Multiscale simulation process and application to additives in porous composite battery electrodes

Accepted Manuscript Multiscale simulation process and application to additives in porous composite battery electrodes Christian Wieser , Torben Prill , Katja Schladitz PII:

S0378-7753(14)01928-4

DOI:

10.1016/j.jpowsour.2014.11.090

Reference:

POWER 20218

To appear in:

Journal of Power Sources

Received Date: 9 September 2014 Revised Date:

7 November 2014

Accepted Date: 18 November 2014

Please cite this article as: C. Wieser, T. Prill, K. Schladitz, Multiscale simulation process and application to additives in porous composite battery electrodes, Journal of Power Sources (2014), doi: 10.1016/ j.jpowsour.2014.11.090. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Multiscale Simulation Process and Application to Additives in Porous

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Composite Battery Electrodes

Christian Wiesera, Torben Prillb, Katja Schladitzb

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a) Adam Opel AG, IPC S1-01, 65423 Rüsselsheim, Germany, [email protected], (corre-

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sponding author: phone +49-6142/7-65773, fax +49-6142/7-78165)

b) Fraunhofer Institut für Techno- und Wirtschaftsmathematik ITWM, Fraunhofer-Platz 1, 67663

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Kaiserslautern, Germany ([email protected], [email protected])

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Abstract

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Structure-resolving simulation of porous materials in electrochemical cells such as fuel cells and lithium ion batteries allows for correlating electrical performance with material morphology. In lithium ion batteries characteristic length scales of active material particles and additives range several orders of magnitude. Hence, providing a computational mesh resolving all length scales is not reasonably feasible and requires

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alternative approaches. In the work presented here a virtual process to simulate lithium ion batteries by bridging the scales is introduced. Representative lithium ion battery electrode coatings comprised of µm-

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scale graphite particles as active material and a nm-scale carbon/polymeric binder mixture as an additive are imaged with synchrotron radiation computed tomography (SR-CT) and sequential focused ion beam/scanning electron microscopy (FIB/SEM), respectively. Applying novel image processing methodologies for the FIB/SEM images, data sets are binarized to provide a computational grid for calculating the

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effective mass transport properties of the electrolyte phase in the nanoporous additive. Afterwards, the homogenized additive is virtually added to the micropores of the binarized SR-CT data set representing the active particle structure, and the resulting electrode structure is assembled to a virtual half-cell for electrochemical microheterogeneous simulation. Preliminary battery performance simulations indicate

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non-negligible impact of the consideration of the additive.

Keywords

lithium ion battery, multiscale simulation, physics-based model, image-processing, porous media

1. Introduction

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In the last two decades, the development of electrified vehicles and electric traction systems gained increasing momentum in advanced automotive engineering to provide sustainable mobility with reduced or zero tailpipe emissions. Namely vehicles with fuel cell and lithium ion battery powertrains demonstrated

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that customer expectations such as performance and range can already be met whilst being efficient and environmentally sound [1]. The simulation-based process for the virtual development of vehicles is well established for conventional vehicle technologies. For electrified vehicles, the process consequently has to

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comprise powertrain electrification including the electrochemical energy converter.

Multi-scale multi-physics simulation is a recent technology trend. Applied to electromobility topics, the

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individual building blocks and scales of the fuel cell or battery system need to be connected from the material scale of the electrochemical cell up to the entire system. In virtual battery engineering, this process starts with material property and physicochemical battery cell simulation resolving the solid/void morphology of the porous electrode (“microheterogeneous scale”). In order to increase computational speed and efficiency for simulations on the length-scale of the technical battery cell, homogenized model mate-

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rial properties are derived from the microheterogeneous scale to provide productive macrohomogeneous tools. For battery module design and system engineering simulation, surrogate models, like equivalent circuit models, are calibrated with test data or physicochemical simulation results to provide electrical and

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thermal battery cell performance predictions like heat source terms for CFD simulations (Figure 1).

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Battery electrodes are typically thin porous coatings made from powders comprising a large fraction of active material with particle sizes in the 10 µm length scale and a small fraction of binding and conductivity-enhancing additives with particle sizes in the 10..100 nm length scale (Figure 2). While the large solid fraction of the active material particles acts as the actual charge storage component, these large particles are bound together by the polymeric portion as well as electrically contacted by the portion of tiny graphitic particles of the small solid fraction of what is called the additive.

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In order to predict macroscopic efficient material properties, such as effective diffusivity of the porous coating, or even the electrochemical performance, such as battery charge/discharge behavior, so-called micro-heterogeneous simulation approaches on the respective length scales have been developed

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[2],[3],[4]. By nature, these approaches require computational domains that resolve the solid/pore structure of the porous material in order to solve the transport equations in the different phases separately. Ideally, computational domains derived from material imaging data sets which have been image-processed

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adequately are provided to the simulation [5]. Other attempts utilize generic structures or simplified geometries. Wang et al., for instance, published a physicochemical mesoscale model of a lithium-ion poly-

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mer half-cell with a surrogate particle model of the composite positive electrode comprised of regular and random arrangements of spherical particles realized by a finite element grid [6]. In contrast to the structure simplifications of macrohomogeneous models, this approach introduced actual solid/void structures in a computational mesh using generic geometries but did not address the structural complexity of a real electrode or the additional transport effects introduced by the binder/carbon additive. Goldin et al. also applies

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differently packaged spheres as model particles in a full-cell arrangement and analyzes particle packing effects on the macroscopic cell performance and local variable distributions [7]. Particularly interesting is the investigation of the impact of differently overlapping spheres as this situation mimics the contact situa-

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tion of real particles. The authors indicate the possibility and relevance of additive consideration but neglect the additive in their work. A similar approach in terms of using generic model structures has been

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published by Zadin et al. who investigated local effects with a finite element model of a three-dimensional trench architecture which deviates strongly from technically relevant particle-based electrode architectures [8]. Besides the above exemplarily described approaches utilizing generic geometric structures, the need to reflect the complex particle/electrolyte geometry, or solid/void morphology, respectively, became obvious. The work of Gupta et al. aimed at investigating effects attributed to the complex particle geometry and the derivation of macroscopic, effective relations and properties for macroscale simulations [9]. They created complex aggregates made from generic ellipsoid base particles and put them into a control volume for succeeding volume-averaging. The domain, hence, apparently was also in kind of a half-cell arrange-

