Interaction energy colloid stability

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). 

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. 

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. 

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. 

A quantitative treatment of the effects of electrolytes on colloid stability has been independently developed by Deryagen and Landau and by Verwey and Over-beek (DLVO), who considered the additive of the interaction forces, mainly electrostatic repulsive and van der Waals attractive forces as the particles approach each other. Repulsive forces between particles arise from the overlapping of the diffuse layer in the electrical double layer of two approaching particles. No simple analytical expression can be given for these repulsive interaction forces. Under certain assumptions, the surface potential is small and remains constant the thickness of the double layer is large and the overlap of the electrical double layer is small. The repulsive energy (VR) between two spherical particles of equal size can be calculated by ... 

---