Bending elasticity of surfactant films: the role of the hydrophobic tails

We study the tail contributions to the elastic constants of an amphiphilic layer. For dense systems the terms arising from the attractive van der Waals interactions prevail, whereas the translational entropy of the liquid layer is essential at lower density. Both the membrane rigidity kappa and the Gaussian bending elastic constant kappa; strongly vary with the density of the hydrocarbon chains; for dense systems, they are of the order 100kT with a ratio kappa;/kappa = -2 / 3. At lower density, partial cancellation of interaction and entropic contributions leads to elastic constants of the order of kT, with a ratio close to the value -2 observed for microemulsions.