We describe a data-driven, multiscale technique to model reactive wetting of a silver–aluminum alloy on a Kovar™ (Fe-Ni-Co alloy) surface. We employ molecular dynamics simulations to elucidate the dependence of surface tension and wetting angle on the drop's composition and temperature. A design of computational experiments is used to efficiently generate training data of surface tension and wetting angle from a limited number of molecular dynamics simulations. The simulation results are used to parameterize models of the material's wetting properties and compute the uncertainty in the models due to limited data. The data-driven models are incorporated into an engineering-scale (continuum) model of a silver–aluminum sessile drop on a Kovar™ substrate. Model predictions of the wetting angle are compared with experiments of pure silver spreading on Kovar™ to quantify the model-form errors introduced by the limited training data versus the simplifications inherent in the molecular dynamics simulations. The paper presents innovations in the determination of “convergence” of noisy MD simulations before they are used to extract the wetting angle and surface tension, and the construction of their models which approximate physio-chemical processes that are left unresolved by the engineering-scale model. Together, these constitute a multiscale approach that integrates molecular-scale information into continuum scale models.
The complex nature of manufacturing processes stipulates electrodes to possess high variability with increased heterogeneity during production. X-ray computed tomography imaging has proved to be critical in visualizing the complicated stochastic particle distribution of as-manufactured electrodes in lithium-ion batteries. However, accurate prediction of their electrochemical performance necessitates precise evaluation of kinetic and transport properties from real electrodes. Image segmentation that characterizes voxels to particle/pore phase is often meticulous and fraught with subjectivity owing to a myriad of unconstrained choices and filter algorithms. We utilize a Bayesian convolutional neural network to tackle segmentation subjectivity and quantify its pertinent uncertainties. Otsu inter-variance and Blind/Referenceless Imaging Spatial Quality Evaluator are used to assess the relative image quality of grayscale tomograms, thus evaluating the uncertainty in the derived microstructural attributes. We analyze how image uncertainty is correlated with the uncertainties and magnitude of kinetic and transport properties of an electrode, further identifying pathways of uncertainty propagation within microstructural attributes. The coupled effect of spatial heterogeneity and microstructural anisotropy on the uncertainty quantification of transport parameters is also understood. This work demonstrates a novel methodology to extract microstructural descriptors from real electrode images through quantification of associated uncertainties and discerning the relative strength of their propagation, thus facilitating feedback to manufacturing processes from accurate image based electrochemical simulations.
Control volume analysis models physics via the exchange of generalized fluxes between subdomains. We introduce a scientific machine learning framework adopting a partition of unity architecture to identify physically-relevant control volumes, with generalized fluxes between subdomains encoded via Whitney forms. The approach provides a differentiable parameterization of geometry which may be trained in an end-to-end fashion to extract reduced models from full field data while exactly preserving physics. The architecture admits a data-driven finite element exterior calculus allowing discovery of mixed finite element spaces with closed form quadrature rules. An equivalence between Whitney forms and graph networks reveals that the geometric problem of control volume learning is equivalent to an unsupervised graph discovery problem. The framework is developed for manifolds in arbitrary dimension, with examples provided for H(div) problems in R2 establishing convergence and structure preservation properties. Finally, we consider a lithium-ion battery problem where we discover a reduced finite element space encoding transport pathways from high-fidelity microstructure resolved simulations. The approach reduces the 5.89M finite element simulation to 136 elements while reproducing pressure to under 0.1% error and preserving conservation.
Lithium dendrite growth hinders the use of lithium metal anodes in commercial batteries. We present a 3D model to study the mechanical and electrochemical mechanisms that drive microscale plating. With this model, we investigate electrochemical response across a lithium protrusion characteristic of rough anode surfaces, representing the separator as a porous polymer in non-conformal contact with a lithium anode. The impact of pressure on separator morphology and electrochemical response is of particular interest, as external pressure can improve cell performance. We explore the relationships between plating propensity, stack pressure, and material properties. External pressure suppresses lithium plating due to interfacial stress and separator pore closure, leading to inhomogeneous plating rates. For moderate pressures, dendrite growth is completely suppressed, as plating will occur in the electrolyte-filled gaps between anode and separator. In fast-charging conditions and systems with low electrolyte diffusivities, the benefits of pressure are overridden by ion transport limitations.
