Constant Potential Model Research Articles

Influence of Copper Surfaces on CO2 vs. CO C−C Coupling Efficiency

AbstractCO2 electrochemical reduction (CO2ER) powered by renewable electricity is critical for transitioning to a carbon‐neutral society by transforming CO2 into essential commodities and fuels. The formation of multi‐carbon compounds through C−C coupling reactions is crucial due to their high energy density and broad industrial uses. Traditionally, C−C coupling was believed to occur through the reaction of *CO (surface‐bound CO) with *C1 intermediates (surface‐bound hydrocarbons with one carbon atom produced during CO2ER). In this study, we used DFT calculations combined with a constant electrode potential model to discover a preference for CO2+*C1 over conventional *CO+*C1 coupling on three commonly observed copper surfaces including Cu(111), Cu(110), and Cu(100). This result demonstrates that CO2 is a more efficient carbon source than *CO for coupling with *C1. Among the nine *C1 species investigated, *CHO, *CHOH, *C, *CH, and *CH2 show greater reactivity towards CO2+*C1 couplings on all the surfaces. Thus, enhancing CO2ER efficiency necessitates increasing the surface concentrations of these five *C1 intermediates, and several strategies have been proposed to accomplish this goal.

Selective methanol production via CO2 reduction on Cu2O revealed by micro-kinetic study combined with constant potential model

High efficiency electrocatalysis of greenhouse gas CO2 to liquid fuel methanol attracts great attentions that allows energy transformation from renewable electric energy to storable chemical energy. Catalytically converting CO2 to methanol using green hydrogen is a promising pathway to achieve carbon neutrality. In this work, the catalytic activity and product selectivity of the electrochemical CO2 reduction reaction on Cu2O were studied using a micro-kinetic model based on Marcus charge transfer theory. The constant potential model under the grand-canonical ensemble enables the accurate description of binding energies and ground-state charge transfer upon surface adsorption as a function of electrode potential. Firstly, the potential-dependent activation energies and rate constants of all possible elementary reactions involved in CO2 reduction are calculated. Then, the surface coverage and its derivative can be obtained in a steady-state approximation. Finally, the total reaction rate and partial reaction rate can be deduced, allowing for direct comparison with catalytic activity (current density) and product selectivity (Faradaic efficiency). It is found that CH3OH is the dominant product on the Cu2O(111) surface, while CO is the main product on the Cu2O(110) surface. Based on the derived total and partial reaction rates under the steady-state approximation, it is demonstrated that Cu2O(111) exhibits the highest electrocatalytic activity and methanol selectivity at U = −0.6 V vs. SHE. This research presents a methodology for predicting apparent electrocatalytic performance from microscopic reaction energy calculations, which can be applied to other important electrocatalytic reaction mechanisms and performance predictions.

Exploring Nitrogen Reduction Reaction Mechanisms with Graphyne-Confined Single-Atom Catalysts: A Computational Study Incorporating Electrode Potential and pH.

This study reconciles discrepancies between practical electrochemical conditions and theoretical density functional theory (DFT) frameworks, evaluating three graphyne-confined single-atom catalysts (Mo-TEB, Mo@GY, and Mo@GDY). Using both constant charge models in vacuum and constant potential models with continuum implicit solvation, we closely mimic real-world electrochemical environments. Our findings highlight the crucial role of explicitly incorporating electrode potential and pH in the constant potential model, providing enhanced insights into the nitrogen reduction reaction (NRR) mechanisms. Notably, the superior NRR performance of Mo-TEB is attributed to the d-band center's proximity to the Fermi level and enhanced magnetic moments at the atomic center. This research advances our understanding of graphyne-confined single-atom catalysts as effective NRR platforms and underscores the significance of the constant potential model for accurate DFT studies of electrochemical reactions.

