The partial charge transfer

Linking Interfacial Structure and Electrochemical Behaviors of Batteries by High-Resolution Electrocapillarity

The electrode-electrolyte interface governs the kinetics and reversibility of all electrochemical processes. While theoretical models can calculate and simulate the structure and associated properties of this intriguing component, their validation by direct experimental measurement has been a long-standing challenge. Electrocapillarity is a classical technique that derives the interfacial structure through potential-dependent surface tensions, but its limited resolution has confined its application to ideal systems such as extremely diluted aqueous electrolytes. In this work, we revive this technique with unprecedented time resolution, which allows fast and precise extraction of intrinsic interfacial structure and properties for a wide spectrum of electrolytes, be it ideal or nonideal, aqueous or nonaqueous, dilute or superconcentrated. For the very first time, this new electrocapillarity enables the measurements of a set of interfacial quantities, such as ion concentration distribution and potential drop across Helmholtz planes. Applying it on Zn-battery electrolytes, we discovered that Cl- specific adsorption at the inner-Helmholtz plane results in unexpected Zn2+ aggregation at the outer-Helmholtz plane, and identified such a unique interfacial structure as the fundamental driving force for fast Zn deposition/stripping kinetics and crystallographic texturing. The renaissance of electrocapillarity brings a new tool to the understanding and design of new electrolytes for future battery systems.

Generalized Helmholtz model describes capacitance profiles of ionic liquids and concentrated aqueous electrolytes

In this work, we propose and validate a generalization of the Helmholtz model that can account for both "bell-shaped" and "camel-shaped" differential capacitance profiles of concentrated electrolytes, the latter being characteristic of ionic liquids. The generalization is based on introducing voltage dependence of both the dielectric constant "ϵr(V)" and thickness "L(V)" of the inner Helmholtz layer, as validated by molecular dynamics (MD) simulations. We utilize MD simulations to study the capacitance profiles of three different electrochemical interfaces: (1) graphite/[BMIm+][BF4-] ionic liquid interface; (2) Au(100)/[BMIm+][BF4-] ionic liquid interface; (3) Au(100)/1M [Na+][Cl-] aqueous interface. We compute the voltage dependence of ϵr(V) and L(V) and demonstrate that the generalized Helmholtz model qualitatively describes both camel-shaped and bell-shaped differential capacitance profiles of ionic liquids and concentrated aqueous electrolytes (in lieu of specific ion adsorption). In particular, the camel-shaped capacitance profile that is characteristic of ionic liquid electrolytes arises simply from combination of the voltage-dependent trends of ϵr(V) and L(V). Furthermore, explicit analysis of the inner layer charge density for both concentrated aqueous and ionic liquid double layers reveal similarities, with these charge distributions typically exhibiting a dipolar region closest to the electrode followed by a monopolar peak at larger distances. It is appealing that a generalized Helmholtz model can provide a unified description of the inner layer structure and capacitance profile for seemingly disparate aqueous and ionic liquid electrolytes.

The electrostatic effect and its role in promoting electrocatalytic reactions by specifically adsorbed anions

The adsorption of anions and its impact on electrocatalytic reactions are fundamental topics in electrocatalysis. Previous studies revealed that adsorbed anions display an overall poisoning effect in most cases. However, for a few reactions such as the hydrogen evolution reaction (HER), oxidation of small organic molecules (SOMs), and reduction of CO₂ and O₂, some specifically adsorbed anions can promote their reaction kinetics under certain conditions. The promotion effect is frequently attributed to the adsorbate induced modification of the nature of the active sites, the change of the adsorption configuration and free energy of the key reactive intermediate which consequently change the activation energy, the pre-exponential factor of the rate determining step etc. In this paper, we will give a mini review of the indispensable role of the classical double layer effect in enhancing the kinetics of electrocatalytic reactions by anion adsorption. The ubiquitous electrostatic interactions change both the potential distribution and the concentration distribution of ionic species across the electric double layer (EDL), which alters the electrochemical driving force and effective concentration of the reactants. The contribution to the overall kinetics is highlighted by taking HER, oxidation of SOMs, reduction of CO₂ and O₂, as examples.