Conversion cathode materials are gaining interest for secondary batteries due to their high theoretical energy and power density. However, practical application as a secondary battery material is currently limited by practical issues such as poor cyclability. To better understand these materials, we have developed a pseudo-two-dimensional model for conversion cathodes. We apply this model to FeS2 – a material that undergoes intercalation followed by conversion during discharge. The model is derived from the half-cell Doyle–Fuller–Newman model with additional loss terms added to reflect the converted shell resistance as the reaction progresses. We also account for polydisperse active material particles by incorporating a variable active surface area and effective particle radius. Using the model, we show that the leading loss mechanisms for FeS2 are associated with solid-state diffusion and electrical transport limitations through the converted shell material. The polydisperse simulations are also compared to a monodisperse system, and we show that polydispersity has very little effect on the intercalation behavior yet leads to capacity loss during the conversion reaction. We provide the code as an open-source Python Battery Mathematical Modeling (PyBaMM) model that can be used to identify performance limitations for other conversion cathode materials.
Jang, Taejin; Mishra, Lubhani; Roberts, Scott A.; Planden, Brady; Subramaniam, Akshay; Uppaluri, Maitri; Linder, David; Gururajan, Mogadalai P.; Zhang, Ji G.; Subramanian, Venkat R.
Electrochemical models at different scales and varying levels of complexity have been used in the literature to study the evolution of the anode surface in lithium metal batteries. This includes continuum, mesoscale (phase-field approaches), and multiscale models. Thermodynamics-based equations have been used to study phase changes in lithium batteries using phase-field approaches. However, grid convergence studies and the effect of additional parameters needed to simulate these models are not well-documented in the literature. In this paper, using a motivating example of a moving boundary model in one- and two-dimensions, we show how one can formulate phase-field models, implement algorithms for the same and analyze the results. An open-access code with no restrictions is provided as well. The article concludes with some thoughts on the computational efficiency of phase-field models for simulating dendritic growth.
Cooper, Samuel J.; Roberts, Scott A.; Liu, Zhao; Winiarski, Bartlomiej
The mesostructure of porous electrodes used in lithium-ion batteries strongly influences cell performance. Accurate imaging of the distribution of phases in these electrodes would allow this relationship to be better understood through simulation. However, imaging the nanoscale features in these components is challenging. While scanning electron microscopy is able to achieve the required resolution, it has well established difficulties imaging porous media. This is because the flat imaging planes prepared using focused ion beam milling will intersect with the pores, which makes the images hard to interpret as the inside walls of the pores are observed. It is common to infiltrate porous media with resin prior to imaging to help resolve this issue, but both the nanoscale porosity and the chemical similarity of the resins to the battery materials undermine the utility of this approach for most electrodes. In this study, a technique is demonstrated which uses in situ infiltration of platinum to fill the pores and thus enhance their contrast during imaging. Reminiscent of the Japanese art of repairing cracked ceramics with precious metals, this technique is referred to as the kintsugi method. The images resulting from applying this technique to a conventional porous cathode are presented and then segmented using a multi-channel convolutional method. We show that while some cracks in active material particles were empty, others appear to be filled (perhaps with the carbon binder phase), which will have implications for the rate performance of the cell. Energy dispersive X-ray spectroscopy was used to validate the distribution of phases resulting from image analysis, which also suggested a graded distribution of the binder relative to the carbon additive. The equipment required to use the kintsugi method is commonly available in major research facilities and so we hope that this method will be rapidly adopted to improve the imaging of electrode materials and porous media in general.
Conversion cathodes represent a viable route to improve rechargeable Li+battery energy densities, but their poor electrochemical stability and power density have impeded their practical implementation. Here, we explore the impact cell fabrication, electrolyte interaction, and current density have on the electrochemical performance of FeS2/Li cells by deconvoluting the contributions of the various conversion and intercalation reactions to the overall capacity. By varying the slurry composition and applied pressure, we determine that the capacity loss is primarily due to the large volume changes during (de)lithiation, leading to a degradation of the conductive matrix. Through the application of an external pressure, the loss is minimized by maintaining the conductive matrix. We further determine that polysulfide loss can be minimized by increasing the current density (>C/10), thus reducing the sulfur formation period. Analysis of the kinetics determines that the conversion reactions are rate-limiting, specifically the formation of metallic iron at rates above C/8. While focused on FeS2, our findings on the influence of pressure, electrolyte interaction, and kinetics are broadly applicable to other conversion cathode systems.