Self-Assembly in Mixtures of Amphiphilic Polymers and Surfactants

We present a model for the joint self-assembly of amphiphilic polymers and small amphiphilic molecules (surfactants) in a dilute aqueous solution. The polymer is assumed to consist of a hydrophilic backbone and a large number of hydrophobic side groups. Preference of the surfactant to bind to hydrophobic microdomains along the polymer induces an effective attraction between bound surfactants. This leads to two distinct binding regimes depending on a single physical parameter, \epsilon, which represents the ratio between surfactant-polymer affinity and polymer hydrophobicity. For small \epsilon the binding is non-cooperative, whereas for large \epsilon it becomes strongly cooperative at a well-defined critical aggregation concentration. Our findings are in accord with observations on diverse experimental systems.