Grand Canonical Approach Research Articles

The Role of Surface Roughening in Improving the Selectivity of Copper for CO2 Electroreduction

Electroreduction of CO2 (eCO2RR) has emerged as a promising alternative for production of renewable fuels and important commodity chemicals such as ethylene and ethanol. Simultaneously, it opens an economically attractive path to mitigate point sources of CO2, a potent greenhouse gas. Despite decades of research efforts, Cu remains the only catalyst capable of producing significant amounts of desirable C2+ products, containing more than one carbon atom. However, further improvement is needed for industrial applications. It is known that roughened copper-based electrocatalysts surfaces exhibit enhanced selectivity towards C2+ products during electroreduction of CO2. This poses a challenge for modeling efforts aiming to find a rationale for the enhanced selectivity. In this work, we use an innovative modeling approach to investigate roughened copper surfaces derived from cuprous oxide on structures of 100x100 nm2 size with atomic resolution and accuracy compared to density functional theory (DFT). We combine semilocal DFT (RPBE) in VASP, effective medium theory (EMT), and linear scaling relationships via the recently proposed alpha parameter scheme to investigate the site-resolved catalytic selectivity of copper sites. Electrode potential-dependence is included via the use of the VASPsol implicit solvation and a grand canonical potential approach. The approach allows us to investigate the effect of varied macroscopic roughness on the intrinsic catalytic activity of copper by comparing surfaces exposed to simulated sputtering and electropolishing, respectively. The study highlights i) the challenge for designing improved copper catalysts for CO2RR with monodisperse active site selectivity, ii) the need for careful experimentation when comparing to theory, and iii) the limitations of macroscopic roughness in controlling atomic scale activity.

Theoretical Investigation of the Potential-Dependent CO Adsorption on Copper Electrodes.

Despite the importance of CO adsorption in many electrocatalytic reaction mechanisms, there has been little investigation of the dependence of the free energy of CO adsorption on the applied potential. Herein, we report on the potential-dependent adsorption of CO on Cu electrodes using a grand-canonical density functional theory approach. We demonstrate that, within the working potential range of electrocatalytic CO2 reduction on Cu(111) and Cu(100), the CO adsorption strength can change by over 0.1 eV. Our analyses explain the potential dependence through an interfacial capacitance loss upon CO adsorption as well as orbital relaxation induced by the electrode potential. Via sensitivity analysis with respect to two electrolyte model parameters (solvent dielectric constant and Debye screening length), we find that the surface excess charge density is a useful descriptor of the CO adsorption free energy.

Molecular modeling of CO2 affecting competitive adsorption within anthracite coal

This study aimed to investigate the adsorption properties of CO2, CH4, and N2 on anthracite. A molecular structural model of anthracite (C208H162O12N4) was established. Simulations were performed for the adsorption properties of single-component and multi-component gases at various temperatures, pressures, and gas ratios. The grand canonical ensemble Monte Carlo approach based on molecular mechanics and dynamics theories was used to perform the simulations. The results showed that the isotherms for the adsorption of single-component CO2, CH4, and N2 followed the Langmuir formula, and the CO2 adsorption isotherm growth gradient was negatively correlated with pressure but positively correlated with temperature. When the CO2 injection in the gas mixture was increased from 1 to 3% for the multi-component gas adsorption, the proportion of CO2 adsorption rose from 1/3 to 2/3, indicating that CO2 has a competing-adsorption advantage. The CO2 adsorption decreased faster with increasing temperature, indicating that the sensitivity of CO2 to temperature is stronger than that of CH4 and N2. The adsorbent potential energies of CO2, CH4, and N2 diminished with rising temperature in the following order: CO2 < CH4 < N2.

Analysis of the adsorption characteristics of SF6 and its decomposition products in ZIF-67: based on GCMC and DFT

Given the superior performance of SF6 in arc extinguishing and its wide application in high voltage fields, the search for new adsorbent materials for SF6 and its main decomposition products holds significant importance in mitigating greenhouse gas potential and its implications for the environment and energy sectors. We chose ZIF-67, an organic framework with a high specific surface area and distinctive pore size structure, to address this important issue. Using the grand canonical Monte Carlo simulation approach, we investigated the adsorption of SF6 and its main decomposer gases by ZIF-67 at GPa. The interaction of ZIF-67 with SF6 and its main breakdown products was then examined at the level of atomic orbital interactions, with the adsorption energy and density of states estimated using density functional theory. The findings reveal that ZIF-67 has the best ability to capture H2S, with a saturation capacity of 3.2 mmol g−1 at room temperature. Its adsorption capacity for SOF2 and SO2F2 is about five to seven times higher than that of industrial adsorbents kdhF-03, and the working conditions are milder. The molecule radius and adsorption capacity are tightly correlated. An innovative method for the widespread recovery and treatment of SF6 and its byproducts is presented in this research. This paper aims to provide new insights and solutions to promote sustainable development in the power industry.

