The role of effective charges in the electrophoresis of highly charged colloids

Abstract

We study the variation of electrophoretic mobilityμ of highly charged spherical colloidal macroions for varying surface charge densityσ onthe colloid using computer simulations of the primitive model for charged colloids. Hydrodynamicinteractions between ions are incorporated by coupling the primitive model of charged colloidsto the lattice Boltzmann model (LB) of the fluid. In the highly charged regime, the mobilityμ of the colloid is known to decrease with the increase of bare chargeQ of the colloid; the aim of this paper is to investigate the cause of this. Wehave identified that the two main factors contributing to the decrease ofμ are counterion charge condensation on the highly charged colloid and an increase ineffective friction of the macroion–counterion complex due to the condensed counterions.Thus the established O’Brien and White theory, which identified the dipolar forceoriginating from distortion of the electric double layer as the cause of decreasingμ, seems to break down for the case of highly charged colloids withσ in the rangeof 30–400 µC cm − 2. To arrive at our conclusions, we counted the number of counterionsq0 moving along with the spherical macroion. We observe in our simulations thatq0 increases with the increase of bare chargeQ, such that theeffective charge Qeff = Q − q0 remains approximately constant. Interestingly for our nanometer-sizedcharged colloid, we observe that, if surface charge densityσ of the colloid is increased by decreasing the radiusRM of the colloid but fixedbare charge Q, the effectivecharge Q − q0 decreaseswith the increase of σ. This behavior is qualitatively different whenσ is increased byincreasing Q keeping RM fixed. Our observations address a controversy about the effective charge of a strongly chargedmacroion: some studies claim that effective charge is independent of the bare charge (Alexanderet al 1984 J. Chem. Phys. 80 5776; Trizac et al 2003 Langmuir 19 4027) whereas others claim thatQeff decreases withincreasing bare charge Q (dos Santos 2009 J. Chem. Phys. 130 124110; Diehl et al 2004 J. Chem. Phys.121 12100; Groot et al 1991 J. Chem. Phys. 95 9191) at relatively high values ofσ.