Towards a Pseudocapacitive Battery: Benchmarking the Capabilities of Quantized Capacitance for Energy Storage

Despite being capable of very fast charging, the pseudocapacitive properties of electrochemical capacitors still require significant research to attain energy densities comparable to that of batteries. Herein we discuss and theoretically benchmark the physics of quantized capacitance as a Faradaic charge storage mechanism, providing near “ideal” pseudocapacitive properties in the context of batterylike energy storage. Through careful electrolyte and reactant engineering, our physical analysis suggests that this less explored “pseudocapacitive battery” mechanism could provide power densities of approximately ${10}^4$ W/L combined with volumetric energy densities in the range of 100 Wh/L (or potentially greater). These benchmarks are arrived at though a comprehensive analysis of two-dimensional (2D) graphitic nanoparticles considering the impact of solvation, electron-electron interactions, and electron transfer processes. In general, our findings indicate that 2D nanomaterials exhibiting quantized capacitance provide a promising and underexplored physical axis within electrochemical capacitors towards realizing very fast charging at energy densities comparable to that of batteries.

Popular Summary

It has long been a goal in the field of energy storage to combine supercapacitors and batteries. At the nexus of these two technologies, one would arrive at a device that is capable of both high power density and high energy density. In the field of supercapacitors, the approach towards increased energy density has been based on incorporating pseudocapacitive faradaic components that store additional charge via redox reactions. In this work, we show how the mechanism of quantized capacitance can theoretically provide a charge storage approach which is pseudocapacitive in terms of its current-voltage characteristics yet theoretically can provide volumetric energy densities comparable to batteries, unlike conventional pseudocapacitive mechanisms. The net result would be a “pseudocapacitive battery” that could exhibit the long-sought dual properties of high power and energy densities.

Figure 1

(Adapted from Ref. [1].) A Ragone plot depicting the volumetric power and energy densities of various energy storage devices. Theoretical energy storage benchmarks for a “pseudocapacitive battery” operating via quantized capacitance (gold region) are discussed and presented in this manuscript.

Figure 2

(a) Operational schematic for a quantized capacitance device similar to (b) (adapted from Ref. [22]) a redox-polymer battery. Both schemes are depicted in the fully charged state and during discharging. Their corresponding cyclic voltammograms are illustrated in the bottom panel of each subfigure. In a quantized capacitance device, graphitic nanoparticles with negative charge states are utilized to store electrons during charging, while graphitic nanoparticles with positive charge states are utilized for electron ($e^{-}$) stripping for charge counter balancing. Here, the stripping or removal of electrons (to realize positively charged states) is denoted by “holes” ($h^{+}$)—just as it is in a redox-polymer battery. This design is provided to explore the possible capabilities of the mechanism; more advanced multiscale designs to aid charge carrier diffusion and transport will likely be important in any practical implementation [38, 39, 40]. Redox-based flow battery analogues may also be similarly applied [41, 42, 43].

Figure 3

(a) Electron density as a function of the ratio of total volume to reactant (nanodisks) volume, assuming a surface electron storage density of $4{\mathrm{q}/\mathrm{nm}}^2$ and the corresponding volumetric energy density at 5 V storage voltage. (b) A schematic that shows the total volume to reactant (nanodisks) volume can be calculated by taking the ratio of the nanodisk thickness $d$ and the supporting medium thickness $L$.

Figure 4

(Adapted from Ref. [10].) (a) Cyclic voltammetry of quantized capacitance up to a maximum applied potential $V_{-,\max }$ on a single electrode that resembles an ideal pseudocapacitive behavior due to the overlapping electron transfer peaks. (b) A schematic of a single negative ($-$) electrode depicting the operation of quantized capacitance Faradaic storage via electron tunneling to each reactant state. Here, the schematic describes the electron storage at a cathode during the charging process (as the electrode electrochemical potential ${\mu }_{\mathrm{eq}}$ is raised). At $V_{-,\max }$ the desired electron density is stored. A similar schematic can be used to understand electron removal at the positive ($+$) terminal during the charging process.

Figure 5

(a) Achieving a target single electrode voltage for adding a target density of electrons via quantized capacitance by tuning the dielectric response and nanoparticle radius. (b) The change in parameter $U$ in response to tuning the dielectric response and nanoparticle radius as described by Eq. (3). (c) The change in reorganization energy $\lambda$ with various dielectric responses and nanoparticle radii. Note that (a) is computed with a target density of electrons of $4{\mathrm{q}/\mathrm{nm}}^2$.

Figure 6

(a) Comparative electronic structure plots against an electrolyte stability window (green) situated between $-2$ and $-7$ eV below vacuum. The left panel shows the electronic structure of ${\mathrm{C}}_{60}$, the middle panel that of graphene, and the right panel that of ${\mathrm{BrC}}_8$ decorated graphene. A dashed line provides the alignment of all electronic structure plots to the Fermi energy ($E_f$) of graphene. The Fermi energy of single-layer ${\mathrm{BrC}}_8$ lies below that of graphene, due to the loss of electrons to Br atoms, but above the stability limit of the electrolyte window. (b) A schematic depicting the position of the open circuit potential ($V_{\mathrm{OC}}$) within the electrolyte stability window (shaded in light blue) dictates the electrode potentials ($|V_{\mathrm{anode}}|$ and $|V_{\mathrm{cathode}}|$) and the maximum cell potential $V_{\max }$ for a system with symmetric electrodes. This schematic assumes the simple case that $V_{\mathrm{OC}}$ lies at the center of the electrolyte stability window with the equally distributed current peaks (shaded in gray) for electron removal at the positive terminal and electron addition at the negative terminal for different charge states on the graphitic nanodisks during a charging process. Here, the equal peak distribution ($U_{+}=U_{-}$) on each terminal is achieved by nanodisks of similar radius on both sides. The inset shows the definitions of anode and cathode for a supercapacitor cell under the charging process [97]. (c) A schematic for a more frequently observed $V_{\mathrm{OC}}$ that lies closer to the limits for the positive electrode. To avoid wasting the wider potential window on the negative electrode, the nanodisks can be engineered to have a smaller radius for a larger $U_{-}$ as compared to $U_{+}$.

Figure 7

(a) The $|M_{\mathrm{ip}}|$ and ${\lambda }_c$ to achieve a specific electron transfer rate $k_{\mathrm{ip}}$, ranging from ${10}^{-3}$ to $100{\mathrm{s}}^{-1}$. (b) The effect of barrier width on the required $M_{\mathrm{ip}}$ to efficiently store the electrons at various barrier heights $V_b$. The value of (c) ${\mathcal{D}}_e$ at 300 K as a function of $|M_{\mathrm{ip}}|$ and ${\lambda }_c$ for a 2.5 eV tunneling barrier.