Simple formula for Marcus–Hush–Chidsey kinetics

Fractional Marcus-Hush-Chidsey-Yakopcic current-voltage model for redox-based resistive memory devices

We propose a circuit-level model combining the Marcus-Hush-Chidsey electron current equation and the Yakopcic equation for the state variable for describing resistive switching memory devices of the structure metal-ionic conductor-metal. We extend the dynamics of the state variable originally described by a first-order time derivative by introducing a fractional derivative with an arbitrary order between zero and one. We show that the extended model fits with great fidelity the current-voltage characteristic data obtained on a Si electrochemical metallization memory device with Ag-Cu alloy.

Advances in Bioelectrode Design for Developing Electrochemical Biosensors

The critical performance factors such as selectivity, sensitivity, operational and storage stability, and response time of electrochemical biosensors are governed mainly by the function of their key component, the bioelectrode. Suitable design and fabrication strategies of the bioelectrode interface are essential for realizing the requisite performance of the biosensors for their practical utility. A multifaceted attempt to achieve this goal is visible from the vast literature exploring effective strategies for preparing, immobilizing, and stabilizing biorecognition elements on the electrode surface and efficient transduction of biochemical signals into electrical ones (i.e., current, voltage, and impedance) through the bioelectrode interface with the aid of advanced materials and techniques. The commercial success of biosensors in modern society is also increasingly influenced by their size (and hence portability), multiplexing capability, and coupling in the interface of the wireless communication technology, which facilitates quick data transfer and linked decision-making processes in real-time in different areas such as healthcare, agriculture, food, and environmental applications. Therefore, fabrication of the bioelectrode involves careful selection and control of several parameters, including biorecognition elements, electrode materials, shape and size of the electrode, detection principles, and various fabrication strategies, including microscale and printing technologies. This review discusses recent trends in bioelectrode designs and fabrications for developing electrochemical biosensors. The discussions have been delineated into the types of biorecognition elements and their immobilization strategies, signal transduction approaches, commonly used advanced materials for electrode fabrication and techniques for fabricating the bioelectrodes, and device integration with modern electronic communication technology for developing electrochemical biosensors of commercial interest.

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.

Nonequilibrium Electrochemical Phase Maps: Beyond Butler-Volmer Kinetics

Accurate models of electrochemical kinetics at electrode-electrolyte interfaces are crucial to understanding the high-rate behavior of energy storage devices. Phase transformation of electrodes is typically treated under equilibrium thermodynamic conditions, while realistic operation is at finite rates. Analyzing phase transformations under nonequilibrium conditions requires integrating nonlinear electrochemical kinetic models with thermodynamic models. This had only previously been demonstrated for Butler-Volmer kinetics, where it can be done analytically. In this work, we develop a software package capable of the efficient numerical inversion of rate relationships for general kinetic models. We demonstrate building nonequilibrium phase maps, including for models such as Marcus-Hush-Chidsey that require computation of an integral, and also discuss the impact of a variety of assumptions and model parameters, particularly on high-rate phase behavior. Even for a fixed set of parameters, the magnitude of the critical current can vary by more than a factor of 2 among kinetic models.

General Kinetic Model for pH Dependence of Proton-Coupled Electron Transfer: Application to an Electrochemical Water Oxidation System

The pH dependence of proton-coupled electron transfer (PCET) reactions, which are critical to many chemical and biological processes, is a powerful probe for elucidating their fundamental mechanisms. Herein, a general, multichannel kinetic model is introduced to describe the pH dependence of both homogeneous and electrochemical PCET reactions. According to this model, a weak pH dependence can arise from the competition among multiple sequential and concerted PCET channels involving different forms of the redox species, such as protonated and deprotonated forms, as well as different proton donors and acceptors. The contribution of each channel is influenced by the relative populations of the reactant species, which often depend strongly on pH, leading to complex pH dependence of PCET apparent rate constants. This model is used to explain the origins of the experimentally observed weak pH dependence of the electrochemical PCET apparent rate constant for a ruthenium-based water oxidation catalyst attached to a tin-doped In2O3 (ITO) surface. The weak pH dependence is found to arise from the intrinsic differences in the rate constants of participating channels and the dependence of their relative contributions on pH. This model predicts that the apparent maximum rate constant will become pH-independent at higher pH, which is confirmed by experimental measurements. Our analysis also suggests that the dominant channels are electron transfer at lower pH and sequential PCET via electron transfer followed by fast proton transfer at higher pH. This work highlights the importance of considering multiple competing channels simultaneously for PCET processes.

