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~ 0.6, in a poor neutral solvent, they found that the ODT between homogenous and microphase-separated phases can be described using the dilution approximation:166

where, for a symmetric diblock the structure factor function F(f)/2 = 10.5 is predicted using Leibler's mean field theory.169 In the dilution approximation it is assumed that the primary role of added solvent is to reduce the number of unfavourable monomer-monomer contacts in a spatially uniform manner. Fredrickson and Leibler provide a justification for Equation (3.8) for neutral good solvents, whilst pointing out that even as 0 —>• 1, the solvent will not be homogeneously distributed, rather it will segregate in the interfacial regions to

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Block Copolymers in Solution: Fundamentals and Applications 1 9^

screen monomer-monomer interactions. It was observed that inhomogeneities in solvent concentration exist whenever the solution is microphase separated,123 a result not obtained by Hong and Noolandi.168 This discrepancy was ascribed to an incorrect description of the solvent concentration field which was assumed to have the same period as the A-B composition profile, whereas it is actually half this period, and is out of phase with it.123 The self-consistent field theory method was later developed to consider the lamellar phase of diblocks in a neutral solvent.159 A slight tendency for solvent segregation to the lamellar interphase was noted, with an initial increase in excess solvent (^s) with increasing copolymer concentration, followed by a decrease in the semidilute and concentrated regimes. This decrease necessarily results as approaches unity and the volume fraction of solvent, 1-0, approaches zero. The resulting maximum in t/>s is enhanced with increasing degree of A-B segregation in the copolymer, ips being approximately proportional to XAB- Competing with this trend is the approximate inverse dependence of ijjs on N in the weak segregation limit.123 Whitmore and Noolandi also obtained approximate scaling relationships for the domain spacing:159

The strongest dependence occurs in the weak segregation limit, with p w 1/3, q w 0.8, r w 0.4, whereas in the strong segregation limit p w 0.2, q « 2/3, r w 0.22. This compares with the values p = 0.l4 and q = 0.64 obtained for strongly segregated block copolymer melts.170'171 Volume fraction profiles were also calculated for PS-&-PI diblocks in the nearly neutral solvent toluene.159 The scaling predictions of the theory were compared with the experimental results of Hashimoto and coworkers, as discussed in the preceding section. Here no distinction was made between the weak and strong segregation limits. Whitmore and Vavasour, also using self-consistent mean field theory, found that phase diagrams for diblocks in a nonselective solvent could be mapped onto essentially the same diagram, when scaled by (f>XARN-172 The mapping onto the melt phase diagram was suggested, although not quantitatively investigated in this limit (0 —> 1). The theories of Fredrickson and Leibler123 and Olvera de la Cruz124 concern microphase separation in semidilute block copolymer solutions in a nonselective good solvent, analysed using the random phase approximation (RPA) and the 'blob' model where monomers are grouped in blobs the size of the correlation length. These authors used Leibler's formulation of the RPA169 for weakly segregated block copolymers. Whereas Olvera de la Cruz only considered the mean field limit, Fredrickson and Leibler also allowed for composition fluctuations, via the method of Brazovskii173 as applied to block copolymer melts.174 Composition fluctuations are important close to the ODT in block copolymer melts, and there is evidence for their existence in semidilute solutions, as discussed in Section 3.4.122 In the semidilute region, excluded volume interactions are important on length scales smaller than the 'blob' size £, but are screened out at distances larger than £. As the

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polymer concentration is increased, the screening becomes more important and the correlation length decreases as ^-VKV+^ ~ 0~°-77,175 where ^ = 0.588 is the excluded volume exponent for good solvents. Because of these excluded volume effects at short distances, the probability of contacts between unlike segments is reduced by a factor of c^2"-1)/^3"-1) ~ 0 023 . Renormalization group studies indicate that the contact probability is even further reduced by an additional factor of XSD, where XSD ~ 0-29 is a crossover exponent given by %SD == Xs/(3^-l), with Xs ~ 0.22.123 (Monte Carlo simulations indicate that xs maY be significantly larger for strongly incompatible blocks.176) In the limit that contributions to the free energy from solvent inhomogeneities are negligible (which is valid for long copolymer chains), mean field theory for semidilute solutions predicts that 0x^V in Equation (3.8) can be replaced by 4>6XN, where 5 = (xs+l )l($v — 1) « 1.6 (the same substitution can be used to relabel the ordinate for phase diagrams within composition fluctuation theory177). This result is valid in the limit that N~°'22
where F differs by a multiplicative constant of order unity from F in Equation (3.8). At the transition, the concentration of copolymer scales as:

Lodge et al. have observed an exponent consistent with this, based on experiments on nearly symmetric PS-b-PI diblocks, as discussed in Section 3.4.121 The position of the structure factor peak, q', for semidilute block copolymer solutions is predicted to scale as:123'124

Mayes et al. tested this prediction using SANS.162 As mentioned in Section 3.6, they did not obtain this scaling, instead a best fit to the data yielded q* ~ 0°'05. This weaker than expected dependence is presently unexplained. However, the expected concentration dependence of the blob size:

was confirmed.162 This scaling was reported earlier for homopolymer solutions in the semidilute regime.178"181 Experimental results for the scaling of q* with 0 yield different exponents. Duplessix et al. found an exponent 0.087 for PS-b-dPS-b-PS triblocks in CS2.182 Daoud et al. obtained the predicted scaling q* ~ <^>a125 for PS solutions in CS2 containing small amounts of dPS.178 Similar experiments by

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King et al. on solutions of dPS in d-toluene containing unlabelled PS produced an exponent 0.078.181 Thus nonuniversal exponents are obtained for homopolymer solutions as well as block copolymers. The Polymer Reference Interaction Site Model (PRISM) theory has also been applied to investigate ordering in block copolymer solutions. The simplest Gaussian thread version of PRISM theory was applied to study the equilibrium properties of diblock copolymer solutions under neutral solvent conditions.183 Analytical predictions were obtained for the influence of local and microdomain scale concentration fluctuations on the relationship between temperature, degree of polymerization and polymer concentration at the ODT. In the semidilute regime, PRISM predictions were found to agree with blob scaling and fluctuation-corrected field-theoretic analyses. However, in concentrated solutions and the melt, strong disagreements were found, and the mean field dilution approximation was found to fail. Apparent scaling laws for the concentration at the ODT with copolymer degree of polymerization were found for concentrated solutions, with effective exponents which depend on solvent quality, melt screening length, chain aspect ratio, and other nonuniversal structural features. The primary reason for failure of the dilution approximation was found to be interchain nonrandom mixing, which is concentration dependent and driven by local entropic packing effects. Composition fluctuations on the microdomain length scale were shown to yield corrections of secondary importance which vanish in the long chain limit. For good solvents, the predicted apparent exponent for the scaling of <^ODT with N is accidentally in close agreement with semidilute blob scaling results, and agrees with the experiments by Lodge et al.121 on PS-b-PI diblocks. Smaller effective exponents were found under 9 solvent conditions. Detailed PRISM calculations for the small-angle scattering intensity and local physical clustering (via contact interchain pair correlation functions) were also presented.183 Distinctive dependences of these quantities on the degree of polymerization, copolymer concentration, solvent quality and polymer screening length were established. In qualitative agreement with TEM experiments on PS-b-PI solutions in neutral solvents,184 significant local clustering of the minority component was anticipated in asymmetric diblocks even very far from the ODT.

3.8 THEORETICAL UNDERSTANDING OF PHASE DIAGRAMS Self-consistent field theory has been used to calulate phase diagrams of ordered micellar solutions. Noolandi et al. compared continuum self-consistent field theory with the lattice version of this theory for triblock copolymers such as the Pluronics in aqueous solution.185 From a different viewpoint, this work represents an extension of the self-consistent field theory employed by Noolandi and coworkers and Matsen and coworkers for the phase behaviour of block copolymer melts34 to block copolymers in solution. The approximations introduced by the adoption of a lattice model are found to lead to some significant differences in the solution phase

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Figure 3.22 Phase diagram for aqueous solutions of Pluronic P94 (EO2i-Z>-PO47-£-EO2i). Notation: LI, isotropic (polymer poor) solution; Ij, cubic phase; H ]5 hexagonal phase; La, lamellar phase; H2, inverse hexagonal phase; I2, inverse cubic phase; L2, isotropic (polymer rich) solution.185 The solid and dashed lines are calculated from the continuum and lattice descriptions, respectively. Reproduced by permission of American Chemical Society.

behaviour compared with the continuum theory, as illustrated by Figure 3.22. For example, the continuum theory predicts ordered phases for Pluronic L64, whereas the lattice theory (neglecting polydispersity) predicts none. Linse and coworkers have also used lattice mean field theory to compute phase diagrams for Pluronic copolymers,10'30'31 as discussed in the preceding section. The approach has also been applied to calculate the phase diagram for a specific ABC triblock in aqueous solution.1 The self-assembly of copolymer ME l4-b-PO \2-b-EOu was examined. Phase boundaries were found to be weakly dependent on copolymer concentration, but strongly dependent on temperature. For each of the ordered phases (hexagonal, lamellar, inverse hexagonal and inverse micellar cubic phases) a three layer structure was determined by analysing volume fraction profiles. Self-consistent field theory has been used to investigate the phase behaviour of block copolymers in solvents of varying selectivity.187 For a neutral good solvent, the dilution approximation is followed. For a symmetric diblock in selective solvent, the sequence lamellar - hexagonal-packed cylindrical micelles - bccpacked spherical micelles - micellar solution - homogeneous solution can be anticipated upon dilution, and self-consistent field theory calculations could reproduce this behaviour (the micellar solution phase was not considered however). For asymmetric copolymers, the theory was able to reproduce transitions from normal to inverse cylinders (and ultimately inverse spheres) via lamellae upon reducing the selectively of a solvent for the majority block.

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There have been surprisingly few computer simulations on mesophase structures in block copolymer solutions, although various mesoscopic simulation techniques have been used to study ordering in block copolymer melts. One exception is dynamic mean field density functional theory calculations performed to simulate the phase behaviour of Pluronic copolymers.188 This method is based on timedependent Ginzburg-Landau equation for the free energy of Gaussian chains. A mapping was made from a coarse-grained polymer bead model onto parameters for two specific Pluronics - L64 and the reverse Pluronic 25R4.188 Good agreement was found when predicted structures for a particular polymer concentration were compared with experimental results. Figure 3.23 shows examples of simulated morphologies. A separate paper focused on the shear-induced structure (and

Figure 3.23 Morphologies for Pluronic L64 from mesoscopic computer simulations. Isosurfaces of EO volume fraction are indicated.188 Polymer concentrations and morphologies as follows: (a) 70%, lamellar structure; (b) 60%, lamellar/hexagonal phase boundary; (c) 55%, hexagonal; (d) 50%, micellar. Reproduced by permission of American Chemical Society.

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calculated scattering patterns) of the hexagonal phase for L64.189 The effect of confinement in a cylindrical slit on the same system was also probed, in particular the orientation of the cylinders was examined as a function of slit width.190 Molecular based computer simulation techniques cannot yet directly be used to simulate block copolymer structures, since the simulation would of necessity contain too many atoms. However, coarse-grained models have been pioneered. Larson has carried out lattice Monte Carlo simulations of 'diblocks' A4B7, A4B6, A4B4 and A6H4, and observed the formation of lyotropic mesophases.191 Phase diagrams were constructed for binary surfactant/water mixtures and ternary surfactant/water/oil systems. Klein and coworkers have simulated bilayer, cylindrical and spherical micellar morphologies.192 The results were mapped onto the behaviour of PEO-&-PEE diblocks, studied experimentally.193 Computed density profiles for bilayer phases were compared with those of a lipid bilayer, and the membrane thickness was found to scale approximately with the molar mass of hydrophobe as d~Afg , i.e. as for weakly segregated block copolymer melts.

3.9 FLOW ALIGNMENT In this section, we consider flow alignment of lyotropic structures, in particular orientation under shear. Shear fields can be conveniently applied in several geometries, and provided the shear rate and/or amplitude are high enough, macroscopic alignment of the sample is possible. Understanding the processes of alignment under flow may also be relevant to applications, where in many cases block copolymer gels are subjected to strong flow fields (for example in drug delivery or in detergent formulations under agitation). Of course, in these applications, the flow field is much more complex so fundamental studies have focused on well-defined shear flow fields. The effect of shear flow on block copolymer mesophases has been extensively reviewed.35'77'194"197 3.9.1

LAMELLAR PHASE

Under shear, the layers in a lamellar block copolymer phase typically align with their normals either along the shear gradient direction, Vv, in the so-called parallel orientation, or with their normals along the neutral direction, e, in the so-called perpendicular orientation (see Figure 3.24). The transverse orientation (layer normals along the shear direction, v) has also been observed, although usually as a transient nonequilibrium state. The effects of shearing the lamellar phase of a concentrated block copolymer solution in a Couette cell have been investigated using SANS.198'199 A solution of a PS-b-PI diblock in DOP was investigated and the lamellar orientation was monitored below and above the ODT temperature with the neutron beam incident either radially or tangentially to the Couette cell. It was found that below the

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Figure 3.24 Orientations of a lamellar structure with respect to the shear plane (v, e). (a) Parallel; (b) perpendicular; (c) transverse.

quiescent ODT, oscillatory shear produced lamellae parallel to the plane of the shear cell walls. However, steady shear resulted in a reorientation of the lamellae into the perpendicular orientation (i.e. lamellar normals in the neutral direction).199 Above the transient ODT, the alignment induced by steady shear above a critical rate, quantified by the anisotropy of the scattering ring, was found to follow a master curve as a function of reduced shear rate (with respect to the shear rate for the onset of orientation) for all temperatures.198'199 The critical shear rate was found to increase exponentially with temperature. The transition between parallel and perpendicular orientations was probed in detail on a similar diblock solution subjected to oscillatory shear.200 The transition between perpendicular and parallel orientation could be initiated at a fixed temperature by increasing frequency. A systematic difference in the defect density between parallel and perpendicular alignments was also noted. In particular, under shear flow a sample with the parallel alignment was largely disordered due to a large number of defects, and it was pointed out that this shear-induced disordering below the quiescent ODT is not in agreement with existing theories.200 It was also proposed that the observed shearinduced disordering of perpendicular lamellar is driven by increasing lamellar undulations. Zryd and Burghardt have investigated the same system in both oscillatory and steady shear via rheology and flow birefringence, and compared their results with those obtained for lamellar PS-b-PI melts.201 They found similar behaviour for either type of flow, i.e. preferential parallel alignment of the lamellae at high reduced frequencies and perpendicular alignment at low reduced frequency. This behaviour is the same as that observed in the melt. At high temperature, the degree of perpendicular alignment induced by steady flow decreased, in contrast to the high degree of orientation maintained under oscillatory shear. This was ascribed to an increased propensity for defect formation and/or formation of mixed orientation states under steady shear. In aqueous solutions of Pluronic P85 (PEO26-&-PPO41-b-PEO26) forming a lamellar phase, Mortensen reported that following shear, parallel and perpendicular orientations coexist with all other lamellar orientations in which layers are parallel to the flow direction.194 Richtering and coworkers have examined using SANS the shear-induced formation of vesicles in solutions of Pluronic block copolymers in

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butanol/water mixtures.202'203 Pluronic P123 and F127 were both studied. Orientation diagrams were constructed showing that a transition from a parallel to a perpendicular alignment of planar lamellae occurred at a certain shear rate for samples in a well defined region of the phase diagram (copolymer concentration and butanol/water ratio).20 Similarly, conditions for shear-induced formation of multilamellar vesicles were identified. This occurred close to the low polymer concentration boundary of the lamellar phase region. The formation of vesicles is signalled by strong shear thickening, whereas the viscosity decreased across the parallel to perpendicular transition in the more concentrated solution.202 SALS data also showed a four-lobe pattern characteristic of vesicles. 3.9.2

HEXAGONAL PHASE

Shear flow leads to alignment of the cylinders in a hexagonal phase parallel to the shear direction. Two possible orientations of the hexagonal lattice in the (Vv, e) plane are possible, and have been observed for block copolymer melts204 although this has not been reported for solutions. A transition from shear-induced order to shear-induced disorder at higher shear rates has been reported above the quiescent ODT of a hexagonal phase in a block copolymer solution.205 The experiments were performed with a solution of a PS-bPI diblock in the neutral solvent DOP, forming cylinders of PS. The samples were investigated by SANS with in situ steady shear. It was pointed out that existing theories for the effects of shear on block copolymers only predict shear-induced ordering due to the suppression of composition fluctuations. However, it was proposed that fluctuations of the cylinders, if characterized by a lifetime larger than the inverse shear rate, lead to the disordering observed at high shear rates. In prior work, Balsara et a/.206 observed a large difference in the ordering transition of this system for shear oriented 'single crystals' and polydomain samples prepared under quiescent conditions. In sheared polydomain samples where the imperfections were partially removed, coexistence of ordered and disordered regions was observed at temperatures between the two limiting ordering transition temperatures. However, these observations have not been satisfactorily accounted for. Shear orientation of the hexagonal-packed cylinder phase formed in aqueous solutions of Pluronic P85 confirmed the long-range nature of the induced alignment.194 A sample was sheared between parallel plates and rotated with respect to the neutron beam. With the neutron beam incident along the shear gradient direction, a SANS pattern with a pair of meridional Bragg reflections is observed, showing orientation of the cylinders along the shear direction. The hexagonal order was confirmed by the hexagonal symmetry observed by SANS when the neutron beam was incident along the shear direction. At lower concentrations of this triblock, shear-orientation of rod-like micelles leads to an aligned nematic phase, as characterized by SANS.194 Richtering and coworkers studied shear orientation in the hexagonal phase of the related Pluronic L64 in aqueous solution via

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birefringence, SALS and SANS.207 The degree of alignment was found to depend on strain, with a common sigmoidal increase in birefringence with strain independent of stress over the range studied. Depolarized light scattering revealed streaks of scattering along the flow direction due to a mesoscopic stripe texture (observed for other surfactant systems208'209 by polarized light microscopy) perpendicular to the flow direction, ascribed to undulations of the director. Zig-zag undulations of cylinders result from a buckling instability that arises from thermal contraction/ expansion. The development of a stripe pattern due to zig-zag undulations of cylinders formed by diblock EO18-&-BO10 in aqueous solution aligned by flow in a capillary has been observed by polarized optical microscopy and analysed through the splitting of SAXS Bragg reflections.210 The effect of large amplitude oscillatory shear on the orientation of a hexagonal phase formed in solution of EO]8-b-BOi0 in 0.2 M K2SO4 has been studied using SAXS on samples subjected to steady shear in a Couette cell.211 The orientation was quantified in terms of order parameters PI, P4 and P6, where Pn denotes an ensemble averaged Legendre polynomial of order n. These order parameters were extracted from the SAXS patterns using a model of scattering from oriented infinitely long cylinders. It was found that the order parameters increased logarithmically with the shear rate. A related study was undertaken for aqueous gels of EO40-^-BO10.212 Here, it was shown that the susceptibility to shear orientation depended on diblock concentration, because a gel containing 25% diblock did not shear orient, whereas gels containing between 30 and 38% diblock did form a shearoriented cylindrical structure. 3.9.3

CUBIC MICELLAR PHASES

The effect of shear on hcp/fcc and bcc phases has been investigated in some detail.77'196 In essence, samples usually align with a close-packed direction along the shear direction, although flow can occur in several possible shear planes depending on shear conditions and geometry. Figure 3.25 presents representative SAXS patterns from shear-aligned PEO-b-PBO diblocks, showing the indexation to hep and bcc structures, respectively.137 One of the first experiments to examine the effect of shear on the orientation of micellar cubic phase was performed on a PS-fr-PEP diblock in dodecane (a selective solvent for the latter block).213 SANS was used to probe the effects of in situ steady shearing, and it was found that long-range order was induced by very low shear rates, whereas shear melting was noted at high shear rates. The data were interpreted on the basis of a distorted fee structure, with an ABC ABC... layer stacking but distorted from a close-packed arrangement due to normal stresses that led to a decreased inter-layer spacing. Distortions from a close-packed structure were also noted for a PEO-b-PSO diblock studied by SAXS under steady shear.214 The distorted lattice was assigned a rhombohedral structure. For the fee phase formed by PS-&-PI micelles in decane, a transition from polycrystallinity to sliding

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Figure 3.25 Schematic of SAXS patterns obtained in the (v, e) plane (shear direction horizontal) following large amplitude oscillatory shear for aqueous diblock solutions.l37 (a) 9 wt% gel of EO96-/?-BOi8 forming a hep structure (indexation to hexagonal lattice), (b) 10 wt% gel of EO315-i'-BOi7 (indexation to a bcc structure). The sample is a multiply twinned, directionally oriented crystal. The labels A, B, C and D correspond to different twins obtained by rotation around the [111 ] direction. Reproduced by permission of American Chemical Society.

hep layers was observed on increasing the shear rate.215 The sliding flow of hep planes observed for such gels at relatively low shear rates has been ascribed215 to a slip-stick mechanism of flow, where the micelles hop from registered (A, B or C) sites (see Figure 3.26). A similar observation has also been made for a diblock containing a polyelectrolyte block, PfBS-b-PNaMA.216 Highly aligned SAXS patterns from fee crystals have been obtained simply by hand shearing cubic phases of PS-&-PI micelles between sliding parallel plates.135

Figure 3.26 Arrangement of spheres in planes in a close-packed structure. With respect to a reference layer A, successive layers can be of type B or C.

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Shear-induced orientation effects in fee structures have also been examined using Pluronic copolymers.217"219 The effect of steady shear, applied using a Couette cell, on the orientation of a fee structure in Pluronic F108 was investigated using SAXS, and transitions between different types of shear flows were elucidated.217 A twinned fee structure with a high density of stacking faults due to flow of sliding layers was observed to transform into large homogeneous single crystals of either twin, separated on a millimetre length scale, upon application of large amplitude oscillatory shear (LAOS).218 The same system was subsequently investigated in more detail using SAXS and SANS.219 Different mechanisms of flow were identified, depending on the shear rate. At low shear rates, the fee structure was locally preserved, and the flow was mediated by defects between crystallites. However, at high shear rates, the melting of the structure was observed through the development of a liquid-like structure factor. Intermediate shear rates (7 w 50 s"1) led to layer sliding, where hep planes were aligned parallel to the Couette cell walls. Creep experiments starting from initially polycrystalline or aligned states have provided a wealth of information on flow mechanisms in an fee gel formed by Pluronic F108.220 It was suggested that the stationary flow curve is associated with the onset of layer sliding of hep planes, although shear thinning occurred at much lower shear rates than those for which layer sliding was detected by SAXS, suggesting nucleation of a fraction of sliding planes below the threshold for detection by SAXS. It was also suggested that the incubation time observed in the creep experiments (above the characteristic stress) was related to the time necessary to reorient initially unoriented grains into sliding hep layers. The effect of shear on an aqueous solution of the diblock EO55-b-BO8 forming a fee structure has been investigated in detail, using SAXS on samples sheared in a Couette cell.221 Steady shear was found to orient the mesophase into a polydomain structure with the hep planes both parallel and perpendicular to the shear plane. At low shear rates, a sliding mechanism of flow of hep layers was identified whereas at higher shear rates, partial melting occurred.221 A common flow-induced state of alignment has been reported from several experiments on different block copolymer solutions forming bcc gels, when subjected to oscillatory or steady shear at moderate shear rates. Flow planes are illustrated in Figure 3.27. In the most common type of flow, a twinned bcc crystal is formed with a <111> close-packed direction along the shear direction, with {110} planes in the shear plane, and a (21 l)-type twinning plane. The bcc twins slip along the twinning planes, allowing the crystal to flow at moderate shear rates.215'222'223 This flow mechanism is the same as that observed for charged colloidal suspensions subjected to steady shear,224 and also observed for a diblock copolymer melt subject to reciprocating shear.225 A transition from an initially aligned twinned bcc structure to a distorted hep structure on increasing shear rate due to the distortion of the twinned structure has been reported for a solution of an PS-£-PI diblock in decane.215 However, the twinned structure is again accessed at higher shear rates (in other words it is the stable state, above a critical shear rate, 7 w 50 s~' in these experiments)215 in contrast to the colloidal system studied earlier.224 At still higher

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Figure 3.27 Flow planes in a bcc lattice.223 (a) bcc lattice with a {110} plane shaded, (b) Section of a bcc lattice showing a {110} plane, (c) bcc lattice with a {211} plane shaded, (d) Section of a bcc lattice showing a {211} plane. Reproduced by permission of American Institute of Physics.

shear rates, melting was observed for the copolymer solution, a process also observed for sheared aqueous solutions of diblock EOgg-b-BO^.226 A more complex orientation than that with {110} planes parallel to the shear plane has been observed for 40 wt% gels of EO86-£>-BOi0 in 0.2 M K2SO4 subjected to either steady226 or oscillatory227 shear. The detailed elucidation of the mechanism was possible because higher order 200, and especially 211 reflections could be resolved. Indexation of the SANS and SAXS patterns including these higher order reflections indicated that flow in {211} and {321} planes is important as well as flow in {110} planes. Thus, it was proposed that the aligned crystal is a 'directionally oriented' crystal, with a [111] direction along the shear direction, but with flow in {110}, {211} and {321} planes (which intersect in a common [111] zone axis). This mechanism is consistent with flow in the three principal slip systems of a bcc crystal, as observed for example for bcc metals.228 Which of these planes are active under particular flow conditions is described in detail elsewhere.77 An interesting point is that the {211} planes are not the most densely packed. A crystallographic study of a shear oriented gel of EO2io-^-BOi6 has shed further light on the orientation state of an aligned bcc gel.229 Here, a gel was subjected to O'7'Z

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large amplitude oscillatory shear (LAOS), and then 'mesoscopic crystallography' was performed, i.e. the gel was rotated with respect to the neutron beam to map out the location of Bragg reflections on the Ewald sphere. In this case flow was observed in {110} and {211} planes only, and not also in {321} planes. A similar alignment state was reported for a 30 wt% gel of EO86-^-BOi0 in 0.2 M K2SO4 subjected to steady shear, and investigated by SAXS.227 Mortensen has presented SANS patterns for Pluronic copolymers F88194'230'231 and P85194'230 which appear to show the same orientation of a twinned bcc crystal, although it was not indexed in detail by him. The work of Riser et a/.223 has also revealed a rich and complex flow behaviour under steady shear in bcc gels formed in an aqueous solution of Pluronic F68. The flow in a Couette cell was inhomogeneous due to the large stress gradient (a decrease of 20% at the outer wall compared with the inner wall). Two successive orientation transitions were observed to occur at very different shear rates but separated by a narrow difference in stress. The stress as a function of shear rate shows two plateaux (Figure 3.28), within each of which two distinct structural

Figure 3.28 Two stress plateaux observed in the flow curve for Pluronic F68 in water (46 wt% polymer) at 20 °C.223 Reproduced by permission of American Institute of Physics.

organizations coexist in the gap of the Couette cell. This phenomenon has been termed 'shear banding', as observed earlier for sheared solutions of wormlike micelles. The structure of the gel as a function of shear rate was elucidated by SAXS. This revealed that at low shear rates, a viscous polycrystalline state filled the gap. At intermediate rates, a first oriented state was observed with {211} planes parallel to the shear plane. The proportion of this state increased across the first stress plateau. At higher rates, in the second plateau, a second oriented state was observed with {110} planes oriented in the shear plane. This is the so-called layer sliding regime, observed earlier for highly charged colloidal latex suspensions.224 In

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both oriented states, the close-packed <111> direction was along the shear direction. Due to the fact that the stress gradient in the Couette cell (20%) was larger than the 2.5% difference in stress separating the two plateaux in the rheology data, the intermediate state with {211} planes parallel to the shear plane was never observed in isolation, but only in combination with the disoriented state (at 7 = 16 s"1, arrowed in Figure 3.28) or with the layer-sliding state (at 7=160 s"1, arrowed). Scanning the X-ray beam across the gap of the Couette cell confirmed that the intermediate orientation state was located close to the outer wall, as expected since the stress was lower there. A question remains as to why stress plateaux were not observed for an fee gel formed by a related Pluronic copolymer (F108) and also studied extensively by Eiser et al.220 despite the observation of strong shear thinning. The difference compared with the bcc gel in Pluronic F68 could be because no purely elastic regime was observed for the fee gel, suggesting a high density of dislocations sufficient to induce flow even for small, applied stresses. The bcc gel may be less defective, alternatively there may be a difference due to the distinct preferred flow planes in bcc compared with fee gels. Hamley and coworkers66 have also compared the flow behaviour of fee and bcc gels subjected to LAOS, and noted the much more elastic response of the bcc gel. In a bcc gel the flow appears to be hindered resulting in a slip-stick motion as planes of micelles shear past one another. In contrast, in a fee gel, sliding of hep layers appears to be unhindered (at least at sufficiently high shear rates). This difference may reflect the difference in the intermicellar potential, which is more long range in the case of a bcc packing of micelles (as discussed in Section 3.5.1). Watanabe et al. have shown that the equilibrium modulus, Ge is hardly affected by shear orientation of a PS-b-PI diblock forming a bcc structure in tetradecane.232 It was noted that this indicates that defects do not have a major influence on Ge. The measured value of Ge is almost an order of magnitude smaller than that predicted on the basis of entropic elasticity theory:

