Liquid-liquid equilibrium calculation in binary water + nonionic surfactant CiEj systems with a new mass-action law model based on continuous thermodynamics

A systematic study of the LLE for a number of aqueous solutions of n-alkyl polyglycol ethers (CiEj) with tail length i from 4 to 12 and head length j from 1 to 6 is presented. For calculation a new thermodynamic model was developed basing on the mass-action law and continuous thermodynamics. Besides the micellization the self association of water is taken into account. The resulting polydisperse mixture of micelles and water associates is described by two continuous aggregation-size distribution functions depending on temperature and surfactant concentration. The Gibbs energy of the mixture is calculated by the Flory-Huggins theory with a temparature dependent parameter χ. The model is applied to 13 water + CiEj systems with LCST behavior and to the three systems water + C4E1, water + C10E4 and water + C10E5 with closed-loop miscibility gaps. For the former 13 systems four parameters were fitted to the experimental equilibrium data. For the systems with closed-loop miscibility gaps two additional parameters were necessary, due two the more extended temperature range. The agreement between calculated and experimental data is very good for nearly all systems of both types.