Schultz-Hardy rule

Humic substances occurring in natural waters in the form of stable negatively charged sols exhibit shielding aetion with respect to colloidal solutions of Si02, Fe(OH)j and Al(OH)3 (Kul skiy, 1960). Colloids shielded by humus do not coagulate and, remaining in the state of sols, can be transported by the waters of rivers, seas, and oceans (Kuznetsov, 1964) for considerable distances, and the Schultz-Hardy rule becomes inapplieable to shielded colloids. 

Coagulation occurs at a critical electrolyte concentration, the critical coagulation concentration (ccc), which in turn depends on the electrolyte valency. At low surface potentials, ccc oo this referred to as the Schultze-Hardy rule. A rate constant... 

As can be seen in Figure 22.6, there is a distiuct difference in the effect of the coagulants depending on the valence of the ions in accord with the Schultz-Hardy rule, which states that the salt couceutratiou required to neutralize an electrostatic charge is inversely proportional to the sixth... 

It can be seen that the effect of indifferent electrolytes on the zeta-potential of the mineral particle depends not only on its concentration but also on the valency of the counterions involved. The Schultz-Hardy rule expresses the dependence of the ability of a coagulant on the valency of the ions as follows ... 

Schultz-Hardy rule can also be applied to organic ions. For example, the coagulation concentration of amine ions depends on the number of alkyl groups linked to the nitrogen atoms of the amine group. In other words, the coagulation concentrations depend in this... 

The flocculation power of polymers depends on the number of ionic groups attached to the long chains of the polymers. Multi-valent flocculants possessing a number of ionic groups in their molecules will adsorb more on oppositely charged mineral surfaces, suggesting the validity of the Schultz-Hardy rule as shown in Table 5.28. 

The above theoretical rationalisation of the Schultze-Hardy rule was claimed as an early success of the DLVO theory. However, among the approximations and assumptions made in reaching equations (9.4) and (9.6) is that the surface potential is high. On the other hand, it is known that flocculation occurs at relatively low surface potentials. In this case the simple theory suggests that the c.c.c. is proportional to z rather than to specific adsorption of ions) may to some extent restore agreement with the Schultze-Hardy rule. 

The studies by Schultze and Hardy led to the formation of the so-called Schultze-Hardy rule, which states that the critical coagulation concentration of a colloid is determined primarily by the valence of the counterions. The early relationship indicated that the ccc varied as the inverse sixth power of... 

The fact that the DLVO theory predicts (roughly at least) the Schultze-Hardy rule would seem to confirm the validity of the theory. However, several approximations and assumptions are included in the derivation that weaken its claim to complete success. For example, at low surface potentials, the theory predicts that the ccc will be proportional to rather than z". A more complete derivation of the theory (i.e., taking into consideration such factors as specific adsorption of ions and hydration effects) can remove some of the discrepancies so far encountered in the simple theory. 

In summary High surface potentials stabilize colloidal systems. The addition of inert salt leads to stronger screening and destabilizes the system. The point at which rapid coagulation (case b) sets in is defined as the critical coagulation concentration (ccc). One key result of DLVO theory is the explanation of the Schultze-Hardy rule, which states that the ccc depends on the counterion valency z like 1/z . 

Critical Flocculation Concentration Schultze-Hardy Rule... 

This is consistent with the empirical Schultze-Hardy rule [2,30]. Based on this relationship, experiments can be designed to evaluate the effectiveness of colloidal dispersions to resist the added electrolytes. 

Specific adsorption phenomena are more pronounced for multivalent ipns because of their liigher structuring strength. Their flocculating strength is aiso markedly higher than that of monovalent ions, and the Schultze-Hardy rule stipulates tliat the cii , z product is constant [21,24],... 

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