Capacitance Contributions

The ionic conductivity of a solvent is of critical importance in its selection for an electrochemical application. There are a variety of DC and AC methods available for the measurement of ionic conductivity. In the case of ionic liquids, however, the vast majority of data in the literature have been collected by one of two AC techniques the impedance bridge method or the complex impedance method [40]. Both of these methods employ simple two-electrode cells to measure the impedance of the ionic liquid (Z). This impedance arises from resistive (R) and capacitive contributions (C), and can be described by Equation (3.6-1) ... 

An interesting special application has been proposed by Schlichthorl and Peter.31,41 It aims at deconvolution of electrochemical impedance data to separate space charge and surface capacitance contributions. The method relies on detection of the conductivity change in the semiconductor associated with the depletion of majority carriers in the space charge region via potential-modulated microwave reflectivity measurements. The electrode samples were n-Si(lll) in contact with fluoride solution. 

The second major advantage of the square-wave procedure is the way that capacitive contributions to the overall current are minimized, and so the scan rate can be increased dramatically - a scan rate v of 1 V s is easily achievable. 

Surface and Double-layer Properties Valette [19] has analyzed earlier experimental data on the inner-layer capacity at PZC for Ag(lll), Ag(lOO), and Ag(llO) surfaces in order to estimate the surface area and capacitance contributions of superficial defects for real electrodes, as compared to ideal faces. Considering the application of surface spectroscopy techniques to single-crystal Ag electrodes, one should note that anisotropy of the SHG response for metal electrode allows one to analyze and correlate its pattern with interfacial symmetries and its variations by changing nonlinear susceptibility and the surface structure. Early studies on Ag(lll) single-crystal electrodes have... 

In Eq. (5) r defines the dielectric relaxation time (r = e/cr) according to which obviously a charge perturbation decays exponentially in a conductor. This defines a parallel R-C circuit as a good approximation of a homogeneous conductor (see Section III). In the following part of this section we consider the steady state, in which the conduction current represents the total current and capacitive contributions have vanished. 

It should also not be forgotten that, from a practical point of view, for small values of t there is a capacitive contribution to the current, due to double layer charging, that has to be subtracted. This contribution arises... 

A faradaic current, 7f, due to the electrode reaction, is registered in the relevant zone of applied potential where electrode reaction occurs. There is also a capacitive contribution on sweeping the potential the double layer charge changes this contribution increases with increasing sweep rate. The total current is... 

The capacitive contribution to the total current as given in (9.1) should also be taken into account. Writing /f = /p,c we have, from (9.1) and... 

High-speed cyclic voltammetry10 can easily be done at microelectrodes, increasing the range of rate constants accessible by the technique. This is because of the reduced capacitive contribution at microelectrodes— sweep rates of up to 106Vs-1 at microelectrodes have been reported. Nevertheless capacitive current subtraction is essential at these rates and instrumental artefacts can appear, which must be taken into account. 

The equations for potential and current steps in reversible systems, neglecting capacitive contributions were derived in Chapter 5. In the present chapter we show the possibilities of using these methods to elucidate electrode processes. We also consider successions of steps, that is pulses, especially with sampling of the response, which in the case of potential control has wide analytical application. 

Figure 10.4 illustrates how to analyse the response. It is important to remember that when t > r there is no capacitive contribution because charge was supplied and then removed. Calling QR the difference between Q(r) and Q(t > r), the charge after t = r is given by... 

In the last section the capacitive contribution was neglected. However, for some galvanostatic experiments this procedure is not possible. Various theoretical treatments have been developed to analyse chrono-potentiograms, but always with approximations that are difficult to justify, such as, for example, Ic constant ... 

By measuring dE/dt we can calculate the transition time, t. The usefulness of these expressions is that they permit the determination of r in a region where the capacitive contribution is small (in fact at its minimum). 

Double-step chronocoulometry is a powerful tool in identifying adsorption phenomena, in obtaining information on the kinetics of coupled homogeneous reactions and for the determination of the capacitive contribution. The double potential step is executed in such a way that after the first step from E to E2, a next step is applied, i.e., the reversal of the potential to its initial value Ei from 2 (see Fig. 3). 

It is important to note that there is no capacitive contribution because the net potential change is zero. 

Second harmonic — Any nonlinear oscillating system produces higher harmonic oscillations. The second harmonic is the response having twice the frequency of the basic oscillation. The - current response of a faradaic electrode reaction (- faradaic reaction) to perturbations of the - electrode - potential is generally nonlinear, and thus higher harmonic oscillations of the - alternating current (AC) are produced in - AC voltammetry. Since the -> capacitive current is a much more linear function of the electrode potential, the capacitive contribution to higher harmonic currents are rather small which allows a desirable discrimination of theses currents in electro-analytical applications. 

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. 

From the electrochemical point of view, the observed micropores are only accessible for the electrolyte cations upon anodic oxidation. The anodic oxidition causes either an opening or a widening of previously inaccessible pores.. As a result of the additional surface the double layer capacitance increases. In addition, electroactive surface groups are developed containing a pseudo capacitive contribution. In order to learn more about the oxidation process, SAXS measurements on the oxidized sample have to be carried out. 

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