Bending moduli of charged membranes immersed in polyelectrolyte solutions

We study the contribution of polyelectrolytes in solution to the bending moduli of charged membranes. Using the Helfrich free energy, and within the mean-field theory, we calculate the dependence of the bending moduli on the electrostatics and short-range interactions between the membrane and the polyelectrolyte chains. The most significant effect is seen for strong short-range interactions and low amounts of added salt where a substantial increase in the bending moduli of order 1 k_BT is obtained. For short-range repulsive membranes, the polyelectrolyte contribution to the bending moduli is small, of the order the 0.1 k_BT up to at most 1 k _BT. For weak short-range attractions, the increase in membrane rigidity is smaller and of less significance. It may even become negative for a large enough amount of added salt. Our numerical results are obtained by solving the adsorption problem in spherical and cylindrical geometries. In some cases, the bending moduli are shown to follow simple scaling laws.