Surface Effects on the Phase Separation of Binary Polymer Blends

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Ind. Eng. Chem. Res. 2004, 43, 354-363

Surface Effects on the Phase Separation of Binary Polymer Blends† Xianfeng Li‡ and Morton M. Denn* Benjamin Levich Institute for Physico-Chemical Hydrodynamics and Department of Chemical Engineering, City College of New York, The City University of New York, New York, New York 10031

The effect of a chemically heterogeneous surface pattern on the microscopic phase separation of a thin film composed of a binary polymer blend has been studied using a three-dimensional self-consistent field method and a Monte Carlo method based on the “bond fluctuation model.” The surface motif can be transferred from the surface into the polymer bulk to a depth of several nanometers, and such transfer alters the morphology of the bulk phase. The presence of the surface motif weakens the repulsion between unlike species and improves the miscibility of the blend. Miscibility enhancement is maximized when the characteristic area of the surface motif is comparable to the area of a polymer coil in the bulk. Blends containing semirigid chains are slightly more effective in the transfer of a surface pattern, but the effect on miscibility is significantly smaller. I. Introduction The phase behavior of polymer mixtures can be controlled by surface interactions.1-10 Functional sites on the surface may interact with portions of one or more polymer components to alter the blend morphology in a nanoscale region near the surface. An example is local phase separation that can be induced in a homogeneous polymer blend by introducing surfaces that are patterned in a way that preferentially attracts one component;5-8 the surface patterning can be recognized by the bulk species and transferred to the bulk phase. An inverse phenomenon is the homogenization of incompatible blends in polymer composites containing exfoliated clays,10 where the presence of the surface-active clay changes the local thermodynamic environment sufficiently to cause the components to mix on a microscopic scale. The common feature of these materials applications is that continuum properties of the blend are determined by surface interactions that occur at the molecular level and extend distances of the order of several radii of gyration into the bulk material. This work was motivated by an interest in mimicking the promotion of blend compatibilization induced by exfoliated clays.10 The system is modeled as a thin film of a binary blend of homopolymers in contact with a chemically patterned surface that has different regions of attraction or repulsion to the various components, and the evolution of morphology and miscibility of the blend due to the presence of the surface motif has been studied. The transfer of chemically heterogeneous surface patterns to the morphology of near surface polymer blends and the modification of the free energy density due to the interaction between the surface and the blend components are of particular interest. We focus on the effects of surface motif, chain rigidity, interactions between each polymer and the surface, and interactions between unlike species on the variations of morphology †

Dedicated to Reuel Shinnar. * To whom correspondence should be addressed. Tel.: 212650-7444. Fax: 212-650-6835. E-mail [email protected]. ‡ Present address: Department of Physiology & Biophysics, Mount Sinai School of Medicine, One Gustave L. Levy Place, Box 1218, New York, NY 10029.

and free energy density of a binary polymer blend. Our tools are a three-dimensional self-consistent field calculation11-13 and a Monte Carlo calculation based on the “bond fluctuation model.” 14,15 Comparisons between the computational results obtained by different methods allow us to examine the effects discussed above and to obtain a detailed picture of the static structure and the thermodynamics of polymer blends in thin films. The simulation method and the model are described in section II. Section III presents a detailed investigation of the dependence of morphology and free energy density on surface pattern for a symmetric flexible blend using the self-consistent field method. The conformational properties near the surface motif and the effect of chain rigidity on phase behavior revealed by the Monte Carlo simulations are also presented in this section. Section IV contains the conclusions. II. Simulation Model A. Self-consistent Field (SCF) Method. In contrast to the conventional one-dimensional SCF model,16 which considers planar averages, the 3-D SCF model computes the segment density at every individual site within a lattice by applying a mean-field approximation. This approach has been successfully used to study copolymer adsorption at a planar chemically heterogeneous surface.11-13 In the framework of the model, for a blend composed of polymers A and B, the probability that a monomer of type i is at a site r ) (x,y,z) with respect to the bulk is given by

(

Gi(r) ) exp -

)

ui(r) k BT

(1)

where kB is the Boltzmann constant and T the absolute temperature. The potential ui(r) for the segment is given by

ui(r) ) R(r) + kBT

χij(〈φj(r)〉 - φbj ) + uext ∑ i (r) j*i

(2)

