Abstract
We analyze twisted membrane structures of chiral surfactants in the framework of the equilibrium theoretical approach based on a continuous elastic model. It is shown that both the surfactant ribbon width and its twist pitch can be defined by equilibrium factors, including the chiral elastic energy. We show however that the theoretically predicted dependencies of the ribbon geometrical parameters on the enantiomeric excess (ee) obtained for the uni-lamellar liquid membrane model are in partial, but qualitative disagreement with experimental data. The surfactant membrane model is then generalized in two directions: (i) we consider also multi-lamellar ribbons (of many bilayers), (ii) we allowed for the crystalline (Lβ) state of the bilayers. The multi-bilayer crystalline structure of self-assembling twisted ribbons is consistent with recent results of X-ray and other experimental studies on gemini surfactants, and, simultaneously, the theory developed for such ribbons yields the ee-dependencies of the twisted ribbon width and pitch that are in reasonable agreement with the data based on TEM images.
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