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The forward problems of pattern formation have been greatly empowered by extensive theoretical studies and simulations, however, the inverse problem is less well understood. It remains unclear how accurately one can use images of pattern formation to learn the functional forms of the nonlinear and nonlocal constitutive relations in the governing equation. We use PDE-constrained optimization to infer the governing dynamics and constitutive relations and use Bayesian inference and linearization to quantify their uncertainties in different systems, operating conditions, and imaging conditions. We discuss the conditions to reduce the uncertainty of the inferred functions and the correlation between them, such as state-dependent free energy and reaction kinetics (or diffusivity). We present the inversion algorithm and illustrate its robustness and uncertainties under limited spatiotemporal resolution, unknown boundary conditions, blurry initial conditions, and other non-ideal situations. Under certain situations, prior physical knowledge can be included to constrain the result. Phase-field, reaction-diffusion, and phase-field-crystal models are used as model systems. The approach developed here can find applications in inferring unknown physical properties of complex pattern-forming systems and in guiding their experimental design.

© 2019 Elsevier Inc. We present a numerical study of electrokinetic transport in porous media, focusing on the role of heterogeneity in a porous microstructure on ion concentration polarization and over-limiting current. For simplicity, the porous medium is modeled as a network of long, thin charged cylindrical pores, each governed by one-dimensional effective transport equations. For weak surface conduction, when sufficiently large potential is applied, we demonstrate that electrokinetic transport in a porous network can be dominated by electro-convection via internally induced flow loops, which is not properly captured by existing homogenized models. We systematically vary the topology and “accessivity” of the pore network and compare with simulations of traditional homogenized parallel-pore (capillary-bundle) models, in order to reveal the effects of regular and hierarchical connectivity. Our computational framework sheds light on the complex physics of electrokinetic phenomena in microstructures and may be used to design porous media for applications, such as water desalination and purification by shock electrodialysis.

We revisit the role of the local solvent structure on the activity coefficients of electrolytes within a nonlocal dielectric function approach. We treat the concentrated electrolyte as a dielectric medium and suggest an interpolation formula for its nonlocal dielectric response. The water dielectric response is approximated based on MD simulations and experimental data, that gives strong over-screening and oscillations in the potential, which are absent in the standard “primitive model” predictions. We obtain mathematically tractable closed-form expressions for the activity coefficients, in reasonable agreement with experimental data.

This study presents a physically-based model for the impedance simulation of the oxygen reduction reaction in porous strontium-doped lanthanum manganite (LSM) cathodes. The model describes the surface mechanism only, taking into account the co-limited adsorption/diffusion of oxygen and the charge-transfer reaction at the three-phase boundary (TPB). After calibration with experimental impedance spectra, the model is used to identify the transition of kinetic regime from the surface to the bulk path mechanism, which occurs at cathodic dc bias of ca. 0.2 V within 700–800 °C. The transition is highlighted by a significant decrease in impedance and the appearance of a low-frequency inductive loop. The model consistently reproduces the impedance spectra before the transition of kinetic regime with a single set of parameters, allowing for the deconvolution of two features, one associated with the co-limited adsorption/diffusion process (ca. 5 Hz) and another minor contribution due to the charge-transfer at the TPB (ca. 35 Hz). The model and its parameters, which quantitatively agree with the literature, can be used as a basis to optimize the microstructural and surface properties of technical LSM-based cathodes, showing that the TPB length is not the main parameter to be maximized. Keywords: LSM; Oxygen reduction reaction; Surface path; Modelling; Impedance spectroscopy

© 2019 Elsevier Inc. We present a numerical study of electrokinetic transport in porous media, focusing on the role of heterogeneity in a porous microstructure on ion concentration polarization and over-limiting current. For simplicity, the porous medium is modeled as a network of long, thin charged cylindrical pores, each governed by one-dimensional effective transport equations. For weak surface conduction, when sufficiently large potential is applied, we demonstrate that electrokinetic transport in a porous network can be dominated by electro-convection via internally induced flow loops, which is not properly captured by existing homogenized models. We systematically vary the topology and “accessivity” of the pore network and compare with simulations of traditional homogenized parallel-pore (capillary-bundle) models, in order to reveal the effects of regular and hierarchical connectivity. Our computational framework sheds light on the complex physics of electrokinetic phenomena in microstructures and may be used to design porous media for applications, such as water desalination and purification by shock electrodialysis.

