Faradaic Quantized Capacitance as an Ideal Pseudocapacitive Mechanism

Abstract

In this work, we provide a theoretical analysis of quantized capacitance (also referred to as solvated Coulomb blockade) as a pseudocapacitive energy storage mechanism. In particular, we examine how redox species exhibiting quantized capacitance might be engineered to satisfy two basic criteria in the design of an “ideal” pseudocapacitive energy storage mechanism: (1) a near-rectangular voltammetric profile which mimics that of double-layer capacitance and (2) a linear rise in the pseudocapacitive current with respect to the voltammetric scan rate. It is demonstrated that nanoparticles exhibiting quantized capacitance may satisfy the first criterion by tailoring their charging and reorganization energies. It is also shown that the second criterion can be satisfied so long as the voltammetric scan rate does not exceed the electron-transfer rate. By formulating a comprehensive theoretical framework for understanding the electron-transfer properties of quantized capacitance, we arrive at a general phenomenological description of how pseudocapacitive properties might be practically engineered through this mechanism.

Benchmarking the ragone behaviour and power performance trends of pseudocapacitive batteries

“…Quantized capacitance (also known as 'solvated Coulomb blockade') relies on energy level quantization within nanoparticles to evenly space ET redox peaks by a constant charging energy over a wide potential range. This allows ET redox peaks to overlap and can theoretically provide a ideal near-rectangular voltammetry profile [27]. Quantized capacitance theories based on the Gerischer-Hopfield formalism have been extensively discussed in previous publications [26,27].…”

“…This allows ET redox peaks to overlap and can theoretically provide a ideal near-rectangular voltammetry profile [27]. Quantized capacitance theories based on the Gerischer-Hopfield formalism have been extensively discussed in previous publications [26,27]. We shall not overview this formalism in detail here [37][38][39][40], but simply state that the effect of quantized capacitance (when U is sufficiently small) is to provide a continuum of redox levels with an energetic density of states (DOS) per electron-volt (eV) that can be reasonably approximated in volumetric units as where V d is the applied potential window, being split equally across both terminals, at which the maximum target concentration of electrons, ρ e,max , is stored [26] (see figures 1(b) and 2).…”

“…Recently, it was proposed that one may dramatically enhance the energy density of supercapacitors through the use of quantized capacitance in the form of device that was termed a 'pseudocapacitive battery' (see the bronze region in figure 1(a)) [26,27]. Such a pseudocapacitive battery consists of an electrolytic media sandwiched between two oppositely charged metal current collectors, where the surface is modified with a volume of deposited nanoparticles as illustrated in figure 1(b)-it is essentially a multiple redox-level variation on a redox-polymer battery [26].…”

Unlocking ion Storage Chemistry in Aqueous Batteries via Operando Smartphone Multispectral Techniques

“…This can be ascribed to the continuous excited electrons from the valence band to the conduction band with increasing electric potential as indicated in Figure 4a (upper scheme). [52,53] Therefore, the delocalized electrons in the conduction band and also the mobile holes in the valence band can move freely, thus contributing to a continuous charge accumulation process with quasi-capacitive behavior. When the MnO 2 continuously encounters oxidative process, the relative reflectance (R) at a specific wavelength varies simultaneously with a small but stable level (proved by Figure 3c).…”

“…In contrast, the PB with larger band gaps exhibited two pairs of distinct peaks in the CV curves related to the K + intercalation/deintercalation behaviors during charge storage. Distinguished from MnO 2 , the electron dislocation process of PB occurs separately over a narrow potential range based on the lack of electron conduction between any neighboring energy sites (shown in Figure 4b) [52,53] that should be responsible for the current peak on the CV scanning path and could result in a different changing rule of the R value. Consequently, the specific variation rule of R following the charge accumulation process depends upon the corresponding energy-storage mechanism.…”