Multi-Scale Modeling of Worm-like Micelle Rheology

We model the dynamics of worm-like micellar rheology using both a slip-spring model and a “pointer algorithm,” both of which account for micellar diffusion within an entanglement network, as well as breakage/fusion of micelles. We check the accuracy of the pointer algorithm using the more highly resolved slip-spring simulations for micelles with limited numbers of entanglements (up to five per average micelle), and find that the terminal region is accurately modeled, while higher frequency processes require more care to model correctly.  Once validated, the pointer algorithm allows prediction of the rheology of more highly entangled micellar solutions, and stiffer micelles, typical of the literature and of commercial formulations. We also show that the simplified estimate of micelle length of Cates only becomes valid for highly entangled, long, micelles, and we demonstrate a simple method of improving the Cates analysis of micelle length from rheology.  We also check and confirm mean-field scaling laws of micelle length and modulus versus surfactant concentration, using micelle parameters extracted from experimental data by fits of the pointer algorithm to rheological data.   Finally, we apply the slip-spring model to the nonlinear rheology of entangled thread-like micelle solutions, including the effects of chain strength, entanglements, and breakage/fusion.