True Double Layer Capacity

It is usually believed that high frequency capacitance obtained from impedance spectroscopy can represent ionic double layer capacity. However in general this is not the case for platinum electrode, this is the reason why one arrow in Fig. 1 (in the left) is crossed. In contrast to Cf measured under equilibrium conditions (by means of isoelectric potential shifts), non-equilibrium impedance response can contain a contribution from Ah (and/or Ao, surface concentration of oxygen-containing species). These contributions are determined by Ah and Ao potential derivatives and their free electrode charge derivatives, and in general can be either positive, or negative. 

The role of true double layer capacity in so-named double layer correction of total capacity was specially considered in a rarely available paper,with illustrations reproduced in Fig.3. Curves 2 demonstrate that ionic contributions to total capacity in the hydrogen potential region are non-monotonous, and deviate from horizontal dashed line (extrapolation of current in double layer region, typically used for approximate correction). For chloride, and especially for bromide solutions, the ionic contribution to total capacity in the hydrogen region surely exceeds the contribution formally estimated from horizontal interpolation In particular, this formal procedme results in pronoimced underestimation of true surface area determined from H-UPD charge (up to 15-20%). 

Probably some unusual voltammetric features of certain polycrystalline platinnm samples, like the third hydrogen peak can result fiom stracture-sensitive sulfate adsorption 

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Figure 3. Cyclic voltammograms representing total capacities Q (1), and true double layer capacities Cf (2) in 1 N H2SO4 (a), HCl (b) and HBr (c). Dashed lines (3) correspond to the difference of curves (1) and (2). In Figure 2a, dashed curve 4 corresponds to formal double layer correction (applied under assumption of purely double layer intermediate region between hydrogen and oxygen adsorption regions). From Ref 54, with modifications.

EXAMPLE 12-2 According to Bockris and Huq the exchange current density for the oxygen electrode in acid solution is of the order of 10 A/cm on a platinum surface. The polarization resistance is RTIAFjo = 6 x 10 fl-cm. The double-layer capacity C j is of the order of 40 p/lcm, based on the true area, or perhaps 100 pjjcm based on the geometric or projected area, on which the current density was based. Thust = 6 X 10 X 100 X 10 = 6 x 10 s, and the time for overpotential decay from 10 to 1 mV is estimated to be 2.3t 4 h. Therefore, measurements accurate to... 

Fig. 7. Analysis of the experimental steady-state current-potential and impedance-potential data from E = - 1300 mV to E = — 600 mV for a titanium rotating-disc electrode (45 Hz) in a solution of 2 M hydrochloric acid, (a) Standard rate constant-potential curve calculated for the hydrogen evolution reaction on titanium assuming that DA = 7.5 x 10 5cm"1s 1 and E° = - 246 mV. The Tafel slope 6C = 211 mV and the measured ohmic resistance was 0.4 ohm cm2. The potentials are the "true potentials, (b) High-frequency double layer capacity-potential curve. The potentials are the measured potentials.

A comparison of the development of the SER intensity with the changes of the true surface area, represented by the double-layer capacity, is shown in Figs. 3 and 4. The two examples measured under similar conditions demonstrate the scattering of the general shape of Raman-time and capacitance-time plots. The good correlation in the shape of the curves found in the experiments leads to the assiunption of a proportionality relation between the SER intensity and the true area of the surface. 

The electrode reaction rate may be controlled by diffusion or by chemical reaction. The impedances associated with these cannot be derived so simply. All that needs to be said here is that they are not pure resistances, i.e. they include a reactive part which, for convenience, is called pseudocapacity to distinguish it from the true capacity of the double layer. The diffusion impedance is also often referred to as Warburg impedance . 

Another important consequence of spatial correlation in electrochemistry is related with double layer theory. It is known that the ratio of the permittivity to the layer thickness is estimated from the capacity of the compact layer. Reasonable model estimates of the layer thickness lead to the conclusion that the effective permittivity of this layer in aqueous solutions is less than 10. Usually, we assume a value of about 6, i.e. only slightly greater than Such a decrease in permittivity is usually explained by the effect of dielectric saturation in the strong electric field of an electrode. However, if this were true, we should expect a more than tenfold increase in the value of permittivity, and hence in the capacity of the compact double layer, as we approach the zero-charge point (at which the field in the double layer vanishes). As a matter of fact, this is not the case. On the other hand, a reasonable explanation for the low effective permittivity in the double layer follows from the concept of spatial correlation between dipoles. The thickness of the compact double layer (-4-5 A), i.e. the distance at which the field changes appreciably, is of the order of the dipole correlation redius, and hence the orientation polarization cannot be noticeably manifested within this layer. This leads to low values of its permittivity[222,223]. 

To estimate the possible concentration limits for adsorbed chlorine, we determined the electrode capacity from the potential decay curves. Similar measurements were made by Stender and Ksenzhek[315] for porous graphite anodes. They found that the true capacity of a unit graphite surface is close to that of a double layer in order of magnitude. 

Before the measurements the working electrode was subjected to step of anodie -cathodic activation in the background solution at potentials E = 0.8 and -1.0 V, respeetively. Current densities were calculated for the true area of the surface of the corresponding working electrode, determined by the desorption charge of atomic hydrogen [27], The results of voltammetry measurements were eorrected for the current of charging of double eleetrie layer idi = Cdi v. The value Cdi was determined by the data of electrochemieal impedanee spectroscopy (phase frequency analyzer FRA-1) the mean capacity value is 30 p,F em. ... 

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