Mobility of a reptating polymer with fast diffusion of stored length

We study a reptation model of polymer electrophoresis in which the diffusion of stored length is very fast compared to the end point model. For long chains we find that the polymer becomes stretched. We demonstrate that the drift velocity in one dimension is higher by a factor 10/3 than would have been expected on the basis of simple estimates. This is caused by the fact that a polymer segment, once created, has a probability of staying that depends on its orientation. The scaling parameter determining the long chain behavior is N${\mathrm{\epsilon }}^2$, where N is proportional to the length of the polymer and ε is the (dimensionless) electric field strength. When N${\mathrm{\epsilon }}^2$≳8 the drift velocity becomes independent on the length of the polymer. For low fields we demonstrate that there is a crossover from a regime where the field can essentially be neglected to a regime where the field significantly changes the dynamics of the polymer. The scaling parameter determining this crossover is shown to be ${\mathit{N}}^3$ ${\mathrm{\epsilon }}^2$.