Theory of coupled ion-electron transfer kinetics

Local reaction environment in electrocatalysis

Beyond conventional electrocatalyst engineering, recent studies have unveiled the effectiveness of manipulating the local reaction environment in enhancing the performance of electrocatalytic reactions. The general principles and strategies of local environmental engineering for different electrocatalytic processes have been extensively investigated. This review provides a critical appraisal of the recent advancements in local reaction environment engineering, aiming to comprehensively assess this emerging field. It presents the interactions among surface structure, ions distribution and local electric field in relation to the local reaction environment. Useful protocols such as the interfacial reactant concentration, mass transport rate, adsorption/desorption behaviors, and binding energy are in-depth discussed toward modifying the local reaction environment. Meanwhile, electrode physical structures and reaction cell configurations are viable optimization methods in engineering local reaction environments. In combination with operando investigation techniques, we conclude that rational modifications of the local reaction environment can significantly enhance various electrocatalytic processes by optimizing the thermodynamic and kinetic properties of the reaction interface. We also outline future research directions to attain a comprehensive understanding and effective modulation of the local reaction environment.

Coupled chemical reactions: Effects of electric field, diffusion, and boundary control

Chemical reactions involve the movement of charges, and this paper presents a mathematical model for describing chemical reactions in electrolytes. The model is developed using an energy variational method that aligns with classical thermodynamics principles. It encompasses both electrostatics and chemical reactions within consistently defined energetic and dissipative functionals. Furthermore, the energy variation method is extended to account for open systems that involve the input and output of charge and mass. Such open systems have the capability to convert one form of input energy into another form of output energy. In particular, a two-domain model is developed to study a reaction system with self-regulation and internal switching, which plays a vital role in the electron transport chain of mitochondria responsible for ATP generation-a crucial process for sustaining life. Simulations are conducted to explore the influence of electric potential on reaction rates and switching dynamics within the two-domain system. It shows that the electric potential inhibits the oxidation reaction while accelerating the reduction reaction.

Differentiating Oxygen Exchange Reaction Mechanisms across Phase Boundaries

Triggering phase transitions by controlling the anion stoichiometry is an effective method of tuning the electrocatalytic activity of the functional oxides. However, understanding the potential differences in the reaction mechanism(s) of different phases requires the accurate mapping of phase boundaries during the electrochemical reactions, which can be quite challenging. In this work, we have established a feasible electrochemical method based on the measurement of chemical capacitance to resolve the critical stoichiometry at phase boundaries under operando conditions. We select a simple binary oxide PrOx as a proof-of-principle model system, which shows excellent activity for high-temperature oxygen incorporation and evolution reactions (OIR/OER). We show that the phase transition can be sensitively probed by quantifying the chemical capacitance, which can be further used for differentiating the OIR/OER mechanisms across the phase boundary of PrOx. Therefore, our findings provide a new framework for exploring phase engineering as a tool for the design of electrocatalysts.

The decisive role of electrostatic interactions in transport mode and phase segregation of lithium ions in LiFePO4

Understanding the mechanism of slow lithium ion (Li+) transport kinetics in LiFePO4 is not only practically important for high power density batteries but also fundamentally significant as a prototypical ion-coupled electron transfer process. Substantial evidence has shown that the slow ion transport kinetics originates from the coupled transfer between electrons and ions and the phase segregation of Li+. Combining a model Hamiltonian analysis and DFT calculations, we reveal that electrostatic interactions play a decisive role in coupled charge transfer and Li+ segregation. The obtained potential energy surfaces prove that ion-electron coupled transfer is the optimal reaction pathway due to electrostatic attractions between Li+ and e- (Fe2+), while prohibitively large energy barriers are required for separate electron tunneling or ion hopping to overcome the electrostatic energy between the Li+-e- (Fe2+) pair. The model reveals that Li+-Li+ repulsive interaction in the [010] transport channels together with Li+-e- (Fe2+)-Li+ attractive interaction along the [100] direction cause the phase segregation of Li+. It explains why the thermodynamically stable phase interface between Li-rich and Li-poor phases in LiFePO4 is perpendicular to [010] channels.

