Aggregation of Colloidal Particles in the Presenceof Multivalent Co-Ions: The Inverse Schulze–Hardy Rule.

Shiftsof the critical coagulation concentration (CCC) in particlesuspensions in salt solutions containing multivalent co-ions and monovalentcounterions are rationalized. One observes that the CCC is inverselyproportional to the valence, and this behavior is referred to as theinverse Schulze–Hardy rule. This dependence is establishedby means of measurements of the stability ratio for positively andnegatively charged latex particles with time-resolved light scattering.The same dependence is equally suggested by calculations of the CCCwith the Derjaguin, Landau, Verwey, and Overbeek (DLVO) theory, wherebythe full Poisson–Boltzmann equation for the asymmetric electrolyteshas to be used. The latter aspect is essential, since in the caseof multivalent co-ions the surface charge is principally neutralizedby monovalent counterions. This rule complements the classical Schulze–Hardyrule, which applies in the case of multivalent counterions, and statesthat the CCC is inversely proportional to the sixth power of the valence. [ABSTRACT FROM AUTHOR]