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ment, even though the counter electrode with adjacent separator has not been modeled explicitly. Hutzenlaub et al. went one important step further by utilizing image-processed 3D tomographical data sets obtained by sequential FIB/SEM as computational meshes for solid/void-resolving physicochemical simu-

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lation of a battery half-cell [11]. Furthermore, they actually considered the existence of the additive (called carbon/binder phase in the publication) and, hence, went further than any previous approaches in considering all components of the composite battery electrode in a spatially resolved simulation. However, the

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impact of the additive has been considered in terms of blocking electrochemically active surfaces of the active material completely thereby neglecting the fact that the additive itself is porous and provides

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transport paths, albeit with additional transport resistance, from the open electrolyte space to the surface of the active particle.

In conclusion of the above brief review, essential elements of a virtual design process for electrochemical cells, namely lithium ion batteries, have been reported, such as solid/void-resolving structure models, ge-

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neric structures as well as utilization of 3D imaging data-sets, scale-bridging considerations, volumeaveraging and physicochemical battery modeling. Missing so far is the comprehensive application of all these individual elements in one single effort to analyze material-scale effects by multi-physics, multi-

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scale battery simulation in a complete electrode/counter-electrode cell arrangement, and in particular the mass transport limitation introduced by the nano-porous carbon/binder additive. This publication aims at

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filling this gap and, in addition to that, provides a preliminary assessment of the consideration of the nanoporous additive as a non-blocking but porous coating on active particle surfaces in such simulations.

From the perspective of designing materials and tailoring properties to requirements, the full virtual vehicle design process still has gaps. To fill these gaps, state-of-the-art porous electrodes need to be imaged accurately, and the imaging data sets need to be image-processed such that accurate computational grids can be provided to the microheterogeneous simulation. Assuming that the relevant physics is considered, the microheterogeneous simulation generates macroscopic results for effective material properties and/or

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performance data that can be compared to component, i.e. cell requirements. In case of deviations to the requirement, the structure can be modified virtually, if need be in several steps, to tune the material to the requirement and formulate material design recommendations for the manufacturing process. Typically, the

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real material that has been manufactured based on the recommendation by the simulation will not exactly match the morphology and, consequently, properties of the recommendation. Hence, the design loop needs to be closed, i.e. the improved real material needs to be imaged and its properties determined. If the devia-

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tion from the recommendation is too large, one or more iterations of the material design loop may be required. Another important customer, besides the material development, is the macrohomogeneous simula-

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tion which requires parameters and constitutive relations that are difficult to measure, such as the tortuosity. A graphical depiction of the process is shown in Figure 3

Due to the fact that the characteristic length scales of the materials composing a battery electrode are orders of magnitude apart, neither one single imaging technique exists to resolve all structures. Even if this was possible, computational grids of the size of an electrode coating (50-100 µm) resolved down to the

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length scale of the additive (10..100 nm) would hardly be computationally manageable. On the other hand, considering both length scales in one simulation case is necessary to analyze interactions between the components. For instance, quantifying the impact of amount and distribution of the conductivity-

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enhancing additive on overall ohmic electrode resistance as well as quantifying the reduction in surface area available for the reaction and additional mass transport resistance by presence of the porous additive

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provides crucial information to design the composite battery electrode.

In order to bridge the scales and enable such an analysis a methodology comprising the key elements of the above virtual material design process is proposed. The process is based on the hypothesis that the additive on the nanometer scale can be imaged in 3D and its effective properties can be determined by microheterogeneous transport simulations based on image-processed data sets. FIB/SEM has been applied to image the porous additive domains in a graphite-based porous composite battery electrode. As a consequence of the high material porosity, the characteristics of the images generate big challenges for standard

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image processing methods. Hence, advanced image processing methods have been developed and applied. After binarization of the grey-scale data set, the transport properties of the additive have been determined by simulation. The active material on the micrometer scale is imaged as well by using synchrotron radia-

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tion computed tomography (SR-CT) and binarized with established image-processing methods. The additive has been introduced to control volumes in the pore space of the electrode structure by setting the effective properties in these control volumes according to the additive properties. The choice of the control

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volumes was made by morphological image processing operations assuming a wetting of the active particles with the additive. Finally, the resulting impact on the electrode performance is calculated with a mi-

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croheterogeneous simulation on the length scale of the active material.

2. Experimental

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2.1. Sample

As mentioned in the introduction, Li-ion battery negative electrodes typically exhibit active carbon parti-

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cles in the 10 µm order of magnitude size and conductivity-enhancing carbon particles in the 10 nm order of magnitude size. In order to have samples providing a broad range of size scales, a carbon-based nega-

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tive Li-ion battery electrode has been chosen to demonstrate the multi-scale process. For that purpose, an 18 µm copper foil has been coated with a 70 µm thick electrode from a slurry comprising 90 % Timcal SLP30 graphite as active material, 6% Timcal Super P Li conductive additive and 4% polymeric binder. The expected porosity based on area loading and coating thickness was 60%. Particle sizes of the raw powders were d50≈16 µm for the active material and d50≈40 nm for the conductive additive, respectively [10],[12].

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The primary functions of the additive are to reduce the electrical contact resistance between adjacent active particles through the conducting carbon and improve the adhesion of adjacent particles and the entire coating, respectively, through the polymer. From a mass transport perspective, the additive can be seen as

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porous coating on some portion of the surface of the active particles and the void between them and, hence, additional transport resistance for the lithium ions in the electrolyte between the open pore and the surface of the active particle. As the additive takes up some of the pore space between the active particles,

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the overall transport resistance of the porous electrode is affected, too. One purpose of this effort therefore is to estimate the quantity of the additional transport resistance by the additive and the impact on battery

2.2. Imaging of Additive

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cell performance, respectively.

