Variational theory of undulating multilayer systems

(Received 5 November 1993, accepted in final form 15 February 1994)

Abstract
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 undulating sheet-like membranes. The method is then applied to lamellar ensembles 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 the bending constant we find an increase in the equilibrium crumpling and 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, appears to be largely unaffected by first order crumpling corrections.