Grand-Canonical Model of Electrochemical Double Layers from a Hybrid Density-Potential Functional

Incorporating Electrolyte Correlation Effects into Variational Models of Electrochemical Interfaces

We propose a way for obtaining a classical free energy density functional for electrolytes based on a first-principle many-body partition function. Via a one-loop expansion, we include coulombic correlations beyond the conventional mean-field approximation. To examine electrochemical interfaces, we integrate the electrolyte free energy functional into a hybrid quantum-classical model. This scheme self-consistently couples electronic, ionic, and solvent degrees of freedom and incorporates electrolyte correlation effects. The derived free energy functional causes a correlation-induced enhancement in interfacial counterion density and leads to an overall increase in capacitance. This effect is partially compensated by a reduction of the dielectric permittivity of interfacial water. At larger surface charge densities, ion crowding at the interface stifles these correlation effects. While scientifically intriguing already at planar interfaces, we anticipate these correlation effects to play an essential role for electrolytes in nanoconfinement.

Origin of Solvent Dependency of the Potential of Zero Charge

Fundamental properties of the Au(111)-KPF6 interface, particularly the potential of zero charge (PZC), exhibit pronounced variations among solvents, yet the origin remains largely elusive. In this study, we aim to link the solvent dependency to the microscopic phenomenon of electron spillover occurring at the metal-solution interface in heterogeneous dielectric media. Addressing the challenge of describing the solvent-modulated electron spillover under constant potential conditions, we adopt a semiclassical functional approach and parametrize it with first-principles calculations and experimental data. We unveil that the key variable governing this phenomenon is the local permittivity within the region approximately 2.5 Å above the metal edge. A higher local permittivity facilitates the electron spillover that tends to increase the PZC on the one hand and enhances the screening of the electronic charge that tends to decrease the PZC on the other. These dual effect lead to a nonmonotonic relationship between the PZC and the local permittivity. Moreover, our findings reveal that the electron spillover induces a capacitance peak at electrode potentials that are more negative than the PZC in concentrated solutions. This observation contrasts classical models predicting the peak to occur precisely at the PZC. To elucidate the contribution of electron spillover to the total capacitance, we decompose the total capacitance into a quantum capacitance of the metal Cq, a classical capacitance of electrolyte solution Cc, and a capacitance Cqc accounting for electron-ion correlations. Our calculations reveal that Cqc is negative due to the promoted electron spillover at more negative potentials. Our work not only reveals the importance of local permittivity in tuning the electron spillover but also presents a viable theoretical approach to study solvent effects on electrochemical interfaces under operating conditions.

An Electrostatically Embedded QM/MM Scheme for Electrified Interfaces

Atomistic modeling of electrified interfaces remains a major issue for detailed insights in electrocatalysis, corrosion, electrodeposition, batteries, and related devices such as pseudocapacitors. In these domains, the use of grand-canonical density functional theory (GC-DFT) in combination with implicit solvation models has become popular. GC-DFT can be conveniently applied not only to metallic surfaces but also to semiconducting oxides and sulfides and is, furthermore, sufficiently robust to achieve a consistent description of reaction pathways. However, the accuracy of implicit solvation models for solvation effects at interfaces is in general unknown. One promising way to overcome the limitations of implicit solvents is going toward hybrid quantum mechanical (QM)/molecular mechanics (MM) models. For capturing the electrochemical potential dependence, the key quantity is the capacitance, i.e., the relation between the surface charge and the electrochemical potential. In order to retrieve the electrochemical potential from a QM/MM hybrid scheme, an electrostatic embedding is required. Furthermore, the charge of the surface and of the solvent regions has to be strictly opposite in order to consistently simulate charge-neutral unit cells in MM and in QM. To achieve such a QM/MM scheme, we present the implementation of electrostatic embedding in the VASP code. This scheme is broadly applicable to any neutral or charged solid/liquid interface. Here, we demonstrate its use in the context of GC-DFT for the hydrogen evolution reaction (HER) over a noble-metal-free electrocatalyst, MoS₂. We investigate the effect of electrostatic embedding compared to the implicit solvent model for three contrasting active sites on MoS₂: (i) the sulfur vacancy defect, which is rather apolar; (ii) a Mo antisite defect, where the active site is a surface bound highly polar OH group; and (iii) a reconstructed edge site, which is generally believed to be responsible for most of the catalytic activity. According to our results, the electrostatic embedding leads to almost indistinguishable results compared to the implicit solvent for the apolar system but has a significant effect on polar sites. This demonstrates the reliability of the hybrid QM/MM, electrostatically embedded solvation model for electrified interfaces.

Comparing Ab Initio Molecular Dynamics and a Semiclassical Grand Canonical Scheme for the Electric Double Layer of the Pt(111)/Water Interface

The theoretical modeling of metal/water interfaces centers on an appropriate configuration of the electric double layer (EDL) under grand canonical conditions. In principle, ab initio molecular dynamics (AIMD) simulations would be the appropriate choice for treating the competing water-water and water-metal interactions and explicitly considering the atomic and electronic degrees of freedom. However, this approach only allows simulations of relatively small canonical ensembles over a limited period (shorter than 100 ps). On the other hand, computationally efficient semiclassical approaches can treat the EDL model based on a grand canonical scheme by averaging the microscopic details. Thus, an improved description of the EDL can be obtained by combining AIMD simulations and semiclassical methods based on a grand canonical scheme. By taking the Pt(111)/water interface as an example, we compare these approaches in terms of the electric field, water configuration, and double-layer capacitance. Furthermore, we discuss how the combined merits of the approaches can contribute to advances in EDL theory.

