Transport Of Charged Species Research Articles

Design and Additive Manufacturing of Electrodes for Electrochemical Energy Storage

Supercapacitors exhibit rapid charge/discharge times and have attracted considerable attention within the automotive, aerospace, and telecommunication industries. The high electrical conductivity and surface area of porous carbons have been attractive for supercapacitor electrodes. Fabricating thick electrodes is one strategy to further increase energy density due to a higher volume fraction of active material. However, thick electrodes suffer from sluggish charged species transport. In this work, we investigate the use of computational optimization and additive manufacturing to design and fabricate thick porous electrodes with improved performance. Electrode performance was maximized by designing their morphologies via topology optimization and printing by projection micro stereolithography (PµSL) using commercial resin (PR48). The PR48 resin was then pyrolyzed (PR48-P) to create the final conductive electrode. The optimized PR48-P electrodes exhibited 99% improvement in capacitance compared to control electrodes printed with cubic lattice morphologies. To further improve performance, we formulated a resin combining graphene oxide (GO) and trimethylolpropane triacrylate (TMPTA). Electrodes printed with 3 wt% GO in TMPTA exhibited improved capacitance retention after pyrolysis compared to the PR48-P electrodes. This work demonstrates the enormous potential of leveraging topology optimization and additive manufacturing to resolve many challenges in the electrochemical storage and renewable energy regimes. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344. Lawrence Livermore National Security, LLC Figure 1

Direct numerical simulation of electrokinetic transport phenomena in fluids: Variational multi-scale stabilization and octree-based mesh refinement

Computational modeling of charged species transport has enabled the analysis, design, and optimization of a diverse array of electrochemical and electrokinetic devices. These systems are represented by the Poisson-Nernst-Planck (PNP) equations coupled with the Navier-Stokes (NS) equation. Direct numerical simulation (DNS) to accurately capture the spatio-temporal variation of ion concentration and current flux remains challenging due to the (a) small critical dimension of the diffuse charge layer (DCL), (b) stiff coupling due to fast charge relaxation times, large advective effects, and steep gradients close to boundaries, and (c) complex geometries exhibited by electrochemical devices.In the current study, we address these challenges by presenting a direct numerical simulation framework that incorporates (a) a variational multiscale (VMS) treatment, (b) a block-iterative strategy in conjunction with semi-implicit (for NS) and implicit (for PNP) time integrators, and (c) octree based adaptive mesh refinement. The VMS formulation provides numerical stabilization critical for capturing the electro-convective flows often observed in engineered devices. The block-iterative strategy decouples the difficulty of non-linear coupling between the NS and PNP equations and allows the use of tailored numerical schemes separately for NS and PNP equations. The carefully designed second-order, hybrid implicit methods circumvent the harsh timestep requirements of explicit time steppers, thus enabling simulations over longer time horizons. Finally, the octree-based meshing allows efficient and targeted spatial resolution of the DCL. These features are incorporated into a massively parallel computational framework, enabling the simulation of realistic engineering electrochemical devices. The numerical framework is illustrated using several challenging canonical examples.

A reasoned general explanation about the concepts of diffusion and reaction layers

The understanding of the implication of the transport of matter is fundamental in the teaching of heterogeneous charge transfers, which are the central element of the electrochemical science and technologies. Thus, even in the absence of intrinsic kinetic complications, the overall rate of such events is frequently conditioned by the mass transport and also by the occurrence of homogeneous coupled chemical reactions. Upon comprehending and accounting for these two effects, the emergent and widely used concepts of the diffusion and reaction layers will be discussed and disentangled under potential-controlled conditions. First, some basic concepts about the transport of charged species in solution are recalled, in order to establish the experimental conditions under which diffusion-only transport can be considered. Under these premises, a fast electron transfer will be considered to introduce the concept of “diffusion layer”, discussing its relationship with the time of the experiment and with the characteristics of the diffusive field that is strongly influenced by the geometry and size of the electrode considered. Next, fast electron transfer reactions “conditioned” by homogeneous chemical reactions undergone by the reactant and/or the product of the redox couple will be analysed. A historical introduction to the concept of “reaction layer” is carried out, pointing out its value in processes with chemical regeneration of the electroactive species and its non-negligible interplay with the mode of diffusion.

