Modeling the microemulsion channel in ternary mixtures of AB diblock copolymer with A and B homopolymers

Ternary mixtures of symmetric AB diblock copolymer and A and B homopolymers exhibit a microemulsion channel in which a strongly correlated disordered phase remains stable over a narrow range of copolymer compositions, where it competes with a highly swollen lamellar phase. We discuss an attempt to model this behavior in a manner inspired by older membrane models of the microemulsion phase in small molecule oil-water-surfactant mixtures. In this approach, we model the free energy of the disordered phase by combining a self-consistent field theory description of a surrogate ordered network with entropic corrections that account for topological entropy and renormalization of the Gaussian rigidity by interfacial fluctuations, and allow for the effect of undulation-induced steric repulsion on the stability of the competing lamellar phase.