End-monomer dynamics in semiflexible polymers

Spurred by an experimental controversy in the literature, we investigate the end-monomer dynamics of semiflexible polymers through Brownian hydrodynamic simulations and dynamic mean-field theory. Precise experimental observations over the last few years of end-monomer dynamics in the diffusion of double-stranded DNA have given conflicting results: one study indicated an unexpected Rouse-like scaling of the mean squared displacement (MSD) 〈r(2)(t)〉 t(1/2) at intermediate times, corresponding to fluctuations at length scales larger than the persistence length but smaller than the coil size; another study claimed the more conventional Zimm scaling 〈r(2)(t)〉 t(2/3) in the same time range. Using hydrodynamic simulations, analytical and scaling theories, we find a novel intermediate dynamical regime where the effective local exponent of the end-monomer MSD, α(t) = d log〈r(2)(t)〉/d log t, drops below the Zimm value of 2/3 for sufficiently long chains. The deviation from the Zimm prediction increases with chain length, though it does not reach the Rouse limit of 1/2. The qualitative features of this intermediate regime, found in simulations and in an improved mean-field theory for semiflexible polymers, in particular the variation of α(t) with chain and persistence lengths, can be reproduced through a heuristic scaling argument. Anomalously low values of the effective exponent α are explained by hydrodynamic effects related to the slow crossover from dynamics on length scales smaller than the persistence length to dynamics on larger length scales.

Duke Scholars

Author Michael Rubinstein Thomas Lord Department of Mechanical Engineering and Materia ...