Efficient screening and catalytic mechanism of TM@β-Te for nitrogen reduction reaction

At present, nitrogen reduction reaction (NRR) has become one critical method for NH3 production through the single-atom catalyst (SAC). A variety of TM@β-Te SACs, constructed by 28 transition metal (TM) atoms anchoring on monovacant β-Te substrate, are systematically investigated by using DFT calculations. An efficient “six-step” screening scheme is proposed to screen out potential NRR catalysts, during which the implicit and explicit solvent models are involved to evaluate competitive reactions of H2O and H+. The final selected (Ta, W)@β-Te catalysts have limiting potentials (UL) of −0.32 V and −0.37 V, respectively. Three intrinsic descriptors of φ (the ratio of number of valence electrons and electronegativity of TM atom), ΔG∗N(adsorption energy of a single N atom on the substrate) and ICOHP (Crystal orbital Hamiltonian integrals for TM-N bonds) are proposed and their correlations with UL are investigated to expound the catalytic activity and mechanism. The relationships of dN≡N ∼ φ, ΔG∗N2∼ φ, ΔG∗N∼ φ and ICOHP ∼ φ resemble “volcanoes”, where (Ta, W)@β-Te are located near the vertex as potential catalysts, which can be verified by scaling relationship of ICOHP and ΔG∗N. Moreover, the UL ∼ φ, UL ∼ ΔG∗Nand UL ∼ ICOHP can be used to determine the potential catalysts from rough catalyst screening to accurate determination of potential determining step (PDS) in catalytic reaction. The constant potential model is adopted to investigate the influences of electrode potentials on adsorption strength of NRR intermediates. This work is informative for the research of NRR process and catalyst design of monoalkenes, which offers an efficient and dependable approach for screening excellent NRR catalysts and revealing the origin of catalytic activity.

Molecular dynamics simulations of ionic liquids confined into MXenes

Two-dimensional (2D) transition metal carbides known as MXenes have been extensively investigated as electrode material of electrochemical devices, including supercapacitors. Here we present a detailed computational study of ionic liquids in contact with Ti3C2F2, both at planar surface and under confinement. The simulations employ an extension of the constant potential model (CPMχ) that can properly deal with materials composed of chemical elements with different electronegativities. The average partial charges of MXene atoms calculated with CPMχ are in excellent agreement with the ones obtained by DFT calculations. The differential capacitance and the charging mechanisms are thoroughly analyzed for two ionic liquids with a common cation, [EMIM][BF4] and [EMIM][NTf2]. By varying the MXene interlayer dimension, the best performance in terms of charge storage is obtained in electrodes with 12.6 Å spacing, with outperformance of [EMIM][BF4]-based cells.

Exploring the impact of S-doped Fe-N-C materials on the ORR mechanism within a constant potential solvation model

The widespread application of S doping in Fe-N-C materials aims to enhance the catalytic activity for oxygen reduction reactions (ORR). However, the current doping strategies are primarily centered on the first coordination layer encompassing Fe atoms. Consequently, this study employs first-principles calculations to compute the formation and binding energies of FeN4 doped with S atom. It further delves into the influence of diverse doping sites on catalyst stability and meticulously analyzes the configurations and corresponding ORR activities of four catalysts, namely FeN4S-N (Number=0∼3), utilizing a constant-potential implicit solvent model to simulate authentic electrocatalytic environments. The findings reveal that under vacuum conditions, FeN4S1 exhibits the utmost ORR activity, boasting a potential of 0.53 V. Conversely, within the constant-potential implicit solvation model, FeN4S2 emerges as the catalyst with the highest ORR activity, achieving a potential of 0.39 V. Therefore, calculations leveraging the constant-potential solvation model offer more realistic insights into catalyst design, thereby guiding the development of superior catalysts.

Diffusiophoretic Behavior of Polyelectrolyte-Coated Particles.

Diffusiophoresis, the movement of particles under a solute concentration gradient, has practical implications in a number of applications, such as particle sorting, focusing, and sensing. For diffusiophoresis in an electrolyte solution, the particle velocity is described by the electrolyte relative concentration gradient and the diffusiophoretic mobility of the particle. The electrolyte concentration, which typically varies throughout the system in space and time, can also influence the zeta potential of particles in space and time. This variation affects the diffusiophoretic behavior, especially when the zeta potential is highly dependent on the electrolyte concentration. In this work, we show that adsorbing a single bilayer (or 4 bilayers) of a polyelectrolyte pair (PDADMAC/PSS) on the surface of microparticles resulted in effectively constant zeta potential values with respect to salt concentration throughout the experimental range of salt concentrations. This allowed a constant potential model for diffusiophoretic transport to describe the experimental observations, which was not the case for uncoated particles in the same electrolyte system. This work highlights the use of simple polyelectrolyte pairs to tune the zeta potential and maintain constant values for precise control of diffusiophoretic transport.