R(r) is a hard-core potential, which ensures that every lattice site is filled. χij is the Flory-Huggins interaction parameter between segments of unlike type i and j,

10.1021/ie030167b CCC: $27.50 © 2004 American Chemical Society Published on Web 08/14/2003

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which measures the energy cost when removing an i unit from its surroundings. φbj is the bulk volume fraction of j segments, and the expression 〈φj(r)〉 is the fraction of contacts that an i segment experiences with unlike species j among its six nearest-neighbor segments on the cubic lattice. When the connectivity of segments in a polymer chain is taken into account, the conditional probability that the kth segment of a chain of type i is located at site r while being connected to the first segment of the chain can be calculated from the following recurrence relation:

Gi(r;k|1) ) 〈Gi(r;k - 1|1)〉 Gi(r;k)

(3)

Similarly, the conditional probability that the kth segment is at site r, given that it is connected to the last (ni) segment of the chain, can be calculated by

Gi(r;k|ni) ) Gi(r;k)〈Gi(r;k + 1|ni)〉

(4)

In eqs 3 and 4, the brackets denote the spatial nearestneighbor average. The total volume fraction of the i molecule at site r can then be obtained from

φi(r) )

φbi ni

ni

∑ k)1

Gi(r;k|1) Gi(r;k|ni)

(5)

Gi(r;k)

The adsorption profile and the equilibrium bulk volume fractions of both species can be solved self-consistently from eqs 1-5, the condition ∑iφi(r) ) 1 at each lattice site, and specific initial and boundary conditions.11,12 Once the concentration profiles are obtained, the free energy density of the binary polymer blend in contact with the patterned surface can be calculated from

F k BT

)

1 Ns

(

[Fm(r) + Fg(r)]i + Fs) ∑ i)1

(6) S)

φA(r) φB(r) ln φA(r) + ln φB(r) + nA nB χABφA(r) φB(r) (7)

where nA and nB are the degrees of polymerization of the two components. Fg(r) in eq 6 is the contribution from the gradient in polymer concentration to the free energy density, which can be expressed by17-20

Fg(r) )

(

)

dφA(r) a2 dr 36φA(r) φB(r)

2

(8)

with a the statistical segment length. Fs in eq 6 is the surface free energy, by which the influence of the surface/polymer interactions can be introduced. In this work, Fs is taken to be a short-range potential in which only those segments directly adjacent to the surface are under the influence of the surface field. Fs is given by21,22

Fs )

∫ dr δ(z) σ(x,y) φ(r)

( ) 4

NS

Ns is the number of sites within the cubic lattice. Fm(r) is the free energy of mixing per lattice site, which is assumed to have the Flory-Huggins form

Fm(r) )

The lattice dimensions are Lx × Ly × Lz ) 24 × 24 × 24 (one lattice spacing represents the length of a statistical segment within a polymer chain), with periodic boundaries in the x-y plane and hard walls in the z-direction; the patterned substrate is located in the x-y plane at z ) 1. The substrate is composed of two types of sites, which experience different chemical affinities toward A and B segments. A symmetric blend of homopolymers A and B with chain lengths nA ) nB ) 64 was considered here. Five values of the volume fraction of polymer A were taken: φA ) 0.1, 0.2, 0.3, 0.4, and 0.5. Correspondingly, the volume fraction of polymer B was taken to be 1 - φA for every realization. The miscibility of the blend is characterized by the Flory-Huggins interaction parameter χAB. Four values of χAB were used: χAB ) 0.01, 0.03125 (the critical value for phase separation without surface effect), 0.05, and 0.1. The short-range interaction between a segment of polymer A and a substrate site is characterized by the potential kBTχS, while there is no interaction between polymer B and the surface. The potential is attractive (kBTχS < 0) if the segment A matches the substrate site; otherwise, it is repulsive (kBTχS > 0). Four values of the strength of the segment-substrate interaction were considered: χS ) 0.01, 0.1, 0.2, and 0.3. The total areas on the substrate that attract and repel segment A were taken to be equal. Four heterogeneous surface patterns were simulated, two ordered arrays of checkerboards ([2 × 2] and [4 × 4] in lattice units) and two uncorrelated disordered realizations denoted as rand(1) and rand(2). A substrate pattern order parameter, following the definition of Genzer,11 was used to describe the spatial distribution and sizes of the surface motif:

(9)

with σ(x,y) the contact potential, which is allowed to vary in strength spatially in the plane of the surface.

