On the Curvature Elasticity Theory of Fluid Membranes

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Abstract
Based on the Oseen-Frank-Nehring-Saupe theory of uniaxial liquid crystals, we give in this report a revised approach that the bending rigidity k, the elastic modulus of Gaussian curvature k − and the spontaneous curvature c 0 may be expressed in terms of the various elastic constants of liquid crystals by k= (k 11–2k 13)d, k − = (2k 13–k 22–k 24)d and c 0 = k 11 s 0(k 11–2k 13)d respectively, where d is the thickness of the membrane and s 0 is the spontaneous splay of the liquid crystal. With another approach based on the Landau-de Gennes theory we find that k, k − and c 0 are closely related to the orientational order parameter of the long chains of the molecules in both layers of the bilayer membrane. Comparison of our calculation with experimental results is also discussed.

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