial

10

orientation

418

426

stretching

245

321

407

oriented

168

245

413

oriented film

387

stretched

284 161

169

226

236

339

372

407

152

390

228

322

Birefringence

130

390

392 Blend stretching Blown film

408 3

Bowing distortion

374

Bowing

270

Bowing ratio

407

Brewster’s angle

166

Bubble instability

153

pressure

389

radius

132

stability

107

109

397

398

stabilizing

390

99

C Cain

144

Cakmak

167

Carreau

8

Cast film

2

195

258

324

Casting

This page has been reformatted by Knovel to provide easier navigation.

433

Index terms

Links

Catenary

181

184

Chill roll

181

195

260

30

Choker bar

18

Chrome

47

Circular die

15

Coat hanger die

20

22

228

234

Coextrusion Control

262

60

systems

62

70

volume

33

49

51

79

183

Convected Oldroyd derivative

11

Cooling air

68

control

238

rate

110

Critical stress

285

Cross point

395

Cross-sectional area

218

Crystal structure

282

Crystalline orientation

137

416

Crystallinity

166

167

Crystallization rate

85

D Deformation rate

10

rate tensor

90

130

Denn

144

Density

166

Diameter range

148

282

Die control

70 This page has been reformatted by Knovel to provide easier navigation.

392

398

434

Index terms

Links

Die (Continued) gap

61

257

lip

22

27

swell

201

Dielectric properties

338

Dimension variation

143

Distortion

372

Double bubble

4 427

245

387

Draw resonance

211

212

215

68

151

Dual lip Dynamics

303

E Edge bead

197

Edge stress

202

Elastic modulus

358

Electric charge

263

Electromagnetic theory

158

Electron microscopy

130

157

Electrostatic pinning

265

power

191

Ellis

8

Elmendorf tear

132

Elongation

421

flow

8

ratio

189

rheology

8

strain rate

261

viscosity

262

Emissivity

75

183

194

This page has been reformatted by Knovel to provide easier navigation.

413

435

Index terms

Links

Energy balance

126

Ethylene glycol

282

Eulerian coordinates

355

EVOH

235

Extension

354

Extra stress tensor

220

321 388

Extruder barrels

46

screws

238

FAN method

50

F Feedblock

228

Feedblock die

36

FEM

51

Film

226

casting

181

density

404

physical properties properties

130 59

stability

144

strain rate

134

temperature

191

thickness

61

velocity

132 46

Finger tensor

11

Finite difference method

366

Finite element method

366

Flat die

186

205 150

184

256

Final land gap

232

378

98

quality

Filter

229

25 This page has been reformatted by Knovel to provide easier navigation.

212

436

Index terms

Links

Flat film

193

Flat sheet

194

Fletcher’s ellipsoid

161

Flexible films

235

Flexlip

60

Flow variation

50

Food packaging

236

403

94

356

Force balance Fourier transform

154

Free surface

360

Freeze line

114

Fresnel’s law

160

119

G Gas permeability

313

400

Gauge

142

299

bands

237

control

67

uniformity

343

variation

64

Gear pumps

240

Giesekus

120

Glass beads

380

Grooved feed

252

H Hardening Haze

47

109

169

174

HDPE, see polyethylene Heat capacity

82

conduction

197

This page has been reformatted by Knovel to provide easier navigation.

437

Index terms

Links

Heat (Continued) conduction equation

193

seal

270

set

327

328

shrinkage

332

407

transfer

145

193

80

183

transfer coefficient Heats of crystallization

166

Helical instability

145

Henky strain rate

10

High-density polyethylene Highly polished

387

387 47

Hookean solid

362

Hydrolysis

282

I Impact strength

99

In-plane birefringence

170

Instability

107

Instron tensile

132

Isotropic

339

Isotropic materials

157

143

K K-BKZ

121

Kinematics

387

L Lagrangian

196

Landing point

191

357

LDPE, see polyethylene

This page has been reformatted by Knovel to provide easier navigation.

212

438

Index terms

Links

Levy-Mises

124

Linear thermoplastic

354

Lip gap

18

46

LLDPE, see polyethylene Longitudinal modulus

344

Lorentz-Lorenz

161

M Machine direction

389

Mandrel design

40

distribution

40

Manifold

21

radius

29

Mathematical Model Maxwell equation Maxwell model

354 11 9

Maxwell-Betti

370

Mean temperature

197

Melt tension

111

Membrane theory

233

93

Mesh point

363

Metastable instability

142

Metzner

130

Mixers

239

118

391

Molecular alignment

326

orientation

344

Momentum equations

356

Monolayer cast film

226

Morphological

175

This page has been reformatted by Knovel to provide easier navigation.

