Publications

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Mesoscale (100s of particles) electrochemical-thermal-mechanical models and simulations of NMC cathodes are a critical outcome of the CABS project. While the mathematical model formulation for these mesoscale simulations is well established, these simulations also require (1) calibrated parameterization of the mathematical model and (2) mesostructure geometries on which to perform the simulations. In this milestone report, we present a parameterized mathematical model, primarily based on parameter values available in the open literature, that will form the basis of future simulations. We also discuss options for obtaining and using representative mesostructure data in these simulations.

Battery performance, while observed at the macroscale, is primarily governed by the bicontinuous mesoscale network of the active particles and a polymeric conductive binder in its electrodes. Manufacturing processes affect this mesostructure, and therefore battery performance, in ways that are not always clear outside of empirical relationships. Directly studying the role of the mesostructure is difficult due to the small particle sizes (a few microns) and large mesoscale structures. Mesoscale simulation, however, is an emerging technique that allows the investigation into how particle-scale phenomena affect electrode behavior. In this manuscript, we discuss our computational approach for modeling electrochemical, mechanical, and thermal phenomena of lithium-ion batteries at the mesoscale. We review our recent and ongoing simulation investigations and discuss a path forward for additional simulation insights.

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As LiCoO2 cathodes are charged, delithiation of the LiCoO2 active material leads to an increase in the lattice spacing, causing swelling of the particles. When these particles are packed into a bicontinuous, percolated network, as is the case in a battery electrode, this swelling leads to the generation of significant mechanical stress. In this study we performed coupled electrochemical-mechanical simulations of the charging of a LiCoO2 cathode in order to elucidate the mechanisms of stress generation and the effect of charge rate and microstructure on these stresses. Energy dispersive spectroscopy combined with scanning electron microscopy imaging was used to create 3D reconstructions of a LiCoO2 cathode, and the Conformal Decomposition Finite Element Method is used to automatically generate computational meshes on this reconstructed microstructure. Replacement of the ideal solution Fickian diffusion model, typically used in battery simulations, with a more general non-ideal solution model shows substantially smaller gradients of lithium within particles than is typically observed in the literature. Using this more general model, lithium gradients only appear at states of charge where the open-circuit voltage is relatively constant. While lithium gradients do affect the mechanical stress state in the particles, the maximum stresses are always found in the fully-charged state and are strongly affected by the local details of the microstructure and particle-to-particle contacts. These coupled electrochemical-mechanical simulations begin to yield insight into the partitioning of volume change between reducing pore space and macroscopically swelling the electrode. Finally, preliminary studies that include the presence of the polymeric binder suggest that it can greatly impact stress generation and that it is an important area for future research.

Electrical conductivity is key to the performance of thermal battery cathodes. In this work we present the effects of manufacturing and processing conditions on the electrical conductivity of Li/FeS2 thermal battery cathodes. We use finite element simulations to compute the conductivity of three-dimensional microcomputed tomography cathode microstructures and compare results to experimental impedance spectroscopy measurements. A regression analysis reveals a predictive relationship between composition, processing conditions, and electrical conductivity; a trend which is largely erased after thermally-induced deformation. The trend applies to both experimental and simulation results, although is not as apparent in simulations. This research is a step toward a more fundamental understanding of the effects of processing and composition on thermal battery component microstructure, properties, and performance.

The polymer-composite binder used in lithium-ion battery electrodes must both hold the electrodes together and augment their electrical conductivity while subjected to mechanical stresses caused by active material volume changes due to lithiation and delithiation. We have discovered that cyclic mechanical stresses cause significant degradation in the binder electrical conductivity. After just 160 mechanical cycles, the conductivity of polyvinylidene fluoride (PVDF):carbon black binder dropped between 45-75%. This degradation in binder conductivity has been shown to be quite general, occurring over a range of carbon black concentrations, with and without absorbed electrolyte solvent and for different polymer manufacturers. Mechanical cycling of lithium cobalt oxide (LiCoO2 ) cathodes caused a similar degradation, reducing the effective electrical conductivity by 30-40%. Mesoscale simulations on a reconstructed experimental cathode geometry predicted the binder conductivity degradation will have a proportional impact on cathode electrical conductivity, in qualitative agreement with the experimental measurements. Finally, ohmic resistance measurements were made on complete batteries. Direct comparisons between electrochemical cycling and mechanical cycling show consistent trends in the conductivity decline. This evidence supports a new mechanism for performance decline of rechargeable lithium-ion batteries during operation - electrochemically-induced mechanical stresses that degrade binder conductivity, increasing the internal resistance of the battery with cycling.