Zooming into the Inner Helmholtz Plane of Pt(111)-Aqueous Solution Interfaces: Chemisorbed Water and Partially Charged Ions

The double layer on transition metals, i.e., platinum, features chemical metal-solvent interactions and partially charged chemisorbed ions. Chemically adsorbed solvent molecules and ions are situated closer to the metal surface than electrostatically adsorbed ions. This effect is described tersely by the concept of an inner Helmholtz plane (IHP) in classical double layer models. The IHP concept is extended here in three aspects. First, a refined statistical treatment of solvent (water) molecules considers a continuous spectrum of orientational polarizable states, rather than a few representative states, and non-electrostatic, chemical metal-solvent interactions. Second, chemisorbed ions are partially charged, rather than being electroneutral or having integral charges as in the solution bulk, with the coverage determined by a generalized, energetically distributed adsorption isotherm. The surface dipole moment induced by partially charged, chemisorbed ions is considered. Third, considering different locations and properties of chemisorbed ions and solvent molecules, the IHP is divided into two planes, namely, an AIP (adsorbed ion plane) and ASP (adsorbed solvent plane). The model is used to study how the partially charged AIP and polarizable ASP lead to intriguing double-layer capacitance curves that are different from what the conventional Gouy-Chapman-Stern model describes. The model provides an alternative interpretation for recent capacitance data of Pt(111)-aqueous solution interfaces calculated from cyclic voltammetry. This revisit brings forth questions regarding the existence of a pure double-layer region at realistic Pt(111). The implications, limitations, and possible experimental confirmation of the present model are discussed.

The review of advances in interfacial electrochemistry in Estonia: electrochemical double layer and adsorption studies for the development of electrochemical devices

The electrochemistry nowadays has many faces and challenges. Although the focus has shifted from fundamental electrochemistry to applied electrochemistry, one needs to acknowledge that it is impossible to develop and design novel green energy transition devices without a comprehensive understanding of the electrochemical processes at the electrode and electrolyte interface that define the performance mechanisms. The review gives an overview of the systematic research in the field of electrochemistry in Estonia which reflects on the excellent collaboration between fundamental and applied electrochemistry.

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.

The Sensitivity of Metal Oxide Electrocatalysis to Bulk Hydrogen Intercalation: Hydrogen Evolution on Tungsten Oxide

Metal oxides are attracting increased attention as electrocatalysts owing to their affordability, tunability, and reactivity. However, these materials can undergo significant chemical changes under reaction conditions, presenting challenges for characterization and optimization. Herein, we combine experimental and computational methods to demonstrate that bulk hydrogen intercalation governs the activity of tungsten trioxide (WO₃) toward the hydrogen evolution reaction (HER). In contrast to the focus on surface processes in heterogeneous catalysis, we demonstrate that bulk oxide modification is responsible for experimental HER activity. Density functional theory (DFT) calculations reveal that intercalation enables the HER by altering the acid-base character of surface sites and preventing site blocking by hydration. First-principles microkinetic modeling supports that the experimental HER rates can only be explained by intercalated H_xWO₃, whereas nonintercalated WO₃ does not catalyze the HER. Overall, this work underscores the critical influence of hydrogen intercalation on aqueous cathodic electrocatalysis at metal oxides.

Implicit Solvation Methods for Catalysis at Electrified Interfaces

Implicit solvation is an effective, highly coarse-grained approach in atomic-scale simulations to account for a surrounding liquid electrolyte on the level of a continuous polarizable medium. Originating in molecular chemistry with finite solutes, implicit solvation techniques are now increasingly used in the context of first-principles modeling of electrochemistry and electrocatalysis at extended (often metallic) electrodes. The prevalent ansatz to model the latter electrodes and the reactive surface chemistry at them through slabs in periodic boundary condition supercells brings its specific challenges. Foremost this concerns the difficulty of describing the entire double layer forming at the electrified solid–liquid interface (SLI) within supercell sizes tractable by commonly employed density functional theory (DFT). We review liquid solvation methodology from this specific application angle, highlighting in particular its use in the widespread ab initio thermodynamics approach to surface catalysis. Notably, implicit solvation can be employed to mimic a polarization of the electrode’s electronic density under the applied potential and the concomitant capacitive charging of the entire double layer beyond the limitations of the employed DFT supercell. Most critical for continuing advances of this effective methodology for the SLI context is the lack of pertinent (experimental or high-level theoretical) reference data needed for parametrization.

