Double-layer capacitance, measurement

Galvanostatic Transient Technique Double-Layer Capacitance Measurements. The value of the fractional surface coverage 9 may be inferred by means of doublelayer capacitance data. As discussed in Section 6.9, the double-layer capacitance C may, in turn, be determined by means of a transient technique. In the galvanostatic transient technique (as in Fig. 6.18), the duration of the constant-current (density) pulse is on the order of microseconds. In the microsecond time range the only process taking place at the electrode is charging of the double layer. Flence, in this case, Eq. (6.96) reduces to... 

The frequency response analyzer may be the best instrument for double-layer-capacitance measurements, but it is also the most expensive one. Other methods are available, which are faster and cheaper, but less accurate. For example, the charge on the double layer is related to the potential as ... 

Figure 17. The double layer capacitance measured with two different metals (Ag and Hg) in an aqueous electrolyte solution as a function of the charge density at the surface. The influence of the nature of the metal phase on the total capacitance is clearest around the point of zero charge. The results are taken from W. Schmickler, Chem. Rev. 96, 3177 (1996).

More information about the ubiquitous presence in seawater of natural organic surfactants has been obtained by the use of seawater/solid interfaces than from studies of the interface between seawater and air. For practical reasons, it is usually very much simpler to study the adsorption of organic matter from solution onto solid surfaces, where a variety of powerful techniques such as electrocapillarity, electrical double-layer capacitance measurements, electrophoresis and ellipsometry can be used to study the progress of adsorption and the nature of the adsorbed layer. Neihof and Loeb (1972, 1974) and Loeb and Neihof (1975, 1977) have demonstrated by electrophoresis and ellipsometry that a wide variety of solid surfaces become covered by a strongly adsorbed film of polymeric acids upon exposure to seawater. Hunter (1977) found the same type of effect and has shown by electrophoretic studies at different pH and metal ion concentrations that phenolic and carboxylic groups are probably responsible. This adsorbed organic material seems hkely to represent an important part of the natural surfactants in seawater and, as such, will adsorb at the air/sea interface as well. 

In the case of the three electrode system (Fig. 7a), the double layer capacitance measured for the working electrode is ... 

Gasteiger and Mathias assume a thin-film structure of the ionomer of 0.5-2 nm covering the entire solid catalyst surface. Experimental support for this electrode structure comes from double-layer capacitance measurements using cyclic voltammetry and AC impedance techniques. Gasteiger and Mathias observed values that are typical of Pt and carbon interfaces with electrolyte and imply that the entire solid surface was in contact with electrolyte for these electrodes. Under several assumptions regarding structure, diffusion, and reactivity, a minimum permeability was derived for a maximum of 20 mV loss. 

The ac bridge is based on a classical Wheatstone (or Wien for ac measurements) bridge in which one part is replaced by an electrochemical cell and the other compensating part by a variable, R or C. The dc potential is supplied by a potentiometer in the center and ac by the external source. The double layer capacitance measurements were initially carried out on a dropping mercury electrode (DME), and the bridge compensation had to be carried out always at the same surface area of the DME, that is, after exactly the same time from the beginning of... 

Historically, it should be noted that double-layer capacitance measurements were first reliably made (at Hg) by Bowden and Rideal [1928] using the dc charging-current method and by Proskumin and Frumkin [1935] by means of ac modulation. Randles [1947,1952] pioneered the examination of impedance of an electrode process (e.g. redox reactions), using phase-sensitive detector instrumentation to record the frequency dependence of the separated real and imaginary components of Z. Under diffusion-control, the dependence of Z" and Z were found due to the Warburg impedance element. 

Fleischmann, M., Graves, PR., HiU, I.R. and Robinson, J. (1983) Simultaneous Raman spectroscopy and dUferential double layer capacitance measurement of pyridine adsorbed on roughened silver electrodes. Chemical Physics Letters, 98, 503. 

Fig. 14. The double layer capacitance vs potential dependence extracted from the impedance measurements for CoNiFe surface. The corresponding coverage of saccharine is calculated from double layer capacitance measurements are shown as dashed line. The additive coverage is estimated using following expression 6 = Reproduced by permission of...

Successfully fabricated diamond fibers were characterized by use of scanning electron microscopy (SEM) and Raman spectroscopy, while the roughness factor of the diamond fiber was calculated based on double-layer capacitance measurements. SEM images of diamond fibers are shown in Figure 18.1. Figure 18.1a shows a suitable diamond fiber for microdisk electrode fiibrication, while... 

The important conclusion to be drawn from this numerical calculation is that great care must be exercised in interpreting double-layer capacitance measurements in systems in which an adsorbed intermediate can be formed. Even a minute fractional coverage can give rise to an adsorption pseudocapacitance comparable to or larger than the double-layer capacitance. 

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. 

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... 

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. 

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. 

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... 

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. 

Variations of resistance with frequency can also be caused by electrode polarization. A conductance cell can be represented in a simplified way as resistance and capacitance in series, the latter being the double layer capacitance at the electrodes. Only if this capacitance is sufficiently large will the measured resistance be independent of frequency. To accomplish this, electrodes are often covered with platinum black 2>. This is generally unsuitable in nonaqueous solvent studies because of possible catalysis of chemical reactions and because of adsorption problems encountered with dilute solutions required for useful data. The equivalent circuit for a conductance cell is also complicated by impedances due to faradaic processes and the geometric capacity of the cell 2>3( . 

We have used voltammetric measurements in the absence of the electroactive species to quantitatively evaluate this heat-sealing procedure. The magnitude of the double layer charging current can be obtained from these voltammograms [25,68-70], which allows for a determination of the fractional electrode area (Table 1). This experimental fractional electrode area can then be compared to the fractional pore area calculated from the known pore diameter and density of the membrane (Table 1). In order to use this method, the double layer capacitance of the metal must be known. The double layer capacitance of Au was determined from measurements of charging currents at Au macro-disk electrodes of known area (Fig. 6, curve A). A value of 21 pF cm was obtained. 

Figure 34. Total impedance (2) and faradaic impedance (Zf) of unsintered porous LSM on YSZ measured in air at 850 °C. Electrolyte resistance (i ) has been subtracted from the total impedance, while both i e and the double-layer capacitance (Cdi) have been subtracted from Zp. (Reprinted with permission from ref 215. Copyright 1998 Elsevier.)...

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