Critical coagulation concentration and the Hofmeister series

The value of y limits to unity for rather high surface potentials. The Hamaker constant, A, must be inserted in J, CCC in mol and z is the counter-ion valency (including sign). Thus, in this case, CCC is proportional to 1/z . At low potentials, y limits to zey/o/ AksT (use of Taylor expansion of exponential function followed by This leads to CCC being 

Equation 11.1 can also be derived from DLVO using the Reerink-Overbeek expression for the electrostatic term (Table 10.5) and the expression for the vdW interactions between two equal-sized spheres  

We see a remarkable agreement with the Schulze-Hardy rule, especially at high potentials. At lower potentials, which represents the often more realistic case, the dependency of the (counter-ion) valency is less pronounced. However, the surface potential is often proportional to 1/z, and thus we can recover the Schulze-Hardy rule. (Higher valency counter-ions adsorb strongly in the Stem layer resulting in a decrease of the surface potential.) 

CCC for spherical particles of a given material is proportional to the third power of the relative permittivity and independent of the particle size. 

Moreover, as shown by Shaw (1992), setting in these equations a typical CCC value equal to 0.1 mol at 25 ° C and z (counter-ion) = -1 for a surface potential equal to 75 mV, we obtain a Hamaker constant equal to 8 X 10 ° J, which is within the expected values from the London/van der Waals theories (as discussed previously). 

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