As a rule of thumb for mass transport calculations, relevant feature sizes need to be resolved by a factor of one tenth in a computational grid. Since the particle size of at least the conductive carbon in the additive is

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40 nm and the pore size in the additive domains is in the 50..100 nm order of magnitude (estimated from comparable coating materials [13]), imaging resolutions in the <10 nm are required to sufficiently resolve the morphology. 3D resolutions on this length-scale cannot be resolved by x-ray computed tomography

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(CT). Hence, sequential focused ion beam nano-tomography with scanning electron microscopy imaging (FIB/SEM) has been applied. FIB/SEM nano-tomography is a serial sectioning technique using an ion

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beam to sequentially erode thin slices from the surface of a sample and take SEM images between two erosion steps. By repeating the erosion and imaging steps, a stack of SEM images is generated containing the 3D information of the material structure. In order to obtain manageable imaging volume sizes and depth information, the sample is typically prepared such that the ion beam is perpendicular to the sample surface and a trench is milled into the sample thereby exposing the volume to be imaged. The electron beam from the SEM is tilted against the ion beam and the excavated surface to be imaged (Figure 4Error! Reference source not found.). A typical and representative image from a such obtained image stack is shown in Figure 5. This image also shows nicely the different length scales of the active particles (part of

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an active particle is visible in the bottom left) and the porous additive. Typical resolutions are some nanometers pixel size of the SEM image and 10 nm for the erosion, i.e. the slice thickness.

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The data set used for this work consists of 370 images with the dimension 1024×884 pixels, generated using an FEI Helios Nano Lab 600 SEM. The lateral resolution of the images was 5 nm × 5 nm and the thickness of the slices was 10 nm. The specimen was tilted for the FIB milling, with a tilt angle of 52°,

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yielding a resolution in the plane of the slicing of 5 nm in x-direction and 6.27 nm in y-direction, leading to a voxel size in the 3 dimensional data of 5 nm x 6.27 nm x 10 nm. A layer of platinum was sputtered on

on top of the porous phase in Figure 5.

2.3. Imaging of Active Material

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the top of the specimen, preventing a curtaining effect during the slicing. The platinum layer can be seen

Due to the length scale of the active material which dominates the porous electrode, synchrotron radiation

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computed tomography has been chosen. A sample of the electrode has been imaged at the ID19 beamline of the European Synchrotron Radiation Facility ESRF in Grenoble, France. For the tomography, 2000 projections have been used taken at 18.5 keV beam energy. The pixel resolution obtained was 0.28 µm.

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The imaged structure has been reconstructed with the PyHST algorithm [14], using inline phase contrast. Figure 6Error! Reference source not found. exemplarily shows a slice of the such obtained grey-scale

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imaging data set. Besides the clearly visible active particles, areas of different grey-scale can be seen in the images. It is assumed that these areas do not represent the nanoporous additive correctly, as the volume fraction exceeds the one assumed for the additive. Instead, we attribute these intermediate grey values partly to imaging artifacts.

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3. Image Processing Some image processing is required for the reconstruction of the pore space between the active particles and the pore space of the nanoporous additive, converting the grey value images from the SEM and the

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SR-CT into a binary images which can be used as a computational grid for the transport and battery simulation. To reconstruct the active particles a simple global thresholding approach was sufficient, while for the reconstruction of the additive, a recently developed workflow has been applied to reconstruct the pore

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space.

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3.1. Image Processing and Segmentation of Additive

A method, recently developed by the authors and Dominique Jeulin at MINES ParisTech has been used to segment the FIB/SEM data set, yielding the voxel grid for the transport resistance calculation. The method combines several morphological transformations of the original image. A flow chart of the segmentation procedure is shown in Figure 7. Base algorithms and choice of parameters are explained in [15]. Here, the

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method is summarized shortly.

First, in a preprocessing step, the SEM images are thoroughly aligned, effects of non-uniform illumination are corrected and contrast differences in the individual SEM images are adjusted for. Then, using morpho-

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logical filters a number of images are computed representing features in the data. These feature images are computed on so called z-profiles of the data, i.e. the grey value of one pixel is tracked through the whole

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image stack. The rationale behind this approach is, the observation, that the z-profile exhibits distinctive characteristics on the pore space and the solid phase, respectively. The features are the grey value of the image and of the morphological gradient, as well as the minima of the z-profiles and a thresholding of a morphological half gradient, computed on the z-profile. These feature images are then used to compute an initial segmentation of the data, separating pore from solid phase. In a final step, the preliminary segmentation is used as input into a constrained watershed transformation, improving the segmentation by fitting the segmented phases to edges in the data. The constrained water-

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shed transformation yields the final result, a binary image, which is used as a voxel grid, for the transport simulation. For details of the segmentation please refer to [15], as the segmentation is laid out in the article in detail,

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including the choice of parameters and a validation of the segmentation using a simulated FIB/SEM data set [16]. Also a geometrical analysis of the reconstructed structure is given.

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3.2. Image Processing and Binarization of Active Material

The SR-CT images of the electrode coating were segmented with the software MAVI [17], using a global

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threshold. As described above, SR-CT cannot resolve the porosity of the nano-porous additive which consequently, at best, will be visible as a grey shadow in contrast to the clearly visible active material particles. As the solid fraction of the active material was known beforehand from the composition of the slurry used to coat the electrode, the threshold was chosen such that desired solid fraction or volume fraction, respectively, is matched. The solid fraction of the porous electrode without consideration of the portion of

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the additive was 40%, thus the threshold was chosen to assign the active particle phase to the 60% of voxels with the highest grey value. A volume rendering of the resulting segmentation is shown in Figure

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8.

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4. Modeling and Simulation As indicated above, due to the fact that the characteristic length scales of the materials composing a battery electrode are orders of magnitude apart, neither one single imaging technique exists to resolve all structures. Even if this was possible, computational grids of the size of an electrode coating (50-100 µm) resolved down to the length scale of the additive (10..100 nm) would hardly be computationally manageable. On the other hand, considering both length scales in one simulation case is necessary to analyze interactions between the components. For instance, quantifying the impact of amount and distribution of the conductivity-enhancing additive on overall ohmic electrode resistance as well as quantifying the reduction

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in surface area available for the reaction and additional mass transport resistance by presence of the porous additive provides crucial information to design the composite battery electrode.

