Application to Charge Regulation between Particles

In Chapter 6, the interaction of colloidal particles by charge regulation was introduced, but its treatment requires use of the concepts developed in Chapter 11 and in this chapter. We will show here the results of a rather recent study (Chan et al. 2006). 

FIGURE 12.18 Schematic representation of the model for two parallel plane snrfaces in the charge regulation approach, assumed to he oxide surfaces in equilihrium with the solution. (Adapted from Journal of Colloid and Interface Science, 296, Chan, D. Y. C. et al.. Electrical double layer interactions between dissimilar oxide surfaces with charge regulation and Stem-Grahame layers, no. 1 (April 1), 150-158, Copyright (2006), with permission from Elsevier.) 

Ion pairing (considering a 1-1 MX electrolyte) occurs through the following reactions (written as dissociations)  

In this work, the activities are approximated by concentrations, so that h = h and x- = u = where c is the electrolyte concentration. The potentials at the respective planes are related through the integral capacitances of the inner part of the double layer, Qj and that of the outer part, Cqj by 

the respective charges are related to the surface concentrations by 

---