Mass transport limitations in concentrated aqueous electrolyte solutions: Theoretical and experimental study of the hydrogen–bromine flow battery electrolyte

Modelling and simulation is a powerful tool to support the development of novel flow cells such as electrolysers and flow batteries. Electrolytes employed in such cells often consist of aqueous solutions of highly concentrated solutes at elevated temperatures. Such conditions pose numerous challenges in conventional model parametrisation because of non-ideal behaviour of the electrolytes. The aim of this work is to study mass transport of electroactive species in highly-concentrated media.We selected the hydrogen–bromine flow battery posolyte, HBr (aq) and Br2, as an exemplary flow battery electrolyte and we leveraged chronoamperometric techniques involving ultramicroelectrodes to study diffusion and migration of bromide and bromine at high concentration and temperature. We successfully simulated the current densities of HBr/Br2 redox reactions in solutions up to 8 mol L–1 using advanced mass transport theory which agreed well with the results obtained with ultramicroelectrodes.While uncharged species transport (Br2) can be credibly modelled using conventional theories such as Fick’s law, charged species (Br–) require special treatment as the diffusion coefficient vary with concentration up to 50 % with respect to the limiting value at infinite dilution. The transport of charged species without added supporting electrolyte occurs via both migration and diffusion and the contribution of migration current may be up to 50 % of the total current. At HBr concentration > 0.6 mol L–1 migration appears to be suppressed due to the “self-screening” effect of the electrolyte.Proper experimental electrolyte characterisation under operating conditions similar to the actual flow cell applications is indispensable to establish predictive models and digital twins of electrochemical devices. Straightforward transfer of concepts known in electro-analytical chemistry to flow cells modelling may lead to erroneous simulations or model overfitting.

Current Leakage and Faradaic Efficiency Simulation of Proton-Conducting Solid Oxide Electrolysis Cells

In this study, we simulated BZY electrolyte-supported proton-conducting solid oxide cell by coupling surface defect chemistry reaction with charged species transport. We validated the model parameters by concentration as a function of temperature, conductivity under dry and wet oxygen as a function of oxygen partial pressure and temperature. The results indicate that the high electron-hole mobility (diffusivity) is mainly responsible for the high leaking current under high temperatures. The Faradaic efficiency stays low or even negative under low operating voltage or high temperature and plateaus as the cell voltage increases. The model developed in this study is a useful tool to understand the leaking current in BZY electrolyte and provide design strategies to avoid/mitigate such significant inefficiency for water electrolysis operation.

Design and additive manufacturing of optimized electrodes for energy storage applications

Supercapacitors exhibit fast charging/discharging ability and have attracted considerable attention within the automotive, aerospace, and telecommunication industries. Porous carbons, prized for their high electrical conductivity and high surface area, have been attractive candidates for supercapacitor electrodes. Moving to thick electrodes is one strategy to further increase energy density due to a higher volume fraction of active material. However, thick electrodes suffer from sluggish charged species transport, which is why thin electrodes are currently favored. In this work, we investigate the use of computational optimization and additive manufacturing to design and fabricate thick porous electrodes with improved performance. Electrode performance was maximized by designing their morphologies via topology optimization and printing by projection micro stereolithography (PμSL) using commercial resin (PR48). The PR48 resin was then pyrolyzed (PR48-P) to create the final conductive electrode. The optimized PR48-P electrodes exhibited 99% improvement in capacitance compared to control electrodes printed with cubic lattice morphologies. To further improve performance, we formulated a resin combining graphene oxide (GO) and trimethylolpropane triacrylate (TMPTA). Electrodes printed with 3 wt% GO in TMPTA exhibited improved capacitance retention after pyrolysis compared to the PR48-P electrodes. This work demonstrates the benefits of using topology optimization to design electrodes and material development to improve functional properties of 3D printable electrodes.

Smoothed Particle Hydrodynamics Modeling of Electrodeposition and Dendritic Growth Under Migration- and Diffusion-Controlled Mass Transport

Abstract In many electrochemical processes, the transport of charged species is governed by the Nernst–Planck equation, which includes terms for both diffusion and electrochemical migration. In this work, a multi-physics, multi-species model based on the smoothed particle hydrodynamics (SPH) method is presented to model the Nernst–Planck equation in systems with electrodeposition. Electrodeposition occurs when ions are deposited onto an electrode. These deposits create complex boundary geometries, which can be challenging for numerical methods to resolve. SPH is a particularly effective numerical method for systems with moving and deforming boundaries due to its particle nature. This paper discusses the SPH implementation of the Nernst–Planck equations with electrodeposition and verifies the model with an analytical solution and a numerical integrator. A convergence study of migration and precipitation is presented to illustrate the model’s accuracy, along with comparisons of the deposition growth front to experimental results.