The Special Activity of Stone–Wales Defect Graphene for the Oxygen Reduction Reaction: A Comparison Study between the Charge-Neutral Model and the Constant Potential Model Calculated by Density Functional Theory

The Special Activity of Stone–Wales Defect Graphene for the Oxygen Reduction Reaction: A Comparison Study between the Charge-Neutral Model and the Constant Potential Model Calculated by Density Functional Theory

Comparative Study of Computational Hydrogen Electrodes and Constant Electrode Potential Models Applied to Electrochemical Reduction of CO2 and Oxygen Evolution Reaction on Metal Oxides/Copper Catalysts

Comparative Study of Computational Hydrogen Electrodes and Constant Electrode Potential Models Applied to Electrochemical Reduction of CO₂ and Oxygen Evolution Reaction on Metal Oxides/Copper Catalysts

Sodium-ion electrolytes based on poly-ethylene oxide oligomers in dual-carbon cells: Anion size drives the charging behavior

Sodium-ion dual-carbon electrochemical cells are an environmentally friendly technology for energy storage purposes. In such systems, the migration of mutual ions in both electrodes is crucial for performance and determines the cell’s behavior. To investigate this effect, we have performed force-field molecular dynamics simulations of dual-carbon sodium-ion systems containing poly-ethylene oxide (PEO6) as the solvent and two different anions, bis(trifluoromethanesulfonyl)imide (TFSI−) and bis(fluorosulfonyl)imide (FSI−). We used a constant potential model that allows simulating the charging behavior of these cells at the potential differences, ΔΨ=1, 2, 3, and 5 volt (V). Our results showed that considering the neat solution, NaTFSIPEO6 exhibited the best transport properties. However, NaFSIPEO6 is a better choice of electrolyte to be employed in dual-carbon cells since it provides higher and faster charge accumulation. Structural analysis also confirmed that the system containing NaFSIPEO6 stored more ions inside their respective electrodes with Na+ cations having fewer molecules composing their first solvation shell. Overall, our findings suggest that the smaller molecular volume of the FSI− anion is the key factor to properly fill the positive electrode, and the NaFSIPEO6 combination is the best choice for electrolytes of dual-carbon cells.

Continuous constant potential model for describing the potential-dependent energetics of CO2RR on single atom catalysts.

In this work, we have proposed a Continuous Constant Potential Model (CCPM) based on grand canonical density functional theory for describing the electrocatalytic thermodynamics on single atom electrocatalysts dispersed on graphene support. The linearly potential-dependent capacitance is introduced to account for the net charge variation of the electrode surface and to evaluate the free energetics. We have chosen the CO2 electro-reduction reaction on single-copper atom catalysts, dispersed by nitrogen-doped graphene [CuNX@Gra (X = 2, 4)], as an example to show how our model can predict the potential-dependent free energetics. We have demonstrated that the net charges of both catalyst models are quadratically correlated with the applied potentials and, thus, the quantum capacitance is linearly dependent on the applied potentials, which allows us to continuously quantify the potential effect on the free energetics during the carbon dioxide reduction reaction instead of confining it to a specific potential. On the CuN4@Gra model, it is suggested that CO2 adsorption, coupled with an electron transfer, is a potential determining step that is energetically unfavorable even under high overpotentials. Interestingly, the hydrogen adsorption on CuN4@Gra is extremely easy to occur at both the Cu and N sites, which probably results in the reconstruction of the CuN4@Gra catalyst, as reported by many experimental observations. On CuN2@Gra, the CO2RR is found to exhibit a higher activity at the adjacent C site, and the potential determining step is shifted to the *CO formation step at a wide potential range. In general, CCPM provides a simple method for studying the free energetics for the electrocatalytic reactions under constant potential.

Theoretical Study on the Mechanism of CO* Electrochemical Reduction on Cu(111) under Constant Potential

In order to understand the mechanism of the electrochemical reduction of CO* on Cu(111), which competitively generates two intermediates, CHO* and COH*, we performed a first principles calculation on these two electrocatalytic reactions, including the solvent effect and imposing a constant potential. The transition states of the two reactions under constant potential conditions were located by the electrochemical nudged elastic band (eNEB) method and the charge effect in the two reactions was elucidated by charge correction in the constant potential model and Bader charge analysis. It was found that the two reactions have different potential dependencies and involve different degrees of partial charge transfer. In addition, we confirmed that the COH* reaction pathway exists only in a certain potential range when using the implicit solvent model.

