DLVO theory limitations

It should be not surprising to find such discrepancies. In the first place, this theory was developed to address the problem of the stability of hydrophobic colloids thus, it only considered from the start long-range interactions. And even within this restriction, there are a number of approximations involved such as the following (the list is not exhanstive)  

The electrostatic and dispersion contribntions are not exactly separable in independent terms (Ninham 1999). 

The electrostatic part is based on the PB equation that implies a number of assumptions (see Section 3.1.2), including treating the solvent as a continuum, and the fact that it does not comply with Maxwell s electromagnetic theory the linearized PB does, but it has limited validity. 

In the dispersion interaction, the Lifshitz theory also treats the electrolyte solution like a continuum, characterized by its frequency-dependent dielectric function, but devoid of any structure. 

FIGURE 6.17 Schematic representation of liquid number density profiles (a) at a vapor-liquid interface 2 is a measure of the molecular-scale surface roughness (b) in the vicinity of a wall-liquid interface (c) between two hard walls at a distance d. (Reprinted from Intermolecular and Surface Forces, 3rd ed., Israelachvili, J.N. Copyright 2010, with permission from Elsevier.) 

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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. 

The limitations of this simplified model have been immediately recognized, and the first criticism [3] even preceded the full development of the DLVO theory. Since then many improvements of the theory have been proposed, to account for the finite size of the ions [4], image forces [5], dielectric corrections [6], ion correlations [7], ion-dispersion [8] and ion-hydration forces [9], to name only a few. Despite the many corrections brought to the traditional DLVO theory, there are some experiments, such as those regarding the stability of neutral lipid multilayers, which could still not be explained within this framework. It is therefore commonly accepted that an additional repulsion occurs when two surfaces approach each other at a distance shorter than a few nanometers. Because this force was initially related to the structuring of water near surfaces, it is commonly named hydration force [10]. 

Because this result has been obtained by solving a generalized Poisson-Boltzmann equation with the linearization approximation, it is necessary to compare it with the DLVO theory in the limit where the Debye approximation holds. In this case, Verwey and Overbeek [2], working in cgs (centimeter-gram-second) units, derived the following approximate equation for the repulsive potential ... 

The same applies to nDLVO-theory yields lower values of ITw for films of small thickness (at least for NaDoS films). If IT, is the cause of the disagreement considered, then the limits of the theory of the double electric layer at high surface charges and electrolyte concentrations should also be accounted for [311],... 

The lower stability of smaller particles which follows from tbe DLVO theory may be one of the factors affecting limited fiocculation of particles during polymerization of polar monomers. The importance of this factor... 

Figure 2.14 Measured electrostatic double-layer and van der Waals forces between two surfaces of curved mica of radius 1 cm in (a) water and (b) dilute KNO3 and Ca(N03)2 solutions. The lines are the predictions of the DLVO theory with a Hamaker constant of 2.2 x 10 J in the limits of constant surface charge and constant surface potential here xfrQ = -(j/s, the particle surface potential. (The lines for constant surface charge are slightly higher than those for constant surface potential at small D.) The inset in (b) is the measured force in 0.1 M KNO3, which shows a force minimum at a distance of around 7 nm. Since this minimum in force occurs away from the deep minimum at the surface, it is called a secondary minimum. (From Israelachvili and Adams 1978 and Israelachvili 1992, reprinted with permission from Academic Press.)...

Appendix 14.1 A Physical Model (DLVO) for Colloid Stability 871 Limitations of the DLVO Theory... 

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. 

The above is only a very brief account of the DLVO theory, since its full development involves rather elaborate mathematics and some necessary approximations which arc probably of limited validity. Nevertheless, the general principles upon which it is based are valuable guides to an understanding of lyophobic colloids. 

Early theories of colloidal dispersions, such as the DLVO theory (Chapter 9) and Einstein s theory of viscosity (Chapter 8). were, of necessity, limited in their applicability to very dilute dispersions. They gave general guidance, however, in the search for att understanding of more concentrated dispersions and formed the basis from which more recent progress has evolved. 

The Derjaguin-Landau-Verwey-Overbeek (DLVO) theory of charged colloids [58] predicts a substantial decrease in stability against flocculation with decreasing particle radius. Most likely the newly formed nuclei are not yet stabilized, and stability sets in only after a certain radius is obtained. After this size is reached, particles grow through monomer addition either reaction- or diffusion-limited, but with an overall rate still depending on the hydrolysis. 

While it has been stated that there are inherent limitations in the DLVO theory, it does appear to be useful in explaining adhesion and contact in some biological cell systems. An early paper by Van den Tempel in 1958 showed that the theory could be used to analyze systems that were similar to colloidal ones. His work on emulsified oil globules, in relation to contact phenomena, enabled him to set up equations of repulsion and attraction resulting from the double layer. These equations, which are a direct result of the DLVO theory, have been applied with great success to biological systems. Van den Tempel was able to measure the thickness of the double layer and he confirmed that the secondary minimum predicted in the DLVO theory does exist. 

Using the surface force apparatus Israelachvili and Adams [38] measured a repulsive force in aqueous solution at short separations that could not be interpreted in terms of DLVO theory. This interaction is due to hydration forces caused by the ordering of water molecules. Its range is very short, typically below 2 nm. For a discussion on the limitations of DLVO theory and possible improvements, see for instance [39]. 

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