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. © 2002 Elsevier Science B.V. All rights reserved.
Girardi, M., & Figueiredo, W. (2003). Monte Carlo simulations for a model of amphiphiles aggregation. Physica A: Statistical Mechanics and Its Applications, 319, 421–431. https://doi.org/10.1016/S0378-4371(02)01390-0