Modeling Electrified Pt(111)-Had/Water Interfaces from Ab Initio Molecular Dynamics

Unraveling the atomistic structures of electric double layers (EDL) at electrified interfaces is of paramount importance for understanding the mechanisms of electrocatalytic reactions and rationally designing electrode materials with better performance. Despite numerous efforts dedicated in the past, a molecular level understanding of the EDL is still lacking. Combining the state-of-the-art ab initio molecular dynamics (AIMD) and recently developed computational standard hydrogen electrode (cSHE) method, it is possible to realistically simulate the EDL under well-defined electrochemical conditions. In this work, we report extensive AIMD calculation of the electrified Pt(111)-Had/water interfaces at the saturation coverage of adsorbed hydrogen (Had) corresponding to the typical hydrogen evolution reaction conditions. We calculate the electrode potentials of a series of EDL models with various surface charge densities using the cSHE method and further obtain the Helmholtz capacitance that agrees with experiment. Furthermore, the AIMD simulations allow for detailed structural analyses of the electrified interfaces, such as the distribution of adsorbate Had and the structures of interface water and counterions, which can in turn explain the computed dielectric property of interface water. Our calculation provides valuable molecular insight into the electrified interfaces and a solid basis for understanding a variety of electrochemical processes occurring inside the EDL.

Impedance response of electrochemical interfaces: part II-chemisorption

Physical modeling helps to acquire fundamental insights from experimental data when electrochemical impedance spectroscopy is employed for mechanistic understandings of electrocatalytic reactions. Herein, we report an analytical model for chemisorption impedance with a consistent treatment of ion transport in the solution and electron transfer on the electrode surface. Our formulation avoids botha prioridecoupling of double-layer charging and electron transfer reaction, and a strict separation of double-layer charging and ion transport. Ion transport in the entire solution region is described by the Poisson-Nernst-Planck theory and electron transfer kinetics on the electrode surface by the Frumkin-Butler-Volmer theory. Surface dipoles caused by partially charged chemisorbates are considered. The classical Frumkin-Melik-Gaikazyan model for chemisorption is retrieved as a limiting case. The obtained formula is validated using experimental data of hydrogen adsorption at Pt(111). Characteristic frequencies and asymptotic behaviors of chemisorption impedance are analyzed.

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

A hybrid density-potential functional of an electrochemical interface that encompasses major effects in the contacting metal and electrolyte phases is formulated. Variational analysis of this functional yields a grand-canonical model of the electrochemical double layer (EDL). Specifically, metal electrons are described using the Thomas-Fermi-Dirac-Wigner theory of an inhomogeneous electron gas. The electrolyte solution is treated classically at the mean-field level, taking into account electrostatic interactions, ion size effects, and nonlinear solvent polarization. The model uses parametrizable force relations to describe the short-range forces between metal cationic cores, metal electrons, and electrolyte ions and solvent molecules. Therefore, the gap between the metal skeleton and the electrolyte solution, key to properties of the EDL, varies consistently as a function of the electrode potential. Partial charge transfer in the presence of ion specific adsorption is described using an Anderson-Newns type theory. This model is parametrized with density functional theory calculations, compared with experimental data, and then employed to unravel several interfacial properties of fundamental significance in electrochemistry. In particular, a closer approach of the solution phase toward the metal surface, for example, caused by a stronger ion specific adsorption, decreases the potential of zero charge and elevates the double-layer capacitance curve. In addition, the ion specific adsorption can lead to surface depolarization of ions. The present model represents a viable framework to model (reactive) EDLs under the constant potential condition, which can be used to understand multifaceted EDL effects in electrocatalysis.

Demystifying the Stern layer at a metal-electrolyte interface: Local dielectric constant, specific ion adsorption, and partial charge transfer

Electric double layer (EDL) represents one of the most basic concepts in electrochemistry and is pertinent to diverse engineering applications ranging from electrocatalysis to energy storage. Whereas phenomenological and coarse-grained models have been long established to describe ionic distributions in the diffuse layer, a faithful prediction of the physicochemical properties of the electrode-electrolyte interface from a molecular perspective remains a daunting challenge. In this work, we investigate the charging behavior of an Ag (111) electrode in NaF aqueous solutions leveraging experimental results and theoretical calculations based on the classical density functional theory for ion distributions in the diffuse layer and on the joint density functional theory (JDFT) for the electronic structure. When the Ag electrode is applied with a negative voltage, the surface charge density can be reasonably described by assuming a neutral Stern layer with the dielectric constant dependent on the local electric field as predicted by the Kirkwood equation. However, the specific adsorption of F^- ions must be considered when the electrode is positively charged and the fluoride adsorption can be attributed to both physical and chemical interactions. Qualitatively, F^- binding and partial charge transfer are supported by JDFT calculations, which predict an increased binding energy as the voltage increases. Our findings shed insight on the molecular characteristics of the Stern layer and the charge behavior of adsorbed species not specified by conventional EDL models.

A possible channel effect of the organics adsorbed to the electrode surface on interfacial electron transfer in the alkaline Pb electrodeposition process

A possible electron transfer channel in solid–liquid interface.