Modulating the Energy Band Structure of the Mg-Doped Sr0.5Pr0.5Fe0.2Mg0.2Ti0.6O3-δ Electrolyte with Boosted Ionic Conductivity and Electrochemical Performance for Solid Oxide Fuel Cells.

Achieving fast ionic conductivity in the electrolyte at low operating temperatures while maintaining the stable and high electrochemical performance of solid oxide fuel cells (SOFCs) is challenging. Herein, we propose a new type of electrolyte based on perovskite Sr0.5Pr0.5Fe0.4Ti0.6O3−δ for low-temperature SOFCs. The ionic conducting behavior of the electrolyte is modulated using Mg doping, and three different Sr0.5Pr0.5Fe0.4–xMgxTi0.6O3−δ (x = 0, 0.1, and 0.2) samples are prepared. The synthesized Sr0.5Pr0.5Fe0.2Mg0.2Ti0.6O3−δ (SPFMg0.2T) proved to be an optimal electrolyte material, exhibiting a high ionic conductivity of 0.133 S cm–1 along with an attractive fuel cell performance of 0.83 W cm–2 at 520 °C. We proved that a proper amount of Mg doping (20%) contributes to the creation of an adequate number of oxygen vacancies, which facilitates the fast transport of the oxide ions. Considering its rapid oxide ion transport, the prepared SPFMg0.2T presented heterostructure characteristics in the form of an insulating core and superionic conduction via surface layers. In addition, the effect of Mg doping is intensively investigated to tune the band structure for the transport of charged species. Meanwhile, the concept of energy band alignment is employed to interpret the working principle of the proposed electrolyte. Moreover, the density functional theory is utilized to determine the perovskite structures of SrTiO3−δ and Sr0.5Pr0.5Fe0.4–xMgxTi0.6O3−δ (x = 0, 0.1, and 0.2) and their electronic states. Further, the SPFMg0.2T with 20% Mg doping exhibited low dissociation energy, which ensures the fast and high ionic conduction in the electrolyte. Inclusively, Sr0.5Pr0.5Fe0.4Ti0.6O3−δ is a promising electrolyte for SOFCs, and its performance can be efficiently boosted via Mg doping to modulate the energy band structure.

Existence and two-scale convergence of the generalised Poisson–Nernst–Planck problem with non-linear interface conditions

The paper is devoted to the existence and rigorous homogenisation of the generalised Poisson–Nernst–Planck problem describing the transport of charged species in a two-phase domain. By this, inhomogeneous conditions are supposed at the interface between the pore and solid phases. The solution of the doubly non-linear cross-diffusion model is discontinuous and allows a jump across the phase interface. To prove an averaged problem, the two-scale convergence method over periodic cells is applied and formulated simultaneously in the two phases and at the interface. In the limit, we obtain a non-linear system of equations with averaged matrices of the coefficients, which are based on cell problems due to diffusivity, permittivity and interface electric flux. The first-order corrector due to the inhomogeneous interface condition is derived as the solution to a non-local problem.

Modeling transport of charged species in pore networks: Solution of the Nernst–Planck equations coupled with fluid flow and charge conservation equations

A pore network modeling (PNM) framework11Computer code available on public repository https://github.com/PMEAL/OpenPNM. for the simulation of transport of charged species, such as ions, in porous media is presented. It includes the Nernst–Planck (NP) equations for each charged species in the electrolytic solution in addition to a charge conservation equation which relates the species concentration to each other. Moreover, momentum and mass conservation equations are adopted and there solution allows for the calculation of the advective contribution to the transport in the NP equations.The proposed framework is developed by first deriving the numerical model equations (NMEs) corresponding to the partial differential equations (PDEs) based on several different time and space discretization schemes, which are compared to assess solutions accuracy. The derivation also considers various charge conservation scenarios, which also have pros and cons in terms of speed and accuracy. Ion transport problems in arbitrary pore networks were considered and solved using both PNM and finite element method (FEM) solvers. Comparisons showed an average deviation, in terms of ions concentration, between PNM and FEM below 5% with the PNM simulations being over 104 times faster than the FEM ones for a medium including about 104 pores. The improved accuracy is achieved by utilizing more accurate discretization schemes for both the advective and migrative terms, adopted from the CFD literature. The NMEs were implemented within the open-source package OpenPNM based on the iterative Gummel algorithm with relaxation.This work presents a comprehensive approach to modeling charged species transport suitable for a wide range of applications from electrochemical devices to nanoparticle movement in the subsurface.

