Adsorbed double-layer capacitance

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. 

The relationship between the fractional surface coverage 9 and the double-layer capacitance C may be better understood in terms of the following model. The doublelayer capacitance at the electrode in the presence of adsorption can be viewed as consisting of two capacitors connected in parallel. One capacitor corresponds to the electrode areas that are unoccupied (free) and the other to the electrode areas that are occupied (covered) with adsorbate (13-15). These two condenser-capacitors have different dielectrics and thus different capacitances. The capacitance of a parallel combination of capacitors is equal to the sum of the individual capacitances. 

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). 

Adsorption phenomena have been studied by means of virtually every electrochemical technique, including recently developed spectroelectrochemical methods. Electrocapillary methods and measurements of double-layer capacitance have played a central role in the understanding of adsorption. AC studies have also been very useful and are very sensitive to adsorption effects. More recently, chronocoulometry (Chap. 3, Sec. II.C) has been applied effectively to the measurement of quantities of adsorbed electroactive species. The interested reader is referred to the sections that deal with these techniques for more detailed information. 

Under ideal conditions, charge consumed by the double-layer capacitance and adsorbed reactants will follow the same time course as discussed earlier for ordinary chronocoulometry. Since the ratio of electrode area to solution volume is larger for thin-layer experiments, charge thus accounted for may represent a much greater proportion of the total. This fact points to an advantage of restricted diffusion experiments for studying some surface phenomena. 

Forming a monolayer involves displacing specifically adsorbed ions and solvent molecules from the interface, which changes the double-layer capacitance from that... 

For processes involving strongly adsorbing reactants, Tp is often sufficiently large to be measured by surface electroanalytical methods (e.g. chronocoulometry, double-layer capacitance), enabling Kt to be evaluated. This allows ket to be determined from kob using eqn. (10). Alternatively, kel can often be evaluated directly in such circumstances by using electrochemi-... 

The final point we would like to emphasize is that the diffusion layer should never be confused with the double layer. The double layer arises because the charge on the electrode is counterbalanced by ions of opposite charge that are specifically adsorbed at the electrode surface. Such a construction resembles a capacitor and gives rise to double-layer capacitance, which will be described in detail later on. The thickness of the double layer is only a few A, much smaller than 6. 

Next we illustrate how electrode reactions differ fundamentally from regular heterogeneous reactions on account of the involvement of electron charge transfer, a process that can be directly modulated in its rate in an instrumen-tally controlled way (by means of a potentiostat and/or an on-line computer). Because of this possibility, the extent of coverage by adsorbed intermediates and the surface electron density of the electrode can also be correspondingly modulated in an experimentally determinable way through measurement of the interfacial double-layer capacitance (7). 

The early stages of experimental transients fit Eq. (43) well, and C is found to have a value consistent with the double-layer capacitance. At longer times, backreaction and especially surface coverage factors cause deviations. Conway and Bourgault (128) took into account the potential dependence of C when C was determined mainly by the pseudocapacitance contribution, C, arising from electroactive adsorbed species. 

In the earliest treatment of open-circuit potential-decay transients (729), C was identified with the double-layer capacitance, C, but it was recognized (cf. Refs. 105, 129) that this formulation did not account for changes in the coverage fractions by any electroactive intermediates involved. Conway and co-workers (126-128) were the first to treat the problem with allowance for changes in coverage of the adsorbed intermediate. However, C was interpreted as the sum of Cj, and C, and the potential-decay behavior for several... 

Capacitance measurements of carbon electrodes have also been made in molten halides, particularly chlorides [30-32], molten nitrates [33, 34], and in cryolite—alumina melts (graphite and glassy carbons). In cryolite—alumina melts, the double-layer capacitance of the basal plane of graphite, in the range 0.7—1.0 V (vs aluminum reference electrode) is about 20[xF/cm at 0.9 V, i.e., in a potential range where no appreciable flow of current has been observed. Data indicate that the capacitance is influenced by adsorbed species from the melt, possibly yielding intercalation compounds, and uncertainty in the true area of the electrode [34]. 

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