Charging a electrochemical double layer supercapacitor exhibiting a distribution of relaxation times

A charging electrochemical double layer supercapacitor can usually be described by a single capacitance and a single resistance in parallel, wherein the latter represents the ohmic losses. Such an ideal behavior may occur if the supercapacitor consists of self-similar porous carbon micro- and nanostructures. However, if the electrochemical double layer supercapacitor consists of a sequence of slices with different relaxation times, a strong deviation from ideal charging curves may occur. Here, it is demonstrated how such charging curves can be interpreted in terms of a distribution of relaxation times. It is found that in the presence of a broad distribution of charge transfer resistances, the voltage initially appears to increase faster than normal during galvanostatic charging. Care should be taken to avoid misinterpretation of the capacitance under such circumstances.