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In order to bridge the scales and enable such an analysis, a methodology comprising the key elements of the above virtual material design process is proposed. The process is based on the hypothesis that the additive on the nanometer scale can be imaged in 3D and its effective properties can be determined by micro-

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heterogeneous transport simulations based on image-processed data sets.

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FIB/SEM has been applied to image the porous additive domains in a graphite-based composite battery electrode. As a consequence of the high material porosity, the characteristics of the images generate big challenges for standard image processing methods. Hence, alternative image processing methods have been developed and applied. After binarization of the grey-scale data set, the transport properties of the additive have been determined by simulation. The active material on the micrometer scale is imaged as

processing methods.

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well using synchrotron radiography computed tomography (SR-CT) and binarized with established image-

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The additive has been introduced to control volumes in the appropriate pore space of the electrode structure by setting the effective properties in these control volumes according to the additive properties. Final-

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ly, the resulting impact on the electrode performance is calculated with a microheterogeneous simulation on the length scale of the active material. Figure 9 is a graphical depiction of this proposed process.

Similar approaches have been applied elsewhere, e.g. to determine the mass transport resistance of electrochemically non-active components of fuel cells [18],[19], however, to the knowledge of the authors, applying such an approach in a coupled electrochemical/transport simulation and, particularly, in the area of lithium ion battery, is novel.

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4.1. Mass Transport Simulation of Porous Media The mass transport resistance for diffusion in porous media is typically described by an expression corre-

bulk or free diffusivity Dbulk [20]:

(1)

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D eff ε = D bulk τ

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lating porosity ε and tortuosity (or, more accurate, tortuosity factor) τ with effective diffusivity Deff and

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Since the fluid in the lithium ion battery is liquid electrolyte, the factor ε/τ is determined by a mass transport simulation using the solid/void-resolving voxel mesh derived from the imaging and imageprocessing described earlier. Knudsen diffusion needs not be considered even in the small pores of the additive as the mean free path in the liquid is close to the molecule size and, hence, much smaller than the

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mean pore diameter of the pores considered here [21].

In order to determine the effective transport parameters or transport resistance, respectively, the GeoDict software application has been used [22]. GeoDict utilizes a voxel grid which reflects the solid/void struc-

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ture of a porous medium and solves the Laplace equation for the concentration c in the pore space

− ∆c = 0

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by applying Newman boundary conditions on the solid/void interfaces and Dirichlet boundary conditions at the domain edges, thereby determining the concentration flux j in the respective direction. With Fick’s law of diffusion

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r N = −Deff ∇c

(3)

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the effective diffusivity Deff and the factor ε/τ can be determined.

As described later, the transport resistance determined by the above simulations in terms of the dimensionless factor ε/τ is applied to set the effective transport properties, namely effective diffusivity and effective

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ion conductivity, in those control volumes of the voxel grid representing the active particle/electrolyte

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structure which act as the additive.

Nano-porous Additive

As a result of the imaging and image-processing as described above, a 3D voxel mesh reflecting the solid/void structure of the nano-porous additive has been imported to GeoDict (Figure 10). The size of the

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mesh was 518×253×256 voxel, and the edge length of the cubic voxels was 5 nm.

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The porosity of the additive has been determined to 59.5%, and the tortuosities have been determined as  τ x   2.5      τ =  τ y  =  2.0  .  τ   1.7   z  

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Apparently, the transport resistance is not isotropic in the sample considered here. To consider the additive as a transport limiting surface coating on the active particles correctly, the actual position of the sample volume relative to the adjacent active particles would be required which is not known. Furthermore, the distribution of the anisotropy in the composite electrode is not known, either. Finally, it is not known whether the properties of the sample volume are representative, or if the volume size itself represents a representative volume element (RVE) from the perspective of macro-homogeneous effective properties. Hence, for the following considerations the anisotropic transport resistance is averaged by τave=2.1 or ε/τave=0.281, respectively.

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Composition Process of Composite Electrode and Transport Simulation As mentioned above, the additive needs to be introduced to control volumes in the appropriate pore space

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of the active particle structure as derived from the SR-CT data set. The choice of the control volumes containing the additive was made by morphological closing of the pore space of the image-processed SR-CT data set using a sphere as structuring element. The closing enlarges the system of the active particles

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slightly into the pore space. Then the active particles were subtracted from the image, leaving the volume added by the closing as additive. The radius of the structuring element was determined, to match the ex-

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pected volume fraction for the additive. Although this is just a geometrical operation, it has a physical analogy as it models a wetting of the active particles with the additive. This assumption is justified by the actual electrode coating fabrication process which usually is a wet process [23][24].

Typically, an ink or paste is made from the solid ingredients, i.e. active material, conductivity-enhancing

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carbon and polymeric binder, and a suspending agent, e.g. NMP, which are mixed thoroughly. The ink or paste is fed to a wet coating process such as die coating or doctor-blading applying a thin electrode layer onto a substrate which usually is the current collector made from copper or aluminum. During the follow-

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ing drying of the coating, the solvent evaporates such that it is removed in the small pores last as it wets the solid surfaces. Consequently, the additive will be deposited in the small pores and in the contact area

tions.

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of the large active particles. The morphological operation mimics this process by geometrical considera-

Since the binder provides only a tiny fraction of the solid and its specific density is not significantly smaller than the graphite that constitutes the active material and conductivity enhancer, the error by assuming that 10 wt% additive constitute 10 vol% of the solid should be negligible. Hence, the morphological opening of the pore space to consider the additive aimed at meeting a 10 vol% additive portion of the solid fraction. Furthermore, the porosity of the additive needs to be considered as the additive is intro-

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duced to the pore space of the active material as an effective property. With approx. 60% porosity, the effective volume of the additive relative to the active material is rather 25%.

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Due to the fact that a voxel mesh has been used, only discrete fractions could be obtained. By using a sphere of six voxels radius, a volume fraction of 11.4% could be obtained which is close to the target number. Figure 11 depicts the resulting composite structure which comprises 47 vol% active material, 12

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vol% effective additive and 41 vol% pores. It is clearly visible that the additive amasses in those locations of the pore space where the local pore size is small, i.e. in small pores and the contact area of the active

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particles.

