The role of added polymer in dilute lamellar surfactant phases

We study theoretically the effect of adding polymer to the dilute lamellar phase of surfactant solutions. The polymer, assumed semidilute and in a good solvent, is taken to have a repulsive or attractive interaction with surfactant bilayers, but has no other effect on their properties. Such polymers can mediate an attractive or repulsive interaction between bilayers which we combine with pre-existing interactions (the Helfrich repulsion, van der Waals, and hydration) using a simple additive model. The polymeric contribution to the free energy is estimated using a blob model (for nonadsorbing chains) and the Cahn-de Gennes scaling functional (for adsorbing chains). Phase diagrams for the system are obtained under various conditions. For a lamellar phase which is bound (i.e., which cannot be indefinitely diluted) as a result of van der Waals forces, nonadsorbing polymer is completely expelled as a semidilute solution, leading to a compression of the lamellar stack. Adsorbing polymer can enter the phase, also tending to cause a slight reduction in the maximum layer spacing. For an unbound lamellar phase controlled by Helfrich forces, nonadsorbing polymer is expelled if the bilayers are stiff, but for flexible enough layers, a significant amount of polymer can be solubilized. At too high a volume fraction of polymer, part of the polymer is expelled as a solution, whereas at high surfactant fractions, a phase separation arises between two lamellar phases (one containing polymer, the other not). For the case of adsorbing chains, small amounts of added polymer cause the system to become bound with expulsion of excess solvent. For large amounts of added polymer, the unbound behavior is recovered, whereas for intermediate polymer content, phase equilibria involve either two lamellar phases (each containing polymer), or one such phase coexisting with a polymer solution.