ONE-DIMENSIONAL MODEL FOR MICROEMULSIONS

In this paper, a model for water-oil-surfactant mixtures, which we have previously studied on two- and three-dimensional lattices, is now studied on a one-dimensional lattice. In this case we are able to obtain exact results, whereas on the higher-dimensional lattices it was necessary to use approximations. This one-dimensional model produces correlation and structure functions that are similar to those obtained for the disordered phase on the two- and three-dimensional lattices. The disorder line is obtained from the water-water correlation function and the Lifshitz line is derived from the water-water structure function. One or the other of these lines is typically used to divide the disordered phase into a region of ordinary disordered fluid and a microemulsion region. Both these lines calculated exactly for the one-dimensional lattice behave similarly to their counterparts on the two- and three-dimensional lattices calculated by various approximations.