Electrophoretic mobility of a highly charged colloidal particle in a solution of general electrolytes

Abstract

For a highly charged particle in an electrolyte solution, counterions are condensed very near the particle surface. The electrochemical potential of counterions accumulated near the particle surface is thus not affected by the applied electric field, so that the condensed counterions do not contribute to the particle electrophoretic mobility. In the present paper we derive an expression for the electrophoretic mobility μ ∞ of a highly charged spherical particle of radius a and zeta potential ζ in the limit of very high ζ in a solution of general electrolytes with large κa (where κ is the Debye–Hückel parameter) on the basis of our previous theory for the case of symmetrical electrolytes (H. Ohshima, J. Colloid Interface Sci. 263 (2003) 337). It is shown that ζ can formally be expressed as the sum of two components: the co-ion component, ζ co-ion, and the counterion component, ζ counterion (where ζ= ζ co-ion+ ζ counterion) and that the limiting electrophoretic mobility μ ∞ is given by μ ∞= ε r ε 0 ζ ∞ co-ion/ η+ O(1/ κa), where ζ ∞ co-ion is the high ζ-limiting form of ζ co-ion, ε r and η are, respectively, the relative permittivity and viscosity of the solution, and ε 0 is the permittivity of a vacuum. That is, the particle behaves as if its zeta potential were ζ ∞ co-ion, independent of ζ. For the case of a positively charged particle in an aqueous electrolyte solution at 25 °C, the value of ζ ∞ co-ion is 35.6 mV for 1–1 electrolytes, 46.0 mV for 2–1 electrolytes, and 12.2 mV for 1–2 electrolytes. It is also found that the magnitude of μ ∞ increases as the valence of co-ions increases, whereas the magnitude of μ ∞ decreases as the valence of counterions increases.