MEMBRANE CURVATURE ELASTICITY IN WEAKLY CHARGED LAMELLAR PHASES

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 as a constant and consider only situations where it is low enough so that the distance 2d between lamellae is the smallest relevant length scale in the problem. In the presence of salt (the short-distance Debye-Huckel regime) we show that the electrostatic contribution to the bending energy of a membrane is in general small, in disagreement with a previous result, is proportional to d3, and is independent of ionic strength. Identical results are obtained for membranes undulating sinusoidally in phase and for concentric cylindrical membranes. The bending constant is also calculated for membranes held at constant electric potential and is compared to the constant charge density case. In the absence of salt, continuity arguments predict an electrostatic contribution to the bending energy that scales as d3. Furthermore, a direct calculation for concentric cylindrical membranes gives exactly the same scaling behavior (including the numerical prefactor) as in the presence of salt.