Methodology of predicting approximate shapes and size distribution of micelles: illustration for simple models

We propose an efficient methodology for predicting approximate shapes and size distribution of micelles. The methodology is a judicious combination of a conventional thermodynamic approach, the reference interaction site model (RISM) theory, and the Monte Carlo (MC) simulated annealing technique. Solvent effects are fully incorporated using the RISM theory with our robust and very efficient algorithm for solving the RISM equations, and the MC technique is applied only to surfactant molecules. The methodology is potentially applicable to realistic models of surfactant and solvent molecules with all-atom potentials. As the first step, however, it is illustrated for simplified models having only essential characteristics of the amphiphiles. We estimate the critical micelle concentration, approximate shapes, and size distributions at some surfactant concentrations. Roles of the solvent and effects due to the type of the surfactant molecule are discussed in detail.