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

We study the variation of electrophoretic mobility μ of highly charged spherical colloidal macroions for varying surface charge density σ on the colloid using computer simulations of the primitive model for charged colloids. Hydrodynamic interactions between ions are incorporated by coupling the primitive model of charged colloids to the lattice Boltzmann model (LB) of the fluid. In the highly charged regime, the mobility μ of the colloid is known to decrease with the increase of bare charge Q of the colloid; the aim of this paper is to investigate the cause of this. We have identified that the two main factors contributing to the decrease of μ are counterion charge condensation on the highly charged colloid and an increase in effective friction of the macroion-counterion complex due to the condensed counterions. Thus the established O'Brien and White theory, which identified the dipolar force originating from distortion of the electric double layer as the cause of decreasing μ, seems to break down for the case of highly charged colloids with σ in the range of 30-400 µC cm (- 2). To arrive at our conclusions, we counted the number of counterions q0 moving along with the spherical macroion. We observe in our simulations that q0 increases with the increase of bare charge Q, such that the effective charge Qeff = Q - q0 remains approximately constant. Interestingly for our nanometer-sized charged colloid, we observe that, if surface charge density σ of the colloid is increased by decreasing the radius RM of the colloid but fixed bare charge Q, the effective charge Q - q0 decreases with the increase of σ. This behavior is qualitatively different when σ is increased by increasing Q keeping RM fixed. Our observations address a controversy about the effective charge of a strongly charged macroion: some studies claim that effective charge is independent of the bare charge (Alexander et al 1984 J. Chem. Phys. 80 5776; Trizac et al 2003 Langmuir 19 4027) whereas others claim that Qeff decreases with increasing 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 of σ.