A new pathway for the re-equilibration of micellar
surfactant solutions

Abstract

Micellar surfactant solutions are generally assumed to undergo restructuring via stepwise monomer loss following a dilution. This process is captured by the Becker–Döring equations, an infinite-dimensional system of ordinary differential equations for the concentration of each aggregate in solution. We reveal certain classes of surfactants, such as the non-ionic family CnEm, for which the predicted re-equilibration times via stepwise monomer loss are far greater than those observed experimentally. We investigate two alternative pathways for re-equilibration, first allowing for micelles to break down into two aggregate fragments rather than stepwise monomer release, and secondly by allowing aggregates to merge together to form large super-micelles that exceed the size of a proper micelle. While the former shows no discernible difference in the predicted time to re-equilibration, the latter provides an alternative pathway to re-equilibration: the formation of unstable super-micelles that break down to proper micelles via a cascade of stepwise monomer release. The new theory is shown to describe the re-equilibration of any surfactant system, with the conventional Becker–D¨oring theory forming a subset of the model that describes the behaviour of a small range of surfactant systems with high critical micelle concentrations and low aggregation numbers. The pathway proposed provides an essential mechanistic route to equilibrium.