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~N^α and the mean-square change of the PT coordinate, ⟨s²(t)⟩~t^β. 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.