Potential energy primary minimum

Coagulation a relatively irreversible aggregation often associated with the primary minimum of a potential energy diagram of two approaching particles. Particles are held together closely. 

FIG. 13.13 Interaction between polymer-coated particles. Overlap of adsorbed polymer layers on close approach of dispersed solid particles (parts a and b). The figure also illustrates the repulsive interaction energy due to the overlap of the polymer layers (dark line in part c). Depending on the nature of the particles, a strong van der Waals attraction and perhaps electrostatic repulsion may exist between the particles in the absence of polymer layers (dashed line in part c), and the steric repulsion stabilizes the dispersion against coagulation in the primary minimum in the interaction potential. 

The identification of the primary ion which is responsible for the secondary product ion can usually be ascertained in simple systems by the coincidence of their appearance potentials. The appearance potential is the minimum energy of the bombarding electrons at which the ion appears. 

An expression for the critical coagulation concentration (c.c.c.) of an indifferent electrolyte can be derived by assuming that a potential energy curve such as V(2) in Figure 8.2 can be taken to represent the transition between stability and coagulation into the primary minimum. For such a curve, the conditions V = 0 and dV/dH = 0 hold for the same value of H. If Vr and VA are expressed as in equations (8.7) and (8.10), respectively,... 

Provided that v > v for most values of h then the form of curve shown in Figure 1 is obtained. When the magnitude of is substantial, say >> 10 kT, a stable dispersion is obtained. The form of the potential energy curve obtained by this approach shows immediately that the stability of a dispersion to electrolyte is kinetic in origin rather than thermodynamic, that is, the lowest free energy state is in the primary minimum and entry into this is prevented by the presence of the large activation energy represented by AV. A more sophisticated and detailed representation of these ideas can be found elsewhere (12,15,16). 

Schematic potential energy diagrams for two particles are depicted in Figure 4.34. As two particles approach, the presence of the adsorbed polymer molecules around the particles leads to a steric interaction in which the thickness of the adsorbed layer is greater than half the surface separation distance. Therefore, the particles do not get close to the primary minimum. The steric interaction Vs is influenced by two parameters ...

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