Interaction Energy and Colloid Stability

Some of the pertinent interactions that affect colloid stability are readily apparent from Figs. 7.4 and 7.12. The main effect of electrolytes is a more rapid decay of the repulsion energy with distance and to compact the double layer (reducing k 1). Experimentally it is known that the charge of the counterion plays an important role. The critical electrolyte concentration required just to agglomerate the colloids is proportional to z 6 Aj for high surface potential, and to z 2 A, 2, at low potentials [(4) and (5) in Table 7.3]. This is the theoretical basis for the qualitative valency rule of Schulze and Hardy. 

With polymers that have ionizable groups, adsorption of a polymer will alter the charge of the surface altering the electrostatic interaction energy and also provide steric protection for the colloid, because the ionized groups will give better than theta conditions for the poisoner in an aqueous solution. This type of polymer stabilization is called electrosteric stabilization because both the electrostatic and the steric play a role in stabilization. The equations for this total interaction are simply the sum of electrostatic and steric terms as well as the van der Waals attraction. 

The hard sphere (HS) interaction is an excellent approximation for sterically stabilized colloids. However, there are other interactions present in colloidal systems that may replace or extend the pure HS interaction. As an example let us consider soft spheres given by an inverse power law (0 = The energy scale Vq and the length scale cr can be com-... 

In a qualitative way, colloids are stable when they are electrically charged (we will not consider here the stability of hydrophilic colloids - gelatine, starch, proteins, macromolecules, biocolloids - where stability may be enhanced by steric arrangements and the affinity of organic functional groups to water). In a physical model of colloid stability particle repulsion due to electrostatic interaction is counteracted by attraction due to van der Waal interaction. The repulsion energy depends on the surface potential and its decrease in the diffuse part of the double layer the decay of the potential with distance is a function of the ionic strength (Fig. 3.2c and Fig. 

Physical model for colloid stability. Net energy of interaction for spheres of constant potential surface for various ionic strengths (1 1 electrolyte) (cf. Verwey and Overbeck). 

As we noted above, the evaluation of W for given values of dispersion properties such as surface potential, Hamaker constant, pH, electrolyte concentration, and so on, forms the goal of classical colloid stability analysis. Because of the complicated form of the expressions for electrostatic and van der Waals (and other relevant) energies of interactions, the above task is not a simple one and requires numerical evaluations of Equation (49). Under certain conditions, however, one can obtain a somewhat easier to use expression for W. This expression can be used to understand the qualitative (and, to some extent, quantitative) behavior of W with respect to the barrier against coagulation and the properties of the dispersion. We examine this in some detail below. 

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