Dynamic relaxation of rodlike micelles

We study theoretically the angular relaxation and translational diffusion of stiff rodlike micelles that can undergo reversible scission reactions, in both the dilute and the entangled regime. The very strong dependence of the angular diffusion constant on rod length leads to an anomalous superdiffusive behavior of the typical angular deflection of a subunit at short times. Despite this, angular correlation functions such as 〈u(t)⋅u(0)〉 (also the linear birefringence and entropic stress response) decay exponentially with a relaxation time that is a power law combination of the time scales for reversible scission and for angular rotation of a (hypothetical) unbreakable rod. This relaxation time corresponds to the waiting time for a subunit to find itself on a rod that is short enough to rotate through an angle of order π before recombining with another rod. The translational diffusion of rodlike micelles shows no anomaly in contrast to the angular case. However, the collective diffusion and self-diffusion constants differ by a factor of 2 at all concentration ranges for which rod micelles exist. The diffusion equation for collective motion is nonlinear (even below the overlap threshold) since the mobility of the rods depends on their local concentration. The dynamic structure factor S(q,t) is calculated to order q4, the quartic terms providing, in principle, a probe of the micellar scission time.