Self-assembly of lipids in water. Exact results from a one-dimensional lattice model

Abstract

We consider a lattice model for amphiphiles in a solvent with molecules chemically similar to one part of the amphiphilic molecule. The dependence of the interaction potential on orientation of the amphiphilic molecules is taken into account explicitly. The model is solved exactly in one dimension by the transfer-matrix method. In particular, pressure as a function of concentration, correlation function and specific heat are calculated. The model is compared with the recently introduced lattice model for colloidal self-assembly, where the particles interact with the isotropic short-range attraction and long-range repulsion (SALR) potential. Similarities between the amphiphilic and the colloidal self-assembly are highlighted.