Thermodynamic and kinetic modeling of electrocatalytic reactions using a first-principles approach.

The computational modeling of electrochemical interfaces and their applications in electrocatalysis has attracted great attention in recent years. While tremendous progress has been made in this area, however, the accurate atomistic descriptions at the electrode/electrolyte interfaces remain a great challenge. The Computational Hydrogen Electrode (CHE) method and continuum modeling of the solvent and electrolyte interactions form the basis for most of these methodological developments. Several posterior corrections have been added to the CHE method to improve its accuracy and widen its applications. The most recently developed grand canonical potential approaches with the embedded diffuse layer models have shown considerable improvement in defining interfacial interactions at electrode/electrolyte interfaces over the state-of-the-art computational models for electrocatalysis. In this Review, we present an overview of these different computational models developed over the years to quantitatively probe the thermodynamics and kinetics of electrochemical reactions in the presence of an electrified catalyst surface under various electrochemical environments. We begin our discussion by giving a brief picture of the different continuum solvation approaches, implemented within the abinitio method to effectively model the solvent and electrolyte interactions. Next, we present the thermodynamic and kinetic modeling approaches to determine the activity and stability of the electrocatalysts. A few applications to these approaches are also discussed. We conclude by giving an outlook on the different machine learning models that have been integrated with the thermodynamic approaches to improve their efficiency and widen their applicability.

Solvation–Reduction Coupling in Ca2+ Electroactivity in Glyme‐Based Electrolytes: A First Principles Study

AbstractThe electrochemical activity of solvated Ca2+ in glyme‐based electrolytes is investigated using grand canonical density functional theory approach and Fukui functions. The obtained results reveal that the length of glyme molecules has little effect on the reduction potentials, but has significant impacts on the effective electron transfer process. In short chain glymes, the transferred electron is located on a Ca2+ center and the organic part of the solvation sphere, leading to a direct Ca2+ reduction and a partial degradation of the glyme molecules. As the glyme's length increases, the reduction process turns into the formation of solvated electrons rather than Ca2+ reduction, unless a partial desolvation occurs. Consequently, an effective Ca2+ reduction in long chain glyme‐based electrolytes is controlled by a (partial) desolvation of the solvation sphere. These results can be used as guiding information to design new electrolytes having the Ca2+ reduction potential in an accessible voltage range together with an effective Ca2+ reduction process. The methodology developed in this study can be universally applied to investigate the thermodynamic and kinetic properties of other battery systems using metal anodes, which might lead to a paradigm shift in the design of prospective electrolytes for future battery technologies.

Band relaxation triggered by modulational instability in topological photonic lattices

Modulational instability in topological photonic lattices enables the selective population of energy bands and generation of steady-state wavefields with well-defined topological invariants. This provides a way to measure bulk topological invariants, which determine the number of robust edge modes appearing at the lattice edges via the bulk-edge correspondence. Here we study numerically the process of wave thermalization arising from modulational instability in topological bands. We apply a grand canonical approach to compute the effective temperature β and chemical potential μ of the steady-state wavefields. The steady-state wavefields exhibit a strong wavevector k -dependence of β and μ throughout the Brillouin zone, suggesting the existence of a long-lived pre-thermal phase and the absence of thermalization for the moderate propagation times accessible using topological photonic lattices.

Electrocatalytic Hydrogen Evolution at Full Atomic Utilization over ITO-Supported Sub-nano-Ptn Clusters: High, Size-Dependent Activity Controlled by Fluxional Pt Hydride Species.