Anomalous Interfacial Electron-Transfer Kinetics in Twisted Trilayer Graphene Caused by Layer-Specific Localization

Interfacial electron-transfer (ET) reactions underpin the interconversion of electrical and chemical energy. It is known that the electronic state of electrodes strongly influences ET rates because of differences in the electronic density of states (DOS) across metals, semimetals, and semiconductors. Here, by controlling interlayer twists in well-defined trilayer graphene moirés, we show that ET rates are strikingly dependent on electronic localization in each atomic layer and not the overall DOS. The large degree of tunability inherent to moiré electrodes leads to local ET kinetics that range over 3 orders of magnitude across different constructions of only three atomic layers, even exceeding rates at bulk metals. Our results demonstrate that beyond the ensemble DOS, electronic localization is critical in facilitating interfacial ET, with implications for understanding the origin of high interfacial reactivity typically exhibited by defects at electrode-electrolyte interfaces.

Origin of Heterogeneous Stripping of Lithium in Liquid Electrolytes

Lithium metal batteries suffer from low cycle life. During discharge, parts of the lithium are not stripped reversibly and remain isolated from the current collector. This isolated lithium is trapped in the insulating remaining solid-electrolyte interphase (SEI) shell and contributes to the capacity loss. However, a fundamental understanding of why isolated lithium forms and how it can be mitigated is lacking. In this article, we perform a combined theoretical and experimental study to understand isolated lithium formation during stripping. We derive a thermodynamic consistent model of lithium dissolution and find that the interaction between lithium and SEI leads to locally preferred stripping and isolated lithium formation. Based on a cryogenic transmission electron microscopy (cryo TEM) setup, we reveal that these local effects are particularly pronounced at kinks of lithium whiskers. We find that lithium stripping can be heterogeneous both on a nanoscale and on a larger scale. Cryo TEM observations confirm our theoretical prediction that isolated lithium occurs less at higher stripping current densities. The origin of isolated lithium lies in local effects, such as heterogeneous SEI, stress fields, or the geometric shape of the deposits. We conclude that in order to mitigate isolated lithium, a uniform lithium morphology during plating and a homogeneous SEI are indispensable.

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.

Understanding Electron Transfer Reactions Using Constrained Density Functional Theory: Complications Due to Surface Interactions

The kinetic rates of electrochemical reactions depend on electrodes and molecules in question. In a flow battery, where the electrolyte molecules are charged and discharged on the electrodes, the efficiency of the electron transfer is of crucial importance for the performance of the device. The purpose of this work is to present a systematic atomic-level computational protocol for studying electron transfer between electrolyte and electrode. The computations are done by using constrained density functional theory (CDFT) to ensure that the electron is either on the electrode or in the electrolyte. The ab initio molecular dynamics (AIMD) is used to simulate the movement of the atoms. We use the Marcus theory to predict electron transfer rates and the combined CDFT-AIMD approach to compute the parameters for the Marcus theory where it is needed. We model the electrode with a single layer of graphene and methylviologen, 4,4'-dimethyldiquat, desalted basic red 5, 2-hydroxy-1,4-naphthaquinone, and 1,1-di(2-ethanol)-4,4-bipyridinium were selected for the electrolyte molecules. All of these molecules undergo consecutive electrochemical reactions with one electron being transferred at each stage. Because of significant electrode-molecule interactions, it is not possible to evaluate outer-sphere ET. This theoretical study contributes toward the development of a realistic-level prediction of electron transfer kinetics suitable for energy storage applications.

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 (Na3.4Zr2Si2.4P0.6O12 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.

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.

Heterogeneous electron transfer reorganization energy at the inner Helmholtz plane in a polybromide redox-active ionic liquid

In ionic liquids (ILs), the electric double layer (EDL) is where heterogeneous electron transfer (ET) occurs. Nevertheless, the relationship between the EDL structure and its kinetics has been rarely studied, especially for ET taking place in the inner Helmholtz plane (IHP). This is largely because of the lack of an appropriate model system for experiments. In this work, we determined the reorganization energy (λ) of Br2 reduction in a redox-active IL 1-ethyl-1-methylpyrrolidinium polybromide (MEPBr2n+1) based on the Marcus-Hush-Chidsey model. Exceptionally fast mass transport of Br2 in MEPBr2n+1 allows voltammograms to be obtained in which the current plateau is regulated by electron-transfer kinetics. This enables investigation of the microscopic environment in the IHP of the IL affecting electrocatalytic reactions through reorganization energy. As a demonstration, TiO2-modified Pt was employed to show pH-dependent reorganization energy, which suggests the switch of major ions at the IHP as a function of surface charges of electrodes.