The difference between the measured Ge and Gj] was ascribed to the correlation between the conformation of the PB blocks (which minimizes the osmotic energy) and the influence of this on the effective number density of strands. The nonlinear response of bcc227 and fee66 gels subject to oscillatory strain has been probed, plotting stress against strain in Lissajous figures. The interpretation of the flow mechanism followed that of Doi et al., who employed a lattice model to analyse the viscoelasticity of a (hexagonal) micellar phase formed by a block copolymer.233 The results show that flow under LAOS in a bcc phase occurs through a slip-stick mechanism, and suggest that this is the process that leads to the observed macroscopic orientation of gels, under steady shear. 226>227 This complements other work that has suggested a slip-stick flow mechanism for fee gels under steady shear.215'216 Lissajous figures obtained for an fee gel of a PEO-£»-PBO

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diblock under LAOS indicated strong shear thinning.66 The onset of strong shear thinning is associated with the development of layer sliding flow of hep layers. As mentioned above, the observation of strong shear thinning from creep experiments on an fee gel was also ascribed to this flow mechanism.220 The influence of oscillatory shear on PS-&-PEB-&-PS triblocks in a solvent selective for the midblock has been investigated by Mortensen et al.234 At the concentration examined, a bcc structure was formed. Flow occurred in both {111} and {110}-type planes along <112> and <111> directions, respectively. An orientation diagram in terms of the flow state as a function of frequency and strain was presented. The influence of the duration of shear was also examined. If shear was stopped after only a short time, rapid relaxation of orientation was observed. However, retention of an oriented scattering pattern was observed after prolonged shearing, and this was ascribed to flow involving relatively large grains. The difference in relaxation behaviour suggests a decrease in slip plane density as shearing progresses. The influence of steady shear on a bcc lattice formed by a PS-b-PB diblock in the PS-selective solvent di-n-butyl phthalate has been examined by shear rheometry.102 The flow behaviour is unsurprisingly non-Newtonian. At low shear rates, steady state was achieved after a significant stress overshoot followed by a thixotropic (time-dependent shear thinning) stress decay. This plastic behaviour reflected mild disruption of the lattice. At high shear rates, the lattice was greatly disrupted, leading to a much weaker dependence of viscosity on shear rate. The pre-sheared system exhibited recovery to an elastic response following cessation of shear. The slowest recovery was observed at a frequency close to that associated with concentration fluctuations. It follows that shear at this (intermediate) frequency was most effective in disrupting the lattice. Thus shear at the highest shear rate does not always lead to the strongest shear-induced disordering. It was noted that the soft nature of the PB core in these micelles allows fluctuations in the number of chains per micelle that varies as defects are created (during shear) or annihilated (during recovery). The shear melting of a bcc lattice has been examined for melts and concentrated solutions of PS-&-PI and PS-&-PEP diblock, triblock and starblock copolymers.235 Steady shear destroys the bcc lattice at a critical shear stress, ac — 0.038G°CC, where G®cc is the low frequency modulus of the bcc lattice. When comparing data at a common reduced temperature, this quantity was found to scale approximately as G£CC ~ RT/d3, where d is the measured domain spacing of the {110} planes. This scaling is consistent with a potential of the form t/(r)~&B71n(l/r), which is similar to that proposed by Witten and Pincus 236 for spheres with interacting grafted polymer layers (see Section 2.9), although the data obtained by Register and coworkers did not scale with / as predicted. A universal scaling was found when G°ccd3/RT was plotted against reduced temperature (this quantity being employed in the absence of quantitative data on x) and found to vary exponentially. In a companion paper, the flow curve (viscosity as a function of shear stress) of bcc block copolymer melts was discussed.237 The melting of the bcc lattice at a critical

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shear stress led to a dramatic reduction in viscosity. The kinetics of the ordering process were also studied.237 The low frequency deformation behaviour was examined via creep and dynamic viscoelasticity measurements.238 Using a model for high temperature creep in metals and ceramics, data for zero shear viscosity as a function of temperature could be rescaled onto a master curve. The resulting Arrhenius plots provided an activation energy that is related to the temperature dependence of the monomeric friction coefficients, with an additional contribution from block segregation. The effect of grain size (controlled through thermal history) on the viscosity was also investigated. The effect of extensional flow applied to orient a bcc gel formed by a PS-&-PEBb-PS triblock in a midblock selective oil has been examined by SAXS.239'240 The deformation was found (by measuring lattice dimensions by SAXS) to be affine for low strains, the onset deformation for nonaffine behaviour decreasing with decreasing polymer concentration.239 At large strains a 'butterfly' pattern was observed, similar to that previously obtained for stretched polymer networks and ascribed either to physical inhomogeneities or anisotropic concentration fluctuations.240 Its observation for the triblock gel was attributed to cluster formation - stretching brings endblock domains closer together in the direction perpendicular to the deformation. The effect of extension rate was also examined. It also found that the deformation was nonaffine at low extension rates, but became affine at higher rates.241

3.10 DYNAMICS 3.10.1

DYNAMIC MODES

DLS has been used to probe the dynamic modes for dilute, semidilute and concentrated solutions of PS-&-PI diblocks in the neutral good solvent toluene.242"244 Three modes have been observed244 - cooperative diffusion (with diffusion coefficient Dc), corresponding to relaxations of fluctuations in polymer concentration, a nondiffusive (q independent) internal mode (with decay rate 1^) that reflects the relative motion of the centres of mass of the blocks on a single chain243 and a heterogeneity mode (DH), due to fluctuations in composition from chain to chain. The observation of these modes is in agreement with theoretical predictions by Benmouna et a/.245'246 and Semenov and coworkers.243 Benmouna et al. predicted cooperative and internal modes, whilst Semenov and coworkers considered a heterogeneity mode. The observation of a fourth mode due to clusters or long-range density fluctuations243 is controversial, and has been ascribed to nonequilibrium or metastable states.244 Lodge and coworkers found that in dilute solution of their PS-b-PI diblocks, a single diffusive mode is present, and is attributed to a superposition of Dc and DH modes. ^ In semidilute and concentrated solutions these two modes are clearly resolved. The decay rate for the cooperative and heterogeneity modes exhibit the predicted dependence on concentration, and molecular weight. Field gradient NMR

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studies were also performed to determine the translational diffusivities (Ds) of the same copolymers. Values of Ds were found to be very similar to DH. The internal mode was hard to resolve, but was observed for the highest molecular weight sample examined. The concentration dependences of DH and Ds were found to be insensitive to the ODT. The relationship of these results to earlier DLS studies of block copolymers in neutral good solvents was discussed in detail (this is not reiterated here). Apparent inconsistencies could be resolved by appropriate assignment of the heterogeneity mode. In a companion paper, index matching of the copolymer was achieved in zero average contrast conditions by the use of appropriate solvents for the PS-&-PI diblocks studied.247 The cooperative diffusion mode could be eliminated, enhancing the relative amplitude of the internal mode, which was observed together with the heterogeneity mode. The decay rate of the internal mode was found to decrease with concentration. Values of DH were again in agreement with those obtained from pulsed field gradient NMR. As the concentration increased towards the ODT, the total scattered intensity increased markedly due to the onset of large amplitude concentration fluctuations. Forced Rayleigh scattering revealed a decrease in diffusivity with increasing concentration for matched asymmetric PS-b-PI and PS-£-PI-b-PS copolymers.248 This was ascribed to the retardation of chain diffusion due to concentration fluctuations. The diffusivity decreased rapidly and discontinuously across the ODT. Since the retardation of mobility due to ordering or concentration fluctuations was larger for the diblock, for which the ordering concentration was greater, the effect was ascribed to the increased monomeric friction in the PS-rich cylindrical domains. A comparison was made to the melt behaviour of the same polymers, and it was noted that the onset of fluctuation effects in the diffusivity occurs at the same relative distance from the ODT in both melts and solutions. The dynamics of giant micelles formed by high molecular weight PS-b-PI diblocks (Mw > 1 x 106 g mol"1) in an unidentified solvent were compared with those of colloidal particles. In contrast to the latter systems, no slow-down in the collective diffusional dynamics is observed in the vicinity of q*, the peak of the static structure factor.249 This was ascribed to nonlocal mobility due to interactions between the tethered corona chains. Since the chains are long enough to be entangled, reptation contributes substantially to the dynamics.250 The same group have also investigated the dynamics of model colloidal particles prepared by crosslinking the PCEMA core of PS-&-PCEMA micelles.251 Two relaxation processes were observed - a fast cooperative diffusion due to interactions among coronal chains and a slow one due to self-diffusion of the core. Analogies with the dynamics of star polymers252 were made, although this is outside the scope of the present text.

3.10.2

DYNAMICS OF GELATION

Gelation is manifest by changes in the intermediate scattering function S(q, i) from the simple exponential relaxation dynamics of a simple liquid. In fact, the system

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Figure 3.29 DLS field correlation function data for a hard gel (o), compared with the single exponential relaxation observed for the dilute liquid phase (n) formed by EO92-^-BOi8 in aqueous solution.262 Reproduced by permission of American Institute of Physics.

becomes nonergodic (i.e. the dynamics vary from point to point in the sample). Nevertheless, by averaging measurements over the sample volume, reliable DLS data can be obtained. A plateau is commonly observed as the dynamics slow down over a certain relaxation time interval (see, for example, Figure 3.29). The dynamics of Pluronic copolymers in structured mesophases provide an early example of the observation of this phenomenon.23'253 In particular, DLS has been used to probe the dynamics of reverse Pluronic 25R8 in aqueous solution.23 At low temperatures and copolymer concentrations the DLS correlation functions were characterized by two dynamic modes. These modes were associated with the presence of free molecules and networks of copolymer strands interconnected through the PPO blocks. At higher copolymer concentrations the correlation functions showed a fast decay followed by a slower relaxation with a much longer decay time. Indeed, a pronounced plateau in the correlation function indicated a nonergodic system in which dynamic fluctuations were suppressed for an intermediate range of timescales. The system was then described as a network of micelles, interconnected by PPO strands. An increase in the polymer concentration of this network at low temperatures, resulted in an ordered solid-like mesophase.23 The dynamics of Pluronic P85 in aqueous solution were also characterized by DLS.253 SANS indicated a single lamellar mesophase at high temperatures. At low temperatures two phases were present, one of which resembled the high temperature phase while the other was similar to the lamellar melt phase.253 The DLS correlation function exhibited a single exponential decay in the concentrated lamellar phase at high temperature. Upon dilution, a fast mode appeared also at

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high temperature as a second lyotropic lamellar phase forms. Here again, a pronounced plateau was observed in the decay of the correlation function. The angular dependence indicated large anisotropic grains in this nonergodic 9^ system. Analogies exist between the dynamics of block copolymer gels and glassy states observed for colloidal systems. A system of hard spheres is dominated by the repulsive interactions between the particles. Particles are increasingly caged by their neighbours (simultaneously each particle makes part of a cage) as the volume fraction of hard spheres increases. At a critical volume fraction, this caging becomes permanent and stops all long-range motion. The system can then be considered nonergodic or glassy.254 However, a hard-sphere glass can be perturbed by the introduction of a short-range particle attraction.255'256 Short-range attractive forces lead to clustering of the particles forming the cage and opens holes, leading to the 'softening' of the hard sphere glasses. This is a qualitatively different glassy state dominated by attractive interactions, where the particles tend to form polydisperse aggregates, some of which can span the whole sample (percolating clusters). Colloidal glassy states dominated by repulsive and/or attractive interactions are well described in terms of the mode-coupling theory (MCT) of supercooled liquids in the vicinity of a glass transition.256"258 Recently DLS has also been used to investigate the application of MCT to the sol-gel transition of block copolymer micellar systems259"261 through the determination of the field correlation function gw(t) via DLS. Dense micellar solutions of Pluronic L64 were studied by DLS.259'261 The field correlation function showed a logarithmic decay, attributed to a higher-order glass transition singularity predicted by MCT, which points to the coexistence of both percolation and structural arrest in the system.259'261 The dynamics of a PEO-bPBO diblock in aqueous solution were studied in micellar, soft gel and hard gel phases.262 Both the liquid and the soft gel phases are micellar phases, although the structural order is higher in the soft gel phase than in the liquid phase. The hard gel phase corresponds to an fee arrangement of micelles. DLS results revealed that the relaxation time in the dilute liquid phase exhibits a single characteristic time associated with the diffusion of the micelles. In addition, a second characteristic time associated with the presence of micellar clusters in the system is identified in the concentrated liquid and in the soft gel phases. It was thus suggested that the structure of the soft gel phase comprises micellar clusters coexisting with micellar fluid, in good agreement with hypotheses from previous work.54'55 The dynamics of the system slows down as the hard gel phase is approached and a plateau is observed in the DLS correlation function (Figure 3.29). The structure of the hard gel is 'softened' upon increasing temperature and/or decreasing concentration. As for the Pluronic copolymers studied by Chen and coworkers,259'261 gelation in these diblock systems is not related to bridging of copolymer chains between micelles, but is due to packing of micelles into cubic structures. The dynamics of micellar solutions of PS-b-PAA block copolymers were investigated by rheology in the vicinity of the gel point263 and in the gel at high

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concentration via rheology and DLS.260 The PAA was not completely hydrolysed, and contained a fraction of hydrophobic ethyl aery late 'stickers'. At the gel point, the expected power law dependence of moduli on frequency, G' ~ G" ~ u;A (Section 3.3.1) was observed. The exponent A was consistent with that predicted by percolation theory.53 A re-entrant liquid-to-glass transition was observed for the PS-b-PAA system. This was in agreement with the MCT phase diagram for a system of hard spheres with short range attractive interactions, which presents a reentrant repulsive glass-to-liquid-to attractive glass transition for a particular range of hydrophobic stickers concentration. In addition, the field correlation function showed an extended logarithmic decay with increasing concentration of sticky soft spheres above the re-entrant transition branch. This, as already mentioned, indicates the coexistence of attractive and repulsive interactions in the system according to MCT. It was therefore concluded that the PS-b-PAA system obeyed all the theoretical predictions of MCT. However not all the DLS results on polymeric micelle or cluster dynamics found in the literature have been explained in terms of MCT. In some cases the DLS data may be reminiscent of supercooled liquids and colloids close to the glass transition, but the final analysis of the results was other than that based on the MCT.264~267 Semidilute micellar solutions of PS-b-PI-b-PS triblock copolymers in a midblock selective solvent were studied by DLS.267 The system could be described as a micellar network where the micelles, well ordered in a cubic structure, were linked by nodes formed by the terminal PS blocks. The correlation function measured by DLS was similar to that expected for supercooled liquid and colloids near the glass transition, but it was interpreted in terms of PS node cooperative diffusion. The dynamics of PS-6-PEB-£-PS micelles in a midblock selective solvent were similarly investigated.265 The dilute solution correlation function only showed the translational diffusion of flower-like micelles. At intermediate concentrations, the correlation functions were characterized by a slow mode and a fast mode. The slow mode was ascribed to the diffusion of polydisperse molecular aggregates, formed by random bridging of triblock copolymer molecules, while the fast mode was associated with the diffusion of flower-like micelles. The semidilute region was identified as a physical gel, characterized by the presence of physical PS nodes. Three dynamic processes were extracted from the correlation function in the semidilute region: a fast mode, corresponding to the collective diffusion of interconnected PS nodes in the physical gel; an intermediate mode, due to the local dynamics of PS nodes trapped in the network of the ordered gel; and a slow mode, associated with the presence of aggregates of insoluble homopolymer impurities (PS) in the system.265 The dynamics of aqueous solutions of a hydrophobically modified poly(oxyethylene) was studied by DLS.266 In this case the time correlation function was described by a single exponential followed by a fractional exponential relaxation function. At short times, the correlation function indicated a diffusive mode whereas at long times, the analysis provided a mean relaxation time, associated with the release of coupled clusters.

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Block Copolymers in Solution: Fundamentals and Applications

The influence of thermal gelation on the dynamics of a giant PS-b-PI diblock (M = 2 x 106 g moF1) in decane was compared with the gelation of star polymers with /= 128 arms (the association number of the diblock micelles was p = 1500).268 The gelation led to a slow down in dynamics due to the overlap of 'arms' (corona chains for the micelles), and a plateau developed in S(q, i). Further details on thermal gelation in the star polymer systems can be found elsewhere.269'270 NMR has also been used to investigate gelation. For example, changes in the proton relaxation times for the the PEO block (in particular the transverse relaxation time r2) were noted at the lower and upper gel transitions for several PEO-b-PEO diblock and PEO-b-PBO-b-PEO triblock copolymers.271 A two-step relaxation model indicated that the slow mode representing large scale motions was affected much more significantly by gelation than the fast mode ascribed to local segmental motions. Transient nuclear Overhauser effect measurements revealed interpenetration of PEO and PBO blocks at the core-corona interface, as for a PEO-b-PPO-bPEO triblock studied earlier.272 For the Pluronic-type copolymer, changes in the relaxation times of both PEO and PPO blocks were observed at the gel transitions (although the fast mode for the PEO block was not sensitive to gelation).272

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4 Polyelectrolyte Block Copolymers 4.1 4.1.1

MICELLIZATION GENERAL REMARKS

As for nonionic block copolymers, micellization occurs in a solvent that is selective for one of the blocks. However, the ionic character introduces new parameters governing the structure and properties of the micellar solution. To date, there have been relatively few reviews focused on the subject.1'2 Early work by Selb and Gallot, largely on PS-b-qP4VP diblocks, was reviewed by them3 and also by Hamley.' The properties of polyelectrolyte block copolymers in solution depend greatly on salt concentration. Regimes of 'salted brush' and 'osmotic brush' behaviour have been identified, depending on whether the added salt concentration is greater or less than the counterion concentration in the corona of the micelle (Figure 4.1).4 A further 'Pincus regime'5 where the Coulombic interaction among coronal chains is unscreened because counterions are located outside the corona has also been identified, as mentioned in Section 4.3 below. The strength of the polyelectrolyte plays an important role in micellization in polyelectrolyte-containing block copolymers.6"8 In strongly charged polyelectrolytes, such as poly(styrene sulfonate), the ionic units are essentially fully dissociated, irrespective of ionic strength or pH. Polyelectrolytes in which the number and arrangement of charges is fixed are termed 'quenched' poly electrolytes. In 'annealed' polyelectrolytes the degree of dissocation depends on pH, as the total number and position of charges is not fixed. For example, for polyacrylic acid, at low pH ~ pKa the degree of dissociation is suppressed due to trapped counterions. Addition of salt can lead to substitution of counterions (e.g. Na+ for H+) and an increase in ionization. Due to the difference in pH within the micelle and in bulk solution, large changes in aggregation number and shape in response to changes in ionic strength are possible for this type of polyelectrolyte. For polyelectrolytes the ionic strength plays an important role in the chain conformation, and the presence of a high charge density leads to some specific properties unique to ionic block copolymers. Many of the studies on ionic block

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Figure 4.1

Block Copolymers in Solution: Fundamentals and Applications

(a) Salted and (b) osmotic brushes in block copolymer micelle coronas.

copolymers have been undertaken with solvents selective for the ionic polyelectrolyte block, generally water or related solvents, such as water/methanol mixtures. However, it has been observed that it is often difficult to dissolve hydrophilic-hydrophobic block copolymers in water. These dissolution problems are far more pronounced than for block copolymers in nonaqueous selective solvents, although they do not always reflect real insolubility. In many cases, dissolution can be achieved if a better solvent is used first, as discussed in the next section. This process however can influence the charge and hence conformation of the polyelectrolyte block, possibly leading to trapped nonequilibrium structures. Other important parameters governing the self-assembly of ionic block copolymers include the nature of the backbone, in particular whether it is hydrophilic (e.g. PAA) or hydrophobic (e.g. PSS). For the former, charge effects govern chain conformation whereas in the latter case, chain configuration depends both on charge and on the effect of hydrophobicity. For polyelectrolytes with a hydrophobic backbone, electrostatic interactions tend to favour an extended conformation, whereas a collapsed configuration reduces hydrophobic interactions. This leads to a pearl necklace conformation.9'10 This consists of regions of charged globules ('pearls') separated by narrow elongated strings. The formation of this conformation has been explained theoretically by analogy with the Rayleigh instability of a charged droplet, whereby addition of charge eventually exceeds the interfacial tension. 11-13 The flexibility of the chain is also important-the influence of charge on flexible chains will differ from that of semi-flexible diblocks or rod-coil systems. The latter type of behaviour is exemplified by block copolymers containing charged peptide 'rod' units, as discussed below. Aggregation into micelles of polyelectrolyte block copolymers modifies the electrostatic component of the interaction potential compared with that for unagreggated polyelectrolytes. In the former case the electrostatic potential is spherically symmetric (and decays inversely with distance), whereas in the latter case it is locally cylindrically symmetric. This has important consequences for counterion condensation.

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4.1.2 MICELLIZATION IN BLOCK COPOLYMERS CONTAINING ANIONIC BLOCKS The main class of anionic polyelectrolytes are polyacrylates and polymethacrylates, usually present as sodium (or other alkali) salts but also in acidic form at sufficiently high pH. Eisenberg and coworkers have investigated micellization of PS-b-PNaA diblock copolyelectrolytes in water over a number of years.14 The PS block length ranged from 6 to 100, while that of the polyelectrolyte varied from ca. 300 to ca. 1400.15 At a constant polyelectrolyte block length, increasing the hydrophobic block length lowered the cmc, as for nonionic block copolymers. Changing the soluble block length from 300 to 1400 typically changed the cmc values by less than a factor of 2, also in agreement with trends for neutral block copolymers. For very short PS blocks, the cmc decreased very rapidly with increasing length of the insoluble block, whereas for more than 12 repeat units, the drop in the cmc was more gradual.15 Micelles formed by PS-b-PC&A and PS-b-PCsMA in toluene, a selective solvent for the PS block, have been characterized using SAXS.16 Comparisons of the micelle core dimensions were made with the Zhulina-Birshtein and Halperin models for type IV polymeric micelles, as discussed in Section 2.7.1. The cmc of a family of PS-£-PNaA diblocks with fixed PS block length (660 repeat units) and 2.6 to 14 ionic block units in THF has been investigated using light scattering.17 Micelles formed by PS-£-PNaA and PS-b-PAA dissolved in this and other organic solvents have been characterized by the same group using a variety of techniques including size exclusion chromatography and static and dynamic light scattering.18 The cmcs and micellar dimensions of the same type of PS-&-PNaA copolymer in aqueous and NaCl salt solutions have been the subject of studies using fluorescence measurements19 and static light scattering experiments.20 A complex dependence of the cmc on block lengths was observed in the fluorescence experiments, with a maximum in the cmc as a function of the soluble PNaA block length.19 The effect of salt concentration on the association numbers, radii of gyration and second virial coefficients of micelles was investigated using static light scattering.20 It was found that the association number p increased as a function of salt concentration at low salt contents, but remained constant above ca. 0.10 M NaCl. The data were compared with the predictions of the neutral star polymer scaling theories, 21-23 and several of the various mean field models for block copolymer micelles (as discussed in Section 2.7).24-26 Good agreement was found with several of the models, although it was not possible to descriminate between the predictions of the theories with the data available.20 'Crew-cut' micelles with a short coronal block attached to a long core block have been the focus of much work by the Eisenberg group.27-32 They first reported the formation of such micelles in aqueous solutions of PS-b-P4VP diblocks quaternized with methyl iodide.32 In subsequent work, crew-cut micelles of highly asymmetric PS-b-PAA28 and nonionic PS-b-PEO31 diblocks in water were studied using TEM. Multiple micellar morphologies for the former were observed28'30 for copolymers

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with 80-98 % PS. Micellization occured in the range 3-6 wt% polymer, depending on its composition.30 For a series of diblocks with a fixed number of PS repeats (200) transitions from spheres to rods to vesicles to compound micelles was observed on decreasing the PAA block length, as illustrated in Figure 4.2. The micrometre-size compound micelles were observed to have an internal structure made up of a core containing reverse micelles and PS in the corona [Figure 4.2(e) and (f)]. Such compound structures have been predicted theoretically for ABC

Figure 4.2 Morphologies formed by PS-b-PAA diblocks in aqueous solution: (a) S200-bAA21; (b) S200-b-AA15; (c) S200-b-AA8; (d) S20o-^-AA4.28 (e) Enlargement of one of the large complex micelles in (d) showing the internal structure. The elongation in one direction was probably caused by the strong shear forces during microtoming. (f) A schematic of the structure of the large complex micelle filled with bulk reverse micelles. Reproduced by permission of Science.

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triblock copolymer melts in the 'superstrong segregation' limit.33 In this limit, segregation between, say, B and C blocks can occur within micelles in the A matrix. A similar effect is likely to underly the observation of compound micelles in block copolymer solutions. Zhang and Eisenberg occasionally observed lamellar structures for compositions where vesicles were otherwise seen (i.e. an alternative bilayer structure), and simple reverse micelle-like aggregates were also noted.28'30 The addition of homopolystyrene was observed to drive transitions from the bilayer or cylindrical morphologies into the spherical micelle structure.30 A transition between morphologies of crew-cut micelles was also observed for nonionic PS-bPEO diblocks, in particular a transition from spherical to rod-like or vesicular structures was induced by increasing the length of the hydrophilic PEO blocks.31 The effect of ionic strength in inducing transitions between micellar structures was also explored for PS-b-PAA and PS-b-PEO diblocks in water.29 It was found that addition of ions in micromolar (CaCl2 or HC1) or millimolar (NaCl) quantities can change the morphology of PS-b-PAA micelles in dilute aqueous solutions. In particular, on increasing the acid or salt concentration, the morphology changed from spheres to rods to vesicles and then to large compound vesicles. Gelation could be also be induced with the addition of ions to the solution.29 Later, morphology diagrams for PS-b-PAA diblocks in dioxane/water were presented.34-36 In general, increasing water content favoured the sequence of morphologies: single chains-spheres - rods-bilayers-inverted structures, with coexistence regions between the various phases. A variety of complex morphologies was also observed for PS-b-PAA31 and PS-b-PEO38 diblocks by Eisenberg et al., as mentioned in Section 2.16. The polymers were dissolved in DMF/water mixtures. DMF is a good solvent for PS, PAA, and PEO whereas water is a nonsolvent for PS. The resulting structures are not in equilibrium when the water content in the mixed solvent is high (the range 7.5-9.5% water was studied), and the aggregate structure depends on the method of preparation.37 The aggregate structure also depends on the addition of electrolytes (which changes the conformation of the water-soluble block) and the preparation temperature.36-38 Structures with combinations of the morphological features mentioned above were also commonly observed.38 The influence of the initial common solvent on the final morphology in aqueous solution was studied by comparing the aggregate structures observed for PS-b-PAA diblocks dissolved in DMF, THF and dioxane and mixtures of these.39 The selectivity of the solvent for either block influences the association number and chain packing. A weakly selective solvent leads to a swollen core. Less polar solvents reduce the PAA-solvent interaction and hence reduce repulsive interactions between corona chains, leading to an increase in association number and the stretching of the PS core chains. The reversibility of morphological transitions upon addition/removal of water to a dioxane solution of diblock PS310-b-PAA52 was studied using cryo-TEM to determine morphology.34 The binary phase diagram for this copolymer is shown in Figure 4.3. The transitions follow the sequence expected based on interfacial curvature/molecular packing considerations. The reversibility of vesicle formation and growth is discussed further in Section 2.17.

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Figure 4.3 Binary morphology diagram for diblock S310-b-AA52 in THF/water mixtures as a function of polymer concentration and water content in the solvent mixture.34,182 Reproduced by permission of Science.

Another interesting morphology observed by Eisenberg and coworkers, again a nonequilibrium structure resulting from the solvent exchange during preparation, is bowl-shaped micelles.40 These were observed for crew-cut micelles formed by PAI-b-PS-b-PAI triblocks initially dissolved in a common solvent and then dialysed against water to induce association of the PS chains. It was proposed that the bowlshaped structure forms from initially spherical compound micelles due to the formation and coalescence (followed by break-through to the surface) of waterfilled bubbles as water is added, and solvent is extracted from the core leading to PS vitrification, as illustrated in Figure 4.4.

Figure 4.4 (a) Proposed mechanism of formation of bowl-shaped structure, (b) Micrographs illustrating the steps (selected from different micrographs) for a PAI-b PS-bPAI triblock.40 Reproduced by permission of American Chemical Society.