Density-Potential Functional Theory of Electrochemical Double Layers: Calibration on the Ag(111)-KPF6 System and Parametric Analysis

The density-potential functional theory (DPFT) of electrochemical double layer (EDL) is upgraded by adopting (generalized) gradient approximations for kinetic, exchange, and correlation functionals of metal electrons. A new numerical scheme that is more stable and converges faster is proposed to solve the DPFT model. The DPFT model is calibrated with existing differential double-layer capacitance (C_dl) data of the EDL at Ag(111)-KPF₆ aqueous interface at five concentrations at room temperature. Metal electronic effects are essential to explain why the two peaks of the camel-shaped C_dl curves are almost symmetric in spite of the size difference of the hydrated cations and anions. A systematic parametric analysis is then conducted in terms of key EDL properties, including the potential of zero charge and the differential capacitance. The parametric analysis, on the one hand, elucidates how quantum mechanical behaviors of metal electrons as well as interactions between metal electrons and the electrolyte solution impact the EDL properties and, on the other hand, identifies key parameters of the DPFT model, which should be calibrated using first-principles calculations and/or advanced experiments in the future.

Essays on Conceptual Electrochemistry: I. Bridging Open-Circuit Voltage of Electrochemical Cells and Charge Distribution at Electrode–Electrolyte Interfaces

We ponder over how an electrochemical cell conforms itself to the open-circuit voltage (OCV) given by the Nernst equation, where properties of the electrodes play no role. We first show, via a pedagogical derivation of the Nernst equation, how electrode properties are canceled and then take a closer look into the electrode–electrolyte interface at one electrode by linking charge and potential distributions. We obtain an equilibrium Poisson–Nernst equation that shows how the charge distribution across an electrode–electrolyte interface can be dictated by the chemical potentials of redox species. Taking a H2/O2 fuel cell as an example, we demystify the formal analysis by showing how the two electrodes delicately regulate their “electron tails” to abide by the Nernst equation. In this example, we run into a seemingly counterintuitive phenomenon that two electrodes made of the same transition metal display two distinct potentials of zero charge. This example indicates that the double layer at transition metals with chemisorption can display distinct behaviors compared to ideally polarizable double layers at sp metals.

Water electrolysis: from textbook knowledge to the latest scientific strategies and industrial developments

Replacing fossil fuels with energy sources and carriers that are sustainable, environmentally benign, and affordable is amongst the most pressing challenges for future socio-economic development. To that goal, hydrogen is presumed to be the most promising energy carrier. Electrocatalytic water splitting, if driven by green electricity, would provide hydrogen with minimal CO2 footprint. The viability of water electrolysis still hinges on the availability of durable earth-abundant electrocatalyst materials and the overall process efficiency. This review spans from the fundamentals of electrocatalytically initiated water splitting to the very latest scientific findings from university and institutional research, also covering specifications and special features of the current industrial processes and those processes currently being tested in large-scale applications. Recently developed strategies are described for the optimisation and discovery of active and durable materials for electrodes that ever-increasingly harness first-principles calculations and machine learning. In addition, a technoeconomic analysis of water electrolysis is included that allows an assessment of the extent to which a large-scale implementation of water splitting can help to combat climate change. This review article is intended to cross-pollinate and strengthen efforts from fundamental understanding to technical implementation and to improve the 'junctions' between the field's physical chemists, materials scientists and engineers, as well as stimulate much-needed exchange among these groups on challenges encountered in the different domains.

Understanding the Electric Double-Layer Structure, Capacitance, and Charging Dynamics

Significant progress has been made in recent years in theoretical modeling of the electric double layer (EDL), a key concept in electrochemistry important for energy storage, electrocatalysis, and multitudes of other technological applications. However, major challenges remain in understanding the microscopic details of the electrochemical interface and charging mechanisms under realistic conditions. This review delves into theoretical methods to describe the equilibrium and dynamic responses of the EDL structure and capacitance for electrochemical systems commonly deployed for capacitive energy storage. Special emphasis is given to recent advances that intend to capture the nonclassical EDL behavior such as oscillatory ion distributions, polarization of nonmetallic electrodes, charge transfer, and various forms of phase transitions in the micropores of electrodes interfacing with an organic electrolyte or ionic liquid. This comprehensive analysis highlights theoretical insights into predictable relationships between materials characteristics and electrochemical performance and offers a perspective on opportunities for further development toward rational design and optimization of electrochemical systems.

Cation Overcrowding Effect on the Oxygen Evolution Reaction

The influence of electrolyte ions on the catalytic activity of electrode/electrolyte interfaces is a controversial topic for many electrocatalytic reactions. Herein, we focus on an effect that is usually neglected, namely, how the local reaction conditions are shaped by nonspecifically adsorbed cations. We scrutinize the oxygen evolution reaction (OER) at nickel (oxy)hydroxide catalysts, using a physicochemical model that integrates density functional theory calculations, a microkinetic submodel, and a mean-field submodel of the electric double layer. The aptness of the model is verified by comparison with experiments. The robustness of model-based insights against uncertainties and variations in model parameters is examined, with a sensitivity analysis using Monto Carlo simulations. We interpret the decrease in OER activity with the increasing effective size of electrolyte cations as a consequence of cation overcrowding near the negatively charged electrode surface. The same reasoning could explain why the OER activity increases with solution pH on the RHE scale and why the OER activity decreases in the presence of bivalent cations. Overall, this work stresses the importance of correctly accounting for local reaction conditions in electrocatalytic reactions to obtain an accurate picture of factors that determine the electrode activity.