Double-layer capacity

Measurements of the adsorption of inhibitors on corroding metals are best carried out using the direct methods of radio-tracer detection and solution depletion measurements . These methods provide unambiguous information on uptake, whereas the corrosion reactions may interfere with the indirect methods of adsorption determination, such as double layer capacity measurements", coulometry", ellipsometry and reflectivity Nevertheless, double layer capacity measurements have been widely used for the determination of inhibitor adsorption on corroding metals, with apparently consistent results, though the interpretation may not be straightforward in some cases. 

Various methods have been employed for the determination of E of liquid and solid metals. Besides purely electrochemical ones (e.g. measurement of the differential double layer capacity (see also chapter 4.2)) further techniques have been used for the investigation of the surface tension at the solid/electrolyte solution phase boundary. The employed methods can be grouped into several families based on the meas-... 

Measurements of the interfaeial eapacitance (the differential double layer capacity Cdl) have been used widely, the method has been labelled tensammetry [46Bre, 52Bre, 51Dosl, 52Dosl, 63Bre]. Various experimental setups based on arrangements for AC polarography, lock-in-amplifier, impedance measurement etc. have been employed. In all reports evaluated in the lists of data below the authors have apparently taken precautions in order to measure only the value of Cdl-... 

When the area A of the eleetrode/solution interface with a redox system in the solution varies (e.g. when using a streaming mercury electrode), the double layer capacity which is proportional to A, varies too. The corresponding double layer eharging current has to be supplied at open eireuit eonditions by the Faradaic current of the redox reaction. The associated overpotential can be measured with respect to a reference electrode. By measuring the overpotential at different capaeitive eurrent densities (i.e. Faradaic current densities) the current density vs. eleetrode potential relationship can be determined, subsequently kinetic data can be obtained [65Del3]. (Data obtained with this method are labelled OC.)... 

In recent years, many types of double-layer capacitors have been built with porous or extremely rough carbon electrodes. Activated carbon or materials produced by carbonization and partial activation of textile cloth can be used for these purposes. At carbon materials, the specific capacity is on the order of 10 J,F/cm of trae surface area in the region of ideal polarizability. Activated carbons have specific surface areas attaining thousands of mVg. The double-layer capacity can thus attain several tens of farads per gram of electrode material at the surfaces of such carbons. 

The total capacity of a ruthenium oxide electrode [the usual double-layer capacity plus the pseudocapacity of reaction (21.4)] is rather high (i.e., several hundred F/g), even more than at the electrodes of carbon double-layer capacitors. The maximum working voltage of ruthenium oxide pseudocapacitors is about 1.4 V. 

Garcia-Araez N, Climent V, Herrero E, Feliu J, Lipkowski J. 2006. Thermodynamic approach to the double layer capacity of a Pt(lll) electrode in perchloric acid solutions. Electrochim Acta 51 3787. 

In an analysis of an electrode process, it is useful to obtain the impedance spectrum —the dependence of the impedance on the frequency in the complex plane, or the dependence of Z" on Z, and to analyse it by using suitable equivalent circuits for the given electrode system and electrode process. Figure 5.21 depicts four basic types of impedance spectra and the corresponding equivalent circuits for the capacity of the electrical double layer alone (A), for the capacity of the electrical double layer when the electrolytic cell has an ohmic resistance RB (B), for an electrode with a double-layer capacity CD and simultaneous electrode reaction with polarization resistance Rp(C) and for the same case as C where the ohmic resistance of the cell RB is also included (D). It is obvious from the diagram that the impedance for case A is... 

Relaxation methods for the study of fast electrode processes are recent developments but their origin, except in the case of faradaic rectification, can be traced to older work. The other relaxation methods are subject to errors related directly or indirectly to the internal resistance of the cell and the double-layer capacity of the test electrode. These errors tend to increase as the reaction becomes more and more reversible. None of these methods is suitable for the accurate determination of rate constants larger than 1.0 cm/s. Such errors are eliminated with faradaic rectification, because this method takes advantage of complete linearity of cell resistance and the slight nonlinearity of double-layer capacity. The potentialities of the faradaic rectification method for measurement of rate constants of the order of 10 cm/s are well recognized, and it is hoped that by suitably developing the technique for measurement at frequencies above 20 MHz, it should be possible to measure rate constants even of the order of 100 cm/s. 

