Theory of Electrophoresis of Polyelectrolytes

The transport of polyions in solutions under an applied electric field is controlled by the three counterion effects: the electrophoresis effect, the field distortion effect and the counterion relaxation effect. Recent experimental and theoretical studies have mainly considered the electrophoresis effect which is a hydrodynamic effect of the medium charged by the counterions. In this paper, the other two effects, which result from the distortion of the counterion atmosphere around the polyion, are evaluated through the strict but simple analysis of the diffusion equations for low molecular ions and the Poisson equation. It was found in this study that these two effects are remarkably important for the system of coiled macroions fairly free‐drained. It was also demonstrated that the applied electric field is strongly depressed near the polyions by the shielding effect of counterions. This result is very different from the various theories which have assumed a constant applied field in the whole space. A cubic free‐volume model was adopted in this theory and the case for infinite dilution of polyion was also discussed as a special case of the free‐volume. The most important factor in our mobility expression is the apparent polyion charge expressed by the counterion activity. The results were compared with the experiments referring to the additivity rule for counterion activity.