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VoltageCapacitance and ESR as a function of the voltageThe supercapacitor capacitance increases with the applied voltage. In the literature the causes of this behavior are explained with different theories: - Reduction of the solvent layer thickness due to the increasing Coulombic forces on the ions when the electric field in the double layer is increasing. - Increase of the solvent dielectric constant due to the compression of the solvent layer, if the concept of dielectric constant has a meaning with such thin layers. Microscopic Maxwell equations formalism would be more appropriate - Increase of the electronic density of states in the carbon pore walls with the tension. Hahn et al. [i] have measured double-layer capacitance and electronic conductance of an activated carbon electrode in an aprotic electrolyte solution, 1 mol/L (C2H5)4NBF4 in acetonitrile. Both quantities show a similar dependence on the electrode potential with distinct minima near the potential of zero charge. This correlation suggests that the capacitance like the conductance is governed substantially by the electronic properties of the solid, rather than by the properties of the solution side of the double layer. - Salitra et al. [ii] attributed this finding to the potential dependence of the ion penetration into nanopores, which was assumed to be minimal at the pzc.
Fig. 1 and 2 show the frequency spectra of 350 F, 3.2 mOhm BCAP0350 supercapacitor capacitance and series resistance for different polarization voltages. It is interesting to observe the low capacitance value when there is no voltage polarization. This phenomenon should be studied as a function of the electrode thickness. If the ionic depletion would be the cause, a thick electrode should exhibit a more pronounce effect. The consequence of a voltage dependency of the capacitance may be also seen in the constant current charge profile. The voltage increase is no more linear. The slope is steeper at low voltage when the capacitance is smaller. See also the theory in the capacitance model which describes the voltage depencency of the capacitance with simple equations. [i] Hahn M, Barbieri O, Campana P, Kötz R, Gallay R. Carbon based double layer capacitors with aprotic electrolyte solutions: the possible role of intercalation/insertion processes. Applied Physics A 2006;82:633-8. [ii] Salitra G, Soffer A, Eliad L, Cohen Y, Aurbach D. Carbon Electrodes for Double-Layer Capacitors. J Electrochem Soc 2000;147:2486-93. Source: Garmanage: Roland Gallay
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