Micellization in di- and triblock copolymers with a PMAA polyelectrolyte block and one or two hydrophobic blocks bearing a perfluorinated side chain has been investigated.41 Despite the expected high hydrophobicity, the copolymers were found not to be very surface active. In exceptional cases, surface tension measurements can be insensitive to micellization. Matsuoka and coworkers have observed micelle formation in

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PS-b-PSS diblocks via dye solubilization and dynamic light scattering.42 However, no decrease in surface tension with increasing concentration over the appropriate range was observed, and no adsorption at the air/water interface was detected by X-ray reflectivity. When salt was added, surface activity was noted and foam formation was detected. For the unscreened solutions, it was proposed that the highly charged nature of PSS was due to an image charge effect. The image charges are significant because of the dielectric contrast between air and water. A strong electrostatic repulsion of PSS from the interface results. Image charge repulsion was considered theoretically by Wittmer and Joanny43 who showed that the corresponding electrostatic energy can exceed thermal energy in the early stage of adsorption when there are lateral variations in charge density. 4.1.3 MICELLIZATION IN BLOCK COPOLYMERS CONTAINING CATIONIC BLOCKS Armes and coworkers have published extensively on the solution properties of tertiary amine methacrylate block copolymers (Figure 4.5). These are prepared by atom transfer radical polymerization or group transfer polymerization. For these ionic block copolymers, the size and association number of the micelles can be systematically controlled by changing the temperature, pH or ionic strength of the solution. The properties are exemplified by the PDMA-b-PDEA system. Diblocks of this type dissolve molecularly at low pH, but as pH is increased deprotonation occurs and the PDEA block becomes hydrophobic, leading to micellization.44'45 At low pH, the copolymers can be considered to be double hydrophilic.44 The micellization of block copolymers containing the permanently hydrophobic PMMA block and PDMA has also been investigated, via static and dynamic light scattering, ultracentrifugation and surface tension measurements.46 For these copolymers, the cmc was found to increase with the length of the hydrophobic block if the hydrophilic block length was fixed, in contrast to the trend for most neutral and ionic block copolymers. Increasing the overall molar mass of the copolymer also increased the cmc for a given composition. Increasing the overall molar mass of the copolymer for a given composition produced larger micelles with a lower association number. Both micelle size and association number decreased with the length of the hydrophobic block if the hydrophilic block length was fixed. Another key concept introduced by Armes and coworkers is that of so-called 'schizophrenic' self-assembly, whereby the core and corona blocks can be interchanged according to solution pH and electrolyte concentration. An example is the PMEMA-b-PDEA system, as illustrated schematically in Figure 4.6, although several other systems exhibit this behaviour, as described in a recent review.47 When the micellar core is charged, ionomer effects become important.48 This is because the concentration of solvent in the core is minimal so that counterions and polyelectrolyte chains remain bound, forming dipoles, as the interaction between charges is not reduced by the dielectric constant of the solvent.

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Figure 4.5 Repeat units in tertiary amine block copolymers studied by Armes and coworkers.183 Reproduced by permission of American Chemical Society.

Work by the Armes group on micellization in tertiary amine methacrylate block copolymers is summarized in Table 4.1. The list covers most aspects of their work, but is not exhaustive. A review from 2001 discusses the development of polymeric amphiphiles by Armes' and other groups up to that date.49

Figure 4.6 Formation of micelles and reverse micelles of a PDEA-b-PMEMA diblock according to solution conditions.59 Reproduced by permission of American Chemical Society.

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Table 4.1 Studies on micellization in tertiary amine methacrylate-based block copolymers by Armes and coworkers Copolymer type

Study

PMMA-b-PDMA

Dependence of cmc and association number on block composition and molar mass Micellization/micelle dimensions and structure pH-dependent micellization. Added salt favours micellization due to charge screening. Detailed SANS study of micelle structure Reversible micellization upon adjustment of pH, temperature or electrolyte concentration

PDMA-b-PDEA PDMA-b-PDEA

PDMA-b-PDEA PDMA-b-PDPA PDMA-b-PMEMA PMDPS-b-PMMA PMDPS-b-poly(alkyl methacrylates) qPDMA-b-PDEA PNaSS-fc-PNaSCOO

PDMA-b-PMAA PDMA-b-PEO PDEA-b-PEO PDMS-b-PDMA

PMEMA-b-PDMA PMEMA-b-PDEA PPO-b-PDEA

PVBA-ZP-PDEA

PVBA-b-PMEMA

Former block obtained by betainization of PDMA. Micellar characteristics obtained Reduced surface activity upon betaine formation. Polydisperse micelle formation, unless dialysed against nonselective solvent Quaternization of PDMA suppresses LCST behaviour and enhances pH range of micelle stability pH responsive micellization of strong/weak acid double hydrophilic diblocks. Polymerization using NaPSS as macro-initiator with other polymers also examinedunsuccessful Zwitterionic system. Thermoreversible micellization Micellization at high temperature Micellization at high pH Micellization in organic solvents as well as water. High surface activity, particularly in alkaline solution. Commercial relevance of silicone surfactants Schizophrenic micellization Schizophrenic micellization Schizophrenic micellization Schizophrenic micellization of a zwitterionic diblock Schizophrenic micellization of a zwitterionic diblock

Reference 46 44, 45 45

51

52 53

54 55

56 57 57 58

59 60 61 62 63

Micellization in related copolymers has been studied by Gohy et a/.50 who prepared P2VP-b-PDMA diblocks. At low pH polydisperse loose aggregates were formed, and micelles with a protonated PDMA corona were observed at intermediate pH. At higher pH, the PDMA corona becomes uncharged, leading to micellar aggregation. Armes and coworkers have also investigated micellization in vinyl ether-based block copolymers prepared by living cationic polymerization. Micellization in aqueous solutions of diblocks of PMTEGVE (hydrophilic) and PIBVE (hydrophobic) has been characterized using dynamic light scattering, aqueous GPC and

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dye solubilization.64 Dihydrophilic block copolymers of PMVE and PMTEGVE65 or PVA66 have been shown to form micelles at elevated temperatures, due to the hydrophobic nature of PVME above the cloud point. Proton NMR spectroscopy confirmed that the PVME block formed the micellar core, and that micellization was reversible. Reversible schizophrenic micellization in neutral-fr-anionic OEGMA-b-PMAA diblocks has also been studied.67

4.1.4

MICELLIZATION OF POLYAMPHOLYTE BLOCK COPOLYMERS

Polyampholytes contain monomers with opposite charges.48 Block copolyampholytes contain blocks with opposite charges. There have been few studies to date on this type of system. The association properties of PDMA-b-PNaMA polyampholyte diblock copolymers has been investigated as a function of pH and the copolymer composition.68 At the isoelectric point aggregation led to phase separation. Moving away from the isoelectric point (balanced charge), charged micelles formed. The size of the aggregates increased with concentration but was almost independent of pH. This has also been noted for nonblock polyampholytes. Addition of salt also did not change the dimensions significantly. Aggregates were also still observed for pH > 10 or pH < 4 where one block was neutral. Schizophrenic micellization has been observed for a PVBA-b-PDEA polyampholyte diblock.62 Gohy et al. investigated the association of PDMA-b-PMAA diblocks.69 Depending on pH, the DMA units can be positively charged and the MAA unit neutral, the MAA units can be negatively charged and the DMA units neutral or both blocks can be charged. At the isoelectric point, strong electrostatic interactions lead to the formation of insoluble complexes. The electrostatic interactions can be screened by the addition of salt. Conditions for the formation of spherical micelles were discussed.

4.1.5 MICELLIZATION OF POLYELECTROLYTE-CONTAINING ABC TRIBLOCKS The solution properties of ABC triblocks containing a hydrophobic midblock and oppositely charged end blocks have been investigated.70 The PAI-b-PS-b-PMAA copolymers behaved as polyampholytes, with two inflection points observed during potentiometric titration (PMAA being deprotonated prior to PAI). Large vesicular structures (Rh = 150-250 nm) were observed, the internal vesicular structure depending on pH. The association properties of an ABC triblock with a polyelectrolyte midblock and short hydrophobic end blocks has been investigated for PS-fr-PNaA-b-PBMA in water.71 The high viscosity in dilute solution was ascribed to the formation of a transient network structure, due to association between the end blocks.

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The pH-dependent changes in micellar structure and intermicellar interactions of P2VP-b-PMMA-b-PAA triblocks in aqueous solution have been investigated in bulk by static and dynamic light scattering and for adsorbed micelles by AFM.72 P2VP is protonated at low pH, and this leads to polyampholytic heteroarm micelles for pH < 1. At higher pH, close to the isoelectric point, electrostatic interactions increase to the extent that phase separation was observed. In alkaline solution, nonequilibrium aggregates of heteroarm star micelles were observed.

4.1.6 MICELLIZATION OF BLOCK COPOLYMERS CONTAINING GRAFTED POLYELECTROLYTES Micellization of Pluronic block copolymers grafted with PAA which confers polyelectrolyte properties has been studied by surface tensiometry,73 viscometry73 and probe solubilization,74 the latter as a function of pH. Gel formation by this type of copolymer is discussed in Section 3.3.5.

4.1.7 MICELLIZATION IN BLOCK COPOLYMERS CONTAINING SULFONATED POLYISOPRENE The micellization of a nonionic PS-b-PI diblock in a PS-selective solvent has been compared with that of a PS-b-PI diblock modified by the addition of a single sulfonate group at the end of the PI block.75 The effect of added salt was also examined. The dimensions of both the micellar core and corona decreased upon addition of the charged endgroup, although addition of salt led to screening and an increase in micellar radius. This was interpreted using a polymer brush model. The micellization of ionically end-capped diblocks prepared from the same parent PS-b-PI diblock was later investigated by SANS.76 The ionic groups were located either on the soluble PS end (quaternary ammonium group) or insoluble PI block (sulfonate group) or both (zwitterionic case). Figure 4.7 schematically presents the findings concerning chain dimensions. The coronal chains in sample Q where the soluble PS chain is end functionalized are extended. In sample S where the insoluble block is end functionalized, the end groups were found to lie on the surface of the micellar core, leading to folding of the chains. The same was found for the zwitterionic end-capped diblock (Z), although here the coronal chain is also folded due to attractive interactions between the ionic end groups. The micellization of block copolymers containing the strong polyelectrolye, sulfonated polyisoprene (sPI) have been reported. Micellization of both PS-6-sPI77 diblock and PS-&-sPI-b-PS78 triblock has been examined. The effect of ionic strength (added NaCl concentration) and polymer concentration on micelle dimensions was studied via light scattering. Fluorescence experiments using pyrene probes were used to locate cmc values.

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Figure 4.7 Schematic of chain configuration deduced from SANS studies on micelles formed by ionically end-capped PS-fe-PI diblocks in a PS-selective solvent.76 Reproduced by permission of American Chemical Society.

4.2

CHAIN CONFORMATION

The structure of polyelectrolyte block copolymer micelles has been examined via SANS, static and dynamic light scattering and cryo-TEM.4 It was reported that at low added salt concentration, the PSSA polyelectrolyte shell in the PEE-b-PSSA diblock examined has typical features of a polymer brush. However, if the added salt concentration exceeds the intrinsic ionic strength of the polyelectrolyte shell, the micellar aggregation number increases due to the screening of the interaction between chains (salted brush behaviour) for this particular copolymer. Guenoun and coworkers suggest that changes in aggregation number depend on copolymer asymmetry79-an increase in association number p has been observed for the symmetric diblock studied by Forster et al., whereas p decreases for a highly asymmetric diblock. In the case of an intermediate asymmetry, p was found to be independent of added salt concentration.79,80 The corona contracts when the added salt concentration exceeds a threshold equal to the inner salt concentration in the corona in the absence of salt.79,81,82 The scaling of corona chain dimensions has been compared with previous results and the predictions of scaling theories. Forster et al. reported L ~ c~°'13, where cs is salt concentration. The exponent reported by Guenoun et al. was -0.14 for ?BS26-£-NaSS404, -0.11 for rBS27-£-NaSS75781 and —0.18 for EP52-b-NaSS25179 (an exponent —0.17 was noted for dense adsorbed layers of this copolymer on polystyrene82). Scaling theory predicts L ~ cs ' in the salted brush regime where salt concentration exceeds the counterion concentra-

Polyelectrolyte Block Copolymers

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tion.83 A scaling L ~ c$ is predicted for polyelectrolyte star micelles with glassy cores, and also for equilibrium micelles in an appropriate regime of salt concentration.84 This scaling has been observed for polyelectrolyte brushes tethered to a flat PS interface in a PS-b-PAA diblock, in the salted brush regime.85 The transition from neutral to osmotic brush on increasing ionization was examined, and the increase in brush thickness probed. The same scaling has also been observed for a PEBS-b-PNaSS diblock adsorbed onto hydrophobized mica,86 as discussed in Section 5.2.2. The scaling behaviour of the association number of micelles ofn neutral-Z?polyelectrolyte diblocks as a function of core block length, p ~ ßB has been investigated by several groups. An exponent (3 = 1.62 or 1.89 was obtained for micelles of PS/PMAA diblock and triblock copolymers in a dioxane/water mixture containing 20% water.87 The dilute solutions were characterized using static and quasi-elastic light scattering. However, it was also found that the association number (and hydrodynamic radius) depended on corona block length NA with an exponent yu = —0.86 or —0.41 for di- and tri-blocks respectively. Since the core radius was not much smaller than the micellar radius, the micelles can be classified in regime III of Zhulina and Birshtein22 (Section 2.7), in which case a dependence of p and micellar radius on NA is expected. However, the exponents (3 and m were not in agreement with the scaling theory predictions (Table 2.3). Other work on PS-b-PAA diblocks in aqueous solution also provided scaling relationships for core radius RB not in agreement with theoretical predictions for nonionic block copolymer micelles.88 In addition to the ionic nature of the solutions studied, thermodynamic equilibrium may not have been reached in the solutions, as shown by the slow exchange kinetics of PS-&-PAA micelles in water such that they remained intact after elution from a GPC column, and as discussed further in Section 4.1.2. Micelles formed by PS-£-PCsA and PS-b-PCsMA in toluene, a selective solvent for the PS block, have been characterized using SAXS.16 Since the scattering was dominated by the cores, which were much smaller than the distance between them, the structure factor and form factor were well separated in the SAXS pattern, enabling detailed information to be extracted on the core dimensions. It was found that the core radius scales as N3/5 B, in agreement with the prediction of the ZhulinaBirshtein and Halperin models for type IV polymeric micelles. Also in agreement with these theories, the association number scaled as NJ and the surface area per 2/5 chain as NE' . Thus, these ionic block copolymer micelles obeyed the same scaling laws with core block length as micelles formed by neutral block copolymers. The conformation of the polyelectrolyte block in PtBS-b-PNaSS diblocks has been probed by SANS with contrast variation using H2O/D2O mixtures.79,89 The PNaSS block was found to adopt a rod-like conformation, as characterized by an intensity variation with wavenumber / ~ q~1 89 This behaviour was observed above a critical wavenumber which increased with salt concentration. The corresponding persistence length was surprisingly long, and proportional to the Debye screening length.79 A high persistence length of worm-like corona chains was observed even

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Block Copolymers in Solution: Fundamentals and Applications

Figure 4.8 SANS intensity profiles obtained for a 1 wt% solution in D2O of a PtBS-&PNaSS diblock for salinities 5= 8.5 x 10~4 M (•), 10~2 M (A), 0.16 M (x) and 1 M (•).89 The critical salt concentration is S — 10~2 M. Deviations from the q~l behaviour can be observed in a Kratky plot (see Guenoun et al.).89 Reproduced by permission of American Physical Society.

for high salt concentrations (up to 1 M NaCl), i.e. despite screening of the charge. This is in striking contrast to the compact coil conformation adopted by uncharged polymer brushes. The extended conformation was adopted, up to a threshold salt concentration corresponding to the free counterion concentration. The free counterions contribute to an osmotic pressure which is reduced by screening when salt is added. The concentration of free counterions was estimated from the Manning model for counterion condensation. Figure 4.8 shows SANS data with the intensity varying as I(q) ~q~l, as expected for rod-like objects. Deviations from this behaviour set in above a salt concentration S « 10~2 M. These can be seen more clearly in a Kratky plot of q2I(q) versus q (not shown). Dan and Tirrell predicted p to be independent of salt concentration,90 whereas the experiments by Guenoun et al. suggested that this was only the case at low ionic strengths, since p decreased with salt concentration for higher ionic strengths.81 Later, the same group showed that the hydrodynamic radius obtained from pulsed field gradient NMR and fluorescence recovery after fringe pattern photobleaching (FRAP) was consistent with that obtained from DLS.91 Cryo-TEM also provided images of the micelles, confirming the existence of both spherical and elongated objects. The distribution of counterions formed by a PrBS-&-PNaSS diblock (with a lengthy polyelectrolyte block and short hydrophobic block) was probed by SAXS, using dialysis to change the counterion and hence the contrast.92 The counterions were found not to be homogeneously distributed in the extended rod-like brush corona. Instead, the

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radial distribution function extracted from the partial structure factor suggested a Poisson-Boltzmann distribution of counterions around a coronal chain. The conformation of the coronal chains in spherical micelles formed by a PS-b-PCsA diblock in toluene (selective for PS) has been analysed by SANS using contrast variation.93 The conformation of PS chains as a function of distance from the ionic core was probed by selective deuteration of segments of the PS block, varying the position of the labelled block. The chains next to the core were rod-like as revealed by the / ~ q~1 variation of small-angle scattering intensity. The power law exponent decreased with distance of dPS blocks from the core. Semidilute behaviour of swollen coils, close to the / ~ g~ 5 / 3 scaling anticipated by the Daoud-Cotton model94 in the intermediate q range, was observed for segments well separated from the core. The contribution from inter-chain scattering also decreased with distance from the core. This scaling behaviour should not be influenced too much by the presence of a pronounced structure factor peak, since this occurred at significantly lower q. The presence of such a feature indicates interactions among the micelles. The chain conformation and distribution of counterions in the corona of a PS-b-PAA diblock have been studied by detailed SANS experiments.95 The polymer contained 50% ionized PAA units. Under these conditions the corona chains were found to be almost fully stretched. The counterions were found to be sequestered within the corona. There was no evidence of charge annealing (recombination and dissociation of the weak polyacid units) and/ or migration of counterions towards the outer coronal layer. The change in PAA coronal layer thickness as a function of degree of ionization was also studied by SANS.96 The core radius and aggregation number were found not to change significantly. In these studies, partial structure factors (PS-PS, PAA-PAA and those for the counterion) were obtained via contrast matching experiments, enabling detailed information about the location of particular species to be obtained. The behaviour of neutral-b-ionic block copolymers has been investigated in semidilute conditions (up to 20 wt% polymer).97 SANS, SAXS and light scattering were used to characterize PEP-b-PNaSS diblocks in aqueous solution. Liquid-like ordering of micelles was observed above a critical concentration, as confirmed by the scaling of SANS peak position with concentration, q* ~ c1/3. The structure of PS-b-PAA diblocks in water has also been investigated via SAXS and SANS up to concentrations where coronal chain overlap occurs.98 The same scaling behaviour of SAXS peak position was noted. The micelle dimensions decrease with increased packing fraction, irrespective of ionic strength and micellar charge. This is due to increased counterion adsorption and/or Donnan salt partitioning between the coronal layer and surrounding medium. At high salt concentration, where charge interactions are screened, the density profile decreases as r~ 4 / 3 , in agreement with scaling theory for star polymers and uncharged block copolymer micelles [Equation (2.23)]. At high charge and in the absence of salt, the polyelectrolyte chains remain almost fully stretched and they interdigitate once the volume fraction of micelles exceeds that for hard sphere crystallization. The interpenetration of the chains leads to the formation of a physical gel, as characterized by measurements of the dynamic

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Block Copolymers in Solution: Fundamentals and Applications

shear moduli. The countenon distribution was determined from SAXS and found to follow closely the radial density profile of the corona segments.98 The distribution of counterions in the corona of PS-b-PAA micelles has been probed by anomalous SAXS." The technique relies on contrast created at the absorption edge of metal atoms/ions-in this case rubidium ions. The ions were found to be closely correlated to the corona chains, much more so than in linear polyelectrolytes due to interactions among the polyelectrolyte brushes 'grafted' to spherical surfaces. The results were compared with recent models for interacting polyelectrolyte brushes and star polyelectrolytes100,101 (this theory is discussed in the following section). The conformation of corona chains in PS-b-PAA micelles has been studied by contrast variation SANS.102 The interaction between the micelles was described using the hard sphere structure factor, for salt-free solutions. In the presence of excess salt, intermicellar interactions were suppressed. The PAA chains were found to contract with increasing polymer concentration, independent of ionic strength. Interpenetration of coronal chains was observed when the packing fraction exceeded a critical value

4.3

THEORY

We focus here on theory developed specifically for block copolymers containing a polyelectrolyte block. When considering adsorption for example, models are often based on polyelectrolyte brushes. The large literature on this subject is not covered here, although suitable reviews can be found elsewhere.103'104 Dan and Tirrell introduced a polymer brush scaling model for diblocks comprising a strongly charged block and a hydrophobic block in aqueous salt solution.90 The system was studied in the regime of high salt concentrations where the electrostatic persistence length is smaller than the range of excluded volume interactions. The formation of micelles in bulk and adsorption on a planar substrate were both considered. The aggregation number of micelles and surface density of the adsorbed layer was predicted to increase with salt concentration, whilst the charged block layer thickness decreased. Micellar properties were predicted to be similar to those of neutral copolymers in nonpolar solvents. Micellization in neutral-b-polyelectrolyte diblocks in a solvent selective for the polyelectrolyte block has been analysed using brush scaling theory for both weakly and strongly charged diblocks.105 Analytical expressions for the cmc and micelle dimensions at the cmc were obtained. For strongly charged diblocks, micellization was suppressed unless the charged block was very short compared with the neutral block. Strong condensation of counterions onto the charged block occurs when the chain is long. The stretching penalty associated with this is high and micelle formation is prevented. In the weakly charged limit, micellization is not hindered in this way. Addition of salt was found not to significantly affect the micelles unless the

Polyelectrolyte Block Copolymers

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screening length was smaller than the micelle size. Wittmer and Joanny used the scaling approach to investigate conditions under which micellization is possible. This occurs provided the charged monomer content is not too high. The model was mainly used to examine adsorption on a solid substrate or at the oil-water interface, as discussed in Section 5.1.2. The scaling approach leads to the following results. The micellar core radius is predicted to scale as given by Equations (2.21) and (2.22):106

The corresponding free energy scales as [in the following, prefactors O(l) are omitted, and expressions are written as equalities]:

where rB is the core-corona interfacial tension. For the polyelectrolyte corona, the free energy comprises a Gaussian elastic energy and an electrostatic energy:43

where Rm is the micellar radius, a is a monomer size, T is the fraction of charged monomers and lB is the Bjerrum length. The thermodynamic potential that governs micellization is the grand canonical free energy and is given by:105

where u is the chemical potential of the solution. By minimizing n, the equilibrium structure of the micelle can be determined. The cmc occurs at a chemical potential:43

The association number at the cmc is:

The size of the micelle is approximately equal to the size of the corona. Micelles only form if the association number is greater than unity, which imposes a condition on the charge fraction43

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If the charge fraction is smaller than Tm, the cmc is roughly given by:43

The foregoing neglects the condensation of counterions within the polyelectrolyte brush (osmotic brush). Allowance for this in the so-called strong charge limit is discussed by Marko and Rabin.105 More general expressions allowing for the density of coronal chains as well as copolymer composition were obtained by Shusharina et al. as summarized in Table 4.2. Table 4.2 Scaling relationships for association number p, corona thickness RA and core radius RB for micelles formed by neutral-b-polyelectrolyte diblocks5 Regime

Labela

p

RA/a

RB/a

z

0mic > e~

Individual quasineutral chains Planar quasineutral brush (1) Planar quasineutral brush (2) Spherical quasineutral brush Individual Pincus chains Planar Pincus brush (1) Planar osmotic brush (1) Planar osmotic brush (2) Spherical osmotic brush 0mic < e~z

Planar Pincus brush (2) Spherical Pincus brush

I(i)

NB

NA'

NB

I(pl)

NB

NA/NB

NB

I(p2)

NB

NB4/5

I(s) II(i) II(pl) III(pl) III(p2) III(s)

2/NA18/11

NA9/11

NB/Na6/11

NA3/5 /NB4//25

NB3/5

NAT4/7 NA7/3T4/3/NB2/9 NAT2/5 NB2/NA3T3 NAr2/5 AB2/NA3T3 N AT 2 / 5

NB NB NB

NB NB2/3 NB2/3 NB/NAr N B /N A T

II(p2) NB2/NA39/8 T15/4 NA5/4T1/2 7 /11 21/22T1511 8/11 2 II(s) N B /N NA N B'11T2/11

NB/NA13/8T5/4 NB8/33/NA7/22T5/11

aI, II and III denote, respectively, regimes with insignificant electrostatic interactions, Pincus regimes and osmotic regimes; i, p and s denote individually grafted polyions, planar brush and spherical brush, respectively (some of which are subdivided into regimes with different scaling properties).

Huang and coworkers have developed the model of Marko and Rabin to consider constraints on counterion condensation in the corona of micelles formed by diblocks with a long charged block and a short hydrophobic chain.107 Huang et al. argue that corona chains will not be fully stretched due to counterion pressure. The association number and the number of condensed counterions per micelle were computed, considering the chemical potentials of copolymer chains and of counterions. The cmc and polydispersity were found to be large in neutralb-polyelectrolyte micelles compared with the analogous uncharged diblock micelles. The number of free chains in the charged diblock decreases above the cmc.

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Figure 4.9 Spherical lattice model used in lattice mean-field theory by Shusharina and coworkers.108 The micelle contains six copolymer chains with solvophobic cores and charged coronas. Counterions are also shown. Solvent is indicated by unfilled cells. Reproduced by permission of American Chemical Society.

Shusharina et al. have performed lattice mean field simulations of micellization in neutral-b-polyelectrolyte diblocks containing a short solvophobic block and a weakly charged poly electrolyte.108 Figure 4.9 illustrates a micelle formed by six chains on the spherical lattice used. The cmc was investigated as a function of charge and length of the hydrophilic block and also as a function of solvent quality and salt concentration. Volume fraction profiles reveal a sharp interface between micellar core and corona. The corona contains very dilute hydrophilic segments. The scaling of micelle aggregation number, core radius and corona thicknesss are in qualitative agreement with scaling predictions. In a subsequent paper, a more detailed comparison with scaling theory was made and a very comprehensive summary of scaling behaviour was provided.5 Three scaling regimes were identified: a quasi-neutral regime at low fractional charge; a Tincus regime'I09 where the Coulomb interaction in the corona is unscreened since the counterions are predominantly outside the charged corona; and an 'osmotic regime' where the Coulomb interactions are screened by counterions which are located within the charged corona. Analytical scaling relations for the micellar aggregation number, the radius of the core, and the thickness of the corona were presented as a function of the length of both blocks, and the fractional charge of the hydrophilic block. These are summarized in Table 4.2. Figure 4.10 summarizes 'phase diagrams' illustrating conditions under which various micellar structures are observed. Diagrams are parameterized in terms of the chain length of the polyelectrolyte block, NA and the fractional charge on each monomer, T. Two limiting cases were considered, depending on the parameter z, the electrostatic

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Polyelectrolyte Block Copolymers

193

interaction energy between the charged micelle and a counterion located on the periphery of the corona. For 0mic > e- z , most counterions are within the spherical corona (osmotic brush), whereas for 0mic < e-z most of the counterions are outside the corona. The composition and grafting density (i.e. interfacial area per block in the case of micelles) leads to a further subdivision of scaling regimes. For very short charged blocks and for low grafting densities, the chains are isolated, and termed 'individual grafted polyions'. If the charged blocks are still short but the grafting density is higher, planar brushes are formed. When the charged block is of significant length compared with the neutral block it forms the corona of micelles, i.e. a spherical brush. The mean-field lattice model provided volume fraction profiles of counterions, as well as coronal layer thickness. Changes in aggregate morphology in neutral-b-polyelectrolyte diblocks as a function of salt concentration have been analysed using a scaling model by Netz.110 The neutral block was hydrophobic. For low salt concentrations, electrostatic interactions are dominant, and a transition from spherical to cylindrical micelles occurs as salt concentration is increased. At high salt concentration, the elastic energy of the hydrophobic block dominates and bilayers are predicted. It was suggested that the presence of coexisting structures at intermediate salt concentrations could indicate the formation of complex interconnected structures such as those observed by Eisenberg and coworkers as discussed in Section 2.16. The endcap energy of cylinders was found to be high, pointing towards the possibility of the formation of closed rings (toroids), as observed experimentally.111 Scaling theory has also been developed by Borisov and Zhulina to describe micellization in diblocks containing a weak polyelectrolyte block and a hydrophobic block.6,84At low pH and/or salt concentration, quasi-neutral micelles in which the corona chains were undissociated were predicted.6 An increase in salt concentration leads to the ionization of the corona chains and hence a decrease in association number. This of course is in contrast to the behaviour of strong or 'quenched' polyelectrolytes. For crew-cut micelles, the corresponding transition occurs continuously, whereas for star-like micelles it occurs discontinuously at a critical salt concentration. The decrease in association number leads to an increase in osmotic repulsion in the corona that cannot be balanced by an increase in free energy of the core interface. The starlike micelles then become unstable and dissociate into smaller ones. This can also occur for crew-cut micelles with short insoluble blocks. Similar jump-like transitions were predicted on changing pH. Phase diagrams were presented in terms of salt concentration and the bulk degree of dissociation, and scaling laws in the various regimes were derived.6 This model was

Figure 4.10 Diagrams as a function of charged block length NA and fraction of singly charged monomers, T, illustrating different scaling regimes for neutral-b-polyelectrolyte diblocks and the location of counterions (dots).5 (a) 0mic > e- z , (b) 0mic < e-z The key to the labels is provided in Table 4.2. Reproduced by permission of American Chemical Society.

