  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.