MAVI has also been applied to determine the specific surfaces of the porous electrode without and with additive, and from the discrete voxel surfaces the real surface area has been estimated [25]. The surface area of the active material exposed directly to the unconstrained pore saturated with electrolyte is 312565

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m²/m³ if no additive is considered and 113422 m²/m³ with additive, respectively. This means that more than 60% of the surface of the active material available to the intercalation reaction are actually covered

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with (pervious) additive.

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4.2. Battery Performance Simulation of Composite Electrode

Physicochemical Battery Model Current physicochemical battery models are typically based on the work of Newman and co-workers who applied concentrated solution theory and porous electrode theory to Li-ion battery simulation [26],[27]. Here, the rigorous derivation from non-equilibrium thermodynamics by Latz and Zausch has been applied [28] considering isothermal conditions, i.e. neglecting heat generation and thermal gradients. The derivation by Latz et al. slightly deviates from the traditional Newman model in the charge transport equation

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and thermal entropy production in the electrolyte thereby rigorously ensuring strictly positive entropy production and thermodynamic consistency.

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As the solid and electrolyte phases are resolved and, consequently, the transport equations for mass and charge are solved individually in the solid active particle control volumes and electrolyte control volumes, respectively, the transport equations to be solved for obtaining the fields for concentration c and electrical

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potential ϕ as given by [28] are as follows:

→ ∂c s →   = ∇⋅  D s ∇ c s  ∂t  

→  →  0 = ∇⋅  κ s ∇ φ s   

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∂ce →  → t → = ∇⋅  D e ∇ ce − + j  ∂t z+F  

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transport equations in the electrolyte:

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transport equations in the solid:

   →  → ( t + − 1)ℜT  ∂ ln f   1 +  ∇(ln ce ) 0 = ∇⋅ κ e ∇ ϕ e + κ e   z + F  ∂ ln ce  14243   "activity term"  

(5)

(6)

(7)

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→

(4)

Note that in the derivation of Latz and Zausch [28] φe is the electrochemical potential in the electrolyte, and not the electrical potential. Electrical potential φe and electrochemical potential φe are coupled relative to the chemical potential of Li metal by the chemical potential µ such that φe=φe+(µ e-µ Li)/(z+·F).

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The interface boundary condition between the solid active particle and the electrolyte describes the electrochemical intercalation reaction which is commonly done by a Butler-Volmer expression for the current

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ise across the interface between solid and electrolyte:

− αc F  α a Fη s ηs  ℜ T ( ise = cs ,max − c s ) e − e ℜT   144424443    exchange current density i0 αc 

α kce a csα a

(8)

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The overpotential ηs is defined by the electrical potential of the solid active material φs, the electrochemi-

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cal potential of the electrolyte φe and the open circuit potential U0:

ηs = φs − ϕe − U0

(9)

At the interface between solid and electrolyte, the electrical current in the solid js has to be fully compensated by the ionic current in the electrolyte je (equaling the Butler-Volmer current ise) to avoid any flux of

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electrons across the interface. It has rather to be ensured that any current across the interface is carried by

r r r r js ⋅ n = je ⋅ n = ise

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the lithium ion flux N+,s and N+,e, respectively:

(11)

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r r r r i N + ,s ⋅ n = N + ,e ⋅ n = se F

(10)

where n is the normal pointing from the solid to the electrolyte.

For the half-cell arrangement used in this study, only one electrode is porous and the counter electrode is represented as a lithium foil. Hence, the open circuit potential at the lithium foil surface is set to 0, and the exchange current density i0 is set to i0 = k ce [3].

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Figure 12 shows the regions where the transport equations for solid and electrolyte are solved individually as well as where the interface boundary condition (Butler-Volmer) is applied. In additive regions, the transport equations for the electrolyte are solved but the transport parameters are adjusted corresponding

tive surface of the solid but only impairs transport in the electrolyte.

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Cell Model – Architecture and Parameterization

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to the effective number as determined previously. Note that in this model the additive does not block ac-

As comprehensive imaging data of active material and respective additive only from one single electrode

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sample, namely a graphite-based electrode coating, was available, the computational case has been set up such that a half-cell arrangement of a Li-ion battery has been modeled (Figure 13). Since the potential of graphite relative to lithium is positive and the counter electrode has been implemented as a solid lithium foil reflecting actual lab arrangements used for material and coating development, the graphite-based electrode acts as the positive and the lithium foil as the negative electrode. This is specific to the half-cell ar-

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rangement with metallic lithium as the counter electrode. As the counter electrodes to graphite-based coatings in technical applications exhibit much more positive potentials than graphite relative to lithium,

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graphite in technical applications is typically acting as the negative electrode.

For reasons of simplicity whilst maintaining a realistic case set-up, a mass transport limiting separator has

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been considered but attributed with the same specific mass transport resistance as the additive. Compared to technical separators, the transport resistance applied here is somewhat lower which will help emphasize effects caused by the mass transport resistance in the additive and not covering it.

The footprint of the virtual half-cell is 200×200 voxel with 0.28 µm voxel edge length resulting in a geometric cross-section of 56×56 µm². The thickness of the porous positive electrode is also 200 voxels or 56 µm, respectively. The solid lithium negative counter electrode is assumed to be only five voxels (1.4 µm)

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thick. Negative and positive electrode are separated by a 25 µm gap filled with electrolyte, i.e. a separator with vanishing transport resistance is assumed.

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To compare the impact of the added mass transport resistance by the additive, two cases (or virtual cells) have been set up. As a reference case, any additive has been removed from the porous electrode, i.e. only active material besides the electrolyte saturating the pores has been considered (reflecting the SR data set).

