Hierarchical Modeling of the Local Reaction Environment in Electrocatalysis

ConspectusElectrocatalytic reactions, such as oxygen reduction/evolution reactions and CO2 reduction reaction that are pivotal for the energy transition, are multistep processes that occur in a nanoscale electric double layer (EDL) at a solid-liquid interface. Conventional analyses based on the Sabatier principle, using binding energies or effective electronic structure properties such as the d-band center as descriptors, are able to grasp overall trends in catalytic activity in specific groups of catalysts. However, thermodynamic approaches often fail to account for electrolyte effects that arise in the EDL, including pH, cation, and anion effects. These effects exert strong impacts on electrocatalytic reactions. There is growing consensus that the local reaction environment (LRE) prevailing in the EDL is the key to deciphering these complex and hitherto perplexing electrolyte effects. Increasing attention is thus paid to designing electrolyte properties, positioning the LRE at center stage. To this end, unraveling the LRE is becoming essential for designing electrocatalysts with specifically tailored properties, which could enable much needed breakthroughs in electrochemical energy science.Theory and modeling are getting more and more important and powerful in addressing this multifaceted problem that involves physical phenomena at different scales and interacting in a multidimensional parametric space. Theoretical models developed for this purpose should treat intrinsic multistep kinetics of electrocatalytic reactions, EDL effects from subnm scale to the scale of 10 nm, and mass transport phenomena bridging scales from <0.1 to 100 μm. Given the diverse physical phenomena and scales involved, it is evident that the challenge at hand surpasses the capabilities of any single theoretical or computational approach.In this Account, we present a hierarchical theoretical framework to address the above challenge. It seamlessly integrates several modules: (i) microkinetic modeling that accounts for various reaction pathways; (ii) an LRE model that describes the interfacial region extending from the nanometric EDL continuously to the solution bulk; (iii) first-principles calculations that provide parameters, e.g., adsorption energies, activation barriers and EDL parameters. The microkinetic model considers all elementary steps without designating an a priori rate-determining step. The kinetics of these elementary steps are expressed in terms of local concentrations, potential and electric field that are codetermined by EDL charging and mass transport in the LRE model. Vital insights on electrode kinetic phenomena, i.e., potential-dependent Tafel slopes, cation effects, and pH effects, obtained from this hierarchical framework are then reviewed. Finally, an outlook on further improvement of the model framework is presented, in view of recent developments in first-principles based simulation of electrocatalysis, observations of dynamic reconstruction of catalysts, and machine-learning assisted computational simulations.

The pH-Induced Increase of the Rate Constant for HER at Au(111) in Acid Revealed by Combining Experiments and Kinetic Simulation

Origins of pH effects on the kinetics of electrocatalytic reactions involving the transfer of both protons and electrons, including the hydrogen evolution reaction (HER) considered in this study, are heatedly debated. By taking the HER at Au(111) in acid solutions of different pHs and ionic concentrations as the model systems, herein, we report how to derive the intrinsic kinetic parameters of such reactions and their pH dependence through the measurement of j-E curves and the corresponding kinetic simulation based on the Frumkin-Butler-Volmer theory and the modified Poisson-Nernst-Planck equation. Our study reveals the following: (i) the same set of kinetic parameters, such as the standard activation Gibbs free energy, charge transfer coefficient, and Gibbs adsorption energy for Had at Au(111), can simulate well all the j-E curves measured in solutions with different pH and temperatures; (ii) on the reversible hydrogen electrode scale, the intrinsic rate constant increases with the increase of pH, which is in contrast with the decrease of the HER current with the increase of pH; and (iii) the ratio of the rate constants for HER at Au(111) in x M HClO4 + (0.1 - x) M NaClO4 (pH ≤ 3) deduced before properly correcting the electric double layer (EDL) effects to the ones estimated with EDL correction is in the range of ca. 10 to 40, and even in a solution of x M HClO4 + (1 - x) M NaClO4 (pH ≤ 2) there is a difference of ca. 5× in the rate constants without and with EDL correction. The importance of proper correction of the EDL effects as well as several other important factors on unveiling the intrinsic pH-dependent reaction kinetics are discussed to help converge our analysis of pH effects in electrocatalysis.

