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© 2020 The Electrochemical Society ("ECS"). Published on behalf of ECS by IOP Publishing Limited. We introduce a framework for analyzing and designing EIS inversion algorithms. Our framework stems from the observation of four features common to well-defined EIS inversion algorithms, namely (1) the representation of unknown distributions, (2) the minimization of a metric of error to estimate parameters arising from the chosen representation, subject to constraints on (3) the complexity control parameters, and (4) a means for choosing optimal control parameter values. These features must be present to overcome the ill-posed nature of EIS inversion problems. We review three established EIS inversion algorithms to illustrate the pervasiveness of these features, and show the utility of the framework by resolving ambiguities concerning three more algorithms. Our framework is then used to design the generalized EIS inversion (gEISi) algorithm, which uses Gaussian basis function representation, modality control parameter, and cross-validation for choosing the optimal control parameter value. The gEISi algorithm is applicable to the generalized EIS inversion problem, which allows for a wider range of underlying models. We also considered the construction of credible intervals for distributions arising from the algorithm. The algorithm is able to accurately reproduce distributions which have been difficult to obtain using existing algorithms. It is provided gratis on the repository https://github.com/suryaeff/gEISi.git.

© The Author(s) 2017. Porous electrode theory, pioneered by John Newman and collaborators, provides a macroscopic description of battery cycling behavior, rooted in microscopic physical models. Typically, the active materials are described as solid solution particles with transport and surface reactions driven by concentration fields, and the thermodynamics are incorporated through fitting of the open circuit potential. However, this approach does not apply to phase separating materials, for which the voltage is an emergent property of inhomogeneous concentration profiles, even in equilibrium. Here, we present a general framework, "multiphase porous electrode theory", based on nonequilibrium thermodynamics and implemented in an open-source software package called "MPET". Cahn-Hilliard-type phase field models are used to describe the active materials with suitably generalized models of interfacial reaction kinetics. Classical concentrated solution theory is implemented for the electrolyte phase, and Newman's porous electrode theory is recovered in the limit of solid solution active materials with Butler-Volmer kinetics. More general, quantum-mechanical models of faradaic reactions are also included, such as Marcus-Hush-Chidsey kinetics for electron transfer at electrodes, extended for concentrated solutions. The full model and implementation are described, and a variety of example calculations are presented to illustrate the novel features of the software compared to existing battery models.

© 2019 The Electrochemical Society. Mathematical models of capacity fade can reduce the time and cost of lithium-ion battery development and deployment, and growth of the solid-electrolyte interphase (SEI) is a major source of capacity fade. Experiments in Part I reveal nonlinear voltage dependence and strong charge-discharge asymmetry in SEI growth on carbon black negative electrodes, which is not captured by previous models. Here, we present a theoretical model for the electrochemical kinetics of SEI growth coupled to lithium intercalation, which accurately predicts experimental results with few adjustable parameters. The key hypothesis is that the initial SEI is a mixed ionelectron conductor, and its electronic conductivity varies approximately with the square of the local lithium concentration, consistent with hopping conduction of electrons along percolating networks. By including a lithium-ion concentration dependence for the electronic conductivity in the SEI, the bulk SEI thus modulates the overpotential and exchange current of the electrolyte reduction reaction. As a result, SEI growth is promoted during lithiation but suppressed during delithiation. This new insight establishes the fundamental electrochemistry of SEI growth kinetics. Our model improves upon existing models by introducing the effects of electrochemical SEI growth and its dependence on potential, current magnitude, and current direction in predicting capacity fade.

© 2019 The Electrochemical Society. Growth of the solid electrolyte interphase (SEI) is a primary driver of capacity fade in lithium-ion batteries. Despite its importance to this device and intense research interest, the fundamental mechanisms underpinning SEI growth remain unclear. In Part I of this work, we present an electroanalytical method to measure the dependence of SEI growth on potential, current magnitude, and current direction during galvanostatic cycling of carbon black/Li half cells.We find that SEI growth strongly depends on all three parameters; most notably, we find SEI growth rates increase with nominal C rate and are significantly higher on lithiation than on delithiation. We observe this directional effect in both galvanostatic and potentiostatic experiments and discuss hypotheses that could explain this observation. This work identifies a strong coupling between SEI growth and charge storage (e.g., intercalation and capacitance) in carbon negative electrodes.

© 2020 The Author(s). There has been significant recent interest in studying multiscale characteristics of current and next-generation batteries, including lithium-metal and lithium-sulfur batteries. Advances in computing power make researchers believe that the detailed multiscale models can be efficiently simulated to arrive at the insights for the degradation and performance loss; however, this is not true and special attention needs to be paid to local singularities, boundary layers, moving boundaries, etc. This article presents 2D examples that illustrate the importance of grid convergence studies, provides well-defined detailed models to test the efficiency of numerical schemes, and discusses the associated simulation challenges.

