The Electric Double Layer and Electrokinetic Phenomena

Let us first make a rough estimate of the thickness of the double layer by assuming that there are no positive ions (coions) present (perfect shielding). Poisson s equation relating spatial variation in electric field to charge distribution for a medium of uniform dielectric constant is 

c is the average molar negative ion (counterion) concentration. Hence, the Poisson equation reduces to 

Assuming that electric field vanishes on one side of the plane layer, that is, we have the boundary condition as 

As electrical potential is the potential energy per charge, the electrical potential energy per mole of negative ion (counterion) can be expressed as 

If we assume planar translational motion of the ions, the value of AW equals to RT/2 and we have 

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D.A. Haydon The electrical double-layer and electrokinetic phenomena, in Progress in Surface Science, vol. I. Academic press., London, 1964. 

Electrokinetic phenomena are only directly related to the nature of the mobile part of the electric double layer and may, therefore, be interpreted only in terms of the zeta potential or the charge density at the surface of shear. No direct information is given about the potentials tf/0 and charge density at the surface of the material in question. 

There are four electrokinetic phenomena (electrophoresis, electroosmosis, streaming potential, and sedimentation potential), all of which involve both the theory of the electric double layer and that of liquid flow. Among them electrophoresis has the greatest practical applicability to the study of biomolecules and biocell surface porperties. In this section, the relation between electrophoretic mobility and its related electrokinetic potential C will be discussed. 

In the following sections, the relationship between surface charge and electrokinetic phenomena is expounded in terms of classical theory. First, a few possible mechanisms and models for the development of charge at a surface in contact with an aqueous solution are described in order to form a basis for the formation of an electrical double-layer at an interface. Secondly, the electrical double-layer is discussed in terms of an equilibrium charge distribution and electrostatic potential near the interface. With an adequate description of the interface, the discussion turns to explication of electrokinetic phenomena according to the charge distribution in the electrical double-layer and the Navier-Stokes equation. A section then follows which describes common methods and experimental requirements for the measurement of electrokinetic phenomena. The discussion closes with a few examples of the use of measurement of the pH dependence of electroosmosis as an analytical characterization technique from this present author s own experience. The intention is to provide... 

Even allowing for the fact that the Debye-Hiickel approximation applies only for low potentials, the above analysis reveals some features of the electrical double layer that are general and of great importance as far as stability with respect to coagulation of dispersions and electrokinetic phenomena are concerned. In summary, three specific items might be noted ... 

The word electrokinetic implies the combined effects of motion and electrical phenomena. Specifically, our interest in this chapter centers on those processes in which a relative velocity exists between two parts of the electrical double layer. This may arise from the migration of a particle relative to the continuous phase that surrounds it. Alternatively, it could be the solution phase that moves relative to stationary walls. 

The surface of shear is the location within the electrical double layer at which the various electrokinetic phenomena measure the potential. We saw in Chapter 11 how the double layer extends outward from a charged wall. The potential at any particular distance from the wall can, in principle, be expressed in terms of the potential at the wall and the electrolyte content of the solution. In terms of electrokinetic phenomena, the question is How far from the interface is the surface of shear situated and what implications does this have on the relation between measured zeta potential and the surface potential ... 

Chapters 11 and 12 in the present edition focus exclusively on the theories of electrical double layers and forces due to double-layer interactions (Chapter 11) and electrokinetic phenomena (Chapter 12). Chapter 11 includes expressions for interacting spherical double layers, and both chapters provide additional examples of applications of the concepts covered. 

In electrokinetic phenomena such as electroacoustics, theoretical models need to consider the induced movement of charge within the electrical double layer (EDL), the surface current , Is, as well as the interaction of the outer portion of the double layer with the applied signal (acoustic or electric field) and with the liquid medium. Hydrodynamic flows generate surface current as liquid moving relative to the particle... 

Many more-sophisticated models have been put forth to describe electrokinetic phenomena at surfaces. Considerations have included distance of closest approach of counterions, conduction behind the shear plane, specific adsorption of electrolyte ions, variability of permittivity and viscosity in the electrical double layer, discreteness of charge on the surface, surface roughness, surface porosity, and surface-bound water [7], Perhaps the most commonly used model has been the Gouy-Chapman-Stem-Grahame model 8]. This model separates the counterion region into a compact, surface-bound Stern" layer, wherein potential decays linearly, and a diffuse region that obeys the Poisson-Boltzmann relation. 

