Journal of Chemical Physics, Vol.111, No.11, 5259-5266, 1999
Dynamics of a polymer surmounting a potential barrier: The Kramers problem for polymers
We study the dynamics of a flexible polymer under a Kramers potential using the multidimensional barrier crossing theory. The activation free energy of the polymer evaluated by a lattice statistics yields the crossing rate as a function of chain length, temperature, and potential parameters. It is found that a long chain has an enhanced crossing rate due to the extended conformation of low free energy it has at the barrier, while a short chain has the crossing dynamics of a Brownian particle. A chain of intermediate length can exhibit a minimum in the crossing rate as chain length varies. For any range of chain lengths and potential parameters, the crossing rate is larger than that of a polymer in the globular state, due to the internal degrees of freedom of the unfolded flexible chain. Our results can be applied to macromolecular separation and DNA electrophoresis.