Role of molecular structure on the thermodynamic properties of melts, blends, and concentrated polymer solutions: comparison of Monte Carlo simulations with the cluster theory for the lattice model

Abstract

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...

Phase Diagrams for Systems Containing Hyperbranched Polymers

“…Using this idea, the exact partition function of a polymer blend where two segments and interacts with the energy can be read as [92]: (19) where is the Kronecker delta function and the vector is pointed from a given lattice site to the nearest neighbour lattice sites. A factor has to be introduced for the indistinguishability of polymer chains of the same species and the factor ½ accounts for the symmetry of each chain.…”

“…Flory and Huggins [84] employed a very simple mean-field approximation that essentially ignores the details of the polymer chain connectivity and, therefore, cannot distinguish between linear, star, branched, and comb polymer architecture. In order to overcome these deficits, Freed and coworkers [87][88][89][90][91][92] developed the lattice cluster theory (LCT), which extends the FH theory. In 1991, Dudowicz and Freed [89][90][91] have developed a systematic expansion of the partition function of a lattice polymer using the LCT.…”

Mixing Properties of Two-Dimensional Lattice Solutions of Amphiphiles

“…[3] to fit the experimental data on polymer solutions (10) so that the dependence of χ = zε (known as the Flory-Huggins parameter) on the temperature, pressure, chain length, and concentration can be obtained. The results thus obtained are, of course, susceptible to the approximations implicit in the lattice picture and to errors arising from specific approximations within the Flory-Huggins theory.…”

“…Despite the simplicity, however, the statistical mechanical treatment of even such idealized models is very complicated, and therefore additional approximations are often required. Examples are common analytical lattice models for polymer solutions, such as the Flory-Huggins theory (1), the quasichemical approximation (2), and lattice cluster theory (3), which permit the prediction of thermodynamic properties and phase equilibrium in a relatively straightforward manner. The study of the lattice theories for polymer solutions is of great importance since these models are sufficient to capture most of the essential features of real polymer solutions.…”

Liquid-Liquid Equilibria in Binary Systems:Monte-Carlo Simulations for Calculating the Effect of Nonrandom Mixing

“…The QC model attempts take nonrandom mixing into account, but it is only accurate for small deviations from random mixing. More recent is the Lattice Ouster (LC) model (Madden, 2 Pesci, & Freed, 1990;Dudowicz, Freed & Madden, 1990) which is a formal method for the exact solution of the lattice model. However, in practice (to date) the LC model remains deficient for the correlation of liquidliquid equilibria.…”