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Elastic free-energy of wormlike micellar chains: theory and suggested experiments

The extensive application of surfactants motivates comprehensive and predictive theoretical studies that improve our understanding of the behaviour of these complex systems. In this study, an expression for the elastic free-energy density of a wormlike micellar chain is derived taking into account interactions between its constituent molecules. The resulting expression incorporates the sum of a quadratic term in the curvature and a quadratic term in the torsion of the centerline of wormlike micelle and thus resembles free-energy density functions for polymer chains and DNA available in the literature. The derived model is applied on a wormlike micelle in the shape of a circular arc, open or closed. A detailed application of the derived model on wormlike micelles of toroidal shape, along with employing necessary statistical-thermodynamical concepts of self-assembly, is performed, and the results are found to be consistent with the ones available in the literature. Steps towards obtaining the material parameters through experiments are suggested and discussed.