DLVO interactions

By assuming additivity of the interactions, the total DLVO potential is simply given by 

In Fig. 1.1 the DLVO interaction potential Wdlvo is schematically sketched together with its two contributions. If the maximum of Wdlvo is sufficiently high (larger than a few kT), flocculation is prevented. Flocculation does occur when the particles can get very close into the socalled primary minimum this minimum is usually deep enough for irreversible flocculation. 

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]. 

In the above descriptions we concentrated on situations where a polar background solvent was implicitly assumed. In apolar solvents double layer repulsion is diflhcult to achieve because dissociation, leading to charged surface groups, is less likely to occur and it becomes essential to stabilize colloids with polymers as to prevent instabilities. In the first decades after the establishment of the DLVO theory most papers on forces between colloidal particles focused on Van der Waals and double layer interactions. Forces of other origin such as polymeric steric stabilization [17], depletion [40] or effects of a critical solvent mixture [41] gained interest at a later stage. 

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Determine the net DLVO interaction (electrostatic plus dispersion forces) for two large colloidal spheres having a surface potential 0 = 51.4 mV and a Hamaker constant of 3 x 10 erg in a 0.002Af solution of 1 1 electrolyte at 25°C. Plot U(x) as a function of x for the individual electrostatic and dispersion interactions as well as the net interaction. 

Fig. 3 —Schematic energy versus distance profiles of DLVO interaction.

Figure 7.9 Some typical DLVO interaction curves for colloidal solutions under different conditions.

The total DLVO interaction energy (Vs) between two spherical colloids (each of radius a and separated by distance H) is given by the following approximate equation ... 

Fig. 1.6 DLVO interactions showing the energetics of colloidal particles as a competition between electrostatic double-layer repulsion and van der Waals attractions. The primary minimum is due to strong short-range electron overlap repulsion (shown in Figure 1.4... 

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.

In this case, the Lewis acid-base approach has been assumed to account for all non-DLVO interactions. The exponential-decay expressions [Eq. (27)] deriving from the work of Pashley and Quirk [51], or other quantitative expressions for non-DLVO interactions, similarly could have been inserted. A major advantage of the Lewis acid-base approach is that all parameters in the expression can be determined a priori, whereas the exponential-decay... 

FIGURE 11.8 DLVO interaction for AI2O3 in water with three different electrolyte concentrations. For low electrolyte concentration the effective barrier can stabilize the particles at distance k ( 9 nm). For larger concentrations a secondary minimum can cause weak coagulation of the suspension at the secondary minimum. Even higher concentrations can completely eliminate any repulsion (fast coagulation). 

Bhattacharjee, S., Elimelech, M., and Borkovecb, M., DLVO interaction between colloidal particles beyond Deijaguin s approximation, Creatica Chem. Acta, 71, 883, 1998. 

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. 

This entry is organized in the following paragraphs First, the advanced determination of van der Waals interaction between spherical particles is described. Second, the relevant approximate expressions and direct numerical solutions for the double-layer interaction between spherical surfaces are reviewed. Third, the experimental data obtained for AFM tips having nano-sized radii of curvature and the DLVO forces predicted by the Derjaguin approximation and improved predictions are compared. Finally, a summary of the review and recommended equations for determining the DLVO interaction force and energy between colloid and nano-sized particles is included. 

Bhattacharjee, S. Elimelech, M. Surface element integration a novel technique for evaluation of DLVO interaction between a particle and a flat plate. J. Colloid Interface Sci. 1997,193 (2), 273-285. 

Andersson, K.M. and Bergstrom, L., DLVO interactions of tungsten oxide and cobalt oxide surfaces measured with the colloidal probe technique, J. Colloid Interf. Sci.. 246, 309, 2002. 

Feiler, A., Jenkins, P., and Ralston, J., Metal oxide surfaces separated by aqueous solutions of linear polyphosphates DLVO and non-DLVO interaction forces, Phys. Chem. Chem. Phys., 2, 5678, 2000. 

Grasso, D., Subramaniam, K., Butkus, M., Strevett, K., and Bergendahl, J. A review of non-DLVO interactions in environmental colloidal systems. Rev. Environ. Sci. Bio/TechnoL, 1, 17, 2002. 

Proteins adsorbed at an oil-water interface may stabilize the oil droplets by the Derjaguin, Landau, Verwey, and Overbeek (DLVO) interactions and/or the steric stabilization mechanism. The proteins may possess or be capable of adopting extended structures, which protrude into a solution for a considerable distance from the interface. This extended hydrated layer may form the basis for steric stabilization of the emulsion. Interactions between the adsorbed protein layers can involve a reduction in conhgurational entropy as molecular chains overlap (Darling and Birkett, 1987). In addition, hydration of adsorbed hydrophilic components can lead to an enthalpic repulsion when two particles are in close proximity. This tends to force the oil droplets apart (Darling and Birkett, 1987). 

Bhattacharjee S., Ko C.-H., Elimelech M. (1998), DLVO interactions between rough surfaces, Langmuir, 14, 12, 3365-3375,... 

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. 

Significant advances have been made over the last three decades in our understanding of steric stabilization, and recently measurements have been reported on the force between two surfaces containing adsorbed polymer ". Data on the measurement of the force due to the electrostatic interaction of surfaces have also been presented, as well as those arising from non-DLVO interactions. 

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... 

Bhardwaj, R., Fang, X., Somasundaran, P., Attinger, D. Self-assembly of colloidal particles from evaporating droplets role of DLVO interactions and proposition of a phase diagram. Langmuir 26, 7833-7842 (2010)... 

Figure 4.6 Calculated energy profiles of DLVO interactions as a function of the distance between particle surfaces, (a) Surfaces repel strongly coUoidal particles remain stable, (b) Surfaces come into stable equilibrium if the secondary minimum is deep enough colloids then aggregate reversibly, (c) The interaction curve approaches the pure van der Waals curve and colloids coagulate irreversibly.

Fig. 1.1 Schematic plot of a typical double layer repulsion between charged colloidal spheres (top), of the Van der Waals attraction (bottom) and their sum, which is the DLVO interaction potential...

FIGURE 6.13 Schematic representation of the relative interaction strength of the different contributions (a), and the resulting total DLVO interaction (b), at different ionic strengths for two identical spheres at constant potential conditions with Ci = fl2 = 10 nm, = aa ... 

Solvation oscillatory forces As described in previous section, they arise from the alterations on the solvent structure as the particles approach. In fact, several experimental measurements of interactions at very short distances have shown an oscillatory behavior (Horn and Israelachvili 1980 Horn and Israelachvili 1981 Christenson and Horn 1983), which were interpreted in terms of electrostatic and oscillatory forces. The oscillations in these measurements clearly are due to the solvent structure discussed in Section 6.6.1, but its treatment as a force, as in other DLVO interactions, has been questioned (Ninham 1999). 

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