Role of Adsorbed Polymer in Bilayer Elasticity

We study theoretically the effect of adsorbed homopolymer on surfactant bilayers. We formulate the energy of adsorption per unit area as a Taylor series in curvature for both spherical and cylindrical surfaces. In the limits of weak adsorption analytic expressions are derived for the polymeric contribution to the elastic moduli of the bilayer, using a scaling functional approach. For stronger adsorption numerical and asymptotic calculations have been made. 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 . For strong adsorption these contributions are comparable to k B T ; thus the presence of adsorbed polymer can strongly influence the elasticity of surfactant bilayers.