Carbonaceous materials play a key role in achieving the necessary performance parameters of electrochemical capacitors (EC). In fact, various forms of carbon constitute more than 95% of electrode composition [1], Double layer capacity and energy storage capacity of the capacitor is directly proportional to the accessible electrode surface, which is defined as surface that is wetted with electrolyte and participating in the electrochemical process. 

Figure 2.9, it can be seen that the interfacial capacitance does show a dependence on concentration, particularly at low concentrations. In addition, whilst there is some evidence of the expected step function away from the pzc, the capacitance is not independent of V. Finally, and most destructive, the Helmholtz model most certainly cannot explain the pronounced minimum in the plot at the pzc at low concentration. The first consequence of Figure 2.9 is that it is no longer correct to consider that differentiating the y vs. V plot twice with respect to V gives the absolute double layer capacitance CH where CH is independent of concentration and potential, and only depends on the radius of the solvated and/or unsolvated ion. This implies that the dy/dK (i.e. straight lines joined at the pzc. Thus, in practice, the experimentally obtained capacitance is (ddifferential capacitance. (The value quoted above of 0.05-0,5 Fm 2 for the double-layer was in terms of differential capacitance.) A particular value of (di M/d V) is obtained, and is valid, only at a particular electrolyte concentration and potential. This admits the experimentally observed dependence of the double layer capacity on V and concentration. All subsequent calculations thus use differential capacitances specific to a particular concentration and potential. 

As was discussed in section 2.1.1, electrocapillarity measurements at mercury electrodes, which have well-defined and measurable areas, allow the double-layer capacitance, CDL, to be obtained as Fm-2. Bowden assumed that the overpotential change at the very beginning of the anodic run in H2-saturated solution was a measure of the double-layer capacity. The slope of the E vs. Q plot in this region was taken as giving 1/CDL, and this gave 2 x 10 5 F. He then assumed that, under these same conditions, the double-layer capacity, in Fm-2, of the mercury electrode is the same. This gave the real surface area of the electrode as 3.3cm 2, as opposed to its geometric area of I cm2. 

Fig. 4. Current density for the reduction of copper and the double layer capacity of a copper electrode in an acidic copper sulfate solution vs. applied overpotential (adapted from ref. 50).

So the double-layer capacity is the same as that of a parallel-plate capacitor with the plate separation given by the Debye length. Since for high concentrations the latter are of the order of a few Angstroms, these capacities can be quite high. 

Figure 7. Comparison of (a, solid) electrochemical and (b, dashed) UHV measurements of the H, coverage/potentiaI differential versus potential on Pt(lll).1.) cathodic sweep (25 mV/s) voltammogram in 0.3 M HF from Ref. 20, constant double layer capacity subtracted, b.) dB/d(A ) versus A plot derived from A versus B plot of Ref. 26. Potential scales aligned at zero coverage. Areas under curves correspond to a.) 0.67 and b.) 0.73 M per surface Pt atom.

The lack of knowledge of precise values of the roughness factor makes it difficult to compare data reported from different studies. This applies in particular to the double-layer capacity data, the values of surface concentration of the adsorbates, and the rates of electrochemical reactions. Therefore, the question of how to determine the real surface of the electrode is of cmcial importance. A survey of various methods for determining roughness was given by Trasatti and Petrii. For noble metal electrodes, the charges of hydrogen deposition and surface oxide formation can be utilized in real-surface determination." ... 

To explain the nature of the hump, the ion-solvent molecule competition modeP can be applied. According to this model, the solvent dipoles oriented with their positive ends toward the electrode are displaced by the anions (for example PFs) that enter the inner layer at the point of maximum double-layer capacity (Cmax)- The value of Cmax is similar in different solvents (Table 5) if the activity of the PFg ions is the same and the adsorption of these anions can be neglected. Thus it is the PF anions rather than solvent molecules that are responsible for the formation of the... 

This leads to the Helmholtz model of the interface (Fig. 10.5) when the other contacting phase is a metal. The Helmholtz model of the interface predicts that the value of the double layer capacity (Q,) will be given by ... 

Variation of the double-layer capacity with applied potential according to the Gouy-Chapman theory is shown in Figure 4.8. Equation (4.10) includes the approximation ifjyi = iIj(x = 0), which is in harmony with the basic assumption of this... 

The double-layer capacity of an electrode immersed in a lO M aqueous solution is found to be 50 /tF/cm. The potential difference at the interphase is 0.1 V. Assume that the dielectric constant e in the double layer is 5.9. 

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