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Approximate lattice model treatments of the energies of mixing and coexistence curves of polymer solutions and melts are compared against Monte Carlo simulations of these properties for the same lattice model. Because the comparisons do not involve adjustable parameters, they represent stringent tests of lattice theories of polymer fluids. The theories considered are those due to Flory, Huggins, and Guggenheim and the recent cluster theory of Freed and co-workers. A new purely algebraic derivation of the latter method, briefly sketched previously, is provided, and additional calculations are performed to extend and correct prior results for polymer solutions, melts, and incompressible blends. The comparison with Monte Carlo simulations for the polymer-solvent (or isomorphic polymer-void) system shows the present cluster theory to produce the most accurate treatment of the energies of mixing and coexistence curves for this system. Given this good agreement between the lattice cluster theory and Monte Carlo calculations for the same lattice model, cluster theory computations are provided for the exhibition of the predicted strong variation of these thermodynamic properties with monomer and solvent molecular structures. IntroductionTheoretical descriptions of thermodynamic properties of polymer blends, melts, and concentrated solutions require the introduction of models to capture the salient physical features of these complicated fluids.lJ For instance, the exact monomer-monomer and monomersolvent interaction potentials are not known, and consequently idealized models are introduced. These models may, for example, use pairwise additive monomermonomer and monomer-solvent interactions, while in reality such interactions most likely contain nonpairwise additive and highly orientation-dependent contributions. Alternative models place monomers and solvent molecules on a lattice. Despite the simplifying nature of these models, the statistical mechanical treatment of even these idealized models of polymeric fluids is very complicated, and, therefore, approximations are required. The necessity for approximations leads to difficulties in comparing theoretical predictions with experimental data: First of all, it is possible that the exact solution of a model would adequately represent the data but that the approximations used in treating the model introduce inaccuracies, which result in poor agreement with experiment. It is also possible that the combination of an inadequate model with approximations in its solution could produce predictions that are in fortuitous accord with experiment. Evidently, the interpretation of the accuracy of a model and its implications for the interpretation of experimental data require the differentiation between the quality of the statistical mechanical model and the quality of the mathematical solution of that model.It is useful to recognize the difference between statistical mechanical models, which are defined by an explicit representation for the configurational potential energy (or its equ...

The graphical theory of Madden and Glandt [J. Stat. Phys. 51, 537 (1988)] for a fluid adsorbed into a quenched medium has been extended to situations in which the distribution of the immobile species has an arbitrary form, not necessarily arising from a thermal quench. The working equations of Madden and Glandt are shown to be applicable to this general case and the approximations common in the theory of equilibrium mixtures are appropriate in this application as well. Extensions to mixtures are considered and the connection with the graphical theory of small molecules is discussed.

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The dynamics of a bead-and-spring polymer chain suspended in a sea of solvent particles are examined by dissipative particle dynamics (DPDJ simulations. The solvent is treated as a structured medium, comprised of particles subject to both solvent-solvent and solvent-polymer interactions and to stochastic Brownian forces. Thus hydrodynamic interactions among the beads of the polymer evolve naturally from the dynamics of the solvent particles. DPD simulations are about two orders of magnitude faster than comparable molecular dynamics simulations. Here we report the results of an investigation into the effects of confining the dissolved polymer chain between two closely spaced parallel walls. Confinement changes the polymer configuration statistics and produces markedly different relaxation times for chain motion parallel and perpendicular to the surface. This effect may be partly responsible for the gap width-dependent rheological properties observed in nanoscale rheometry.