Unified quantum theory of electrochemical kinetics by coupled ion-electron transfer

A general theory of coupled ion-electron transfer (CIET) is presented, which unifies Marcus kinetics of electron transfer (ET) with Butler-Volmer kinetics of ion transfer (IT). In the limit of large reorganization energy, the theory predicts normal Marcus kinetics of "electron-coupled ion transfer" (ECIT). In the limit of large ion transfer energies, the theory predicts Butler-Volmer kinetics of "ion-coupled electron transfer" (ICET), where the charge transfer coefficient and exchange current are connected to microscopic properties of the electrode/electrolyte interface. In the ICET regime, the reductive and oxidative branches of Tafel's law are predicted to hold over a wide range of overpotentials, bounded by the ion-transfer energies for oxidation and reduction, respectively. The probability distribution of transferring electron energies in CIET smoothly interpolates between a shifted Gaussian distribution for ECIT (as in the Gerischer-Marcus theory of ET) to an asymmetric, fat-tailed Meixner distribution centered at the Fermi level for ICET. The latter may help interpret asymmetric line shapes in x-ray photo-electron spectroscopy (XPS) and Auger electron spectroscopy (AES) for metal surfaces in terms of shake-up relaxation of the ionized atom and its image polaron by ICET. In the limit of large overpotentials, the theory predicts a transition to inverted Marcus ECIT, leading to a universal reaction-limited current for metal electrodes, dominated by barrierless quantum transitions. Uniformly valid, closed-form asymptotic approximations are derived that smoothly transition between the limiting rate expressions for ICET and ECIT for metal electrodes, using simple but accurate mathematical functions. The theory is applied to lithium intercalation in lithium iron phosphate (LFP) and found to provide a consistent description of the observed current dependence on overpotential, temperature and concentration. CIET theory thus provides a critical bridge between quantum electrochemistry and electrochemical engineering, which may find many other applications and extensions.

Advantages of a Solid Solution over Biphasic Intercalation for Vanadium-Based Polyanion Cathodes in Na-Ion Batteries

The efficient operation of metal-ion batteries in harsh environments, such as at temperatures below -20 °C or at high charge/discharge rates required for EV applications, calls for a careful selection of electrode materials. In this study, we report advantages associated with the solid solution (de)intercalation over the two-phase (de)intercalation pathway and identify the main sources of performance limitations originating from the two mechanisms. To isolate the (de)intercalation pathway as the main variable, we focused on two cathode materials for Na-ion batteries: a recently developed KTiOPO4-type NaVPO4F and a well-studied Na3V2(PO4)2F3. These materials have the same elemental composition, operate within the same potential range, and demonstrate very close ionic diffusivities, yet follow different (de)intercalation routes. To avoid any interpretation uncertainties, we obtained these materials in the form of particles with merely identical morphology and size. A detailed electrochemical study revealed a much lower capacity and energy density retention for phase-transforming Na3V2(PO4)2F3 compared to NaVPO4F, which exhibits a single-phase behavior over a wide range of Na concentrations. The reasons for the inferior rate capability and temperature tolerance for the phase-separating Na3V2(PO4)2F3 material should be affiliated with slow phase boundary propagation. We hope that the comprehensive information on limiting factors provided for both mechanisms is useful for the further optimization of electrode materials toward a new generation of high-power and low-temperature metal-ion batteries.

Learning heterogeneous reaction kinetics from X-ray videos pixel by pixel

Reaction rates at spatially heterogeneous, unstable interfaces are notoriously difficult to quantify, yet are essential in engineering many chemical systems, such as batteries1 and electrocatalysts2. Experimental characterizations of such materials by operando microscopy produce rich image datasets3-6, but data-driven methods to learn physics from these images are still lacking because of the complex coupling of reaction kinetics, surface chemistry and phase separation7. Here we show that heterogeneous reaction kinetics can be learned from in situ scanning transmission X-ray microscopy (STXM) images of carbon-coated lithium iron phosphate (LFP) nanoparticles. Combining a large dataset of STXM images with a thermodynamically consistent electrochemical phase-field model, partial differential equation (PDE)-constrained optimization and uncertainty quantification, we extract the free-energy landscape and reaction kinetics and verify their consistency with theoretical models. We also simultaneously learn the spatial heterogeneity of the reaction rate, which closely matches the carbon-coating thickness profiles obtained through Auger electron microscopy (AEM). Across 180,000 image pixels, the mean discrepancy with the learned model is remarkably small (<7%) and comparable with experimental noise. Our results open the possibility of learning nonequilibrium material properties beyond the reach of traditional experimental methods and offer a new non-destructive technique for characterizing and optimizing heterogeneous reactive surfaces.