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In contrast to that, the test case considers the additive in the above explained manner (reflecting the combined SR data set and structure model for additive distribution, i.e. the composite electrode). The additive is considered such that in those voxels or control volumes, respectively, that are dedicated additive control

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volumes, diffusion and ion conduction are reduced by the above transport resistance factor ε/τave. The surface of the active material is not affected, i.e. the surface available for the intercalation reaction remains unchanged. However, as the concentration of lithium is expected to be lower in surface areas covered by additive due to the higher transport resistance in the control volumes adjacent to these surface areas com-

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pared to the reference case, locally higher overpotentials and, consequently, some impact on the terminal voltage is expected.

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The material parameters for the negative electrode and the electrolyte and separator, respectively, are listed in Table 1. Since the negative electrode is considered as a lithium foil, maximum and initial concen-

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tration and diffusion constant are irrelevant, and open circuit potential is set to zero. 25°C have been chosen as operating temperature.

5. Results and Discussion

In order to compare low and high transport regimes, two load cases have been chosen: 1 C discharge for “low transport rates” and 5 C discharge for “high transport rate”. In contrast to the technical definition of

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C rate, the physical definition has been applied, i.e. the physical capacity of the cell given by the theoretical capacity of the anode has been used as the reference to calculate the current needed to completely dis-

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charge the electrode within one hour (or in one fifth of an hour for the 5 C rate, respectively).

Figure 14 shows the result in terms of the terminal voltages of both cases at low and high discharge rate and the voltage difference of the cases without and with additive for both low and high discharge rate. At

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the low discharge rate of 1 C, the impact of the additive is negligible as the transport resistance introduced by the additive adds only a couple of millivolts to the overall overpotential. However, with increasing load

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the portion of the added transport loss increases. At a 5 C discharge rate, the potential difference of the two cases rises to approx. 35 mV. The initial increase of the overpotential added by the transport resistance in the additive is characteristic for the transient behavior of the processes in the cell as it takes some time to establish concentration gradients from the initial situation of homogeneous lithium ion dis-

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tribution prior to drawing current from the cell.

It needs to be mentioned that while a discharge rate of 5 C may be considered high in battery electric vehicles without (BEV) or with range extender (EREV), other applications like plug-in electric vehicles

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(PHEV) or hybrids may experience much higher discharge rate of several 10 C. It has to be expected that in these cases, the impact of considering (or not considering) the additive may be pronounced dispropor-

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tionally as indicated by these results. In this case, increasing the load fivefold translates to a tenfold increase of the potential discrepancy.

Furthermore, having in mind that this study considers half-cell situations only, non-negligible impact of the additive may require more attention in full cells as both electrodes will comprise additives and the effect thereof may add up. Hence, these results indicate an error of performance prediction in the several ten millivolt, if not 100 mV, order of magnitude by inappropriate consideration of the mass transport resistance in the additive alone. From a battery system engineering perspective, 100-300 mV overall error

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(3-10% for typical cells) for the performance prediction of a given cell may be tolerable. However, the design process is typically vice versa, i.e. performance is specified and needs to be met by the cell supplier, possibly resulting in an adaption of cell architecture. For instance, 10% change in cell thickness to

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meet a performance or capacity requirement translate to 1 mm absolute change of a 10 mm thick cell (which is a representative cell thickness). 100 cells stacked would require a 10 cm packaging tolerance which is very demanding (for comparison, in the Opel Ampera, 288 cells are stacked in a T-shaped battery

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[33]).

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Figure 15 shows the through-plane evolution of the local Li-ion flux magnitude as an average across one cross-sectional slice and the maximum fluxes in these respective slices for both cases. The average fluxes are almost identical, minor differences may be explained by through-plane redistributions of the fluxes caused by the addition of additive. The average flux needs to be the same in both cases as the load boundary condition is the same.

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The maximum Li-ion fluxes, though, deviate distinctly. The local redistribution of the Li-ion flux in the electrolyte (in open pores as well as in the additive) caused by the local existence of additive causing a local resistance for lithium ions to migrate from the electrolyte to the surface of the active particles, appar-

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ently causes local flux peaks exceeding those of the reference case by a factor of up to two. This is particularly remarkable as the increase of the transport resistance by the factor of 1/(ε/τave)=1/0.281=3.6 does

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not appear to be distinctively high. However, the large portion of active material surface covered with pervious additive (approx. 60%, see above) may explain the magnitude. The local analysis of the discharge situation in the above cases indicates differences of the Butler-Volmer overpotential of only a few millivolts. However, in a charge situation, notably at high charge currents, such redistributions of local lithium ion flux and, hence, of the local overpotential may cause local deposition of metalic lithium, i.e. Li plating, not indicated by the overall cell potential thereby generating degradation seeds. It may be hypothesized that the transport resistance and distribution of the additive might have an impact on both, cell performance and life.

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The quantitative assessment of the relevance of the reported observations related to additional mass transport resistance introduced by the nanoporous additive needs to be seen in the context of the model

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depth of the physicochemical performance model and its parameterization applied here. Further analysis is needed with regard to (i) uncertainties of the parameterization of the model and (ii) the model simplifications.

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Important examples for parameterization uncertainties are the Butler-Volmer rate constants or exchange current densities, respectively, and the diffusivities of lithium in the solid active material. Lithium diffu-

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sivities reported in literature, for instance, range across orders of magnitude, and a dependency of lithium diffusivity on lithium concentration is known [34]. This may be due to the circumstance of the high anisotropy of diffusive mass transport in graphite depending on whether transport takes place along or perpendicular to the basal planes of graphite. Dedicated transport analysis exhibited basal-plane lithium diffusivities of 9⋅10-12 cm²/s compared to 4⋅10-6 cm²/s in the edge-plane [35]. The exposition of basal-plane or

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edge-plane surfaces of the active material with regard to the electrolyte furthermore also determine the local exchange current density which enters the Butler-Volmer relationship. For instance, Tran et al. reported almost two orders of magnitude higher current density for electrochemical processes on exposed

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edge planes compared to exposed basal planes [36]. All told, it may have an impact for the microheterogeneous considerations presented in this paper whether the surface area of the active particle exposed to

