EDL interaction

The electrical double layer interaction is a key feature of a great many colloidal systems that are of technological significance. In the preparation and useful shelf-life of paints, and/or inks, or in the area of detergency where the properties of charged surface active compounds come into consideration the stabilizing influence of the edl interaction is important. Special mention... 

The first reported uses of an AFM to study EDL interactions using the colloid probe technique were the studies by Ducker et al. [29,301 and by Butt [311... 

In 1942 Deqaguin and Landau and Verwey and Overbeek (DLVO) suggested that the total energy of a colloidal system is the summation of van der Waals (vd W) and EDL interactions. For the case of spherical particles of radius R, this has the form... 

In Eq. (15), the electrostatic potential, iJ/, is for the overlapping electric double layer of the interacting particles. Numerous models have been created to predict the overlapping field electrostatic potential between parallel plates. However, calculation of the EDL interaction for the common geometry of two spheres has not been satisfactorily resolved, due mainly to the nonlinear partial differential terms in Eq. (13) arising because of the three-dimensional geometry of the system. As a consequence, a number of approximate and numerical models have been developed for the calculation of the EDL interaction between two spheres. These models are briefly described below. 

Exact Numerical Solutions for EDL Interaction Between Two Spheres... 

The interaction forces and potentials between two charged surfaces in an electrolyte are fundamental to the analysis of colloidal systems and are associated with the formation of electrical double layers (EDLs) in vicinity of the solid surfaces. The charged surfaces typically interact across a solution that contains a reservoir of ions, as a consequence of the dissociation of the electrolyte that is already present. In colloid and interfacial sciences, the EDL interaction potential, coupled with the van der Waals interaction potential, leads to the fimdamental understanding of inter-siuface interaction mechanisms, based on the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory [1]. In practice, the considerable variations in the EDL interaction, brought about by the variations in electrolytic concentration of the dispersing medium, pH of the medium, and the siuface chemistry, lead to a diverse natiue of the colloidal behavior. A fundamental understanding of the physics of EDL interactions, therefore, is of prime importance in... 

To begin with the fundamental analysis of EDL interactions, let us first consider the distribution of potential between two charged infinite parallel plates at a distance of 2H apart and subjected to constant surface potentials (refer to Eig. 1). Assuming a Boltzmann distribution of the respective ionic concentrations, one can write, for a symmetric 1 1 electrolyte (see entry Electrical Double Layers ),... 

The corresponding EDL interaction force per unit area, F2H, can be calculated as... 

Equation 9 can be conveniently utilized to derive the interaction potential between two spherical EDLs, following the Derjaguin s method [2]. This is done by utilizing the fact that the EDL interactions between two thin parallel slices of the spherical surfaces are essentially governed by Eq. 9. For the sake of analysis, let us consider two spherical surfaces at a minimum distance of separation of Hq, as depicted in Fig. 2. From Fig. 2, the total potential energy of interaction between two infinitesimally small parallel rings of width dx and radius x can be described as... 

Fig. 2 Geometrical features used for the calculation of the EDL interaction potential between two spherical surfaces of radii oi and 2...

Equation 15 can be utilized to derive the EDL interaction potential between a sphere of radius a and a flat plate by setting ai = a, U2 oo, to obtain... 

It is important to mention here that the EDL interaction potentials described by Eqs. 15 and 16 are only applicable under the following restricted conditions ... 

The methodology described as above has recently been extended [4] to estimate the EDL interaction between a spherical particle (of radius a) and a cylinder (of radius R). The details of the derivations are presented elsewhere [4], and only the final results are summarized below. 

The fundamental theories on EDL interactions have been substantially advanced by several researchers in the recent past in order to incorporate the effects of other pertinent physicochemical phenomena in the mathematical model and to generalize the underlying postulates. Kjellander and Mitchell [5] employed the dressed ion theory for EDL structure and interactions, which is nothing but an exact statistical mechanical formahsm for electrolyte systems. In their theory, the dressed ions took equivalent roles as the bare ions in the Poisson-Boltzmann approximation. A practical method was also derived for evaluating the effective surface charge densities of the particles. Behrens and Borkovec [6] proposed... 

When the EDL interaction occurs in nanofluidic channels, a traditional bulk ionic concentration does not even exist. The local electroneutrality may never be obtained at the middle of channel for these cases. People have found the counterion enrichment when the EDL overlap occurs in the nanochannels. A few methods have been proposed to determine the effective bulk ionic concentration in nanochannels. A reasonable determination for the effective bulk ionic concentration with double-layer interactions in nanochannels requires (i) to reflect the dominating ions effects on transport and (ii) to transform to the traditional bulk concentration automatically when the double-layer interaction vanishes. Based on these requirements, we present a new enrichment coefficient, a, to calculate the... 

Electrokinetic phenomena arise when the mobile layer of the EDL interacts with an externally applied electric field resulting in relative motion between the solid and liquid phases. There are three types of electrokinetic phenomena relevant to microfluidics electroosmotic flow, streaming potential, and electrophoresis. In aU of these cases, the zeta potential is a key parameter that defines either the fluid flow or particle motion. Since it is not possible to probe the zeta potential directly, measurements are based on indirect readings obtained from electrokinetic experiments. The following discussion focuses on modem methods of measuring the zeta potential using electroosmotic flow, electrophoresis, and streaming potential. 

Fig. 3.13 Principal dependency of the total interaction energy k, between two particles from the surface distance curves for EDL interaction (Vdl). van-der-Waals interaction (Vvdw) and Bom repulsion (Vb) are shown additionally example for repelling EDLs and two local minima...

In nature, electrokinetics is used, in the form of electro-osmosis, by earthworms to allow them to move over soil. The flow within a micro-thin liquid layer near the worm s body surface is induced by what is known as the electric double layer (EDL) interaction. This is essentially electro-osmosis at the micro-scale providing lubrication between its body and moist soil, thus reducing surface adhesion (Yan et al., 2007). The reader will find similar research using the term biomimetics in his or her search engine. 

The counterions form a diffuse cloud that shrouds each particle in order to maintain electrical neutrality of the system. When two particles are forced together their counterion clouds begin to overlap and increase the concentration of counterions in the gap between the particles. If both particles have the same charge, this gives rise to a repulsive potential due to the osmotic pressure of the counterions which is known as the electrical double layer (EDL) repulsion. If the particles are of opposite charge an EDL attraction will result. It is important to realize that EDL interactions are not simply determined by the Columbic interaction between the two charged spheres, but are due to the osmotic pressure (concentration) effects of the counterions in the gap between the particles. 

In the 1940s Derjaguin, Landau, Verwey and Overbeek (DLVO), developed the hypothesis that the total particle interaction could be determined by simply summing the contributions from the van der Waals interaction and the EDL interaction. In the meantime, the DLVO theory has been widely verified experimentally. Furthermore, it has been found that many other forces may be combined in the same way to determine the overall interparticle interaction. Examples of some net interparticle interaction forces are shown in Figure 5.9. 

Since the EDL adhesion is not equal to the acid-base (or donor-acceptor) interaction, it is possible that in some systems both interactions can coexist. However, the increase of the acid-base interaction on the same surface can reduce the EDL interaction due to the decrease of the surface charge density )... 

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