Effects of double-layer polarization and counterion condensation on the electrophoresis of polyelectrolytes

The electrophoretic behavior of an entirely porous, charged entity such as DNA, protein, or a synthetic polymer is modeled. Adopting a spherical polyelectrolyte on the axis of a narrow, long cylindrical pore as the model system, we show that, in addition to the effects of boundary, double-layer polarization arising from the deformation of the ionic cloud surrounding the polyelectrolyte due to the convective flow of ionic species, and electroosmotic retardation flow coming from the motion of unbalanced amount of counterions in the double layer, the effect of counterion condensation also plays a role, yielding behaviors that are different both quantitatively and qualitatively with those of the corresponding rigid and soft particles. The present analysis predicts the presence of several unexpected and interesting results. For instance, the electrophoretic mobility of the polyelectrolyte may show a local maximum as the amount of its fixed charge varies, and the amount of fixed charge at which the local maximum occurs depends upon the thickness of double layer, the relative size of the pore, and the friction coefficient of the polyelectrolyte. These findings are consistent with the experimental observations in the literature, but the relevant mechanisms have not been proposed and/or explained satisfactorily. The results gathered in this study provide valuable information for both the design of an electrophoresis apparatus and the interpretation of experimental data.