Bending energy of surfactant films

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Abstract
The phenomenological theory of the bending energy in a surfactant membrane is analysed and extended to account for the case of spontaneously curved membranes. The original form of the bending energy, due to Helfrich can be recovered if the differences in the principal curvatures from the spontaneous values are used, rather than the actual curvatures. The linear saddle splay term then vanishes for all spontaneously curved membranes, resulting in a pure splay form (to lowest order). The implications of this modified form for physical models of membrane bending are discussed, and it is shown that a wide variety of models result in the same form, and these models can be distinguished only by their higher-order behaviour (cubic and higher in the curvatures). In particular, it is shown that the description of surfactant aggregation in terms of the surfactant parameter is consistent with the requirements of bending theory.

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