Phase equilibria in systems containing both an anionic and a cationic amphiphile. A thermodynamic model calculation

Abstract

We have studied the equilibrium between a lamellar phase and crystalline salts in a four-component system containing both a cationic and an anionic surfactant in water. The chemical potentials for the different components have been derived from a thermodynamic model for the free energy.

In our model system there are four salts that can precipitate: A ⁺ X ⁻, A ⁻X⁺, A ⁺ A ⁻ and X ⁺ X ⁻. A ⁺ and A ⁻ are, respectively, a cationic and an anionic surfactant; X ⁻ and X ⁺ are the corresponding counterions. The system is represented as a trigonal bipyramid. We have calculated the equilibrium between a lamellar phase and crystalline phases A ⁺ A ⁻, A ⁻ X ⁺ and A ⁺ X ⁻ with different weight fractions of A ⁺ A ⁻.

The observed instability gap between the two lamellar regions around equal amounts of A ⁺ X ⁻ and A ⁻ X ⁺ can be explained by the fact that dispersion attraction between the amphiphilic plates dominates over the electrostatic repulsion. The high entropy in the lamellar liquid crystal compared with a common crystal can be the reason for the extension of the lamellar stability region to very low water contents in the vicinity of the instability gap.