Temporal evolution of micellar aggregates in the temperature jump experiments

We study a model for amphiphilic aggregation on a square lattice through Monte Carlo simulations. We consider the temporal evolution of the aggregates of an equilibrium micellar solution after a sudden change in temperature. The amphiphiles are represented by chains of five interconnected sites on the lattice, one site accounting for the hydrophilic part of the molecule while the others are related to its hydrophobic part. The remaining sites of the lattice are filled with water molecules, one molecule per site. Our simulations are performed in the NVT ensemble, and when the temperature is changed, we follow in time all the aggregates of the system until the new equilibrium state is reached. For each aggregate size we measured two well-separated relaxation times, a shorter one that is related to the quick exchange of amphiphiles with aggregates and a longer one, which is associated with the formation and disintegration of the micelles. We have seen that for all the aggregate sizes the longer relaxation time is around ten times the shorter one. We also show that the relaxation time to equilibrium of the mean size aggregate is longer in the cooling than in the heating process.