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The extensive application of surfactants motivates comprehensive andpredictive theoretical studies that improve our understanding of the behaviourof these complex systems. In this study, an expression for the elasticfree-energy density of a wormlike micellar chain is derived taking into accountinteractions between its constituent molecules. The resulting expressionincorporates the sum of a quadratic term in the curvature and a quadratic termin the torsion of the centerline of wormlike micelle and thus resemblesfree-energy density functions for polymer chains and DNA available in theliterature. The derived model is applied on a wormlike micelle in the shape ofa circular arc, open or closed. A detailed application of the derived model onwormlike micelles of toroidal shape, along with employing necessarystatistical-thermodynamical concepts of self-assembly, is performed, and theresults are found to be consistent with the ones available in the literature.Steps towards obtaining the material parameters through experiments aresuggested and discussed.

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