Elasticity of fluctuating charged membranes probed by X-ray grazing-incidence diffuse scattering

Abstract : We have investigated the structure, fluctuations and elasticity parameters of charged fluid membranes composed of didodecyldimethylammonium halide bilayers (DDAX) with different counterions (X = Cl− or Br−) by non-specular (diffuse) X-ray scattering. The samples have been prepared as highly aligned thick stacks on silicon support and have been swollen at controlled osmotic pressures. From line-shape analysis of the diffuse scattering, we can determine the fluctuation amplitudes of the membranes in the Łα phase and the characteristic correlation lengths. According to the Caillé model, the measured structural parameters have been expressed in terms of the exponent η and smectic penetration length λ, from which the smectic compression modulus B (J/m3) and the bending modulus K (J/m) have been determined, as a function of the swelling state. We show that the results are in quantitative agreement with the mean-field electrostatic Poisson-Boltzmann calculations, controlled by the bilayers surface charge density (surfactant head groups with free or condensed counterions).