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later developed to consider changes in morphology for crew-cut micelles, driven by changes in ionic strength.7 Increasing salt concentration (or decreasing degree of ionization of corona blocks) was predicted to lead to transitions from spherical micelles to cylindrical micelles to lamellar aggregates. Morphology diagrams were presented in terms of block length (for either block) and the second virial coefficient which describes short-range interactions between charged monomers (which depends quadratically on the degree of ionization). The influence of salt on the association number was also investigated for diblocks containing strong polyelectrolyte blocks.84 An increase in p with salt concentration was observed, together with a small decrease in micelle radius due to screening of charges on coronal chains. Scaling laws for micelle dimensions and association numbers for different regimes of salt concentration were presented. The association properties of a diblock polyampholyte have been analysed using random phase approximation theory.112 When the charges on the polycationic block and polyanionic block are balanced, the solution phase separates into a polyelectrolyte network and almost pure solvent. However, above a certain charge asymmetry ratio, spherical micelles are formed. For weakly charged diblocks, the excess charge varies with pH. Changes in the dimensions of the micelles were found to be in qualitative agreement with experiments on adsorbed weakly charged diblocks.113 The association behaviour of telechelic polyelectrolytes has been examined using an analytical model based on an extended Flory network model. Telechelic polyelectrolytes are ABA triblocks with a lengthy charged solvophilic midblock and short hydrophobic endblock 'stickers'. The swelling and collapse of gels formed by telechelic polyelectrolytes was investigated, and phase diagrams constructed.114 The formation of a gel leads to phase separation since concentrated gel phase coexists with a dilute supernatant phase. Increasing the degree of ionization leads to destabilization of gels. Added salt screens the interactions between the charged end groups and facilitates the association of telechelic molecules. The formation of physical clusters instead of a macroscopic physical gel was also considered.115 Depending on the attraction energy between stickers, clusters are found to be stabilized if the Coulomb interaction and translational entropy of counterions are sufficiently large. The association of multiblock ionomers, i.e. chains comprising a small fraction of charged units inserted into neutral chains led to the concept of superstrong segregation.116 In this regime the ionic units and counterions form an ion pair with a dipole moment. Interaction between these dipoles causes attraction between them to form 'multiplets'. The limiting size and spacing of of multiplets was analysed in the melt limit. The analysis will also apply to solutions of ionomers, and other systems of copolymers with strongly interacting groups.117 This work predicted the formation of disk-like and ultimately lamellar structures as the multiplet interaction parameter increases. Such structures were considered in the analysis of superstrong segregation in ABC triblocks (Section 2.7.6) and have been observed by Lodge et al. in micelles formed by ABC block copolymers.118,119

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195

Little theoretical or simulation effort has been devoted to the behaviour of concentrated solutions of polyelectrolyte block copolymers. Microphase separation of concentrated solutions of associating polyelectrolytes has been investigated using strong segregation limit theory.120 Spherical, cylindrical and lamellar structures were all predicted for a concentration range lower than that at which physical gelation occurred. Dynamic mean field density functional theory has been used to compute the phase behaviour of concentrated solutions of a weakly charged triblock polyelectrolyte in the case that a Donnan equilibrium is established, i.e. long-range electrostatic interactions are screened.121 The lyotropic phase diagram was found to be modified depending on the charge on the solvophilic end-blocks. Likos and coworkers have recently used the interaction potential they derived for polyelectrolyte solutions to investigate the structure and phase behaviour of polyelectrolyte star solutions.100'101 As for the comparison between neutral star polymers and block copolymer micelles,122 analogies may be expected with the structure of concentrated solutions of polyelectrolyte stars and micelles. The theory led to phase diagrams containing multiple ordered phases, including simple cubic, fcc and bcc phases as well as interesting body-centred orthogonal and diamond packings of stars.101 Micellization in dilute solutions of a neutral-b-polyelectrolyte diblock with oppositely charged linear homopolymers was examined using a brush model to calculate contributions to the free energy of micelles.123 The system was studied in the limit that the polyelectrolyte block was large relative to the neutral block, whilst the homopolymer chains were shorter than the charged block in the copolymer. Polyelectrolyte complexes with different compositions were found to coexist with well-defined micelles. The micelles comprise the polyelectrolyte block and the oppositely charged homopolymer polyelectrolyte surrounded by a corona of the hydrophilic block.

4.4

POLYION COMPLEXES

Electrostatic interactions between a pair of neutral-b-polyelectrolyte block copolymers containing blocks with equal but opposite charges can lead to the formation of a polyion complex (PIC). When the charge is not balanced, overcharging and charge reversal of micellar aggregates are possible. To form PIC micelles, it was shown that the charge on oppositely charged segments has to be matched.124,125 This is illustrated in Figure 4.11 which shows complex formation by PEG-b-PAsp and PEG-b-PLys diblocks, with oppositely charged polyelectrolyte blocks.125 Chains with matched polyelectrolyte block length can form micelles, whereas unmatched chains form charge neutralized bimolecular complexes. Kataoka and coworkers have investigated PIC micellization in this system in a series of papers.124-126 The core radius and volume fraction of PEG at the core/corona interface were obtained from light scattering experiments, and the importance of these two parameters in determining micellar size was emphasized.126 The volume

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Block Copolymers in Solution: Fundamentals and Applications

Figure 4.11 Polyion complex formation by pairs of block copolymers with oppositely charged polyelectrolyte blocks.125 When the polyelectrolyte chain length is matched, micelles can self-assemble, whereas for unmatched chains, bimolecular complexation is observed. Reproduced by permission of Science.

fraction of PEG at the interface was shown to be proportional to the length of the PAsp block. Polyion complexes have also been prepared by the Kataoka group in which the micelles have been functionalized by the incorporation of aldehyde groups at the end of the PEG corona block.127 These ligands could assist in targeted delivery. The core-forming block was PDMA, to which plasmid DNA is complexed thus entrapping the DNA for use in gene delivery. It is established that the resistance of plasmid DNA against nuclease digestion is increased remarkably when it was incorporated into the core of PIC micelles.128 The incorporation of the model protein, chicken egg white lysozyme (positively charged over a wide pH range) into PIC micelles formed with PEG-b-PAsp diblocks was also studied via light scattering.129 The stoichiometry between aspartic acid residues and the total number of lysine and arginine residues in lysozyme in the micelle core was quantified. Further details on drug delivery applications of PIC micelles can be found in Section 6.3. The co-preciptation of P2VP blocks in PS-b-P2VP and P2VP-b-PEO blocks leads to the formation of onion-type micelles with a PS core, a P2VP inner shell and a PEO outer shell (see Figure 2.27). 13° The PS-b-P2VP polymer was dissolved in a methanol/dioxane/water mixture and then dialysed against 0.1 M HC1, leading to micelles with a protonated P2VP corona. Addition of P2VP-b-PEO at pH > 10 leads to the formation of onion micelles. These were investigated later by SANS 131 (see Section 2.12.2). Kabanov and coworkers have investigated micelles formed in several types of block ionomer complex. For example, they have investigated micellization in mixtures of diblock cations with anionic surfactant. The diblocks contained a

Polyelectrolyte Block Copolymers

197

cationic block such as PE4VP) and a PS132 or PAMS133 block. The anionic surfactant was bis(2-ethylhexyl)sulfosuccinate (AOT). The micelle characteristics (dimensions and aggregation numbers) were found to be similar to those of neutral block copolymers in a selective solvent. They also observed polyion complexes in mixtures of a diblock containing an anionic block, PEO-b-PNaMA, and the cationic homopolymer PE4VP.134 They showed that micelles containing a core consisting of stoichiometric neutralized polyion complex and a PEO corona form in water, in contrast to the interpolyelectrolyte complexes formed by the homopolymers which lose solubility when the charge is neutralized. This points to the important role of the PEO corona in enhancing solubility. It was also shown that the PIC micelles are highly salt sensitive, since dissociation was observed at high salt concentration. Similar conclusions were reached from a study on complexes of the same diblock system (although a different composition) but with cationic ammonium and pyridinium bromide salts.135-137 The influence of temperature on the dehydration of the PEO chain was also examined.137 At room temperature, dispersions were stable, but on increasing temperature aggregation occurred due to the dehydration of the PEO 'steric stabilization' layers. The onset temperature for aggregation decreased with increasing salt concentration, depending also on the nature of the salt anion, following the Hofmeister series (cf. Section 2.6.3). Diblocks containing an insoluble block such as PS-b-PNaA formed complexes with N-cetylpyridinium cations-the nonstoichiometric complexes being swollen with ionized PAA chains.138 Complexes between PEO-b-PNaMA diblock copolymers and single, double or triple cationic surfactants have been found to lead to stable dispersions with particle size in the range 100-200 nm, the stability depending on the length of the blocks.139 Complexation between block copolymers containing a cationic block and DNA, which is anionic, to yield so-called polyplexes is relevant to drug delivery applications.140,141 The cationic block copolymer should charge compensate the DNA, inducing a coil-globule transition so that the DNA condenses and has enhanced stability under physiological conditions. It is also necessary that the polymer has sufficiently low molar mass (<30 000 g mol"1)141 so that it can be eliminated from the body. Addition of a hydrophobic block is believed to enhance cell interactions and tissue permeability. Hydrophilic polyethylene glycol on the other hand enhances solubility of the polyplex. Further details are provided in Section 6.3. Polyelectrolyte complexation between a neutral-b-cationic PEO-b-PDEA diblock and an anionic PMAA homopolymer leads to the formation of three types of aggregate structure, depending only on solution pH.142 Above pH 8.5, simple micelles are formed with hydrophobic PDEA cores and PEO corona chains, the PMAA not participating in micelle formation. However, at pH 6-8.5, polyion complex micelles with charge-compensated PDEA/PMAA cores and PEO coronas are observed. Below pH 3, a third micelle structure is formed with a core comprising hydrogen bonded PEO and PMAA with a PDEA corona. Complexation between an ABC triblock with a cationic inner shell B block and a neutral-anionic

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Block Copolymers in Solution: Fundamentals and Applications

diblock (or an anionic homopolymer) has been used to prepare shell cross-linked micelles.143 Onion-type micelles were prepared from PEO-b-qPDMA-b-DEA triblocks in alkaline solution. Sodium polystyrene sulfonate homopolymer or PEO-b-PNaSS diblock were added to effect ionic cross-linking. The diblock copolymer cross-linker proved to be much more effective than the homopolymer.

4.5

COPOLYMER-SURFACTANT COMPLEXES

The interaction between polymers and surfactants is described by two critical concentrations. The first is the critical aggregation concentration (cac, sometimes denoted C1) at which point the binding of surfactant and polymer first occurs. The cac is generally lower than the cmc of the surfactant alone. The second critical concentration (often denoted C2) is associated with the saturation of polymer with surfactant aggregates (Figure 2.34). The cmc of the surfactant (Cm) may also be observed. For some polymer/surfactant systems, Cm and C2 are coincident.144,145 However, in other cases, Cm is less than C2.144'145 Complex formation between P2VP-b-PEO diblocks and fluorinated anionic surfactants has been investigated in aqueous solution.146 The two types of fluorinated surfactant and P2VP have opposite charges at pH 3, leading to strong electrostatic interactions. TEM revealed the presence of vesicles as well as other complex polymicellar aggregates. Berret and coworkers have performed small-angle scattering (SANS and SAXS) and DLS studies of colloidal complexes resulting from the self-assembly of neutralb-polyelectrolyte diblocks and oppositely charged surfactants.147-150 An aggregate with a core-shell structure forms, as sketched in Figure 4.12. The core is described as a coacervated microphase comprising surfactant micelles linked by the polyelectrolyte blocks. The corona formed by the lengthy neutral chains forms a stabilizing coating. The complexes form when the stoichiometric charge ratio Z (equal to the ratio of surfactant and polyelectrolyte repeat unit concentrations) is in the range Z = O.l-l.150 Copolymers with both type of charged block were studied. Cationic polyelectrolyte blocks of PTMEMS formed complexes with the surfactant SDS, and anionic PNaA or PSS blocks formed complexes with DTAB.150 The neutral block was polyaerylamide. The complexes have hydrodynamic radii in the range 13-58 nm. The cores contain typically a few hundred micelles.148 There is no evidence of crystalline order in the core, in contrast to very well ordered cubic or hexagonal lattices observed for the precipitate formed from the phase-separated polyelectrolyte homopolymer/surfactant mixtures when Z = 1.150 Indeed, Monte Carlo simulations of aggregation within the core indicate hard sphere interactions among the micelles in the core,149 which lead to the observed structure factor peak at large q. The phase separation observed for the homopolymer/surfactant complex is prevented in the block copolymer/surfactant complex by the neutral micellar corona.148 The scaling properties of the colloidal complexes differ from those of conventional block copolymer micelles.150 The core radius decreases more slowly

Polyelectrolyte Block Copolymers

199

Figure 4.12 Schematic of core-shell structure formed by complexation between a diblock comprising an anionic poly(sodium acrylate) block and neutral poly(acrylamide) and the cationic surfactant DTAB.147 Reproduced by permission of EDP.

with core block length than predicted and the neutral block does not significantly influence the core radius. The nonequilibrium nature of the self-assembly process was emphasized by the observed dependence of the size of complexes on the initial mixing conditions.148 Cryo-TEM on the complexes provided direct evidence for internal structure within the micelles, as well as providing dimensions for comparison with the indirect scattering techniques.149 It is possible that the systems studied by Kabanov and coworkers discussed above also form structures with microphaseseparated core structures. Examination of this requires the use of a probe sensitive to internal micellar structure, such as SANS.

4.6 COMPLEXATION WITH OTHER MOLECULES The complexation of PEl-b-PPG-b-PEl and PEl-b-PEG-b-PEl triblock copolymers with cyclodextrins leads to fascinating pseudo-polyrotaxanes, in which the cyclodextrins thread over the hydrophobic block domains, since the cavity in the cyclodextrin molecules is itself hydrophobic. In the PEI-b-PPG-b-PEI system, B-cyclodextrins moved away from fluorescein-4-isothiocyanate end caps towards the PPG block as temperature increased, due to increased hydrophobicity of the midblock.151,152 In the PEl-b-PEG-b-PEl system, pH responsiveness was observed.153 At pH < 8, a-cyclodextrin (a-CD) molecules selectively thread over

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Block Copolymers in Solution: Fundamentals and Applications

Figure 4.13 Formation of pseudo-polyrotaxanes by threading of a-cyclodextrin molecules around a PEl-b-PEG-b-PEl triblock.153 The self-assembly is pH responsive due to protonation of PEI below pKa = 8.9. Reproduced by permission of American Chemical Society.

the PEG midblock due to repulsive electrostatic interactions (Figure 4.13), since PEI is protonated under these conditions. At pH 11, all blocks threaded a-CD molecules (Figure 4.13). Using these two systems, thermoresponsive and pH-responsive formation of pseudo-polyrotaxanes is possible via a self-assembly process.

4.7

GELATION

As in neutral block copolymers (Section 3.3), block copolymers containing polyelectrolyte chains can undergo gelation at sufficiently high concentration. At low pH, electrostatic interactions dominate the self-assembly of PAA-b-P2VP-b-PAA triblocks in aqueous solution.154 The P2VP units are protonated, and the PAA units are negatively charged. As sketched in Figure 4.14, an increase in concentration leads to interactions between the oppositely charged units and hence gelation. The resulting gel exhibits interesting rheological behaviour, including strain hardening and shear thickening. These shear-induced changes in network structure were ascribed to an increase in the number of elastically active chains due to an increase in the extent of intermolecular bridging.

4.8 HIERARCHICAL ORDER IN PEPTIDE BLOCK COPOLYELECTROLYTE SOLUTIONS Block copolymers composed of a synthetic block and a charged polypeptide block are a particularly interesting class of polyelectrolyte block copolymer. Hierarchical order and additional functionality can be programmed into the self-assembly of

Polyelectrolyte Block Copolymers

201

Figure 4.14 Schematic of self-assembly in a PAA-b-P2VP-b-PAA triblock polyelectrolyte as a function of concentration.154 Here cg denotes the critical concentration for gelation and c' is a concentration at which percolation is observed. Reproduced by permission of American Chemical Society.

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Block Copolymers in Solution: Fundamentals and Applications

Figure 4.15 Peptide sequence of samples of PEG-peptide block copolymers containing switch peptide sequences shown in B-strand conformation (a) and as a-helical wheel representation (b).160 Rectangles and ovals mark hydrophobic and hydrophilic amino acids, respectively. Reproduced by permission of Royal Society of Chemistry.

block copolymers by incorporating one or more polypeptide chains. These can form secondary structures-a helices due to intramolecular hydrogen bonding or (3 sheets due to intermolecular hydrogen bonding. Furthermore, by appropriate positioning of amino acid residues it is possible to design structures with localized hydrophobicity or hydrophilicity, for example a helices with hydrophobic and hydrophilic faces (see Figure 4.15). The solution self-assembly of block copolymers containing peptide units has been reviewed.155,156 4.8.1

a HELIX STRUCTURES

A range of aggregate structures of PS-b-polypeptide diblocks in aqueous solution have been revealed by TEM and AFM on dried films.157 The synthetic poly (isocyanide) peptides studied form a-helices. Poly(isocyano-L-alanine-L-alanine)

Polyelectrolyte Block Copolymers

203

forms a right-handed helix, whereas poly(isocyano-L-alanine-L-histidine) forms a left-handed helix. The aggregate structure was found to depend on the length of the poly(isocyanide) block, the pH and the anion-headgroup interactions. Micelles, vesicles and bilayer aggregates were all observed. In addition, superhelices were imaged, and ascribed to coiled rods. The superhelices had an opposite twist to that of the constituent blocks, a puzzling observation that was not explained. The influence of PEG chains on the aggregation of peptides containing heptad sequences designed to form coiled coil superstructures has been investigated by two groups.158-160 Klok and coworkers employed the coiled coil sequence LAEIEAK designed de novo by Hodges and coworkers.161 Incorporation of PEG chains in hybrid diblocks significantly enhanced the stability of coiled coil superstructures towards denaturing, an effect ascribed to the formation of a hydrophilic, protective shell of PEG around the hydrophobic interior. The ability of the peptide to form an a helix was not disturbed. Pechar et al. reached a similar conclusion for their diblocks comprising PEG(2000) and (VSSLESK)n, n = 3-6.158 Based on evidence from CD and analytical ultracentrifugation, the self-organization in the PEGpeptides containing the LAEIEAK sequence was described as an equilibrium between copolymer unimers and dimeric and tetrameric coiled coil aggregates, as illustrated in Figure 4.16. The relative amounts of these species are temperature and concentration dependent. The helix content decreases with temperature, suggesting cooperative unfolding. The process is reversible. Increasing concentration favours the formation of dimeric and tetrameric aggregates. In the peptides containing the (VSSLESK)n sequence with n = 5 or 6, dimers were observed. The helix content increased with n. Electron paramagnetic resonance on spin-labelled samples of the LAEIEAK-containing polymers confirmed that the PEG chains are folded closely around the peptide core, as sketched in Figure 4.16.162 The self-assembly of

Figure 4.16 Model for the self-assembly of PEG-b-peptide diblocks containing the heptad sequence LAEIEAK.160-162 Reproduced by permission of American Chemical Society.

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Block Copolymers in Solution: Fundamentals and Applications

homopolypeptides and PEG-peptide diblocks containing one or two heptad repeat sequences was later compared.160 The helix content was similar whether the peptide contained one or two heptad repeats. On the other hand, for the peptides containing the (VSSLESK)n sequence, the helix content increased with n. For the LAEIEAKcontaining polymers, the helix content was enhanced in the polypeptide compared with the diblocks (and decreased with PEG content) due to steric hindrance caused by the conjugated PEG which probably hampers association and folding of the peptide.160,163 The helix content increased with concentration, and decreased with temperature. Nanostructure formation in aqueous solutions of PEG-peptide diblocks and PEG-b-peptide-£-PEG triblocks containing 'switch' peptide sequences has also been explored.160 Switch peptides are patterned with hydrophobic and hydrophilic substituents in such a way that they can form either amphiphilic a-helices or amphiphilic B-strands, depending on pH,164 as illustrated in Figure 4.15. TEM and AFM suggested the formation of fibrillar structures, which is particularly interesting since circular dichroism (CD) indicated that in the low pH conditions, the a-helical structure of the peptide was retained upon conjugation to PEG. A model for the formation of fibrils based on side-to-side stacking of the 'Janus' helices [Figure 4.15(b)] was presented. The solution self-assembly of PS-b-PLys diblocks was investigated by SANS and light scattering.165 Extended micellar structures were observed, whilst the a helix conformation of the PLys was retained. Changing solvent conditions can induce a transition in the conformation of PBLG from a random coil to a rod-like helical conformation. This has been studied via SANS on PBLG-b-PS diblocks for which a transition from a coil-coil to a rod-coil conformation has been detected.166 4.8.2

(3 SHEET STRUCTURES

It has been shown that conjugation to PEG can be used to control the lateral aggregation of B-sheet forming peptides into fibrils. This is relevant to fibril formation in amyloidosis, which is responsible for diseases such as BSE and Alzheimer's. Lynn and coworkers observed fibril formation in aqueous solutions of PEG-peptide diblocks where the peptide block was based on the central domain of the B-amyloid peptide. 167-169 They found from SANS and TEM that the PEG forms a coating around the fibril-thus acting as a 'steric stabilization' layer. Stupp and coworkers have studied fibril formation in diblocks with a peptide block linked to fatty acid 'tail groups'.170 The peptides were designed to contain terminal cysteine residues to facilitate intramolecular cross-linking via disulfide bonds. This enabled the reversible polymerization of nanofibres. By controlling the pH, gelation was also observed due to intermolecular cross-linking. In a subsequent paper,171 it was shown that it was possible to mineralize a nanostructured fibrous scaffold prepared by the self-assembly of a fatty acid-b-peptide diblock, to produce artificial bone.

Polyelectrolyte Block Copolymers

205

Collier and Messersmith have investigated the effect of conjugation to PEG on peptide fibril width for PEG-b-peptide and peptide-b-PEG-b-peptide Copolymers containing ß-sheet forming sequences.172 The self-assembly in aqueous solution of a number of hybrid block Copolymers containing amphiphilic ß strand sequences flanked by one or two PEG terminal chains was investigated via CD spectroscopy, SAXS and TEM.173 CD revealed primarily ß-strand secondary structures. In comparison with the native peptide sequence, it was found that the secondary structure was stabilized against pH and temperature variation in the di- and triblock Copolymers with PEG. SAXS indicated the presence of fibrillar structures, and the dimensions of these are comparable with the estimated width of a (3 strand (with terminal PEG chains in the case of the Copolymers). Transmission electron microscopy on selectively stained and dried specimens shows directly the presence of fibrils (Figure 4.17). It was proposed that

Figure 4.17 TEM image of dried films of a PEG/peptide block eopolymer in which the peptide forms a ß-sheet structure.173 Reproduced by permission of American Chemical Society.

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Block Copolymers in Solution: Fundamentals and Applications

these fibrils result from the hierarchical aggregation of B strands into helical tapes which then stack into fibrils. Details on nanofibre formation, due in part to B-sheet hydrogen bonding, in PEG-peptide amphiphiles,170-172,174 is not discussed in detail here, since the chains are too short for them to be considered as block copolymers. 4.8.3

HYDROGELS

Hybrid hydrogels have been prepared via the self-assembly of a water soluble synthetic polymer and coiled-coil peptides, which were genetically engineered, and expressed using Escherichia coli.115,176 The peptides were linked via a pendant metal-chelating ligand to a hydrophilic copolymer of HPMA and the metalchelating monomer DAMA (Figure 4.18). Two coiled coil peptides were employed-

Figure 4.18 Hybrid hydrogels in which a water soluble copolymer is linked via coiled coil peptide domains.176 The structure of the cross-link is shown enlarged. Reproduced by permission of Wiley-VCH.

one based on a natural sequence from the motor protein kinesin (containing a six histidine tag), and the other a block copolymer HHHHHH-b-(noncoiled 30 amino acid sequence)-b-(VSSLESK)6. The heptad sequence favours coiled coil formation. The histidine block acts as a tag for Ni2+ chelation. Hydrogels containing the wild type peptide cross-linker underwent a volume phase transition driven by thermal unfolding. Those containing the block polypeptide did not show a volume phase transition. However, for hydrogels containing either type of cross-linker, gel

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swelling was observed by replacement of the histidine tag by a metal-chelating ligand.177 Later, peptides containing block sequences were studied, comprising noncoiled regions (A) alternating with sequences from the kinesin stalk protein with a tendency to form coiled coils.178 Histidine-tagged AB diblock, ABAB tetrablock and ABABAB hexablock polymers were prepared via recombinant DNA techniques. Size exclusion chromatography revealed the presence of multimer aggregate structures (mainly dimers and tetramers). The degree of swelling decreased with temperature as unfolding occurred. The use of synthetic polypeptide block Copolymers to create hydrogels has been explored by Deming and coworkers.179,180 They investigated gelation for a range of diblocks containing a hydrophilic PLys [or poly(L-glumatic acid)] Polyelectrolyte block and a hydrophobic block based on an a-helix for poly(L-leucine) or a ß-sheet in the case of poly(L-valine).179 It was found that a high degree of conformational order of the hydrophobic chain was required to observe gelation, and that gelation occurred slightly better with a-helical domains. The importance of chain packing was highlighted by the fact that gelation was not observed in a mixture containing racemic L-leucine at a concentration at which gelation occurred for a copolymer containing the enantiomeric form. Hierarchical ordering was observed with a nanoscale interpenetrating network structure and a porous bicontinuous morphol1 80 ogy comprising gel matrix and water channels at the microscale. Laser scanning confocal microscopy and Cryo-TEM were used to probe the cellular structure for a PLys-&-poly(L-leucine-,stat-L-valme) diblock (Figure 4.19). SANS confirmed a nanoscale ordered structure.

Figure 4.19 Cryo-TEM image showing cellular structure in a gel formed by a poly(Llysine)-b-poly(L-leucine-stat-L-valine) diblock.180 Reproduced by permission of American Chemical Society.

4.8.4

POLYPEPTIDE BLOCK COPOLYMER-BASED COMPLEXES

Complexes of a PEO-b-PLys diblock with retinoic acid (vitamin A) have been investigated via a number of techniques.181 In aqueous solution, micelles comprised

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5 Adsorption 5.1

INTRODUCTION

Adsorption of block copolymers is relevant to their interfacial activity and hence applications for example in lubrication, coatings technology, emulsification or as templates for patterning inorganic materials. Adsorption of block copolymers has been discussed in a review of polymers at interfaces.1 The subject is also briefly covered in several texts.2,3

5.2 ADSORPTION AT THE AIR-WATER INTERFACE 5.2.1

ADSORPTION OF NEUTRAL BLOCK COPOLYMERS

Adsorption is typically studied as a function of surface area, often correlated to surface pressure-area (n-A) isotherms measured using a Langmuir trough. Two types of conformational transition are observed upon compression of adsorbed block copolymer layers, depending on the interaction of the soluble block with the surface. In the case of no preferable interaction, a gradual transition between noninteracting polymer mushrooms and stretched polymer brushes is observed upon compression. These systems are studied as models for 'tethered chains'. Representative data obtained for a PEO-b-PFMA diblock are shown in Figure 5.1.4 In contrast, when the soluble block has a tendency to adsorb to the interface then at low surface density an adsorbed pancake conformation is observed. Upon compression, this block is repelled from the surface and a brush is formed in which the insoluble block acts as a 'buoy' (Figure 5.2). The continuous change of conformation is exemplified by PDMS-b-PS diblocks at the surface of ethyl benzoate5 or DOP.6 The surface-active PDMS block acts as a buoy for the PS block (Figure 5.2), which is consequently depleted from the surface (the range of the depletion layer increases with chain length6). The scaling behaviour of tethered layer thickness with surface coverage and copolymer chain length was probed, and compared with theory. Good agreement was found with numerical self-consistent field (SCF) calculations,7,8 although not with analytical

Block Copolymers in Solution: Fundamentals and Applications © 2005 John Wiley & Sons, Ltd.

I. W. Hamley

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Figure 5.1 Representative surface pressure-area isotherm for a PEO-b-PFMA diblock film at the air-water interface, with schematic of the monolayer structures. Figure adapted from Hussain et al. Reproduced by permission of American Chemical Society.

