Multiphase separation model for binary mixed micelles

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, (X-i(mM)/X-j(mM))(P, T) = const., at some temperatures and pressures. However, if (X-i(mM)/X-j(mM))(P, T) is a function of the content of a binary mixture of surfactants, (X-i(mM)/X-j(mM))(P, T) = f(alpha(i)), then instead of the micellar mono-pseudophase, a multi-pseudophase picture for the binary mixed micelle should be accepted. We proved that (X-i(mM)/X-j(mM))(P, T) = n * const., 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: (X-i(mM)/X-j(mM))(P, T) = const. The model-independent methods give the total molar fraction of surfactant i in the micellar multiphases (X-i(mMT)).X-j(mMT) corresponds to the mean value of the activity coefficient (<(f(i)(mM))over bar>). If the regular solution theory (RST) is applied, then <(f(i)(mM))over bar> does not correspond to X-i(mMT). 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. (C) 2019 Elsevier B.V. All tights reserved.