439

Index terms

Links

Multilayer films

226

flat die

36

stretching

407

408

Multimanifold die

36

229

Multistage biaxial

402

Multistretching

245

N Neck down

325

Neck-in

197

Necking

307

stress

340

Neutral stability

221

Newton-Raphson

95

Newtonian viscosity

7

Nickel plated

47

Non-Newtonian

51

185

Numerical analysis

361

simulation

35

solutions

364

Nusselt number

84

Nylon

235

film

388

polystyrene

354

Nylon-6

181

404 387

O Oldroid’s convected derivative

220

OPP films

388

This page has been reformatted by Knovel to provide easier navigation.

440

Index terms

Links

Optical characteristics

158

Optical clarity

169

Optimization

263

Orientation

162

Orientation factor

162

Oscillation

214

Oxygen barrier

313

168

P Packaging

245

Parallel plate die

16

PEEK

288

Permeability

336

PET

118 321

film

400

235 354

416

Phan

120

Piezo-translators

60

Pinning methods

259

Planar extension

12

Plane Couette flow

7

Plane stress

370

Plastic strain

130

135

Plastic-elastic transition

122

130

51

53

Poiseuille flow Poisson ratio

376

Polarized wave

159

Pole figure

169

417

413

426

Poly(ethylene) terephthalate, see PET Polyamide-6

This page has been reformatted by Knovel to provide easier navigation.

249 387

282 414

441

Index terms Polyethylene naphthalate

Links 110

136

354

426

181

195

288

Polyphenylene sulfide

413

419

288

387

Polypropylene

181

354

387

425

Polystyrene

195

387

Polyvinyl alcohol

388

chloride

412

Polyvinylidene chloride

235

387

413

fluoride

413

426

Power law

7 216

8 217

53

288

332

Preland gap

28

length

28

Pressure differences

33

Principal stresses

173

Principle strain rates

131

Process control

241

Q Qualitative

145

R Radial ports

42

Radiation

194

energy

324

Refractive index

166

Regrind

233

Relaxation heat setting

343

This page has been reformatted by Knovel to provide easier navigation.

93

442

Index terms

Links

Relaxation

306

Residual stress

369

Retort

403

Reynolds number

84

Rubber elasticity

358

Rubber film

354

Runge-Kutta-Verner

24

S SAXS

157

302

Scaleup

74

100

107

Screen changer

46

Second bubble

389

Semirigid sheet

234

Sequential biaxial stretching

323

53

436

Shear flow

74

modulus

376

rate

7

rheology

7

stress

33

thinning

45

Sheet

226

228

Shrink film

323

388

SIC

297

298

Single lip

151

Single-screw

251

Single-stretching

245

Single crystals

282

Small-angle x-ray, see SAXS Snell's law

165

This page has been reformatted by Knovel to provide easier navigation.

404

443

Index terms

Links

Specific heat

183

Spencer impact

132

Spirals

42

43

distribution

49

54

mandrel

47

mandrel die

40

Spreading

230

Squeezing

230

Stability

110

analysis system

146

characteristics

151

improvement

149

limit

142

Stiffness matrix

45

111 152

371

Strain rate

135

184

tensor

182

359

Stress

135

pattern

394

tensor

182

Stress-strain

328

Stress-induced crystallization

298

Stretching

354

ratio

392

stress

392

Structural anisotropy

157

Structural characteristics

175

Structure development

171

Super drawing

270

Supertensilized film

347

424

Surface Of rolls

325 This page has been reformatted by Knovel to provide easier navigation.

145

416

444

Index terms

Links

Surface (Continued) roughness

176

transmissivity

175

treatments

273

286

T T-die

18

Tandem extruder

253

Tanner

120

Tas

135

Tear strength

136

256

Temperature control

66

effect

33

fields

387

profiles

134

Tenetering

245

Tensile strength

421

stress

355

testing

378

Tenter

322

clips

267

frame

388

process

322

Tentering Terephthalic acid

402

3

245

282

321

Thermal bolts

60

conductivity

34

crystallization stability

82

297 45

342

This page has been reformatted by Knovel to provide easier navigation.

445

Index terms

Links

Thermal (Continued) rheological Thermosetting zone

115 342

349

Thickness gauge

70

limits

350

profiles

63

uniformity variation

394 59

Thinning technology

349

Total stress

355

Transient

186

elongational viscosity

78

Transverse direction

389

modulus

344

stretching

327

stretching stress

340

Traversing

70

Triclinic unit cell

417

Tubular film

74

process

157

322

Two-phase model

115

U Uniaxial stretching

326

Unit cell

282

V Vector wave

159

Video camera

145

This page has been reformatted by Knovel to provide easier navigation.

373

446

Index terms

Links

Visco-plastic-elastic

115

Viscoelastic

201

fluids

218

models

118

Viscous dissipation

122

33

Visualization

214

Void formation

384

Volume conservation

355

Volumetric flow rate

33

W Water vapor transmission

337

WAXS

130

157

403

WAXS pole figure

289

419

423

Weld lines

40

White

120

Wide-angle X-ray diffraction, see WAXS

X X-ray diffraction

166

Y Yeow

144

Yield strengths

136

Young moduli

376

This page has been reformatted by Knovel to provide easier navigation.