Dynamics of a polymer surmounting a potential barrier: The Kramers problem for polymers

Abstract

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. (C) 1999 American Institute of Physics. [S0021-9606(99)51835-7].