Figure 5.2 Adsorption of block copolymers at the air-water interface in the case that the hydrophobic block forms a 'buoy' to which the hydrophilic block is tethered.

results in the strong segregation limit.9 Figure 5.3 shows fits to neutron reflectivity data for a PS-b-PDMS diblock on ethyl benzoate, along with model density profiles.5 These are based on parabolic functions, as anticipated for tethered polymer brushes. The quality of fit can be improved by allowing for an exponential tail and a depletion layer near the air-liquid interface. The adsorption behaviour of amphiphilic block copolymers at the air-water interface has mainly been studied for copolymers containing PEO. In particular, experiments have largely focused on two main classes: PS-b-PEO diblocks10-16 and PMMA-b-PEO17-20 diblocks. Phase transitions in monolayers of these block

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Figure 5.3 Neutron reflectivity data and model fits for a PDMS-b-PS diblock on ethyl benzoate.5 (a) Neutron reflectivity, shown normalized by the reflectivity from the solvent, (b) Corresponding PS density profiles. The long dashed line corresponds to a parabolic function with exponential tail, the solid line to a parabolic function with a depletion layer and the short dashed line to a parabolic function with both an exponential tail and a depletion layer. Reproduced by permission of American Institute of Physics.

copolymers at the air-water interface have been investigated via surface pressurearea isotherm measurements, neutron reflectivity and Brewster angle microscopy. In the PS-b-PEO system, at low coverage, the favourable interaction between PEO and water leads to adsorption of PEO at the interface.11,14-16 As the layer is compressed, the repulsive interactions between PS and PEO lead to desorption of PEO from the interface. Upon further compression, the PEO is pushed out of the surface layer into the water subphase to form a brush, and the surface is covered with PS blocks.12,15 This surface phase transition has a first order character,11,15 although SCF theory predicts it to be second order.10 Due to the effective repulsive interaction between the PEO and the interface, a depletion region develops near the

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Figure 5.4 Surface pressure-area isotherms for a series of PS-b-PEO diblocks with constant PS chain length (NPS = 31) and increasing PEO chain length, as indicated.14 Reproduced by permission of Springer Verlag.

interface. The depletion layer is particularly evident for longer PEO chains. Indeed, for shorter chains the plateau in the n-A isotherm is much less pronounced,4,14,15 as shown in Figure 5.4. It was shown that such n-A curves collapse into a master curve when the area per monomer is normalized by the PEO chain length.14,16 Brewster angle microscopy confirmed a first-order transition from an adsorbed PEO layer to a PEO brush in the plateau region of the n-A isotherm for copolymers with long PEO blocks.15 The concentration profiles obtained from neutron reflectivity have been compared with those computed using various 'brush' models, especially SCF theory.10,14 Similarly, the adsorbed amount and the hydrodynamic layer thickness (determined via optical microscopy and dynamic light scattering, respectively) have been compared with SCF calculations.21 The organization at the air-water interface of a PS-b-PEO diblock as a function of bulk copolymer concentration has been probed via neutron reflectivity, using selectively labelled chains to obtain the full set of partial structure factors.20 Surface micelles were observed well below the bulk cmc. The PS cores form buoys (lenses) at the surface [Figure 5.5(a)]. As the copolymer concentration increases towards and over the bulk cmc, the adsorbed amount increases and the thickness of the PS

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Figure 5.5 (a) Schematic of structure of adsorbed PS-b-PEO diblocks at the air-water interface on increasing copolymer concentration (A-C).20 (b) Schematic of structure of diblock EE 21 2-b-EOn2 as a function of increasing surface pressure.23 Reproduced by permission of American Chemical Society.

top layer decreases (and its density increases) as the PS forms less curved lenses. The PEO chains are consequently forced to adopt conformations that extend more into the aqueous subphase. At these concentrations, the reflectivity data on selectively labelled chains indicates structuring of the PS layer, which may result from a phase transition to a structure with in-plane order. The concentration at

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which an onset of layering in the PS is observed corresponds to a point at which an apparent kink in the surface tension data is observed. Surface quasi-elastic light scattering (SQELS) has been used to probe the viscoelasticity of adsorbed layers, in particular to determine the shear moduli and associated relaxation times.22 This technique was also used to obtain the dynamic elasticity and dilational viscosity of a series of PS-b-PEO and PEO-b-PS-b-PEO copolymers.16 In the PMMA-b-PEO system, detailed contrast variation neutron reflectivity revealed that the adsorbed layer contains both components at low surface coverage whereas upon compression the PEO extends into the aqueous subphase and the PMMA is expelled into the air phase.18,22 In the case of an asymmetric PEE-b-PEQ diblock, compression leads initially to the formation of finite domains.23 When the area fraction of domains reaches about 95%, corresponding to a surface area of around 6 A2 per EO monomer, PEO desorption is observed. This surface area is lower than values typically observed for other (symmetric) diblocks. The resulting layer structure is indicated in Figure 5.5(b). Ultimately a homogeneous PEE surface layer is formed, the thickness of which increases linealy with grafting density. Adsorption of amphiphilic silicon-containing diblock copolymers at the air/water interface has been investigated by Matsuoka and coworkers.24-26 Using n-A measurements, and X-ray reflectivity, they confirmed that a monolayer can be formed at an appropriate surface pressure.25 An interesting observation has been made for a diblock containing a highly ionic hydrophilic block, PDESCB attached to a hydrophobic PMMA block.26 It was found by SAXS, DLS and dye solubilization that micelles were formed in bulk, and yet no decrease of surface tension and no evidence of adsorption at the air-water interface was observed. This puzzling observation has yet to be fully explained, although it was suggested that destabilization of the amphiphilic monolayers due to electrostatic repulsion might play a role (however, in this case, micelles should also not be stable). The structure of an adsorbed monolayer of a PhI-b-PSSA at the air-water interface has been studied by X-ray reflectivity by Matsuoka and coworkers.27 The PhI forms a buoy to which the PSSA brush is tethered. Surface pressure-area isotherms for monolayers of telechelic PEO-based block copolymers (with C12 and C16 end groups) at the air-water interface reveal two plateaux.28 The first is ascribed to loops in the PEO midblock (and is observed for the homopolymer alone). Following this plateau the pressure rises rapidly as the end groups anchor onto the substrate. The second plateau at high density is due to dissolution of the polymer chains into bulk water. Brush theory was used to calculate isotherms which were in reasonable agreement with the experiments. In addition, polymer adsorption and desorption kinetics were calculated. The structure of aggregates formed at the air-water interface by copolymers with more complex architectures has also been investigated for mixed arm PEO-b-PS3 and PEO-b-PS2 star copolymers.29 Langmuir-Blodgett deposition of the monolayers onto silicon substrates enabled the surface morphology, comprising circular domains, to be imaged. As the surface pressure increased, the packing density of circular domains increased.

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ADSORPTION OF POLYELECTROLYTE BLOCK COPOLYMERS

Adsorption of diblock copolymers containing a polyelectrolyte at the air-water interface has been studied by neutron reflectivity. Thomas and coworkers have studied the adsorption of a number of PDMA-b-PMMA diblocks as a function of concentration and pH.30-32 Reducing pH increases the positive charge on the PDMA block, which has a pKa of about 7.3. Considering the effect of concentration at a fixed high pH, at low concentration the adsorbed layer was found to consist of a mix of the two blocks, with about half of the layer immersed in the underlying water. At higher concentration, a multilayer structure was formed with a central layer rich in the more hydrophobic PMMA and the outer layers comprising PDMA. This structure was ascribed to the formation of surface micelles with a PMMA core and PDMA extending up into the air-water interface and down into the aqueous subphase. A transition to this structure, characterized by a large increase in adsorbed layer thickness, is induced by increasing pH or by increasing concentration at a fixed high pH. Increasing the fractional charge on the polyelectrolyte however disfavours the formation of micelles.31 A study of the structure of adsorbed layer of a PDMA-b-PnBMA was undertaken using neutron and X-ray reflectivity suggested a similar structure with a submerged PDMA block attached to a PnBMA 'buoy'.33 Ellipsometry was used to probe the pH-controlled adsorption of diblocks comprising hydrophobic PDEA or PDPA and methyl- or benzyl-quaternized PDMA or sulfopropyl betainized PDMA.34 At low solution pH, where the copolymers are molecularly dissolved, low adsorbed amounts were observed. At higher solution pH, a pronounced increase in adsorbed amount accompanied the formation of micelles. Changes in the conformation of polyelectrolyte brushes in PtBS-b-PSS diblocks upon varying the interfacial area/molecule have been investigated by neutron reflectivity.35 For salted brushes, i.e. those for which charge is screened by the added NaCl, a parabolic density profile was observed (cf. Figure 5.3), as for uncharged polymer brushes. An additional excess density observed near the interface is due to adsorption of the hydrophobic backbone of the polyelectrolyte. The density profile was also measured for so-called 'osmotic brushes' in which the brush is swollen by its own trapped counterions. The profiles could be fitted using Gaussian functions, in agreement with the predictions of SCF calculations.36 However, the thickness of the brush was dependent on grafting density, in contrast to the SCF calculations but in agreement with models that account for the lateral inhomogeneity of counterion distribution37,38 and the reduction in entropy of counterions due to the space occupied by the polymer backbone (which is compensated by an extension of chains with increasing grafting density38). The latter is supposed to be the main factor. Forster and coworkers investigated the adsorption of a PEE-b-PSSA diblock at the air-water interface using X-ray reflectivity.39 The polyelectrolyte block was shown to form an osmotically swollen brush with thickness independent of polymer concentration (the hydrophobic block stretched in proportion to grafting density).

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At high salt concentration the contraction of the brush was observed, the thickness scaling as L ~ cs-1/3, as discussed further in Sections 4.2 and 5.3.2.

5.3 ADSORPTION ON SOLID SUBSTRATES The adsorption of surfactants and copolymers onto solid substrates is relevant to their use in applications including detergency, oil recovery and lubrication.40,41 The adsorption isotherm has been investigated for neutral and polyelectrolyte block copolymers on different substrates. In addition, the morphology of surface micelles has been examined, and the use of these in patterning inorganic materials (metals, metal oxides) explored. 5.3.1

ADSORPTION OF NEUTRAL BLOCK COPOLYMERS

The adsorption of PEO-containing block copolymers on solid substrates has been extensively investigated. Non-fouling surfaces coated with PEO are of interest since protein, plasma adsorption, etc., is reduced. There has been controversy as to whether surface micellization is correlated to the bulk cmc.42 Ellipsometry on Pluronic copolymers adsorbed onto (hydrophilic) silica provided evidence for an increase in adsorbed amount just below the bulk cmc.43 Surface association was discussed, especially since the increase in adsorbed amount occurred cooperatively but since the adsorbed layer was substantially less thick than the hydrodynamic radius, adsorption of intact micelles did not occur. It was concluded that PEO rather than PPO has the stronger tendency to adsorb,43 although the PPO block will have a stronger tendency to adsorb onto hydrophobic substrates.44,45 For PEO-b-PTHF-b-PEO and PEO-b-PPO-b-PEO copolymers, Tiberg and coworkers found that the amount of adsorbed copolymer increases two orders of magnitude below the cmc for the former system, and close to the cmc for the latter one.46 This increase was related to the cooperative formation of surface micellar structures on hydrophilic surfaces. In contrast, at hydrophobic surfaces, monolayers were observed. AFM on related alcohol ethoxylate surfactants provided direct evidence for the formation of surface micelles on a hydrophilic substrate and a monolayer on a hydrophobic substrate.47 Measurements using the surface forces apparatus on a PEO-£-PTHF-/?-PEO triblock also provided evidence for short-range attractions between surface aggregates due to bridging of the gap between hydrophilic quartz surfaces.48 In contrast to these findings, Muller and coworkers reported no correlation between the adsorption of PEO-b-PDLL diblocks onto hydrophilic silica and micellization in bulk.49 By comparing the adsorption of the diblock and that of PEO homopolymer, it was found that the hydrophobic block drives adsorption (in contrast to the conclusions of Malmsten et al. on PEO-b-PPOb-PEO triblocks43). On hydrophobized silica, the same diblocks formed a monolayer, anchored by the adsorbed PDLL blocks.50

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Adsorption of PEQ-b-PPO-b-PEO block copolymers onto hydrophobic surfaces has been studied by surface plasmon resonance (SPR). SPR exploits the coupling between incident photons from a laser and surface electrons (plasmons) at the metal/solution interface. The angle at which there is a minimum in the intensity of internally reflected light is sensitive to the dielectric properties of the substrate. Using this technique, Green et al. found a dense layer of PPO adsorbed at the hydrophobic substrate.51 Adsorption of a series of Pluronics onto model hydrophobic self-assembled monolayer surfaces has been studied by AFM and SPR.45 Adsorption isotherms were obtained from SPR, and the adsorbed amount was found to go through a maximum near the cmc, contrary to the Langmuir isotherm. The adsorption process was found to be partly irreversible. Surface micelle structures were only observed (by AFM) for the more hydrophobic copolymers, the more hydrophilic ones adsorbing as unimers to form a uniform layer. Force-distance curves suggested a brush-like structure of adsorbed micelles. The surface structure was shown to depend on the tip force applied. It was suggested that higher force scans revealed the micellar core structure, in contrast to low force scans which probe the polymer brush coronas. In a sister paper,52 the kinetics of adsorption was analysed by SPR. Enhanced adsorption rates for more hydrophobic triblocks was observed above the cmc, due to adsorption of micelles. Adsorption of unimers was inferred for more hydrophilic copolymers. Adsorption of Pluronics P105, F108, F88 and F68 onto PS latex particles has been investigated by sedimentation field-flow fractionation and dynamic light scattering.53 The thickness and density of the adsorbed layer was studied as a function of particle size. The mobility of the adsorbed chains was studied by electron spin resonance (ESR) using spin-probe labelled polymers. For a given particle size, the layer thickness was found to increase with PEO endblock chain length, and the dynamics to speed up, i.e. the rotational correlation rate from ESR increased. Later, Hariharan et al. analysed the adsorption data and showed it was consistent with the star-like polymer model (Section 2.7.1), i.e. the layer thickness L and particle radius R satisfied the relationship:54

Here a is the surface chain density, k is a constant (close to unity), v is a binary cluster integral characterizing the polymer-solvent interaction, lc is the contour length of the chains and aK is the statistical segment or Kuhn length. A plot of (LIR + 1)5/3 against vo 1 / 3 /R provided a straight line with a slope that yielded v/aK.54 It has been shown using neutron reflectivity that layering of block copolymer micelles occurs at a hard wall.55 Adsorption of Pluronic P85 onto quartz from solution in D2O was studied. Monte Carlo simulations of interacting hard spheres were able to account for the observed density profiles.55,56 Later, the model was refined to account for the tethered chains.56

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Emoto et al. studied adsorption of PEG-b-PLA micelles onto SAM-coated Si, glass and plasma-treated PDMS.57 They found that the micelle structure was disrupted upon deposition. However, cross-linking the PLA core via terminal methacryloyl moieties led to stable micelles that adsorbed intact. This group have reviewed the applications of PEG-based block copolymers at surfaces for biomedical applications.58 Their own work involves the used of PEG-b-PLA in which the PEG chain is end-terminated with an acetal or aldehyde group (Figure 5.6),59 which can be used to immobilize ligands including proteins, peptides and sugars. The PLA can be cross-linked (via end-functionalization with methacryloyl units) and confers additional biodegradability. Similarly, surfaces with biorecognition properties have been developed using PEG-b-PLA diblocks with biotinylated PEG chains.60,61

Figure 5.6 Functionalized PEG layer on a biodegradable PLA substrate, prepared from the self-assembly of PEG-b-PLA diblocks.59 Reproduced by permission of American Chemical Society.

The adsorption of copolymers with more complex architectures has also been investigated. For example, AFM has been used to probe the adsorption of PS7P2VP7 heteroarm polymers on silicon and mica.62 In acidic aqueous solutions, adsorption of single molecules and of micelles was noted, the rigid PS micellar core forming pronounced 'humps'. Addition of toluene, a good solvent for PS, lead to a conformational transition that caused flattening of the micelles as the PS chains extended from the micellar core. Surface micellar structures at the air-water

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interface have also been imaged (by deposition of the film onto silicon wafers) for a PEO-b-PS3 starblock copolymer.29 Responsive polymer surfaces sensitive to humidity have been prepared from PS-b-PI diblocks with hydrophilic dimethylamine or sulfobetaine end groups.63 The PS block adsorbed onto the silicon substrate, leaving dangling end groups. The reduction in the contact angle was monitored upon exposure to water vapour. The stratification resulting from adsorption of bidisperse mixtures of PS-b-P2VP diblocks onto silicon in good solvent conditions has been investigated by neutron reflectivity.64 The system was considered as a model bidisperse 'polymer brush'. The volume fraction profiles were compared with analytical self-consistent mean field theory. Experiments in poorer, near-6, conditions in cyclohexane showed much reduced layering of long and short chains. Tao et al. determined adsorption isotherms for a series of near symmetric PS-bPCEMA diblocks, adsorbing as brushes onto silica from a PS-selective solvent.65 The brush areal densities were compared with the predictions of the model due to Marques et al. (Section 5.5). The influence of a surface on the isotropic-nematic transition in a solution of cylindrical micelles formed by PB-b-PEO diblocks in aqueous solution has been compared with the bulk behaviour using neutron reflectivity to probe the surfaceinduced ordering and SANS to probe the bulk phase transition.66 The phase transition was shifted to lower polymer volume fractions in the layer close to the silicon-solution interface. 5.3.2

ADSORPTION OF POLYELECTROLYTE BLOCK COPOLYMERS

The adsorption of polyelectrolyte block copolymers has also been investigated, for polyampholyte diblocks and also for neutral-b-polyelectrolyte copolymers. Obviously for this type of copolymer, adsorption will be strongly influenced by the charge on the copolymer relative to the surface. Surface micellization by these types of copolymer has also been observed, as discussed in the following section. The adsorption of a PtBS-b-PSS diblock onto PS latices from water has been studied via gravimetric determination of the adsorbed amount, following centrifugation.54 The adsorbed amount increases with ionic strength (added NaCl) to give a dense polyelectrolyte brush. The thickness of the adsorbed layer was compared with scaling theories, as discussed in the previous section. A simple blob model for polyelectrolyte brushes on spherical surfaces was developed, leading to scaling predictions for brush layer thickness L ~ cs-m with m = —1/6 for brushes adsorbed on a sphere with infinite radius (m = —0.17 was observed for dense adsorbed layers) and m — —1/10 for adsorption on a sphere with zero radius (m = —0.11 was observed for bulk micelles). This behaviour depends much less weakly on salt concentration than predicted by earlier scaling models. The adsorption of this type of diblock (PtBS-b-PNaSS) on hydrophobized mica in the salted brush regime was reported to be consistent with L ~ cs-1/3.67 The same behaviour was reported earlier for a PEE-b-PSSA diblock adsorbed at the air-water interface.39

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Stamm and coworkers have investigated the adsorption of PDMA-b-PMAA polyampholyte diblocks from solution onto silicon substrates.68,69 The adsorbed amount determined via ellipsometry using the Langmuir isotherm was measured as a function of pH, polymer concentration and salt concentration. The adsorption was maximal at the isoelectric point (Figure 5.7). At a fixed pH, increasing salt

Figure 5.7 Amount of PDMA-b-PMAA diblock adsorbed as a function of pH at a fixed polymer concentration.69 The arrows indicate where the silicon surface and the polyampholyte carry a positive or negative charge. Reproduced by permission of Springer Verlag.

concentration increased the adsorbed amount.68 Adsorption kinetics were also analysed, allowing the diffusion coefficient for the early stage of adsorption to be measured.68 Later, the structure of dried adsorbed layers was imaged by AFM.69 This confirmed the presence of surface micelles, the size of which was weakly dependent on pH, although the adsorbed amount was strongly pH dependent. An and coworkers have used neutron reflectivity to investigate the conformation of the PDMA block in aqueous salt solutions of a PDMA-b-PMMA diblock, where the PMMA is adsorbed onto a SAM layer (of octadecyl trichlorosilane) on silica.70 The adsorption of the same diblock at the air-water interface was also studied (see Section 5.2.2). It was found that the PDMA chain was not ionized in the vicinity of the PMMA anchor, in agreement with a SCF theory model for weakly grafted poly electrolytes.1}J2 5.3.3

SURFACE MICELLES

Under appropriate conditions, it is possible for adsorption of micelles to occur, rather than single chains. This provides a route, for example, for the controlled

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Figure 5.8 AFM topographic image of a PS-P2VP diblock micellar film loaded with HAuCl4 deposited onto a Si wafer.74 Reproduced by permission of American Chemical Society.

deposition of inorganic nanoparticles, prepared from precursors (such as metal salts) sequestered within the micellar core.73,74 The structure of block copolymer micelles on solid substrates has been probed on dried films by AFM.74-76 Figure 5.8 shows a representative topography image. In addition, TEM can be applied for specimens that have been suitably cryo-cooled (sometimes the specimens are also stained to enhance contrast).75,77-82 Eisenberg and coworkers have imaged surface micelles formed by amphiphilic diblocks deposited by the Langmuir-Blodgett technique at the air-water interface.83-85 The films were picked up onto supported TEM grids, then dried and shadowed with metal vapour and examined by TEM. The same group has also performed AFM on dried micelles on glass.86 Images were first obtained for PS-bqP4VP diblocks, quaternized with decyl iodide, spread as a monolayer at the airwater interface. TEM images revealed self-assembled circular surface micelles at low surface pressures (<2mNm~ 1 ). For a S26o-b-q4VP240 diblock, the surface micelles were quite regular and had an aggregation number of 131 ± 35.87 The distance between micelles (at low surface pressures) was found to be consistent with fully extended qP4VP chains extending from a central core of PS coils. An apparent first-order phase transition was detected at high pressures from a plateau in n-A isotherms. This was correlated to TEM images which suggested that the polyelectrolyte block changed from a surface adsorbed two-dimensional (2D) state 83 to a submerged aqueous state with less order (quasi-2D) at this transition. This transition was more graphically termed as being between 'starfish' micelles and 'jellyfish' micelles (Figure 5.9).86,88 In subsequent work, Langmuir films of more asymmetric copolymers of the same type at the air-water interface were investigated.84,88 Circular or starfish micelles were observed for copolymers with less than 86% PS, rod or ribbon-shaped surface micelles were observed for copolymers with between 86% and 94% PS, and planar micelles were observed for PS contents between 94% and 97% PS. These structures are shown in Figure 5.10. This sequence of phase transitions is distinct from phase

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Figure 5.9 Schematic of 'starfish' and 'jellyfish' micelles. Typical association numbers are actually p ~ 100.129 Reproduced by permission of Oxford University Press

Figure 5.10 Transmission electron micrographs of thin films of Sm-b-4VPn/C10H21I. (a) Circular surface micelles; m = 480, n = 200.89 (b) Ribbon surface micelles; m = 480, n = 34; (c) Planar surface micelles; m = 480, n = 13. Reproduced by permission of Royal Society of Chemistry.

transitions in the bulk, where the sequence lamellae - cylinders - spheres is observed on increasing the asymmetry of strongly segregated block copolymers. The rod micelles were found to be made up of two layers of the diblocks, whilst the planar aggregates appeared to be one PS block thick, although they extend up to several microns in width.86 In parallel with bulk observations, addition of PS homopolymer was found to induce changes in the morphology of the surface micelles (circle, ribbon or plane). For example, addition of homopolymer PS was observed to induce a transition from ribbon surface micelles to planar micelles in a

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S260-b-qVP24o diblock. A cellular or foam morphology (i.e. the inverse of the circular surface micelle phase) was observed in some areas (up to 10%) of Langmuir-Blodgett films formed by PS-b-PNaA and PS-b-PNaMA block copolymers. The cell areas of these nanofoams ranged from 100 to 5000 nm2.89 Circular surface micelles have also been observed for nonionic block copolymers. Li et al. reported observations via TEM and AFM of starfish micelles formed by PS-b-PnBMA, PS-b-PtBMA, PS-b-PtBA and PS-b-PDMS diblock copolymers.85 Plateaux observed in n-A isotherms of the Langmuir-Blodgett films at the air-water interface were consistent with the formation of surface micelles. Meiners et al.90 and Spatz et al.14,15 have observed surface micelles of PS-bP2VP on mica or carbon. Samples were prepared by drying dip coated films of diblocks (dissolved in toluene), vitrification on solvent evaporation leading to trapping of micellar structures. Regenbrecht et al.91 probed the structure of micelles of the neutral-b-polyelectrolyte diblock copolymer PEE-b-PSSA adsorbed on solid substrates in aqueous solution by AFM on dried samples. A comparison was made between adsorption onto a neutral hydrophobic graphite substrate, and onto mica modified to be positively charged by a coating of PEI, or by ion exchange. A range of structures from spherical micelles to network-like structures, was observed upon varying ionic strength. Adsorption of micelles and vesicles was observed onto graphite. Adsorption onto strongly charged substrates led to the formation of structures not found in the bulk.76,91 The ordering of micelles of a PS-b-P2VP diblock from pH = 1 aqueous solution (where the P2VP block is protonated) has been studied for films dip coated onto silicon.92 Even in these highly acidic conditions, the deposited micelles were strongly adsorbed, and could not be removed by washing. The highest density and ordering of micelles was achieved by controlling the solvent evaporation rate, the most important experimental variable. The rate of substrate withdrawal also influenced the ordering. Surface micellar structures (stripe and spherical domain patterns) have been imaged for dried PB-b-PS diblocks using TEM.81 Webber et al.93 investigated the adsorption of PDMA-b-PMMA diblocks onto mica as a function of pH. They observed surface micelles at low pH, where PDMA is protonated, and regions of close-packed structure at higher pH for this polyelectrolyte diblock. Subsequently, they have observed hcp structures in an adsorbed layer of a related diblock, qPDMA-b-PDEA.94 The structure of the polymer layer was influenced by the electrostatic interaction between the PDMA block and the negatively charged mica. Surface plasmon resonance experiments revealed a correlation between the rate of adsorption of PS-b-P2VP diblocks from toluene and the bulk cmc - the initial rate of adsorption increasing above this concentration.95 According to Tassin et al., the adsorbed surface micelles act as a barrier that slow down the subsequent adsorption of unimers, observed as an additional slow process. A study of the adsorption kinetics of two PS-b-PEO copolymers onto dielectric substrates (glass and sapphire) using optical interferometry provided evidence for the adsorption of micelles above the cmc.96 The adsorbed amount increased steeply to the cmc,

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however it then decreased sharply and then a slower increase was observed (Figure 5.11). The rate of adsorption also showed a discontinuity at the cmc (Figure 5.11). Adsorption from very dilute solution (well below the cmc) has been found to occur via a two-step process. Ellipsometry has been used to probe the

Figure 5.11 Data from adsorption experiments (using optical interferometry to measure the surface concentration) of a PS-b-PEO diblock from cyclopentane onto dielectric substances.96 (a) Adsorbed concentration as a function of bulk copolymer concentration for adsorption onto glass (A) and sapphire (o, •), (b) Initial rate of adsorption as a function of bulk copolymer concentration. Symbols as for (a). Reproduced by permission of American Chemical Society.

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adsorption of PS-b-PEO diblocks from toluene - the initial rapid adsorption was ascribed to the diffusive transport of individual chains.97 The later slower growth in thickness of adsorbed layers corresponded to strongly overlapped chains, and brush-like behaviour was then observed. A similar study on PS-b-P2VP diblock adsorption from toluene reached similar conclusions.98 The adsorption of a PPO-b-PEO diblock from aqueous solution onto hydrophilic mica and hydrophobic silica substrates has been studied using in situ AFM.42'44 Adsorption was studied as a function of concentration - close to and below the bulk cmc the copolymers adsorb as single chains or 'pre-micelle aggregates'. As concentration was increased, micelles formed densely packed structures (Figure 2.2). At a given concentration, the ordering was higher for the strongly adsorbed micelles on silica. Adsorption onto the hydrophilic silicon nitride AFM tip was observed to compete with adsorption onto either substrate (although this was a particularly strong effect when imaging weakly adsorbed layers on mica). The substrate coverage with micelles on mica increased roughly linearly with scan time at low micelle concentration. Weak adsorption on mica was analysed to provide a 2D diffusion coefficient. The effect of tip oscillation frequency on the AFM images was investigated - higher frequencies were required to image more weakly adsorbed polymer aggregates on mica. Finally, force-distance curves provided information on the nanomechanical properties of the adsorbed polymer layers. It was suggested that micelles and aggregates adsorb to silica via the hydrophobic PPO block, whilst they adsorb to mica via the hydrophilic PEO block. A model for the adsorbed structure is shown in Figure 5.12. Adsorption of shell cross-linked knedel (SCK) nanoparticles onto mica has been investigated by Wooley and coworkers. Dried films have been imaged by tappingmode AFM. The role of the charge on adsorption was explored by modification of the negatively charged mica surface with a self-assembled monolayer to make it positively charged, and also variation of the charge on the SCK nanoparticles (varying as a function of the extent of cross-linking).99 In situ measurements in a liquid cell of pH-induced changes in the adsorbed 2D array structure have also been performed.100 Further details on related structures can be found in Section 2.12.4.