1

Ns′

∑

N ′s i)1

sisj ∑ j)1 4

(10)

where N ′s is the total number of surface sites and si and sj are Ising-like spin numbers. The internal summation runs over the four nearest-neighbors of site i. sisj ) 1 if sites i and j are of the same type; otherwise, sisj ) -1. S can change from -1 (the finest 1 × 1 pattern) to 1 (all surface sites are of the same type). For the four patterns applied in this work, the corresponding values of S are 0([2 × 2]), 0.5 ([4 × 4]), -0.03 [rand(1)], and 0.52 [rand(2)], respectively. The two disordered surfaces were selected with average motif sizes corresponding to those of the ordered surfaces to elucidate the effect of spatial distribution of the surface pattern on the phase behavior of the blends. We did not carry out the quenched average over different random realizations of the surface pattern.1 Figure 1 shows the pattern structures of the substrates, where the light and dark regions correspond to the areas that are attractive and repulsive to polymer A, respectively. B. Bond Fluctuation Model (BFM) and Monte Carlo (MC) Method. The BFM-MC method has been extensively used to study phase behavior23-26 and interfacial properties27-32 of polymers, and the results have been compared to mean field calculations.26,32-34 In the framework of the model, each monomer occupies eight sites of a unit cell in a simple cubic lattice.

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Figure 1. Four heterogeneous surface patterns, two ordered checkerboard patterns of [2 × 2] and [4 × 4], and two uncorrelated disordered patterns denoted as rand(1) and rand(2). The light and dark regions correspond to the areas that are attractive and repulsive to polymer A, respectively.

Monomers along a chain are connected via 1 of 108 bond vectors within the set

B ) P(2, 0, 0) ∪ P(2, 1, 0) ∪ P(2, 1, 1) ∪ P(2, 2, 1) ∪ P(3, 0, 0) ∪ P(3, 1, 0) (11) where P(a, b, c) stands for the set of all permutations and sign combinations of (a, (b, (c. The allowable bond length can therefore take any one of the five values 2, x5, x6, 3, and x10 in units of lattice spacing. A randomly selected monomer can jump to one of six nearest lattice neighbors; a permissible jump must satisfy the excluded volume constraint to avoid overlap of monomers at the same lattice site and the bond length constraint to avoid intersections of chain segments. A pairwise interaction was imposed by a short-range square well potential between monomers that are within x6 lattice units, a distance extending over 54 neighboring sites. The contact of monomers of the same type does not change the energy, whereas contacts between unlike monomers increase the energy by AB. To simulate a completely phase-separated system, AB was taken to be 1kBT (corresponding to a Flory-Huggins parameter χAB ) 5.625) and was fixed in the MC simulations. Four heterogeneous surface patterns were simulated, consisting of ordered arrays of checkerboards of [2 × 2], [4 × 4], [8 × 8], and [16 × 16] in units of lattice spacing, respectively. The polymeric chain segments interact with the surface motifs as in the SCF calculation. The

strength s of the short-range interaction equaled 5AB, AB, and 0.5AB, respectively; s is negative if the square is attractive to chain segments and positive if the square is repulsive. For calculations in which polymer A was taken to be semirigid, an intrachain bending energy, f(1 + cos θi)2, was imposed, where f is the bending rigidity and θi is the angle between successive bonds. The stiffness of chain is proportional to f, which was taken to equal 2.5kBT. (f ) 0 for a flexible chain.) The lattice dimensions for the MC calculations were Lx × Ly × Lz ) 64 × 64 × 40, with periodic boundaries in the x-y plane and hard walls in the z-direction; the patterned substrate was located at z ) 1. Fifty percent of the lattice sites were occupied, and the volume fraction of each species was 50%; previous simulations based on the BFM have shown that this volume fraction is large enough to represent a polymer melt.35 The sample volume contained 642 chains with chain lengths nA ) nB ) 16. Assuming that a bond in the BFM corresponds to roughly 3-5 chemical monomers in a real polymer,36 a chain length of 16 corresponds to 48-80 real monomers; such a chain length is too short to describe entanglement dynamics, but it should reflect equilibrium properties of the polymer blend adequately.25,37 The Metropolis important sampling criterion38 was used, wherein the acceptable transition probability exp(-δE/kBT) must exceed a random number uniformly