Multicomponent Ionic Transport Modeling in Physically and Electrostatically Heterogeneous Porous Media With PhreeqcRM Coupling for Geochemical Reactions

AbstractLow‐permeability aquitards, such as clay layers and inclusions, are of utmost importance for contaminant transport in groundwater systems. Although most dissolved species, contaminants, and clay surfaces are charged, the role of electrostatic interactions in subsurface flow‐through systems has not been extensively investigated. This study presents a two‐dimensional multicomponent reactive transport investigation of diffusive/dispersive and electrostatic processes in homogeneous and heterogeneous clay systems. The proposed approach is based on multiple continua and is capable to accurately describe charge interactions during ionic transport in the free water, diffuse layer, and interlayer water of charged porous media. The diffuse layer composition is simulated by considering a mean electrostatic potential following Donnan approach, whereas the interlayer composition is calculated by adopting the Gaines‐Thomas convention. Diffusive/dispersive fluxes within each subcontinuum (free water, diffuse layer, and interlayer) are calculated solving the Nernst‐Planck equation while maintaining a net zero‐charge flux. Furthermore, the multidimensional flow and transport model is coupled with the geochemical code PHREEQC, by utilizing the PhreeqcRM module, thus enabling great flexibility to access all PHREEQC's reaction capabilities. The code is benchmarked in 1‐D systems against other software and previously published experimental data. Successively, reactive transport simulations are performed in 2‐D clayey‐sandy flow‐through domains with spatially variable physical and electrostatic properties at both laboratory and field scales. The results reveal that different properties of surface charge, diffuse layer, and Coulombic interactions impact the transport of charged species and lead to distinct spatial distribution of the ions in the different subcontinua and to significantly different breakthrough curves.

A spectral deferred correction strategy for low Mach number reacting flows subject to electric fields

We propose an algorithm for low Mach number reacting flows subjected to electric field that includes the chemical production and transport of charged species. This work is an extension of a multi-implicit spectral deferred correction (MISDC) algorithm designed to advance the conservation equations in time at scales associated with advective transport. The fast and nontrivial interactions of electrons with the electric field are treated implicitly using a Jacobian-Free Newton Krylov approach for which a preconditioning strategy is developed. Within the MISDC framework, this enables a close and stable coupling of diffusion, reactions and dielectric relaxation terms with advective transport and is shown to exhibit second-order convergence in space and time. The algorithm is then applied to a series of steady and unsteady problems to demonstrate its capability and stability. Although developed in a one-dimensional case, the algorithmic ingredients are carefully designed to be amenable to multi-dimensional applications.

Interdisciplinary Relationship Models for Complementary and Integrative Health: Perspectives of Chinese Medicine Practitioners in the United States

The combination of low intensity electric fields and plants, named as electrokinetic-assisted phytoremediation, to carry out the decontamination of polluted soils has been proposed as a more ecological alternative to the addition of chelating agents in order to increase the availability of pollutants. It results from the electrolysis of water, which generates redox and acid/base reactions in the soil, and the transport of charged species throughout the liquid phase of the soil. EK-phytoremediation allows to reduce the time of treatment as compared to that of phytoremediation and may be applied to both metal(loid)s and organic pollutants. In this chapter, the multiple aspects concerning the applicability of EK-phytoremediation, such as the electrochemical processes and the physicochemical changes occurring in the soil, along with the effects of electric current on plant biomass and some practical issues of the technique, have been extensively discussed based in the literature published to date.

Open‐mouth spherical g‐C3N4/Fe‐2, 5‐thiophenedicarboxylic acid hybrid photocatalyst for dye degradation and bacterial inactivation

AbstractBACKGROUNDPhoto‐remediation of water is seen as an economical and sustainable solution to undertake the rampant pollution by dyes and bacterial pathogens. Despite significant advances made in semiconductor mediated photocatalysis, the search for cheap, efficient, eco‐friendly and robust photocatalyst has underachieved.RESULTSThis paper reports the use of graphitic carbon nitride (g‐C3N4) supported open‐mouth spherical iron (III) based metal‐organic framework (MOF) hybrid photocatalyst for rapid degradation of acidic dyes and bacterial pathogens. Open‐mouth Fe‐2,5‐thiophenedicarboxylic acid (Fe‐TDA) MOF was prepared by microwave‐heating and coupled with g‐C3N4 using methanol as solvent. Compared with the parent g‐C3N4 and Fe‐TDA, the resultant g‐C3N4/Fe‐TDA(x) hybrids have shown nearly 4‐fold increase in acid violet 7 (AV7) dye degradation and Escherichia coli bacterial growth inhibition. The improvement in photo‐response of g‐C3N4/Fe‐TDA(x) hybrids is ascribed to the exceptional specific surface area of the open‐mouth MOF structure, rapid diffusion, transport of charged species and improved dissociation of photo‐excitons. The present work may offer new directions for the synthesis of g‐C3N4/MOF hybrid photocatalysts for visible light‐driven applications.CONCLUSIONA new open‐mouth nanospherical g‐C3N4/Fe‐TDA2wt% photocatalyst developed by microwave heating, produced a high specific surface area of 114 m2 g−1, and improved rate kinetics of AV 7 dye photodegradation and E. coli inactivation. © 2018 Society of Chemical Industry