Population effects driving active material degradation in intercalation electrodes

In battery modeling, the electrode is discretized at the macroscopic scale with a single representative particle in each volume. This lacks the accurate physics to describe interparticle interactions in electrodes. To remedy this, we formulate a model that describes the evolution of degradation of a population of battery active material particles using ideas in population genetics of fitness evolution, where the state of a system depends on the health of each particle that contributes to the system. With the fitness formulation, the model incorporates effects of particle size and heterogeneous degradation effects which accumulate in the particles as the battery is cycled, accounting for different active material degradation mechanisms. At the particle scale, degradation progresses nonuniformly across the population of active particles, observed from the autocatalytic relationship between fitness and degradation. Electrode-level degradation is formed from various contributions of the particle-level degradation, especially from smaller particles. It is shown that specific mechanisms of particle-level degradation can be associated with characteristic signatures in the capacity-loss and voltage profiles. Conversely, certain features in the electrode-level phenomena can also provide insight into the relative importance of different particle-level degradation mechanisms.

Capacitive deionization performance of asymmetric nanoengineered CoFe2O4 carbon nanomaterials composite

Capacitive deionization (CDI) is a relatively new technique that uses electric double layer (EDL) effects, high-affinity chemical groups, redox-active materials, and membrane capacitive electrosorption principle for the desalination. In this paper, hydrothermal synthesis of cobalt ferric oxide (CFO) metal oxide nanoparticles (NPs) coupled with the vacuum filtration method, or the freeze-drying method is used to fabricate high-performance nanocomposites: CFO-graphene, CFO-CNTs, and CFO-3DrGO. Two times of hydrothermal reaction methods were conducted to fabricate the CFO-3DrGO nanoengineered as a pseudocapacitive/EDL electrode. The results have demonstrated that the SAC of CFO-3DrGO/CFO (64.5 mg g^-1) is greater than that of the CFO-graphene/CFO (55.16 mg g^-1) and CFO-CNTs/CFO (21.5 mg g^-1) due to the better surface area of the CFO-3DrGO nanocomposite (330 m² g^-1). The higher surface area of the CFO-3DrGO is due to the porous and interconnected 3D structure of the 3DrGO, and it provides a larger surface area to form EDL capacitance. In addition, the added porous 3DrGO entangled with the spinel crystals (CoFe₂O₄) in the composite allowed for a quick ion diffusion across the interconnected open macroporous structures.

Operando Characterization and Theoretical Modeling of Metal|Electrolyte Interphase Growth Kinetics in Solid-State Batteries. Part II: Modeling

Understanding the interfacial dynamics of batteries is crucial to control degradation and increase electrochemical performance and cycling life. If the chemical potential of a negative electrode material lies outside of the stability window of an electrolyte (either solid or liquid), a decomposition layer (interphase) will form at the interface. To better understand and control degradation at interfaces in batteries, theoretical models describing the rate of formation of these interphases are required. This study focuses on the growth kinetics of the interphase forming between solid electrolytes and metallic negative electrodes in solid-state batteries. More specifically, we demonstrate that the rate of interphase formation and metal plating during charge can be accurately described by adapting the theory of coupled ion-electron transfer (CIET). The model is validated by fitting experimental data presented in the first part of this study. The data was collected operando as a Na metal layer was plated on top of a NaSICON solid electrolyte (Na_3.4Zr₂Si_2.4P_0.6O₁₂ or NZSP) inside an XPS chamber. This study highlights the depth of information which can be extracted from this single operando experiment and is widely applicable to other solid-state electrolyte systems.

