Limitations of the DLVO Theory

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

The most important limitation of the DLVO theory is that it does not account for other important repulsive forces such as the steric and solvation ones at close distances. Natural and synthetic polymers, especially block and graft copolymers, can provide steric stabilization. It is best if one part of the stabilizer has a high tendency to adsorb onto the particle surface and the other has a high affinity for the solvent. 

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]. 

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.)...

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. 

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. 

Several extensions and modifications of the electrolyte theory in the first half of the twentieth century should be mentioned Bjeiium [14] introduced the concept of limited electrostatic dissociation (ion pair formation), Onsager and Fuoss extended the DH approach and the ideas of Debye about the electrophoretic and the relaxation effect on transport properties such as electrical conductivity and diffusion coefficients [15]. As already mentioned, the DH description is also the basis of one of the two constituting parts of the DLVO theory in colloidal chemistry. 

Here, we will limit our discussion to electrostatic double-layer forces and van der Waals forces. Thus, other interaction forces important in special cases are neglected. This means that we start with a discussion of the DLVO theory. 

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],... 

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. 

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. 

In general, it is observed that DLVO works reasonably well for ionic strengths no higher than about 0.01 M and interparticle distances not less than a few nanometers. Outside these limits, the theory shows important discrepancies with experiments. Fortunately, in soil-related problems, these conditions hold thus, DLVO can give, most of the time, correct predictions however, in some cases, such as highly saline soils, it can fail severely. In view of the discrepancies, there have been diverse proposals to improve/replace the DLVO theory, as mentioned in the following sections. 

We have not studied all types of colloidal systems in detail but limited ourselves to suspensions, siufac-tants, emulsions and foams. In terms of properties, the stability and associated concepts (double layer, van der Waals forces, steric effects) as well as the DLVO theory have been presented in detail, while kinetic and especially the optical properties have been discussed more briefly. 

---