DLVO interaction theory

The total interaction potential for charged colloids win be thus given by a combination of van der Waals attraction and electrostatic repulsion, which is known as DLVO interaction theory [4,5]. Figme 51.1 shows the total interaction energy as a function of the interparticle distance for different ionic strengths. It can be observed that attraction always wins out at short distances and at large distances, while repulsion may win at intermediate distances (77 1/k), which is represented as a... 

Fig. 4. Attractive force law deduced from forces measured between mica surfaces immersed in CTAB solutions. Each point is the difference between the measured force and the expected DLVO interaction. For comparison, from Lifshitz theory calculated van der Waals force-law for two mica surfaces and two hydrocarbon surfaces in water is shown as shaded area. Adapted from Ref. [81]. 1984, with permission from Elsevier.

It is customarily assumed that the overall particle-particle interaction can be quantified by a net surface force, which is the sum of a number of independent forces. The most often considered force components are those due to the electrodynamic or van der Waals interactions, the electrostatic double-layer interaction, and other non-DLVO interactions. The first two interactions form the basis of the celebrated Derjaguin-Landau-Verwey-Overbeek (DLVO) theory on colloid stability and coagulation. The non-DLVO forces are usually determined by subtracting the DLVO forces from the experimental data. Therefore, precise prediction of DLVO forces is also critical to the determination of the non-DLVO forces. The surface force apparatus and atomic force microscopy (AFM) have been used to successfully quantify these interaction forces and have revealed important information about the surface force components. This chapter focuses on improved predictions for DLVO forces between colloid and nano-sized particles. The force data obtained with AFM tips are used to illustrate limits of the renowned Derjaguin approximation when applied to surfaces with nano-sized radii of curvature. 

Earlier experimental and theoretical studies of systems in which particles interact through Van der Waal s attraction and electrostatic repulsion led to the development of Derjaguin-Landau-Verwey-Overbeek theory (DLVO). This theory has been successful in providing a quan-... 

Adsorption of enteric viruses on mineral surfaces in soil and aquatic environments is well recognized as an important mechanism controlling virus dissemination in natural systems. The adsorption of poliovirus type 1, strain LSc2ab, on oxide surfaces was studied from the standpoint of equilibrium thermodynamics. Mass-action free energies are found to agree with potentials evaluated from the DLVO-Lifshitz theory of colloid stability, the sum of electrodynamic van der Waals potentials and electrostatic double-layer interactions. The effects of pH and ionic strength as well as electrokinetic and dielectric properties of system components are developed from the model in the context of virus adsorption in extra-host systems. 

Application of DLVO Theory. Our approach to determine the contribution of double-layer interaction and van der Waals potentials to AGads involves comparing differences in the magnitudes of AGads found on the same solid but with different solution conditions, to potentials (U), or theoretical free energy components, evaluated from the DLVO-Lifshitz theory of colloid stability. 

This suggests that if covalent-ionic interactions control adsorption, we could expect viruses to be strongly adsorbed to CuO, but only weakly adsorbed, if at all, to our other oxide surfaces. This is clearly inconsistent with observed trends in virus adsorption, suggesting that here, covalent-ionic interactions are not involved to any major extent, especially considering the good correspondence obtained with the DLVO-Lifshitz theory. 

Poliovirus adsorption to many oxide surfaces is controlled principally by the combination of electrodynamic van der Waals interactions and electrostatic double-layer interactions, as demonstrated by the excellent correspondence of the DLVO-Lifshitz theory with experimentally determined adsorption free energies. 

Many experimental studies have shown DLVO theory is not sufficient to describe particle stability in environmental systems, and additional non-DLVO interactions (hydrophobic/hydrophilic and steric) have been applied to an extended DLVO theory. The unique and size-dependent properties of nanoparticles may require additional modification of DLVO theory to model their interactions in aqueous environments. 

Despite these efforts, no coherent theory of the non-DLVO interactions has emerged yet. The existing approaches are, in principle, based on a simple extension of DLVO interactions derived by considering the local geometry of the interacting bodies or local rather than macroscopic charge distribution. 

Fig. XrV-6. (a) The total interaction energy determined from DLVO theory for n-hexadecane drops for a constant ionic strength - 5.0 nm) at various emulsion pH (b) enlargement of the secondary minimum region of (a). (From Ref. 39.)...

The combined effect of van der Waals and electrostatic forces acting together was considered by Derjaguin and Landau (5) and independently by Vervey and Overbeek (6), and is therefore called DLVO theory. It predicts that the total interaction energy per unit area, also known as the effective interface potential, is given by V(f) = ( ) + dl ( )- absence of externally imposed forces, the equiHbrium thickness of the Hquid film... 

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. 

Fig. 1 Illustration of the DLVO theory interaction of two charged particles as a function of the interparticle distance (attractive energy curve, VA, repulsive energy curve, VR and net or total potential energy curve, Vj).

The DLVO theory, with the addition of hydration forces, may be used as a first approximation to explain the preceding experimental results. The potential energy of interaction between spherical particles and a plane surface may be plotted as a function of particle-surface separation distance. The total potential energy, Vt, includes contributions from Van der Waals energy of interaction, the Born repulsion, the electrostatic potential, and the hydration force potential. [Israelachvili (13)]. 

In filtration, the particle-collector interaction is taken as the sum of the London-van der Waals and double layer interactions, i.e. the Deijagin-Landau-Verwey-Overbeek (DLVO) theory. In most cases, the London-van der Waals force is attractive. The double layer interaction, on the other hand, may be repulsive or attractive depending on whether the surface of the particle and the collector bear like or opposite charges. The range and distance dependence is also different. The DLVO theory was later extended with contributions from the Born repulsion, hydration (structural) forces, hydrophobic interactions and steric hindrance originating from adsorbed macromolecules or polymers. Because no analytical solutions exist for the full convective diffusion equation, a number of approximations were devised (e.g., Smoluchowski-Levich approximation, and the surface force boundary layer approximation) to solve the equations in an approximate way, using analytical methods. 

To what extent can theory predict the collision efficiency factor Two groups of researchers, Derjagin and Landau, and Verwey and Overbeek, independently of each other, have developed such a theory (the DLVO theory) (1948) by quantitatively evaluating the balance of repulsive and attractive forces that interact most effective tool in the interpretation of many empirical facts in colloid chemistry. 

The DLVO theory is a theoretical construct that has been able to explain many experimental data in at least a semiquantitative manner it illustrates plausibly that at least two types of interactins (attraction and repulsion) are needed to account for the overall interaction energy as a function of distance between the particles. 

The presence of polymers or polyelectrolytes have important effects on the Van der Waal interaction and on the electrostatic interaction. Bacterial adhesion, as discussed in Chapter 7.9 may be interpreted in terms of DLVO theory. Since the interaction in bacterial adhesion occurs at larger distances, this interaction may be looked at as occurring in the secondary minimum of the net interaction energy (Fig. 7.4). Particle Size. The DLVO theory predicts an increase of the total interaction energy with an increase in particle size. This effect cannot be verified in coagulation studies. 

In summary, the DLVO theory seems to break down at very close separation where interfacial phenomena such as particle-particle interaction (coagulation) and particle-surface interaction (deposition) are important. 

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... 

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