In this paper, we investigate the microscopic dynamics of a polymer of length $N$ translocating through a narrow pore. Characterization of its purportedly anomalous dynamics has so far remained incomplete. We show that the polymer dynamics is anomalous until the Rouse time $\tau_{ R}\sim N^{ 1+2\nu}$, with a mean square displacement through the pore consistent with $t^{ (1+\nu)/(1+2\nu)}$, with $\nu\approx0.588$ the Flory exponent. This is shown to be directly related to a decay in time of the excess monomer density near the pore as $t^{ -(1+\nu)/(1+2\nu)}\exp(-t/\tau_{ R})$. Beyond the Rouse time translocation becomes diffusive. In consequence of this, the dwell-time $\tau_{ d}$, the time a translocating polymer typically spends within the pore, scales as $N^{ 2+\nu}$, in contrast to previous claims.
Categories: cond-mat.soft cond-mat.stat-mech physics.bio-ph q-bio.BM