Kramers problem for a polymer in a double well

Abstract

The generalization of the Kramers escape over a barrier problem to the case of a long chain molecule is investigated. It involves the motion of chain molecule of N segments across a region where the free energy per segment is higher, so that it has to cross a barrier. The limit where the width of the barrier w is large in comparison with the Kuhn length l, but small in comparison with the total length Nl of the molecule is considered. The free energy of activation was calculated, which shows a square root dependence on the temperature T, leading to a non-Arrhenius form for the rate.