Abstract
The translocation of polymer through a channel with a gradient interaction between the polymer and the channel is studied. The interaction is expressed by E = E0 + kx, where E0 is the initial potential energy at the entrance, x is the position of the monomer inside the channel, and k is the energy gradient. The mean first passage time τ is calculated by using Fokker-Planck equation for two cases (1) N > L and (2) N < L under the assumption that the diffusion rate D is a constant, here N is the polymer length and L is the length of channel. Results show that there is a minimum of τ at k = k(c) for both cases, and the value kc is dependent on E0 and driving force f. At large f, the scaling relation τ ∼ N is observed for long polymer chains. But the scaling relation is dependent on the energy gradient k for an unforced driving translocation.
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