Coil-to-stretch transition, kink formation, and efficient barrier crossing of a flexible chain

We study the thermally activated barrier crossing of a linear, flexible chain (polymer) under the Kramers bistable potential using the multidimensional barrier crossing theory and the functional integral method. We find that above a critical chain length or below a critical chain spring constant the chain at the barrier top undergoes coil-to-stretch transition, resulting in the formation of a kink. The emergence of the kink mode renormalizes the activation energy to a smaller value so as to facilitate the barrier crossing. In addition to this, the larger fluctuation of the polymer in the unstable region of the potential (compared to that in the confining well) further reduces the free energy barrier, and greatly enhances the crossing rate of a flexible chain. We calculate analytically the crossing rates and confirm the results by numerical simulations. The polymer in barrier crossing thus reveals its conformational flexibility and adjustment to external forces as characteristic features of soft matter dynamics.