Quantitative molecular interpretation of mesoscopic correlations in bicontinuous microemulsions

The charge frustrated Ising model is used as the basis for understanding bicontinuous oil-water-surfactant mixtures. The elemental energy of the model is related to the surface tension between oil and water in the absence of surfactant. The two elemental lengths of the model are related to the volume of a water molecule (or oil segment) and the length of a surfactant molecule. The model is analyzed analytically with approximations justified for homogeneous mixtures on length scales that are larger than these microscopic lengths. The symmetry and discreteness of the underlying lattice are physically irrelevant in this regime. The local mean field approximation is applied to the model yielding a theory that is consistent with the Landau-Ginzburg phenomenology of microemulsions. Corrections to the mean field treatment are required for a quantitative description of the correlations of bicontinuous microemulsions. In analyzing these corrections, a theory is derived that is related to the random wave model, but with all phenomenological coefficients now determined in terms of temperature, surfactant density, and surfactant chain length. A comparison with existing experimental data is successful. Predictions and suggestions are made for future experiments.