Explicit-and implicit-solvent simulations of micellization in surfactant solutions

In this article, we focus on simulation methodologies to obtain the critical micelle concentration (cmc) and equilibrium distribution of aggregate sizes in dilute surfactant solutions. Even though it is now relatively easy to obtain micellar aggregates in simulations starting from a fully dispersed state, several major challenges remain. In particular, the characteristic times of micelle reorganization and transfer of monomers from micelles to free solution for most systems of practical interest exceed currently accessible molecular dynamics time scales for atomistic surfactant models in explicit solvent. In addition, it is impractical to simulate highly dilute systems near the cmc. We have demonstrated a strong dependence of the free surfactant concentration (frequently, but incorrectly, taken to represent the cmc in simulations) on the overall concentration for ionic surfactants. We have presented a theoretical framework for making the necessary extrapolations to the cmc. We find that currently available atomistic force fields systematically underpredict experimental cmc's, pointing to the need for the development of improved models. For strongly micellizing systems that exhibit strong hysteresis, implicit-solvent grand canonical Monte Carlo simulations represent an appealing alternative to atomistic or coarse-grained, explicit-solvent simulations. We summarize an approach that can be used to obtain quantitative, transferrable effective interactions and illustrate how this grand canonical approach can be used to interpret experimental scattering results.