Ion Induced Lamellar-Lamellar Phase Transition in Charged Surfactant Systems

TL;DR

This paper presents a model combining electrostatic and non-electrostatic interactions to explain a discontinuous liquid-liquid phase transition in charged lamellar systems, aligning with experimental observations for specific surfactants.

Contribution

It introduces a self-consistent model integrating Poisson-Boltzmann and Langmuir-Frumkin-Davies theories to explain phase transitions in charged lamellae.

Findings

Discontinuous phase transition observed with combined electrostatic and adsorption effects.

Transition depends on area per headgroup and counterion interactions.

Qualitative explanation for phase behavior of DDABr surfactant.

Abstract

We propose a model for the liquid-liquid phase transition observed in osmotic pressure measurements of certain charged lamellae-forming amphiphiles. The model free energy combines mean-field electrostatic and phenomenological non-electrostatic 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 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 Poisson-Boltzmann theory is self-consistently augmented by Langmuir-Frumkin-Davies adsorption. This phase transition depends on the area per amphiphilic headgroup, as well as on non-electrostatic interactions of the counterions with the lamellae, and interactions between counterion-bound and counterion-dissociated surfactants. Coupling lateral phase transition in the bilayer plane with electrostatic interactions in the bulk, our results offer a qualitative explanation for the existence of the phase-transition of DDABr (didodecyldimethylammonium bromide), but its apparent absence for the chloride and the iodide homologues. More quantitative comparisons with experiment require better understanding of the microscopic basis of the phenomenological model parameters.