INTEGRAL-EQUATION THEORY FOR COMPRESSIBLE POLYMER ALLOYS - THERMODYNAMICS, SCATTERING, AND MISCIBILITY OF GAUSSIAN CHAINS

A series of numerical calculations are performed on binary mixtures of Gaussian chains using our recently developed integral equation theory of polymer blends. The intermolecular radial distribution function, structure factor, chi-parameter, spinodal temperature, and compressibility are investigated over a range of molecular parameters. Structurally symmetric (the symmetric isotope blend) and various structurally asymmetric mixtures were studied. We find that the integral equation approach, which includes the effects of concentration fluctuations and nonrandom packing, leads to an increase in miscibility relative to the Flory-Huggins theory. For the symmetric isotope blend the chi-parameter, calculated at fixed temperature and composition, decreases linearly with N-1/2 for large degrees of polymerization N. Our calculations of chi as a function of composition for the symmetric isotopic blend are in good qualitative agreement with recent SANS measurements of Bates and co-workers. The wave vector dependence of the effective chi-parameter is calculated and the implications with regard to block copolymers is discussed. The dependence of chi on temperature, composition, and N is systematically studied. We find that the incompressible random phase approximation (RPA) agrees with fully compressible calculations for the partial structure factors in the case of the symmetric isotope, but progressively deterioriates as structural asymmetry between the components is increased due to compressibility effects. Whereas the RPA predicts a large increase in miscibility as the disparity in segment lengths between the components increases, calculations of the critical temperature which include density fluctuations show only a relatively small enhancement. A striking result from this integral equation theory of polymer blends is that the upper critical solution temperature is proportional to square-root N rather than a linear N dependence predicted by the Flory-Huggins theory. This unexpected molecular weight dependence, which is a consequence of the correlation hole, is found for both structurally symmetric and weakly asymmetric blends.