ALBERT

Notes: We recently proposed a concentration fluctuation model to describe the segmental dynamics of miscible polymer blends [Kumar et al., J. Chem. Phys. 105, 3777 (1996)]. This model assumes the existence of a cooperative volume, similar to that in the Adam-Gibbs picture of the glass transition, over which segments have to reorganize in a concerted fashion to facilitate stress relaxation. No molecular theory exists for the cooperative volume. Consequently, here we critically compare two alternative functional dependences for this quantity in the context of the segmental dynamics of the most extensively studied miscible polymer blend, 1,4-polyisoprene (PI) and polyvinylethylene (PVE): (a) The Donth model, which assumes the Vogel form for the temperature dependence of relaxation processes, with a relaxation time that diverges at the Vogel temperature, roughly 50 K below the glass transition, and (b) a more recent dynamic scaling model that predicts the relaxation time diverges algebraically, only about 10 K below the glass transition. We find that the dynamic scaling model provides a near-quantitative description of the segmental relaxation in PI/PVE blends. In contrast, the Donth model predicts that the relaxation time spectrum for PI, the faster relaxing component, is bimodal, in qualitative disagreement with NMR experiments and our dielectric measurements reported here. Our results therefore emphasize two findings. First, our model can describe the segmental relaxations of the components of a polymer blend in a near-quantitative manner. Second, and more fundamentally, it appears that the dynamic scaling model describes segmental dynamics of polymers near their glass transition. © 1999 American Institute of Physics.

Notes: The surface segregation from free space polymer blends based on purely entropic effects is investigated using computer simulation and integral equation theory. Computer simulations are performed for tangent-hard-sphere chains of length ranging from short 10 bead chains to experimentally realistic 500 bead chains. The chain segments of one species experience a bending potential which is introduced between any two consecutive bonds and this serves to make this component stiffer than the other blend component. Computer simulations and numerical wall polymer reference interaction site model (wall-PRISM) integral equation calculations for finite hard core athermal chains demonstrate that at liquidlike densities the segments of the stiffer polymer always partition to a neutral surface, apparently independent of the length of the polymer chains in question. Although the primary factor affecting this segregation is the better local packing of the stiff chains at the surface, lattice mean-field calculations suggest that local conformational changes in the molecules also favor the stiff chains at the surface under these conditions. Further, nonlocal effects appear to be irrelevant in this context. Recently, field theoretic based models have suggested in the context of an incompressible approximation that stiffness disparity is the underlying cause for the experimentally observed surface segregation of branched molecules from blends of linear and branched hydrocarbon polymers (the branched molecules were considered more "flexible'' or "conformationally smaller'').The segregation observed in the simulations, however, is both much smaller in magnitude and of the opposite sign to that seen in the field theoretic calculations. Coupled with results of independent work on the bulk behavior of these athermal mixtures, which do not capture the experimentally observed phase separation, we suggest that hydrocarbon blends, at least over the chain lengths examined, cannot be modeled in terms of purely entropic effects, but rather through the incorporation of energetics. Analytic wall-PRISM results for a thread like model of the polymer molecules are also presented, and show that the various approximations made in deriving analytical theories critically affect the magnitude and the sign of the predicted athermal segregation. The connections of our analytical work to recent field theoretic analyses is also discussed. © 1995 American Institute of Physics.

