Formation of large micellar aggregates before equilibrium in diluted solutions

We study the formation of premicelles for different values of the concentration of amphiphile molecules in water. Our model consists of a square lattice with water molecules occupying one cell of the lattice while the amphiphilic molecules, represented by chains of five interconnected sites, occupy five cells of the lattice. We perform Monte Carlo simulations in the NVT ensemble, for a fixed temperature and different concentration of amphiphiles, ranging from below to above the critical micelle concentration. We start our simulations from a monomeric state and follow in time all the aggregates sizes until the equilibrium state is reached. We pay particular attention to two aggregate sizes, one related to the minimum and the other to the maximum of the aggregate-size distribution curve obtained at equilibrium. We show that these aggregates evolve in time exhibiting a maximum concentration well before the equilibrium state, revealing the formation of premicelles. The times to reach these maximum concentrations decrease exponentially with the total concentration of the system.