Coagulation by multivalent counterions and the Schulze–Hardy rule
Graphical abstract
Highlights
► Adsorption of complex ions and its effect on colloid stability is revisited. ► The quantitative Schulze–Hardy rule must be reinterpreted. ► Specific ion adsorption tends to increase with valency. ► Charge reversal is not a proof for ion correlation theory.
Introduction
More than half a century ago Egon Matijević and his coauthors published a plethora of experimental papers, all dealing with the adsorption of multivalent complex molecules on hydrophobic colloids and its consequences for the stability against coagulation. The valency of counterions plays a dominant role in the stability of hydrophobic sols. According to the classical Schulze–Hardy rule, the stability very strongly decreases with increasing counterion valency. Egons basic idea was that, once the Schulze–Hardy rule is quantified, even if only empirically, it must in principle be possible to establish the valency of the counterion from colloid stability measurements. If this counterion is a complex, its valency can help to establish the chemical composition of that complex in the adsorbed state.
As a corollary of the strong adsorption of multivalent complexes, such ions have a strong propensity for superequivalent adsorption, leading to overcharging. This phenomenon was also experimentally investigated by the Matijević team.
We are now many decades further, and one may wonder to which extent the ideas developed by this team are qualitatively and quantitatively still valid. It will be shown that, although much can be said about this approach, it also has something significant to offer to modern colloid science. This issue will be the leading principle of the present paper, and at the same time, it is intended to appreciate the contributions of Matijević to colloid science.
Section snippets
The Schulze–Hardy rule
The Schulze–Hardy (SH) rule is an empirical rule, stating that the coagulation concentration ccr of hydrophobic sols decreases very strongly with the valency z of the counterion. It stems from the end of the nineteenth century, and its qualitative validity has since been confirmed over and again for a variety of sols and conditions. At issue was, and still is, its quantification. Finding this requires an underlying theory.
Nowadays, DLVO theory is generally accepted to be valid under the
Review of some experiments from the Matijević School
In line with his ancestry, many experiments from this School have been carried out using in statu nascendi silver bromide and silver iodide sols [3], [4]. The components from which the sols are made, say KBr and AgNO3 in the case of AgBr sols, are mixed together with the indifferent electrolyte, and the turbidity is measured after a certain time, often about 10 min. The difference between the AgNO3 and KBr concentrations is a very rough measure of the surface charge. For given initial
Extrapolation to modern issues
Let us emphasize the important conclusion that, depending on pH, many multivalent cations hydrolyze. As a result, the valency of the dominant species changes, (often it decreases), whereby the specific adsorption in the Stern layer increases, so that overcharging can occur.
The first question is as follows: are these conclusions still valid, that is, are they qualitatively and quantitatively substantiated by modern studies? For several reasons, the Matijević-type of measurements cannot stand
Conclusion
Multivalent cations tend to adsorb on solid particles by specific binding of hydrolyzed products, rather than by ion correlations. For the interpretation of the Schulze–Hardy rule, this implies that the coagulation concentration is determined by a combination of specific ion adsorption and diffuse double layer overlap. The higher the valency, the higher the contribution of specific adsorption.
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