Double layer charge—transfer reaction

Consider mercury as the liquid metal under study. One of the advantages of this metal is that the mercuiy/solution interface approaches closest to the ideal polarizable interface (see Section 6.3.3) over a range of 2 V. What this means is that this interface responds exactly to all the changes in the potential difference of an external source when it is coupled to a nonpolarizable interface, and there are no complications of charges leaking through the double layer (charge-transfer reactions). 

Reaction 5.1 is meant to represent a nonspecific electrostatic interaction (presumably responsible for double-layer charge accumulation) Reaction 5.2 symbolizes specific adsorption (e.g., ion/dipole interaction) Reaction 5.3 represents electron transfer across the double layer. Together, these three reactions in fact symbolize the entire field of carbon electrochemistry electric double layer (EDL) formation (see Section 5.3.3), electrosorption (see Section 5.3.4), and oxidation/reduction processes (see Section 5.3.5). The authors did not discuss what exactly >C, represents, and they did not attempt to clarify how and why, for example, the quinone surface groups (represented by >CxO) sometimes engage in proton transfer only and other times in electron transfer as well. In this chapter, the available literature is scrutinized and the current state of knowledge on carbon surface (electrochemistry is assessed in search of answers to such questions. 

In electrode kinetics a relationship is sought between the current density and the composition of the electrolyte, surface overpotential, and the electrode material. This microscopic description of the double layer indicates how stmcture and chemistry affect the rate of charge-transfer reactions. Generally in electrode kinetics the double layer is regarded as part of the interface, and a macroscopic relationship is sought. For the general reaction... 

If the electrolyte components can react chemically, it often occurs that, in the absence of current flow, they are in chemical equilibrium, while their formation or consumption during the electrode process results in a chemical reaction leading to renewal of equilibrium. Electroactive substances mostly enter the charge transfer reaction when they approach the electrode to a distance roughly equal to that of the outer Helmholtz plane (Section 5.3.1). It is, however, sometimes necessary that they first be adsorbed. Similarly, adsorption of the products of the electrode reaction affects the electrode reaction and often retards it. Sometimes, the electroinactive components of the solution are also adsorbed, leading to a change in the structure of the electrical double layer which makes the approach of the electroactive substances to the electrode easier or more difficult. Electroactive substances can also be formed through surface reactions of the adsorbed substances. Crystallization processes can also play a role in processes connected with the formation of the solid phase, e.g. in the cathodic deposition of metals. 

The problem of ion transfer across the interface has been treated in detail by Sato,26,27 Scully,28 and also Valand and Heus-ler,29 following the general theory of Vetter.30 Valand and Heusler assumed the same type of activation-controlled charge transfer kinetics, except that the dominant charge here is that on the O2-ions (or OH- ions) obtained by splitting water at the interface. The electrochemical double layer here is of the usual type for aqueous systems and the equilibrium p.d. is determined by the main charge transfer reaction... 

Many of the processes that are familiar from ordinary electrochemistry have an analog at ITIES so these form a wide field of study. We limit ourselves to a brief introduction into a few important topics thermodynamics, double-layer properties, and charge-transfer reactions. Further details can be found in several good review articles... 

A related technique is the current-step method The current is zero for t < 0, and then a constant current density j is applied for a certain time, and the transient of the overpotential 77(f) is recorded. The correction for the IRq drop is trivial, since I is constant, but the charging of the double layer takes longer than in the potential step method, and is never complete because 77 increases continuously. The superposition of the charge-transfer reaction and double-layer charging creates rather complex boundary conditions for the diffusion equation only for the case of a simple redox reaction and the range of small overpotentials 77 [Pg.177]

Figure 2. A complete adsorption reaction, including transfer of counter charge to the solution part of the electric double layer. While the reaction is usually divided conceptually into four steps, it is usually only the total energy of reaction that is observed experimentally.

In electrochemistry, the electrode current is conventionaUy classified into the faradaic current and the nonfaradaic current. The former is the electric current associated with charge transfer reactions at nonpolarizable electrodes and the latter is the current that is required to establish the electrostatic equilibrium at the interfacial double layer on both polarizable and nonpolarizable electrodes. The nonfaradaic ciurent, sometimes called a transient current, flows also in the course of establishing the adsorption of ions on electrodes. 

