Molecular modeling of binary mixtures of amphiphiles in a lattice solution

We examine the behavior of binary surfactant mixtures using Monte Carlo simulations with a three-dimensional lattice model of a binary surfactant mixture, in which the surfactants are represented by a series of connected beads. The range of amphiphile concentrations used is around the critical micelle concentration. The quasichemical approximation, a mean-field lattice theory, has also been used to determine the phase equilibrium for these types of solutions. The simulations allow direct determination of micellar properties such as the composition of the aggregates and dispersed phase as well as the individual size distribution of the amphiphiles in the aggregates. Properties of the aggregates such as their shapes, sizes, and volume fraction profiles have also been calculated. The simulation results are analyzed in light of the phase separation model, which considers the micelles as a separate bulk pseudo-phase. The Monte Carlo calculations show that even though the thermodynamic assumptions behind the regular solution theory are not correct, it can be very useful in approximating the prediction of the monomer-micelle compositions and the amphiphile activity coefficients in micelles for mixed amphiphile systems. The results of the simulations do not satisfy fully a thermodynamic consistency test based on the Gibbs–Duhem relationship. This raises questions about the application of the pseudo-phase model to mixed surfactant systems at the concentrations investigated in this work. One potential reason for the noncompliance of this test is that the aggregates might be too small to be considered a pseudo-phase.