Dynamics of micelle formation from temperature-jump Monte Carlo simulations

In the present work we perform temperature jumps in a surfactant solution by means of Monte Carlo simulations, investigating the dynamics of micelle formation. We use a lattice model that allows orientational freedom and hydrogen bonding for solvent molecules, which can make a connection between the different time scales of hydrogen bond formation and amphiphilic aggregation. When we perform a large jump between a high-temperature nonmicellized state and a micellized state, there is strong hysteresis between the heating and cooling processes, the latter showing the formation of premicelles that act as nucleation centers for the assembly of larger aggregates and the former is a drive for dissociation of the existing aggregates. Hysteresis is not seen when we perform a small jump between two states that can be both micellized or nonmicellized. Looking for a more detailed analysis of the hydrophobic effect that drives aggregation, we compare the time evolution of the solvent hydrogen bonds in our system close and far from micelles and how that is affected by the formation of large clusters at low temperatures. We find a strong connection between them, with the total number of hydrogen bonds in the system always increasing when micelles are formed. To gain insights into the mechanism of premicellar formation and growth, we measure the lifetime of micellized amphiphiles as a function of the aggregate size and the stage of the aggregation process. Our results indicate that the premicelles are always unstable, quickly exchanging amphiphiles with the solution due to their low probabilty in equilibrium. Furthermore, we find that the stability of individual surfactants in micelles increases with the aggregate size, with the lifetime of amphiphiles in large micelles being as much as 35 times longer than in the case of the unstable premicellar region.