Electrostatics of Curved Fluid Membranes: The Interplay of Direct Interactions and Fluctuations in Charged Lamellar Phase

Abstract

Our understanding of the Poisson-Boltzmann electrostatics of curved fluid monolayers and bilayers of ionic amphiphiles, and its status within the Helfrich bending-energy formulation, is reviewed and subsequently extended. The two limiting scenarios, namely excess salt (non-overlapping interfaces) and zero salt (counterions only) are briefly discussed to couch their generalization to intermediate screening. This general situation of arbitrary composition is treated first within the cylindrical and spherical cell models, to harmonic order in their curvatures, leading on to the geometry of undulating planar confinement, now harmonic in amplitude but covering the entire spectrum of wavelengths. The latter derivation extends previous results, and moreover, provides analytic expressions for the electrostatic free energy using theta function developments. This in turn supplies the Hamiltonian for the generalized harmonic theory of fluctuating lamellar phases with added salt. Finally, the statistical mechanical predictions for the area increase, and relative amplitudes, of bilayer thermal undulations are compared to existing light-scattering data from dilute lamellar phases doped with anionic surfactant.