Double-layer interactions, experimental

More dramatic are the long-range consequences of the van der Waals attraction, even when a cut-off is included. As shown by Bostrom et al. [16], the double layer interactions in electrolytes of physiological concentrations become in this case attractive at distances less than 30 A. This unexpected theoretical prediction has yet to be verified experimentally. 

At low electrolyte concentrations, the experimental results can be explained within the DLVO theory. A well-known approximation for the double layer interaction between weakly charged spheres, at constant surface charge, is1... 

Determination of the Electrophoretic Mobility, To evaluate the equation for the double-layer interaction (eq 5), the zeta potential, must be known it is calculated from the experimentally measured electrophoretic mobility. For emulsions, the most common technique used is particle electrophoresis, which is shown schematically in Figure 4. In this technique the emulsion droplet is subjected to an electric field. If the droplet possesses interfacial charge, it will migrate with a velocity that is proportional to the magnitude of that charge. The velocity divided by the strength of the electric field is known as the electrophoretic mobility. Mobilities are generally determined as a function of electrolyte concentration or as a function of solution pH. 

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. 

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. 

Both the magnitude and range of the electrical double layer interactions on the peaks are greatly reduced compared with those in the valleys. In both cases the range is very different from that at a planar surface, both experimentally (data for mica are shown for comparison) and theoretically (the Debye length). It is also possible to quantify the adhesive interaction between colloid probe and membrane surface at different locations, as shown in Figure 6.18 and Table 6.4. 

More recent experimental data [4] show that considerable deviations from the conventional DLVO theory appear for short surface-to-surface distance hydration repulsion) and in the presence of bivalent and multivalent counterions ionic correlation force). Both effects can be interpreted as contributions to the double-layer interaction not accounted for in the DLVO theory see Sec. VLB. 

By far, the greatest amount of theoretical and experimental work on colloid attachment or deposition has as its roots DLVO theory (e.g., Kretzchmar et al., 1999 Ryan Elimelech, 1996 and references therein). Filtration theory (e.g., Yao et al., 1971), which is usually expressed in terms of a single collector (i.e., the immobile phase) efficiency, works well for systems with well-defined geometry and in which repulsive double layer interactions are absent, that is, for fast deposition. Although filtration theory quickly evolved to include DLVO type interactions (i.e., repulsive forces and slow deposition), large discrepancies between experimental results and theory typically arise if double-layer interactions are required (e.g., Elimelech O Melia, 1990). As a consequence, predicting colloid deposition in response to... 

To fit the experimental data it was necessary to set Wgi equal to -0.3 and -0.46 yN for the 3.4 and 8.5 mM SDS solutions respectively (middle and lower curves of Fig. 9). Bell Peterson have developed a comprehensive theory to account for the electrical double layer interaction forces between spheres. Peterson44 has calculated for the asperity radii found in this work, that such values of Wgi can be generated using reasonable estimates for the surface potential at the contact. His calculations also show that the predominate repulsion occurs outside the contact zone. 

Relaxations in the double layers between two interacting particles can retard aggregation rates and cause them to be independent of particle size [101-103]. Discrepancies between theoretical predictions and experimental observations of heterocoagulation between polymer latices, silica particles, and ceria particles [104] have promptetl Mati-jevic and co-workers to propose that the charge on these particles may not be uniformly distributed over the surface [105, 106]. Similar behavior has been seen in the heterocoagulation of cationic and anionic polymer latices [107]. 

The parameter a in Equation (11.6) is positive for electrophobic reactions (5r/5O>0, A>1) and negative for electrophilic ones (3r/0Oelectrochemical promotion behaviour is frequently encountered, leading to volcano-type or inverted volcano-type behaviour. However, even then equation (11.6) is satisfied over relatively wide (0.2-0.3 eV) AO regions, so we limit the present analysis to this type of promotional kinetics. It should be remembered thatEq. (11.6), originally found as an experimental observation, can be rationalized by rigorous mathematical models which account explicitly for the electrostatic dipole interactions between the adsorbates and the backspillover-formed effective double layer, as discussed in Chapter 6. 

At present it is impossible to formulate an exact theory of the structure of the electrical double layer, even in the simple case where no specific adsorption occurs. This is partly because of the lack of experimental data (e.g. on the permittivity in electric fields of up to 109 V m"1) and partly because even the largest computers are incapable of carrying out such a task. The analysis of a system where an electrically charged metal in which the positions of the ions in the lattice are known (the situation is more complicated with liquid metals) is in contact with an electrolyte solution should include the effect of the electrical field on the permittivity of the solvent, its structure and electrolyte ion concentrations in the vicinity of the interface, and, at the same time, the effect of varying ion concentrations on the structure and the permittivity of the solvent. Because of the unsolved difficulties in the solution of this problem, simplifying models must be employed the electrical double layer is divided into three regions that interact only electrostatically, i.e. the electrode itself, the compact layer and the diffuse layer. 

---