Linking molecular timescales to linear viscoelastic response in dilute and semidilute unentangled wormlike micelle solutions

Unentangled wormlike micelle solutions relax stress through a dynamic interplay of reversible scission and intrachain relaxation involving a hierarchy of molecular timescales whose relationship to linear viscoelastic response remains incompletely resolved. A multiparticle mesoscopic Brownian dynamics framework has been developed in which persistent worms, represented by bead-spring chains with sticky ends, assemble to form wormlike micelles via reversible scission and fusion. Both linear and ring-like micelles are formed across the dilute and semidilute concentration regimes. Accurate predictions of dynamic properties are obtained through inclusion of hydrodynamic interactions using a RPY tensor. We identify and quantify characteristic timescales governing micellar dynamics, including bond lifetimes, self- and non-self-recombination times, breakage times of wormlike micelles of length $L$, relaxation times of various contributions to stress, and the longest relaxation time. The dependence of these timescales on sticker strength, concentration, micellar topology and hydrodynamic interactions is established. The presence of ring micelles is found to moderately prolong recombination and breakage processes, while hydrodynamic interactions are shown to affect some of the timescales by reducing sticker mobility. When appropriately scaled, the dependence on mean length of the non-self-recombination and micelle breakage times collapse onto master curves. Storage and loss moduli exhibit distinctive features in the intermediate-frequency regime that are absent in homopolymer solutions. A clear connection is made between micellar timescales and these signatures in the dynamic moduli at various characteristic frequencies, providing a direct link between microscopic dynamics and macroscopic rheology in unentangled wormlike micellar solutions, in dilute and semidilute concentration regimes.