Capacitance double-layers

Figure Bl.28.8. Equivalent circuit for a tliree-electrode electrochemical cell. WE, CE and RE represent the working, counter and reference electrodes is the solution resistance, the uncompensated resistance, R the charge-transfer resistance, R the resistance of the reference electrode, the double-layer capacitance and the parasitic loss to tire ground.

Electrically, the electrical double layer may be viewed as a capacitor with the charges separated by a distance of the order of molecular dimensions. The measured capacitance ranges from about two to several hundred microfarads per square centimeter depending on the stmcture of the double layer, the potential, and the composition of the electrode materials. Figure 4 illustrates the behavior of the capacitance and potential for a mercury electrode where the double layer capacitance is about 16 p.F/cm when cations occupy the OHP and about 38 p.F/cm when anions occupy the IHP. The behavior of other electrode materials is judged to be similar. 

From an electroanalytical point of view, the double-layer capacitance is a nuisance resulting in the charging current, which has no analytical value. 

Active electrochemical techniques are not confined to pulse and linear sweep waveforms, which are considered large ampHtude methods. A-C voltammetry, considered a small ampHtude method because an alternating voltage <10 mV is appHed to actively couple through the double-layer capacitance, can also be used (15). An excellent source of additional information concerning active electroanalytical techniques can be found in References 16—18. Reference 18, although directed toward clinical chemistry and medicine, also contains an excellent review of electroanalytical techniques (see also... 

Even in the absence of Faradaic current, ie, in the case of an ideally polarizable electrode, changing the potential of the electrode causes a transient current to flow, charging the double layer. The metal may have an excess charge near its surface to balance the charge of the specifically adsorbed ions. These two planes of charge separated by a small distance are analogous to a capacitor. Thus the electrode is analogous to a double-layer capacitance in parallel with a kinetic resistance. 

Figure 1-13 displays the experimental dependence of the double-layer capacitance upon the applied potential and electrolyte concentration. As expected for the parallel-plate model, the capacitance is nearly independent of the potential or concentration over several hundreds of millivolts. Nevertheless, a sharp dip in the capacitance is observed (around —0.5 V i.e., the Ep/C) with dilute solutions, reflecting the contribution of the diffuse layer. Comparison of the double layer witii die parallel-plate capacitor is dius most appropriate at high electrolyte concentrations (i.e., when C CH). 

FIGURE 1-13 Double-layer capacitance of a mercury drop electrode in NaF solutions of different concentrations. (Reproduced with permission from reference 5.)... 

Measurements of the double-layer capacitance provide valuable insights into adsorption and desorption processes, as well as into the structure of film-modified electrodes (6). 

For (ideally) polarizable metals with a sufficiently broad double-layer region, such as Hg, Ag, Au, Bi, Sn, Pb, Cd, H, and others, Ea=to can be obtained from measurements of the double-layer capacitance in dilute... 

Measurements based on the Gouy-Chapman-Stem theory to determine the diffuse double-layer capacitance 10, 24,72, 74... 

A new approach to the double-layer capacitance of rough electrodes has been given by Daikhin et al.m m The concept of a Debye length-dependent roughness factor [i.e., a roughness function R LD) that deter-... 

Daikhin, double layer capacitance of solid at rough electrodes, 52 of the double layer, of non-aqueous solutions, 61... 

Daikhin s analysis, 52, 53 double layer capacitance of solid at, 52 semi conductor, diffusion length, 492... 

This does not imply that this double layer is at its point of zero charge (pzc). On the contrary, as with every other double layer in electrochemistry, there exists for every metal/solid electrolyte combination one and only one UWr value for which this metal/gas double layer is at its point of zero charge. These critical Uwr values can be determined by measuring the dependency onUWR of the double layer capacitance, Cd, of the effective double layer at the metal/gas interface via AC Impedance Spectroscopy as discussed in Chapter 5.7. 

Figure 5.32. Double layer capacitance as a function of overpotential of the system a) Pt/YSZ, b) Au/YSZ, c) Ni/YSZ and d) Au/YSZ before ( ) and after (O) prolonged anodic overpotential application.55 Reprinted with permission from the National Institute of Chemistry, Ljubljana, Slovenia.

Figure 8.13. (a) Cyclic voltammetric investigation of the Ir02/YSZ interface (inset shows the circuit used to model the data)19 and (b) Effect of catalyst-electrode mass on the polarization resistance Rp and the double layer capacitance Cd.19 Scan rate 20 mV/s, T=380°C, pO2=20 kPa. 

The origin of the observed correlation was not established, and the relation was not interpreted as causal. It could be argued that a sustained elevated potential due to as-yet unknown microbial processes altered the passive film characteristics, as is known to occur for metals polarized at anodic potentials. If these conditions thickened the oxide film or decreased the dielectric constant to the point where passive film capacitance was on the order of double-layer capacitance (Cji), the series equivalent oxide would have begun to reflect the contribution from the oxide. In this scenario, decreased C would have appeared as a consequence of sustained elevated potential. 

Mortari, A., Maaroof A., Martin, D. and Cortie, M.B. (2007) Mesoporous gold electrodes for measurement of electrolytic double layer capacitance. Sensors and Actuators B, 123, 262-268. 

Both terms affect whether the double layer capacitance can become negative. 

Nonfaradaic components associated with the uncompensated resistance between reference electrodes (7 ) and the double layer capacitance (Qi) can be accurately determined by AC impedance measurements. In this technique, a small AC potential perturbation is superimposed to the DC bias, and the resulting AC current is measured as a function of the frequency of modulation. The simplest circuit considered for a polarizable... 

FIG. 7 Simplified equivalent circuit for charge-transfer processes at externally biased ITIES. The parallel arrangement of double layer capacitance (Cdi), impedance of base electrolyte transfer (Zj,) and electron-transfer impedance (Zf) is coupled in series with the uncompensated resistance (R ) between the reference electrodes. (Reprinted from Ref. 74 with permission from Elsevier Science.)... 

Under this electrochemical configuration, it is commonly accepted that the system can be expressed by the Randles-type equivalent circuit (Fig. 6, inset) [23]. For reactions on the bare Au electrode, mathematical simsulations based on the equivalent circuit satisfactorily reproduced the experimental data. The parameters used for the simulation are as follows solution resistance, = 40 kS2 cm double-layer capacitance, C = 28 /xF cm equivalent resistance of Warburg element, W — R = 1.1 x 10 cm equivalent capacitance of Warburg element, IF—7 =l.lxl0 F cm (

charge-transfer resistance, R = 80 kf2 cm. Note that these equivalent parameters are normalized to the electrode geometrical area. On the other hand, results of the mathematical simulation were unsatisfactory due to the nonideal impedance behavior of the DNA adlayer. This should... 

This impedance response, in general, is similar to that elicited from an Armstrong electrical circuit, shown in Figure 3, which we represent by Rfl+Cd/(Rt+Ca/Ra). Rfl is identified with the ohmic resistance of the solution, leads, etc. Cj with the double-layer capacitance of the solution/metal interface Rfc with its resistance to charge transfer and Ca and Ra with the capacitance and resistance... 

Kinetic parameters can also be obtained by using the zero-point method as described earlier.40 The advantage of this method is that the values of a and k° can be deduced independent of the determination of values of the double-layer capacitance, electrode impedance, and potential difference across the electrode/solution... 

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