Enhanced membrane rigidity in charged lamellar phases

Abstract

We calculate the electrostatic contribution to the bending energy of charged surfactant membranes in lamellar phases when the electrostatic interactions are not screened by added salt. In the limit of high charge densities (when the Gouy-Chapman length λ is smaller than the membrane separation d) we find that the bending constant is proportional to the intermembrane spacing : kc ∼ d/l kB T, where l is the Bjerrum length. This is calculated both from the electrostatic free energy of two membranes undulating symmetrically and from the free energy of two concentric cylindrical membranes. The value of the bending energy is potentially very large compared to kB T, hence the membranes are extremely flat and rigid. We also consider the case of small charge densities (λ > d), and the case of screened interactions with the Debye length κ -1 > d, and show that the bending energy does not scale in the same way for the undulating surface and the cylindrical geometry. We give the scaling behavior of kc in all these limits