Charge regulation of nonpolar colloids

Individual colloids often carry a charge as a result of the dissociation (or adsorption) of weakly-ionized surface groups. The magnitude depends on the precise chemical environment surrounding a particle, which in a concentrated dispersion is a function of the colloid packing fraction $\eta$. Theoretical studies have suggested that the effective charge $Z_{\rm{eff}}$ in regulated systems could, in general, decrease with increasing $\eta$. We test this hypothesis for nonpolar dispersions by determining $Z_{\rm{eff}}(\eta)$ over a wide range of packing fractions ($10^{-5} \le \eta \le 0.3$) using a combination of small-angle X-ray scattering and electrophoretic mobility measurements. We find a complex dependence of the particle charge as a function of the packing fraction, with $Z_{\rm{eff}}$ initially decreasing at low concentrations before finally increasing at high $\eta$. We attribute the non-monotonic density dependence to a crossover from concentration-independent screening at low $\eta$, to a high packing fraction regime in which counterions outnumber salt ions and electrostatic screening becomes $\eta$-dependent. The efficiency of charge stabilization at high concentrations may explain the unusually high stability of concentrated nanoparticle dispersions which has been reported.