The effect of adsorbed polymer on the elastic moduli of surfactant bilayers

We study theoretically the effect of adsorbed homopolymer on surfactant bilayers, restricting ourselves to homogeneous equilibrium adsorption of polymer on both sides of the bilayer, with no penetration. We formulate the energy of adsorption per unit area as a Taylor series in curvature for both spherical and cylindrical surfaces. In the limit of weak adsorption analytic expressions for the polymeric contribution to the mean and Gaussian elastic moduli of the bilayer are derived, using both a mean-field and a scaling functional approach. For stronger adsorption numerical calculations have been made, and in the limit of very strong adsorption, asymptotic functional forms for the elastic moduli found. In all cases the presence of the polymer leads to a decrease in the mean curvature rigidity K and an increase in the Gaussian rigidity $\bar {K}$. At the mean-field level these contributions are always small compared to the thermal energy kB T. However the scaling theory predicts qualitatively similar, but quantitatively larger effects; thus the presence of adsorbed polymer can strongly influence the elasticity of surfactant bilayers