DLVO forces

In the SFBLA approach, the interaction potential near the electrode is composed of the traditional DLVO forces and the electrophoretic and diffusiophoretic contributions. The flux of particles is given by... 

W.A. Ducker, Z. Xu, and J.N. Israelachvili Measurements of Hydrophobic and DLVO Forces in Bubble-Surface Interactions in Aqueous Solutions. Langmuir 10, 3279 (1994). 

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 ... 

Non DLVO forces in water deserve a special subchapter because they are important and far from being understood. They are important because water is the universal solvent in nature. Also, in more and more industrial processes water is used instead of organic solvent since it is harmless to the environment. 

Non-DLVO forces also occur when the aqueous medium contains surfactants, which form micelles, or polyelectrolytes. A discussion of the complex interaction is, however, beyond the scope of this book. We recommend Ref. [199],... 

Figure 5.15 shows an example of a disjoining pressure isotherm in which the steric force contributions have been superimposed on the classical DLVO force contributions. It can be seen that this creates two regions for meta-stable foam films. One region is the thick, common black film region, with film thicknesses of approximately 50 nm or so. The other region is the thin, Newton black film region, with film thicknesses of approximately 4 nm. While the common black films are mostly stabilized by electrostatic forces, the Newton black films are at least partly stabilized by the steric forces. 

Because the double layer force vanishes in the absence of surface charges, one expects the attractive van der Waals force to cause the coagulation of all neutral (or even weekly charged) colloids. The absence of such a behavior has been explained by the existence of an additional (non-DLVO) force, the hydration interaction, which is due to the structuring of water in the vicinity of hydrophilic surfaces. This chapter is devoted to the identification of the microscopic origin of the hydration force, and to the presentation of a unified treatment of the double layer and hydration forces, the Polarization Model. 

The effect of electrolyte concentration on the transition from common to Newton black films and the stability of both types of films are explained using a model in which the interaction energy for films with planar interfaces is obtained by adding to the classical DLVO forces the hydration force. The theory takes into account the reassociation of the charges of the interface with the counterions as the electrolyte concentration increases and their replacements by ion pairs. This affects both the double layer repulsion, because the charge on the interface is decreased, and the hydration repulsion, because the ion pair density is increased by increasing the ionic strength. The theory also accounts for the thermal fluctuations of the two interfaces. Each of the two interfaces is considered as formed of small planar surfaces with a Boltzmannian distribution of the interdistances across the liquid film. The area of the small planar surfaces is calculated on the basis of a harmonic approximation of the interaction potential. It is shown that the fluctuations decrease the stability of both kinds of black films. 

In fact, the SFA was initially developed for practically probing the DLVO theory, and DLVO forces were successfully measured in electrolyte solutions and colloidal systems [4,22]. However, the applications of the apparatus were not restricted to this. Detailed and accurate information was obtained on thickness and refractive index profiles of thin films [6], simple liquid molecular structuring... 

Fig. 11. (A) Force normalised by radius as a function of surface separation between mica surfaces in 0.01 wt.% acetic acid solution (pH 3.8). The arrow indicates a jump from a force barrier into molecular contact. (B) Forces between mica surfaces coated with chitosan across 0.01 wt.% acetic acid solution (pH 3.8). Two sets of measurements are shown. Filled and open symbols represent the forces measured on approach and separation, respectively, after 24 h of adsorption. The crosses represent the forces measured at pH 3.8 after the cycle of exposing chitosan adsorption layers for solutions of increasing alkalinity and measuring forces at pH 4.9, 6.2 and 9.1. The solid lines represent theoretically calculated DLVO forces. Redrawn with permission from Ref. [132]. 1992, American Chemical Society.

Attempts to utilize traditional DLVO approaches to quantify the Schulze-Hardy Rule have found limited and qualified success [23,59]. Although a qualitative agreement of the predicted dependence of ccc on counterion valence can be demonstrated, non-DLVO forces are typically ignored and analytical solutions of the DLYO equations predict unrealistically large ccc values [23,59]. 

Formation and stability studies of black foam films can be summarised as follows 1) surface forces in black foam films direct measurement of disjoining pressure isotherm DLVO- and non-DLVO-forces 2) thin foam film/black foam film transition establishing the conditions for the stability of both types of black films and CBF/NBF transition 3) formation of black foam films in relation to the state of the adsorption layers at the solution/air interface 4) stability of bilayer films (NBF) theory and experimental data. 

The analysis of the above techniques (Section 3.4.2.2) developed to estimate the conditions under which stable CBF and NBF exist, and reveals the equilibrium character of the transition between them and the particular features of the two types of black films. Furthermore the difference between the techniques of investigation as well as the difference between their intrinsic characteristics proves to be a valuable source of information of these thinnest liquid formations. The transition theory of microscopic films evidences the existence of metastable black films. Due to the deformation of the diffuse electric layer of the CBF, the electrostatic component of disjoining pressure 1 L( appears and when it becomes equal to the capillary pressure plus Ylvw, the film is in equilibrium (in the case of DLVO-forces). As it is shown in Section 3.4.2.3, CBF exhibit several deviations from the DLVO-theory. The experimentally obtained value of ntheoretically calculated. This is valid also for the experimental dependence CeiiCr(r). Systematic divergences from the DLVO-theory are found also for the h(CeiXr) dependence of NaDoS microscopic films at thickness less than 20 nm. 

In Section 3.4.1.3 it was discussed that the surface forces in black films from ionic surfactants deviate considerably from the DLVO-forces. 

Non-DLVO Forces. Although DLVO theory worked very well for the electrolyte-induced coagulation of bitumen-in-water emulsions, it cannot be applied in some cases. 

In a simple foam film the thickness of the interface is similar to the length of a surfactant molecule. The thickness of the so-called common black film (CBF) is determined by the DLVO forces, and the thinner Newton black film (NBF) is stabilized by steric repulsion and does not contain any free solvent molecules. A transition from a CBF to a NBF can be induced by the addition of salt leading to a screening of the surface potential. This confirms the electrostatic nature of the repulsive force stabilizing the CBF. The transition from a CBF to a NBF corresponds to an oscillation of the disjoining pressure because of the attractive van-der-Waals forces. This attractive part of the isotherm is mechanically unstable, and it cannot be measured by a TFPB. But a step in film thickness from the thicker CBF to a thinner NBF is detected. 

Particle-Particle Interaction Improvements in the Prediction of DLVO Forces... 

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. 

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