Journal of Molecular Liquids | 2019
Multiphase separation model for binary mixed micelles
Abstract
Abstract Starting from the equilibrium between a micellar binary monophase and a water solution of surfactants i and j, we found that the ratio between the molar fraction of surfactant i of the micellar pseudophase and the molar fraction of surfactant j of the micellar pseudophase is a constant value, (ximM/xjmM)P, T\u202f=\u202fconst., at some temperatures and pressures. However, if (ximM/xjmM)P, T is a function of the content of a binary mixture of surfactants, (ximM/xjmM)P, T\u202f=\u202ff(αi), then instead of the micellar mono-pseudophase, a multi-pseudophase picture for the binary mixed micelle should be accepted. We proved that (ximM/xjmM)p, T\u202f=\u202fn\u202f∗\u202fconst., with n being the element from the set of all positive rational numbers. In the multiphase model, the following equation is applied for each phase: (ximM/xjmM)P, T\u202f=\u202fconst. The model-independent methods give the total molar fraction of surfactant i in the micellar multiphases (ximMT). ximMT corresponds to the mean value of the activity coefficient ( f i mM ¯ ). If the regular solution theory (RST) is applied, then f i mM ¯ does not correspond to ximMT. This means that if the micellar multi-pseudophases exist at the critical micelle concentration, then using the RST and the model-independent methods for determining the excess Gibbs free energy give different values even in the case where the binary mixture of surfactants is symmetric.