Colloidal suspensions, potential energies

Often the van der Waals attraction is balanced by electric double-layer repulsion. An important example occurs in the flocculation of aqueous colloids. A suspension of charged particles experiences both the double-layer repulsion and dispersion attraction, and the balance between these determines the ease and hence the rate with which particles aggregate. Verwey and Overbeek [44, 45] considered the case of two colloidal spheres and calculated the net potential energy versus distance curves of the type illustrated in Fig. VI-5 for the case of 0 = 25.6 mV (i.e., 0 = k.T/e at 25°C). At low ionic strength, as measured by K (see Section V-2), the double-layer repulsion is overwhelming except at very small separations, but as k is increased, a net attraction at all distances... 

FIGURE 8.25 The stability of a sol (a suspension of colloidal particles) may be evaluated from the balance of repulsive (electrostatic) interaction forces and attractive (dispersive) interaction forces, e.g., by applying the DLVO theory (Equation 8.103). If a potential energy barrier exists the system is stable (left). If the barrier is removed, the coagulation of the particles is contolled by diffusion alone. (Courtesy of Jean Le Bell.)... 

Repulsive Forces. In the simplest example of colloid stability, suspension particles would be stabilized entirely by the repulsive forces created when two charged surfaces approach each other and their EDLs overlap. The repulsive potential energy VR for spherical particles is given approximately as... 

Figure 5 shows the calculated potential energy of interaction Vt of AI2O3 particles (t/ = 0.25 pm, A = 4.5 x 10 J, and 0.01 M ionic strength) as a function of the surface-to-surface distance of separation for various conditions of potential in an aqueous suspension. Note that the height of the potential energy barrier increases quite sharply as the potential becomes larger than a certain critical value ( 30 mV in Fig. 5). Therefore, the potential is a very good index of the magnitude of the repulsive interaction between colloid particles. Because of this, measurements of potential are most commonly used to assess the stability of a given colloidal sol.

Let us tinaily mention that the assumption of the existence of the three contributions to the total potential energy is known as extended DLVO theory of the stability of colloidal suspensions, as opposed to the classical model, originally developed by Derjaguin and Landau, and Verwey and Overbeek. universally called DLVO theory of stability. 

Consider a suspension of colloidal particles. The particles undergo Brownian motion (similar to the motion of pollen in a liquid) and will eventually collide. The potential energy of attraction Va between two particles with radius a and a... 

With reference to Figure 10.21c, if the attractive potential dominates, then the colloidal suspension will not he stable (curve 5 and also 4). The system will minimize its energy by coagulation and will fall into the well indicated by the primary minimum, which implies an irreversible destmction. 

The type of interaction between colloidal electrically charged particles in a liquid medium can be estimated by the DLVO theory (1 -4,23). According to this theory, the extent of agglomeration in colloidal suspensions depends on the total potential energy of interaction between particles (Ut), which consists basically of a balance among the attractive ( /a) and repulsive Ur) potential energies, as follows ... 

Fig. 16. Computed dependence of the free-energy barrier AG for crystal nucleation of poly-disperse suspensions of hard, colloidal spheres. The free energy is expressed in terms ofkgT, where is Boltzmann s constant and T is the absolute temperature. A/i (also in units of is the absolute difference between the chemical potential of the liquid and the solid. It is a measure for the degree of supersaturation. The curves are fits that have been drawn as a guide to the eye. To facilitate comparison with experiment, we have collected in Table 2, the relation between A,u and the volume fraction of the liquid, for the different systems that we studied...

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