  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.
