Primary minimum state

The introduction of the van der Waals potential in combination with a Yukawa potential produces a curve in which the primary minimum is always deeper than the secondary minimum. This must be so because the primary minimum state is that for which the particles have coalesced and the valency of the nth plate Zn has dropped to zero since Z —> 0 as Xmn —> 2a, —> 0 as —> 2a, and the van der Waals force... 

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). 

Neutral molecules, dissolved, dispersed or suspended in a liquid medium, are in continuous random motion (Brownian motion) with a mean free path (x) and collision diameter (xe), depending on c and vex effects. At a far separation distance, is negative, increasing to 0 at xe, where repulsion counterbalances attraction and the amphiphiles are at dynamic equilibrium in a primary minimum energy state. At x High concentrations shorten x and make the collision rate nonlinear with c, (Hammett, 1952). A separation distance of x < xe is sterically forbidden without fusion. 

At steady state, the number density of adsorbed particles is KyCo/Kr, regardless of the initial density n j. Thus, if n2i < Kycn/K a net adsorption will take place, whereas if 2i > KyCg/Kr, a net desorption occurs. From Equation (13), Kj/Kr depends primarily on the depth of tlie primary minimum which in turn is influenced significantly by the ionic strength (Figure 3). 

When the Interaction forces establish an energy barrier that reduces adsorption and desorption rates significantly, particles around the primary minimum (0 h St) have time Co achieve quasi equilibrium before their population changes. Then, assuming a quasi steady state lor the remainder of tie region, we have (alternative A)... 

Kinetic equations for reversible adsorption and reversible coagulation are established when the interaction potential has primary and secondary minima of comparable depths. The process is assumed to occur in two successive steps. First the particles move from the bulk of the fluid to the secondary minimum. A fraction of the particles which have arrived al the secondary minimum move further to the primary minimum. Quasi-steady state is assumed for each of the steps separately. Conditions are identified under which rates of reversible adsorption or coagulation at the primary minimum can be computed by neglecting the rate of accumulation at the secondary minimum. The interaction force boundary layer approach has been improved by introducing the tangential velocity of the particles near the surface of the collector into the kinetic equations. To account for reversibility a short-range repulsion term is included in the interaction potential. 

In essence, inequalities [25] and [27] give the conditions under which, after a short transient, the rate of accumulation at the primary minimum can be computed assuming steady state between the bulk and the primary minimum. 

Similarly, denoting by the quasi-steady-state flow-rate of particles between the secondary and the primary minimum, one can write... 

A definite prediction of DLVO theory is that charge-stabilized colloids can only be kinetically, as opposed to thermodynamically, stable. The theory does not mean anything at all if we cannot identify the crystalline clay state (d 20 A) with the primary minimum and the clay gel state (d 100 to 1000 A) with the secondary minimum in a well-defined model experimental system. We were therefore amazed to discover a reversible phase transition of clear thermodynamic character in the n-butylammonium vermiculite system, both with respect to temperature T and pressure P. These results rock the foundations of colloid science to their roots and... 

In the case of films with high stability the overcoming of potential barrier does not result in a rupture of film, but leads to another metastable state corresponding to the primary minimum (Fig. VII-10, point B). This results in the formation of a rather stable, very thin Newtonian black films [15]. The investigation of the nature of stability of black films is one of the central problems in colloid science nevertheless, at present there is no commonly accepted opinion concerning the nature of forces that are responsible for high stability of black films (see Chapter VIII). 

In this case, the particles can exist in three possible states gas-tike particles undergoing Brownian motion at long range, soft adhesion in the secondary minimum and hard adhesion in the primary minimum. There is also the energy barrier between these adhesive states, slowing the approach to the primary minimum. 

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