Many properties of disperse systems are related to the distribution of charges in the vicinity of the interface due to the adsorption of electrolytes. The adsorption of molecules is driven by the van der Waals attraction, while the driving force for the adsorption of electrolytes is the longer-range electrostatic (Coulomb) interaction. Because of this, the adsorption layers in the latter case are less compact than in the case of molecular adsorption (i.e., they are somewhat extended into the bulk of the solution), and the discontinuity surface acquires noticeable, and sometimes even macroscopic thickness. This diffuse nature of the ionized adsorption layer is responsible for such important features of disperse systems as the appearance of electrokinetic phenomena (see Chapter V) and colloid stability (Chapters VII, VIII). Another peculiar feature of the adsorption phenomena in electrolyte solutions is the competitive nature of the adsorption in addition to the solvent there are at least two types of ions (even three or four, if one considers the dissociation of the solvent) present in the system. Competition between these ions predetermines the structure of the discontinuity surface in such systems -i.e. the formation of spatial charge distribution, which is referred to as the electrical double layer (EDL). The structure and theory of the electrical double layer is described in detail in textbooks on electrochemistry. Below we will primarily focus on those features of the EDL, which are important in colloid... 

The spatial charge distribution in the electrical double layer is exactly what causes the electrokinetic phenomena, namely the mutual displacement of the phases in contact in an applied external electric field (electrophoresis and electroosmosis) or the charge transfer that occurs upon the mutual motion of phases (streaming and sedimentation potentials and currents). The following consideration, the simplest consistent with the Helmholtz model, establishes the relationship between the rate of the phase shift, e.g. that of electroosmosis, and the strength of the external electric field, E, directed along the surface3. 

The studies of electrophoresis and other electrokinetic phenomena as well as the investigation of ion exchange (Chapter III), have shown a strong influence of electrolyte composition on the structure of electrical double layer and intensity of electrokinetic phenomena. One may subdivide electrolytes capable of causing such an influence into the following groups [13] ... 

The bulk transport of ions in electrochemical systems without the contribution of advection is described by Poisson-Nernst-Planck (PNP) equations (Rubinstein, 1990).The well-known Nernst-Planck equation describes the processes of the process that drives the ions from regions of higher concentration to regions of lower concentration, and electromigration (also referred to as migration), the process that launches the ions in the direction of the electric field (Bard and Faulkner, 1980). Since the ions themselves contribute to the local electric potential, Poisson s equation that relates the electrostatic potential to local ion concentrations is solved simultaneously to describe this effect. The electroneutrality assumption simplifies the mathematical treatise of bulk transport in most electrochemical systems. Nevertheless, this no charge density accumulation assumption does not hold true at the interphase regions of the electric double layer between the solid and the Uquid, hence the cause of most electrokinetic phenomena in clay-electrolyte systems. 

Induced-charge and second-kind electrokinetic phenomena arise due to electrohydrodynamic effects in the electric double layer, but the term nonlinear electrokinetic phenomena is also sometimes used more broadly to include any fluid or particle motion, which depends nonlinearly on an applied electric field, fit the classical effect of dielectrophoresis mentioned above, electrostatic stresses on a polarized dielectric particle in a dielectric liquid cause dielectro-phoretic motion of particles and cells along the gradient of the field intensity (oc VE ). In electrothermal effects, an electric field induces bulk temperature gradients by Joule heating, which in turn cause gradients in the permittivity and conductivity that couple to the field to drive nonlinear flows, e.g., via Maxwell stresses oc E Ve. In cases of flexible solids and emulsions, there can also be nonlinear electromechanical effects coupling the... 

ElGCtrokinetiC Phenomena. Electrokinetic motion occurs when the mobile part of the electric double layer is sheared away from the inner layer (charged surface). There are several types of electrokinetic measurements, electrophoresis, electroosmosis, streaming potential, sedimentation potential, and two electroa-coustical methods. The first four methods are described in References 35 and 62. Of these the first finds the most use in industrial practice. The electroacoustical methods involve detection of the sound waves generated when dispersed species are made to move by an imposed alternating electric field, or vice versa (63). In all of the electrokinetic measurements either the liquid is made to move across a... 

Induced-charge and second-kind electrokinetic phenomena arise due to electrohydrodynamic effects in the electric double layer, but the term nonlinear electrokinetic phenomena is also sometimes used more broadly to include any fluid or particle motion, which depends nonlinearly on an applied electric field. In the classical effect of... 

The electrostatic component of the disjoining pressure is given by the positive term describing the interaction between the electrical double layers of the two surfaces in contact. The detailed description of the electrical double layer can be found in textbooks on colloid science and in specialized textbooks on electrokinetic phenomena at interfaces [5,8-13]. We will restrict ourselves to a very brief revision of the basic concepts associated with the electrical double layer. 

Electrokinetic phenomena arise from movement of ions in the electric double layer under a pore pressure gradient. In the case of a steady-state fluid circulation and for a saturated porous media, a linear relation exists between the electrical potential difference AV and the pressure difference AP. This ratio is called the electrokinetic coupling coefficient [11-12] ... 

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