5.4 SURFACE FORCES EXPERIMENTS Experiments using the surface forces apparatus (SEA) provide information on the interaction between polymer brushes tethered to locally flat surfaces (the actual geometry comprises curved half cylinders, oriented to be mutually orthogonal). The first report on the use of the surface force apparatus for measuring forces betwen adsorbed layers of block copolymers was by Hadziioannou et al.101 They attached symmetric PS-b-PVP diblock copolymers via adsorption of the PVP block, the PS block being nonadsorbing, to mica surfaces in the good solvent toluene. It was demonstrated that the PS chains were strongly stretched normal to the adsorbing surface forming a polymer brush at the liquid-solid interface. A force-distance

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Figure 5.12 Models for adsorption of diblock PO94-b-EO316 onto silica and mica at the concentrations indicated.42 The gray triangle represents the AFM tip. The grey corona chains are PEO and PPO chains (black) from the micelle cores. Reproduced by permission of American Chemical Society.

profile for a PS-b-P2VP diblock adsorbed on mica from a cylcohexane solution is illustrated in Figure 5.13. This shows that well below the 6 temperature for PS in cyclohexane (70 — 34°C) there was pronounced attraction at large plate separations, whereas at higher temperatures the force was purely repulsive.101 To mimic a layer of end-grafted polymer chains more closely, Taunton et al. investigated highly asymmetric diblock copolymers and demonstrated that PS-b-PEO diblock copolymer chains with a short PEO block can be terminally anchored on mica through the adsorption of ethylene oxide segments on the mica surface with the PS blocks dangling freely into the solvent (e.g. toluene).102,103 At high surface coverage, the PS chains were found to be strongly stretched, and the monotonically repulsive interaction profiles of two such polymer brushes were in good agreement with theoretical predictions.102,103 The interaction of end-adsorbed diblock and triblock copolymers in toluene against a bare mica surface was investigated by surface force measurements.104

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Figure 5.13 Force-distance profile obtained from surface forces experiments on a symmetric P2VP-b-PS diblock adsorbed on mica in cyclohexane at 21 °C.101 Reproduced by permission of American Chemical Society.

Only monotonically repulsive forces were observed when a bare mica sheet interacted with a single layer of PS-b-PEO diblock, end adsorbed at a toluene mica interface. In contrast, clearly detectable attractive forces were found for PEOb-PS-b-PEO triblock copolymers under similar conditions. The attraction was attributed to polymer bridges in which the two PEO end blocks of a single triblock chain simultaneously adsorbed onto the two mica surfaces. The experimentally detected evolution of the force profiles from attractive to repulsive with successive compression-decompression cycles was proposed to result from the dynamics of conformational rearrangements and the subsequent migration of chains between the surfaces. The results further indicated that the relative populations of chains adsorbed in a loop or tail conformation depend on the adsorption energy of the anchoring blocks, as does the degree of stretching of the bridging chains before rupture upon separation of the mica surfaces.104 Surface force experiments were

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combined with simultaneous neutron reflectivity experiments on PS-b-PEO diblocks adsorbed on glass plates.105 Adsorption from toluene led to preferential adsorption of PEO, however due to the very high asymmetry of the copolymers studied, and the favourable adsorption energy, PS was also adsorbed. On the approach of a second coated plate, the PS volume fraction increased near the interface, indicative of strong interlayer repulsion.105 Surface force measurements on a PEO-b-PBO diblock in aqueous solution have revealed purely monotonic repulsive forces between the BO8-b-EO41 layers adsorbed onto hydrophobically modified mica (to which PBO is adsorbed).106 Ellipsometry was used to determine adsorption isotherms (adsorbed amount as a function of concentration), and the adsorbed amount as a function of time. The range of the steric repulsion was found to increase with increasing bulk copolymer concentration, whereas the concentration of an inert salt (up to 0.1 M KBr) did not influence the surface forces profiles. The adsorption kinetics were found to be described by two adsorption regimes. Initially, diffusion of polymer to the interface to the solid surface dominated, thus this was a diffusion-controlled regime. When the surface was fully covered, a crossover into a second regime occurred and the increase in surface coverage was less rapid due to interactions between block copolymer molecules at the surface. Measurements using the surface forces apparatus on a PEO-b-PTHF-b-PEO triblock also provided evidence for shortrange attractions between surface aggregates due to bridging of the gap between hydrophilic quartz surfaces.48

5.5 MODELLING ADSORPTION The adsorption of block copolymers to solid substrates has been investigated extensively by lattice self-consistent mean field calculations.7,106-110 These models consider adsorption of polymer chains, rather than micelles, and properties such as surface density, segment density profiles and adsorbed layer thickness can be calculated. Calculations for specific Pluronic copolymers (P85, P103, P104 and P105) provided concentration- and temperature-dependent data on surface tension in good agreement with measured values.111 In addition, information on the distribution of PPO and PEO segments was obtained that indicated a top layer of PPO, with little water pentration and a thicker PEO layer underneath, extending into the aqueous subphase. Allowing for polydispersity of the block copolymer led to a less clear discontinuity in surface tension data at the cmc, in agreement with experimental observations. Schillen and coworkers examined the adsorption of BO8-b-EO41 using experiment (as mentioned above) and theory.106 The theory was able to reproduce the observed adsorption isotherm, especially when allowance was made for polydispersity. In a polydisperse polymer, preferential adsorption of the chains with longer hydrophobes was noted. Lattice Monte Carlo simulations have been employed to investigate block copolymer adsorption onto solid substrates. Balazs et al. investigated the adsorption of ABA triblocks with solvophobic endblocks onto flat substrates, and compared it

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with that of AB diblocks.112 They explored the optimal conditions for adsorption of a 'steric stabilization' layer, and found that this could be achieved by adsorption from dilute solution of relatively short polymers, since these adsorb in a loop conformation. The presence of two hydrophobes per chain for the triblock leads to stronger adsorption than for the case of diblocks. Later, they investigated adsorption onto a corrugated surface and found selective adsorption of the end blocks of an ABA triblock onto the ridges, whilst the midblock spanned the intervening wells.113 Consequently, the adsorption of triblocks acts to smooth a rough surface. Zhan and Mattice performed lattice Monte Carlo simulations of adsorption of model A10B10 diblocks in a selective solvent for A.114,115 They found that below and close to the cmc, adsorption of free chains only occurs. In contrast, at concentrations much higher than the cmc, adsorption of micelles predominates.115 They were able to reproduce the observations of Munch and Cast concerning the adsorbed mass per unit area, F, as a function of concentration - in particular a linear increase in F below the cmc, followed by a drop to a lower adsorbed amount above the cmc (only weakly dependent on concentration) (Figure 5.11). At a concentration about ten times the cmc, the adsorption of micelles was marked by an increase in the concentration dependence of adsorbed polymer.115 This regime was not encountered by Munch and Gast, who suggest adsorption of micelles commences at the cmc. Zhan and Mattice suggest that the increased adsorption rate above the cmc observed by Munch and Gast can be interpreted as arising from collisions of micelles with the surface, that do not subsequently adsorb. Wang and coworkers have developed the lattice Monte Carlo simulation approach to model adsorption of di- and triblocks from aqueous solution by considering the interaction between the blocks as well as that between each block and the substrate.116 This is in contrast to the work by Balazs et al. who only considered the interaction between the adsorbing block and the substrate (Zhan and Mattice did allow for nonzero interaction parameters in their study of adsorption from a selective solvent,115 although not for a nonselective solvent117,118). Wang et al. found that a strongly adsorbed diblock behaves like an adsorbed homopolymer. The formation of a collapsed 'globule' structure in a poor solvent was also examined, and found to be inhibited somewhat by the presence of the substrate. Binder and coworkers performed off-lattice Monte Carlo simulations (using a bead-spring model for the polymer chains) of asymmetric diblocks (/= 0.25) with short-range attraction to the surface for the minority block.119 Depending on surface coverage and surface interaction energy, the formation of mushrooms, brushes or surface micelles were observed. The cmc was found to be similar to that in bulk. Large surface micelles were found to contain very dense micellar cores containing crystalline layers. On the basis of a scaling argument (also the Daoud-Cotton model), Johner and Joanny have suggested that even from a micellar solution, only free chains adsorb and never complete micelles, due to the potential barrier for micellar adsorption.120 On the other hand, the formation of surface micelles by adsorption of diblocks at a solid surface from a selective solvent has been predicted on the basis of a modified 'brush' theory.121 The result of Johner and Joanny is also contradicted by experiment. Earlier work by this group discussed the adsorption of brush layers

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from micellar and lamellar solutions.122 Again adsorption of micelles was not considered. Adsorption was strongly influenced by the balance of van der Waals attraction between the adsorbed block and the stretching energy of the 'buoy' brush, which depends on copolymer asymmetry. The adsorption of neutral-b-polyelectrolyte diblocks was analysed in a subsequent paper.123 The formation of a dense brush layer was found to be possible only if the charge on the polyelectrolyte block was not too high. The formation of micelles in bulk was also constrained by the fraction of charged monomers. Adsorption at the oil-water interface was also discussed, and a range of parameters identified for which the interfacial tension was reduced to zero in the presence of added copolymer. Monte Carlo simulations have also been performed of the adsorption of triblock copolymers from a nonselective solvent onto a flat surface from a nonselective solvent.124 The results were compared with Langmuir adsorption studies using ellipsometry to probe adsorption via the end blocks of a PEO-b-PS-b-PEO triblock copolymer from a nonselective solvent (toluene).125 Haliloglu et al. additionally calculated Langmuir adsorption isotherms and analysed adsorption kinetics.124 Comparison was also made with the simulations for diblocks, and it was found that the adsorbed amount is lower for the diblock than for the triblock at low concentration. However, the surface coverage is the same for both copolymers when weakly adsorbed to the surface. Surface density profiles were also compared. Finally, scaling relationships for triblock copolymer adsorption under weak adsorption conditions were derived.124 In a related paper,126 adsorption and bridging of BAB copolymers in an athermal solvent and confined between two parallel flat surfaces was studied, and the dynamic response of the system to sinusoidal and step shear was examined. The dimensions of surface micelles have been analysed using a brush model, modelling adsorbed blocks as a 2D melt. The surface micelles were approximated by part of a sphere. The association number, radius and height of the micelles were 1 /2 all shown to scale with the length of the nonadsorbed block as NA 1/2(i.e. a melt-like 127 scaling). Adsorption of diblocks comprising a highly charged block and a hydrophobic block onto planar substrates has been analysed using a brush scaling model, in the case of high salt concentration where interactions between charged blocks are screened.128 Layers adsorbed from dilute solution below the bulk cmc were found to be much denser than layers in equilibrium with micellar solutions. The adsorbed layer thickness was found to decrease with increasing salt concentration, whereas the surface density increased.

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6

Applications

As mentioned in Chapter 1, industrial applications of block copolymer surfactants have been discussed by industrial researchers from the United States.1-3 The texts edited by Nace4 and by Alexandridis and Lindman5 cover many aspects of the behaviour and properties of PEO-based amphiphilic block copolymers, with several chapters devoted to applications. Biomedical applications of block copolymers have been reviewed extensively, as discussed in Section 6.3. From an academic perspective, a number of reviews6-9 have covered the selfassembly of amphiphilic block copolymers, and the numerous potential applications of the resulting nanostructures. This is the main focus of the present chapter, which is concerned with the science underpinning several key applications. It is not intended to provide an overview of industrial products or processes.

6.1 SURFACTANCY/DETERGENCY The major application of amphiphilic block copolymers by value and volume is of course detergency. The PEO-b-PPO-b-PEO copolymers are widely used as nonionic polymeric surfactants in aqueous solution. As the properties of these systems have been extensively discussed in Chapters 2 and 3, further details are not provided here.

6.2 SOLUBILIZATION, EMUSIFICATION AND STABILIZATION 6.2.1 6.2.1.1

SOLUBILIZATION Experiments

There have been numerous studies on the use of amphiphilic block copolymers to solubilize molecules, in particular the use of water soluble block copolymers to solubilize organic compounds ('oils') which are immiscible in water. In fact, industrial applications of block copolymers, such as agrochemical dispersions or pharmaceutical formulations,3 relies on this solubilization capacity. Solubilization for applications in drug delivery is discussed in detail in Section 6.3. Block Copolymers in Solution: Fundamentals and Applications © 2005 John Wiley & Sons, Ltd.

I. W. Hamley

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Solubilization of benzene in solutions of PS-b-PMAA diblocks in aqueous solution was investigated via fluorescence spectroscopy (using tagged chains) and quasi-elastic light scattering.10 Solubilization of organic substances in micelles formed by PMMA-b-PAA copolymers neutralized to various degrees with Li+, Na+, or K+ counterions, has been studied by SANS and NMR. 11 Chloroform or chlorobenzene were solubilized in the PMMA core, to an extent that depends on the charge on the polyelectrolyte block. Solubilization of various organic solutes in PS-b-PEO diblocks has also been quantitatively studied.12 The Solubilization of perfluorinated compounds within block copolymer micelles in aqueous solution has been shown to be more efficient when the micelles are formed from a block copolymer with a partly fluorinated hydrophobic block.13 Furthermore, when a mixture of perfluorinated and hydrocarbon compounds was added, selective Solubilization of each type into the corresponding micelle was observed. Pluronic copolymers have been extensively used to solubilize aromatic hydrocarbons - see for example papers by Hurter and Hatton14 and others.15 Gadelle et al. investigated the Solubilization of aromatic solvents in micelles formed by PEO/PPO (Pluronic type) triblocks in water using head-space gas chromatography and determined Solubilization isotherms and solute partition coefficients.16 They found that the addition of apolar solubilizates promotes association of the copolymer, and that Solubilization is initially a replacement process in which water molecules in the core are displaced from the micellar core by the solubilizate. The partitioning of hydrophobic solutes into micelles of Pluronic block copolymers has been studied using fluorescence probe techniques.17 The partition coefficient, P, defined as the ratio of solute concentration in the micelle microphase and in the aqueous phase were determined for a series of copolymers. A simple inverse relationship between P and the cmc was found using pyrene as a probe (Figure 6.1). An increase in partition coefficient with hydrophobic block content was noted for a number of Pluronic copolymers.14,15 The Solubilization capacity also increases with polymer concentration.14,15 By varying the length of the alkyl chain in alkyl fluorescein probes, the incremental contribution of methylene groups to the free energy (of transfer from aqueous phase into micelle) could be determined - values ranged from —1.3 to —3.0 kJ mol -1 , increasing with the length of the hydrophobic PPO block.17 The Solubilization of water within reverse micelles formed by Pluronics (and related PEO-b-PBO-b-PEO triblocks) in p-xylene has been probed by gravimetry.18 The Solubilization capacity increased considerably when the PEO content in the copolymers decreased. Solubilization of alkyl cyanobiphenyl liquid crystals in the core of micelles formed by PEO-b-PPO diblock copolymers has been examined via light scattering and SAXS.19-22 The Solubilization capacity of hydrocarbon solutes in PEO-b-PPO diblocks and PEO-b-PPO-b-PEO triblocks was also compared.23 The Solubilization was measured by mixing aqueous micellar solutions with the hydrocarbons, separating the aqueous phase from the unsolubilized material and analysing the amount of

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Figure 6.1 Linear relationship between logP and log (cmc) where P is the partition coefficient of pyrene into micelles of a series of Pluronic PEO-b-PPO-b-PEO triblocks (sample codes indicated).17 Reproduced by permission of American Chemical Society.

solubilized hydrocarbon by direct gas chromatography.24 The presence of solubilizate was shown to lower the cmc. The polymerization of monomer within block copolymer micelles has been studied. Kriz et al. showed25 using !H NMR that methyl methacrylate segregates to the core-shell interface of PS-b-PMA diblocks in aqueous solution, where it can undergo polymerization to produce an 'onion' structure with a core surrounded by two shells. Solubilization of large molecules such as fullerenes is possible in large block copolymer assemblies (hollow micelles with a monolayer shell,26 rather than a bilayer as in vesicles).26,27 Hollow spheres formed by two poly(phenylquinoline)-b-PS diblocks in binary organic solvent mixtures were able to solubilize C60 and C70 fullerenes. The aggregate dimensions increased from 1-5 (um initially to over 30 um upon solubilization. Block copolymers have been used as dispersants for pigments. For example, P4VP-b-PNaMA diblocks and PNaMA-b-P4VP-£-PNaMA triblocks have been used to disperse alumina-coated titanium dioxide.28 Gemini-type block copolymers, with two hydrophilic PEO blocks linked at a single junction point to a hydrophobic PS block have been prepared.29 They are expected to have superior wetting, foaming and dispersing properties than linear copolymers. Their use as surfactant stabilizers in emulsion polymerization was examined.29 6.2.1.2 Theory and Computer Simulation A scaling analysis based on the star polymer model of Daoud and Cotton for the solubilization of a low molecular weight solute in spherical micelles formed by an

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AB diblock in selective solvent was presented by Nagarajan and Ganesh.30 Scaling relations for the association number, the core radius, the coronal layer thickness L and the volume fraction of copolymer in the core, 0B were derived for a number of situations, including the case where the solvent S is a good or 0 solvent for the shell block A, and the solute J being a good or G solvent for the core block. The solubilization of low molecular weight solute J in micelles of AB diblocks formed in a selective solvent S was considered theoretically by Nagarajan and Ganesh.31 Predictions were made for the cmc, the size and composition distribution of the micelles containing solute J, the association number of the micelles, the maximum extent of solubilization, and the core radius and shell thickness of the micelles. Calculations indicated that micelles containing solubilizate tend to be essentially monodisperse in size and in the extent of solubilization. The solubilization behaviour of the micelles and their geometrical characteristics were found to be significantly influenced by the interactions between the solute and the solventincompatible B block of the copolymer as well as the J-S interfacial tension. The micellar structure was also found to be affected by the interactions between S and the coronal A block, though to a somewhat lesser degree when compared with the corresponding solute-free systems. The predictions of the theory were compared with experimental data for water-soluble PEO-b-PPO diblocks.24 The solubilization of hydrocarbons in PEO-b-PPO-b-PEO has also been examined theoretically, focusing on aggregates with different shape (spherical, cylindrical, lamellar) and transitions between different morphologies induced by solubilization.32 Theory and experiments on the solubilization of hydrophobic substances by block copolymer solvents have been reviewed by Nagarajan.33 Block copolymer micellization in a mixture with two immiscible solvents was considered by Cogan et al.,34 also employing modified Scheutjens-Fleer theory. They considered the case where each of the solvents is selective for one of the blocks and found that for highly incompatible solvents, one segregates in the centre of the micelle whilst the other selectively solvates the corona. The capacity of the micelle to disperse a second solvent was found to be controlled by the size of the core block. It was reported that the number of dispersed molecules and copolymer chains assembled in a micelle change most rapidly as the background solvent concentration approaches saturation levels. The theory was applied to interpret earlier experimental results35,36 on PEO-b-PS diblock copolymers in cyclopentane with trace amounts of water, which is a selective solvent for the PEO block that forms the micellar core. A simple thermodynamic model to describe solubilization in block copolymer micelles was developed by Munk and coworkers.37 The theory assumed that the association number of copolymer molecules within the micelle is not affected by the process of solubilization. The extent of solubilization represents an equilibrium between the favourable interaction of the core component with the solubilizate (with both enthalpic and entropic contributions) and the surface tension at the core boundary that acts against solubilization. The theoretical predictions were found to agree reasonably well with experimental results for neutral-b-polyelectrolyte PS-bPMAA diblocks in solution in 80:20 dioxane/water mixtures (selective for PMAA),

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with a variety of organic solubilizates. In the experiments, static light scattering was used to determine the extent of solubilization and dynamic light scattering was used to obtain the micellar hydrodynamic radius.37 Dan and Tirrell presented a model for the phase diagram of a diblock copolymer in a mixture of incompatible and highly selective solvents using a mean field scaling theory approach.38 The properties of the diblock copolymer as an emulsifier were investigated, and the microdomain geometry and size were determined by an analysis of the interfacial layer. They found that solvent selectivity leads to copolymer association at the liquid-liquid interface and the formation of stable microdomains. Symmetric copolymers were found to form lamellae at all copolymer concentrations, whereas asymmetric copolymers were shown to associate in spherical micelles in equilibrium with the two bulk solvent phases. The interfacial curvature and surface density was found to increase, and the volume of the emulsion phase to decrease, with the copolymer degree of asymmetry. The cac, above which chains assemble at the liquid-liquid interface and microdomains form, was found to be significantly lower than the cmc. The emulsion phase volume was found to increase linearly with copolymer concentration until, when one of the solvents is exhausted, cylindrical domains appear. At high copolymer concentrations lamellae replace the cylindrical domains. As noted by Dan and Tirrell,38 this sequence of phase transitions is similar to that predicted for block copolymer/homopolymer blends.39,40 Earlier work by Cantor addressed diblock copolymers as emulsifiers in mixtures of immiscible solvents using mean field Flory-type theory for semidilute solutions.41 However, only a lamellar phase was considered. Emulsification in polymer blends containing block copolymers is discussed elsewhere.42 Pepin and Whitmore have investigated homopolymer solubilization limits in diblock copolymer micelles via Monte Carlo simulations.43 The distribution of low molecular weight homopolymer solubilized in the core of the micelles (formed by near symmetric diblocks) was found to be relatively uniform. This conclusion is in agreement with prior experimental and theoretical results on homopolymer solubilization in block copolymers.44 A threshold volume fraction of homopolymer beyond which it was no longer solubilized, and instead macrophase separated was identified and found to decrease with increasing chain length of homopolymer relative to the corresponding core block in the micelle. Monte Carlo simulations of solubilization in triblock copolymers revealed that solubilization enhances micellization - the fraction of chains associated into micelles and the association number are both increased.45 Structure formation in block copolymer + solvent + solubilizate systems has also been simulated, considering both solubilization in micelles and also microemulsion formation.46 6.2.2

EMULSIFICATION AND STABILIZATION

Amphiphilic block copolymers are widely used to stabilize emulsions and microemulsions. Due to their interfacial activity, they segregate to the oil-water interface, reducing the interfacial tension to facilitate mixing.

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The structure of the adsorbed layer of PEO-b-PBO diblocks at the interface in a perfluorodecalin-in-water microemulsion has been studied by SANS. Volume fraction profiles were obtained and found to resemble those for polymer brushes calculated using SCF theory.47 Block copolymers have been used as stabilizers in microemulsion polymerization to prepare hollow PS nanospheres.48 Methyl methacrylate was solubilized in the core of Pluronic micelles, and then polymerized. Styrene was then added with divinylbenzene as cross-linker. The PMMA core was removed by methylene chloride etching to leave PS nanospheres, as illustrated in Figure 6.2. The particle diameter was 15-30 nm, with a shell thickness 2-5 nm. Similarly, near monodisperse PS microspheres have been prepared by dispersion polymerization using PDMA-bpoly(alkyl methacyrylate) diblocks as stabilizers.49

Figure 6.2 Fabrication of hollow polystyrene nanospheres using block copolymer micelles as nanoreactors for sequential polymerization of PMMA, followed by PS, and subsequent removal of PMMA.48 Reproduced by permission of American Chemical Society.

Addition of PEP-b-PEO diblocks has been shown to dramatically improve the solubilization capacity of nonionic surfactants such as CioEO4 in water/ decane amphiphile microemulsions.50,51 The structure of PEP-b-PEO is of course chemically similar to that of the alcohol ethoxylate surfactants (although with branching) - for example, PEP10-b-PEO10 corresponds roughly to C715EO210.51 The interfacial tension is reduced dramatically upon addition of the block copolymer and the microemulsion can swell to a greater extent. The surfactant volume fraction required to form a balanced one-phase microemulsion is reduced by a factor of about four by using the surfactant/block copolymer mixture. The formation of lamellar mesophases, usually observed when the hydrophobic content of the amphiphiles is increased, is not observed using the block copolymer additive. The effect was ascribed to the ability of the polymer chains to extend further into the adjacent subphases. Contrast variation SANS was used to probe the curvature of the amphiphilic

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membrane and the dependence of membrane volume fraction on block copolymer number density and chain dimensions was probed.51 PEO-based block copolymers have been used as stabilizers to prevent flocculation of PMMA microparticles sprayed into liquid CO2.52 Reverse Pluronics PPO-b-PEO-b-PPO (and also Tetronic stars) and PEO-b-PEO diblocks were used, the PEO acting as steric stabilizer, the hydrophobic block anchoring on the PMMA. The stabilization of foams by block copolymers has been investigated.53 For example, measurements of the disjoining pressure in films containing PEO-b-PEO diblock or PEO-b-PEO-b-PEO triblock copolymer have been combined with timeresolved ellipsometric determination of the adsorption rate and time-resolved surface tensiometry. Measurements of the interactions between the two air-liquid interfaces in the foam were performed via the thin film balance technique, in which the film thickness and disjoining pressure isotherm are monitored. It was found that film stability at high pressure was higher for the films containing diblock copolymers due to more efficient packing at the interface. Micellization of block copolymers in supercritical CO2 has been studied by several groups.54-58 The work has been motivated by the fact that block copolymers containing CO2-philic blocks have been shown to be very effective surfactants in emulsion polymerization.59,60 The micellar corona is usually formed by CO2-philic perfluorinated55-58 or partially fluorinated blocks. The use of block copolymers as stabilizers in supercritical fluids has been reviewed.61 Micellization of fluorinecontaining block copolymers to form particles with highly hydrophobic cores has been investigated.13,62

6.3 DRUG DELIVERY Applications of block copolymers in the pharmaceutical industry have been extensively reviewed, in particular in several special issues of Advanced Drug Delivery Reviews, 63-71 but also elsewhere.72-77 It is not intended to reiterate all of this information here, but salient features will be highlighted. The main types of polymer investigated have been PEO-based block copolymers, either PEO-b-PPO-b-PEO Pluronics, PEO-b-polyesters or PEO-£-poly(L-amino acid)s.76 Pluronics are readily available commercially, PEO-b-polyesters benefit from the susceptibility of the polyester block to hydrolytic degradation and PEO-b-poly(L-amino acid)s contain functional groups that may be used for targeted delivery. All of these copolymers can be used as drug delivery systems, sustained release agents, coatings, adjuvants (materials that increases the immune response to an antigen when combined with it), emulsifiers and dispersants and anti-hemolytic agents among other applications. Polymeric micelles containing PEO offer advantages compared with other systems (microspheres, liposomes, etc.) of greater stability, decreased uptake by the reticulo-endothelial system (RES, a system of cells responsible for removal of foreign substances and pathogens from the bloodstream) and thus longer circulation

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times and enhanced passive accumulation in tumours via the enhanced permeability and retention (EPR) mechanism.78 Several reviews cover specific applications such as the use of PEG-based micelles as carriers for contrast agents in medical imaging (MRI or computed tomography)68 or for delivery of photosensitizers for photodynamic therapy.71 Another example is the use of polyether-b-polyester diblocks in formulations of paclitaxel, due to problems of hypersensitivity with the current formulation of taxol, the anti-cancer drug.69 The development of Pluronic copolymers for applications in drug delivery has largely been pioneered by Kabanov and coworkers.79 These materials are attractive due to the ready commercial availability of a wide range of copolymers (with different composition and molar mass), low toxicity, and well characterized physicochemical properties. They investigated the use of Pluronic micelles as delivery agents for drug targeting across the blood-brain barrier.80,81 They have also shown that unimers inhibit immune response. They have recently studied block ionomer complexes as carriers for DNA, as reviewed in detail elsewhere63,82 (and mentioned in Section 4.4). Kataoka et al. have studied the biomedical and pharmaceutical applications of PEG-b-PLA diblocks with functional group terminated PEG corona chains. The relevant papers are cited in a comprehensive review.70 A schematic summarizing various applications exploiting micelles in bulk and also for surface modification is shown in Figure 6.3. PLA is biodegradable and nontoxic and is widely used in implant materials. The PEG corona block bears an acetal or aldehyde end group to

Figure 6.3 Schematic showing applications of PEG-b-PLA block copolymers for biomedical applications.70 Reproduced by permission of Elsevier.

