Integral equation theory of polymer blends : numerical investigation of molecular closure approximations

The thermodynamics of symmetric polymer blends is investigated using the polymer reference interaction site model integral equation theory with the new molecular closures presented in the previous paper. In contrast to the atomic mean spherical approximation reported earlier by Schweizer and Curro [J. Chem. Phys. 91, 5059 (1989); Chem. Phys. 149, 105 (1990)] (in which the critical temperature is proportional to the square root of the degree of polymerization), the molecular closures predict a linear dependence of the critical temperature on the degree of polymerization, in agreement with classical mean field theory. Detailed numerical calculations using the reference molecular mean spherical approximation (R-MMSA) and the reference molecular Percus–Yevick (R-MPY) closures are presented for the intermolecular structure and effective chi parameter in symmetric blends of semiflexible chains. For the symmetric blend, the R-MMSA closure is almost an integral equation realization of mean field theory, consistent with the analytical results presented in the previous paper. With the R-MPY closure, at low densities, the effective chi parameter is significantly renormalized down from its mean field value and displays a strong composition dependence. As the density is increased, both the renormalization of the effective chi parameter and its composition dependence become weaker. These trends are consistent with recent computer simulations. The influence of chain aspect ratio and the precise choice of intermolecular potentials on blend thermodynamics and phase separation are also explored. With the exception of the composition dependence of the effective chi parameter in the R-MPY theory, the analytical thread calculations are shown to be in qualitative, and sometimes quantitative, agreement with all the numerical results for symmetric blends.