Curvature elasticity models of microemulsions

Abstract

We review the theory of curvature elasticity of thin, fluid films starting with a phenomenological formalism motivated by microscopic, physical examples. The effects of finite compressibility of the layer, exchange of molecules between the film and the solution, and the intrinsic bending stiffness of the film are taken into account; these degrees of freedom account for all the important molecular modes of the system. The effects of fluctuations of the number of molecules in the film (which is in equilibrium with surfactant molecules or micelles in solution) and in the area per molecule about its equilibrium value is shown to soften the curvature elastic moduli. The relationship of the bending moduli to the pressure distribution in the film is discussed and it is demonstrated that isotropic liquid films have no bending modulus, in the continuum limit. The bending moduli for charged membranes and for block copolymers are estimated. Finally, some recent experimental measure of curvature elasticity are discussed and compared with the theory.