The drift velocity in reptation models for electrophoresis

The drift velocity (diffusion constant) in the Rubinstein–Duke model with periodic boundary condition is calculated analytically to lowest order in the applied electric field and numerically for the whole scaling regime. The model is modified by restricting the polymer-storing capacity of the cells and for this case again the diffusion constant is determined. The periodic boundary condition decouples the different tube configurations. Thus, with the process of tube renewal removed, only the diffusion of length defects through the tube remains. The effect of the periodic boundary condition on the value of the diffusion constant and the behavior of the scaling function is discussed on the basis of numerical results for both models with free endpoint motion. The results strongly suggest that to linear order in the field the drift velocity is unaffected by the process of tube renewal, i.e., is only determined by the transport of reptons along the tube.