Surfactant binding and micellisation in polymer solutions and gels: Binding isotherms and their consequences

Transient networks are formed by many pairs of polymer and surfactant that associate into mixed micelles. Generally, for a given polymer concentration, the viscosity or the elastic shear modulus of such mixtures first increases and then decreases with the concentration of added surfactant. We point to the importance of considering the general features of the isotherm for the binding of the surfactant to the polymer when analysing these effects. We argue that a break-down of mixed micellar crosslinks between polymers should typically occur only when the added surfactant dominates in the mixed micelles. At this point, the concentration of monomeric surfactant should be of the same order as the relevant c.m.c. of the surfactant. The relevant c.m.c. is not generally the bulk c.m.c. but, rather, the c.m.c. in the same system but in the absence of those hydrophobic parts of the polymer that are responsible for the interpolymer crosslinking. We use this approach to analyse new and previously published experimental data on a range of ionic and non-ionic hydrophobically modified polymers mixed with surfactants that form spherical micelles, but have widely different c.m.c.s. A consistent picture of the mixed micellar stoichiometries at the point of the maximum viscosity, and at the point of final dissolution of the mixed micellar crosslinks, emerges from this analysis.