Contact interactions DLVO theory

Several models have been developed to describe these phenomena quantitatively, the main difference being the interaction potential between the particles. There are two major approaches the hard sphere and the soft sphere. The hard sphere assumes that the only interaction between particles is a strong repulsion at the point of contact. The soft sphere is more realistic and assumes a potential with a barrier and a primary minimum like in DLVO theory (Figure 11.8). 

DLVO theory explained major principles of coagulation of hydrosols by electrolytes and brought to common grounds all previous observations (primarily of qualitative nature) that related to individual cases and often seemed to be contradictory. In years that followed further extensions of DLVO theory that took into account the possibility of reversible particle aggregation were developed. At very small distances between particles in addition to the usual long-range interaction, molecular attraction and electrostatic repulsion, one must account for other factors that play role at a direct particle contact. The formation of peculiarly structured hydration layers in the vicinity of solid surface, the appearance of elastic forces that are responsible for the Born repulsion between surface atoms at the point of contact, the repulsion between the adsorbed surfactant molecules in contact zone between two particles, all represent the so-called non-DLVO stability factors . This means that more or less deep primary minimum remains finite. 

For practical systems, when the particle concentration is high, the validity of the DLVO theory is open to question. Particle-particle interaction might not begin at infinite distance of separation, i.e. one particle is, on average, sufficiently close to another to reduce the effective energy barrier which must be overcome for the particles to come into contact. This is particularly relevant to dispersions in hydrocarbon media for which the double-layer thickness is large compared with the average distance between the particles. 

In order to establish reasons for the limited sensitivity of Aa, (i.e., of the measured force / ,) to the presence of electrolytes in experiments with hydrophobic particles in hydrocarbon/alcohol mixtures, one can compare these results with the results of measuranents in the aqueous medium. The latter represent the main subject of DLVO theory. The final diseussion in this chapter is devoted to addressing the relationship between the contact interactions (i.e., cohesion forces at the primary potential energy minimum) and the results of DLVO theory (i.e., mainly long-range forces). Some of these experiments were conducted by Yaminskiy [30,50-52]. In addition to the contact forces, the Pi(fi) and Ao((fi) isotherms shown in Figure 4.46 were also determined. 

The DLVO theory of stability takes into account the interaction of two kinds of long-range forces which determine the closeness of contact of two particles approaching as a result of Brownian movement. The forces concerned are (i) the London-van der Waals forces of attraction, and (ii) the electrostatic repulsion between electrical double layers. 

In conclusion, we have shown that the phase diagram of charged colloids, where the interactions are given within the DLVO theory by hard-core repnlsive Yukawa pair potential, can be obtained for any snfficiently high contact valne Pe by mapping the well-known phase boundaries of the point Yukawa particles onto those of the hard-core repulsive Yukawa system and bearing in mind that the stable bcc region is bounded by a bcc-fcc coexistence at ti 0.5. 

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