Electric Fields and Charge Separation for Solid Oxide Fuel Cell Electrodes

Activation losses at solid oxide fuel cell (SOFC) electrodes have been widely attributed to charge transfer at the electrode surface. The electrostatic nature of electrode-gas interactions allows us to study these phenomena by simulating an electric field across the electrode-gas interface, where we are able to describe the activation overpotential using density functional theory (DFT). The electrostatic responses to the electric field are used to approximate the behavior of an electrode under electrical bias and have found a correlation with experimental data for three different reduction reactions at mixed ionic-electronic conducting (MIEC) electrode surfaces (H₂O and CO₂ on CeO₂; O₂ on LaFeO₃). In this work, we demonstrate the importance of decoupled ion-electron transfer and charged adsorbates on the performance of electrodes under nonequilibrium conditions. Finally, our findings on MIEC-gas interactions have potential implications in the fields of energy storage and catalysis.

Electrochemical Methods for Water Purification, Ion Separations, and Energy Conversion

Agricultural development, extensive industrialization, and rapid growth of the global population have inadvertently been accompanied by environmental pollution. Water pollution is exacerbated by the decreasing ability of traditional treatment methods to comply with tightening environmental standards. This review provides a comprehensive description of the principles and applications of electrochemical methods for water purification, ion separations, and energy conversion. Electrochemical methods have attractive features such as compact size, chemical selectivity, broad applicability, and reduced generation of secondary waste. Perhaps the greatest advantage of electrochemical methods, however, is that they remove contaminants directly from the water, while other technologies extract the water from the contaminants, which enables efficient removal of trace pollutants. The review begins with an overview of conventional electrochemical methods, which drive chemical or physical transformations via Faradaic reactions at electrodes, and proceeds to a detailed examination of the two primary mechanisms by which contaminants are separated in nondestructive electrochemical processes, namely electrokinetics and electrosorption. In these sections, special attention is given to emerging methods, such as shock electrodialysis and Faradaic electrosorption. Given the importance of generating clean, renewable energy, which may sometimes be combined with water purification, the review also discusses inverse methods of electrochemical energy conversion based on reverse electrosorption, electrowetting, and electrokinetic phenomena. The review concludes with a discussion of technology comparisons, remaining challenges, and potential innovations for the field such as process intensification and technoeconomic optimization.

Interfacial Resistive Switching by Multiphase Polarization in Ion-Intercalation Nanofilms

Nonvolatile resistive-switching (RS) memories promise to revolutionize hardware architectures with in-memory computing. Recently, ion-interclation materials have attracted increasing attention as potential RS materials for their ion-modulated electronic conductivity. In this Letter, we propose RS by multiphase polarization (MP) of ion-intercalated thin films between ion-blocking electrodes, in which interfacial phase separation triggered by an applied voltage switches the electron-transfer resistance. We develop an electrochemical phase-field model for simulations of coupled ion-electron transport and ion-modulated electron-transfer rates and use it to analyze the MP switching current and time, resistance ratio, and current-voltage response. The model is able to reproduce the complex cyclic voltammograms of lithium titanate (LTO) memristors, which cannot be explained by existing models based on bulk dielectric breakdown. The theory predicts the achievable switching speeds for multiphase ion-intercalation materials and could be used to guide the design of high-performance MP-based RS memories.

Reconciling the Volcano Trend with the Butler-Volmer Model for the Hydrogen Evolution Reaction

The volcano trend has been widely utilized to forecast new optimum catalysts in computational chemistry while the Butler-Volmer relationship is the norm to explain current-potential characteristics from cyclic voltammetry in analytical chemistry. Herein, we develop an electrochemical model for hydrogen evolution reaction exchange currents that reconciles device-level chemistry, atomic-level volcano trend, and the Butler-Volmer relation. We show that the model is a function of the easy-to-compute hydrogen adsorption energy invariably obtained from first-principles atomic simulations. In addition, the model reproduces with high fidelity the experimental exchange currents for elemental metal catalysts over 15 orders of magnitude and is consistent with the recently proposed analytical model based on a data-driven approach. Our findings based on fundamental electrochemistry principles are general and can be applied to other reactions including CO2 reduction, metal oxidation, and lithium (de)intercalation reactions.