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Figure 2. Illustration of the recognition and transfer of a surface motif. The volume fraction profile map shows polymer A at z ) 2, 5, and 10. The simulation was carried out with χAB ) 0.03125, χS ) 0.2, and φA ) φB ) 0.5.

distributed between 0 and 1; δE is the change of energy. The simulation was started from a fully compatible configuration corresponding to a system at infinite temperature and then annealed to the desired temperature with complete phase separation. Monte Carlo steps (3 × 109) were required for the blend to reach equilibrium; samples were taken thereafter at every 2 × 104-th successful configuration in the run for each set of energetic parameters, and 5000 equilibrium configurations were used in the statistics. III. Results and Discussion A. Self-consistent Field Calculation. Surface Motif Transfer. For both copolymer and polymer blend systems, it is well known1-9,11-13,22 that the surface motif can be recognized and transcribed to the bulk through the interaction between a chain segment and its matching lattice site on the substrate. The processes of motif recognition and transcription can be understood by visualizing the profile of the volume fraction of chain segments in each layer away from the substrate. An illustrative example of the mean-field simulation is shown in Figure 2, in which the surface motif and the volume fraction profile map of polymer A at z ) 2, 5, and 10 are displayed. The simulation was carried out with χAB ) 0.03125, χS ) 0.2, and φA ) φB ) 0.5. It can be seen from the profile of φA in each panel that the specific pattern of the surface is detected by the blend and transferred to the bulk phase. The transcription of the surface motif becomes indistinct after about 10 layers from the surface. Using a physical lattice spacing of a ≈ 4 Å, which is roughly the statistical segment length for a chain in a polyethylene melt,39 the transference depth of the surface motif is about 4 nm. The volume fraction profile maps of polymer A at z ) 2, the layer next to the substrate, are shown for the various patterned substrates of Figure 1 in Figure 3, from which the transfer of the surface pattern from the substrate into the bulk phase can be clearly observed. As can be seen by comparing the scales for the 2 × 2 and 4 × 4 checkerboards, there is more contrast with the larger motif. With specific architecture and length of chains, two factors control the response of the blend to the surface motif: energetics, the interactions between the different species in the blend and between chain segments and the patterned substrate, and geometry, the spatial distribution and dimension of the pattern. The pattern transfer parameter defined by Genzer12,13 is a convenient way to characterize the recognition capability and

the transfer depth of the surface pattern; for polymer A it can be calculated as

∑ φA(x,y,z)

(xa,ya)

PA(z) )

∑ φA(x,y,z)

-

(xr,yr)

Sa

Sr

∑

(12)

φa(x,y,z)

(x,y)

Sa + Sr where Sa and Sr are the substrate areas occupied by sites attractive and repulsive to polymer A, respectively. The summations are carried out over the (x, y) sites above the corresponding substrate site; PA ) 2 denotes perfect positive substrate motif transfer. (A more general definition of PA can be found elsewhere.13,40) The relative effects of the energetic parameters on the transfer of the surface pattern are displayed in Figure 4 for the 4 × 4 checkerboard pattern. PA is a maximum in the layer adjacent to the substrate and monotonically decays to the bulk value. The effect of the surface affinity χS on PA is much more significant than that of the interaction χAB between the two species, although the system exhibiting stronger segregation leads to slightly deeper transfer of the surface motif. Only 1.5% of the surface motif is retained in the fifth layer from the substrate for even the strongest surface affinity in Figure 4, however. The effects of the spatial distribution and scale of the surface pattern on PA are shown in Figure 5 for φA ) φB ) 0.5, χAB ) 0.03125, and χS ) 0.2 for the four surface motifs given in Figure 1. PA decays exponentially with distance away the substrate, and the transfer of the pattern is sensitive to the geometrical distribution on the surface. The larger disordered pattern decays more slowly than the smaller, and the larger checkerboard pattern decays more slowly than the smaller, as would be expected. The two disordered patterns decay more slowly than the two checkerboard patterns. The behavior of rand(1) is more interesting; although this pattern has the smallest value of S, its surface motif transfers deeper than the 2 × 2 and 4 × 4 checkerboards, indicating that the slower decay of the motif transfer is caused by patches that have greater than average size. The lines in Figure 5, which were added to guide the eye, suggest two linear regions for each pattern. The slope at small z is smaller than that at large z for the 2 × 2 and 4 × 4 ordered patterns, indicating that the decay of PA becomes more rapid after z ) 2. For the disordered motifs, in contrast, PA decays more rapidly in the region close to the surface; the small patches

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Figure 3. Recognition of the surface motif by checkerboard and disordered patterns. The volume fraction profile maps of polymer A are given at z ) 2 for various patterns.

