Our recent work on modeling electrochemical (EC) energy storage devices has indicated more clearly the similarities and differences between ultracapacitors and batteries.  In addition, the introduction of nanostructures into such EC storage devices introduces new physics based on the consideration of the density of states (DoS), especially in the form of quantum capacitance C_Q [1].  Here, we propose an equivalent circuit model which describes EC storage deploying either traditional three-dimensional electrodes or lower-dimensional electrodes.  The circuit has two separate branches: the ultracapacitor branch which involves the device double-layer capacitance and C_Q (the latter being chiefly for low DoS electrodes), and a battery related branch which was modeled through diode-like characteristics with the diode characteristic of charging and discharging current in response to overpotential.  It will be shown how the equivalent circuit closely models and agrees with experimental data on carbon nanotube based electrodes [1], and details related to the model validation will be discussed.  The proposed equivalent circuit would explain, for the first time, the intrinsic capacitor-like and battery-like characteristics of any EC device in a unified manner.

[1] H. Yamada and P. R. Bandaru, Appl. Phys. Lett. 102, 173113 (2013), ibid 104, 213901 (2014).