Calculation of the phase equilibrium for systems of the type water + nonionic surfactant + alkane

We present a new thermodynamic model describing the phase behavior of systems water + nonionic surfactant + alkane. This is a generalization of our theory for aqueous solutions of nonionic surfactants published previously. The treatment is based on the mass action law and continuous thermodynamics. Besides the aggregation of the surfactant molecules the self-association of water is taken into account. The resulting polydisperse mixture of aggregated surfactant molecules and water associates is described by continuous aggregation-size distribution functions depending on temperature and composition of the system. The shape of the aggregates is not considered. Furthermore, all surfactant aggregates are assumed to be governed by the same temperature-dependent aggregation constant. The Gibbs energy of the ternary mixture is calculated by the Flory–Huggins theory with three temperature dependent χij parameters. We apply our extended model to the system H2O + C4E1 + n-C12H26. Here, the χij parameter of the binary subsystem water + C4E1 and the micellization constant of C4E1 are known from one of our previous papers. Moreover, there are numerous experimental phase equilibrium data in the literature. The comparison of the calculated results with the experimental ones is satisfactory considering the simplicity of the model and the only few parameters fitted.