Formation of spherical micelles in a supercritical solvent: Lattice Monte Carlo simulation and multicomponent solution model

We modify Larson's lattice model [Larson, R.G., Scriven, L.E. and Davis, H.T. (1985). J. Chem. Phys., 83, 2411-2420] and use it to study formation of spherical micelles in a supercritical solvent by large-scale Monte Carlo (MC) simulations and by the multicomponent solution model. Carbon dioxide and perfluoroalkylpoly(ethylene oxide) serve as prototypes for the solvent and surfactant, respectively. Larson-model type parameters for carbon dioxide and perfluoroalkylpoly(ethylene oxide) are obtained using experimental values of critical parameters and solubility along with a modified Berthelot combining rule. We perform canonical MC simulations at a supercritical temperature and low surfactant concentrations, varying the number of surfactant head and tail segments and the solvent density. Various properties such as the critical micelle concentration, the aggregate size distribution and the size of the micelles is evaluated. The multicomponent solution model and the simulation results for the aggregate size distribution are then combined to determine the standard state chemical potential for the spherical micelles and the intermicellar interaction; we present a novel approach to model this standard state chemical potential. The implications of these results for the thermodynamics of the formation of the spherical micelles in supercritical solvents are explored.