Microscopic Insights into Cation-Coupled Electron Hopping Transport in a Metal-Organic Framework

Electron transport through metal-organic frameworks by a hopping mechanism between discrete redox active sites is coupled to diffusion-migration of charge-balancing counter cations. Experimentally determined apparent diffusion coefficients, D_e^app, that characterize this form of charge transport thus contain contributions from both processes. While this is well established for MOFs, microscopic descriptions of this process are largely lacking. Herein, we systematically lay out different scenarios for cation-coupled electron transfer processes that are at the heart of charge diffusion through MOFs. Through systematic variations of solvents and electrolyte cations, it is shown that the D_e^app for charge migration through a PIZOF-type MOF, Zr(dcphOH-NDI) that is composed of redox-active naphthalenediimide (NDI) linkers, spans over 2 orders of magnitude. More importantly, however, the microscopic mechanisms for cation-coupled electron propagation are contingent on differing factors depending on the size of the cation and its propensity to engage in ion pairs with reduced linkers, either non-specifically or in defined structural arrangements. Based on computations and in agreement with experimental results, we show that ion pairing generally has an adverse effect on cation transport, thereby slowing down charge transport. In Zr(dcphOH-NDI), however, specific cation-linker interactions can open pathways for concerted cation-coupled electron transfer processes that can outcompete limitations from reduced cation flux.

Cation- and pH-Dependent Hydrogen Evolution and Oxidation Reaction Kinetics

The production of molecular hydrogen by catalyzing water splitting is central to achieving the decarbonization of sustainable fuels and chemical transformations. In this work, a series of structure-making/breaking cations in the electrolyte were investigated as spectator cations in hydrogen evolution and oxidation reactions (HER/HOR) in the pH range of 1 to 14, whose kinetics was found to be altered by up to 2 orders of magnitude by these cations. The exchange current density of HER/HOR was shown to increase with greater structure-making tendency of cations in the order of Cs⁺ < Rb⁺ < K⁺ < Na⁺ < Li⁺, which was accompanied by decreasing reorganization energy from the Marcus-Hush-Chidsey formalism and increasing reaction entropy. Invoking the Born model of reorganization energy and reaction entropy, the static dielectric constant of the electrolyte at the electrified interface was found to be significantly lower than that of bulk, decreasing with the structure-making tendency of cations at the negatively charged Pt surface. The physical origin of cation-dependent HER/HOR kinetics can be rationalized by an increase in concentration of cations on the negatively charged Pt surface, altering the interfacial water structure and the H-bonding network, which is supported by classical molecular dynamics simulation and surface-enhanced infrared absorption spectroscopy. This work highlights immense opportunities to control the reaction rates by tuning interfacial structures of cation and solvents.

Thermodynamics, Charge Transfer and Practical Considerations of Solid Boosters in Redox Flow Batteries

Solid boosters are an emerging concept for improving the performance and especially the energy storage density of the redox flow batteries, but thermodynamical and practical considerations of these systems are missing, scarce or scattered in the literature. In this paper we will formulate how these systems work from the point of view of thermodynamics. We describe possible pathways for charge transfer, estimate the overpotentials required for these reactions in realistic conditions, and illustrate the range of energy storage densities achievable considering different redox electrolyte concentrations, solid volume fractions and solid charge storage densities. Approximately 80% of charge storage capacity of the solid can be accessed if redox electrolyte and redox solid have matching redox potentials. 100 times higher active areas are required from the solid boosters in the tank to reach overpotentials of <10 mV.

Theory of the electrostatic surface potential and intrinsic dipole moments at the mixed ionic electronic conductor (MIEC)-gas interface

The local activation overpotential describes the electrostatic potential shift away from equilibrium at an electrode/electrolyte interface. This electrostatic potential is not entirely satisfactory for describing the reaction kinetics of a mixed ionic-electronic conducting (MIEC) solid-oxide cell (SOC) electrode where charge transfer occurs at the electrode-gas interface. Using the theory of the electrostatic potential at the MIEC-gas interface as an electrochemical driving force, charge transfer at the ceria-gas interface has been modelled based on the intrinsic dipole potential of the adsorbate. This model gives a physically meaningful reason for the enhancement in electrochemical activity of a MIEC electrode as the steam and hydrogen pressure is increased in both fuel cell and electrolysis modes. This model was validated against operando XPS data from previous literature to accurately predict the outer work function shift of thin film Sm0.2Ce0.8O1.9 in a H2/H2O atmosphere as a function of overpotential.