Lattice-gas with two- and three-body couplings as a model for amphiphilic aggregation

In this paper we studied a lattice-gas model with two- and three-body interactions in linear, square and cubic lattices. We observed that, at low concentrations, the model presents some aggregation characteristics similar to micellar solutions. These peculiarities include a plateau in the plane of concentration of isolated molecules as a function of the total concentration (CMC), and a local minimum and maximum in the aggregate-size distribution curve (ADC). The transfer matrix technique, Monte Carlo simulations, and the independent cluster approximation were employed to find the ADC, CMC and the micellization temperature of the model. The one-dimensional case was solved exactly and a transition between a micellized and a non-micellized state is displayed. For the two- and three-dimensional versions of the model, extensive Monte Carlo simulations were performed in order to find the exponent γ associated with the difference between the local minimum and maximum heights in the aggregate-size distribution curve. We have found that γ is 1, independent of the spatial dimension.