Benchmarking the Ragone behaviour and power performance trends of pseudocapacitive batteries

The "holy grail" of energy storage is to achieve both high energy and high power densities (≧100 Wh/L and ~104 W/L, respectively) as characterized in a Ragone plot. However, across the macroscopic dimensions over which energy storage systems operate, power performance is fundamentally limited by both drift and diffusion processes. In this work a macroscopic variation on the Gerischer-Hopfield formalism is applied to explore how the motion of electrical charges, moving between redox species, and screening counter-ions might be engineered in a pseudocapacitive system employing quantized capacitance (in the form of a pseudocapacitive battery) to reach this long-sought metric. Our theoretical findings show that the electron diffusion timescale between redox species generally determines power performance trends when pseudocapacitive coatings are applied monolithically. This electron-diffusion--dominated timescale, in turn, is shown to scale with the square of the coating thickness. However, when conducting pathways (or shunts) are introduced to substantially reduce the mean distance for electron diffusion the Ragone performance becomes dominated by ion drift and diffusion --- even when the diffusion constants of all species are held equal. The resulting trends, for this shunting regime, show a power performance timescale that scales in a more linear fashion with increasing thickness of the redox-active region. By analyzing the Ragone performance metrics for realistic coating thicknesses between these two operational regimes, the resulting findings suggest that the diffusion constants needed to achieve the aforementioned high-performance metrics are plausibly achievable for both electronic and ionic charges in this proposed class of pseudocapacitive systems.