© 2020 Elsevier Ltd The microscopic theory of chemical reactions is based on transition state theory, where atoms or ions transfer classically over an energy barrier, as electrons maintain their ground state. Electron transfer is fundamentally different and occurs by tunneling in response to solvent fluctuations. Here, we develop the theory of coupled ion-electron transfer, in which ions and solvent molecules fluctuate cooperatively to facilitate non-adiabatic electron transfer. We derive a general formula of the reaction rate that depends on the overpotential, solvent properties, the electronic structure of the electron donor/acceptor, and the excess chemical potential of ions in the transition state. For Faradaic reactions, the theory predicts curved Tafel plots with a concentration-dependent reaction-limited current. For moderate overpotentials, our formula reduces to the Butler–Volmer equation and explains its relevance, not only in the well-known limit of large electron-transfer (solvent reorganization) energy, but also in the opposite limit of large ion-transfer energy. The rate formula is applied to Li-ion batteries, where reduction of the electrode host material couples with ion insertion. In the case of lithium iron phosphate, the theory accurately predicts the concentration dependence of the exchange current measured by in operando X-Ray microscopy without any adjustable parameters. These results pave the way for interfacial engineering to enhance ion intercalation rates, not only for batteries, but also for ionic separations and neuromorphic computing.

© 2018 Elsevier B.V. We couple the Leaky Membrane Model, which describes the diffusion and electromigration of ions in a homogenized porous medium of fixed background charge, with Butler-Volmer reaction kinetics for flat electrodes separated by such a medium in a simple mathematical theory of voltammetry. The model is illustrated for the prototypical case of copper electro-deposition/dissolution in aqueous charged porous media. We first consider the steady state with three different experimentally relevant boundary conditions and derive analytical or semi-analytical expressions for concentration profiles, electric potential profiles, current-voltage relations and overlimiting conductances. Next, we perform nonlinear least squares fitting on experimental data, consider the transient response for linear sweep voltammetry and demonstrate good agreement of the model predictions with experimental data. The experimental datasets are for copper electrodeposition from copper(II) sulfate solutions in a variety of nanoporous media, such as anodic aluminum oxide, cellulose nitrate and polyethylene battery separators, whose internal surfaces are functionalized with positively and negatively charged polyelectrolyte polymers.

Shock electrodialysis (shock ED), an emerging electrokinetic process for water purification, leverages the new physics of deionization shock waves in porous media. In previous work, a simple leaky membrane model with surface conduction can explain the propagation of deionization shocks in a shock ED system, but it cannot quantitatively predict the deionization and conductance (which determines the energy consumption), and it cannot explain the selective removal of ions in experiments. This two-part series of work establishes a more comprehensive model for shock ED, which applies to multicomponent electrolytes and any electrical double layer thickness, captures the phenomena of electroosmosis, diffusioosmosis, and water dissociation, and incorporates more realistic boundary conditions. In this paper, we will present the model details and show that hydronium transport and electroosmotic vortices (at the inlet and outlet) play important roles in determining the deionization and conductance in shock ED. We also find that the results are quantitatively consistent with experimental data in the literature. Finally, the model is used to investigate design strategies for scale up and optimization.

