Theory of Collapse and Overcharging of a Polyelectrolyte Microgel Induced by an Oppositely Charged Surfactant

We report on the theoretical study of interaction of ionic surfactants with oppositely charged microgel particles in dilute solutions. Two approaches are proposed. Within the first approach, the micellization of the surfactants inside the microgel is taken into account while the second model focuses on the hydrophobic interactions of the surfactant tails with the hydrophobic parts of microgel subchains. It has been shown that microgels effectively absorb surfactant ions. At low surfactant concentration this absorption is realized due to an ion exchange between microgel counterions and surfactant ions. The ion exchange is significantly affected by the amount of the microgel counterions initially trapped within the microgel particles which depends on the size of the microgel, its ionization degree, cross-linking density as well as polymer concentration in the solution. Increase of the surfactant concentration causes contraction of the microgels, which can be realized as either a continuous shrinking or a jumplike collapse transition depending on the system parameters. In the collapsed state additional absorption of surfactants by microgels takes place due to an energy gain from micellization or hydrophobic interactions. This leads to microgel precipitation and successive microgel overcharging at an excess of the surfactant in the solution. The theoretical results are compared with the existing experimental data, in particular, on photosensitive surfactant/microgel complexes.