Theory for nanoscale curvature induced enhanced inactivation kinetics of SARS-CoV-2

We develop a novel theory for the nanomorphology dependent outer sphere heterogeneous electron transfer (ET) rate constant () based on an energy level alignment approach. is modelled through the activation free energy, which is a product of the water monolayer covered metal work function (WF) and the fractional electronic charge exchanged at the transition state (attained through the alignment of the metal Fermi and HOMO/LUMO energy levels of the electroactive species). The theory shows that is an exponentially increasing and decreasing function of the mean curvature in concave and convex nanomorphologies, respectively, for electroactive species or proteins involving their HOMO energy. For the specific spike protein of SARS-CoV-2, we have estimated the half lifetime (t_1/2) and degree of inactivation as a function of the metal WF, nanostructure mean curvature, spike protein HOMO energy, and the environmental temperature (T). By varying the metal from Ag to Au, t_1/2 is reduced from 7 h to 4 min, respectively. The reduction in the copper nanoparticle size from 50 to 5 nm increases the degree of inactivation from 60 to 99.6% (with a reduction factor of 10 in t_1/2). Similarly, the increase in T from 10 °C to 65 °C causes a 100 times lowering of the t_1/2 and t_99.9% of SARS-CoV-2 on Cu metal. The theory predicts that involving the HOMO energy level of a protein follows the surface nanostructure shape dependent order as follows: spherical nanoparticle > cylindrical nanorod > cylindrical nanopore > spherical nanocavity, while the opposite trend is observed in the case of the LUMO energy level participation. Finally, the theory shows agreement with the reported experimental data of the degree of inactivation of SARS-CoV-2 on Ag and Cu nanoparticles.

Purification and preparation of Rhodobacter sphaeroides reaction centers for photocurrent measurements and atomic force microscopy characterization

The formation of defined surfaces consisting of photosynthetic reaction centers (RCs) in biohybrid solar cells is challenging. Here, we start with the production of engineered RCs for oriented binding. RCs are deposited onto gold electrodes, and 6-mercapto-1-hexanol (MCH) is used to displace multilayers and non-specifically adsorbed RCs. The resulting electrode surfaces are analyzed for photocurrent generation using an intensity-modulated light and lock-in amplifier. Atomic force microscopy (AFM) is used to characterize the surface and the formation of RC structural assemblies.

For complete details on the use and execution of this profile, please refer to Jun et al. (2021).

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Express and purify RC membrane proteins from Rhodobacter sphaeroides

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Deposit RCs and MCH on gold electrodes for formation of structural assemblies

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Measure RC photocurrents with an intensity-modulated LED and lock-in detection

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Prepare single crystal gold electrodes for AFM of RCs and image processing

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.

Singlet Oxygen in Electrochemical Cells: A Critical Review of Literature and Theory

Rechargeable metal/O₂ batteries have long been considered a promising future battery technology in automobile and stationary applications. However, they suffer from poor cyclability and rapid degradation. A recent hypothesis is the formation of singlet oxygen (¹O₂) as the root cause of these issues. Validation, evaluation, and understanding of the formation of ¹O₂ are therefore essential for improving metal/O₂ batteries. We review literature and use Marcus theory to discuss the possibility of singlet oxygen formation in metal/O₂ batteries as a product from (electro)chemical reactions. We conclude that experimental evidence is yet not fully conclusive, and side reactions can play a major role in verifying the existence of singlet oxygen. Following an in-depth analysis based on Marcus theory, we conclude that ¹O₂ can only originate from a chemical step. A direct electrochemical generation, as proposed by others, can be excluded on the basis of theoretical arguments.

