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

TL;DR

This paper derives an elastic free-energy model for wormlike micellar chains considering molecular interactions, applying it to various shapes, and discusses experimental methods to determine material parameters.

Contribution

It introduces a new elastic free-energy expression for wormlike micelles that accounts for molecular interactions and applies it to different micellar geometries.

Findings

Model aligns with existing literature on micellar shapes

Application to toroidal micelles demonstrates model's versatility

Proposes experimental approaches to measure material parameters

Abstract

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.