Interfacial behavior of compressible polymer blends

We develop a new density functional treatment for the liquid–liquid interface of phase separated binary polymer blends. In contrast to previous density functional theory studies of these interfaces, we incorporate the compressibility (i.e., ‘‘equation of state effects’’) of the system through use of a compressible version of Flory–Huggins theory. The introduction of compressibility is demonstrated to severely complicate the mathematical description. The coupled, nonlinear Euler–Lagrange equations for the interfacial profile and tension are shown to become numerically unstable and permit analytic solution in the asymptotic profile wings. Our computations are limited to symmetric binary blends because this restriction enables us to compute numerically the central portion of the interfacial profile and thereby test more general variational methods (applicable also to unsymmetric blends) that we develop for computing the full interfacial profile and the interfacial tension. The total density of the symmetric blend is found to be reduced in the profile center relative to the bulk density by 0.4%–1.5%. While this total density fluctuation costs free energy, it reduces unfavorable polymer–polymer contacts, thereby diminishing the total interfacial tension. The applicability of our approximate scheme is tested.