Figure 4. Influence of the energetic parameters on the transfer of the surface pattern for the 4 × 4 checkerboard.

Figure 5. Effects of spatial distribution and dimension of the surface pattern on the pattern transfer parameter.

become unimportant after about z ) 4 and the remaining images of the large patches on the surface dominate the transfer. Free Energy Density. The excess free energy of a blend interacting with a patterned surface relative to that of a blend in contact with a neutral surface (no interaction between polymer and surface) is a useful measure of the effect of the surface patterning on the phase separation. With the volume fraction of each component available from the computation, the excess free energy can be calculated from eqs 6-9. The SCF

calculations of excess free energy were carried out for the four patterned surfaces shown in Figure 1, with χAB ) 0.01, 0.03125, 0.05, and 0.1; χAB ) 0.03125 corresponds to the critical transition point of a blend in contact with a free surface, above which phase separation occurs. The calculated free energy densities are shown in Figure 6a-c for affinities χS ) 0.1, 0.2, and 0.3, respectively. The solid lines in the figures are calculated from the Flory-Huggins expression [eq 7] and correspond to a system in contact with a neutral surface. A decrease in excess free energy results from

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Figure 7. Dependence of AB* on χS for three blends (χAB ) 0.03125, χAB ) 0.05, and χAB ) 0.1) in contact with various surface patterns.

adsorption and greater reduction of the free energy. The free energy density reduction for a given surface pattern and value of χS is relatively insensitive to χAB. The imposition of the surface motif decreases the free energy because of a rearrangement of the spatial distribution of chain segments in the vicinity of the surface. We can define an apparent interaction parameter χAB* that takes the surface energetics into account, and χAB* was estimated through fitting the calculated free energy with eq 7. Since the interaction parameter is a measure of the chemical mismatch between the different components of the mixture, χAB* < χAB denotes an increased possibility of chain segments overcoming the chemical mismatch to create a homogeneous mixture. χAB* is defined as

χ/AB )

Figure 6. Free energy densities for different affinities between the surface motif and the chain segment of polymer A: (a) χS ) 0.1, (b) χS ) 0.2, and (c) χS ) 0.3. The solid lines are directly calculated by the Flory-Huggins expression [eq 7], corresponding to a system in contact with a neutral surface.

chain segment adsorption onto the matching surface areas. The reduction of the free energy density depends on the spatial distribution and the dimension of the surface pattern for each χAB and χS pair, with the free energy decreasing as free surface > 2 × 2 > rand(1) > 4 × 4 > rand(2). Increasing the interaction between the chain segments and the surface motif leads to stronger

m / 1  - (/ + /BB) kBT AB 2 AA

[

]

(13)

where m is the coordination number and AB*, AA*, and BB* are apparent potentials between A-B, A-A, and B-B monomers, respectively. AA* and BB* are taken to be zero; hence, the effective interaction potential between unlike components can be directly estimated from χAB*. The dependence of AB* on χS for three blends (χAB ) 0.03125, 0.05, and 0.1) is shown in Figure 7 for various surface patterns. The magnitude of the decrease in AB* with increasing χS depends strongly on the surface pattern but is insensitive to χAB. Hence, the effect is greatest for the smallest interaction parameter. For χAB ) 0.03125 and χS )0.01, 0.1, 0.2, and 0.3, respectively, the calculated AB* decreases about 0.1%, 5%, 20%, and 40% with respect to the neutral surface. These decreases are sufficient to create a homogeneous mixture in a thin film that would otherwise phase separate. B. Monte Carlo Calculations. Typical equilibrium conformations near the patterned substrate with checkerboards of various sizes are shown in Figure 8a-d. The respective influences of the size of the surface motif and chain rigidity on the surface pattern transfer parameter PA are displayed in Figure 9 with S ) 5AB. The Monte Carlo results are consistent with those using the SCF method, in that a larger characteristic size of the surface pattern induces deeper transfer. The radius of gyration Rg of the flexible chain in the bulk is 4.6 in lattice units, so the transfer depth of the surface motif is 3-4 times

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Figure 8. Typical equilibrium configurations near the substrate consisting of ordered arrays of checkerboards of (a) [2 × 2], (b) [4 × 4], (c) [8 × 8], and (d) [16 × 16], with AB ) kBT and S ) 5AB. “A” monomers are dark.