Electrochemistry at Electrodes is concerned with the structure of electrical double layers and the characteristic of charge transfer reactions across the electrode/electrolyte interface. The purpose of this text is to integrate modem electrochemistry with semiconductor physics this approach provides a quantitative basis for understanding electrochemistiy at metal and semiconductor electrodes. 

The rate of the charge-transfer reaction across the membrane/solution interface, leading to charging of the electrical double layer at this interface [87]. 

Galvanostatic Transient Technique. In the galvanostatic method a constant-current pulse is applied to the cell at equilibrium state and the resulting variation of the potential with time is recorded. The total galvanostatic current ig is accounted for (1) by the double-layer charging, /ji, and (2) by the electrode reaction (charge transfer), i. ... 

The overpotential 77 is required to overcome hindrance of the overall electrode reaction, which is usually composed of the sequence of partial reactions. There are four possible partial reactions and thus four types of rate control charge transfer, diffusion, chemical reaction, and crystallization. Charge-transfer reaction involves transfer of charge carriers, ions or electrons, across the double layer. This transfer occurs between the electrode and an ion, or molecule. The charge-transfer reaction is the only partial reaction directly affected by the electrode potential. Thus, the rate of charge-transfer reaction is determined by the electrode potential. 

The application of electrochemical methods for the study of the kinetics and mechanisms of reactions of electro chemically generated intermediates is intimately related to the thermodynamics and kinetics of the heterogeneous electron transfer process and to the mode of transport of material to and from the working electrode. For that reason, we review below some basics, including the relationship between potential and current (Section 6.5.1), the electrochemical double layer and the double layer charging current (Section 6.5.2), and the... 

Note that this capacitance is linked to the electron transfer reaction and therefore has a faradaic origin and is not related to the double-layer charging process (this last capacitance corresponds to a pure capacitor see Sect. 6.4.1.5). In this sense, it has been called pseudo-capacitance [56]. The normalized current i/rCv is a ratio of capacitances since, from Eq. (6.161), y ev = (Icv/v)/(Qf F/RT)) = Ccv/Cf [48, 57],... 

This chapter intends to discuss the fundamental role played by carbons, taking particularly into account their nanotexture and surface functionality. The general properties of supercapacitors are reviewed, and the correlation between the double-layer capacitance and the nanoporous texture of carbons is shown. The contribution of pseudocapacitance through pseudofaradaic charge transfer reactions is introduced and developed for carbons with heteroatoms involved in functionalities able to participate to redox couples, e.g., the quinone/hydroquinone pair. Especially, we present carbons obtained by direct carbonization (without any further activation) of appropriate polymeric precursors containing a high amount of heteroatoms. 

Faradic impedance (//) is directly related to the rates of charge transfer reactions at and near the electrode/electrode interface. As shown in Figure 3.1, the Faradaic impedance acts in parallel with the double-layer capacitance Cd, and this combination is in series with the electrolyte resistance Rei The parameters Rei and Cd in the equivalent circuit are similar to the idea of electrical elements. However, X/ is different from those normal electrical elements because Faradaic impedance is not purely resistive. It contains a capacitive contribution, and changes with frequency. Faradaic impedance includes both the finite rate of electron transfer and the transport rate of the electroactive reagent to the electrode surface. It is helpful to subdivide Zj into Rs and Cs, and then seek their frequency dependencies in order to obtain useful information on the electrochemical reaction. 

The technique of AC impendance spectroscopy, one of the most common techniques in aqueous and solid-state electrochemistry, was used recently to confirm the formation of the effective double layer on metal surfaces interfaced with YSZ [43,95]. An example for the case of Pd/YSZ is shown in Figure 20. The semicircle labeled Ci is associated with the charge-transfer reaction... 

For heavily doped materials, either notp type, the surface is degenerated and the material behaves like a metal electrode, meaning that the charge transfer reaction in the Helmholtz double layer is the rate-determining step. This is supported by the lack of an impedance loop associated with the space charge for the heavily doped materials. Also, for heavily doped n-Si large current in the dark is due to electron injection, which is not characterized by a slope of 60 mV/decade. For p-Si, electron injection into the conduction band may also occur during the anodic dissolution. 

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