A theoretical analysis of the surface tension profiles of strongly interacting polymer-surfactant systems

Measurements of the surface tension of static polymer-surfactant mixtures as the concentrations of polymer and surfactant are varied produce interesting and surprising profiles. It is well known how the critical points in the surface tension profile of a weakly interacting system relate to the formation of complexes in the bulk. However the critical points in the profiles of strongly interacting systems are much less well understood, and an important open question is what conditions are required for the formation of a peak. Here, using a model for the surface tension developed in a previous article (Bell et al., Langmuir 23 (2007) 6042), we apply asymptotic techniques to show explicitly how the structure of the surface tension profile and the critical concentrations depend on the relative stability of the underlying polymer-surfactant complexes. We derive the interesting result that none of the critical concentrations is at the critical aggregation concentration (CAC). We also identify a criterion for the appearance of a peak in the surface tension profile, expressed in terms of the physical and chemical parameters of the system.