Verwey-Overbeek potential

This figure compares with an electrical barrier of 0.28 eV estimated from the point charge model. These values would coincide for a = 0.34. Hence the theory based on the Verwey-Overbeek potential is consistent with experiment. From (4) and (5) the experimental plot of In v versus AF should yield a straight line with the so-called Liley slope. Inserting the numerical values, we find that this slope, with a = 0.34, corresponds to a tenfold increase in frequency of MEPP for each 15.0 mV depolarization. The most recent experimental value on the rat muscle preparation was 12.5 mV, and Liley reported about 16 mV. We can thus conclude that a discussion of the approach of a synaptic vesicle to a presynaptic membrane, which is based on the Verwey-Overbeek theory of the interaction of two double layers, gives reasonable quantitative agreement with the available data on the dependence of V of MEPP on depolarization of the presynaptic membrane. 

Monomers interact with the particle according to the Verwey-Overbeek potential ... 

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

Throughout most of this chapter the emphasis has been on the evaluation of zeta potentials from electrokinetic measurements. This emphasis is entirely fitting in view of the important role played by the potential in the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory of colloidal stability. From a theoretical point of view, a fairly complete picture of the stability of dilute dispersions can be built up from a knowledge of potential, electrolyte content, Hamaker constants, and particle geometry, as we discuss in Chapter 13. From this perspective the fundamental importance of the f potential is evident. Below we present a brief list of some of the applications of electrokinetic measurements. 

Ruckenstein and Schiby derived4 an expression for the electrochemical potential, which accounted for the hydration of ions and their finite volume. The modified Poisson-Boltzmann equation thus obtained was used to calculate the force between charged surfaces immersed in an electrolyte. It was shown that at low separation distances and high surface charges, the modified equation predicts an additional repulsion in excess to the traditional double layer theory of Deijaguin—Landau—Verwey—Overbeek. 

For interactions at constant surface potential, y>s(0 = ips(°°)=Vs and using the corresponding Verwey—Overbeek choice C = —cKHVsO00), one obtains, integrating by parts the first, right-hand side term of eq 10, the expression... 

The free energy of the system is always defined up to an arbitrary constant the choice C = 0 in the Verwey— Overbeek approach leads to positive values for the free energy of the system at constant surface charge and negative at constant surface potential. However, the interaction free energy (the difference between the free energy of the system at the final separation distance and the free energy of the system at infinite separation) is not affected by the choice of the constant C. 

When speculating about the colloidal stability of a monomer droplet dispersion in water, one could use the Deryaguin-Landau-Verwey-Overbeek theory, also known as DLVO theory, to analyze the stability of the system. This has been done in Fig. 10a, where we show the effect of different surface potentials upon the rate of coagulation, fi, defined in the case of two droplets of the same size as ... 

The physical stability of a colloidal system is determined by the balance between the repulsive and attractive forces which is described quantitatively by the Deryaguin-Landau-Verwey-Overbeek (DLVO) theory. The electrostatic repulsive force is dependent on the degree of double-layer overlap and the attractive force is provided by the van der Waals interaction the magnitude of both are a function of the separation between the particles. It has long been realized that the zeta potential is a good indicator of the magnitude of the repulsive interaction between colloidal particles. Measurement of zeta potential has therefore been commonly used to assess the stability of colloidal systems. 

Though the theory of Derjaguin-Landau-Verwey-Overbeek (DLVO) [17, 18] was essentially designed for hydrophobic colloids, it is often applied to the analysis of the stability of polyelectrolyte solutions. According to this approach an overlap of the electrical double-layers of two charge-like colloidal spheres in an electrolyte solution always yields a repulsive screened Coulomb interaction, and the van der Waals forces are responsible for the attraction. A number of experiments in the recent decades, however, provide evidence that the effective interparticle potential shows a long-range attraction which cannot be ascribed to the van der Waals forces [15, 88-93], In spite of numerous theoretical attempts to explain this phenomena (for a review see [7, 8, 10, 94,... 

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 role of electrostatic repulsion in the stability of suspensions of particles in non-aqueous media is not yet clear. In order to attempt to apply theories such as the DLVO (Derjaguin-Landau-Verwey-Overbeek) theory (to be introduced in Section 5.2), one must know the electrical potential at the surface, the Hamaker constant and the ionic strength to be used for the non-aqueous medium these are difficult to estimate. The ionic strength will be low so the EDL will be thick, the electric potential will vary slowly with separation distance and so will the net electric potential as the double layers overlap. For this reason, the repulsion between particles can be expected to be weak. A summary of work on the applicability or lack of applicability of DLVO theory to non-aqueous media has been given by Morrison [33]. 

The interaction forces and potentials between two charged surfaces in an electrolyte are fundamental to the analysis of colloidal systems and are associated with the formation of electrical double layers (EDLs) in vicinity of the solid surfaces. The charged surfaces typically interact across a solution that contains a reservoir of ions, as a consequence of the dissociation of the electrolyte that is already present. In colloid and interfacial sciences, the EDL interaction potential, coupled with the van der Waals interaction potential, leads to the fimdamental understanding of inter-siuface interaction mechanisms, based on the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory [1]. In practice, the considerable variations in the EDL interaction, brought about by the variations in electrolytic concentration of the dispersing medium, pH of the medium, and the siuface chemistry, lead to a diverse natiue of the colloidal behavior. A fundamental understanding of the physics of EDL interactions, therefore, is of prime importance in... 

The destabilisation of colloidal systems can also be described with the DLVO (Deryagin-Landau-Verwey-Overbeek) theory. This theory has been proposed for lyophobic colloidal systems but can also be applied qualitatively to lyophilic colloidal systems. If the potential energy is plotted as a function of the distance of two particles, a curve is obtained as shown in Fig. 18.8. 

When particles approach each other, a result of the attractive van der Waals forces and the repulsive electrostatic forces is the generation of a potential energy barrier which tends to keep particles apart (see Figure 3.2). The Deryagin-Landau and Verwey-Overbeek theory describes the formation of the barrier such that for two spherical particles... 

Electrostatic stabilization is of importance in solution synthesis as another way to stabilize dispersions.1 1 Colloidal particles almost always have charged surfaces that tend to repel each other. One of the most common charging processes is the adsorption of charged species on the surface of the particle. To maintain electroneutrality, a diffuse cloud of counter ions forms in the fluid around the suspended particle. This phenomenon is described by the diffuse double-layer theory. When the diffuse ion clouds of particles interpenetrate, the particles tend to repel each other electrostatically. The electrostatic repulsive forces are opposed by attractive van der Waals forces that are always present between particles in suspension. The description of the potentials created by these two opposing forces is known as the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. The DLVO theory predicts... 

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