Correlating structural assemblies of photosynthetic reaction centers on a gold electrode and the photocurrent - potential response

The use of biomacromolecules is a nascent development in clean alternative energies. In applications of biosensors and biophotovoltaic devices, the bacterial photosynthetic reaction center (RC) is a protein-pigment complex that has been commonly interfaced with electrodes, in large part to take advantage of the long-lived and high efficiency of charge separation. We investigated assemblies of RCs on an electrode that range from monolayer to multilayers by measuring the photocurrent produced when illuminated by an intensity-modulated excitation light source. In addition, atomic force microscopy and modeling of the photocurrent with the Marcus-Hush-Chidsey theory detailed the reorganization energy for the electron transfer process, which also revealed changes in the RC local environment due to the adsorbed conformations. The local environment in which the RCs are embedded significantly influenced photocurrent generation, which has implications for electron transfer of other biomacromolecules deposited on a surface in sensor and photovoltaic applications employing a redox electrolyte.

Kinetics of lithium electrodeposition and stripping

Electrodeposition and stripping are fundamental electrochemical processes for metals and have gained importance in rechargeable Li-ion batteries due to lithium metal electrodes. The electrode kinetics associated with lithium metal electrodeposition and stripping is crucial in determining the performance at fast discharge and charge, which is important for electric vertical takeoff and landing (eVTOL) aircraft and electric vehicles (EV). In this work, we show the use of Marcus-Hush-Chidsey (MHC) kinetics to accurately predict the Tafel curve data from the work of Boyle et al. [ACS Energy Lett. 5(3), 701 (2020)]. We discuss the differences in predictions of reorganization energies from the Marcus-Hush and the MHC models for lithium metal electrodes in four solvents. The MHC kinetic model is implemented and open-sourced within Cantera. Using the reaction kinetic model in a pseudo-2D battery model with a lithium anode paired with a LiFePO₄ cathode, we show the importance of accounting for the MHC kinetics and compare it to the use of Butler-Volmer and Marcus-Hush kinetic models. We find significant deviation in the limiting currents associated with reaction kinetics for the three different rate laws for conditions of fast charge and discharge relevant for eVTOL and EV, respectively.

Understanding attenuated solvent reorganization energies near electrode interfaces

In this manuscript, we examine the role of image charge effects on the electrostatic potential fluctuations experienced by ionic species in the vicinity of an electrode surface. We combine simulation and theory to quantify these fluctuations and how they vary with distance from the electrode surface. We observe that the potential distribution narrows significantly for species within a few electrolyte screening lengths of the electrode. We attribute this narrowing to the effects of image charge fluctuations originating from the polarization response of the electrode. We show that the physical consequences of these image charge effects can be captured in the context of a simple analytical field theory with anti-symmetric boundary conditions. We contextualize these results by discussing their implications for rates of Marcus-like outer-sphere interfacial electron transfer.

Fundamental principles of battery design

With an increasing diversity of electrical energy sources, in particular with respect to the pool of renewable energies, and a growing complexity of electrical energy usage, the need for storage solutions to counterbalance the discrepancy of demand and offer is inevitable. In principle, a battery seems to be a simple device since it just requires three basic components – two electrodes and an electrolyte – in contact with each other. However, only the control of the interplay of these components as well as their dynamics, in particular the chemical reactions, can yield a high-performance system. Moreover, specific aspects such as production costs, weight, material composition and morphology, material criticality, and production conditions, among many others, need to be fulfilled at the same time. They present some of the countless challenges, which make battery design a long-lasting, effortful task. This chapter gives an introduction to the fundamental concepts of batteries. The principles are exemplified for the basic Daniell cell followed by a review of Nernst equation, electrified interface reactions, and ionic transport. The focus is addressed to crystalline materials. A comprehensive discussion of crystal chemical and crystal physical peculiarities reflects favourable and unfavourable local structural aspects from a crystallographic view as well as considerations with respect to electronic structure and bonding. A brief classification of battery types concludes the chapter.

Review-Mathematical Formulations of Electrochemically Gas-Evolving Systems

Electrochemically gas-evolving systems are utilized in alkaline water electrolysis, hydrogen production, and many other applications. To design and optimize these systems, high-fidelity models must account for electron-transfer, chemical reactions, thermodynamics, electrode porosity, and hydrodynamics as well as the interconnectedness of these phenomena. Further complicating these models is the production and presence of bubbles. Bubble nucleation naturally occurs due to the chemical reactions and impacts the reaction rate. Modeling bubble growth requires an accurate accounting of interfacial mass transfer. When the bubble becomes large, detachment occurs and the system is modeled as a two-phase flow where the bubbles can then impact material transport in the bulk. In this paper, we review the governing mathematical models of the physicochemical life cycle of a bubble in an electrolytic medium from a multiscale, multiphysics viewpoint. For each phase of the bubble life cycle, the prevailing mathematical formulations are reviewed and compared with particular attention paid to physicochemical processes and the impact the bubble. Through the review of a broad range of models, we provide a compilation of the current state of bubble modeling in electrochemically gas-evolving systems.

