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Figure 7.5 The energy of interaction of two spherical particles as a function of the distance, H, between the surfaces. For monovalent ions c (mol dm"3) = 10"15k2 (cm_1). In this example, a # 10"5 cm, A # 10"19 J and # RT/F # 26.5 mV.

Reproduced from J. Th. Overbeek, J. Colloid Interface Sci, 58, 408 (1977).

secondary minimum and the small primary maximum would be sufficient to prevent coagulation in the primary minimum. At high concentrations of added electrolyte, the range of VR would be so small that the van der Waals attractive forces would dictate the shape of the total energy curve. As a consequence, this curve has no primary maximum and the dispersion would consequently be unstable since there would be no energy barrier to prevent coagulation of the particles in the primary minimum. The practical importance of this can be seen when nanoparticles are dispersed in cell culture media with high levels of electrolyte and flocculate as a result.

We can see from equation (7.3) that the magnitude of the effect of an electrolyte of a given concentration on VR also depends on the valence of the ion of opposite charge to that of the particles (the counterion): the greater the valence of the added counterion, the greater its effect on VR. These generalisations are known as the Schulze-Hardy rule.

Notice that it does not matter which particular counterion of a given valence is added.

Effect of surface potential on stability

A second parameter which influences the shape of the total energy curve is the surface potential of the particles. We can see from equation (7.4) that VR will increase with an increase in the changes which occur in the total curve are seen in Fig. 7.6. There is a decrease in the primary maximum as the surface potential decreases and you should note the appearance of a secondary minimum at the intermediate value of (see C).

7.2.2 Repulsion between hydrated surfaces

The increasing use of nonionic macromol-ecules as stabilisers, which has occurred since the development of the DLVO theory, has led to the awareness of other stabilising forces. The approach of particles with hydrated macromolecules adsorbed to their surfaces leads, on the interaction of these layers, to repulsion (Fig. 7.7), because of the consequent positive enthalpy change (+A H) which ensues. In more general terms, the approach of two particles with adsorbed stabilising chains leads

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