Ion induced lamellar-lamellar phase transition in charged surfactant systems.

We propose a model for the liquid-liquid (L(alpha)-->L(alpha(') )) phase transition observed in osmotic pressure measurements of certain charged lamellae-forming amphiphiles. The model free energy combines mean-field electrostatic and phenomenological nonelectrostatic interactions, while the number of dissociated counterions is treated as a variable degree of freedom that is determined self-consistently. The model, therefore, joins two well-known theories: the Poisson-Boltzmann theory for ionic solutions between charged lamellae and the Langmuir-Frumkin-Davies adsorption isotherm modified to account for charged adsorbing species. Minimizing the appropriate free energy for each interlamellar spacing, we find the ionic density profiles and the resulting osmotic pressure. While in the simple Poisson-Boltzmann theory the osmotic pressure isotherms are always smooth, we observe a discontinuous liquid-liquid phase transition when the Poisson-Boltzmann theory is self-consistently augmented by the Langmuir-Frumkin-Davies adsorption. This phase transition depends on the area per amphiphilic head group, as well as on nonelectrostatic interactions of the counterions with the lamellae and interactions between counterion-bound and counterion-dissociated surfactants. Coupling the lateral phase transition in the bilayer plane with electrostatic interactions in the bulk, our results offer a qualitative explanation for the existence of the L(alpha)-->L(alpha(') ) phase transition of didodecyldimethylammonium bromide (DDABr), but the transition's apparent absence for the chloride and the iodide homologs. More quantitative comparisons with experiment require better understanding of the microscopic basis of the phenomenological model parameters.