Date Published: April 24, 2017
Publisher: John Wiley and Sons Inc.
Author(s): Cheng Zhan, Cheng Lian, Yu Zhang, Matthew W. Thompson, Yu Xie, Jianzhong Wu, Paul R. C. Kent, Peter T. Cummings, De‐en Jiang, David J. Wesolowski.
Supercapacitors such as electric double‐layer capacitors (EDLCs) and pseudocapacitors are becoming increasingly important in the field of electrical energy storage. Theoretical study of energy storage in EDLCs focuses on solving for the electric double‐layer structure in different electrode geometries and electrolyte components, which can be achieved by molecular simulations such as classical molecular dynamics (MD), classical density functional theory (classical DFT), and Monte‐Carlo (MC) methods. In recent years, combining first‐principles and classical simulations to investigate the carbon‐based EDLCs has shed light on the importance of quantum capacitance in graphene‐like 2D systems. More recently, the development of joint density functional theory (JDFT) enables self‐consistent electronic‐structure calculation for an electrode being solvated by an electrolyte. In contrast with the large amount of theoretical and computational effort on EDLCs, theoretical understanding of pseudocapacitance is very limited. In this review, we first introduce popular modeling methods and then focus on several important aspects of EDLCs including nanoconfinement, quantum capacitance, dielectric screening, and novel 2D electrode design; we also briefly touch upon pseudocapactive mechanism in RuO2. We summarize and conclude with an outlook for the future of materials simulation and design for capacitive energy storage.
In this section, we briefly review the most commonly used classical methods to simulate EDL and EDLCs. These include classical density functional theory (CDFT), classical molecular dynamics (CMD), and grand canonical Monte Carlo (GCMC). In both CDFT and GCMC, coarse‐grained models are commonly used for the electrolyte, while in CMD all‐atom models are usually employed.
When the electron or the electronic structure plays an important role at the electrochemical interfaces, ab initio simulations are necessary. The electronic effect can originate from the electron‐solvent repulsion at the charged interface and influence the structure and screening potential of the EDL, as revealed by ab initio MD simulations of the aqueous electrolyte/Pt interface.126 For carbon‐based EDLCs, the main concern is due to the low electronic density of states at the Fermi level; in this review, we mainly focus on this quantum capacitance (CQ) effect, which has been briefly introduced in 1.6.1. One can compute the total capacitance (Ctot) by combining CEDL from classical simulation and CQ from the electronic structure calculation. At the same surface charge density, the total electrode potential drop can be divided into contributions from CQ and CEDL.80, 127 Methods have also been developed to capture the polarization effect self‐consistently at the electronic‐structure level. Here, the electronic chemical potential shift Δμe is treated as the electrode potential drop and has contributions from band filling/emptying in the electrode and ionic screening in the electrolyte. Currently, there are two methods that can capture the electronic structure of the electrode in contact with the EDL: the effective screening medium (ESM) method and joint density functional theory (JDFT).
Having introduced the simulation methods, now we can review how they have been applied to understand capacitive energy storage. The most interesting feature of an EDLC is the structure and capacitance of the double layer confined inside the nanopores. In this section we focus our narrative on the double layer confined in different pore size/geometry from classical simulations, while leaving the electrode chemistry for the next section.
Besides EDL structure and pore size/geometry, the next important factor in EDLCs is the electrode’s electronic structure and chemistry. The electronic structure for an EDLC electrode is typically dictated by the electronic density of states (DOS) near the Fermi level. A limited DOS contributes to the charging of an EDLC unfavorably due to the band filling/emptying, leading to quantum capacitance, which is a focus of discussion in this section.
Activated carbon electrodes have diverse structure and form, but most theoretical studies still focus on graphene‐based model. Although the slit pore surface of a porous carbon can be simulated by a graphene basal plane, pore mouth is better represented by an edge plane. Moving beyond the graphene‐based models requires simulating the amorphous structure of a carbon electrode. In this section, we will first introduce several recent experimental and theoretical studies on the edge effect in carbon electrode, and then focus on the reverse Monte‐Carlo and MD techniques for modeling structure and EDL capacitance of amorphous carbon electrodes.
Understanding pseudocapacitors is more challenging due to the complexity of interfacial physics and chemistry. There are two main ways to simulate their behavior: (a) numerical solution and scaling analysis of classical equations (such as PNP and PB equations) to describe the solid/liquid interface with specified boundary conditions; (b) atomistic modeling based on quantum mechanics and molecular mechanics.
Traditional materials for supercapacitors include mainly carbons, transition‐metal oxides, and redox‐reactive organic compounds. Novel materials such as MXene and borophene may have great potential in supercapacitor applications.
In this review, we summarized recent computational insights into capacitive energy storage to address several important issues in supercapacitors especially EDLCs. The fundamental physics of EDLCs is ion separation and sorption on the electrode surfaces. Built upon conventional interfacial double‐layer theory (Helmholtz, GC and GCS models), a more accurate interfacial description has been obtained analytically,10, 12, 13 in terms of the shape of the differential capacitance vs potential for different ionic concentrations next to a planar electrode. Coarse‐grained models, such as CDFT and coarse‐grained MD or GCMC, provided microscopic insights into the ionic response and EDL structure more accurately than analytical modeling.65, 143 In particular, CDFT allows one to efficiently examine how the ion size, ion valence, ion concentration, and the electrode pore size/geometry influence the capacitive performance. The atomic level information of the electrolyte response behavior could be obtained from CMD with all‐atom force fields. With this tool, one could study the influence of electrode geometry and electrolyte chemistry on the capacitive performance. Moreover, CMD is also applicable to more realistic and complex porous carbon models with the constant potential method.101 Thus, the capacitance determined by electrolyte property and electrode geometry can be well understood by the classical simulation techniques (CDFT, GCMC and CMD). Charging kinetics can be simulated by time‐dependent CDFT, while CMD can provide insights into how pore size impacts ion diffusivity at different electrode potentials.
The authors declare no conflict of interest.