Dynamics of a polymer surmounting a potential barrier: The Kramers problemfor polymers

We study the dynamics of a flexible polymer under a Kramers potential using the multidimensional barrier crossing theory. The activation free energy o f the polymer evaluated by a lattice statistics yields the crossing rate as a function of chain length, temperature, and potential parameters. It is f ound that a long chain has an enhanced crossing rate due to the extended co nformation of low free energy it has at the barrier, while a short chain ha s the crossing dynamics of a Brownian particle. A chain of intermediate len gth 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 l arger than that of a polymer in the globular state, due to the internal deg rees of freedom of the unfolded flexible chain. Our results can be applied to macromolecular separation and DNA electrophoresis. (C) 1999 American Ins titute of Physics. [S0021-9606(99)51835-7].