Double layer charge transfer

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). 

For oxides to become dispersions with relaxed double layers, charge transfer through the interface should take place. Experience has shown that such transport is usually realized via uptake or release of protons, which leads to equilibria such as I3.6.38a and/or b]. For that, some hydration of the surface, leading to surface hydroxyl groups, is needed. Most oxides exhibit this phenomenon. As a consequence, H and OH" ions may be considered charge-determining. This premise is supported by the observation that several oxides, if made into electrodes demonstrate Nemst or pseudo-Nemst behaviour as a function of pH. Such behaviour has never been observed as a function of the metal ions apparently these are too deeply embedded in the solid to be liberated without any... 

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]

Double-layer charging current and ohmic drop are likely to interfere at high scan rates. The procedures for extracting the Faradaic component of the current and correcting the potential axis from the effect of ohmic drop described earlier (see Sections 1.3.2 and 1.4.3) should then be applied. The same is true for the double-layer effect on the electron transfer kinetics (Section 1.4.2). 

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 two interfacial processes, charge transfer and double-layer charging, proceed in parallel and so the total current density is the sum of the faradaic and the charging (sometimes called non-faradaic) current densities... 

In the case of a simple system considered throughout Sect. 2, it is already clear that both the faradaic charge transfer and the non-faradaic double-layer charging will contribute to the impedance of the electrode-solution interface. In addition to this, we have to account for the ohmic resistances between the connections to indicator and counter electrodes. This was already illustrated in Sect. 1.1, Fig. 1. The first conclusion is therefore that the total impedance can be written as the summation... 

Both the double-layer charging and the faradaic charge transfer are non-linear processes, i.e. the charging current density, jc, and the faradaic... 

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],... 

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. 

The selection of impedance or admittance for presentation of experimental results and data analysis is dependent on the type of equivalent electric circuit. For instance, for the analysis of -> charge-transfer processes and -> double-layer charging, the impedance may be preferred, while for the resonance circuits (e.g., in piezometric systems) the admittance may offer advantages. 

Therefore the electrochemical response with porous electrodes prepared from powdered active carbons is much increased over that obtained when solid electrodes are used. Cyclic voltammetry used with PACE is a sensitive tool for investigating surface chemistry and solid-electrolyte solution interface phenomena. The large electrochemically active surface area enhances double layer charging currents, which tend to obscure faradic current features. For small sweep rates the CV results confirmed the presence of electroactive oxygen functional groups on the active carbon surface. With peak potentials linearly dependent on the pH of aqueous electrolyte solutions and the Nernst slope close to the theoretical value, it seems that equal numbers of electrons and protons are transferred. 

When the potential of a planar electrode is suddenly shifted from a value at which no current flows to a value where the electron transfer, Eq. (1), proceeds at the diffusion-controlled rate, the current-time behavior is given by Eq, (64), where ic is the double layer charging current [1,2],... 

This asymptotic expansion forms a part of a semicircle in the complex plane of a Cole-Cole plot. This kind of response indicates charge-transfer limitations, bypassed through the double-layer charging. The center of the semicircle is located on the real axis at... 

For L-p/l y>> 1 the limitations due to proton transport are practically absent and the impedance response forms a perfect semicircle in the Cole - Cole representation with M = R = 9tdiff/2, due to the parallel processes of charge-transfer and double-layer charging, which are distributed homogeneously within the layer. The frequency in the turning point of the semicircle is 2p, the approximation being the better the larger the ratio L-p/l. For Lp/l = 1 the error of this estimate is about 10%. 

The EIS response depends on the flhn thickness and morphology, applied potential, and, obviously, the nature of the components of the hybrid system. The hydro-phobic nature of the polymer, the level of doping within the film, and the size of ions in contact with the polymer surface are factors to be considered for studying the response of such materials. In short, the kinetics of the overall charge transfer process should take into account (1) electron hopping between adjacent redox sites (Andrieux et al., 1986) usually described in terms of a Warburg diffusion impedance element (Nieto and Tucceri, 1996) and (2) double-layer charging at the metal-flhn interface, represented in terms of a double-layer capacitance element. 

Electrochemical capacitors, also called supercapacitors, are very attractive electricity sources because of their high power, very long durability, and intermediate energy between the classical dielectric capacitors and batteries. The performance of a typical electrochemical capacitor is based on the accumulation of charges in the electrical double layer without faradaic reactions (no electron transfer The electrons involved in double layer charging are the delocalized conduction-band electrons of the electrode material. As shown in Fig. 23.9, an electrochemical capacitor contains one positive electrode with electron deficiency and the second one with electron excess (negative). The capacitance C of one electrode due to a pure electrostatic attraction of ions is proportional to the surface area S of the electrode-electrolyte interface, according to the formula (23.3) ... 

Most SECM measurements involve steady-state current measurements. This can be a significant advantage in the measurement of kinetics, even for rapid processes, because factors like double-layer charging and adsorption do not contribute to the observed currents. However, one can also carry out transient measurements, recording iT as a function of time. This can be of use in measurements of homogeneous kinetics (Chapter 7) and for systems that are changing with time. It can also be used to determine the diffusion coefficient, D, of a species without knowledge of the solution concentration or number of electrons transferred in the electrode reaction (23). 

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