A combination of density functional theory (DFT) and experiments with atomically size-selected Ptn clusters deposited on indium-tin oxide (ITO) electrodes was used to examine the effects of applied potential and Ptn size on the electrocatalytic activity of Ptn (n = 1, 4, 7, and 8) for the hydrogen evolution reaction (HER). Activity is found to be negligible for isolated Pt atoms on ITO, increasing rapidly with Ptn size such that Pt7/ITO and Pt8/ITO have roughly double the activity per Pt atom compared to atoms in the surface layer of polycrystalline Pt. Both the DFT and experiment find that hydrogen under-potential deposition (Hupd) results in Ptn/ITO (n = 4, 7, and 8) adsorbing ∼2H atoms/Pt atom at the HER threshold potential, equal to ca. double the Hupd observed for Pt bulk or nanoparticles. The cluster catalysts under electrocatalytic conditions are hence best described as a Pt hydride compound, significantly departing from a metallic Pt cluster. The exception is Pt1/ITO, where H adsorption at the HER threshold potential is energetically unfavorable. The theory combines global optimization with grand canonical approaches for the influence of potential, uncovering the fact that several metastable structures contribute to the HER, changing with the applied potential. It is hence critical to include reactions of the ensemble of energetically accessible PtnHx/ITO structures to correctly predict the activity vs Ptn size and applied potential. For the small clusters, spillover of Hads from the clusters to the ITO support is significant, resulting in a competing channel for loss of Hads, particularly at slow potential scan rates.

Sulfur-deficient edges as active sites for hydrogen evolution on MoS2.

A grand-canonical approach is employed to calculate the voltage-dependent activation energy and estimate the kinetics of the hydrogen evolution reaction (HER) on intrinsic sites of MoS2, including edges of varying S-coverage as well as S-vacancies on the basal plane. Certain edge configurations are found to be vastly more active than others, namely S-deficient edges on the Mo-termination where, in the fully S-depleted case, HER can proceed with activation energy below 0.5 eV at an electrode potential of 0 V vs. SHE. There is a clear distinction between the performance of Mo-rich and S-rich adsorption sites, as HER at the latter sites is characterized by large (generally above 1.5 eV) Heyrovsky and Tafel energy barriers despite near-thermoneutral hydrogen adsorption energy. Thus, exposing Mo-atoms on the edges to which hydrogen can directly bind is crucial for efficient hydrogen evolution. While S-vacancies on the basal plane do expose Mo-rich sites, the energy barriers are still significant due to high coordination of the Mo atoms. Kinetic modelling based on the voltage-dependent reaction energetics gives a theoretical overpotential of 0.25 V and 1.09 V for the Mo-edge with no S atoms and the weakly sulfur-deficient (2% S-vacancies) basal plane, respectively, with Volmer-Heyrovsky being the dominant pathway. These values coincide well with reported experimentally measured values of the overpotential for the edges and basal plane. For the partly Mo-exposed edges, the calculated overpotential is 0.6-0.7 V while edges with only S-sites give overpotential exceeding that of the basal plane. These results show that the overpotential systematically decreases with increased sulfur-deficiency and reduced Mo-coordination. The fundamental difference between Mo- and S-rich sites suggests that catalyst design of transition metal dichalcogenides should be focused on facilitating and modifying the metal sites, rather than activating the chalcogen sites.

Interpretation of particle yields in pp interactions at √S = 8.8, 12.3 and 17.3 GeV within statistical hadronization model

The statistical hadronization model ThermalFist was applied to numerous hadron yields measured in p+p collisions at √S = 8.8, 12.3 and 17.3 GeV, including recently published yields ofϕ-mesons, measured by the NA61/SHINE Collaboration. We consistently used the energy-dependent widths of Breit-Wigner mass distributions of hadronic resonances, as this approach was generally found to provide better agreement with experimental data. The well-established experimentalϕmeson yields are consequently accounted for (although neglecting this particle was found to improve the fit quality). The canonical treatment of particles with open strangeness with the grand canonical approach for non-strange particles gave a moderately reasonable agreement with the measured yields, only when the volume of strange particles was allowed to vary freely. In all the studied cases this volume is found to be greater than the canonical one.

Reversible vs Standard Hydrogen Electrode Scale in Interfacial Electrochemistry from a Theoretician’s Atomistic Point of View

It is a general notion in interfacial electrochemistry that the stability of adsorbate phases that only contain hydrogen atoms should be independent of the pH value of the electrolyte on the scale of the reversible hydrogen electrode, whereas the stability of adsorbate phases that do not contain any hydrogen should be independent of the pH value on the scale of the standard hydrogen electrode. In this Perspective, it will be argued on the basis of a grand-canonical approach that such a Nernstian behavior can only be reproduced if the free energy of the adsorbate phase is independent of the electrochemical control parameters. In general, this should not be true, so that the Nernstian behavior should be the exception rather than the rule. Still, structural and chemical factors will be discussed that might lead to a Nernstian behavior. This requires an analysis of the electrochemical electrolyte/electrode interface on the atomistic level. At the same time, this analysis also provides a guideline for the validity of grand-canonical simulations using the concept of the computational hydrogen electrode in which the dependence of the energy of adsorbate phases on pH and electrode potential is neglected.