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enable functionalization. Nanospheres have been prepared by core cross-linking of heterobifunctional diblocks.83 The polylactide block was terminated by a methacryloyl moiety for cross-linking of the core. The micelles with polymerized core could be adsorbed intact onto a coated surface (in contrast to micelles without polymerized cores).84 Applications of PEO-b-poly(L-amino acid) micelles for drug delivery have been reviewed by Kataoka et al.65 Kwon and coworkers also discuss such systems.67 The core-forming poly(L-amino acid) is nonpolar and can solubilize hydrophobic drugs. Conjugates of the drug molecules with the block copolymer have also been prepared. This type of copolymer has also been used for DNA delivery applications. A PEG-b-PAsp diblock has been used as steric stabilizer in the coprecipitation of DNA with calcium phosphate, to control the growth of Ca3(PO4)2 crystals containing DNA.85,86 Controlling the size distribution is essential since transfection efficiency is strongly influenced. Calcium phosphate/DNA coprecipitates have attracted interest in transfection of plasmid DNA for applications in gene therapy. The copolymer solution containing phosphate ions was mixed with DNA in the presence of calcium ions and crystals with a relatively narrow size distribution were formed. Kataoka and coworkers have studied the properties of PEO-b-PAsp block copolymers, and potential applications which arise from the fact that both blocks are biocompatible and the steric stabilization conferred by PEG.87-89 Conjugation with adriamycin (ADR) to give PEO-b-poly(Asp(ADR)) diblocks enables the preparation of an anticancer drug delivery system. Conjugation inhibits side reactions which can damage ADR - unconjugated material can be removed from the micelles formed in aqueous solution by dialysis.89 The antitumour action in vivo, long blood circulation times (conferred by the PEG micellar coating) and cytotoxicity have been extensively characterized.87-89 The same group earlier investigated the effect of modification of secondary structure through side group substitution in PEG-PLys diblocks.90 The substitution (to a varying extent) of hydrocinnamoyl groups in the N£ position of the amino acid afforded control of the hydrophilic/hydrophobic balance, and of TT-TT interactions. Increasing the degree of substitution, or pH, led to a transition from a random coil to a (3 sheet structure (which is stabilized by side-chain interaction between aromatic groups). Micellization of polymers with a ß-strand structure was also observed. Applications of block copolymer gelation in the development of thermally controlled delivery systems for slow drug release have also been explored. A micellar solution containing solubilized drug molecules is injected into the body at a suitable temperature (Figure 6.4). Gelation then occurs at body temperature (37 °C), providing a matrix for slow release. The use of PEO-based copolymers in this context has been widely reported, and several reviews are available.2,3,79 In particular, PEO-bPPO-b-PEO triblocks are commercially available materials suitable for such applications. The concept has also been demonstrated with block copolymer micelles containing biodegradable polylactide blocks, which further facilitates elimination of the polymeric drug delivery system following release. Jeong et al. have shown that by adjusting the length of the biodegradable PLLA block in PLLA-b-PEO

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Figure 6.4 Principle for a slow release drug delivery system using a block copolymer gel.91 A sol of block copolymer micelles containing solubilized drug is injected at room temperature. It then forms a gel in vivo (gel temperature Tt), which is slowly degraded to release the drug. Reproduced by permission of Nature.

diblocks, and the copolymer concentration, the transition from a high temperature solution to a gel can be manipulated to achieve this.91,92 They further demonstrated the slow release in vitro of a model drug. By use of a different copolymer, PEG-bPLGA-b-PEG [PLGA = poly(D,L-lactic acid-co-glycolic acid], a system exhibiting a sol at room temperature and a gel at body temperature was demonstrated.93,94 Control of the sol-gel phase transition boundary through the addition of salts was also explored.93 The integrity of the gels was examined in vivo using a rat model.94 The same group has also examined the use of graft copolymers, for example PEG grafted with PLGA.95 The use of (PEO-b-polylactide)n (n = 4 or 8) star-block copolymers has also been suggested,96 because it has been shown that degradation is slower for this architecture than for linear copolymer, due presumably to steric effects. The hydrophobic polylactide was either poly(L-lactide) or poly(L-lactide-coglycolide). Micellization of PEO-b-poly(ethyl acrylate) diblocks has also been studied in the context of drug delivery systems.97 Poly(ethyl acrylate) is moderately hydrophobic and has a low glass transition temperature, facilitating dynamic micellization. Micellization of PEG-b-poly(lactide) block copolymers has also been investigated by other groups, who have highlighted the enhanced blood circulation times and reduced uptake by the liver of these PEG-coated micelles, compared with poly(lactide) nanoparticles.98'99 The biodegradability of the poly(lactide) block is also important. Booth and coworkers have also studied block copolymer systems in which the micellar solution can be injected at room temperature, gelation occurring at high temperature.100,101 In particular, they have demonstrated sustained release of salicylic acid from a gel formed by a PEO-b-PBO-b-PEO triblock in aqueous

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solution102 and have investigated the solubilization of another model hydrophobic drug, griseofulvin, in micelles formed by diblocks and triblocks of EO with PO or SO.103 They have also investigated the gelation of PEO-£-poly(D,L-lactic acid) diblocks - only a high temperature gel - sol transition was observed, i.e. cold gelation necessary for applications was not observed.104 Drug release properties were not examined. Armes and coworkers have recently developed biocompatible, stimulusresponsive gelators based on triblock copolymers containing 2-methacryloyloxyethyl phosphorylcholine (MPC).105,106 The phosphorylcholine motif is an important component of cell membranes and surface coatings containing it are remarkably resistant to protein adsorption and bacterial/cellular adhesion. The triblocks with symmetric DEA or DPA end blocks are molecularly dissolved at low pH, but form flower micelles or gels at pH 8, depending on polymer concentration (Figure 6.5).106 The microstructure and rheology of the gels and solutions were later studied in detail.107 It was noted that the dynamic elastic moduli were considerably

Figure 6.5 Schematic showing flower micelle formation and gelation in PDPA-b-PMPC-bPDPA triblocks.106 Reproduced by permission of American Chemical Society.

lower than those of Pluronic triblock gels in aqueous solution at similar concentrations, an effect ascribed to reduced bridging of micelles in the MPC-based block copolymers. Release studies using a model hydrophobic drug indicated that PDPAb-PMPC-b-PDPA gels retain the drug longer than PDEA-b-PMPC-b-PDEA gels, probably due to the greater hydrophobicity of PDPA than PDEA.106 Triggered release is possible because gel dissolution occurs at low pH. Polyion complex micelles have also been exploited to encapsulate charged molecules, such as DNA or certain enzymes due to electrostatic interactions with an oppositely charged core-forming block.63,65,66 The PEG block forms a steric stabilization layer, also termed 'palisade'. PEG-b-cationic block copolymers employed to form PIC micelles with DNA include PEG-b-PLys, PEG-b-PEI and PEG-b-PDMA.66 Further information is provided in Section 4.4. Shuai et al. examined DNA condensation using PEG-b-PLys diblocks.108 The transfection using complexes containing monomethoxyl PEG-b-PCL has also been examined, also for copolymers in which these blocks are grafted onto hyperbranched PEL109

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The development of neutral-b-cationic block copolymers for gene therapy applications has been explored by Kabanov and coworkers. Several systems with PEO as the neutral block and different cationic polymer blocks have been investigated.63,79 Compared with cationic homopolymers used for gene delivery, incorporation of PEO in a block copolymer confers improved solubility (even if all electrostatic charges are neutralized63) and steric stabilization. A proposed mechanism for transfection of plasmid DNA via endocytosis is illustrated in Figure 6.6.

Figure 6.6 Schematic showing transfection of plasmid DNA into a cell via endocytosis using a block polyelectrolyte.258 Reproduced by permission of Royal Society of Chemistry.

The incorporation of sugar units onto PEG chain ends that form the coronas of micelles has been reported for PEG-b-PDLL diblocks.110 The sugar groups (e.g. glucose or galactose) should enable cellular-specific targeting via glycol receptors on the cell membrane. The potential use of such sugar-coated micelles in drug delivery is evident. The Kataoka group has shown that specific recognition of lectin proteins (i.e. those that specifically bind carbohydrates) is possible with this type of micelle.111 Surface plasmon resonance has been used to investigate the interaction between lectins immobilized on a gold surface and lactose-coated PEG-b-PDLL diblock micelles, adsorbing from solution.112,113 Micelles from diblock copolymers containing glucose and galactose groups end groups have been characterized, and

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their interaction with lectin immobilized on a GPC column was examined.114 Diblocks were prepared using protected glucose and galactose containing initiators, used for ATRP of PEGMA-b-PBzMA. The preparation of sugar-coated shell crosslinked micelles is discussed in Section 2.12.4. Vesicles may also be used in drug delivery applications, as discussed in Section 6.7 and reviewed elsewhere.74 Other applications of block copolymers in medicine are discussed elsewhere.3,79 Examples include the use of Pluronic copolymers in artificial blood formulations, anti-tumour and anti-inflammatory agents and surgical dressings.

6.4 BIODEGRADABLE BLOCK COPOLYMER MICELLES Applications of biodegradable block copolymers have recently been reviewed.115 The main class of biodegradable copolymer contains polyesters or polyester sequences. Applications include surface modification, hydrogel formation and micelles for drug delivery. The latter subject is discussed in detail above. Surface modification generally involves coating with PEG chains by adsorption of a block copolymer. PEG can prevent biofouling. As mentioned in the preceding section, Kataoka and coworkers have investigated end-functionalization of the PEG as a route to conjugate proteins to the surface, for example.70,116 Biodegradable hydrogels based on polylactide-containing copolymers have been extensively studied,91,117,120 due to potential applications in drug delivery. The copolymers comprise a water soluble PEG midblock with hydrophobic polylactide end blocks. The gelation transition depends on copolymer composition and concentration. Further details are provided in the preceding section. Gelation of triblock copolymers containing a PLGA midblock and short PEO endblocks has been investigated by Char and coworkers.121,122 A particular focus was rheological and structural characterization of the turbid gels formed at high temperature, as well as transparent gels formed at low temperature. The turbidity results from aggregation of micelles, which leads to complex dynamics, as manifested for example by a plateau in the decay of the intensity autocorrelation function obtained from DLS122 (see also Section 3.10.2). This was ascribed to a phase separated structure containing heterogeneities resulting from the percolation of micelle clusters. These copolymers were contrasted to Pluronic copolymers in that the PLGA midblock is more hydrophobic than PPO, leading to enhanced attractive interactions between micellar cores. Tew and coworkers have examined the gelation of PLLA-b-PEO-b-PLLA triblocks via rheological experiments.123 Biodegradable micelles formed from block copolymers containing PCL have been investigated by Nie et al.124 The enzymatic degradation kinetics were investigated and it was noted that simply monitoring pH provided a good measure of degradation rate. The enzymatic biodegradation of the PCL core in PCL-b-PEO micelles has been probed by light scattering.125

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6.5 THERMORESPONSIVE MICELLAR SYSTEMS Thermoresponsive block copolymers have been prepared using PNIPAM as the thermosensitive hydrophobic block. PNIPAM exhibits a lower critical solution temperature (LCST) at Tc= 32 °C. Cross-linked gels pass through a volume phase transition at this temperature, shrinking dramatically as water is expelled.126'127 Although there is an extensive literature on random copolymers with NIPAM (for recent examples see references127-129 there have been fewer studies on block copolymers. The micellization of PNIPAM-b-PEO, poly(NIPAM-co-HPMA)-b-PEO and poly(NIPAM-co-HPMA-lactate)-fr-PEO diblocks has been investigated.130 PHPMA is interesting since it was originally developed as a biocompatible polymer for drug delivery applications. Increasing the PHPMA content enables the cloud point to be reduced, indicating an increase in the hydrophobicity of the corresponding block. On the other hand, the hydrolysed block containing PHPMA lactate becomes more hydrophilic. By varying the composition of the copolymer it was possible to engineer a system forming micelles at body temperature that break up during hydrolysis. Furthermore, the hydrolysis kinetics can be controlled through the number and length of oligolactate grafts in the copolymer. This is attractive for drug delivery applications. In a similar vein, the thermoresponsive behaviour of PHPMA-b-PNIPAM diblocks has been studied.131 Large increases in hydrodynamic radius and aggregate molar mass were observed above the LCST of PNIPAM. This was ascribed to enhanced hydrogen bonding in the collapsed state, leading to the formation of aggregates. Several groups have investigated micellization in PNIPAM-b-PEO diblocks.130'132'133 Topp et al. also prepared PNIPAM-b-PEO-bPNIPAM triblocks.132 These studies report that the PEO block increases the LCST and stabilizes micelles. Okano and coworkers have investigated the micellization of diblocks comprising PNIPAM with hydrophobic blocks - either PS 134 or biodegradable PDLL.135 Micelles were formed below the LCST. Above the LCST clouding was observed due to micellar aggregation as the PNIPAM chains collapsed. The aggregation process was found to be reversible. It was noted that the low cmc values observed would favour long circulation times of the micelles in blood and that the hydrated outer shell (below the LCST) would hinder uptake by the RES.134 Since the micelles can also solubilize hydrophobic molecules including an anti-cancer drug, they have potential as drug carriers. Since tumour sites may have a locally higher temperature, the thermoresponsivity of the PNIPAM shell can be exploited to target delivery above the LCST where binding interactions with cell membrane surfaces are favoured.134 In a further development of PNIPAM-based copolymers, double responsive PNIPAM-b-PAA diblocks have been prepared.136 Since PAA is a pH-sensitive polyelectrolyte, the system exhibits thermal and pHresponsiveness. Micelles with a PNIPAM core and PAA corona are formed at high pH and T > Tc where the PAA is deprotonated and PNIPAM is collapsed. For pH < 4 and T < Tc, micelles with a protonated PAA core and PNIPAM corona are formed. At pH < 4, T > Tc aggregation is observed.

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Cationic polymerization has been used to prepare another type of thermoresponsive diblock copolymer based on poly(vinyl ethers.137 The hydrophilic block is PHOVE, and the thermoresponsive hydrophobic block was one of three types of poly(vinyl ether) with a pendant terminal alkyl unit. A transition from a micellar solution to a gel (ordered cubic micellar structure) was observed on heating. A practical disadvantage of the system may be the closeness of the critical micelle temperature and critical gel temperature, these being separated by less than 0.5 °C. The sol-gel transition in thermoresponsive lactide-based linear91'94 and star96'138 block copolymers has also been mapped out, as discussed in the previous section.

6.6 METAL-CONTAINING COPOLYMER MICELLES AND NANOREACTORS Block copolymer domains can be used as 'nanoreactors' for the synthesis of inorganic nanoparticles. Reviews of the subject are available.8'139'140 Two basic approaches have been developed. The first involves the binding of inorganic species to the monomer prior to polymerization or to one of the blocks of a copolymer prior to micellization (which may be induced by the ion binding ). The most important approach, however, involves the loading of preformed micelles, whether in solution or in bulk. Cohen et al. have systematically examined the preparation of diblock copolymer nanoreactors, which are subsequently loaded with salt that is then reduced to form metal nanodomains. They have demonstrated the patterning of complexes of silver,141-143 gold141 and zinc.144 The metal salt is added after formation of the diblock, and coordinates to a norbornene-based block, whilst the other block is built from PMTD. The copolymer/metal salt solution is then dried and the thin film morphology observed. For the silver and gold systems, spherical, cylindrical and lamellar metallic domains were observed, after heat treatment.141-143-145 Using zinc-containing complexes, zinc fluoride and zinc sulfide clusters were obtained, within spherical domains 144 and also lamellae.146 This concept was later generalized by creating carboxyl-functionalized nanoreactors within which a variety of metal salts can be sequestered (Figure 6.7).147'148 The carboxyl moiety was again a norbornene derivative. Metal oxide nanoparticles such as CoFe2O4 (of interest for high-density magnetic recording applications) have been prepared in a similar way.149 NaOH was used to form the oxide from the chloride salt precursor. Metal sulfides have also been produced by reaction of the precursor complexes with H2S.147'150'151 Particularly relevant to quantum dot applications of semiconductor nanoparticles, Moffitt et al. described the preparation of CdS nanoparticles within the cores of PS-b-poly(cadmium acrylate) diblocks from organic solvents.152'153 The particle size could be controlled in the range 2.9-5 nm by changing the length of the ionic poly(cadmium acrylate) block. The preparation of PbS nanoparticles was also described.152 An alternative approach to the preparation of CdS

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Figure 6.7 Schematic of block copolymer nanoreactors, whereby a carboxy functionalized domain is loaded with metal ions or complexes.148 Reproduced by permission of Elsevier.

nanoparticles exploits complexation with the P2VP core of PS-b-P2VP micelles.154 Here, the nanoparticles are aggregated into 'raspberry' morphology clusters. A disadvantage of the methods introduced by Cohen et al. is the need to synthesize polynorbornene-based block copolymers, which furthermore are not available commercially. Other complexation chemistries may be preferred. A useful compilation of functional blocks for the complexation of inorganic materials is available.8 The same authors also attempt to rationalize the ability of polymers to solubilize inorganic molecules by reference to hard-soft acid-base interactions. Spatz et al. have produced titania nanoparticles within block copolymer micelle nanoreactors.155 Titania nanoparticles are interesting for applications such as catalysis, water purification and UV blocking. They prepared micelles from a PS-b-PEO diblock in a nonpolar solvent with a PS corona and a PEO core. HC1 was mixed with the micelle solution to create reservoirs within the micelle cores. Titanium alkoxides were then added, the reaction with the acid and subsequent

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heating leading to the formation of TiO2 particles. Individual particles and chains were both obtained. The same group have also used aqueous solutions of PS-bP2VP diblocks to form gold nanoparticles by reduction of HAuCl4 solubilized in the micellar core (as discussed also in Section 5.3.3). Below the cmc, nonspherical agglomerated particles were observed, showing that it is necessary for the reduction to occur in micellar 'nanoreactors' to get well defined spherical nanoparticles. Figure 6.8 illustrates the low polydispersity of nanoparticles that can be obtained in

Figure 6.8 TEM image showing well-defined gold nanoparticles in a dried film of goldcontaining PS-b-P2VP micelles.259 Reproduced by permission of American Chemical Society.

this way. Sakai and Alexandridis have shown that gold nanoparticles can be fabricated from HAuCl4.3H2O using Pluronic block copolymers, without additional reducing agents.156 The AuCl-4 ions are reduced by the PEO (the mechanism for this is discussed), and the block copolymer stabilizes the colloidal dipersion of the resulting nanoparticles. The effect of copolymer composition and molar mass on the nanoparticle formation was also investigated. Micellar nanoreactors for metallic nanoparticles based around several different block copolymers have been investigated by Bronstein and coworkers. In many cases, the ability of poly(vinylpyridine), P2VP or P4VP, to form complexes with metal salts due to the presence of an N atom is exploited.157-159 For example, Pd

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clusters have been produced by reduction of Pd(CH3COO)2 that coordinates to the P4VP micellar core formed by PS-b-P4VP diblocks in toluene.157,160 Other metal nanoclusters including cobalt,161 gold,157,159,160 rhodium157 and platinum157 have been prepared in a similar way. The catalytic hydrogenation properties of the nanoclusters have been compared.157,160 Bimetallic colloids have also been prepared.157 The methods may be extended to thin films where surface interactions may be exploited to prepare highly aligned nanostructures. Antonietti and coworkers have extended the range of amphiphilic diblocks that act as nanoreactors by demonstrating the production of metal nanoparticles within micelles of diblocks derived from PS-b-PB.162 The PB was first epoxidized, then the oxirane ring was opened to introduce a variety of functional side groups (nucleophiles, acids, acid chlorides), designed to complex with metal salts. Loaded micelles were formed by dissolution in toluene and mixing with the metal salts. Colloidal gold, silver, palladium and rhodium were all prepared by reduction of the metal salts in the block copolymer micelles. The formation of metal complexes with the double bonds in PB in block copolymers with PS has been examined via 1H NMR and IR spectroscopy.163 It has been shown that a core consisting of PB complexed to metal can be prepared by dissolution in a solvent selective for PS.164 In a variant of the method for nanoparticle templating introduced by Bronstein et al., the patterning of palladium particles at the domain interface in a PI-b-P2VP diblock has been demonstrated, and ascribed to 'polarization' of the nanoparticle at the interface.165 Using PS-b-PEO12 or P4VP-b-PEO166 diblocks, it is possible to prepare nanoparticles in aqueous media, although the micellization is influenced by pH and by the presence of the metal salts. The same group have also developed mixed micelles containing a nonionic PS-b-PEO diblock and a cationic surfactant (cetylpyridinium chloride).167 The aim was to prepare nanoreactors based on charged micellar cores (similar to the concept introduced by Clay and Cohen; (Figure 6.7). The counterions in the micellar corona are exchanged by anions such as PtCl2-6 and PdCl26-. The concept can be extended to mixed micelles containing anionic surfactants with cationic counterion exchange, as exemplified by the system PS-b-PEO/SDS.168 Exchange of the Na+ cation with a rhodium species enabled the loading of the corona with the latter. Reduction using NaBH4 led to clusters of rhodium nanoparticles within micellar aggregates. Nanoreactors containing transition metal binding sites in the core have been prepared from amphiphilic poly(2-oxazoline) block copolymers in aqueous solution.169'170 The sequestered triphenylphosphine moieties were expected to lead to catalytic activity. These hydrophobic groups were introduced into the block copolymer by a polymer analogous Pd-catalyzed phosphorus–carbon coupling reaction, leading to a statistical copolymer with pendant functional groups. Double hydrophilic block copolymers have also been used to template the production of metal hydrous oxide nanoparticles.171'172 The block copolymers contained a PAA anionic metal-binding block and a neutral block of PAM or PHEMA that conferred colloidal stability. Elongated and spherical lanthanum and aluminium hydrous oxide particles were observed.

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Rod-like block copolymer micelles can be used as scaffolds to prepare metal nanowires. This has been demonstrated using diblock copolymers consisting of a carbosilane dendrimer and a polyisocyanopeptide, silver ions preferentially forming complexes with the peptide units that form the micellar core.134 The concept can presumably be extended to simpler block copolymers containing a polyelectrolyte block. Polymer/palladium nanowire hybrids have been prepared using nanotubes fabricated from core-shell tetrablock copolymer cylinders, as illustrated in Figure 6.9.174 The procedure is illustrated in Figure 6.10.174 Tetrablock

Figure 6.9 TEM image showing Pd-loaded nanofibres prepared from nanotubes prepared by cross-linking of the P(CEMA-ran-HEMA) domain and removal of the PI cores formed in core-shell cylinders of PI-b-PfBA-b-P(CEMA-ran-HEMA)-6-PSMA tetrablock copolymers.174 Reproduced by permission of American Chemical Society.

Figure 6.10 Procedure for preparation of Pd-loaded nanotubes from PI-b-PtBA-b-P(CEMAra«-HEMA)-b-PSMA tetrablock copolymers (A). (B) Micelle formation. (C) Cross-linking of the P(CEMA-rarc-HEMA) domain. (D) Removal of the PI cores. (E) Loading of nanotubes with PdCl2. (F) Reduction to form Pd-plated nanotubes.174 Reproduced by permission of American Chemical Society.

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PI-b-P?BA-b-poly(CEMA-ran-HEMA)-b-PGMA copolymers self-assembled into cylindrical aggregates in aqueous solution. The core comprised core-shell cylinders of PI then PtEA then P(CEMA-ran-HEMA). The PGMA formed the water soluble corona. The P(CEMA-ran-HEMA) layer was cross-linked followed by ozone etching to remove the PI core to form nanotubes, which may then be coated with Pd using an electroless method. An alternative approach has been used by this group in which bulk nanostructures formed by an ABC triblock are fixed by shell cross-linking.175 The nanocylinders formed are then dispersed in solvent. PBMA-bPCEMA-b-PriBA triblocks formed cylinders with PtBA cores and PCEMA shells in a PBMA matrix. The PCEMA was photochemically cross-linked, prior to dissolving the polymer film in the THF to produce nanofibres. The PtBA units were finally hydrolysed to PAA to produce PAA-lined nanotubes. It was shown that the nanotubes could be loaded with Fe2O3 due to ion exchange of Fe2+ with the protons of the acrylic groups. The concept of fixing bulk structures formed by ABC triblocks and then dissolving in a selective solvent was used to prepare Janus micelles, as discussed in Section 2.12.5. An alternative approach has been developed by Stamm and coworkers using the concept of dissolution of a melt structure (see Section 2.12.5) to prepare isolated PS nanoparticles.176 In this case the melt structure comprising shear-aligned cylinders of PS in a matrix of P4VP (to which the amphiphile pentadecylphenol was conjugated) were dissolved in a P4VP-selective solvent. This led to the formation of PS cylinders coated with P4VP. Pd nanoclusters could be deposited directly onto the nanorod templates by electroless deposition due to a direct redox reduction with the P4VP. In a similar fashion, CdSe nanowires could be fabricated. The harnessing of supramolecular chemistry to prepare diblocks containing a metal complex has recently been used to create metal-containing micelles.177,178 Diblocks were formed by complexation between PS and PEO homopolymers, each of which was end-capped with a terpyridine ligand that forms a tri-coordination complex with ruthenium. The result is a diblock, denoted PS-[Ru]-PEO that contains a Ru complex linking group (Figure 6.11). In aqueous solution, micelles are formed with a PS core surrounded by a Ru complex shell, to which PEO corona chains are tethered. The micellization was compared with that of a covalently bonded PS-b-PEO diblock.178 The presence of the charged metal-ligand complex at the interface between the blocks was found to lead to a large increase in hydrodynamic radius. Addition of salt screens the charge on the Ru complex and leads to a reduction in radius towards that of the covalently bound copolymer. This was ascribed to reduced stretching of the PEO block which appeared to have certain characteristics of polyelectrolyte chains. The concept has been extended to ABC triblocks - spherical core-shell-corona micelles were observed for PS-b-P2VP[Ru]-PEO in aqueous solution in which the P2VP shell is pH sensitive.179 The micellization of block copolymers containing the organometallic block PFS has been investigated by Manners and coworkers. 180-184 Block copolymers containing PFS are of interest because PFS has intriguing charge transport properties, and has been investigated as a precursor material to magnetic ceramics. Spherical

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Figure 6.11 Schematic of a PS-[Ru]-PEO diblock that contains a Ru complex linking group.178 Reproduced by permission of American Chemical Society.

and rod-like micelles were observed for a PFS-b-PDMS-b-PFS triblock 180,183 and several PFS-b-PDMS diblocks 181,184 in n-alkanes, which are selective solvents for PDMS. By varying the temperature of micelle formation with respect to the melting point of the crystalline PFS block, it was found that crystallization has a major influence on micelle shape - spherical micelles were observed above Tm, and rodlike ones below. Flower-like aggregates of rod-like micelles were also noted,180,183 again being ascribed to the effect of PFS crystallization. Cylinders of these diblocks deposited onto GaAs substrates by aerosol spraying have been used as templates for patterning of lines into ceramic materials.185 Hydrogen plasma etching removed the organic material leaving a ridge of ceramic containing Si, Fe, O and C. Spherical micelles were also observed for a PFS-b-PEO diblock in water.186 Spherical micelles were observed for several PFS-b-PI diblocks in THF, a selective solvent for PI.182 In addition, the PI corona of the micelles was cross-linked using UV radiation to yield polymer shells containing a dense metal-containing core.

