Pore-blockade times for field-driven polymer translocation

We study pore-blockade times for a translocating polymer of length N, driven by a field E across the pore in three dimensions. The polymer performs Rouse dynamics, i.e., we consider polymer dynamics in the absence of hydrodynamical interactions. We find that the typical time for which the pore remains blocked during a translocation event scales as similar to N(1+ 2 nu)/(1+nu)/E, where nu similar or equal to 0.588 is the Flory exponent for the polymer. We show, in line with our previous work, that this scaling behavior stems from polymer dynamics in the immediate vicinity of the pore - in particular, the memory effects in the polymer chain tension imbalance across the pore. This result, like numerical results from several other groups, violates the lower bound similar to N1+nu/E suggested earlier in the literature. We discuss why this lower bound is incorrect and show, on the basis of the conservation of energy, that the correct lower bound for the pore-blockade time for field-driven translocation is given by eta N-2 nu/E, where eta is the viscosity of the medium surrounding the polymer.