The differential capacitance comprises the most relevant thermodynamic information about an electrochemical system. Classical approaches to describe electrochemical capacitance have difficulties to combine the treatment of the ionic contribution of the electrolyte with the electronic contribution of the electrode. Moreover, different approaches are typically required for the description of the double-layer capacitance, on the one hand, and the pseudocapacitive contribution due to adsorption or intercalation of reactive species, on the other. In the present work, a new approach to describe electrochemical capacitance from first principles is developed. The treatment of a general electrochemical system at the level of multicomponent density-functional theory (MCDFT) yields an exact analytical expression for the total capacitance of the system, which corresponds to a formal series-circuit partitioning into "quantum" capacitance contributions of the density of states of electrons and ions, the (mean-field) electrostatic capacitance, as well as capacitance contributions of exchange and correlation among all active species. It is shown that the classical expression of the double-layer capacitance involving the interfacial Galvani potential is obtained in the limit of extended electrode and electrolyte regions. Importantly, the present formalism also describes systems with confined electrode and electrolyte phases, where the definition of the (classical) inner potentials of the electrode and electrolyte domains becomes problematic. Moreover, the new approach unifies the treatment of double-layer capacitance and pseudocapacitance resulting from reactive processes.
Controlling electrochemical reactivity requires a detailed understanding of the charging behavior and thermodynamics of the electrochemical interface. Experiments can independently probe the overall charge response of the electrochemical double layer by capacitance measurements, and the thermodynamics of the inner layer with potential of maximum entropy (PME) measurements. Relating these properties by computational modeling of the electrochemical interface has so far been challenging due to the low accuracy of classical molecular dynamics (MD) for capacitance and the limited time and length sc…
The distribution of electric fields within the electrochemical double layer depends on both the electrode and electrolyte in complex ways. These fields strongly influence chemical dynamics in the electrode-electrolyte interface, but cannot be measured directly with sub-molecular resolution. We report experimental capacitance measurements for aqueous interfaces of CO-terminated Pt(111). By comparing these measurements with first-principles density-functional theory (DFT) calculations, we infer microscopic field distributions and decompose contributions to the inverse capacitance from various sp…
Reliable first-principles calculations of electrochemical processes require accurate prediction of the interfacial capacitance, a challenge for current computationally-efficient continuum solvation methodologies. We develop a model for the double layer of a metallic electrode that reproduces the features of the experimental capacitance of Ag(100) in a non-adsorbing, aqueous electrolyte, including a broad hump in the capacitance near the Potential of Zero Charge (PZC), and a dip in the capacitance under conditions of low ionic strength. Using this model, we identify the necessary characteristic…
Confinement-controlled Water Engenders High Energy Density Electrochemical-double-layer Capacitance
Skolkovo Institute of Science and Technology（斯克隆沃科学技术研究所）；Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）；Max Planck Institute for Polymer Research（马克斯·普朗克高分子研究所）
Surfaces of metal oxides at working conditions are usually electrified due to the acid-base chemistry. The charged interface compensated with counterions forms the so-called electric double layer. The coupling of surface chemistry and electric double layer is considered to be crucial but poorly understood because of lacking the information at the atomistic scale. Here, we used the latest development in density functional theory based finite-field molecular dynamics simulation to investigate pH-dependence of the Helmholtz capacitance at electrified rutile TiO$_2$ (110)-NaCl electrolyte interfac…
Discovery of electrocatalytic materials for high-performance energy conversion and storage applications relies on the adequate characterization of their intrinsic activity, which is currently hindered by the dearth of a protocol for consistent and precise determination of double layer capacitance (CDL). Herein, we propose a seven-step method that aims to determine CDL reliably by scan rate-dependent cyclic voltammetry. The method considers three aspects that strongly influence the outcome of the analysis: measurement settings, data collection, and data processing. To illustrate the proposed me…
Electrochemical impedance spectra for battery electrodes are usually interpreted using models that assume isotropic active particles, having uniform current density and symmetric diffusivities. While this can be reasonable for amorphous or polycrystalline materials with randomly oriented grains, modern electrode materials increasingly consist of highly anisotropic, single-crystalline, nanoparticles, with different impedance characteristics. In this paper, analytical expressions are derived for the impedance of anisotropic particles with tensorial diffusivities and orientation-dependent surface…
The use of aqueous electrolytes in energy storage devices is traditionally limited by the voltage stability window of water at 1.23 V. We present the use of a microemulsion based electrolyte which, although mostly water by mass, has a voltage stability window of up to 5 V. This allows the cost and safety benefits of aqueous electrolytes to finally be realised in high-voltage systems. Supercapacitors constructed using this electrolyte were able to achieve and maintain a capacitance of ~40 F/g and an energy density ~40 Wh/kg of with a Coulombic efficiency of 99\% for over 10,000 cycles on activa…
We apply first principles computational techniques to analyze the two-electron, multi-step, electrochemical reduction of CO2 to CO in water using cobalt porphyrin as a catalyst. Density Functional Theory calculations with hybrid functionals and dielectric continuum solvation are used to determine the steps at which electrons are added. This information is corroborated with ab initio molecular dynamics simulations in an explicit aqueous environment which reveal the critical role of water in stabilizing a key intermediate formed by CO2 bound to cobalt. Using potential of mean force calculations,…
