Onset of Self-Assembly in Polymer-Surfactant Systems

Amphiphilic molecules (surfactants) consist of two opposing parts - a water-soluble moiety and a water-insoluble one - which are chemically bonded. Consequently, above a certain threshold concentration in aqueous solution (critical micellar concentration, cmc) surfactants self-assemble into aggregates. Aqueous solutions containing linear, flexible chain molecules (polymers) and surfactants exhibit self-assembly at much lower surfactant concentrations. This feature offers a delicate control over the physical properties of the solution, which is used in numerous applications. We study theoretically the onset of self-assembly in such polymer-surfactant systems. Focusing on the effect of the surfactant on polymer conformation and using a conjecture of local instability of the polymer at the onset of self-assembly, we obtain several simple predictions: (i) the threshold concentration required for polymer-surfactant self-assembly (critical aggregation concentration, cac) is always lower than the cmc; (ii) in charged systems the cac increases with the concentration of added salt and is almost independent of polymer charge; (iii) in weakly interacting systems the cac follows changes in the cmc roughly linearly. We further use the special case of interactions between surfactants and amphiphilic polymers to demonstrate the crucial role of chain conformation in the self-assembly. The predictions are supported by available experiments