Simple theoretical framework for a systematic molecular dynamics study of the interfacial properties of oil/water systems in the presence of surfactant molecules

This paper presents a simple theoretical methodology for a systematic molecular dynamics study of the interfacial properties of oil/water/surfactant systems. This formalism is based on the appropriate definition and classification of the different energy terms which contribute to the free energy of the ternary system, and thus, to the chemical potentials of the surfactants in oil, water, and at the oil/water interface. Using molecular dynamics techniques over interfacial and bulk models atomistically described, series expansions fittings of those energy terms as a function of surfactant concentration can be obtained, and a simple thermodynamic expression for the free energy of the whole system results. This report is solely related with the development of that free-energy expression along with analytical formulae for the surface excess, the interfacial tension, and the chemical potentials of a surfactant in oil, water, and at the oil/water interface. The application of this theoretical approach to the study of the interfacial properties produced by chemically different surfactants, and a systematic study of the effect of the formulation variables on the interfacial behaviour of an oil/water system, will be forwarded in future reports.