Figure 9. Effects of active surface area and chain rigidity on the pattern transfer parameter with S ) 5AB. Results for f ) 0 and f ) 2.5kBT are displayed with solid and open symbols, respectively.

Rg; using the results of Baschnagel et al.,36 one BFM lattice unit corresponds to 2 Å for a polyethylene melt; hence, the transfer depth can reach 3-4 nm. The effect of chain rigidity (f ) on PA is not large, but, as might be

expected, a semirigid chain is more efficient in transferring the pattern than a flexible chain. The intermolecular heterogeneous contact number nAB, which is the average number of unlike monomers within 54 neighboring lattice sites around a particular monomer,25 is a useful parameter for exploring the effect of the surface motif. The effects of active surface area, surface affinity, and chain rigidity on nAB are shown in Figure 10, where nAB was calculated within the range in which the surface effect can be felt by the chain segments (i.e., 20 layers away from the substrate) and was scaled by the bulk average n0AB. The characteristic area Sc of the surface motif was scaled by the crosssectional area of a flexible chain in the bulk. The calculations show that the effect of the patterned surface is to increase the contacts between monomers of different type, indicating a decrease of phase domain size and increase in miscibility. Up to Sc/πRg2 ∼ 2, stronger interaction between the substrate and polymer leads to increased miscibility. The effect of the surface on the miscibility is maximized when the characteristic area is about the same size as the area of the flexible coil, with some variability depending on the interaction strength, since large areas on the substrate can host one or more molecules of the same type and induce phase separation. (Sc/πRg2 < 0.5 for all of the surface

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can be measured by the asymmetry parameter, λ,41 defined by

λ)

Figure 10. Effects of active surface area, surface affinity, and chain rigidity on nAB. The calculations were carried out within 20 layers from the substrate.

motifs in the SCF calculations, so the monotonic change of free energy density with motif size in Figure 6 is consistent with the predictions of Monte Carlo simulations.) The change in miscibility for a blend in which component A is semirigid is significantly less than for a flexible blend since the surface activation is partially offset by the distortions of the semirigid chain. The conformations of polymer chains adsorbed on the surface pattern are important in determining the phase behavior. The conformation is reflected in the average chain orientation relative to the surface normal, which

2〈Rgz2〉z - 〈Rgx2〉z - 〈Rgy2〉z 2(〈Rgz2〉z + 〈Rgx2〉z + 〈Rgy2〉z)

(14)

〈Rgs2〉z (s ) x, y, z) denotes the s component of the meansquare radius of gyration of a chain at position z. The profiles of the asymmetry parameter in the direction away from the surface motif for flexible chains in which at least one monomer is adsorbed to the surface with S ) 5AB are shown in Figure 11, where zc is the z component of the center of mass of the adsorbed chain. The populations of adsorbed chains at various zc are shown in the insert. Nearly 55% of the adsorbed chains populate the region around zc ) 3, where λ ∼ -0.25, indicating that half of the adsorbed chains adopt conformations orientated parallel to the substrate (a value of -0.5 would indicate complete orientation parallel to the substrate). About 30% of the adsorbed chains populate the region around zc ) 5, where λ vanishes, reflecting the isotropy of the flexible coils. Fewer than 15% of the adsorbed chains have values of λ from 0.1 to 0.7, corresponding to conformations extending in the direction normal to the substrate. IV. Conclusions The presence of a chemically heterogeneous surface with attractive and repulsive regions can significantly alter phase separation in a thin film of a binary polymer blend. The selective interaction between the surface motif and chain segments induces changes in both the blend morphology and the free energy density. Selfconsistent mean field calculations show that the adsorption of a blend component onto the active substrate

Figure 11. Profiles of the asymmetry parameter of adsorbed A chains. Here, zc is the z component of the center of mass of a chain. The populations of adsorbed chains of various zc are given in the insert; S ) 5AB.

