DLVO Schulze-Hardy rule

Attempts to utilize traditional DLVO approaches to quantify the Schulze-Hardy Rule have found limited and qualified success [23,59]. Although a qualitative agreement of the predicted dependence of ccc on counterion valence can be demonstrated, non-DLVO forces are typically ignored and analytical solutions of the DLYO equations predict unrealistically large ccc values [23,59]. 

The essentials of the Schulze-Hardy rule are readily derived from the DLVO theory presented in this section. With reference to Fig. 8.1.3 it can be seen that the primary maximum of the curve V(2) is the demarcation point between stability and instability. At that point... 

CCC is one of the most significant characteristics of cell dispersion. The experimental observations for inorganic colloidal suspension reveal that the variation of CCC as a function of the valence of counterion follows roughly the inverse sixth power law, the classic Schulze-Hardy rule [74,75]. For negatively charged colloids, the CCC ratio of cations of valences 3, 2, and 1 is 3 2 1 , or roughly 1 11 729. Based on the DLVO theory, which considered the electrical repulsive force... 

This expression is the principal result of DLVO theory. The steep r dependence of the critical coagulation concentration has been observed experimentally for strongly charged surfaces and is commonly known as the Schulze-Hardy rule. In the case of weakly charged surfaces, a less steep dependence of the critical coagulation concentration on the valence (z" ) is observed. In fact, it was the empirical dependence of the c.c.c. on the valence established in the course of experimental studies on coagulation that inspired the development of DLVO theory. 

According to the DLVO theory, coagulation results from reduction in the double-layer repulsion, which results from decreasing the surface potential (by changing pH) or from increasing the concentration of electrolyte (counterions). The effectiveness of a counterion in reducing the repulsion depends very strongly on the valence of the ion, as shown in Fig. 6. The empirical Schulze-Hardy rule indicates that the concentration of electrolyte... 

The effect of salts and especially of the counter-ions on the coUoid stability can be demonstrated via the so-called Schulze-Hardy rule. We will see in Chapter 11 that this rule has been verified by the DLVO theory, but it appeared many years before the DLVO. As shown in Figure 10.19, salts, even in small amounts, can reduce drastically the diffuse double layer and thus the stability of colloids. Adding salt leads to coagulation. 

The DLVO theoiy thus enabled theoretical significance to be given to the valence sequence in coagulation experiments that bad been observed many years earher by Schulze (1882) and Hardy (1900). Although expre ions of this type are useful in a qualitative predictive sense, the implication that there is a simple rule applicable to alt systems must be treated with considerable caution. It must be borne in mind that coagulation is a complicated phenomenon involving quite a range of kinetic and specific ion effects. 

---