Interfacial studies of incompressible binary blends

Abstract

Density functional theory is used to investigate two of the possible reasons for the discrepancy between theory and experiment for the interfacial width and tension of phase separated binary blends. The two reasons are the inadequacy of the density functionals used previously and the neglect of the composition dependence of the Flory interaction parameter χ. For the sake of algebraic simplicity, our computations are restricted to symmetric, incompressible binary blends with correlation functions taken in the random phase approximation. We extend the analysis in Paper I [Tang and Freed, J. Chem. Phys. 94, 1572 (1991)] on the validy of density functionals for binary blends to the strong segregation limit with narrow interfaces by studying the conditions under which the Roe free energy functional is appropriate. Our derivation in this limit resums a rigorous Landau expansion to show that the Roe functional is appropriate only for infinite molecular weights. Nevertheless, even in the strong segregation limit this functional becomes incorrect in the wings of the concentration profile where a Landau expansion is valid despite the current unavailability of a local density functional. Interfacial properties in the theoretically simplest weak segregation limit are in accord with those of previous workers, but we are able to suggest an interpolation form for the interfacial width and tension of symmetric blends that crosses over between the weak and strong segregation limits. The composition dependence of the Flory interaction parameter χ poses several problems when experimental χeff are substituted into theories that ignore this composition dependence. We therefore investigate the errors incurred by the use of different experimental measures of χ and by the use of χ measured at different compositions for two simple models in which χ varies linearly or quadratically with blend composition. Situations arise where there exists an experimental χeff that yields the correct interfacial width in the composition independent theory, but other examples produce substantial errors. Dimensionless combinations of the interfacial width and tension are constructed that should be weakly dependent on molecular weight and temperature unless ignored factors, such as blend compressibility, have a significant influence on interfacial properties. The relevance of the composition dependece of χ to interfacial profiles suggests a similar relevance of blend compressibility because compressibility influences χ and its composition dependence.