Micro-mechanical, continuum-mechanical, and AFM-based descriptions of elasticity in open cylindrical micellar filaments
We present theoretical and experimental descriptions of the elasticity of cylindrical micellar filaments using micro-mechanical and continuum theories, and atomic force microscopy. Following our micro-mechanical elasticity model for micellar filaments [M. Asgari, Eur. Phys. J. E: Soft Matter Biol. Phys., 2015, 38(9), 1–16], the elastic bending energy of hemispherical end caps is found. The continuum description of the elastic bending energy of a cylindrical micellar filament is also derived using constrained Cosserat rod theory. While the continuum approach provides macroscopic description of the strain energy of the micellar filament, the micro-mechanical approach has a microscopic view of the filament, and provides expressions for kinetic variables based on a selected interaction potential between the molecules comprising the filament. Our model predicts the dependence of the elastic modulus of the micellar filaments on their diameter, which agrees with previous experimental observations. Atomic force microscopy is applied to estimate the elastic modulus of the filaments using force volume analysis. The obtained values of elastic modulus yield the persistence length of micellar filaments on the same order of the previously reported values. Consistent with previous studies, our results indicate that semi-flexible linear micelles have a relatively large local strain energy at their end points, which explains their tendency to fuse to minimize the number of end caps at relatively low total surfactant volume fractions. Also, the elastic modulus of micellar filaments was found to increase when the indentation frequency increases, a finding which agrees with previous rheological observations on the bulk shear modulus of micellar solutions.