Electric Double Layer Effects in Electrocatalysis: Insights from Ab Initio Simulation and Hierarchical Continuum Modeling

Structures of the electric double layer (EDL) at electrocatalytic interfaces, which are modulated by the material properties, the electrolyte characteristics (e.g., the pH, the types and concentrations of ions), and the electrode potential, play crucial roles in the reaction kinetics. Understanding the EDL effects in electrocatalysis has attracted substantial research interest in recent years. However, the intrinsic relationships between the specific EDL structures and electrocatalytic kinetics remain poorly understood, especially on the atomic scale. In this Perspective, we briefly review the recent advances in deciphering the EDL effects mainly in hydrogen and oxygen electrocatalysis through a multiscale approach, spanning from the atomistic scale simulated by ab initio methods to the macroscale by a hierarchical approach. We highlight the importance of resolving the local reaction environment, especially the local hydrogen bond network, in understanding EDL effects. Finally, some of the remaining challenges are outlined, and an outlook for future developments in these exciting frontiers is provided.

Steering Selectivity in the Four-Electron and Two-Electron Oxygen Reduction Reactions: On the Importance of the Volcano Slope

In the last decade, trends for competing electrocatalytic processes have been largely captured by volcano plots, which can be constructed by the analysis of adsorption free energies as derived from electronic structure theory in the density functional theory approximation. One prototypical example refers to the four-electron and two-electron oxygen reduction reactions (ORRs), resulting in the formation of water and hydrogen peroxide, respectively. The conventional thermodynamic volcano curve illustrates that the four-electron and two-electron ORRs reveal the same slopes at the volcano legs. This finding is related to two facts, namely, that only a single mechanistic description is considered in the model, and electrocatalytic activity is assessed by the concept of the limiting potential, a simple thermodynamic descriptor evaluated at the equilibrium potential. In the present contribution, the selectivity challenge of the four-electron and two-electron ORRs is analyzed, thereby accounting for two major expansions. First, different reaction mechanisms are included into the analysis, and second, G _max(U), a potential-dependent activity measure that factors overpotential and kinetic effects into the evaluation of adsorption free energies, is applied for approximation of electrocatalytic activity. It is illustrated that the slope of the four-electron ORR is not constant at the volcano legs but rather is prone to change as soon as another mechanistic pathway is energetically preferred or another elementary step becomes the limiting one. Due to the varying slope of the four-electron ORR volcano, a trade-off between activity and selectivity for hydrogen peroxide formation is observed. It is demonstrated that the two-electron ORR is energetically preferred at the left and right volcano legs, thus opening a new strategy for the selective formation of H₂O₂ by an environmentally benign route.

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

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

Sensitivity Analysis in the Microkinetic Description of Electrocatalytic Reactions

A methodology to determine how the variation in a kinetic parameter affects the global kinetic response of an electrochemical reaction is proposed. The so-called sensitivity analysis is applied to quantify the contribution of single reaction steps of an electrocatalytic system under an oscillatory regime using microkinetic analysis.

Pt utilization in proton exchange membrane fuel cells: structure impacting factors and mechanistic insights

It is essential to realize an expected low usage of platinum (Pt) in proton exchange membrane fuel cells (PEMFCs) for the large-scale market penetration of PEMFC-powered vehicles. As well as seeking Pt-based catalysts with a high specific activity, improving Pt utilization through structure optimization of the catalyst layer (CL) has been the main route and apparently a more practical way so far to develop high-performance low-Pt PEMFCs. Despite the significant progress achieved in the past 2-3 decades, a visible gap remains between the current Pt demand of automobile PEMFCs and the target value. To further increase Pt utilization, insights from previous studies are necessary. This review analyzes the structural factors that impact the current-generation efficiency of Pt in PEMFC electrodes in great detail, with emphasis particularly put on the mechanistic and molecule-level insights into the structural effects. The contents include the so-called local transport resistance associated with the permeation and diffusion of oxygen molecules in the ionomer film covering the Pt surface, regulation of ionomer aggregation through molecular interactions between ink components, modulation of ionomer distribution through pore size exclusion and surface electrostatic interaction of the carbon support, optimization of the coupling between the reaction and transport processes through graded composition, and the formation of highways of protons, electrons, and gas molecules through component alignment. We provide a critical analysis of the measurement methods and theoretical models assessing the local transport resistance, which is considered as a crucial issue in the current-generation efficiency of Pt in ultralow-Pt CL. Finally, new opportunities toward the further promotion of Pt utilization are proposed. These subjects and discussions should be of great significance in the rational design and precise fabrication of PEMFC electrodes, and may also inspire similar subjects in other electrochemical energy technologies such as water electrolysis, CO₂ reduction, and batteries.

