Double layer, electric heterogeneity

Electric double layers are formed in heterogeneous electrochemical systems at interfaces between the electrolyte solution and other condncting or nonconducting phases this implies that charges of opposite sign accumnlate at the surfaces of the adjacent phases. When an electric held is present in the solntion phase which acts along snch an interface, forces arise that produce (when this is possible) a relative motion of the phases in opposite directions. The associated phenomena historically came to be known as electrokinetic phenomena or electrokinetic processes. These terms are not very fortunate, since a similar term, electrochemical kinetics, commonly has a different meaning (see Part 11). 

This series covers recent advances in electrocatalysis and electrochemistry and depicts prospects for their contribution into the present and future of the industrial world. It illustrates the transition of electrochemical sciences from a solid chapter of physical electrochemistry (covering mainly electron transfer reactions, concepts of electrode potentials and stmcture of the electrical double layer) to the field in which electrochemical reactivity is shown as a unique chapter of heterogeneous catalysis, is supported by high-level theory, connects to other areas of science, and includes focus on electrode surface structure, reaction environment, and interfacial spectroscopy. 

The central issue which has to be addressed in any comprehensive study of electrode-surface phenomena is the determination of an unambiguous correlation between interfacial composition, interfacial structure, and interfacial reactivity. This principal concern is of course identical to the goal of fundamental studies in heterogeneous catalysis at gas-solid interfaces. However, electrochemical systems are far more complicated since a full treatment of the electrode-solution interface must incorporate not only the compact (inner) layer but also the boundary (outer) layer of the electrical double-layer. The effect of the outer layer on electrode reactions has been neglected in most surface electrochemical studies but in certain situations, such as in conducting polymers and... 

Problems 2 and 3 are of direct relevance for an adequate understanding of concentration polarization at, respectively, composite heterogeneous and homogeneous permselective membranes. The main difference between these formulations is that in Problem 2, relevant for a composite heterogeneous membrane, the motion in a pore of the support is induced by the electro-osmotic slip due to the interaction of the applied electric field with the space charge of the electric double layer which is present already at equilibrium. 

The recorded current is caused not only by the heterogeneous electron transfer to the substrate (the Faradaic current ), but also by the current used to charge the electrical double layer, which acts as a capacitor. The measured potentials include the potential drop caused by the ohmic resistance in the solution, the iR drop. Both the charging current ic and the iR drop grows with the sweep rate it is always desirable to compensate for ic and iR drop, but it becomes imperative at higher sweep rates. There exist different ways to compensate electrically for these phenomena, and this makes it possible to operate up to about 103 V sec-1. It is assumed below that the data are obtained with proper compensation. 

The impedance for the study of materials and electrochemical processes is of major importance. In principle, each property or external parameter that has an influence on the electrical conductivity of an electrochemical system can be studied by measurement of the impedance. The measured data can provide information for a pure phase, such as electrical conductivity, dielectrical constant or mobility of equilibrium concentration of charge carriers. In addition, parameters related to properties of the interface of a system can be studied in this way heterogeneous electron-transfer constants between ion and electron conductors, or capacity of the electrical double layer. In particular, measurement of the impedance is useful in those systems that cannot be studied with DC methods, e.g. because of the presence of a poor conductive surface coating. 

Surface heterogeneity means that the chemical contribution to the double layer formation varies from site to site along the surface. This chemical heterogeneity is partly obliterated by the electric field. 

Composition. While the average environment of a molecule in solution is well represented by the bulk concentrations of the various constituents of a reaction mixture, the environment of a molecule bound to a heterogeneous interface may be strongly perturbed. The properties of the motionally restricted phase may dictate. rather large deviations in the local concentrations of ions, reactants, and other mobile species from their respective bulk concentrations. The most important examples of this have been demonstrated for electrode-solution interfaces where, for example, the pH in the electrical double layer may differ significantly from its value in the bulk solution and can change with applied potential (1). A similar, though less extreme,example involves the interface between aqueous solutions and hydrophobic polymers. 

Electrochemical reactions at an electrode snrface differ from normal heterogeneous chemical reactions in that they involve the participation of one or more electrons that are either added to (reduction) or removed from (oxidation) the reactant species. The explicit inclusion of electrons as reactants or products means that the reaction rate depends on the electric potential. Electron transfer processes occur within a small portion of the double layer immediately adjacent to the electrode surface (10 to 50 mn in thickness) where solution-phase electroneutrality does not hold and where very strong electric fields (on the order of 10 V/cm) exist during a charge transfer reaction. We begin the analysis of electrochemical kinetics by defining a generic electrode reaction ... 

However, as we noted early in this chapter, numerous assumptions are employed in the field applications of surface complexation models. Davis et al. (1998) noted that surface complexation models are mainly developed from well-controlled laboratory experiments. It is unclear how the models can be applied to soil and sediments where the double layers of the heterogenous particles may interact and the competitive adsorption of many different ions can cause significant changes in the electrical properties of mineral-water interfaces. 

A model predicting electrode response with time must therefore consider the following (1) the double-layer capacitance, (2) the concentration of electroactive species at the electrode surface (which in turn is affected by the diffusion coefficients), (3) the values of the formal potentials (E ), (4) the heterogeneous rate constants of the redox species (with respect to the electrode material and electrolyte composition), and (5) the electrical potential of the electrode itself. 

The electrical double layer (edl) at the oil-water interface is a heterogeneous interfacial region that separates two bulk phases of polarized media and maintains a spatial separation of charges. EDLs at such interfaces determine the kinetics of charge transfer across phase boundaries, stability and electrokinetic properties of lyophobic colloids, mechanisms of phase transfer or interfacial catalysis, charge separation in natural and artificial photosynthesis, and heterogeneous enzymatic catalysis [1-5]. 

Two general theoretical approaches have been applied in the analysis of heterogeneous materials. The macroscopic approach, in terms of classical electrodynamics, and the statistical mechanics approach, in terms of charge-density calculations. The first is based on the application of the Laplace equation to calculate the electric potential inside and outside a dispersed spherical particle (11, 12). The same result can be obtained by considering the relationship between the electric displacement D and the macroscopic electric field Em a disperse system (12,13). The second approach takes into account the coordinate-dependent concentration of counterions in the diffuse double layer, regarding the self-consistent electrostatic poton tial of counterions via Poisson s equation (5, 16, 17). Let us consider these approaches briefly. 

Electroosmotic flow is the bulk liquid motion that results when an externally applied electric field interacts with the net surplus of charged ions in the diffused part of an electrical double layer (EDL). In the presence of nonuniform or heterogeneous -potential, the net charge density in the EDL changes locally, resulting in an irregular... 

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