Electrical Stabilization of Particle Dispersions

The detailed argument, DLVO theory, for the stability of colloidal dispersions was originally worked out by Derjaguin and Landau in the Soviet Union and by Vervey and Overbeek ° in the Netherlands. However, the first convincing direct tests of these theories were not carried out until the work of Israelachvili and Adams using molecularly smooth mica sheets immersed in various liquids with electrolytes present. 

Pashley and Israelachvili measured the force as the gap was varied. Fig. 10.7(b), and compared the results with the sum of the van der Waals attractive force and the repulsion given by Equation (10.3). They obtained good agreement, but when the gap was reduced to about 5 nm, the surfaces jumped into contact, because the van der Waals force exceeded the electrical double layer repulsion. 

The results fitted the theoretical curve, danonstrating that this was a method with high force resolution, because it used kT as a gauge to measure 0.001 pN, 

This detailed potential curve can be modeled more simply by the square well approximation of Fig. 10.9(b). Widely separated particles give no interaction. But at a certain range the particle experiences a repulsive barrier of energy Ej, and if it is sufficiently energetic, the particle can leap over the barrier to adhere in the square well of range and depth where it then meets the hard sphere repulsion as the particles make molecular contact 

The stability of the colloid may be interpreted as the difficulty which the particles experience in getting over the energy battier. Particles which have been prepared in the fully dispersed state, for example by precipitation, have a distribution of velocities with an average thermal energy 3kT/2. Particles in the distribution with energy greater than Sj have sufficient impetus to cross the barrier, so then doublets will form in the adhesive potential well. Treating the formation of doublets as a reaction 

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