Molecular origin of negative component of Helmholtz capacitance at electrified Pt(111)/water interface

Electrified solid/liquid interfaces are the key to many physicochemical processes in a myriad of areas including electrochemistry and colloid science. With tremendous efforts devoted to this topic, it is unexpected that molecular-level understanding of electric double layers is still lacking. Particularly, it is perplexing why compact Helmholtz layers often show bell-shaped differential capacitances on metal electrodes, as this would suggest a negative capacitance in some layer of interface water. Here, we report state-of-the-art ab initio molecular dynamics simulations of electrified Pt(111)/water interfaces, aiming at unraveling the structure and capacitive behavior of interface water. Our calculation reproduces the bell-shaped differential Helmholtz capacitance and shows that the interface water follows the Frumkin adsorption isotherm when varying the electrode potential, leading to a peculiar negative capacitive response. Our work provides valuable insight into the structure and capacitance of interface water, which can help understand important processes in electrocatalysis and energy storage in supercapacitors.

Sulfate, Bisulfate, and Hydrogen Co-adsorption on Pt(111) and Au(111) in an Electrochemical Environment

The co-adsorption of sulfate, bisulfate and hydrogen on Pt(111) and Au(111) electrodes was studied based on periodic density functional calculations with the aqueous electrolyte represented by both explicit and implicit solvent models. The influence of the electrochemical control parameters such as the electrode potential and pH was taken into account in a grand-canonical approach. Thus, phase diagrams of the stable coadsorption phases as a function of the electrochemical potential and Pourbaix diagrams have been derived which well reproduce experimental findings. We demonstrate that it is necessary to include explicit water molecules in order to determine the stable adsorbate phases as the (bi)sulfate adsorbates rows become significantly stabilized by bridging water molecules.

Some Questionable Approaches in Interfacial Electrochemistry—The Charged State of Adsorbed Species and Their Involvement in Redox Processes

On the basis of a survey on the relevant literature it can be stated that some views and approaches concerning the charged state of adsorbed species and the charge transfer processes occurring with them are far from being unambiguous even in some respect they contradict fundamental physical and physicochemical principles. The meaning of the electrosorption valency, the misleading formulation of the Gibbs adsorption equation, and the interpretation of redox processes occurring with adsorbed species, is discussed in detail. It has been concluded that although the electrosorption valency of an adsorbed species as usually defined is an extra-thermodynamic and self-contradictory concept, experimental determined formal partial charge numbers can be a useful tool for scientists investigating adsorption phenomena, since the observed deviation between its value and the charge number of the same species in the solution phase unequivocally indicates a non-simple mechanism of the adsorption process, which should be taken into account in theoretical interpretation of the experimental data. It has been emphasized that the evaluation of voltammetric curves obtained in the presence of adsorbed redox partners requires a cautious analysis of the accompanying chemical transformations. In the framework of a critical analysis it is demonstrated that probably one of the most important sources of the misinterpretations and misunderstandings is the inadequate approach to the concept of electrode charge. The possibility of a general and straightforward presentation of the Gibbs adsorption equation has also been discussed.

Grand-canonical approach to density functional theory of electrocatalytic systems: Thermodynamics of solid-liquid interfaces at constant ion and electrode potentials

Properties of solid-liquid interfaces are of immense importance for electrocatalytic and electrochemical systems, but modeling such interfaces at the atomic level presents a serious challenge and approaches beyond standard methodologies are needed. An atomistic computational scheme needs to treat at least part of the system quantum mechanically to describe adsorption and reactions, while the entire system is in thermal equilibrium. The experimentally relevant macroscopic control variables are temperature, electrode potential, and the choice of the solvent and ions, and these need to be explicitly included in the computational model as well; this calls for a thermodynamic ensemble with fixed ion and electrode potentials. In this work, a general framework within density functional theory (DFT) with fixed electron and ion chemical potentials in the grand canonical (GC) ensemble is established for modeling electrocatalytic and electrochemical interfaces. Starting from a fully quantum mechanical description of multi-component GC-DFT for nuclei and electrons, a systematic coarse-graining is employed to establish various computational schemes including (i) the combination of classical and electronic DFTs within the GC ensemble and (ii) on the simplest level a chemically and physically sound way to obtain various (modified) Poisson-Boltzmann (mPB) implicit solvent models. The detailed and rigorous derivation clearly establishes which approximations are needed for coarse-graining as well as highlights which details and interactions are omitted in vein of computational feasibility. The transparent approximations also allow removing some of the constraints and coarse-graining if needed. We implement various mPB models within a linear dielectric continuum in the GPAW code and test their capabilities to model capacitance of electrochemical interfaces as well as study different approaches for modeling partly periodic charged systems. Our rigorous and well-defined DFT coarse-graining scheme to continuum electrolytes highlights the inadequacy of current linear dielectric models for treating properties of the electrochemical interface.

