Miscibilities in binary copolymer systems

Abstract

A lattice theory is presented for liquid-liquid equilibria in binary systems containing random copolymers. This theory takes into account deviations from random mixing through a non-randomness factor which follows from a generalization of Monte-Carlo calculations for the three-dimensional Ising model. While the lattice remains incompressible, the effect of specific interactions (hydrogen bonding) is introduced by superimposing on the non-random (Ising model) expression for the Helmholtz energy of mixing a correction based on the lattice-gas model by ten Brinke and Karasz. The resulting theory can predict immiscibility caused by lower critical solution temperatures. Several theoretical miscibility maps at fixed temperature were computed; these are compared with those predicted by the random-mixing Flory-Huggins theory. Theoretical miscibility maps are also compared with experiment for a few systems with strong specific interactions.