To improve the understanding of the relation between electrode curvature and energy storage mechanisms, a systematic investigation of the correlation between convex and concave electrode surfaces and the differential capacitance of an electrochemical double layer capacitor using molecular dynamics simulations is presented. Each electrode consists of three layers of curved graphene sheets with a convex and concave surface to which the constant potential method was applied. The differential capacitance shows a fluctuating behavior with respect to the curvature radius of the convex and concave ar…
Most of the performances of electrochemical devices are governed by molecular processes taking place at the solution-electrode interfaces and molecular simulation are the main way to study these processes. Aqueous electrochemical systems have often been studied using classical DFT but with too crude approximations to consider the system description to be realistic. We study the interface between graphene electrodes and liquid water at different applied voltage using molecular DFT, improving the state of the art by the following key points: 1) electrodes have a realistic atomic resolution, 2) c…
Rethinking Balance Sheets: A Poisson-Nernst-Planck Based Approach for Modeling Concentration and Flux Profiles Inside an Electrochemical Cell
University of Colorado Boulder（科罗拉多大学博尔德分校）；National Laboratory of the Rockies（落基山国家实验室）；Renewable and Sustainable Energy Institute, University of Colorado Boulder（科罗拉多大学可再生与可持续能源研究所）
Unveiling the Influence of Graphitic Nanocarbon Structures, Defects, and Surface Functional Groups on Supercapacitive Performance in LiTFSI Electrolyte
Sirindhorn International Institute of Technology, Thammasat University（诗琳通国际理工学院，坦布拉大学）；Université de Haute-Alsace, Institut de Science des Matériaux de Mulhouse (IS2M), CNRS UMR 7361（上阿尔萨斯大学，米卢斯材料科学研究所 (IS2M)，法国国家科学研究中心 UMR 7361）；Université de Strasbourg（斯特拉斯堡大学）；Réseau sur le Stockage Electrochimique de l’Energie (RS2E), CNRS FR3459（电化学储能网络 (RS2E)，法国国家科学研究中心 FR3459）；International Research and Education Center for Element Science, Faculty of Science and Technology, Gunma University（群马大学理学院元素科学国际研究与教育中心）；Division of Chemical Engineering, Faculty of Engineering, Rajamangala University of Technology Krungthep（曼谷皇家理工大学工程学院化学工程系）
Continuum electrolyte models represent a practical tool to account for the presence of the diffuse layer at electrochemical interfaces. However, despite the increasing popularity of these in the field of materials science it remains unclear which features are necessary in order to accurately describe interface-related observables such as the differential capacitance (DC) of metal electrode surfaces. We present here a critical comparison of continuum diffuse-layer models that can be coupled to an atomistic first-principles description of the charged metal surface in order to account for the ele…
Electrochemical devices often consist of multicomponent electrolyte solutions. Two processes influence the overall dynamics of these devices: the formation of electrical double layers and chemical conversion due to redox reactions. However, due to the presence of multiple length and time scales, it is challenging to simulate both processes directly from the Poisson-Nernst-Planck equations. Therefore, common modeling approaches ignore one of the processes, assume the two are independent, or extrapolate the results from reaction-free systems. To overcome these limitations, we formulate and deriv…
We use molecular dynamics simulations in a constant potential ensemble to study the effects of solution composition on the electrochemical response of a double layer capacitor. We find that the capacitance first increases with ion concentration following its expected ideal solution behavior, but decreases upon approaching a pure ionic liquid in agreement with recent experimental observations. The non-monotonic behavior of the capacitance as a function of ion concentration results from the competition between the independent motion of solvated ions in the dilute regime and solvation fluctuation…
Current supercapacitors present several distinct limitations that severely inhibit the efficiency, power, and electrical capacitance of energy storage devices. Supercapacitors present an exciting prospect that has countless applications in renewable energy storage and modern day electronic devices. In recent years the exciting development of carbon nanotubes (CNTs) has presented an advantage in electrode development. CNTs, however beneficial for their increased electrode surface area, have severe limitations regarding conductivity and electrode density. Creating a nanocomposite hybrid out of a…
We investigate a nanoscale dielectric capacitor model consisting of two-dimensional, hexagonal h-BN layers placed between two commensurate and metallic graphene layers using self-consistent field density functional theory. The separation of equal amounts of electric charge of different sign in different graphene layers is achieved by applying electric field perpendicular to the layers. The stored charge, energy, and the electric potential difference generated between the metallic layers are calculated from the first-principles for the relaxed structures. Predicted high-capacitance values exhib…
The frequency-dependent impedance is a fundamental property of electrical components. We show that it can be determined from the equilibrium dynamical fluctuations of the electrode charge in constant-potential molecular simulations, extending in particular a fluctuation-dissipation for the capacitance recovered in the low-frequency limit and provide an illustration on water/gold nanocapacitors. This work opens the way to the interpretation of electrochemical impedance measurements in terms of microscopic mechanisms, directly from the dynamics of the electrolyte, or indirectly via equivalent ci…
Biredox ionic liquids are a new class of functionalized electrolytes that may play an important role in future capacitive energy storage devices. By allowing additional storage of electrons inside the liquids, they can improve device performance significantly. However current devices employ nanoporous carbons in which the diffusion of the liquid and the adsorption of the ions could be affected by the occurrence of electron-transfer reactions. It is therefore necessary to understand better the thermodynamics and the kinetics of such reactions in biredox ionic liquids. Here we perform ab initio …
The technique presented here for the measurement of electrical conductivity is based on the principle that the current converges on a small disk electrode. Most of the ohmic resistance therefore lies within a narrow region surrounding the disk. If the reference electrode is kept outside this zone, the potential difference between the working and the reference electrode includes practically all ohmic potential drops occurring in the solution. Moreover, this ohmic drop can be related to the conductivity of the solution by an analytical expression derived by Newman. At sufficiently high overpoten…
