Electrophoretic mobility of a cylinder with high surface charge density

Abstract

The electrophoretic mobility of a cylindrical particle is calculated by combining the solution of the complete Poisson-Boltzmann equation in cylindrical coordinates with the equations of Henry. Results are obtained for pointlike counterions (Gouy-Chapman picture) and for counterions having a finite diameter (Stern layer model). The deformation of the ionic atmosphere under the influence of the external field (relaxation effect) is not taken into account. In application to actual data a correction procedure for the relaxation effect, such as the semiempirical method proposed by W. J. H. M. Möller, G. A. J. van Os, and J. Th. G. Overbeek (Trans. Faraday Soc. 57, 312, 325, 1961), should be combined with the present treatment. Results can be applied to stiff (e.g., DNA) and to flexible (e.g., vinylic polyacids) polyelectrolytes.