Unveiling the mutual ion-storage mechanism of dual-carbon NaTFSI-WiSE Cells: A molecular dynamics study

The application of sodium cation in electrochemical devices has been considered an alternative technology for energy storage applications. Water-in-salt electrolyte (WiSE) combined with dual-carbon electrodes can be considered an emerging eco-friendly alternative, however, several problems remain in debate, e.g., what is the ion-storage mechanism? Thus, we carried out molecular dynamics investigations considering three different dual-carbon sodium-WiSE cells at different salt/water concentrations, namely, 4.50, 6.76, and 9.25molkg−1. Furthermore, we employed the constant potential model to simulate the charging behavior of these systems at two potential differences, namely, ΔΨ=1V and 2V. The best results for the total accumulated charge at 2V were from the 6.76m and 9.25m systems. From the analysis of the evolution of the local charge on the electrodes, we identified a crucial role in the mutual ions migration inside both the positive and negative sides of the dual-carbon. In general, cations are driven into the pores coordinated by water molecules and keep their solvation shell during all the simulation time. Except when they are highly confined into narrow pores, where they have fewer water molecules in their surroundings. Therefore, from our simulations and analyses, the storage mechanisms are associated with sodium adsorption together with H2O co-embedding.

Single-Atom Electrocatalysis for Hydrogen Evolution Based on the Constant Charge and Constant Potential Models.

DFT calculations are performed at constant charge, while practical electrochemical reactions often take place under constant potential. To unravel the effect of the model difference on single-atom electrocatalysis, we implement benchmarked DFT and grand-canonical DFT calculations to systematically investigate the hydrogen adsorption on 99 single-atom M-NxCy motifs. We find that the initial electrode potentials for all M-NxCy are negative, leading to the loss of system electrons once their electrode potentials are fixed at 0 V/SHE. We prove that the quantitive difference of ΔG(*H) between the CCM and CPM is proportional to the square difference of total charge change before and after H adsorption, which originates from the adjustment of electronic occupation states. Our work provides theoretical insight into the differential capacitance model in the graphene-confining SACs for the HER and emphasizes the importance of CPM for in silico design of electrocatalysts.

Energy and power performances of binary mixtures of ionic liquids in planar and porous electrodes by molecular dynamics simulations

Binary mixtures of ionic liquids are interesting alternatives to tailor ionic liquids properties. Some of them have been proposed as electrolytes for supercapacitors. Herein, we performed molecular dynamics simulations of planar and porous electrodes with binary mixtures of ionic liquids comprising the 1-ethyl–3-methyl–imidazoliumbis(trifluoromethane–sulfonyl)imide ([EMIM][NTf2]) and 1-ethyl–3-methyl–imidazoliumtetrafluoroborate ([EMIM][BF4]), increasing the mole fraction of the latter (xBF4) from 0 to 1. The energy densities calculated from the simulations increase monotonically with xBF4, accordingly with available experimental results [Angew. Chem. Int. Ed. 2015, 54, 1 – 5]. Considering that the electrode simulations were dealt with the constant potential model, the characteristic charging times were calculated for planar and porous electrodes. The devices containing only [EMIM][NTf2] charge slower than electrolytes with xBF4 > 0.0, and the fastest charging happens in xBF4 = 1.0 V. These features are related to the higher [NTf2]-electrode interaction and also to the smaller size of [BF4]−. For porous electrode, the calculated Ragone plot indicates that [EMIM][BF4] outperforms all the other electrolytes with a voltage of 3.0 V in terms of energy and power densities. In the system of best performance, there are considerable contributions of co-ion desorption and counter-ion adsorption mechanisms in the negative and positive electrodes, respectively.

Examination of the Brønsted-Evans-Polanyi relationship for the hydrogen evolution reaction on transition metals based on constant electrode potential density functional theory.