Fermions on a torus knot

In this work, we investigate the effects of a nontrivial topology (and geometry) of a system considering \textit{interacting} and \textit{noninteracting} particle modes, which are restricted to follow a closed path over the torus surface. In order to present a prominent thermodynamical investigation of this system configuration, we carry out a detailed analysis using statistical mechanics within the grand canonical ensemble approach to deal with \textit{noninteracting} fermions. In an analytical manner, we study the following thermodynamic functions in such context: the Helmholtz free energy, the mean energy, the magnetization and the susceptibility. Further, we take into account the behavior of Fermi energy of the thermodynamic system. Finally, we briefly outline how to proceed in case of \textit{interacting} fermions.

Simulations of the Electrochemical Oxidation of Pt Nanoparticles of Various Shapes

The activity and stability of a platinum nanoparticle (NP) are not only affected by its size but additionally depend on its shape. To this end, simulations can identify structure–property relationships to make a priori decisions on the most promising structures. While the activity is routinely probed by electronic structure calculations on simplified surface models, modeling the stability of NP model systems in electrochemical reactions is challenging due to the long time scale of relevant processes such as oxidation beyond the point of reversibility. In this work, a routine for simulating electrocatalyst stability is presented. The procedure is referred to as GREG after its main ingredients─a grand-canonical simulation approach using reactive force fields to model electrochemical reactions as a function of the galvanic cell potential. The GREG routine is applied to study the oxidation of 3 nm octahedral, cubic, dodecahedral, cuboctahedral, spherical, and tetrahexahedral platinum NPs. The oxidation process is analyzed using adsorption isobars as well as interaction energy heat maps that provide the basis for constructing electrochemical phase diagrams. Onset potentials for surface oxidation increase in the sequence cube ≈ dodecahedron ≤ octahedron ≤ tetrahexahedron < sphere < cuboctahedron, establishing a relationship between the oxidation behavior and the surface facet structure. The electrochemical results are rationalized using structural and electronic analyses.

Deprotonation and cation adsorption on the NiOOH/water interface: A grand-canonical first-principles investigation

Nickel-based oxides are highly active, cost-effective materials for the oxygen evolution reaction in alkaline conditions. Recent experimental studies have revealed the importance of surface deprotonation and alkali metal cation adsorption on the activity of Ni oxide surfaces, in contact with aqueous alkaline electrolyte. As a first step to elucidate the role of the alkali adsorption for the activity, we performed first-principles electronic structure calculations to address the stable surface structures of β-NiOOH(0001) as a function of the operating conditions in an electrochemical environment. We present a grand-canonical approach to compute the surface Pourbaix diagram of the β-NiOOH/water interface for the processes of deprotonation and alkali metal cation adsorption. The results of this study emphasize the importance of double-layer effects, including the adsorbate-induced change of surface dipole moments and the rearrangement of water molecules due to their strong interaction with the adsorbed species, for the most stable interface structure.

Multi-objective optimization of alkali/alkaline earth metals doped graphyne for ultrahigh-performance CO2 capture and separation over N2/CH4

Adsorbents with excellent CO2 capture and separation performances are critical in reducing the excessive CO2 concentration in the atmosphere. Herein, alkali/alkaline earth metals doped graphynes (AMn-GYs, AM = Li, Na, K, Mg and Ca; GY = graphyne; n = 0.5, 1, and 2) were evaluated by employing grand canonical Monte Carlo and density functional theory approaches. The results showed that AMs were strongly bonded on GY with binding energies of −0.09 to −2.52 eV and diffusion barriers of 5.20–16.32 eV. Electronic structure analyses proved that there was a strong covalent bond, large charge transfer, and distinct orbital overlap characters between the AMs and GY, thus constructing a stable and feasible gas adsorption environment. Among all structures, AM1-GYs with one AM doping in a GY unit cell displayed the best CO2 adsorption behavior. Thereafter, Li1/Na1/K1-GY with a pore size of 6.60 Å and Mg1/Ca1-GY with a pore size of 6.50 Å were screened as the potential adsorbents. In comparison, the best performing Ca1-GY had an ultra-high CO2 adsorption capacity of 9.01 mmol/g at 298 K and 1 bar, which was superior to most of the previously reported adsorbents. At 298 K and 1 bar, the CO2 selectivity over N2/CH4 for Ca1-GY reached 2246 and 5602, respectively. Interaction and gas distribution analysis confirmed that comparing to other AM1-GYs, Ca1-GY has a stronger affinity with CO2 and larger isosteric heat differences between CO2 and other gases, rendering Ca1-GY to possess excellent adsorption capacity and selectivity.

