A molecular model for the free energy, bending elasticity, and persistence length of wormlike micelles

An expression for the elastic free-energy density of a wormlike micelle is derived taking into account interactions between its constituent molecules. The resulting expression is quadratic in the curvature and torsion of the centerline of micelle and thus resembles free-energy density functions for polymer chains and helical filaments such as DNA. The model is applied on a wormlike micelle in the shape of a circular arc, open or closed. Conditions under which linear chains in dilute systems transform into toroidal rings are analyzed. Two concrete anisotropic soft-core interaction potentials are used to calculate the elastic moduli present in the derived model, in terms of the density of the molecules and their dimensions. Expressions for the persistence length of the wormlike micelle are found based on the flexural rigidities so obtained. Similar to previous observations, our results indicate that the persistence length of a wormlike micelle increases as the aspect ratio of its constituent molecules increases. A detailed application of the model on wormlike micelles of toroidal geometry, along with employing statistical-thermodynamical concepts of self-assembly is performed, and the results are found to be well consistent with the literature. Steps to obtain the material parameters through possible experiments are discussed.