In the search for efficient and inexpensive electrocatalysts for the hydrogen evolution reaction (HER), the hydrogen binding energy is often used as a descriptor to represent the catalytic activity. The success of this approach relies on the Brønsted-Evans-Polanyi (BEP) relationship. In this study, we used constant electrode potential density functional theory calculations to examine this relationship. Eight fcc metals with a low hydrogen adsorption concentration of 1/9 were used as the model systems. We found that the HER kinetic barriers are indeed correlated to the . Both the s of the hollow site and less favourable top site correlate to the kinetic barriers; however, the correlation is better for the latter. This behaviour leads to a set of equations for estimating the HER kinetic barriers with improved accuracy that can be used to predict the HER performance of the materials with a low hydrogen adsorption concentration. This work demonstrates the importance of calculating the of a suitable adsorption site to establish good BEP relationships.

Understanding potential-dependent competition between electrocatalytic dinitrogen and proton reduction reactions

A key challenge to realizing practical electrochemical N2 reduction reaction (NRR) is the decrease in the NRR activity before reaching the mass-transfer limit as overpotential increases. While the hydrogen evolution reaction (HER) has been suggested to be responsible for this phenomenon, the mechanistic origin has not been clearly explained. Herein, we investigate the potential-dependent competition between NRR and HER using the constant electrode potential model and microkinetic modeling. We find that the H coverage and N2 coverage crossover leads to the premature decrease of NRR activity. The coverage crossover originates from the larger charge transfer in H+ adsorption than N2 adsorption. The larger charge transfer in H+ adsorption, which potentially leads to the coverage crossover, is a general phenomenon seen in various heterogeneous catalysts, posing a fundamental challenge to realize practical electrochemical NRR. We suggest several strategies to overcome the challenge based on the present understandings.

Comparing Graphite and Graphene Oxide Supercapacitors with a Constant Potential Model

Electric double-layer capacitors store energy because of the adsorption of ions on the surface of electrodes. A realistic model to describe the electrolyte–electrode interface is based on the const...

(Invited) Quantum Mechanical Screening of Metal-N4-Functionalized Graphenes for Electrochemical Anodic Oxidation of Light Alkanes to Oxygenates

Developing processes that allow partial oxidation of light alkanes (C1-C4) to more valuable oxygenates is important from both industrial and academic perspectives. In this study, quantum mechanics combined with a constant potential model were employed to evaluate the ability of metal-N4-functionalized graphene (gMN4) to catalyze anodic partial oxidation of light alkanes to oxygenates via electrochemical means while considering both the reactivity and selectivity. During the reaction, reactive oxo (*O) is generated through water electrochemical oxidation. This reactive oxo is used to oxidize light alkanes (represented by methane and propane). Based on investigating the systems with different Ms (Cr, Mn, Fe, Co, Ru, Rh, Os, and Ir) in a wide range of electrode potentials (U, 0.0 to 2.0 VSHE) and pH values (0.0 to 14.0), only gIrN4 and gFeN4 were capable of catalyzing this oxidation with acceptable reaction rates. The other catalysts were unable to form *O or inert to C-H bonds. Both alkanes can be oxidized but the rate for methane is slower. gIrN4 oxidizes methane to formaldehyde under proper Us. For propane, this catalyst generates iso-propanol at low Us and acetone at high Us. gFeN4 only oxidizes propane to acetone. Our theoretical investigation along with known experimental results suggest a high probability for experimental realization of this anodic partial oxidation, which would allow for utilization of natural gas discovered in remote oil fields.

Scalar field solutions for anisotropic universe models in various gravitation theories

In this study, we have investigated homogeneous and anisotropic Marder and Bianchi type I universe models filled with normal and phantom scalar field matter distributions with [Formula: see text] in [Formula: see text] gravitation theory (T. Harko et al., Phys. Rev. D 84 (2011) 024020). In this model, [Formula: see text] is the Ricci scalar and [Formula: see text] is the trace of energy–momentum tensor. To obtain exact solutions of modified field equations, we have used anisotropy feature of the universe and different scalar potential models with [Formula: see text] function. Also, we have obtained general relativity (GR) solutions for normal and phantom scalar field matter distributions in Marder and Bianchi type I universes. Additionally, we obtained the same scalar function values by using different scalar field potentials for Marder and Bianchi type I universe models with constant difference in [Formula: see text] gravity and GR theory. From obtained solutions, we get negative cosmological term value for [Formula: see text] constant scalar potential model with Marder and Bianchi type I universes in GR theory. These results agree with the studies of Maeda and Ohta, Aktaş et al. also Biswas and Mazumdar. Finally, we have discussed and compared our results in gravitation theories.