Cation Overcrowding Effect on the Oxygen Evolution Reaction

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

Modelling electrocatalytic reactions with a concerted treatment of multistep electron transfer kinetics and local reaction conditions

A physicochemical model is developed for electrocatalytic reactions involving multiple electron transfer steps occurring in the electric double layer (EDL). The local reaction conditions are calculated using a mean-field EDL model, which is derived from a comprehensive grand potential that considers the steric effects, solvent polarization, and chemisorption-induced surface dipoles. Macroscopic mass transport in the so-called diffusion layer is controlled by the same set of controlling equations of the EDL model, without imposing the electroneutrality assumption as usual. The Gerischer's formulation of electron transfer theory, corrected with local reaction conditions, is used to describe the kinetics of elementary steps. Multistep kinetics of the electrocatalytic reaction is treated using microkinetics modelling, without resorting to the usual rate-determining step approximation. In formal analysis of the model, we retrieve canonical models with additional assumptions. Self-consistent numerical implementation of the model is demonstrated for oxygen reduction reaction (ORR) at Pt(111) in acidic solution, and the aptness of the model is verified by comparison with experimental data. A comparative study of the full model and its simplified versions allows us to examine how the ORR is influenced by asymmetric steric effects, finite concentration of ions, solvent polarization, surface charge effects, and metal electronic structure effects. We find that the difference in terms of the overpotential between the full model and the simplest model can be up to ∼0.1 V at a current density of -6 mAcm-2.

Properties of the Pt(111)/electrolyte electrochemical interface studied with a hybrid DFT-solvation approach

Self-consistent modeling of the interface between solid metal electrode and liquid electrolyte is a crucial challenge in computational electrochemistry. In this contribution, we adopt the effective screening medium reference interaction site method (ESM-RISM) to study the charged interface between a Pt(111) surface that is partially covered with chemisorbed oxygen and an aqueous acidic electrolyte. This method proves to be well suited to describe the chemisorption and charging state of the interface at controlled electrode potential. We present an in-depth assessment of the ESM-RISM parameterization and of the importance of computing near-surface water molecules explicitly at the quantum mechanical level. We found that ESM-RISM is able to reproduce some key interface properties, including the peculiar, non-monotonic charging relation of the Pt(111)/electrolyte interface. The comparison with independent theoretical models and explicit simulations of the interface reveals strengths and limitations of ESM-RISM for modeling electrochemical interfaces.

Cross-Sphere Electrode Reaction: The Case of Hydroxyl Desorption during the Oxygen Reduction Reaction on Pt(111) in Alkaline Media

Hydroxide ion is a common electrolyte when electrode reactions take place in alkaline media. In the case of oxygen reduction reaction on Pt(111), we demonstrate by ab initio molecular dynamics calculations that the desorption of hydroxyl (OH*) from the electrode surface to form a solvated OH^- is a cross-sphere process, with the OH* reactant in the inner sphere and the OH^- product directly generated in the aqueous outer sphere. Such a mechanism is distinct from the typical inner sphere and outer sphere reactions. It is dictated by the strong hydrogen bonding interactions between a hydroxide ion and water molecules and is facilitated by proton transfer through solvation layers. It should play a significant role whenever OH* desorption, or its reverse, OH^- adsorption, is involved in an electrochemical reaction.

Pore-Scale Modeling of Anode Catalyst Layer Tolerance upon Hydrogen Sulfide Exposure in PEMFC

A pore-scale contamination model is developed to resolve the physicochemical processes in the anode catalyst layer for a deeper insight into the hydrogen sulfide (H2S) contamination mechanism. The present model is based on lattice Boltzmann method (LBM) and a novel iteration algorithm is coupled to overcome the time-scale issue in LBM which can extend its application. The microstructure of CL is stochastically reconstructed considering the presence of carbon, Pt, ionomer, and pores. The proposed model is validated by comparing the experimental data and can accurately predict the effect of H2S contamination on performance with time. The results show that the fuel cell performance is not sensitive to the anode Pt loading under the clean fuel condition as the hydrogen oxidation reaction is easy to activate. However, higher Pt loading can effectively prolong the operation time under the H2S contamination by providing a larger buffer reactive area and a lower H2S concentration condition. Furthermore, the H2S contamination in the fuel gas should be strictly restricted as it directly affects the poisoning rate and significantly affects the operation time.

Graphical abstract

Physicochemical processes in the ACL with reactant transport through micro porous layer (MPL) to active Pt sites

Solvated proton and the origin of the high onset overpotential in the oxygen reduction reaction on Pt(111)

For the hydrogenation of O atoms on Pt(111), protonation can be bypassed by hydrolysis as the electrode potential rises.