Modeling of the electrochemical double layer and its impact on intercalation reactions

We deduce a generic interface theory to describe charge and electron transfer reactions at electrified interfaces based on fundamental principles.

Theory of linear sweep voltammetry with diffuse charge: Unsupported electrolytes, thin films, and leaky membranes

Linear sweep and cyclic voltammetry techniques are important tools for electrochemists and have a variety of applications in engineering. Voltammetry has classically been treated with the Randles-Sevcik equation, which assumes an electroneutral supported electrolyte. In this paper, we provide a comprehensive mathematical theory of voltammetry in electrochemical cells with unsupported electrolytes and for other situations where diffuse charge effects play a role, and present analytical and simulated solutions of the time-dependent Poisson-Nernst-Planck equations with generalized Frumkin-Butler-Volmer boundary conditions for a 1:1 electrolyte and a simple reaction. Using these solutions, we construct theoretical and simulated current-voltage curves for liquid and solid thin films, membranes with fixed background charge, and cells with blocking electrodes. The full range of dimensionless parameters is considered, including the dimensionless Debye screening length (scaled to the electrode separation), Damkohler number (ratio of characteristic diffusion and reaction times), and dimensionless sweep rate (scaled to the thermal voltage per diffusion time). The analysis focuses on the coupling of Faradaic reactions and diffuse charge dynamics, although capacitive charging of the electrical double layers is also studied, for early time transients at reactive electrodes and for nonreactive blocking electrodes. Our work highlights cases where diffuse charge effects are important in the context of voltammetry, and illustrates which regimes can be approximated using simple analytical expressions and which require more careful consideration.

Thermodynamic stability of driven open systems and control of phase separation by electro-autocatalysis

Motivated by the possibility of electrochemical control of phase separation, a variational theory of thermodynamic stability is developed for driven reactive mixtures, based on a nonlinear generalization of the Cahn–Hilliard and Allen–Cahn equations. The Glansdorff–Prigogine stability criterion is extended for driving chemical work, based on variations of nonequilibrium Gibbs free energy. Linear stability is generally determined by the competition of chemical diffusion and driven autocatalysis. Novel features arise for electrochemical systems, related to controlled total current (galvanostatic operation), concentration-dependent exchange current (Butler–Volmer kinetics), and negative differential reaction resistance (Marcus kinetics). The theory shows how spinodal decomposition can be controlled by solo-autocatalytic charge transfer, with only a single faradaic reaction. Experimental evidence is presented for intercalation and electrodeposition in rechargeable batteries, and further applications are discussed in solid state ionics, electrovariable optics, electrochemical precipitation, and biological pattern formation.

Quantitative phase-field modeling of dendritic electrodeposition

A thin-interface phase-field model of electrochemical interfaces is developed based on Marcus kinetics for concentrated solutions, and used to simulate dendrite growth during electrodeposition of metals. The model is derived in the grand electrochemical potential to permit the interface to be widened to reach experimental length and time scales, and electroneutrality is formulated to eliminate the Debye length. Quantitative agreement is achieved with zinc Faradaic reaction kinetics, fractal growth dimension, tip velocity, and radius of curvature. Reducing the exchange current density is found to suppress the growth of dendrites, and screening electrolytes by their exchange currents is suggested as a strategy for controlling dendrite growth in batteries.

Recent Advances in Voltammetry

Recent progress in the theory and practice of voltammetry is surveyed and evaluated. The transformation over the last decade of the level of modelling and simulation of experiments has realised major advances such that electrochemical techniques can be fully developed and applied to real chemical problems of distinct complexity. This review focuses on the topic areas of: multistep electrochemical processes, voltammetry in ionic liquids, the development and interpretation of theories of electron transfer (Butler-Volmer and Marcus-Hush), advances in voltammetric pulse techniques, stochastic random walk models of diffusion, the influence of migration under conditions of low support, voltammetry at rough and porous electrodes, and nanoparticle electrochemistry. The review of the latter field encompasses both the study of nanoparticle-modified electrodes, including stripping voltammetry and the new technique of 'nano-impacts'.