Kink motion in the barrier crossing of a chain molecule

We consider the activated escape of chain molecule of N segments over a barrier, a generalization of the classic Kramers problem. Using the Rouse model, we show that the free energy of activation has a square root dependence on the temperature T, leading to a non-Arrhenius form for the rate. We further show that there is a special time dependent solution of the model, which corresponds to a kink in the chain, confined to the region of the barrier. The polymer goes from one side to the other by the motion of the kink in the reverse direction. If there is no free energy difference between the two sides of the barrier, then the kink moves by diffusion and the time of crossing $t_{\mathrm{cross}}\sim N^2{/T}^{3/2}.$ If there is a free energy difference, then the kink moves with a nonzero velocity from the lower free energy side to the other, leading to $t_{\mathrm{cross}}\sim N/\sqrt{T}.$