Constitutive Modeling of Soft Materials: Wormlike Micelles

Self-assembly of amphiphilic molecules into various supramolecular nano-structural aggregates has drawn the attention of chemists, physicists, and engineers in recent decades. Examples of such aggregates include wormlike micelles, which are important in a wide range of applications, including lubrication, templating of nano- and micro-structured materials, oil recovery, and also biological applications such as  targeted diagnostic and drug delivery. A sound theoretical understanding of the behaviour of self-assembled aggregates can be achieved using statistical mechanics, continuum mechanics, and mathematical techniques such as differential geometry. The current work is concerned with using a microphysical approach to derive a model for the free-energy density of wormlike micelles based on the interactions between their constituent molecules. In doing so, the relevant concepts of the differential geometry of curves have been applied. This approach is unique in the sense that it relates the interactions between the molecules comprising the micelle to its continuum-based elastic energy. The derivation of the model gives rise to integral representations for the elastic moduli of the wormlike micelle in terms of the interaction potential, and the molecular dimensions. Anisotropic soft-core interaction potentials were applied on the derived model to obtain expressions for the elastic moduli of the wormlike micelle. The results were further used to find the persistence length of the wormlike micelle in terms of molecular dimensions, and the distribution of the molecules.