Electrical irreversibility in electrochemical capacitor charging and discharge: rate effects
It was stated earlier in this article that charging and discharging of electrochemical capacitors has commonly been perceived as a process much more reversible than that for batteries and hence being capable of operation at high power densities. While, in practice, this is largely true, charging of the high-area, porous-electrode structures that are required for achieving large capacitance densities (farads/g or farads/cm3) encounters limitations of rate due to the distributed electrolytic and contact resistances within the pore structure of such materials.
In the simplest analysis, any practical capacitor device behaves as if an ohmic resistance is in series with it, the so-called equivalent (or real) series resistance (Figure 3).
The presence of real or equivalent series resistance in the operating equivalent circuit of any capacitor introduces an ir potential drop in the process of charging or discharging and this drop depends, of course, on the charging rate (current) leading to distortion of the charging curve of accumulated charge against voltage, in time. When the distributed resistance effect also operates, as it normally does, the distortion effect becomes more complex but has been experimentally and computationally evaluated (de Levie, 1963).
The above effect causes limitation of rates at which the capacitor can be charged or discharged and, for ac modulated charging, it also introduces a frequency-dependent phase angle (normally -90o) between the modulated applied voltage and the resultant charging current. This also applies to other, non-constant charging modes.
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