Derjaguin—Landau—Verwey—Overbeek interaction energy

The force between particles is the sum of a pH-independent van der Waals component, which is always attractive, and a pH-dependent electrostatic component, which can be attractive or repulsive. In Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, the potential is used to calculate the interaction force or energy as a function of the distance between the particles. Atomic force microscopy (AFM) makes it possible to directly measure the force between the particles as a function of the distance, and commercial instruments are available to perform such measurements. Different approaches have been proposed to utilize the results obtained by AFM to determine the pHq. The quantity obtained by AFM corresponds to the lEP rather than the PZC. AFM was used to measure the force between SiO2 (negative potential over the entire studied pH range) and Si,N4 (lEP to be determined) in [681]. The pH at which the force at a distance of 17 nm was equal to zero was identified with the lEP. The van der Waals forces are negligible at such a distance, and the force is governed by an electrostatic interaction. The experimental results were consistent with DLVO theory. 

The forces acting on a colloidal system include gravitational, diffusion, viscous, inertial, attractive Van der Waals, and electrical repulsive forces. Because most of these forces are functions of the particle size, it is important to know both particles size and size distribution. The classical Derjaguin-Landau-Verwey-Overbeek (DLVO) theory describes colloid stability on the basis of pair interaction, considering only attractive van der Waals forces and repulsive electrostatic forces (Molina-Bolfvar and Ortega-Vinuesa, 1999). The total potential energy of interaction, Ujc, between two particles is defined as ... 

The pair potential of colloidal particles, i.e. the potential energy of interaction between a pair of colloidal particles as a function of separation distance, is calculated from the linear superposition of the individual energy curves. When this was done using the attractive potential calculated from London dispersion forces, Fa, and electrostatic repulsion, Ve, the theory was called the DLVO Theory (from Derjaguin, Landau, Verwey and Overbeek). Here we will use the term to include other potentials, such as those arising from depletion interactions, Kd, and steric repulsion, Vs, and so we may write the total potential energy of interaction as... 

The first quantitative theory of interactions in thin liquid films and dispersions is the DLVO theory called after the names of the authors Derjaguin and Landau [407] and Verwey and Overbeek [399], In this theory, the total interaction is supposed to be a superposition of van der Waals and double layer interactions. In other words, the total disjoining pressure and the total interaction energy are presented in the form ... 

The most widely used theory of suspension stability, the DLVO theory, was developed in the 1940s by Derjaguin and landau (1941) in Russia and by Verwey and Overbeek (1948) in Holland. According to this theory, the stability of a suspension of fine particles depends upon the total energy of interaction, Vt, between the particles. Vf has two components, the repulsive, electrostatic potential energy, Vr, and the attractive force, Va, i. e. 

The development of the thermodynamics of thin films is related to the problem of stability of disperse systems. An important contribution to its solving are the works of the Russian scientists Derjaguin and Landau [1] and the Dutch scientists Verwey and Overbeek [2], known today as the DVLO theory. According to their concept the particular state of the thin liquid films is due to the change in the potential energy of molecular interaction in the film and the deformation of the diffuse electric layers. The thermodynamic characteristic of a state of the liquid in the thin film, as shown in Section 3.1, appears to be the dependence of disjoining pressure on film thickness, the n(/t) isotherm. The thermodynamic properties of... 

In the theory developed by Derjaguin and Landau (24) and Verwey and Overbeek (25.) the stability of colloidal dispersions is treated in terms of the energy changes which take place when particles approach one another. The theory involves estimations of the energy of attraction (London-van der Walls forces) and the energy of repulsion (overlapping of electric double layers) in terms of inter-oarticle distance. But in addition to electrostatic interaction, steric repulsion has also to be considered. 

The central theory for colloidal, and therefore latex, stability is because of the complimentary work of Derjaguin and Landau in Moscow and Verwey and Overbeek in Holland. This has become known as DLVO theory.The idea is to represent a total energy of interaction as the sum of individual attractive and repulsive potentials. Fig. 4 sketches out the van der Waals and electrostatic potentials, as well as the total interaction for a particular particle size, surface potential, and electrolyte concentration. 

It is well known that Verwey and Overbeek and Derjaguin and Landau " " (DLVO) have given a quantitative treatment of the interaction of electrical double layers. According to them, the free energy of a double layer may be expressed as a difference between the surface energy G, of the system in its equilibrium state and the surface free energy G of a standard state in which no double layer is present ... 

By using the above equations, Derjaguin and Landau, and Verwey and Overbeek (DLVO) proposed a system for the process of adhesion. According to the work of Derjaguin and Landau, the interaction of two diffused electrical double layers would cause the formation of an energy barrier between the two interacting particles. This energy barrier would lie between two minima. 

This approach (comprising, however, only the LW and EL forces) was developed independently by Derjaguin and Landau (1941) and Verwey and Overbeek (Verwey and Overbeek, 1948, 1999), and became known, after these authors, as the DLVO theory, and the corresponding energy vs. distance plots as DLVO plots. In the absence, or virtual absence, of polar (AB) interactions (i.e., in mainly apolar media), the DLVO theory correlates admirably with the stability of particle suspensions. However, in the cases of particle suspensions in polar and especially aqueous media, disregarding the influence of polar interactions by using simple DLVO plots usually leads to severely unrealistic models (van Oss et ai, 1990a). In other words, in all polar systems one should take into account AG j, as a function of , as ... 

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