Self-assembly of ionic surfactants in polyelectrolyte solutions: A model for mixtures of opposite charge

A thermodynamic model of polyelectrolyte/surfactant interactions is derived. The model considers the binding of polyion chains to the surface of oppositely charged surfactant micelles. The electrostatic interactions are treated within the Poisson-Boltzmann cell model. The nonelectrostatic interactions are described as in earlier phenomenological models of charged micelles. An explicit expression for the chemical potential of the surfactant in the micelles is derived. It is used to calculate the critical aggregation concentration (cac) in solutions of hydrophilic anionic polyelectrolytes with flexible backbones. The results are compared with experimental data for cationic surfactants, both monovalent and divalent. A reasonable agreement is obtained when the repulsive energy between surfactant headgroups is assumed to vary as a constant/area per headgroup. The model explains why monovalent and divalent surfactants with the same hydrocarbon chain length have about the same cac. It accounts for the increase of the cac with increasing salt and polyelectrolyte concentrations and explains a previously found correlation between the cac and the aggregation number for a given surfactant interacting with different polyelectrolytes. The paper contains a summary of experimental results and a detailed discussion of the nature of the interaction between polyions and surfactants. A mechanism for the suppression of overcharging of the micelles by the polyion is discussed.