Prediction of the critical micelle concentration in a lattice model for amphiphiles using a single-chain mean-field theory

A single-chain mean-field theory is used to predict the properties of binary surfactant solutions including the critical micelle concentration (cmc). In particular, the cmc of two symmetric nonionic amphiphiles is calculated as a function of temperature in order to analyze the validity of the ideal mixing assumption, often employed in the mass action model. On comparing against literature Monte Carlo results for the same lattice model we find that although it is applicable at low temperatures and hence cmcs at low amphiphile concentrations, at higher temperatures it becomes necessary to correct for the nonideal mixing of the free chain-free chain bulk interaction. We find that a simplistic model taking into account only the repulsive interaction is sufficient to restore the excellent quantitative agreement found between a single-chain mean-field theory calculations and literature molecular simulation results at the low temperature limit.