DOUBLE-LATTICE MODEL FOR BINARY POLYMER-SOLUTIONS

Freed's lattice-field theory provides a basis for a double-lattice model for the Helmholz energy of mixing for binary polymer solutions. When Freed's series-expansion terms for the simple Ising lattice and for the Flory-Huggins lattice with r1 = 1 and r2 = 100 are revised slightly, predicted liquid-liquid coexistence curves are in excellent agreement with those calculated from Scesney's Pade-approximant coefficients and from computer simulation results by Madden, Pesci, and Freed; here r1 and r2 are the numbers of sites required by molecule 1 and molecule 2, respectively. For real systems, the interchange energy (epsilon/k) and r2 are adjusted to fit the experimental concentration dependence of the Flory-Huggins parameter chi determined by vapor sorption, osmotic pressure, light scattering, or sedimentation. To account for highly oriented interactions between segments, a secondary lattice is introduced. This secondary lattice requires an additional parameter (delta-epsilon/k) related to the energy of the oriented interaction and one empirical parameter c10. With the double-lattice theory, coexistence curves can be reproduced for systems having an upper critical solution temperature (UCST), a lower critical solution temperature (LCST), or a miscibility loop with both UCST and LCST.