Effects of multivalent salt addition on effective charge of dilute colloidal solutions

The effective charge Z* is often invoked to account for the accumulation of counterions near the colloid with intrinsic charge Z. Although the ion concentrations c(i) are not uniform in the solution due to the presence of the charged particle, their chemical potentials are uniform everywhere. Thus, on the basis of ion chemical potential, effective ion concentrations c(i)*, which can be experimentally measured by potentiometry, are defined with the pure salt solution as the reference state. The effective charge associated with the charged particle can then be determined by the global electroneutrality condition. Monte Carlo simulations are performed in a spherical Wigner-Seitz cell to obtain the effective charge of the colloid. In terms of the charge ratio alpha=Z*/Z, the effects of added salt concentration, counterion valency, and particle charge are examined. The effective charge declines with increasing salt concentration and the multivalent salt is much more efficient in reducing the effective charge of the colloidal solution. Moreover, the extent of effective charge reduction is decreased with increasing intrinsic charge for a given concentration of added salt. Those results are qualitatively consistent with experimental observations by electrophoresis.