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the electrolyte and available to lithium intercalation addresses the differences of intercalation kinetics and mass transport resulting from the high anisotropy of graphite structure. From a perspective of pragmatism, though, selecting the “right” lumped or effective number or constitutive relation for lithium diffusivity in the graphite and exchange current density or rate constant, respectively, appears to be a reasonable approach. Besides parameterization uncertainties, model form error or model simplifications also needs to be considered to reliably quantify the impact of singular mechanisms. For instance, the impact of intercalation induced change of specific active material volume and its impact on macroscopic cell thickness is known

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but with regard to microscopic pore morphology changes not well understood. With reported swelling of more than 14% in the first cycle of the pristine material (so-called formation) and 4-5% swelling swings between succeeding cycling for graphite (and several 100% for silicon-based negative electrode materials)

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[37], a significant impact and state-of-charge-related effect on the pore structure and, hence, transport resistance needs to be expected and considered in future model improvements. Another mechanism which so far has not been considered in the performance model presented here is the solid/electrolyte interphase

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(SEI). The SEI is a film generated on the surface of the active material exposed to the electrolyte, typically by a decomposition reaction of the electrolyte under consumption of lithium [38]. Pristine electrodes form

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this film already in the first cycle, and the film slowly growths with cycle life. This mechanism is desired on one hand as the surface film acts as a protective layer, e.g. by suppressing graphite exfoliation due to electrolyte absorption. On the other hand, the SEI binds lithium which reduces the battery cell capacity and it further adds resistance to the lithium migration from the electrolyte to the solid active material. Colclasure et al., for instance, analyzed the chemistry of SEI formation and provided a model for additional

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overpotentials in the order of several 10 mV introduced by the SEI [39]. The SEI being more and more in the focus of improved lithium battery performance models apparently adds overpotentials that are in the same order of magnitude as the additional transport resistances introduced by the additive analyzed in this

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publication. Further comparative analysis of the additive effect compared to the SEI, hence, requires model improvement by SEI consideration, e.g. as commonly done by introducing an additional ohmic re-

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sistance attributed to the SEI in the Butler-Volmer equation [11],[39],[40]. The complexity of potentially existing mechanisms and the difficulty to quantify their impact on the macroscopic battery cell performance, let alone to reflect them in the equation system of the model, in the end justifies the simplification of the overall model to investigate the individual impact of single mechanisms like the transport resistance introduced by the additive.

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Conclusions A comprehensive and multi-scale process for physicochemical simulation of lithium ion batteries down to the scale of the composite porous electrode has been developed and demonstrated. Building blocks of the

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process comprise three-dimensional imaging of the porous constituents of the electrodes, i.e. the porous nanometer-scale additive and the porous micrometer-scale active material, image processing, homogenization on small scale and consideration of small scale transport properties as effective properties on large

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scale and, finally, electrochemical performance simulation resolving the large scale of the porous lithium

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battery electrode.

Tentative simulation results based on a half-cell configuration indicate negligible impact of mass transport limitations introduced by the distribution of the nanometer-scale additive in the void of the pore structure generated by the active material at low electric loads. However, elevated electric loads that are occurring in battery electric vehicles increasingly emphasize lithium ion transport resistances in the porous battery

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electrode with visible impact on the performance behavior. Higher electric loads which occur in hybrid vehicles and full battery cell arrangements (instead of half-cell configurations) where effects at both the positive and the negative electrode add up promise to reveal a non-negligible impact of the transport re-

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sistance introduced by the additive in the porous composite battery electrode. Further studies consequently need to analyze this transport resistance in more detail. In addition to that, as discussed above, the valida-

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tion of the overall physicochemical model by a detailed, consistent and comprehensive material characterization and model validation effort is required to enable a quantitative assessment of the sensitive mechanisms in the established models as well as reveal additional mechanisms to be implemented. Important next steps of model refinement definitely comprise (i) the consideration of the SEI either indirectly in the parameterization of the kinetic model or by direct addition of an SEI growth model and (ii) the consideration of the impact of changing solid/void morphology by intercalation-induced variation of specific active material volume. Any reasonable next step associated with the introduction of new mechanisms should certainly also comprise experimental work to validate the findings obtained by modeling and simulation.

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Nomenclature concentration, mol/l

ce

concentration in the electrolyte, mol/l

cs

concentration in the solid, mol/l

cs,max

maximum concentration in the solid, mol/l

Dbulk

bulk diffusion coefficient, cm²/s

De

diffusion coefficient in the electrolyte, cm²/s

Deff

effective diffusion coefficient, cm²/s

Ds

diffusion coefficient in the solid, cm²/s

f

activity coefficient

F

Faraday constant, 96487 C/mol

i0

exchange current density, A/m²

ise

Butler-Volmer current, A/m²

N

concentration flux, mol/(cm²·s)

N+,e

concentration flux of Li ions in the electrolyte, mol/(cm²·s)

N+,s

concentration flux of Li ions in the solid, mol/(cm²·s)

j

electrical current

js k

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je

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c

electrical current in the electrolyte

electrical current in the solid

reaction rate constant, A·m5/2·mol3/2

n

normal pointing from the solid to the electrolyte

U0

open circuit voltage, V

ℜ

gas constant, 8.314 J/(mol·K)

t

time, s

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transference number

z+

number of elementary charge per ion (z+=1 for Li+)

α

charge transfer coefficient

αa

charge transfer coefficient in the anode

αc

charge transfer coefficient in the cathode

ε

porosity (volume fraction of void)

κ

specific conductivity, S/cm

κe

specific (ion) conductivity in the electrolyte, S/cm

κs

specific (electron) conductivity in the solid, S/cm

η

overpotential, V

ηs

Butler-Volmer overpotential of charge transfer, V

φ

electrical potential, V

φe

electrical potential in the electrolyte, V

φs

electrical potential in the solid, V

φ

electrochemical potential, V

φe

electrochemical potential in the electrolyte, V

µ

chemical potential, J/mol

µe

chemical potential in the electrolyte, J/mol

µ Li

chemical potential of Li metal, J/mol

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τ

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t+

tortuosity factor

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Acknowledgement The imaging and development of image-processing algorithms and methodologies has been supported by

(05M10AMA) which is thankfully acknowledged.

