A Theory on the Bending Moduli of Thin Membranes by the Use of a Simple Molecular Model

The nature of the bending elasticity of monolayer membranes was studied by the use of the free energy model, in which the energy of the surface dilations of head, chain, and intermediate surface of the molecule was assumed. The intermediate surface was introduced to reproduce the frustrated internal stresses within individual molecules. Under given curvatures, the area of the neutral surface and its position were determined so as to minimize the free energy. We have shown that there exists a neutral surface where the saddle bending modulus becomes zero when the intermediate part does not exist. This result is due to the fact that the free energy does not possess any term that is resistant to shear and it represents the liquid phase of membranes. For frustrated membranes with the intermediate surface, saddle bending moduli of finite values, but much smaller than the cylindrical modulus in magnitude, were obtained, the sign of which is either positive or negative depending on the spontaneous area and the position of the intermediate surface