Dynamical Scaling Exponents for Polymer Translocation through a Nanopore

We determine the scaling exponents of polymer translocation (PT) through a nanopore by extensive computer simulations of various microscopic models for chain lengths extending up to N=800 in some cases. We focus on the scaling of the average PT time τ∼Nα and the mean-square change of the PT coordinate, ⟨s2(t)⟩∼tβ. We find α=1+2ν and β=2∕α for unbiased PT in two dimensions (2D) and three dimensions (3D). The relation αβ=2 holds for driven PT in 2D, with a crossover from α≈2ν for short chains to α≈1+ν for long chains. This crossover is, however, absent in 3D where α=1.42±0.01 and αβ≈2.2 for N≈40−800.