Theory and Analytical Solutions to Coupled Processes of Transport and Deformation in Dual-Porosity Dual-Permeability Poro-Chemo-Electro-Elastic Media

The linear theory of dual-porosity and dual-permeability poro-chemo-electro-elasticity is presented. The theory outlines the dual-continuum formulation of multiple coupled processes involving solid deformation, pore fluid flow, and electrically charged species transport, within and in between two coexisting porosity systems of a fluid-saturated, poro-elastic medium. The described formulation is used to derive the analytical solutions to the inclined wellbore problem and axisymmetric Mandel-Type problem of dual-porosity, dual-permeability poro-chemo-electro-elasticity. The effects of chemical and electrical potentials on the distributions of stress and pore pressure are demonstrated by numerical examples pertaining to the considered problems. It is shown that the fully coupled nature of the solutions rigorously captures the seemingly anomalous time variations of the effective stress as driven by the pore fluid pressure disturbances, as well as the distribution and movement of anions/cations within the dual-porosity porous medium. The existing subset of published solutions on the subject is successfully reproduced as special cases of the solutions presented in this paper.

Differential Cationization of Fatty Acids with Monovalent Cations Studied by ESI-MS/MS and Computational Approach.

The intercellular and intracellular transport of charged species (Na+ /K+ ) entail interaction of the ions with neutral organic molecules and formation of adduct ions. The rate of transport of the ions across the cell membrane(s) may depend on the stability of the adduct ions, which in turn rely on structural aspects of the organic molecules that interact with the ions. Positive ion ESI mass spectra were recorded for the solutions containing fatty acids (FAs) and monovalent cations (X=Li+ , Na+ , K+ , Rb+ and Cs+ ). Product ion spectra of the [FA+X]+ ions were recorded at different collision energies. Theoretical studies were exploited under both gas phase and solvent phase to investigate the structural effects of the fatty acids during cationization. Stability of [FA+X]+ adduct ions were further estimated by means of AIM topological analyses and interaction energy (IE) values. Positive ion ESI-MS analyses of the solution of FAs and X+ ions showed preferential binding of the K+ ions to FAs. The K+ ion binding increased with the increase in number of double bonds of FAs, while decreased with increase in the number of carbons of FAs. Dissociation curves of [FA+X]+ ions indicated the relative stability order of the [FA+X]+ ions and it was in line with the observed trends in ESI-MS. The solvent phase computational studies divulged the mode of binding and the binding efficiencies of different FAs with monovalent cations. Among the studied monovalent cations, the cationization of FAs follow the order K+ >>Na+ >Li+ >Rb+ >Cs+ . The docosahexaenoic acid showed high efficiency in binding with K+ ion. The K+ ion binding efficiency of FAs depends on the number of double bonds in unsaturated FAs and the carbon chain length in saturated FAs. The cationization trends of FAs obtained from the ESI-MS, ESI-MS/MS analyses were in good agreement with solvent phase computational studies.

Nernst‐Planck‐based Description of Transport, Coulombic Interactions, and Geochemical Reactions in Porous Media: Modeling Approach and Benchmark Experiments

