The DLVO theory

In the case shown schematically, thermodynamic equilibrium occurs at the minimum value of Ft, when the particles are in contact (aggregation distance). However, if we were to take two particles separated by a distance s Smax, they would not be able to approach one another because there is a net repulsive force in this region (Ft increases as s decreases). The barrier at Fmax must be crossed in order to reach the attractive region. If the particles do not dispose of an energy (either thermal or kinetic) greater than F ax, the system will not evolve. It is in fact metastable. 

Although it is highly schematised, this description provides a good model for the normal behaviour of colloidal suspensions. The main features here are  

The resulting deposits silt up estuaries and favour the formation of deltas. 

It has been known for more than 100 years that many aqueous dispersions precipitate upon addition of salt. Schulze and Hardy observed that most dispersions precipitate at concentrations of 25-150 mM of monovalent counterions [154,155]. For divalent ions they found far 

Roughly 60 years ago Derjaguin, Landau, Verwey, and Overbeek developed a theory to explain the aggregation of aqueous dispersions quantitatively [66,157,158], This theory is called DLVO theory. In DLVO theory, coagulation of dispersed particles is explained by the interplay between two forces the attractive van der Waals force and the repulsive electrostatic double-layer force. These forces are sometimes referred to as DLVO forces. Van der Waals forces promote coagulation while the double layer-force stabilizes dispersions. Taking into account both components we can approximate the energy per unit area between two infinitely extended solids which are separated by a gap x  

For small distances DLVO theory predicts that the van der Waals attraction always dominates. Please remember the van der Waals force between identical media is always attractive irrespective of the medium in the gap. Thus thermodynamically, or after long periods of time, we expect all dispersions to precipitate. Once in contact, particles should not separate again, unless they are strongly hit by a third object and gain a lot of energy. 

A closer look at the interaction at large distances shows the weak attractive energy. This secondary energy minimum can lead to a weak, reversible coagulation without leading to direct molecular contact between the particles. 

For many systems this is indeed observed. There are, however, important exceptions. One such exception is the swelling of clay [159-161], In the presence of water or even water vapor, clay swells even at high salt concentrations. This cannot be understood based on DLVO theory. To understand phenomena liken the swelling of clay we have to consider the molecular nature of the solvent molecules involved. 

It has been known for more than 100 years that many aqueous dispersions precipitate upon addition of salt [438]. Schulze and Hardy observed that most dispersions precipitate at concentrations of 25-150 mM of monovalent counterions [439, 440]. For divalent ions, they found far smaller precipitation concentrations of 0.5-2 mM. Trivalent counterions lead to precipitation at even lower concentrations of 0.01-0.1 mM. For example, gold colloids are stable in NaCl solution, as long as the NaCl concentration does not exceed 24 mM. If the solution contains more NaCl, then the gold particles aggregate and precipitate. The appropriate concentrations for KNO3, CaCl2, and BaCl2 are 23, 0.41, and 0.35 mM [441], respectively. 

This coagulation can be understood as follows. The gold particles are negatively charged and repel each other. With increasing salt concentration, the electrostatic repulsion decreases. The particles, which move around thermally, have a higher 

About seven decades ago, Derjaguin, Landau, Verwey, and Overbeek developed a theory to explain the aggregation of aqueous dispersions quantitatively [413, 442, 

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The theory has certain practical limitations. It is useful for o/w (od-in-water) emulsions but for w/o (water-in-oil) systems DLVO theory must be appHed with extreme caution (16). The essential use of the DLVO theory for emulsion technology Hes in its abdity to relate the stabdity of an o/w emulsion to the salt content of the continuous phase. In brief, the theory says that electric double-layer repulsion will stabdize an emulsion, when the electrolyte concentration in the continuous phase is less than a certain value. 

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. 

The DLVO theory [88,89], a landmark in the study of colloids, interprets stability as dependent on the competition between the long-range repulsion forces of similarly charged... 

The physicochemical forces between colloidal particles are described by the DLVO theory (DLVO refers to Deijaguin and Landau, and Verwey and Overbeek). This theory predicts the potential between spherical particles due to attractive London forces and repulsive forces due to electrical double layers. This potential can be attractive, or both repulsive and attractive. Two minima may be observed The primary minimum characterizes particles that are in close contact and are difficult to disperse, whereas the secondary minimum relates to looser dispersible particles. For more details, see Schowalter (1984). Undoubtedly, real cases may be far more complex Many particles may be present, particles are not always the same size, and particles are rarely spherical. However, the fundamental physics of the problem is similar. The incorporation of all these aspects into a simulation involving tens of thousands of aggregates is daunting and models have resorted to idealized descriptions. 

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)]. 

The DLVO theory provides a qualitative explanation of the ionic strength and solution pH effects on particle release. 

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. 

In a number of recent publications (1, 2) microcrystailine cellulose dispersions (MCC) have been used as models to study different aspects of the papermaking process, especially with regard to its stability. One of the central points in the well established DLVO theory of colloidal stability is the critical coagulation concentration (CCC). In practice, it represents the minimum salt concentration that causes rapid coagulation of a dispersion and is an intimate part of the theoretical framework of the DLVO theory (3). Kratohvil et al (A) have studied this aspect of the DLVO theory with MCC and given values for the CCC for many salts, cationic... 

The DLVO theory, a quantitative theory of colloid fastness based on electrostatic forces, was developed simultaneously by Deryaguin and Landau [75] and Verwey and Overbeek [76], These authors view the adsorptive layer as a charge carrier, caused by adsorption of ions, which establishes the same charge on all particles. The resulting Coulombic repulsion between these equally charged particles thus stabilizes the dispersion. This theory lends itself somewhat less to non-aqueous systems. 

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... 

The DLVO theory is thus found to be useful to predict and estimate colloidal stability behavior. Of course, in such systems with many variables, a simplified theory is to be expected to fit all kinds of systems. 

In the past decade, much development has taken place in regard to measuring the forces involved in these colloidal systems. In one method, the procedure used is to measure the force present between two solid surfaces at very low distances (less than micrometer). The system can operate under water, and thus the effect of addictives has been investigated. These data have provided verification of many aspects of the DLVO theory. Recently, the atomic force microscope (AFM) has been used to measure these colloidal forces directly (Birdi, 2002). Two particles are brought closer, and the force (nanoNewton) is measured. In fact, commercially available apparatus are designed to perform such analyses. The measurements can be carried out in fluids and under various experimental conditions (such as added electrolytes, pH, etc.). 

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. 

Derjaguin and Landau, and Verwey and Overbeek (1941-8) developed the DLVO theory of colloid stability. 

Historical deveiopment of van der Waais forces. The Lennard-Jones potentiai. intermoiecuiar forces. Van der Waais forces between surfaces and coiioids. The Hamaker constant. The DLVO theory of coi-loidal stability. 

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