Metal double layer capacitance, determination

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. 

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. 

Electrodeposition of lead-tin alloy films is usually performed in the presence of peptone as an additive. Peptone is adsorbed on the metal surface during the electrodeposition process. The fractional surface coverage Q of the lead-tin electrode may be determined from the double-layer capacitance C measurements, and/or chronopotentiometric measurements. For a solution containing 9.0 g/L of tin and 13.0 g/L of lead, the following relationship between the concentration of peptone, the double-layer capacitance C, and the transition time At is observed (8). 

There is a similar quantity called the inner Helmholtz plane, where the potential is ( )j. This is determined by the radius of the anions in solution, which tend to be specifically adsorbed on the metal surface. A discussion of this phenomenon and its effect on the double-layer capacitance is outside the scope of this book. 

The presence of a Faradaic electrode reaction of any kind competing with the double layer charging presents a problem in determining the purely capacitive current needed to calculate the surface charge. From a plot of 1 vs. (/ = total electrode current) with a fixed concentration of the ions of the electrode metal dissolved in solution, the surface charge can be obtained [65Butl]. (Data obtained with this method are labelled TC). 

Amokrane and Badiali proposed a semiempirical approach to the determination of the solvent contribution C, to the capacitance of the double layer in aqueous and nonaqueous " solutions. They used the relation C = Cf - C m, where Q is the experimentally determined capacity of the inner layer and Cm is the contribution of the metal. The plots ofC, vs. (Tm were presented for various solvents and correlated with their properties.However, the problem of the supporting electrolyte was entirely neglected in the quoted papers. It was shown recently that the height and position of the maximum on the C, vs. Gm plots depend on the type of the supporting electrolyte. Experimental differential capacity data obtained on the Hg electrode in methanol and ethanol containing various electrolytes with nonadsorbing anions (F , PFg, ClOi) indicate that the type as well as concentration of the electrolyte influences the position and the height of the maximum on the C, vs. plots (Fig. 13). 

So far we have established in a qualitative way the importance of the metal properties on the characteristics of the interfacial region through two properties, the relation of Omvs. pzc and the capacitance of the double layer. What is next At this point it would be good to obtain a detailed model of the metal region and then determine—now in a quantitative way—the influence of the metal on the interfacial properties, similarly to the procedure followed when studying the solution region (Section 6.6.1). 

Valuable information about the properties of electrical double layers can be obtained from electrocapillary experiments. In an electrocapillary experiment the surface tension of a metal surface versus the electrical potential is measured. The capacitance and the point of zero charge are obtained. Surface charge densities for disperse systems can be determined by potentiometric and conductometric titration. 

Differential capacitance measurements were used to determine the extent that DMSA adsorbsonto the metal surface as a function of its concentration in solution. In this approach the metal-solution interface is modelled as a resistor and capacitor in series and if the diffuse part of the double layer is neglected, the measured capacitance can be expressed as ... 

In all reactions given above, we have oxygen ions O on the right part of the equations. Corresponding to these reactions, the current discharge density 7 can be determined by the kinetic equations (2.12)-(2.16). Furthermore, the capacitance of the electric double layer at the TPB among gas-oxide-SE-YSZ is different from that of the electric double layer at the TPB among gas-metal-SE-YSZ [38, 61]. In fact, for SEs, based on metal Pt or Au, the capacitance of the electric double layer is about 50-150 juC/cm and basically independent of temperature and Pq2 fluctuations. However, for... 

The method developed here for the description of chemical equilibria including adsorption on charged surfaces was applied to interpret phosphate adsorption on iron oxide (9), and to study electrical double-layer properties in simple electrolytes (6), and adsorption of metal ions on iron oxide (10). The mathematical formulation was combined with a procedure for determining constants from experimental data in a comparison of four different models for the surface/solution interface a constant-capacitance double-layer model, a diffuse double-layer model, the triplelayer model described here, and the Stem model (11). The reader is referred to the Literature Cited for an elaboration on the applications. 

The use of in situ FTIR spectroscopy to study ions adsorption is related to the need of experimental tools to access the doublelayer structure with molecular specificity. This is especially true for the solid metals, where the study of the double layer using the classical capacitance studies is not easy. Spectroscopy combined with in situ scanning tunneling microscopy (STM) [42, 43] constitutes a very powerful approach, allowing the determination of the molecular identity and organization of the doublelayer components. However, it is not the purpose of this chapter to review in detail the double-layer structure, but rather, to show how in situ infrared spectroscopy can contribute to the understanding of the double layer at molecular specificity. 

In conclusion, it appears that few metal-molten salt systems behave in the ideally polarizable sense generally associated with the mercury/aqueous solution interface at 298 K. Possible exceptions include some noble liquid metal/melt systems such as mercury/molten nitrates and lead/molten halides at low temperatures (<773 K), but only when the molten electrolyte is extensively purified. Otherwise, systems need to be analyzed as complex impedances, using ac or pulse techniques, to determine whether the minimum interfacial capacitance is affected by extensive factors, leading to parallel pseudocapacitances and Faradaic components. The range of potentials and measuring frequencies for which the interface approaches ideally polarizable behavior also needs to be established. It now seems clear that the multilayer ionic model of charge distribution at the metal/melt interface is more pertinent to molten media than the familiar double layer associated with aqueous solutions. However, the quantitative theories derived for the former model will have to be revised if it is confirmed that the interfacial capacitance is, indeed, independent of temperature in the ideally polarizable region. 

Figure 3.51 schematically shows how the charge of the double layer can be determined by (a) electrocapillary measurements and (b) by capacitance measurements. We may keep in mind that an anionic excess in the double layer corresponds to a positive charge at the metal and therefore to a positive value of q. 

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