Capacitance mercury electrode

Fig. 20.7 Differential capacitance/mercury electrode potential relationships for potassium chloride at different concentrations showing (a) how minima are obtained only at low concentrations and (6) the constant capacitance at negative potentials (after Bockris and Drazic )...

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. 

Fig. 4. Capacitance—potential relationship at a mercury electrode for a nonspecific absorbiag electrolyte where regions A and B represent inner layer anions...

Fig. 4. Differential capacitance-potential curves for various concentrations of aniline in 1-0 M aqueous potassium chloride and at a mercury electrode-frequency 400 Hz.

FIGURE 10.1 (a) Differential capacitance of a mercury electrode as a function of potential... 

Several methods exist that can be used to measure changes of ESE for solid electrodes as a function of potential or other factors, but the accuracy of such measurements is much lower than that for Uquid electrodes. A plot of ESE vs. potential is called the electrocapillaty cutye (ECC). Typical ECCs measured at a mercury electrode in NaF solutions of different concentration are shown in Fig. 10.6. Also shown in this figure is a plot of values vs. potential calculated via Eq. (10.27). This plot almost coincides with that obtained from capacitance measurements (Fig. lO.lfc). This is evidence for the mutual compatibility of results obtained by these two methods of measurement. 

The differential capacity can be measured primarily with a capacity bridge, as originally proposed by W. Wien (see Section 5.5.3). The first precise experiments with this method were carried out by M. Proskurnin and A. N. Frumkin. D. C. Grahame perfected the apparatus, which employed a dropping mercury electrode located inside a spherical screen of platinized platinum. This platinum electrode has a high capacitance compared to a mercury drop and thus does not affect the meaurement, as the two capacitances are in series. The capacity component is measured for this system. As the flow rate of mercury is known, then the surface of the electrode A (square centimetres) is known at each instant ... 

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. 

A similar conclusion arises from the capacitance data for the mercury electrode at far negative potentials (q 0), where anions are desorbed. In this potential range, the double-layer capacitance in various electrolytes is generally equal to ca. 0.17 F Assuming that the molecular diameter of water is 0.31 nm, the electric permittivity can be calculated as j = Cd/e0 = 5.95. The data on thiourea adsorption on different metals and in different solvents have been used to find the apparent electric permittivity of the inner layer. According to the concept proposed by Parsons, thiourea can be treated as a probe dipole. It has been cdculated for the Hg electrode that at (7 / = O.fij is equal to 11.4, 5.8, 5.1, and 10.6 in water, methanol, ethanol, and acetone, respectively. 

The electrode roughness factor can be determined by using the capacitance measurements and one of the models of the double layer. In the absence of specific adsorption of ions, the inner layer capacitance is independent of the electrolyte concentration, in contrast to the capacitance of the diffuse layer Q, which is concentration dependent. The real surface area can be obtained by measuring the total capacitance C and plotting C against Cj, calculated at pzc from the Gouy-Chapman theory for different electrolyte concentrations. Such plots, called Parsons-Zobel plots, were found to be linear at several charges of the mercury electrode. ... 

Anastopoulos et al. [47] have analyzed interfacial rearrangements of triphenyl-bismuth and triphenylantimony at mercury electrode in nonaqueous solvents of high dielectric constant. These phenomena were detected as the peaks in the capacitance-potential curves at intermediate negative potentials for triphenyl-bismuth and triphenylantimony in N-methylformamide, A,A-dimethylforma-mide, dimethyl sulfoxide, propylene carbonate, and methanol solutions. 

Current spikes that are attributable to rapid adsorption or desorption of an adsorbate are sometimes observable for strongly adsorbing but electroinactive species such as camphor at a mercury electrode. The spike is a nonfaradaic current caused by the change in capacitance resulting from the sudden alteration in double-layer structure when the molecule adsorbs or desorbs. 

Figure 3.4 Faradaic (a), capacitive (b), and total (c) current at the dropping-mercury electrode.

The external leads from the potentiostat to the electrodes may also contribute significant resistance and capacitance that must be taken into account if the cell currents are large and if fast response is desired. Most metallic working electrodes will have very low resistance, but a typical diopping-mercury electrode (DME) may have a resistance as large as 100 Q because the mercury-filled lumen of the capillary is so small (— 0.005-cm diameter). This resistance makes a contribution to the total cell resistance and to the uncompensated resistance in a three-electrode circuit. 

At the dropping mercury electrode the fact that DPV is better than NPV is due to the residual capacitive current contribution, which is subtracted out in the differential technique. It is relatively easy to demonstrate that the diminution factor, f, is given by... 

---