AbstractTransport of multicomponent electrolyte solutions in saturated porous media is affected by the electrostatic interactions between charged species. Such Coulombic interactions couple the displacement of the different ions in the pore water and remarkably impact mass transfer not only under diffusion, but also under advection‐dominated flow regimes. To accurately describe charge effects in flow‐through systems, we propose a multidimensional modeling approach based on the Nernst‐Planck formulation of diffusive/dispersive fluxes. The approach is implemented with a COMSOL‐PhreeqcRM coupling allowing us to solve multicomponent ionic conservative and reactive transport problems, in domains with different dimensionality (1‐D, 2‐D, and 3‐D), and in homogeneous and heterogeneous media. The Nernst‐Planck‐based coupling has been benchmarked with analytical solutions, numerical simulations with another code, and high‐resolution experimental data sets. The latter include flow‐through experiments that have been carried out in this study to explore the effects of electrostatic interactions in fully three‐dimensional setups. The results of the simulations show excellent agreement for all the benchmarks problems, which were selected to illustrate the capabilities and the distinct features of the Nernst‐Planck‐based reactive transport code. The outcomes of this study illustrate the importance of Coulombic interactions during conservative and reactive transport of charged species in porous media and allow the quantification and visualization of the specific contributions to the diffusive/dispersive Nernst‐Planck fluxes, including the Fickian component, the term arising from the activity coefficient gradients, and the contribution due to electromigration.

Low-Frequency Electrical Conductivity of Aqueous Kaolinite Suspensions II: Counterion Effects and Estimating Stern Layer Mobilities of Counterions

AbstractThe electrical state of the interface between a kaolinite-dominated clay sample and aqueous electrolyte solutions was characterized using low-frequency conductance measurements. From these measurements, the ζ-potential and surface conductivity contributions from the diffuse and non-diffuse parts of the electrical double layer were obtained. The suspensions were studied as a function of volume fraction, electrolyte concentration, and electrolyte type (LiCl, NaCl, KCl, CsCl, CaCl2, SrCl2, and BaCl2). Interpretation in terms of the surface conductance revealed that a substantial part of the surface conductivity originates in the inner part of the double layer. Electrokinetic potentials and related diffuse double layer properties are highly dependent on the nature of monovalent counterions, whereas divalent counterions do not show such clear dependencies. Further presented was a simple way to estimate the order of magnitude of counterion mobilities in the inner part of the electrical double layer. All counterions were shown to have a substantial mobility in the inner part of the double layer. Finally, we suggest that the apparent ion-specific effects observed in the diffuse part of the double layer are at least in part related to the finite size of the counterions. Our findings are relevant to scenarios where fluid flow in porous media is accompanied by charged species transport, e.g., in electro-osmotic remediation, spectral-induced polarization, or permeability measurements.

The Effect of Ionic Aggregates on the Transport of Charged Species in Lithium Electrolyte Solutions

In this investigation we focus on the problem of modeling the transport of the charged species (lithium ions) in electrolyte solutions with moderate and high salt concentrations (0.1M to > 2M), and consider the Nernst-Planck equation as a model of such processes. First, using a combination of magnetic resonance imaging (MRI) and inverse modeling (IM) we demonstrate that at higher concentrations the Nernst-Planck equation requires negative transference numbers in order to accurately describe the concentration profiles obtained from experiments. The need for such a physically inconsistent constitutive relation indicates the loss of validity of the Nernst-Planck equation as a model for this process. Next we consider the formation of ion pairs and clusters as a possible effect responsible for the appearance of negative transference numbers and derive an extended version of the Nernst-Planck system which accounts for these additional species. However, a careful analysis of this model reveals that incorporation of ion-pairing effects into the modeling will not change the transference numbers inferred from the experimental data via inverse modeling. This demonstrates that physical effects other than formation of ion pairs and clusters must be incorporated into the Nernst-Planck model in order for it to correctly describe ion transport at higher salt concentrations. One prime candidate for such effects is the motion of the reaction surface resulting from dendrite growth.

On the Fundamental and Practical Aspects of Modeling Complex Electrochemical Kinetics and Transport

Numerous technologies, such as batteries and fuel cells, depend on electrochemical kinetics. In some cases, the responsible electrochemistry and charged-species transport is complex. However, to date, there are essentially no general-purpose modeling capabilities that facilitate the incorporation of thermodynamic, kinetic, and transport complexities into the simulation of electrochemical processes. A vast majority of the modeling literature uses only a few (often only one) global charge-transfer reactions, with the rates expressed using Butler–Volmer approximations. The objective of the present paper is to identify common aspects of electrochemistry, seeking a foundational basis for designing and implementing software with general applicability across a wide range of materials sets and applications. The development of new technologies should be accelerated and improved by enabling the incorporation of electrochemical complexity (e.g., multi-step, elementary charge-transfer reactions and as well as supporting ionic and electronic transport) into the analysis and interpretation of scientific results. The spirit of the approach is analogous to the role that Chemkin has played in homogeneous chemistry modeling, especially combustion. The Cantera software, which already has some electrochemistry capabilities, forms the foundation for future capabilities expansion.