The forward problems of pattern formation have been greatly empowered by extensive theoretical studies and simulations, however, the inverse problem is less well understood. It remains unclear how accurately one can use images of pattern formation to learn the functional forms of the nonlinear and nonlocal constitutive relations in the governing equation. We use PDE-constrained optimization to infer the governing dynamics and constitutive relations and use Bayesian inference and linearization to quantify their uncertainties in different systems, operating conditions, and imaging conditions. We discuss the conditions to reduce the uncertainty of the inferred functions and the correlation between them, such as state-dependent free energy and reaction kinetics (or diffusivity). We present the inversion algorithm and illustrate its robustness and uncertainties under limited spatiotemporal resolution, unknown boundary conditions, blurry initial conditions, and other non-ideal situations. Under certain situations, prior physical knowledge can be included to constrain the result. Phase-field, reaction-diffusion, and phase-field-crystal models are used as model systems. The approach developed here can find applications in inferring unknown physical properties of complex pattern-forming systems and in guiding their experimental design.

Ion transport in extremely narrow nanochannels has gained increasing interest in recent years due to unique physical properties at the nanoscale and the technological advances that allow us to study them. It is tempting to approach this confined regime with the theoretical tools and knowledge developed for membranes and microfluidic devices, and naively apply continuum models, such as the Poisson-Nernst-Planck and Navier-Stokes equations. However, it turns out that some of the most basic principles we take for granted in larger systems, such as the complete screening of surface charge by counter-ions, can break down under extreme confinement. We show that in a truly one-dimensional system of ions interacting with three-dimensional electrostatic interactions, the screening length is exponentially large, and can easily exceed the macroscopic length of a nanotube. Without screening, electroneutrality breaks down within the nanotube, with fundamental consequences for ion transport and electrokinetic phenomena. In this work, we build a general theoretical framework for electroneutrality breakdown in nanopores, focusing on the most interesting case of a one-dimensional nanotube, and show how it provides an elegant interpretation for the peculiar scaling observed in experimental measurements of ionic conductance in carbon nanotubes.

© 2021 Acta Materialia Inc. Although lithium-metal anodes are being extensively examined in research projects aiming at pushing the energy density of lithium batteries to its limit, the knowledge about the mechanical properties of pure lithium is insufficient in two aspects. First, most of the available data focuses either on nano- and micro-scale single-crystalline lithium or on macro-scale bulk material. Second, those tests were commonly performed via uniaxial tests in which the stress states were simple or nanoindentation. This work aims at bridging these gaps by performing a systematic experimental program under various stress states on small-sized specimens and by developing a plasticity model that can capture the important characteristics. Based on these experimental and computational findings, the added value on the understanding of the deformation and failure mechanisms of lithium under various stress states and a first quantitative description on the plasticity anisotropy on lithium is provided. In order to manufacture the required complex-shaped specimens for the five different stress states (uniaxial tension, notched tension with two different radii, central hole tension, and simple shear), a method which allows safe laser cutting of thick lithium foil in argon atmosphere is developed. The tensile tests are conducted in pure argon as well as in air to quantify the effect of oxidation on the strength of lithium. By means of post-mortem microstructural examinations, two active slip systems and cross-slip are observed. Lithium fractures in a perfectly ductile manner when the specimen thickness is reduced to zero due to localized necking. Digital image correlation analysis shows that the lithium foil is highly anisotropic in the through-thickness direction although it is in-plane isotropic. By using a rate-dependent transverse isotropic model, a satisfactory prediction of the five experiments is provided.

Lithium iron phosphate (LiFePO4) is the prototypical two-phase battery material whose complex patterns of lithium ion intercalation provide a testing ground for theories of electrochemical thermodynamics. Using a depth-averaged (a-b plane) phase-field model of coherent phase separation driven by Faradaic reactions, we reconcile conflicting experimental observations of diamond-like phase patterns in micron-sized platelets with observations of surface-controlled patterns in nanoparticles. Elastic analysis predicts this morphological transition for particles whose a-axis dimension exceeds twice the bulk elastic stripe period. We also simulate a rich variety of non-equilibrium patterns, influenced by size-dependent spinodal points and electro-autocatalytic control of thermodynamic stability.

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