Ab initio modelling of interfacial electrochemical properties: beyond implicit solvation limitations

First-principles calculations are an important tool to investigate the complex processes occurring at solid/liquid interfaces which are at the heart of modern technologies. Currently, capturing the whole electrochemical environment at an interface, including the applied potential and solvation, still remains challenging as it necessitates to couple different approaches whose interactions are not fully understood. In this work, a grand canonical density functional theory approach is coupled with solvation models to investigate the electrochemical interfaces under applied potential. We show that a parametrized polarizable continuum model (PCM) which represent solvation in a mean field approach by a continuous polarizable media, possesses catastrophic limitations for the modelling of ionic and charged interfaces. We reveal the origin of PCM instabilities under chemical or electrochemical strong oxidation to be the consequence of a phase transition in the surface Li electronic structure. Thus, PCM undergoes an unphysical response to this phase transition by penetrating within the atomic radius of surface Li atoms. To recover a physical response, an explicit first solvation shell has to be included in addition to the PCM in order to properly describe the electrochemistry of the interface. The Fukui functions show that the first solvation shell becomes involved in the redox process as solvent electron doublet is transferred to the acidic Li+. If another explicit solvent layer is added, the interface electrochemical properties become independent of the PCM parameters: in particular capacitance can then be computed from a parameter-free electrochemical approach. This is an important conclusion as the experimental electrochemical capacitance are not easily found and thus the parametrization of the PCM for electrochemical interface can be difficult. This approach can easily be applied to investigate electrochemical properties at the atomic scale and generalized to any electrochemical device for which interfaces play a crucial role.

In Search of the Active Sites for the Selective Catalytic Reduction on Tungsten-Doped Vanadia Monolayer Catalysts Supported by TiO2

Tungsten-doped vanadia-based catalysts supported on anatase TiO2 are used to reduce hazardous NO emissions through the selective catalytic reduction of ammonia, but their exact atomistic structure is still largely unknown. In this computational study, the atomistic structure of mixed tungsta-vanadia monolayers on TiO2 support under typical operating conditions has been addressed by periodic density functional theory calculations. The chemical environment has been taken into account in a grand-canonical approach. We evaluate the stable catalyst structures as a function of the oxygen chemical potential and vanadium and tungsten concentrations. Thus we determine structural motifs of tungsta-vanadia/TiO2 catalysts that are stable under operating conditions. Furthermore, we identify active sites that promise high catalytic activity for the selective catalytic reduction by ammonia. Our calculations reveal the critical role of the stoichiometry of the tungsta-vanadia layers with respect to their catalytic activity in the selective catalytic reduction.

Grand canonical ensemble approach to electrochemical thermodynamics, kinetics, and model Hamiltonians

The unique feature of electrochemistry is the ability to control reaction thermodynamics and kinetics by the application of electrode potential. Recently, theoretical methods and computational approaches within the grand canonical ensemble (GCE) have enabled to explicitly include and control the electrode potential in first principles calculations. In this review, recent advances and future promises of GCE density functional theory and rate theory are discussed. Particular focus is devoted to considering how the GCE methods either by themselves or combined with model Hamiltonians can be used to address intricate phenomena such as solvent/electrolyte effects and nuclear quantum effects to provide a detailed understanding of electrochemical reactions and interfaces.

Grand-canonical approaches to understand structures and processes at electrochemical interfaces from an atomistic perspective

Electrochemical interfaces between an electrode and an electrolyte are often covered by ions from the solution. These adsorbed ions can strongly modify the properties of the interfaces. Furthermore, in electrocatalysis, the reacting species typically have to get into contact with the surface of the electrocatalyst, where the reaction then proceeds. Hence the understanding of the interaction of solvated species with electrode surfaces and the determination of the resulting adsorbate structures as a function of electrochemical control parameters such as electrode potential and electrolyte concentrations are crucial in electrochemistry. Here, grand-canonical theoretical approaches to derive adsorbate structures at electrochemical interfaces from an atomistic perspective will be reviewed. Special emphasis will be put on the distinction between the validity of the approach and the approximations that are typically made when using this approach.

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.