6.7

VESICLES

The preparation and properties of block copolymer vesicles are discussed in Section 2.17. Here we focus on proposed applications. The use of block copolymer assemblies as synthetic cell elements has been discussed.187 Vesicle bilayers are analogous to cell membranes, and giant wormlike micelles may be synthetic models for filaments in the cell. Due to their enhanced toughness and rigidity, block copolymer 'polymersomes' are much more robust than conventional liposomes. The ability to cross-link the chains of course enables significant additional enhancement in mechanical properties, as discussed below. Liu and coworkers have investigated a number of routes to the preparation of hollow polymer nanospheres for controlled release applications using cross-linked

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block copolymer vesicles. 188 They prepared PI-b-PCEMA vesicles in THF/hexane solutions. The PCEMA shell was photo cross-linked. 188 The PI chains were then hydroxylated to give water soluble vesicles with a hydrophilic coating on both sides of the shell (Figure 6.12). These were used to solubilize a dye compound, the

Figure 6.12 Vesicles formed from PI-b-PCEMA diblocks, following PCEMA shell crosslinking and hydroxylation of the PI core.188 Reproduced by permission of American Chemical Society.

release of which was studied via measurements of fluorescence intensity. The potential of nanocapsules with a cross-linked diblock shell for drug delivery applications was highlighted.188 The enhanced stability of cross-linked nanoparticles (for example in the bloodstream) and the ability to tune the capsule size and to incorporate responsive and/or functional moieties are additional advantages offered by the use of polymers. In an alternative approach, micelles of PSMA-b-PDMA were formed in aqueous solution with PDMA coronas and PSMA cores.189 The PDMA coronas were then chemically cross-linked. Finally the cores of the nanospheres were made hydrophilic by hydrolysis of the nitroxide groups in PSMA. It should be noted that this approach does not produce hollow spheres, and it is not clear how the uptake and release of hydrophilic compounds across the cross-linked shell can be decoupled. Methods to prepare hollow nanospheres have also been

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developed for ABC triblocks. PI-b-PCEMA-b-PtBS micelles were formed in THF/ methanol mixtures.190 The PCEMA shell was cross-linked, and the PI core removed by ozonolysis to leave PCEMA shells with a PtBS coating. In contrast to the two-stage procedure used by Liu et al. (cross-linking of the shell plus hydrolysis or ozone etching of the core), Meier and coworkers have pioneered a one-step route to prepare nanoshells from block copolymer vesicles.191,192 Vesicles were formed upon dispersion of an ethanolic solution of PMOXA-b-PDMS-b-PMOXA triblocks into aqueous solution. The PMOXA shell bears polymerizable end groups which can then be photo cross-linked,191 as illustrated in Figure 6.13. The resulting nanocapsules are mechanically stable, and also

Figure 6.13 Schematic showing polymerization of PMOXA-b-PDMS-b-PMOXA block copolymer vesicles.191 Reproduced by permission of American Chemical Society.

retain their shape upon dispersion in organic solvents. Free-standing planar membranes with areas of approximately 1 mm2 were also prepared using this chemistry, and the enhanced mechanical properties (stability against electric field-induced rupture) of these films were compared with those of lipid bilayers.193 In a beautiful concept demonstration, pore-forming transmembrane proteins have been incorporated within triblock copolymer planar membranes194 and vesicles (Figure 6.14).195 The functionality of the bacterial porin OmpF is retained after its incorporation into the block copolymer membrane. When incorporated into the membrane, this protein forms channels that exclude molecules with molecular weights above 400 Da. Responsive nanocapsules can be fabricated containing these channels, and these have great potential for targeted drug delivery and diagnostics.192 It has further been shown that such porous nanocapsules can be used to prepare calcium phosphate nanoparticles, where the Ca2+ is transported across the shell through the ion channels.196 Another application uses the cross-linked vesicles as nanoreactors. The

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Figure 6.14 Nanoreactor comprising a cross-linked block copolymer vesicle encapsulating the enzyme ß-lactamase which catalyses the hydrolysis of ampicillin.197 Reproduced by permission of Royal Society of Chemistry.

enzyme ß-lactamase was encapsulated and used to hydrolyse ampicillin, which is a ß-lactam antibiotic.195,197 The concept is illustrated in Figure 6.14. Application of a transmembrane voltage above a certain threshold causes a reversible gating action of the OmpF.195 Polyelectrolyte added to the solution was shown to trigger the gating transition. The Donnan equilibrium established leads to a concentration difference of polyelectrolyte chains either side of the membrane. If this exceeds the gating potential, the channels are closed and the nanoreactor is deactivated. Incorporation of the bacterial channel forming protein LamB into block copolymer vesicle membranes enables DNA to be transported into the nanocontainer, since LamB serves as a receptor for A phage to trigger the ejection of A phage DNA.198 If the compositional asymmetry is large enough, PMOXA-b-PDMS-b-PMOXA triblocks self-assemble into hollow nanotubes in aqueous solution.199 The tube diameter was relatively uniform (40 nm) with a length extending to several tens of microns. As discussed in Section 2.17, Discher et al. prepared block copolymer vesicles using PEO-b-PEE diblocks.200 The nanocapsules possess enhanced toughness and reduced water permeability compared with liposomes. The use of these particles in protein encapsulation has been comprehensively studied.201 The vesicles exhibit good long-term stability in blood plasma, i.e. phagocytosis is inhibited. Cell viability was also shown not to be adversely affected by addition of the polymersomes. In contrast to liposomes, the block copolymer vesicles can withstand harsh thermal treatments, to some extent although the vesicles shrink and leak their contents. It was proposed that these properties result from steric stabilization

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conferred by PEG. Compared with PEG-lipids, the polymersomes offer much improved mechanical stability and stability against dilution. Polymer vesicles formed by block copolymers containing polypeptide blocks, i.e. so-called 'peptosomes' have been developed based on PB-b-poly(7-L-glutamic acid) (Figure 6.15).202-204 The helix-coil transition of the peptide does not change

Figure 6.15 Proposed structure of a PB-b-poly(7-L-glutamic acid) vesicle. by permission of Wiley-VCH.

Reproduced

the dimensions of the peptosome. In contrast, Checot et al. showed that the size of their PB-b-poly(7-L-glutamic acid) peptosomes could be reversibly manipulated as a function of both pH and ion strength. The vesicle hydrodynamic radius increased by 50% when the peptide underwent a transition from an a-helix to a random coil conformation, driven by increasing pH.203,204 These authors also demonstrated UVinduced cross-linking of the PB to produce 'shape persistent stimuli-responsive nanocapsules'. Purely peptide block copolymers have also been shown to selfassemble into peptosomes.205 Poly{Nb-2-[2-(2-methoxyethoxy)-ethoxy]acetyl-Llysine}-b-PLys diblocks self-assembled into giant unilamellar vesicles. Vesicle size could be controlled by adjustment of hydrophobic content or overall copolymer chain length. No release of solubilized dye was observed, over a period of weeks. A copolymer was prepared in which 70% of the L-leucine residues of the hydrophobic domain of the block copolymer were replaced in a statistical manner with L-lysine. At high pH, PLys is not water soluble and it adopts an a-helical conformation. Vesicles similar to those formed by the unmodified copolymers were observed. However, a helix-to-coil transition driven by a reduction in pH caused destabilization of the vesicles and release of their contents. Thus pH-responsiveness was

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demonstrated. The cooperative self-assembly of poly(L-lysine)- b-poly(L-cysteine) block copolymers in the presence of silica and gold nanoparticles can be used to prepare hollow spheres coated with a shell of gold and a shell of silica (Figure 6.16). The cysteine block facilitates disulfide links and these act as attachment points for gold nanoparticles. Introduction of silica nanoparticles then drove the formation of a silica coating. These hollow nanoshells were formed without the use of emulsions or a sacrificial core.

Figure 6.16 Schematic suggested for the hierarchical self-assembly of gold and silica nanopartices into hollow spheres with a two-layer shell structure, using poly(L-lysine)-bpoly(L-cysteine) block copolymers.260 Reproduced by permission of American Chemical Society.

Triblock copolymer vesicles which are unstable to oxidation have been prepared with the aim of developing a responsive system for drug delivery.206 PEG-b-PPS-bPEG triblocks were used, PEG being hydrophilic and poly(propylene sulfide) being hydrophobic but readily oxidized to poly(propylene sulfoxide) and ultimately poly(propylene sulfone), both of which are hydrophilic. This conversion results in the breakup of the vesicles. The resulting individual copolymer chains were short enough to be expected to be readily eliminated from the body. Biodegradable polymersomes have been reported based on PEG-b-PLLA diblocks. 207 The poration of PEG-b-PLLA and PEG-b-PCL vesicles (and mixed vesicles) due to hydrolysis has been investigated.208 Encapsulation of the anticancer agent doxorubicin was also studied. Release kinetics from giant vesicles were studied for model hydrophilic fluorescent encapsulants via phase contrast and fluorescence microscopy. The release (over a timescale from hours to days) was found to occur in a quantized manner, as each vesicle porates and disintegrates individually. A mechanism for the poration process is illustrated in Figure 6.17.

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Figure 6.17 Mechanism proposed for membrane poration due to hydrolysis of polyester in PEG-b-polyester vesicles.208 Polyester chains are shown in light grey. Reproduced by permission of Elsevier.

Release kinetics can be controlled via the PEG content of the copolymer and the hydrophobicity of the other block (PCL is more hydrophobic than PLLA). Porous polymer microspheres have been prepared by using Pl-b-PAA diblocks to solubilize chloromethane containing PI-b-PtBA and homopolymer PtEA as oil droplets in water.209 The PtBA was then hydrolysed and the resulting PAA extracted to leave porous spheres (diameter 0.3-1 u.m). The shape and connectivity of pores could be controlled through the relative content of PtBA in the homopolymer versus diblock. Conjugation of block copolymers to liposomes leads to two scenarios, as shown in Figure 6.18.210 Addition of PEO-b-PPO-b-PEO block copolymer after lipid vesicle formation leads to adsorption, if the block copolymer does not contain too much hydrophobic block (if it does, micellization of the block copolymer predominates). If the polymer is present at low concentration during vesicle formation, however, it can be incorporated into the vesicle membrane, the PPO blocks being incorporated into the hydrophobic compartment.210 In contrast to this work, Johnsson and coworkers found significant morphological changes in liposome structure upon addition of Pluronic copolymers.211 Cryo-TEM was essential in elucidating morphology of the phosphatidylcholine vesicles upon addition of block copolymer. Pluronics with long PEO blocks were found to induce the formation of bilayer disks, whereas those with shorter PEO blocks tend to promote a reduction in liposome size. The Pluronics were found to increase the porosity of the liposomes, as revealed by fluorescence experiments on solubilized dye. Inclusion of cholesterol into the lipid membrane was found to reduce the incorporation of copolymer.

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Figure 6.18 Schematic for interaction between a unilamellar lipid vesicle and a PEO-bPPO-6-PEO triblock copolymer.210 Reproduced by permission of American Chemical Society.

6.8

SEPARATION MEDIA

The use of amphiphilic copolymers in gel electrophoresis has been examined. The selective partitioning between aqueous and hydrophobic domains in two-phase systems with Pluronic and dextran polymer components leads to a distribution between the two phases depending on the hydrophobicity or hydrophilicity of the protein.212-215 The partitioning has been investigated, with the Pluronic in both the unimer and micellar states. The partitioning was found to depend strongly on temperature, but not on micellization per se. Selective partitioning has also been exploited in capillary gel electrophoresis of nucleotides and DNA fragments, as investigated by the groups of Rill216-218 and Chu.219-221 In concentrated solution, Pluronic F127 was shown to form an fcc cubic micellar phase in the buffer solution used for the electrophoretic separations.219,221 Separation of nucleotides up to a few thousand base pairs in length has been demonstrated using this technique,216 and separation of individual nucleotides from standard mixtures (Figure 6.19).217

6.9

TEMPLATING

Block copolymers have been extensively used to template the formation of 'mesoporous' materials.7,140,222 Since the pore size is typically 5-25 nm, these

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Figure 6.19 Separation via gel electrophoresis of double stranded DNA (123 base pairs) using gels of Pluronic F127 (gel concentration indicated).218 Reproduced by permission of AAAS.

materials should probably be termed 'nanoporous'. Compared with conventional nonionic surfactants, amphiphilic block copolymers offer the advantage of larger pore sizes. The templating of silica by amphiphilic block copolymers was first performed using commercially available PEO-b-PPO-b-PEO triblocks.223 A representative TEM image of a hexagonal structure is shown in Figure 6.20. Lamellar or bicontinuous structures have been prepared in a similar manner. Since the pore size and wall thickness can be varied according to the processing conditions, it is evident that the nanoporous silica is not generally a 'cast' of the lyotropic mesophase formed by the triblocks in solution, rather that the copolymers act as structuredirecting agents of the tetraalkoxysilane precursors. Other research teams have investigated the production of mesoporous silica from different PEO-b-PPO-b-PEO triblocks,224-226 and also related PEO-b-PBO-b-PEO copolymers.227,228 The patterning of silica and other metal oxides including TiO2, ZrO2, WO3, etc., was performed in a related procedure, although using chloride salts in ethanol rather than metal alkoxides in acidic aqueous solutions.229,230 It is proposed that complexation occurs between the oxygen atoms in PEO and the multivalent metal

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Figure 6.20 Hexagonal structure of calcined mesoporous silica, templated using a PEO-bPPO-b-PEO triblock copolymer.223 Reproduced by permission of Science.

species in the alkoxides. The production of mesoporous silica in thin films using PS-b-PEO diblocks has been achieved via selective solvent evaporation, which leads to cooperative self-assembly of the diblock and silicate to produce mesoporous silica with hexagonally arranged pores, vesicular structures or rods.231,232 The use of CH3-Si(OCH2CH3)3 with the PS-b-PEO diblock in the synthesis reduces the siloxane condensation rate, allowing cooperative self-assembly of the silica and amphiphile.232 True nanocasting can be achieved starting from a high concentration liquid crystal phase, where the continuous liquid phase undergoes a sol-gel transition. The use of block copolymers in the preparation of mesoporous materials has been discussed in a review of nanocasting methods.233 This route has been explored using block copolymers in which one block is a polyelectrolyte234 or both blocks are non-ionic.235,236 In the former case,234 both cationic and anionic diblocks have been used as structure-directing agents to produce materials with irregular arrays of spherical pores. In the latter case,235,236 diblock copolymers based on PEO have been used. Sol-gel chemistry has also been exploited to prepare metal oxide-containing mesoporous silica with well-defined lamellar and cylindrical structures using Pl-bPEO diblock solutions to template the structure formation.235 It is proposed that the metal alkoxide precursors preferentially swell the PEO block. Condensation then leads to mesoporous silica containing metal oxide. By dissolving the organic component, spherical, cylindrical and plate-like nanoparticles could be prepared.237 These are coated with PEO chains (so-called 'hairy' nano-objects), which can be removed by thermal treatment. A schematic showing the synthetic approach used to prepare these nano-objects is shown in Figure 6.21. In subsequent work, the same team has reported the preparation of a mesoporous silicon/aluminium oxide ceramic

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Figure 6.21 Schematic of the sol-gel approach to synthesize PEO-coated nanoparticles of different shape using a sol-gel synthesis of metal alkoxides templated by PI-PEO diblocks.237 The symbol A indicates thermal treatment. Reproduced by permission of Wiley-VCH.

material with a bicontinuous 'plumbers nightmare' pore structure.238 It is interesting to note the analogous approach using the 'ball-at-the-wall' morphology formed by ABC triblocks in the melt to prepare Janus micelles upon crosslinking the PB 'balls', and dissolution of the lamellar matrix,239 as noted in Section 2.12.5. Antonietti and coworkers used PEO-b-PEB diblock copolymers to prepare porous silica.236 Either a disordered or a regular packing of spherical pores was obtained, depending on polymer concentration. In another variation, the lyotropic phase structure can be fixed by cross-linking the gel structure prior to the templating of silica.240 Diblocks containing PB (with PEO) were used for this purpose, since PB can be cross-linked by 7-radiation. In a related approach, photopolymerization of water and oil-soluble monomers in lyotropic mesophases formed by Pluronic copolymers has been studied.241 The influence of the order in the mesophase on the polymerization kinetics was examined. The resulting materials were polymeric hydrogels. A biomimetic route to the preparation of mesoporous silica has been demonstrated by Cha et al.242 They have developed poly(L-lysine)-b-poly(L-cysteine) hydrophilic-hydrophobic diblock copolypeptides that mimic the properties of the protein silicatein, involved in the condensation of tetraethyoxysilane into silica in, for example, sponges and diatoms. The hydrolysis of silica occurs at neutral pH, in

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contrast to conventional methods that rely on acidic conditions, or the use of organic solvents. Porous silica beads and rods were produced, depending on the copolymer composition. Ordering on multiple length scales can be achieved by confining the mesoporous silica synthesis using Pluronic copolymer templates within the interstices between colloid particles,243 using soft lithography with elastomeric stamps (Figure 6.22),243

Figure 6.22 Soft lithographic moulding of a sol-gel block copolymer precursor solution.243 Reproduced by permission of Science.

or within a macroporous polymer foam.244 Using the soft lithography approach, together with the templated synthesis of mesoporous silica, mirrorless lasing has been demonstrated.243 Arrays of mesas (1-3 um wide, 1-2 um high, 2-8 um spacing, several centimetres long) were patterned, containing mesoporous silica. When doped with laser dye, amplification of stimulated emission within the waveguides was noted. Hollow spheres formed by rod-coil diblocks in a selective solvent can aggregate directly into microporous materials provided the solvent casting conditions are properly optimized.245 Figure 6.23 schematically shows the process, and Figure 6.24 shows a fluorescence photomicrograph of an ordered microporous film prepared in this way. Block copolymers have been used to control the growth of calcium carbonate crystals, in either vaterite or calcite forms.246 Various types of diblock with a PEG hydrophilic block and a second hydrophilic polyacid were employed, the latter interacting strongly with the calcium ions. The crystal size and shape could be

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Figure 6.23 Schematic showing diblock structure and process of formation of microporous material from hollow microspheres formed by its self-assembly in a coil-selective solvent.245 Reproduced by permission of Science.

controlled by appropriate choice of polymer. A PEG-b-PAsp diblock has similarly been used to control the growth of calcium phosphate crystals,85,86 as discussed in Section 6.3. Ikkala and coworkers have demonstrated hierarchical self-assembly in PS-bP4VP diblocks to which the amphiphile pentadecylphenol is conjugated via hydrogen bonds to the P4VP block.247,248 The surfactant can form a lamellar structure, independent of the microphase separation of the block copolymer. However, as yet, the concept has been investigated for melt systems although it seems natural to extend it to solutions. In an extension of this concept, Valkama et al. have shown

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Figure 6.24 Ordered microporous structure formed in a dried film245 prepared as shown in Figure 6.23. Reproduced by permission of Science.

that mesoporous materials can be prepared by solvent extraction of amphiphiles complexed to PS-b-P4VP diblocks. Zinc dodecylbenzene forms coordination complexes with P4VP. This approach offers the advantage that high molecular weight amphiphiles can be bonded, in comparison to complexes formed via hydrogen bonding. Following microphase separation, the amphiphile was extracted using methanol, leaving a porous lamellar structure, which was mechnically stable due to defects connecting the PS lamellae.

6.10

MEMBRANES

Sulfonated block copolymers have applications as polymer electrolyte membranes for use in fuel cells. Proton conduction occurs through the ionic channels of the membranes, formed by microphase separation between the hydrophilic proton exchange site and the hydrophobic domain. Such membranes have been prepared from sulfonated SEBS, polystyrene-b-poly(ethylene-ran-butylene)-b-polystyrene triblocks.250 These materials complement other well-studied polymers such as Nafion™ (DuPont) which is not a block copolymer, but which is a perfluorosulfonic acid. It has been proposed that this forms a porous structure from a percolating array of ionic clusters swollen by water dispersed in a continuous polymeric matrix. However, Diat and coworkers have suggested a model of elongated polymeric bundles.251,252 Won et al. have shown that cross-linking PS-b-PB-b-PS copolymers prior to sulfonation enables the swelling of the membrane, and hence ionic channel size, to be controlled.250 The proton conductivity was shown to be as good as Nafion, but the undesirable permeability of methanol was reduced. The latter is relevant to direct methanol fuel cells where the transport of methanol across the membrane needs to be minimized.

Applications

275

6.11 OTHER APPLICATIONS Other applications of block copolymers including uses in oil and coal recovery, agricultural applications, emulsification, lubrication and surface treatment among others are discussed elsewhere.2,3 The use of block copolymers as gelators of lipid lamellar phases has been explored by Safinya and coworkers.253'254 Gelation is observed with as little as 0.5% added amphiphilic block copolymer. The block copolymers comprise a hydrophilic PEG chain and hydrophobic double chain 3,4-(alkoxy)benzoic moieties. Gelation occurs for AB diblocks or ABA triblocks,253'254 showing that copolymer bridging is not essential (Figure 6.25). However, swelling in water is hindered in the ABA system due to bridging. The same group have also explored hydrogel formation by addition of PEG lipids to fluid lamellar phases.255,256

Figure 6.25 Lipid membranes decorated with block copolymers.253 (a) Amphiphilic AB diblocks in mushroom conformations, (b) ABA triblock copolymer in bridging conformation, (c) ABA triblock copolymer in looping conformation. Reproduced by permission of American Chemical Society.

As mentioned in Section 6.9, soft lithography has been used to prepare patterned films of porous silica from Pluronic solution precursors.243 Micropatterning of block copolymer solutions using elastomeric stamps has also been investigated by Thomas and coworkers, who point out the necessity of avoiding swelling of the

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mould by the solvent.257 In their case, this was achieved by use of a thin layer of amorphous fluorinated polymer coating the mould surface.

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Index ABC triblock 45-47, 62-66, 147, 176-177, 182-183 Adsorption kinetics 226, 229-231, 234 Alpha helix 202-204, 206-208, 265 Amyloid 204 Aniansson-Wall theory 53-55 Annealed polyelectrolyte 173 Anomalous micellization 21 Anomalous SAXS 188 Association number 23, 26, 29-30, 31, 43-44, 47-50, 53, 77, 175, 184-185, 189, 194 Associative thickener 60, 62 Atomic force microscopy (AFM) 11-12 Baxter model 14, 51 Beta sheet 202, 204-206, 207, 249 Bicontinuous sponge 116 Bidisperse polymer brush 225 Biocompatibility 224, 251 Biodegradable surface 224, 248 Birefringence 133, 140, 150 Blob model 34, 144, 152 Block copolymer/lipid complex 267-268, 275 Block copolymer/surfactant complex 76-78, 128, 198-199 Block copolymer/surfactant conjugate 273-274 Bowl-shaped micelle 178 Brewster angle microscopy 217-218 Bridging 29, 60-61, 129-131, 162-163, 233 Brush model 33-40, 48, 90-91, 188-190, 216-218, 220, 232, 235-236 Caging 162 Capillary gel electrophoresis 268 Carnahan-Starling equation 16

Chain dynamics 56-60 Coiled coil 203, 206-207 Cold gelation 126 Composition fluctuations 133-135, 144-146, 151 Compound micelles 79, 83, 176 Compound vesicles 82 Computer simulation 44-45, 148-149, 234-236 CONTIN 9 Cooperative diffusivity 159-160 Corona layer thickness 48-49, 184-185, 222, 225 Counterion distribution 187, 188, 191 Creep experiments 154, 158-159 Critical aggregation concentration (cac) 62, 76, 198 Critical gel concentration (cgc) 124-126, 201 Critical micelle concentration (cmc) 20-25, 29, 32-33, 42, 43, 175, 190 Critical micelle temperature (cmt) 24, 32-33, 40, 42-44 Cross-linking 62-66, 68-71, 79, 84-85, 116, 131-132, 206, 249, 259-260, 261-263 Cryo-TEM 7 Crystallization in micelles 90-91 Cubic-cubic phase transition 137-139 Cyclic copolymers 28-30 Daoud-Cotton model 34-35, 48, 187, 235, 243 Debye plot 15 Demicellization 132 Dendrimer-containing block copolymer 32 Density functional theory 136-137, 148 Density profile 35, 48, 217, 221, 246 Detergency 241

Block Copolymers in Solution: Fundamentals and Applications © 2005 John Wiley b Sons, Ltd.

I. W. Hamley

286 Dielectric spectroscopy 119, 130 Differential scanning calorimetry 8 Diffusion coefficient 9 Dilution approximation 106-107, 133-134, 143, 147 Disk-shaped micelle 63, 68, 91 DNA complexation 196-197, 249, 251-252 Domain spacing scaling 115, 140-143, 187 Double hydrophilic copolymers 132, 179, 182, 258 Dynamic density functional theory 149, 195 Dynamic light scattering 8-10 Dynamic modes 56-60, 135, 159-160 Dynamic shear moduli 117-119 Dynamic structure factor 57, 164 Elastic modulus Electric-field alignment 140 Ellipsometry 10 Emulsification 215, 241, 245-246 Enthalpy of gelation 126 Enthalpy of micellization 8, 23-25, 32-33, 77 Enzymatic degradation 253 EPR (enhanced permeability and retention) mechanism 248 Exchange kinetics 53-56 Flower-like micelles 29, 45, 60-61, 129, 163, 261 Fluorescence probe experiments 10, 52, 56, 77, 90 Fluorinated chains 60, 62, 64, 130-131 Form factor 13, 51, 63, 72, 74, 114 Gelation 117-132, 200 Gelation dynamics 160-164 Gel point 119, 163 Gel structure 75, 124-126 Gene therapy 252 Gibbs energy of micellization 23-25, 29 Grafted polyelectrolyte 183 Grain growth 139-140 Guinier equation 13 H-shaped copolymers 31 Halperin model 37, 175, 185 Hard gel 117, 124-126

Index Hard spheres 14, 16, 51, 105, 124, 162, 188 Heterogeneity mode 159-160 Hockey puck micelle 90 Hot gelation 126 Hydrogels 206-207 Hydrogen bonding 74-75, 79, 87, 126, 127, 206 Image charge effect 179 Intermicellar interactions 51-52, 158 Internal mode 57, 151-160 lonically end-capped copolymers 183-184 Jamming 129 Janus micelles 66, 71, 260 Langmuir isotherm 16, 223, 226 Large amplitude oscillatory shear (LAOS) 156-157 Layer sliding 156, 158 Leibler model 37-40, 143 Looping entropy 40 Lower critical solution temperature (LCST) 254 Lyotropic mesophase 105-117, 269 Manning condensation 186 Maxwell-Voigt model 118, 123 Mean field lattice model 115, 147, 191, 234 Membrane protein 263-264 Mesoporous material 269-274 Metal complexation 257-258 Micellar fusion 55-56 Micelle dimensions 27, 28, 33-37, 39, 41-44, 47-50 Micellization kinetics 52-56 Micellization thermodynamics 22-25, 126 Microemulsion 246 Mixed micelles 75-76, 139 Mode-coupling theory 162-163 Monte Carlo simulations 44-45, 149, 234-236 Multiblock ionomer 194 Nagarajan-Ganesh model 43, 49-50, 244 Nanocage 69 Nanocapsule 263 Nanocasting 270

Index Nanodroplet 87-88 Nanoreactor 255-258 Nanotube 260, 264 Nanowire 259-261 Neutron reflectivity 18 Neutron spin echo 59-60 Newtonian flow 120 Nuclear magnetic resonance (NMR) 10-11, 57-60, 164 Octopus structure 82 Onion micelle 63, 70, 79, 116, 198, 243 Order-disorder transition 106, 132-135 Order-order transition 106, 134, 135-143 Ordering kinetics 139-140 Oscillatory shear 122-123, 150, 152, 154-156 Osmotic brush 173, 185, 191, 221 Ozonolysis 69 Parallel orientation 150 Partition coefficient 242-243 Pearl necklace 174 Peptosome 265 Percolation transition 52, 119, 162, 253 Perpendicular orientation 150 pH-responsiveness 132, 173, 179-183, 204, 251, 265 Phase cube 110 Photon correlation spectroscopy, see Dynamic light scattering Pincus regime 173, 191 Pluronic 18-22, 24-27, 32-33, 42-43, 52, 53, 72, 75, 76-78, 86-87, 110-117, 126, 127-128, 131, 139, 146-147, 150-151, 154, 156, 161, 183, 242, 244, 247, 251, 253, 267, 268, 269, 272, 275 Polyampholyte 63, 182 Polydispersity 42 Polyion complex 195-198, 251 Polymer electrolyte 274 Polymersome 83, 87, 261 PRISM theory 146 Quenched polyelectrolyte 173, 193

287 Rheology 11, 117-124 Rod-coil copolymer 66-68, 174, 272 Rod-like micelle 66-68, 71-74, 151-152, 259-261 Salt effect on micellization 32-33, 127, 182, 184-186, 191-194, 197, 234 Salted brush 163, 185, 221, 225 Scaling theory 33-37 Scanning probe microscopy 11-12 Schizophrenic micellization 179-181 Self-consistent mean field theory 40-43, 51, 136, 141, 143, 146-147, 217-218, 22, 234, 246 Self-diffusion coefficient 11 Shape transition 72-74, 177 Shear alignment 86-87, 149-159 Shear banding 156 Shear melting 158 Shell cross-linked knedel (SCK) 68-71, 231 Slip-stick mechanism 153, 158 Slow release system 250 Small-angle neutron scattering (SANS) 12-14 Small-angle x-ray scattering (SAXS) 12-14 Soft gel 117 Soft lithography 272, 275 Sol-gel transition 119, 126, 127, 130, 135, 255 Solubilization 42, 75, 128, 241-245 Solvent distribution 142-143 Solvent effect on micellization 32 Stabilization 246-247 Static light scattering (SLS) 14-16 Sticky hard sphere model, see Baxter model Stokes-Einstein equation 9 Stopped flow experiments 52, 54 Stress plateaux 156-157 Stress relaxation 120-122 Structure factor 13-14, 51-52, 72, 114, 119, 120, 134 Styrenic block copolymer 20 Sugar-coated micelle 70, 252-253 Supercritical CO2 247 Superstrong segregation 47, 64, 177 Surface activity 21-22 Surface forces experiments 231-234

288 Surface micelle 218-219, 221, 224, 226-231, 236 Surface plasmon resonance 223, 229 Surface pressure-area isotherm 16, 215-220 Surface quasi-elastic light scattering 220 Surface tensiometry 16 Surface tension 21-22, 178 Swelling 142 Switch peptide 204 Tapered block copolymer 31-32 Telechelic 4, 60-62, 129-132, 194, 220 definition 4 Ternary phase diagram 111, 115 Tethered chains 45, 90-91, 215 Tetronic 123 T-jump experiments 52-55 Thixotropic stress decay 158 Time-stain separability 122 Toroidal structure 83, 193 Trajectory map 106-110, 143 Transmission electron microscopy (TEM) 7 Tube inversion test 117, 135 Tube theory 120

Index Tubules 79, 83 Ultrasonic absorption 55 Vesicles 68, 79, 83-90, 150-151, 261-268 Virial coefficient 9, 52, 57, 194 Viscometry 17 Viscosity modifier 91 Vitamin A 207 Wilhelmy plate 16-17 Wormlike micelles 64-65, 71-74, 79-80 X-ray photon correlation spectroscopy (XPCS) 59 X-ray reflectivity 17-18 Y junction 80-81 Yield stress 11, 117, 120 Zhulina-Birshtein model 35-37, 50, 175, 185 Zwitterionic copolymer 181, 183