Lattice model of microemulsions

Publisher Website
Google Scholar
Abstract
A lattice model of microemulsions is proposed. It proves to be equivalent to a spin-1/2 Ising model in a magnetic field, with ferromagnetic nearest-neighbor, antiferromagnetic next-nearest-neighbor (next-nearest defined as two lattice steps, regardless of the metrical distance), and three-spin interactions. The respective interaction constants H, J, M, and L in the Ising model are related to the ratios zBB/zAA and zAB/(zAAzBB)1/2 of the activities of the oil (AA), water (BB), and surfactant (AB), to the surfactant-film-curvature energy (surfactant–surfactant interaction energy) K, and to the curvature-bias parameter (Bancroft parameter) λ, in the microemulsion model. A table of translations is given. In mean-field approximation the symmetrical version of the model, in which H=L=0 (or zBB/zAA =1 and λ=0 in microemulsion language), is equivalent also to the ANNNI (anisotropic, or axial, next-nearest-neighbor Ising) model. The analog of the three-phase (Winsor III) equilibrium of surfactant solutions is identified in the ANNNI model’s phase diagram. States of vanishing tension of the microscopic surfactant film are identified in the symmetrical model. They prove to be the same as those in which the tension of the interface between (metastable) bulk oil and water phases (the ferromagnetic phases in the Ising model) vanishes. Those states are reflected in the phase diagram, and also in the ultralow tensions of the interfaces between stable phases in their neighborhood.