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Lithium-ion battery particle-scale (non-porous electrode) simulations applied to resolved electrode geometries predict localized phenomena and can lead to better informed decisions on electrode design and manufacturing. This work develops and implements a fully-coupled finite volume methodology for the simulation of the electrochemical equations in a lithium-ion battery cell. The model implementation is used to investigate 3D battery electrode architectures that offer potential energy density and power density improvements over traditional layer-by-layer particle bed battery geometries. Advancement of micro-scale additive manufacturing techniques has made it possible to fabricate these 3D electrode microarchitectures. A variety of 3D battery electrode geometries are simulated and compared across various battery discharge rates and length scales in order to quantify performance trends and investigate geometrical factors that improve battery performance. The energy density and power density of the 3D battery microstructures are compared in several ways, including a uniform surface area to volume ratio comparison as well as a comparison requiring a minimum manufacturable feature size. Significant performance improvements over traditional particle bed electrode designs are observed, and electrode microarchitectures derived from minimal surfaces are shown to be superior. A reduced-order volume-averaged porous electrode theory formulation for these unique 3D batteries is also developed, allowing simulations on the full-battery scale. Electrode concentration gradients are modeled using the diffusion length method, and results for plate and cylinder electrode geometries are compared to particle-scale simulation results. Additionally, effective diffusion lengths that minimize error with respect to particle-scale results for gyroid and Schwarz P electrode microstructures are determined.

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Li/FeS2 thermal batteries provide a stable, robust, and reliable power source capable of long-term electrical energy storage without performance degradation. These systems rely on the electrical conductivity of FeS2 cathodes for critical performance parameters such as power and lifetime, and on permeability of the electrolyte through the solid FeS2 particles for ion transfer. The effects of component composition, manufacturing conditions, and the mechanical deformation on conductivity and permeability have not been studied. We present simulation results from a finite element computer model compared with impedance spectroscopy electrical conductivity experiments. Our methods elucidate the combined effects of slumping, particle size distribution, composition, and pellet density on properties related to electrical conduction in Li/FeS2 thermal battery cathodes.

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Temperature histories on the surface of a body that has been subjected to a rapid, highenergy surface deposition process can be di cult to determine, especially if it is impossible to directly observe the surface or attach a temperature sensor to it. In this report, we explore two methods for estimating the temperature history of the surface through the use of a sensor embedded within the body very near to the surface. First, the maximum sensor temperature is directly correlated with the peak surface temperature. However, it is observed that the sensor data is both delayed in time and greatly attenuated in magnitude, making this approach unfeasible. Secondly, we propose an algorithm that involves tting the solution to a one-dimensional instantaneous energy solution problem to both the sensor data and to the results of a one-dimensional CVFEM code. This algorithm is shown to be able to estimate the surface temperature 20 C.

