Colloidal dispersions interaction energies

In the theory developed by Derjaguin and Landau (24) and Verwey and Overbeek (25.) the stability of colloidal dispersions is treated in terms of the energy changes which take place when particles approach one another. The theory involves estimations of the energy of attraction (London-van der Walls forces) and the energy of repulsion (overlapping of electric double layers) in terms of inter-oarticle distance. But in addition to electrostatic interaction, steric repulsion has also to be considered. 

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.)... 

In calculating the repulsive interaction energy between colloidal particles [Eq. (22)] it is usually assumed that a complete equilibrium exists between the particle surface and the dispersion medium at any separation between the particles. This is not necessarily correct, however, because the adjustment of equilibrium takes a finite time and this time may be longer than the time involved in a collision or longer even than the coagulation time. The time needed for adjusting the structure of the diffuse double layer (the relaxation time of the double layer) is equal to the average time needed for the displacement of ions across the double layer. 

The potential energy-osmotic pressure transformation formula. The measurement of the osmotic pressure of colloidal dispersions, in principle, provides a relatively straightforward method for determining the distance dependence of the steric repulsion. As Ottewill (1980) has pointed out, the relatively small osmotic pressures involved render the actual measurements difficult to accomplish. None the less, it is worth establishing how to transform osmotic pressures into potential energies of interaction between the particles involved and vice versa. 

Stabilization of Polymer Colloid Dispersions 3.6.3 The steric interaction energy Vj... 

It is therefore of interest to estimate the dependence of the attractive interaction, b d,T) on the sphere size. For relatively short-range interactions between spheres, the attractive interaction per sphere can be approximately obtained from the interaction between two flat plates. As we now show, this approximation results in an effective attraction between spheres that increases linearly with the sphere radius. Once the interaction energy per sphere is known, the virial coefficient can be calculated from Eq. (7.4) and the stability of the system to phase separation is related to the magnitude of this coefficient. Thus, the general plan is to (i) find the effective interaction between two flat plates, (ii) relate this interaction energy to an interaction between spheres via the Derejaguin approximation, (iii) calculate the virial coefficient for the spheres in order to assess the stability of the single-phase colloidal dispersion. 

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