Transition in three-dimensional micellar systems

We have studied the thermal behavior of aggregates of amphiphilic molecules in water for a three-dimensional lattice model. We have employed extensive Monte Carlo simulations to find the distribution curve for aggregate size as a function of temperature. Our model consists of amphiphile molecules with a single polar head and three monomers in its hydrophobic tail. In this lattice model each amphiphile occupies four sites of the lattice, and the water molecules occupy only one site. We determine the free amphiphile concentration and the aggregate-size distribution P(n) as functions of total surfactant concentration for different temperatures. As for the two-dimensional case, the degree of micellar organization is characterized by Δ≡P(nmax)−P(nmin), where nmin and nmax>nmin are the aggregate sizes at which P exhibits its local minimum and maximum. For this three-dimensional model we also show that Δ vanishes continuously as we increase the temperature. However, the exponent associated with the micellar to nonmicellar transition is twice that found in the two-dimensional simulations.