Verwey

The calculation involved here is conceptually a complex one, and for the necessarily detailed discussion needed to do it justice, the reader is referred to Verwey and Overbeek [5] and Kruyt [6] or to Hamed and Owen [10]. Qualitatively, what must be done is to calculate the reversible electrostatic work for the process ... 

Often the van der Waals attraction is balanced by electric double-layer repulsion. An important example occurs in the flocculation of aqueous colloids. A suspension of charged particles experiences both the double-layer repulsion and dispersion attraction, and the balance between these determines the ease and hence the rate with which particles aggregate. Verwey and Overbeek [44, 45] considered the case of two colloidal spheres and calculated the net potential energy versus distance curves of the type illustrated in Fig. VI-5 for the case of 0 = 25.6 mV (i.e., 0 = k.T/e at 25°C). At low ionic strength, as measured by K (see Section V-2), the double-layer repulsion is overwhelming except at very small separations, but as k is increased, a net attraction at all distances... 

Here we consider the total interaction between two charged particles in suspension, surrounded by tlieir counterions and added electrolyte. This is tire celebrated DLVO tlieory, derived independently by Derjaguin and Landau and by Verwey and Overbeek [44]. By combining tlie van der Waals interaction (equation (02.6.4)) witli tlie repulsion due to the electric double layers (equation (C2.6.lOI), we obtain... 

Verwey E J W and Overbeek J Th G 1948 Theory of the Stabiiity of Lyophobic Coiioids (New York Elsevier)... 

E. J. W. Verwey and. T. G. Overbeek, Theory of the Stability ofEyophobic Colloids, Elsevier Publishing Co., Amsterdam, 1948. 

DLVO Theory. The overall stabiUty of a particle dispersion depends on the sum of the attractive and repulsive forces as a function of the distance separating the particles. DLVO theory, named for Derjaguin and Landau (11) and Verwey and Overbeek (12), encompasses van der Waals attraction and electrostatic repulsion between particles, but does not consider steric stabilization. The net energy, AGp between two particles at a given distance is the sum of the repulsive and attractive forces ... 

The Yukawa potential is of interest in another connection. According to the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, colloidal... 

The kinetics outlined above, first observed empirically by Giintherschulze and Betz, were modelled by Verwey" with the rate-controlling energy barrier being that between to adjacent cation sites within the oxide film. The same basic form can be derived if the rate-controlling energy barrier is that between a metal atom on the metal surface and an adjacent cation site in the film. The rate is then limited by ion injection into the film rather than... 

Hence, for two similarly charged surfaces in electrolyte, interactions are determined by both electrostatic doublelayer and van der Waals forces. The consequent phenomena have been described quantitatively by the DLVO theory [6], named after Derjaguin and Landau, and Verwey and Over-beek. The interaction energy, due to combined actions of double-layer and van der Waals forces are schematically given in Fig. 3 as a function of distance D, from which one can see that the interplay of double-layer and van der Waals forces may affect the stability of a particle suspension system. 

Overbeek, JTG, Quantitative Interpretation of the Electrophoretic Velocity of Colloids. In Advances in Colloid Science Mark, H Verwey, EJW, eds. Interscience New York, 1950 Vol. 3, p 97. 

---