Self-assembly of ionic surfactant in cross-linked polyelectrolyte gel of opposite charge. A physical model for highly charged systems

A physical model is presented for the self-assembly of ionic surfactants in oppositely charged polyelectrolyte gels. The basic idea is that the formation of a micelle in an initially water-swelled gel is accompanied by a collapse of the surrounding polyion chains resulting in the formation of a complex. The strong electrostatic interaction between the micelle and the highly charged polyion produces a short-range perturbation of the gel structure in the vicinity of the micelle, leaving the complex-free regions of the gel essentially unchanged. With a fixed volume of the complex and a fixed stoichiometry of the surfactant and the polyion in the complex, a linear change in the gel volume is predicted as a function of the number of micelles in the gel. Experiments with dodecyltrimethylammonium bromide in cross-linked sodium polyacrylate support this for weakly cross-linked gels, but deviations are found at higher cross-linking densities.The distribution of the surfactant between gels and equilibrium aqueous phases is investigated and presented as binding isotherms. It is found that prior to micelle formation the surfactant binding can be described as an exchange of sodium ions in the gel with a preferential binding of the sodium ion (Delta G degrees: 1-2 RT/mol). Cooperative binding is observed when the surfactant concentration in the gels exceeds the critical aggregation concentration in solutions of linear polyacrylate of the corresponding polyelectrolyte concentration. The details of the cooperative part of the binding isotherm are investigated by means of a simple law of mass action analysis. It is found that a pronounced effect of small additions of salt is well described at moderate degrees of surfactant binding to the gels. The abrupt reduction of the cooperativity at high degrees of binding is found to coincide with the gels reaching their fully collapsed state, which is characterized by an ordered packing of the complexes. At this point each micelle is surrounded by an excess of polyelectrolyte units.