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induces a decrease in the excess free energy and equivalently reduces the apparent Flory-Huggins interaction parameter between unlike species. Monte Carlo calculations show that the enhancement in miscibility is maximized when the characteristic size of the surface motif is comparable to the area of a flexible coil in the bulk. Semiflexible chains are more efficient than flexible chains in transferring a surface motif to the polymer, but they are less effective in improving miscibility. About 55% of the adsorbed chains adopt a conformation parallel to the substrate, and fewer than 15% adopt a conformation normal to the surface. Finally, we return to the experiments10 on exfoliated clay platelets with immiscible blends that motivated this study. The surface-to-volume ratio in these systems is large because of the large aspect ratios of the exfoliated platelets, so much of the polymer exists in thin films near a planar surface. The calculations reported here are therefore consistent with the notion that the adsorption of polymer chains onto the clay platelets can induce compatibilization. We offer the caveat, however, that compatibilization can only be realized with a suitable combination of motif size, phase domain size, and surface-polymer and polymer-polymer interaction strengths. Acknowledgment This work was supported in part by the donors of the Petroleum Research Fund under Grant ACS-PRF 36563AC7. Literature Cited (1) Chakraborty, A. K. Disordered Heteropolymers: Models for Biomimetic Polymers and Polymers with Frustrating Quenched Disorder. Phys. Rep. 2000, 342, 1. (2) Chakrabarti, A.; Chen, H. Block Copolymer Films on Patterned Surfaces. J. Polym. Sci., Part B: Polym. Phys. 1998, 36, 3127. (3) Petera, D.; Muthukumar, M. Effect of Patterned Surface on Diblock-Copolymer Melts and Polymer Blends Near the Critical Point. J. Chem. Phys. 1997, 107, 9640. (4) Petera, D.; Muthukumar, M. Self-Consistent Field Theory of Diblock Copolymer Melts at Patterned Surfaces. J. Chem. Phys. 1998, 109, 5101. (5) Karim, A.; Douglas, J. F.; Lee, B. P.; Glotzer, S. C.; Rogers, J. A.; Jackman, R. J.; Amis, E. J.; Whitesides, G. M. Phase Separation of Ultrathin Polymer-Blend Films on Patterned Substrates. Phys. Rev. E 1998, 57, R6273. (6) Ermi, B. D.; Nisato, G.; Douglas, J. F.; Rogers, J. A.; Karim, A. Coupling between Phase Separation and Surface Deformation Modes in Self-Organizing Polymer Blend Films. Phys. Rev. Lett. 1998, 81, 3900. (7) Bo¨ltau, M.; Walheim, S.; Mlynek, J.; Krausch, G.; Steiner, U. Surface-Induced Structure Formation of Polymer Blends on Patterned Substrates. Nature 1998, 391, 877. (8) Karim, A.; Douglas, J. F.; Nisato, G.; Liu, D. W.; Amis, E. J. Transient Target Patterns in Phase Separating Filled Polymer Blends. Macromolecules 1999, 32, 5917. (9) Winesett, D. A.; Ade, H.; Sokolov, J.; Rafailovich, M.; Zhu, S. Substrate Dependence of Morphology in Thin Film Polymer Blends of PS and PMMA. Polymer 2000, 49, 458. (10) Winesett, D. A.; Ade, H.; Rafailovich, M.; Sokolov, J.; Zhang, W. X-Ray Microscopy of Polymer Blends Compatibilized with Clay Nanocomposites. Microscopy and Microanalysis 2000 Conference, August 17, 2000, Philadelphia, PA. (11) Genzer, J. Self-Consistent Field Study of Copolymer Adsorption at Planar Chemically “Rough” Surfaces: An Interplay between the Substrate Chemical Pattern and Copolymer Sequence Distribution. Adv. Colloid Interface Sci. 2001, 94, 105. (12) Genzer, J. Copolymer Adsorption on Planar Substrates with a Random Distribution of Chemical Heterogeneities. J. Chem. Phys. 2001, 115, 4873.

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Received for review February 24, 2003 Revised manuscript received June 6, 2003 Accepted June 10, 2003 IE030167B