END-GRAFTED POLYMERS WITH SURFACTANTS - A THEORETICAL-MODEL

A mean-field analytical model is developed for end-grafted polymers in contact with a solution containing surfactants. At concentrations abo ve the critical association concentration, the surfactants are capable of cooperative association in a micellar form with the polymer chains . For single-grafted coils it is found that the coverage of the polyme r chain by micelles increases continuously with increasing adsorption strength or bulk surfactant concentration. The size of the coils can i ncrease, decrease, or have a maximum with increasing micellar coverage , depending on the relative strength of the monomer-monomer, monomer-m icelle, and micelle-micelle excluded volume interactions. The amount o f surfactants adsorbed on densely grafted polymer chains (brushes) is found to increase either continuously or discontinuously with increasi ng adsorption strength or decreasing grafting density. The character o f the transition is determined by the interplay of the adsorption ener gy and the excluded volume interactions. When the adsorbed amount decr eases continuously with increasing grafting density, the brush height increases at small and large grafting densities and has a local maximu m in the intermediate range. In the case of an abrupt transition in th e adsorbed amount the coexistence of stretched and collapsed chains is predicted in the transition regime. Critical adsorption strengths and grafting densities are discussed. Where possible, the numerical resul ts are compared to experimental data.