  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.
