PHASE-SEPARATION IN BULK STATISTICAL COPOLYMERS AND THEIR MIXTURES WITH HOMOPOLYMERS .1. THEORY

A method based on the Flory-Huggins thermodynamics is presented for modeling phase equilibria in bulk statistical copolymers of two monomers. For a given phase separation, a component's preference for one of the phases depends only on its composition, and there always exists a balanced composition which shows no preference at all and assumes equal concentrations in both phases. In contrast, the degree of enrichment depends exponentially on the component's chain length and the magnitude of the deviation of its composition from the balanced one. A fast two-loop iteration scheme is devised for numerical computation of phase equilibria for any distribution of chain length and composition. Critical state formulas can be cast succintly in terms of averages of deviations from the balanced composition (which here equals the z-average composition). At the critical composition, the (z+1)-average of cubed deviations has to be zero, whereas the critical value of the interaction parameter is inversely proportional to the z-average of squared deviations and to the w-average chain length. Thus, e.g., a copolymer with a symmetrical distribution always constitutes a critical mixture.