Total Potential Energy and the Schulze-Hardy Rule

Total Potential Energy and the Schulze-Hardy Rule 

For colloidal particles of larger size, Eqs. (7.57) and (7.64 ) are applicable for Vr and Va, respectively. The total energy V, then becomes 

When is large ( 200 mV) or g = 1, the flocculation concentration Cc is inversely proportional to the sixth power of the valency of the ions. Therefore, for the concentration ratio of C one-to-one, two-to-two, and three-to-three types of electrolytes, the following equation is given  

This is the well-known empirical Schulze-Hardy rule of coagulation concentration, which has been confirmed experimentally in many colloidal systems. The above theory of dispersion and coagulation of colloidal particles, based on the repulsive interaction between two diffuse layers and on the attractive interaction owing to the van der Waals-London force, is called the Deijaguin-Landau-Verwey-Overbeek (D.L.V.O.) theory. 

We know that Va is inversely proportional to d, whereas Vr decreases exponentially with the distance 2d. Thus, at short and long distances of d, Va becomes larger than Vr, but at intermediate distances the two particles repel each other strongly due to the repulsion of Bom and Mayer. Thus, Vt has two minima, as shown in Fig. 7.7 a deep one at a short interparticle distance and a shallow one at a relatively long interparticle distance. Coagulation takes place at the first deep minimum. The secondary minimum plays an important role for plate- or rod-like particles that have a wide interparticle contact area. However, because the second minimum is relatively shallow, the coagulation induced by it is easily broken by an external force. This effect is closely related to rheological phenomena of colloidal suspensions. 

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