Density functional theory has been used to describe the ordering phenomena of amorphous A-B diblock copolymers. The resulting formalism was then used to study the ordering of a symmetric diblock copolymer to the lamellar morphology for values of above the microphase separation transition value. The number of statistical segments per diblock copolymer chain is denoted by N and is the Flory interaction parameter. We have identified three distinct regimes for the N dependence of the domain spacing D. For 10.495 < < 12.5, the weak segregation limit of Leibler is realized where the domain spacing D is proportional to JV0•6. For > 100, the strong segregation limit is achieved where D is proportional to JV0•67. In the newly discovered intermediate regime (15 < < 95), D is proportional to IV0•72 and the domain boundaries support substantial fluctuations. The distinct features of the microscopic density profiles in the various regimes are discussed. In addition, the present theoretical results are compared with the most recent experimental investigations reported in the literature.

Liquid-liquid demixing in a binary polymer blend driven solely by the component-selective crystallizabilityA theory for the thermodynamic properties of binary polymer blends was developed and applied to predict the compositional dependence of the effective chi parameter S in model isotopic polyethylene mixtures. The theory is a generalization of the optimized cluster theory for single component molecular fluids. Starting from exact cluster expansions for the Helmholtz free energy and pair-correlation functions in a molecular mixture developed by Chandler et al., a series of transformations was performed to yield approximate expressions for these quantities. The resulting theory was demonstrated to be equivalent to a set of diagrammatically proper integral equations. For model isotopic polyethylene blends, we calculated the various partial structure factors in the mixture and used them to predict the compositional dependence of S . The calculated values of S were found to be in reasonable agreement with recent neutron-scattering measurements but the theory underestimates the compositional dependence relative to the experiment. Deviations from random mixing that extend well beyond monomeric length scales were predicted in this blend system.

Self-consistent RISM integral equation theory of polymeric liquids is used to investigate the equilibrium properties of polymer solutions and melts. Density functional formalism is employed to derive the effective medium-induced potential between two sites on a polymer chain. The resulting expression leads to a coupling between the interchain and intrachain pair correlation functions. An approximate method for the calculation of the effective intrachain pair correlations is examined. The method employs Monte Carlo computer simulations of a single polymer chain interacting via local chemical interactions, long-range excluded volume, and the self-consistently determined medium-induced potential in the condensed phase to compute the intrachain pair correlations which are consistent with the interchain packing. Results for solutions of tangent hard-sphere chains are compared to recent off-lattice Monte Carlo simulations for various chain lengths and densities. In particular, it was found that the theory slightly overestimates the average size of the polymers in solution, while the density dependence of the average size of the chains is in good agreement with the Monte Carlo simulations. The inclusion of the self-consistent determination of the intrachain correlations is found to significantly alter the interchain pair correlation function at low and intermediate densities.

Approximate solutions to the self-consistent reference interaction-site model (RISM) integral equation theory of polymer liquids are employed to study the conformational properties of flexible polymers as a function of density and chain length. The nonlinear nature of the expression describing the medium-induced potential between two sites along the polymer chain necessitates the use of approximate methods to determine the intrachain pair-correlation function consistent with the interchain packing. In the limiting case where the polymer segment hard-core diameter approaches zero and the number of interaction sites comprising the chain goes to infinity, with the segment volume fraction held fixed, the intrachain pair correlation function is determined through a Feynman variational procedure for the effective free energy of a single chain in solution. The screening of the excluded volume interactions and the corresponding reduction of the polymer dimensions as a function of both polymer density and chain length is systematically studied with the results being in good agreement with scaling predictions. In addition, the variational method is successfully extended to chains having finite hard-core diameters, with the predictions of the theory comparing favorably with existing theories for polymer solutions based on field theoretic approaches.

The small-angle neutron scattering (SANS) interaction parameter χ NS in isotope blends almost always exhibits pronounced upward curvature when plotted as a function of concentration at any given temperature. Optimized cluster theory (OCT), which accounts for blend compressibility and for fluctuations, is used to address this effect in blends of conventional and perdeuterated polyethylene. Structure factors are calculated for symmetric systems having a concentration independent χ bare ) 2.09 × 10 -4 and chains of N ) 3290 or N ) 8746 monomers. When analyzed in terms of incompressible RPA approach, exactly as done in experiments, the model returns an interaction parameter that is practically indistinguishable from χbare for all blends concentrations between 0.01 and 0.99. Trivial departures from the energetic χbare are attributed to equation-of-state effects. These results, combined those from compressible lattice models, show clearly that compressibility has no significant role in determining the composition dependence of the interaction parameter. The experimental behavior of isotope blends cannot be ascribed to any theoretical reason (i.e., compressibility or density fluctuations) and is therefore attributed to measurement errors.