Electrochemical double-layer capacitance

The actual value of the double-layer capacitance depends on many variables including electrode type, electrochemical potential, oxide layers, electrode surface heterogeneity, impurity adsorption, media type, temperature, etc. [1, pp. 45-48]. Capacitance of the double layer also largely depends on the intermolecular structure of the analyzed media, such as the dielectric constant (or high-frequency permittivity), concentration and types of conducting species, electron-pair donicity, dipole moment, molecular size, and shape of solvent molecules. Systematic correlation with dielectric constant is lacking and complex, due to ionic interactions in the solution. In ionic aqueous solutions with supporting electrolyte ( supported system ) the values of -10-60 pF/ cm are typically experimentally observed for thin double layers and solution permittivity e - 80. The double-layer capacitance values for nonpolar dielec- 

The double-layer thickness influencing the is different than the diffusion layer ( 10 -10 cm thick), which plays a role in the diffusion-limited mass transport and will be discussed in Section 5-6. The principles behind the two parameters are also very different—the diffusion layer is driven by a gradient of concentration that extends far into solution as the species are being consumed in the electrochemical reaction. The double-layer thickness results from an electrochemical potential difference between the media and the electrode, which decays over a much smaller distance from the electrode surface. 

Total double-layer capacitance is composed of a series combination of the compact Helmholtz layer and the diffuse-layer capacitances as  

The Helmholtz capacitor C eu holtz (P/ m ) is potential-independent and is expressed by a capacitor formula  

The thickness of the compact Helmholtz layer (L 1-2 ran) is approximately equal to the length of closest proximity where the discharging ions can approach the interface. For aqueous media with relative permittivity e = 80 and a 2 nm thick Helmholtz layer, fiF/cm. While the Helm- 

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Figure 18. Estimation of the capacitance of the electrochemical double layer Cstiso as a function of the charge density, using a series connection of the capacitance of the double layer of the metal surface [Cm < 0) and the molecular Helmholtz layer (Csoi). It is found that the electrochemical double layer capacitance shows a maximum at around the point of zero charge, where the influence of the metal phase is strongest. This is in qualitative agreement with the experimental results (Fig. 17). The bars on the capacitance axis indicate 2 x 10 F/cm, the bars on the horizontal axis indicate 5 x 10 C/cm. ...

Fiset, E., J. S. Bae, T. E. Rufford, S. Bhatia, G. Q. Lu, and D. Hulicova-Jurcakova. 2014. Effects of structural properties of silicon carbide-derived carbons on their electrochemical double-layer capacitance in aqueous and organic electrolytes. Journal of Solid State Electrochemistry 18 703-711. 

Chen, R. J., Z. Y. He, L. Li, F. Wu, B. Xu, and M. Xie. 2012. Pore size effect of carbon electrodes on the electrochemical double-layer capacitance in LiTFSI/2-oxazolidinone complex electrolyte. Journal of Physical Chemistry C 116 2594—2599. 

This last point, which has been ignored until now, in fact imposes limitations on all transient techniques. Essentially, in addition to the faradaic current flowing in response to a potential perturbation, there is also a current due to the charging of the electrochemical double-layer capacitance (for more details see Chapter 5). In chronoamperometry this manifests itself as a sharp spike in the current at short times, which totally masks the faradaic current. The duration of the double layer charging spike depends upon the cell configuration, but might typically by a few hundred microseconds. Since It=o cannot be measured directly it is necessary to resort to an extrapolation procedure to obtain its value, and whilst direct extrapolation of an /Vs t transient is occasionally possible, a linear extrapolation is always preferable. In order to see how this should be done we must first solve Pick s 2nd Law for a potential step experiment under the conditions of mixed control. The differential equations to be solved are... 

Yamada, H., Nakamura, H., Nakahara, F, Moriguchi, L, and Kudo, T. 2007. Electrochemical study of high electrochemical double layer capacitance of ordered porous carbons with both meso/macropores and micropores. J h s Chettj, 111(1), 227-233. 

Fig. 1 Schematic of charge storage via the process of either a electrochemical double-layer capacitance or b pseudocapacitance [17] (Reprinted with permission from Ref. [17] Cop5ulght (2011) by Cambridge University Press)...

High-Frequency Resistance A more sophisticated approach to measurement of the ohmic losses is the HFR measurement, as discussed in the previous section. In this approach, an AC signal is superposed on the DC from the fuel cell. At very high fiequencies, the AC will render the various electrochemical double-layer capacitances to zero, and only the purely ohmic resistance will be measured. Typical frequencies high enough to successfully use this technique are > 1 kHz for PEFCs. This approach only measures the path of least resistance however, and care should be taken to properly understand results. For example, in the electrodes, the HFR will normally measure the electrical resistance only, since it is generally much less than the ionic loss in the mixed conductivity stracture. Therefore, HFR could not generally be used to determine electrode ionomer performance. 

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