Understanding the apparent fractional charge of protons in the aqueous electrochemical double layer

A detailed atomic-scale description of the electrochemical interface is essential to the understanding of electrochemical energy transformations. In this work, we investigate the charge of solvated protons at the Pt(111) | H₂O and Al(111) | H₂O interfaces. Using semi-local density-functional theory as well as hybrid functionals and embedded correlated wavefunction methods as higher-level benchmarks, we show that the effective charge of a solvated proton in the electrochemical double layer or outer Helmholtz plane at all levels of theory is fractional, when the solvated proton and solvent band edges are aligned correctly with the Fermi level of the metal (E_F). The observed fractional charge in the absence of frontier band misalignment arises from a significant overlap between the proton and the electron density from the metal surface, and results in an energetic difference between protons in bulk solution and those in the outer Helmholtz plane.

A detailed atomic-scale description of the electrochemical interface is essential to the understanding of electrochemical energy transformations. Here, the authors investigate the solvated proton at the electrochemical interface and show that it unexpectedly carries a fractional charge.

Probing the charge distribution at the electrochemical interface

The electrode/electrolyte interface is central to many electrochemical systems; however, gaining insight into the electronic structure at the interface is challenging. Due to its buried nature it is difficult to employ traditional techniques that provide spectroscopic information of localised atoms. To gain new insight into the charge distribution at the interface, we used resonant surface X-ray diffraction to select atoms at the interface via the diffraction conditions and obtained spectroscopic information simultaneously. Coupling the polarisation of the incident X-ray beam with the electron density at the interface allows direct probing of the charge transfer between the metal electrode and the adsorbing species in the electrolyte solution. Results for the adsorption of halide anions onto Cu and Au single crystal electrode surfaces reveal that there is significant modification of the charge distribution of both the surface and sub-surface atomic metal adlayers in the case of ionic bond formation. This has potential impact both in developing a theoretical understanding of the interface structure and in designing new materials for electrochemical applications.

Determining Potentials of Zero Charge of Metal Electrodes versus the Standard Hydrogen Electrode from Density-Functional-Theory-Based Molecular Dynamics

We develop a computationally efficient scheme to determine the potentials of zero charge (PZC) of metal-water interfaces with respect to the standard hydrogen electrode. We calculate the PZC of Pt(111), Au(111), Pd(111) and Ag(111) at a good accuracy using this scheme. Moreover, we find that the interface dipole potentials are almost entirely caused by charge transfer from water to the surfaces, the magnitude of which depends on the bonding strength between water and the metals, while water orientation hardly contributes at the PZC conditions.

Partial oxidation of step-bound water leads to anomalous pH effects on metal electrode step-edges

The design of better heterogeneous catalysts for applications such as fuel cells and electrolyzers requires a mechanistic understanding of electrocatalytic reactions and the dependence of their activity on operating conditions such as pH. A satisfactory explanation for the unexpected pH dependence of electrochemical properties of platinum surfaces has so far remained elusive, with previous explanations resorting to complex co-adsorption of multiple species and resulting in limited predictive power. This knowledge gap suggests that the fundamental properties of these catalysts are not yet understood, limiting systematic improvement. Here, we analyze the change in charge and free energies upon adsorption using density-functional theory (DFT) to establish that water adsorbs on platinum step edges across a wide voltage range, including the double-layer region, with a loss of approximately 0.2 electrons upon adsorption. We show how this as-yet unreported change in net surface charge due to this water explains the anomalous pH variations of the hydrogen underpotential deposition (Hupd) and the potentials of zero total charge (PZTC) observed in published experimental data. This partial oxidation of water is not limited to platinum metal step edges, and we report the charge of the water on metal step edges of commonly used catalytic metals, including copper, silver, iridium, and palladium, illustrating that this partial oxidation of water broadly influences the reactivity of metal electrodes.

Electrical double layer effects on ion transfer reactions

The effects of the electrical double layer on ion transfer reactions and their voltammetry are investigatedviaGibbs energy surfaces.

Non-covalent interactions in water electrolysis: influence on the activity of Pt(111) and iridium oxide catalysts in acidic media

Electrolyte components, which are typically not considered to be directly involved in catalytic processes at solid–liquid electrified interfaces, often demonstrate a significant or even drastic influence on the activity, stability and selectivity of electrocatalysts.