Reptation dynamics with random local interactions

We generalize the reptation model to treat cases where the N segments of the primitive chain can interact with a static environment (such as a gel). The rates of tube segment renewal are calculated taking into account both an external field and local interaction energies. This model can be used, e.g., to study the migration of polymers in a random environments (where local entropic and elastic effects can play a role). We then present a study of polymer reptation in a tube with a random (annealed) energy landscape, similar to the one described by Lumpkin and Zimm. In particular, if an external field is applied, the predictions of the biased reptation model are modified. We find that for low field intensities, the electrophoretic mobility mu scales like 1/N1+alpha where the exponent alpha greater than or equal to 0 increases with the strength of the random energies.