Potential-Dependent Volcano Plot for Oxygen Reduction: Mathematical Origin and Implications for Catalyst Design

Climbing up the volcano peak stands as a challenging problem for oxygen reduction. Repeated efforts have been made to fine-tune the binding energy of oxygen reaction intermediates within a narrow region of 0.2 eV by adjusting the catalyst electronic structure. Herein, we address ourselves to two different, oft-neglected but nontrivial questions: (a) Does a superior oxygen reduction reaction catalyst in rotating disk electrode experiments still work well in practical fuel cells (usually at a different potential)? (b) For a given catalyst, can we place it on the volcano peak by adjusting the electrode potential (ϕ^M), which can be easily varied within 0.5 V in experiments, and the potential at the reaction plane in solution (ϕ^OHP), which is modulated by double-layer electrostatic effects? To answer these two questions, we articulate the mathematical origin of the volcano plot and reveal its dependence on ϕ^M and ϕ^OHP by combining a microkinetic model for the oxygen reduction reaction and a mean-field model for the double layer. Furthermore, we explore possible approaches of adjusting ϕ^OHP, for instance, by varying electrolyte concentration and particularly by tuning the electrostatic properties of the support material in a supported catalyst system. The investigation of how electrostatic properties of the support material affect the volcano plot of a supported catalyst opens an additional channel of catalyst-support interactions.

Interface Properties of the Partially Oxidized Pt(111) Surface Using Hybrid DFT-Solvation Models

This article reports a theoretical-computational effort to model the interface between an oxidized platinum surface and aqueous electrolyte. It strives to account for the impact of the electrode potential, formation of surface-bound oxygen species, orientational ordering of near-surface solvent molecules, and metal surface charging on the potential profile along the normal direction. The computational scheme is based on the DFT/ESM-RISM method to simulate the charged Pt(111) surface with varying number of oxygen adatoms in acidic solution. This hybrid solvation method is known to qualitatively reproduce bulk metal properties like the work function. However, the presented calculations reveal that vital interface properties such as the electrostatic potential at the outer Helmholtz plane are highly sensitive to the position of the metal surface slab relative to the DFT-RISM boundary region. Shifting the relative position of the slab also affects the free energy of the system. It follows that there is an optimal distance for the first solvent layer within the ESM-RISM framework, which could be found by optimizing the position of the frozen Pt(111) slab. As it stands, manual sampling of the position of the slab is impractical and betrays the self-consistency of the method. Based on this understanding, we propose the implementation of a free energy optimization scheme of the relative position of the slab in the DFT-RISM boundary region. This optimization scheme could considerably increase the applicability of the hybrid method.

Controlling the mixed potential of polyelectrolyte-coated platinum electrodes for the potentiometric detection of hydrogen peroxide

The use of a Pt electrode coated with a layer of Nafion has been described in previous works as an attractive way to perform the potentiometric detection of hydrogen peroxide. Despite of the attractive features of this approach, the nature of the non-Nernstian response of this system was not properly addressed. In this work, using a mixed potential model, the open circuit potential of the Pt electrode is shown to be under kinetic control of the oxygen reduction reaction (ORR). It is proposed that hydrogen peroxide acts as an oxygenated species that blocks free sites on the Pt surface, interfering with the ORR. Therefore, the effect of the polyelectrolyte coating can be understood in terms of the modulation of the factors that affects the kinetics of the ORR, such as an increase of the H⁺ concentration, minimization of the effect of the spectator species, etc. Because of the complexity and the lack of models that accurately describe systems with practical applications, this work is not intended to provide a mechanistic but rather a phenomenological view on problem. A general framework to understand the factors that affect the potentiometric response is provided. Experimental evidence showing that the use of polyelectrolyte coatings are a powerful way to control the mixed potential open new ways for the development of robust and simple potentiometric sensors.

Ultrafine and highly dispersed platinum nanoparticles confined in a triazinyl-containing porous organic polymer for catalytic applications

The fabrication of stable porous organic polymers (POPs) with heteroatoms that can firmly anchor noble metal nanoparticles (NPs) is a challenging and significant task for heterogeneous catalysis. In the current work, we used piperazine and cyanuric chloride as precursors and successfully fabricated a PC-POP material. Then, through the impregnation method and subsequently the reduction method, ultrafine Pt NPs were confined in the PC-POP with a high dispersion. The Pt NP active sites are accessible due to the uniform mesopores of the PC-POP that facilitate diffusion and mass transfer. The organic cages and nitrogen atoms in the PC-POP frameworks can make the Pt NPs stably anchored in the PC-POP during the catalytic process. The obtained Pt@PC-POP nanocatalyst showed excellent catalytic activity and good recyclability in the selective hydrogenation of halogenated nitrobenzenes and catalytic hydrolysis of ammonia borane as compared with many other reported noble metal catalysts.