Origin of Asymmetric Electric Double Layers at Electrified Oxide/Electrolyte Interfaces

PiNN: Equivariant Neural Network Suite for Modeling Electrochemical Systems

Electrochemical energy storage and conversion play increasingly important roles in electrification and sustainable development across the globe. A key challenge therein is to understand, control, and design electrochemical energy materials with atomistic precision. This requires inputs from molecular modeling powered by machine learning (ML) techniques. In this work, we have upgraded our pairwise interaction neural network Python package PiNN via introducing equivariant features to the PiNet2 architecture for fitting potential energy surfaces along with PiNet2-dipole for dipole and charge predictions as well as PiNet2-χ for generating atom-condensed charge response kernels. By benchmarking publicly accessible data sets of small molecules, crystalline materials, and liquid electrolytes, we found that the equivariant PiNet2 shows significant improvements over the original PiNet architecture and provides a state-of-the-art overall performance. Furthermore, leveraging on plug-ins such as PiNNAcLe for an adaptive learn-on-the-fly workflow in generating ML potentials and PiNNwall for modeling heterogeneous electrodes under external bias, we expect PiNN to serve as a versatile and high-performing ML-accelerated platform for molecular modeling of electrochemical systems.

Electronic Response and Charge Inversion at Polarized Gold Electrode

We have studied polarized Au(100) and Au(111) electrodes immersed in electrolyte solution by implementing finite-field methods in density functional theory-based molecular dynamics simulations. This allows us to directly compute the Helmholtz capacitance of electric double layer by including both electronic and ionic degrees of freedom, and the results turn out to be in excellent agreement with experiments. It is found that the electronic response of Au electrode makes a crucial contribution to the high Helmholtz capacitance and the instantaneous adsorption of Cl can lead to a charge inversion on the anodic polarized Au(100) surface. These findings point out ways to improve popular semi-classical models for simulating electrified solid-liquid interfaces and to identify the nature of surface charges therein which are difficult to access in experiments.

Molecular-scale insights into the electrical double layer at oxide-electrolyte interfaces

The electrical double layer (EDL) at metal oxide-electrolyte interfaces critically affects fundamental processes in water splitting, batteries, and corrosion. However, limitations in the microscopic-level understanding of the EDL have been a major bottleneck in controlling these interfacial processes. Herein, we use ab initio-based machine learning potential simulations incorporating long-range electrostatics to unravel the molecular-scale picture of the EDL at the prototypical anatase TiO2-electrolyte interface under various pH conditions. Our large-scale simulations, capable of capturing interfacial water dissociation/recombination reactions and electrolytic proton transport, provide unprecedented insights into the detailed structure of the EDL. Moreover, the larger capacitance of the EDL under basic relative to acidic conditions, originating from the higher affinity of the cations for the oxide surface, is found to give rise to distinct charging mechanisms on negative and positive surfaces. Our results are validated by the agreement between the computed EDL capacitance and experimental data.

Machine learning the electric field response of condensed phase systems using perturbed neural network potentials

The interaction of condensed phase systems with external electric fields is of major importance in a myriad of processes in nature and technology, ranging from the field-directed motion of cells (galvanotaxis), to geochemistry and the formation of ice phases on planets, to field-directed chemical catalysis and energy storage and conversion systems including supercapacitors, batteries and solar cells. Molecular simulation in the presence of electric fields would give important atomistic insight into these processes but applications of the most accurate methods such as ab-initio molecular dynamics (AIMD) are limited in scope by their computational expense. Here we introduce Perturbed Neural Network Potential Molecular Dynamics (PNNP MD) to push back the accessible time and length scales of such simulations. We demonstrate that important dielectric properties of liquid water including the field-induced relaxation dynamics, the dielectric constant and the field-dependent IR spectrum can be machine learned up to surprisingly high field strengths of about 0.2 V Å-1 without loss in accuracy when compared to ab-initio molecular dynamics. This is remarkable because, in contrast to most previous approaches, the two neural networks on which PNNP MD is based are exclusively trained on molecular configurations sampled from zero-field MD simulations, demonstrating that the networks not only interpolate but also reliably extrapolate the field response. PNNP MD is based on rigorous theory yet it is simple, general, modular, and systematically improvable allowing us to obtain atomistic insight into the interaction of a wide range of condensed phase systems with external electric fields.

Molecular picture of electric double layers with weakly adsorbed water

Water adsorption energy, Eads, is a key physical quantity in sustainable chemical technologies such as (photo)electrocatalytic water splitting, water desalination, and water harvesting. In many of these applications, the electrode surface is operated outside the point (potential) of zero charge, which attracts counter-ions to form the electric double layer and controls the surface properties. Here, by applying density functional theory-based finite-field molecular dynamics simulations, we have studied the effect of water adsorption energy Eads on surface acidity and the Helmholtz capacitance of BiVO4 as an example of metal oxide electrodes with weakly chemisorbed water. This allows us to establish the effect of Eads on the coordination number, the H-bond network, and the orientation of chemisorbed water by comparing an oxide series composed of BiVO4, TiO2, and SnO2. In particular, it is found that a positive correlation exists between the degree of asymmetry ΔCH in the Helmholtz capacitance and the strength of Eads. This correlation is verified and extended further to graphene-like systems with physisorbed water, where the electric double layers (EDLs) are controlled by electronic charge rather than proton charge as in the oxide series. Therefore, this work reveals a general relationship between water adsorption energy Eads and EDLs, which is relevant to both electrochemical reactivity and the electrowetting of aqueous interfaces.

