PHASE-EQUILIBRIA OF LATTICE POLYMER AND SOLVENT - TESTS OF THEORIES AGAINST SIMULATIONS

Computer simulations are performed to determine the coexistence curve for an incompressible polymer –solvent mixture on a simple cubic lattice in three dimensions. This model is isomorphic to that of a compressible pure polymer when the solvent molecules are regarded as vacancies. Coexistence is established by letting the system separate into two phases, with the polymer-rich phase condensed against an adhesive boundary. A slight degree of polydispersity (Mw/Mn = 1.084) is included to take advantage of an especially efficient simulation algorithm. Comparison is made against the theories of Flory, of Guggenheim, and of Freed and co-workers. The Guggenheim quasichemical approximation is found to be in best agreement with the simulation results. The standard Flory lattice theory (“Flory-Huggins theory”) proves accurate at very high polymer volume fractions but is poor at lower concentrations. The simulations reveal deficiencies in existing implementations of the Freed theory that can be eliminated by the inclusion of additional diagrams. Bulk-phase simulations were conducted to evaluate the term-by-term accuracy of the approximate theories in their predicted corrections to the Helmholtz free energy and internal energy of mixing. The Guggenheim and Freed theories are found to give good representations of the first-order perturbation term in the cohesive forces. They also agree well with one another in their predictions for the athermal Helmholtz free energy of mixing. However, the most elaborate implementation of the Freed theory now available gives a second-order term that is incorrect in both sign and magnitude. The quasichemical approximation in the Guggenheim theory gives a reasonable estimate of this term, but a cruder version of the Freed theory (“extended mean field theory”) is in best overall agreement with simulation. This result suggests refinements of the systematic Freed theory that are necessary to reproduce the simulations. It is shown that the second-order term from extended mean field theory can be used in conjunction with accurate lower-order results to give improved agreement with simulations at intermediate densities. © 1990, American Chemical Society. All rights reserved.