The dimension dependence of gel electrophoresis

We study the significance of self-avoidance on the dynamics of a reptating polymer in a field. We show that in two dimensions the drift velocity decreases with field above a certain field strength due to self-trapping of the polymer. This phenomenon does not occur in more than two dimensions. We conclude that there is a crucial difference between electrophoresis in two and electrophoresis in more than two dimensions and that electrophoresis in a plane has the potential for a much better size-selectivity than gel electrophoresis in three dimensions. Moreover, we establish a scaling law for the drift velocity of a two-dimensional polymer, and show that the scaling variable is N2.5±0.03ε