VARIATIONAL THEORY OF UNDULATING MULTILAYER SYSTEMS

We use a variational approach to determine the equilibrium properties of lamellar surfactant phases. The variational theory yields a general expression for the renormalization of the bending constant of undulat ing sheet-like membranes. The method is then applied to lamellar ensem bles characterized by conserved surfactant film area and the full, non -linear bending Hamiltonian. In the limit of large bending modulus the theory converges towards Helfrich's model. For realistic values of th e bending constant we find an increase in the equilibrium crumpling an d layer separation and characteristic changes in the structure factor and swelling law due to film area conservation and non-linear terms in the Hamiltonian. The scaling of the free energy density, however, app ears to be largely unaffected by first order crumpling corrections.