Why impedance model/characteristics of porous electrodes for supercapacitors can be formulated into single pore mode?

There have existed several multi-scale impedance models for the porous electrode of supercapacitors (SCs) in literature. However, sometimes the multi-scale impedance model is too complex in mathematics to be easily used in the impedance diagnosis for SCs. Actually, impedance models and the corresponding characteristics of porous electrodes for SCs more often adopt single pore mode instead of the bi-scale mode to simplify the model construction and facilitate the understanding. Currently, there is one doubt for above degeneration, i.e., is this simple and rough approximation for the bi-scale impedance model reasonable and feasible? Based on the rigorous numerical calculations, this work gives a theoretical deduction for the bi-scale impedance model to be formulated into single pore mode. The numerical calculations yield two aspects of important understandings over the whole interested frequency range of 0.01 Hz ∼ 10 kHz under actual application background: (i) impedance model for the single pore can be degenerated into a pure resistor connected in series with a pure capacitor; and (ii) the impedance from the equivalent capacitor is three-order larger than that from the equivalent resistor. Based on the above understandings, the bi-scale impedance model for the porous electrode can be successfully formulated into single pore mode. The degenerated impedance model of the porous electrode not only contains rich information at the multiple scales, but is also mathematically easy to apply.