Monte Carlo simulations for a model of amphiphiles aggregation

In this work we employed Monte Carlo simulations to study a spin-like lattice model that resembles some properties observed in micellar systems. This simple model for molecular aggregation was studied in dimensions d=1,2 and 3. The interaction energy favors the formation of a well-defined optimal aggregate of size n, where n is the number of possible states of the amphiphiles. In this model, both the amphiphiles and the water molecules (we treated aqueous solutions) occupy only a single site in the lattice. The simulations and numerical calculations in one dimension agree with the exact ones obtained in previous works. The minimum and the maximum in the aggregate-size distribution curve and the critical micellar concentration, which are the fingerprints of micellar aggregation, are obtained. The two- and three-dimensional cases also exhibit these features. We calculated the exponent γ that measures the dependence of the difference in height between the maximum and the minimum in the aggregate-size distribution curve on temperature. We found γ≅1, for all values of n we considered, independently of d.