ON THE DISTRIBUTION OF SURFACTANTS AMONG MIXED MICELLES

Composition distributions of mixed micelles are analyzed using basic p rinciples of classical statistical mechanics with special emphasis on potential application to fluorescence quenching experiments in such sy stems. The problem is formulated as a lattice model with nearest-neigh bor interactions between surfactant hydrophilic moieties. Firstly, the mean-field approximation is discussed in some detail with focus on it s general character. Deeper analysis, involving direct evaluation of t he lattice partition function, shows how substantial the deviations fr om the mean-field predictions can be. The situation is dramatically im proved when the truncated cumulant expansion is introduced. Two specia l cases are distinguished, where the so-called interchange energy take s positive or negative values. In the former case, a binary mixture ca n separate into two phases of different composition, while in the latt er micelles can undergo structural ordering. Finally, mixtures with ex cess of one component are considered and a useful approximation for th e grand partition function is derived.