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We present a phenomenological constitutive model that describes the macroscopic behavior of pressed-pellet materials used in molten salt batteries. Such materials include separators, cathodes, and anodes. The purpose of this model is to describe the inelastic deformation associated with the melting of a key constituent, the electrolyte. At room temperature, all constituents of these materials are solid and do not transport cations so that the battery is inert. As the battery is heated, the electrolyte, a constituent typically present in the separator and cathode, melts and conducts charge by flowing through the solid skeletons of the anode, cathode, and separator. The electrochemical circuit is closed in this hot state of the battery. The focus of this report is on the thermal-mechanical behavior of the separator, which typically exhibits the most deformation of the three pellets during the process of activating a molten salt battery. Separator materials are composed of a compressed mixture of a powdered electrolyte, an inert binder phase, and void space. When the electrolyte melts, macroscopically one observes both a change in volume and shape of the separator that depends on the applied boundary conditions during the melt transition. Although porous flow plays a critical role in the battery mechanics and electrochemistry, the focus of this report is on separator behavior under flow-free conditions in which the total mass of electrolyte is static within the pellet. Specific poromechanics effects such as capillary pressure, pressure-saturation, and electrolyte transport between layers are not considered. Instead, a phenomenological model is presented to describe all such behaviors including the melting transition of the electrolyte, loss of void space, and isochoric plasticity associated with the binder phase rearrangement. The model is appropriate for use finite element analysis under finite deformation and finite temperature change conditions. The model reasonably describes the stress dependent volume and shape change associated with dead load compression and spring-type boundary conditions; the latter is relevant in molten salt batteries. Future work will transition the model towards describing the solid skeleton of the separator in the traditional poromechanics context.

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Liquid droplets flowing through a rectangular microfluidic channel develop a vortical flow field due to the presence of shear forces from the surrounding fluid. In this paper, we present an experimental and computational study of droplet velocities and internal flow patterns in a rectangular pressure-driven flow for droplet diameters ranging from 0.1 to 2 times the channel height. Our study shows excellent agreement with asymptotic predictions of droplet and interfacial velocities for infinitesimally small droplets. As the droplet diameter nears the size of the channel height, the droplet velocity slows significantly, and the changing external flow field causes a qualitative change in the location of internal vortices. This behavior is relevant for future studies of mass transfer in microfluidic devices. © 2014 AIP Publishing LLC.

Ductile metals and other materials typically deform plastically under large applied loads; a behavior most often modeled using plastic deformation constitutive models. However, it is possible to capture some of the key behaviors of plastic deformation using only the framework for nonlinear elastic mechanics. In this paper, we develop a phenomenological, hysteretic, nonlinear elastic constitutive model that captures many of the features expected of a plastic deformation model. This model is based on calculating a secant modulus directly from a materials stress-strain curve. Scalar stress and strain values are obtained in three dimensions by using the von Mises invariants. Hysteresis is incorporated by tracking an additional history variable and assuming an elastic unloading response. This model is demonstrated in both single- and multi-element simulations under varying strain conditions.

Lithium-ion battery electrodes rely on a percolated network of solid particles and binder that must maintain a high electronic conductivity in order to function. Coupled mechanical and electrochemical simulations may be able to elucidate the mechanisms for capacity fade. We present a framework for coupled simulations of electrode mechanics that includes swelling, deformation, and stress generation driven by lithium intercalation. These simulations are performed at the mesoscale, which requires 3D reconstruction of the electrode microstructure from experimental imaging or particle size distributions. We present a novel approach for utilizing these complex reconstructions within a finite element code. A mechanical model that involves anisotropic swelling in response to lithium intercalation drives the deformation. Stresses arise from small-scale particle features and lithium concentration gradients. However, we demonstrate, for the first time, that the largest stresses arise from particle-to-particle contacts, making it important to accurately represent the electrode microstructure on the multi-particle scale. Including anisotropy in the swelling mechanics adds considerably more complexity to the stresses and can significantly enhance peak particle stresses. Shear forces arise at contacts due to the misorientation of the lattice structure. These simulations will be used to study mechanical degradation of the electrode structure through charge/discharge cycles.

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Goma 6.0 is a finite element program which excels in analyses of multiphysical processes, particularly those involving the major branches of mechanics (viz. fluid/solid mechanics, energy transport and chemical species transport). Goma is based on a full-Newton-coupled algorithm which allows for simultaneous solution of the governing principles, making the code ideally suited for problems involving closely coupled bulk mechanics and interfacial phenomena. Example applications include, but are not limited to, coating and polymer processing flows, super-alloy processing, welding/soldering, electrochemical processes, and solid-network or solution film drying. This document serves as a user's guide and reference.