We study the effect of electrostati

We study the effect of electrostatic interactions on the membrane bending energies of weakly charged,swollen, lamellar phases of surfactant solutions. We treat the surface charge density of the lamellae asa constant and consider only situations where it is low enough so that the distance 2d between lamellaeis the smallest relevant length scale in the problem. In the presence of salt (the short-distance DebyeHuckel regime) we show that the electrostatic contribution to the bending energy of a membrane is ingeneral small, in disagreement with a previous result, is proportional to d3,and is independent of ionicstrength. Identical results are obtained for membranes undulating sinusoidally in phase and for concentriccylindrical membranes. The bending constant is also calculated for membranes held at constant electricpotential and iscompared to the constant chargedensity case. In the absenceof salt,continuity argumentspredict anelectrostatic contribution tothebendingenergythat scalesasd3. Furthermore,adirect calculationfor concentric cylindrical membranes gives exactly the same scaling behavior (including the numericalprefactor) as in the presence of salt.