Barrier crossing of a semiflexible ring polymer

Motivated by the dynamics of a membrane in response to an external force, we study the thermally activated crossing of a semiflexible ring polymer over a potential barrier. For the bistable potential of Kramers type smoothly varying over a long length scale, we calculate the crossing rate using the multidimensional Kramers' rate theory and the functional integral method. We find that, due to its conformational fluctuation, the rate for a flexible ring is much larger than that for a stiff ring. For a sufficiently long chain length or a sufficiently weak bending modulus, the ring undergoes a compact-stretch transition. The stretched conformation of the chain results in a decrease of the activation energy and so the further increase of the rate. This result implies that the soft matter conformational flexibility and adaptability facilitate the barrier crossing.