Micellar aggregation dynamics on a lattice

In this work, we present some results concerning the dynamical behavior of a lattice model for micellar aggregation. The model we study here, is a lattice-gas with two- and three-body interactions on a linear lattice, which exhibits the essential features of micellar aggregation in equilibrium: a critical micellar concentration, and a local minimum and maximum in the aggregate-size distribution curve. We investigate the kinetics of micellar formation by means of two different approaches. The first one is the Becker-Döring approximation, which accounts only for the process of entering/exiting of a single particle at a time into/from aggregates. In the second approach, we employ Monte Carlo simulations, where we use short- and long-range movements of particles to explore the phase space of the system. The time evolution of each aggregate-size concentration is monitored after temperature- and concentration-jump experiments, and the residence time of the amphiphiles in aggregates of different sizes are obtained. The results are compared with the typical relaxation times found in the micellization processes.