© The Author(s) 2019 We study the linear stability of transient electrodeposition in a charged random porous medium, whose pore surface charges can be of any sign, flanked by a pair of planar metal electrodes. Discretization of the linear stability problem results in a generalized eigenvalue problem for the dispersion relation that is solved numerically, which agrees well with the analytical approximation obtained from a boundary layer analysis valid at high wavenumbers. Under galvanostatic conditions in which an overlimiting current is applied, in the classical case of zero surface charges, the electric field at the cathode diverges at Sand’s time due to electrolyte depletion. The same phenomenon happens for positive charges but earlier than Sand’s time. However, negative charges allow the system to sustain an overlimiting current via surface conduction past Sand’s time, keeping the electric field bounded. Therefore, at Sand’s time, negative charges greatly reduce surface instabilities and suppress dendritic growth, while zero and positive charges magnify them. We compare theoretical predictions for overall surface stabilization with published experimental data for copper electrodeposition in cellulose nitrate membranes and demonstrate good agreement between theory and experiment. We also apply the stability analysis to how crystal grain size varies with duty cycle during pulse electroplating.

© 2020 The Electrochemical Society ("ECS"). Published on behalf of ECS by IOP Publishing Limited. The control of the dielectric and conductive properties of device-level systems is important for increasing the efficiency of energy- A nd information-related technologies. In some cases, such as neuromorphic computing, it is desirable to increase the conductivity of an initially insulating medium by several orders of magnitude, resulting in effective dielectric breakdown. Here, we show that by tuning the value of the applied electric field in systems with variable permittivity and electric conductivity, e.g. ion intercalation materials, we can vary the device-level electrical conductivity by orders of magnitude. We attribute this behavior to the formation of filament-like conductive domains that percolate throughout the system, which form only when the electric conductivity depends on the concentration. We conclude by discussing the applicability of our results in neuromorphic computing devices and Li-ion batteries.

© 2020 The Electrochemical Society ("ECS"). Published on behalf of ECS by IOP Publishing Limited. We introduce a framework for analyzing and designing EIS inversion algorithms. Our framework stems from the observation of four features common to well-defined EIS inversion algorithms, namely (1) the representation of unknown distributions, (2) the minimization of a metric of error to estimate parameters arising from the chosen representation, subject to constraints on (3) the complexity control parameters, and (4) a means for choosing optimal control parameter values. These features must be present to overcome the ill-posed nature of EIS inversion problems. We review three established EIS inversion algorithms to illustrate the pervasiveness of these features, and show the utility of the framework by resolving ambiguities concerning three more algorithms. Our framework is then used to design the generalized EIS inversion (gEISi) algorithm, which uses Gaussian basis function representation, modality control parameter, and cross-validation for choosing the optimal control parameter value. The gEISi algorithm is applicable to the generalized EIS inversion problem, which allows for a wider range of underlying models. We also considered the construction of credible intervals for distributions arising from the algorithm. The algorithm is able to accurately reproduce distributions which have been difficult to obtain using existing algorithms. It is provided gratis on the repository https://github.com/suryaeff/gEISi.git.

© The Author(s) 2017. Porous electrode theory, pioneered by John Newman and collaborators, provides a macroscopic description of battery cycling behavior, rooted in microscopic physical models. Typically, the active materials are described as solid solution particles with transport and surface reactions driven by concentration fields, and the thermodynamics are incorporated through fitting of the open circuit potential. However, this approach does not apply to phase separating materials, for which the voltage is an emergent property of inhomogeneous concentration profiles, even in equilibrium. Here, we present a general framework, "multiphase porous electrode theory", based on nonequilibrium thermodynamics and implemented in an open-source software package called "MPET". Cahn-Hilliard-type phase field models are used to describe the active materials with suitably generalized models of interfacial reaction kinetics. Classical concentrated solution theory is implemented for the electrolyte phase, and Newman's porous electrode theory is recovered in the limit of solid solution active materials with Butler-Volmer kinetics. More general, quantum-mechanical models of faradaic reactions are also included, such as Marcus-Hush-Chidsey kinetics for electron transfer at electrodes, extended for concentrated solutions. The full model and implementation are described, and a variety of example calculations are presented to illustrate the novel features of the software compared to existing battery models.

© The Author(s) 2017. Published by ECS. All rights reserved. Lithium forms ordered stages when it reacts with graphite. These stages have distinct colors; therefore, optical microscopy gives direct information about the lithium concentration in the graphite. Here we present in situ optical images during charging and discharging of a graphite electrode. Stages are observed to coexist with each other even after extended rest. There is considerable spatial nonuniformity on the microscale. To predict this concentration distribution, we employ a model which combines porous-electrode theory and Cahn-Hilliard phase-field theory to describe the flux of lithium within the graphite. The model closely matches the experimental voltage and concentration distribution. The spatial nonuniformity can be approximated with a relatively simple model of distributed resistances. Finally, we discuss the implications of using the phase-field model instead of a solid-solution model for prediction of lithium plating. The two models give similar predictions of cell voltage and risk of lithium plating under many operating conditions, with the main difference being the relaxation of concentration gradients within particles during rest. The distributed-resistance model shows a higher risk of lithium plating because well-connected particles are overworked as their more-resistive neighbors require a higher driving force for passage of current.