Onset of Self-Assembly in Polymer-Surfactant Systems

The onset of self-assembly in a dilute aqueous solution containing a flexible polymer and surfactant is theoretically studied. Focusing on the effect of the surfactant on polymer conformation and using a conjecture of partial collapse of the polymer at the onset of self-assembly, we obtain results which agree with known experimental observations: (i) polymer-surfactant self-assembly always starts at a lower concentration (cac) than the one required for surfactant-surfactant self-assembly (cmc); (ii) in charged systems the cac increases with salt concentration and is almost independent of polymer charge; (iii) in weakly interacting systems the cac remains roughly proportional to the cmc over a wide range of cmc values. The special case of amphiphilic side-chain polymers strongly supports our basic conjecture. A similarity is found between the partial collapse induced by the surfactant and general results concerning the effect of impurities on critical phenomena.