Notes: Off-lattice Monte Carlo computer simulations and numerical polymer reference interaction site model (PRISM) integral equation calculations were performed to quantitatively probe the origins of entropic corrections to Flory–Huggins theory for athermal polymer blends with stiffness disparity. This model system is of interest since it has been recently proposed for describing commercially relevant hydrocarbon polymer mixtures. The novelty of the simulations is that the chemical potential changes on mixing for both components are evaluated. We have considered mixing under constant density conditions, and find surprisingly that the stiffer component is stabilized on blending, while the flexible component is characterized by a positive interaction or χ parameter. The net effective single χ parameter describing these blends, however, is close to zero suggesting that they are completely miscible over a wide range of stiffness disparities and chain lengths. PRISM theory is found to be in good agreement with the simulations for both structural and mixing thermodynamic properties. While purely entropic nonrandom mixing effects could be relevant in determining system thermodynamics, especially for large stiffness disparity, the dominant contribution to the chemical potential changes on mixing arise from equation-of-state (EOS) effects since the two pure components and the mixture are at different pressures when examined at the same density. The EOS contribution to the mixing free energy for small stiffness mismatch is shown to be quantitatively reproduced through an extension of the generalized Flory approach. Through the use of PRISM theory we find that athermal, nonlocal entropy-driven phase separation can occur for long enough chains and high enough stiffness disparity. However, since no phase separation is predicted for stiffness disparities relevant to experimental hydrocarbon systems, regardless of chain length, we suggest that enthalpic effects have to be evoked to explain the limited miscibility of these commercially important mixtures. © 1995 American Institute of Physics.

Notes: We report results of off-lattice Monte Carlo simulations on randomly grafted polymer layers in poor solvent. The results of the investigations show that the conformations of polymer chains in these matrices undergo a gradual transition from a mushroom to brush shape with increases in grafting density, in agreement with expectations. We also find that the location of this transition can be predicted quantitatively with a knowledge of the isolated chain dimensions. Analysis of the detailed structure of the grafted layers supports recent theories which predict that clusters will form not only at low grafting densities, but also at higher densities in which the layer covers the entire surface. The segment density profiles evolve from a monotonic decay to the shape of a step function at moderate grafting densities, but show little agreement with analytical self-consistent field theories for brushes in poor solvent. Finally, we have examined brush structures at high grafting densities and find that the segments of these chains arrange into layers parallel to the surface due to packing constraints, but do not crystallize since the model employed is too simple to permit this possibility. Consequently, we find the formation of a kinetically controlled configurational glass phase, especially for long chain brushes.

Notes: We present the first comprehensive theory for the phase behavior of thin polymer blend films. Based on the Landau–Ginzburg free energy functional, our mean field analysis incorporates the influence of finite size effects and surface interactions, and explicitly considers surface segregation. The procedure for calculating the full phase diagram is provided. In symmetric blends with neutral surfaces, the reduced critical temperature shifts t are obtained in exact analytical forms. Our predictions are in good agreement with our simulations. For polymers with N(approximately-greater-than)100 (N being the polymerization index) in films much thinner than fully extended chain dimensions Nl, a unique scaling behavior t∝L−1 (i.e., the inverse film critical temperature depends linearly on 1/L) is found. When L(very-much-greater-than)Nl, an Ising-type behavior t∝N0.59L−1.59 is expected.

Notes: The chain increment method and configurational bias Monte Carlo methods are used to test the approximations made in the derivation of the generalized Flory-Dimer (GF-D) theory for tangent hard sphere chains. Insertion probabilities and residual chemical potentials are calculated for hard chain fluids containing chains of length n=4, 8, 16, and 32 at monomer densities, ρM, up to 0.8. We find that the largest errors in the GF-D theory are those associated with assuming that the probability of inserting a monomer into a chain fluid is approximately equal to the probability of inserting a monomer into a monomer fluid, as predicted by the Carnahan–Starling equation of state. The errors in the incremental compressibility factor of the second segment associated with assuming that the conditional probability of inserting a second bead next to the first bead in a chain fluid is approximately equal to the probability of inserting a second bead next to the first bead in a dimer fluid as predicted by combining the Carnahan–Starling and Tildesley–Streett equations of state are relatively small. Consistent with the findings of Mooij and Frenkel, we find that these two approximations lead to an overprediction of the incremental contributions to the compressibility factor. Despite the overprediction of the incremental contributions to the compressibility factor of the first segment, the GF-D equation of state accurately predicts the compressibility of hard chains; this accuracy is traced to (1) the insensitivity of the compressibility factor to errors in the insertion probability and (2) cancellation of errors in the incremental compressibility factor of the first segment with small cumulative errors in the incremental compressibility factors of the third and subsequent segments. © 1996 American Institute of Physics.