A Monte Carlo simulation of the micellar phase of an amphiphile and solvent mixture

Results are presented from Monte Carlo simulations of a three-dimensional lattice model of a binary mixture of solvent and amphiphile chains in which free self-assembly of the chains is allowed. The use of a lattice model allows good statistics to be collected for clusters containing up to 100 chains. The model exhibits a critical micelle concentration and a cluster size distribution with a minimum and maximum in the micellar region. The dependence of the weight average aggregation number on the total amphiphile concentration is found to obey theoretical predictions. The dilute solution excess chemical potential μ⁰_n - μ⁰₁ is determined from the cluster size distribution, where n is the number of monomers in a cluster. A single analytical expression is found to describe the cluster size distribution and the behaviour of the monomer concentration with total amphiphile concentration in the concentration range from 0 to 10 vol%. The excess chemical potential is found to be a monotonically decreasing function of n with different functional forms for large and small n. The form of the excess chemical potential is compared with the empirical forms which are used commonly in the literature. It is necessary to introduce an activity coefficient to describe accurately the behaviour of the model for amphiphile concentrations in the range 5–10 vol%. The dependence of the excess chemical potential on temperature and head-solvent interaction is reported.