Modeling of Nanomaterials for Supercapacitors: Beyond Carbon Electrodes

Capacitive storage devices allow for fast charge and discharge cycles, making them the perfect complements to batteries for high power applications. Many materials display interesting capacitive properties when they are put in contact with ionic solutions despite their very different structures and (surface) reactivity. Among them, nanocarbons are the most important for practical applications, but many nanomaterials have recently emerged, such as conductive metal-organic frameworks, 2D materials, and a wide variety of metal oxides. These heterogeneous and complex electrode materials are difficult to model with conventional approaches. However, the development of computational methods, the incorporation of machine learning techniques, and the increasing power in high performance computing now allow us to tackle these types of systems. In this Review, we summarize the current efforts in this direction. We show that depending on the nature of the materials and of the charging mechanisms, different methods, or combinations of them, can provide desirable atomic-scale insight on the interactions at play. We mainly focus on two important aspects: (i) the study of ion adsorption in complex nanoporous materials, which require the extension of constant potential molecular dynamics to multicomponent systems, and (ii) the characterization of Faradaic processes in pseudocapacitors, that involves the use of electronic structure-based methods. We also discuss how recently developed simulation methods will allow bridges to be made between double-layer capacitors and pseudocapacitors for future high power electricity storage devices.

PiNNwall: Heterogeneous Electrode Models from Integrating Machine Learning and Atomistic Simulation

Electrochemical energy storage always involves the capacitive process. The prevailing electrode model used in the molecular simulation of polarizable electrode-electrolyte systems is the Siepmann-Sprik model developed for perfect metal electrodes. This model has been recently extended to study the metallicity in the electrode by including the Thomas-Fermi screening length. Nevertheless, a further extension to heterogeneous electrode models requires introducing chemical specificity, which does not have any analytical recipes. Here, we address this challenge by integrating the atomistic machine learning code (PiNN) for generating the base charge and response kernel and the classical molecular dynamics code (MetalWalls) dedicated to the modeling of electrochemical systems, and this leads to the development of the PiNNwall interface. Apart from the cases of chemically doped graphene and graphene oxide electrodes as shown in this study, the PiNNwall interface also allows us to probe polarized oxide surfaces in which both the proton charge and the electronic charge can coexist. Therefore, this work opens the door for modeling heterogeneous and complex electrode materials often found in energy storage systems.

Microscopic Simulations of Electrochemical Double-Layer Capacitors

Electrochemical double-layer capacitors (EDLCs) are devices allowing the storage or production of electricity. They function through the adsorption of ions from an electrolyte on high-surface-area electrodes and are characterized by short charging/discharging times and long cycle-life compared to batteries. Microscopic simulations are now widely used to characterize the structural, dynamical, and adsorption properties of these devices, complementing electrochemical experiments and in situ spectroscopic analyses. In this review, we discuss the main families of simulation methods that have been developed and their application to the main family of EDLCs, which include nanoporous carbon electrodes. We focus on the adsorption of organic ions for electricity storage applications as well as aqueous systems in the context of blue energy harvesting and desalination. We finally provide perspectives for further improvement of the predictive power of simulations, in particular for future devices with complex electrode compositions.

Double-Edged Sword of Ion-Size Asymmetry in Energy Storage of Supercapacitors

The advanced supercapacitor is of great significance for renewable energy storage. Achieving its high energy and high power densities remains a huge challenge. Herein, the contribution of ion-size asymmetry to the charging behavior of a supercapacitor is systematically studied using time-dependent density functional theory (TDDFT). We track the time evolution of the ionic microstructure inside the porous electrode and its reservoir and reveal a kinetic charge inversion in the asymmetrical ion-size cases. Compared with the symmetrical ion-size case, we find that the ion-size asymmetry has a double-edged sword effect on the energy storage of a supercapacitor: it accelerates the charging process yet reduces the differential capacitance. Additionally, the energy density and power density can simultaneously increase in the asymmetrical cases, which provides important insights toward the experimental design of supercapacitors with high energy and high power densities.

Dynamics of Heterogeneous Catalytic Processes at Operando Conditions

The rational design of high-performance catalysts is hindered by the lack of knowledge of the structures of active sites and the reaction pathways under reaction conditions, which can be ideally addressed by an in situ/operando characterization. Besides the experimental insights, a theoretical investigation that simulates reaction conditions-so-called operando modeling-is necessary for a plausible understanding of a working catalyst system at the atomic scale. However, there is still a huge gap between the current widely used computational model and the concept of operando modeling, which should be achieved through multiscale computational modeling. This Perspective describes various modeling approaches and machine learning techniques that step toward operando modeling, followed by selected experimental examples that present an operando understanding in the thermo- and electrocatalytic processes. At last, the remaining challenges in this area are outlined.

Recent Progress toward Ab Initio Modeling of Electrocatalysis

Electrode potential is the key factor for controlling electrocatalytic reactions at electrochemical interfaces, and moreover, it is also known that the pH and solutes (e.g., cations) of the solution have prominent effects on electrocatalysis. Understanding these effects requires microscopic information on the electrochemical interfaces, in which theoretical simulations can play an important role. This Perspective summarizes the recent progress in method development for modeling electrochemical interfaces, including different methods for describing the electrolytes at the interfaces and different schemes for charging up the electrode surfaces. In the final section, we provide an outlook for future development in modeling methods and their applications to electrocatalysis.