[1]

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References

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the German Federal Ministry of Education and Science BMBF in the context of the funded project AMiNa

U.Eberle, R. v. Helmolt, Fuel Cell Electric Vehicles, Battery Electric Vehicles, and their Impact

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on Energy Storage Technologies: An Overview, Electric and Hybrid Vehicles (2010), Chapter 9, 227-245 [2]

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J. Becker, R. Flückiger, M. Reum, F. Büchi, F. Marone, M. Stampanoni, Determina-tion of Ma-

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rous materials of electrochemical cells in the CAE design process, SIMVEC 2010

terial Properties of Gas Diffusion Layers: Experiments and Simulations Us-ing Phase Contrast Tomographic Microscopy, Journal of The Electrochemical Society, 156 (10) B1175-B1181 (2009)

[6] C.-W. Wang et al., Mesoscale Modeling of a Li-Ion Polymer Cell, Journal of The Electrochemical Society, 154 (11) A1035-A1047 (2007)

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[7] G.M.Goldin et al., Three-dimensional particle-resolved models of Li-ion batteries to assist the evaluation of empirical parameters in one-dimensional models, Electrochimica Acta 64 (2012) 118– 129

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[8] V. Zadin et al., Modelling electrode material utilization in the trench model 3D-microbattery by finite element analysis, Journal of Power Sources 195 (2010) 6218–6224

[9] Gupta et al., Effective Transport Properties of LiMn2O4 Electrode via Particle-Scale Modeling,

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Journal of The Electrochemical Society, 158 (5) A487-A497 (2011)

[10] Carbon powders for Lithium battery systems, Timcal product brochure 2005

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[11] T. Hutzenlaub et al., Three-dimensional electrochemical Li-ion battery modelling featuring a focused ion-beam/scanning electron microscopy based three-phase reconstruction of a LiCoO2 cathode, Electrochimica Acta 115 (2014) 131– 139 [12] MatWeb material Property Data

(http://www.matweb.com/search/datasheettext.aspx?matid=2690)

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[13] M. Martinez-Rodriguez, Characterization of Microporous Layer in Carbon Paper GDL for PEM Fuel Cell, ECS Transactions 33 (2010) 1133-1141 [14] Mirone, A., Brun, E., Gouillart, E., Tafforeau, P., Kieffer, J., The PyHST2 hybrid distributed

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code for high speed tomographic reconstruction with iterative reconstruction and a priori knowledge capabilities, Nuclear Instruments and Methods in Physics Research Section B: Beam

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Interactions with Materials and Atoms, Volume 324, 1 April 2014, Pages 41-48 [15] Prill, T., Schladitz, K., Jeulin, D., Faessel, M. and Wieser, C. (2013), Morphological segmentation of FIB-SEM data of highly porous media. Journal of Microscopy, 250: 77–87. doi: 10.1111/jmi.12021

[16] Prill, T. and Schladitz, K. (2013), Simulation of FIB-SEM Images for Analysis of Porous Microstructures. Scanning, 35: 189–195. [17] Fraunhofer ITWM, Department of Image Processing. MAVI – modular algorithms for volume images. http://www.mavi-3d.de, 2005.

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[18] Ch. Wieser, Nanoporous and Microporous Materials in Fuel Cell Applications, New Congress Materials Science and Engineering, Nuremberg, September 4, 2008 [19] J. Becker, Ch. Wieser, S. Fell, K. Steiner, A multi-scale approach to material modeling of fuel

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cell diffusion media, International Journal of Heat and Mass Transfer 54 (2011) 1360–1368 [20] N. Epstein, On tortuosity and the tortuosity factor in flow and diffusion through porous media, Chemical Engineering Science 44 (1989)779-781

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[21] P. Ganesh et al., Accurate Static and Dynamic Properties of Liquid Electrolytes for Li-Ion Batteries from ab initio Molecular Dynamics, J. Phys. Chem. B 115 (2011) 3085–3090

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[24] M. Wolter, S. Börner, U. Partsch, ELEKTRODENFERTIGUNG FÜR LITHIUMBATTERIEN

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IM TECHNIKUMSMASSSTAB, Fraunhofer IKTS Jahresbericht 2012/13, 110-111 [25] J. Ohser, K. Schladitz, 3d Images of Materials Structures - Processing and Analysis, Wiley 2009 [26] M. Doyle, Modeling of Galvanostatic Charge and Discharge of the Lithium/Polymer/Insertion

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Cell, Journal of the Electrochemical Society 140 (1993) 1526-1533 [27] T. Fuller, Simulation and Optimization of the Dual Lithium Ion Insertion Cell, Journal of the

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Electrochemical Society 141 (1994) 1-10 [28] A. Latz, J. Zausch, Thermodynamic consistent transport theory of Li-ion batteries, Journal of Power Sources 196 (2011) 3296-3302

[29] C.J. Wen at al., Thermodynamic and Mass Tansport Properties of “LiAl”, Journal of the Electrochemical Society 126 (1979) 2258-2266 [30] P. Albertus et al., Experiments on and Modeling of Positive Electrodes with Multiple Active Materials for Lithium-Ion Batteries, Journal of The Electrochemical Society 156 (2009) A606A618

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[31] L.O. Valøen, Transport Properties of LiPF6-Based Li-Ion Battery Electrolytes, Journal of the Electrochemical Society 152 (2005) A882-A891 [32] C.M. Doyle, Design and Simulation of Lithium Rechargeable Batteries, PhD Thesis University

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of California UC-210 (LBL-37650) 1995 [33] Roland Matthé and Ulrich Eberle, The Voltec System – Energy Storage and Electric Propulsion, In: Lithium-Ion Batteries, edited by Gianfranco Pistoia, Elsevier, Amsterdam, 2014, Pages 151-

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176, ISBN 9780444595133, http://dx.doi.org/10.1016/B978-0-444-59513-3.00008-X.

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(2004)

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for a Composite Graphite Anode, Journal of The Electrochemical Society, 151 (8) A1247-A1250

[35] K. Persson et al., Lithium Diffusion in Graphitic Carbon, The Journal of Physical Cehmistry Letters 2010, 1, 1176-1180

[36] T. Tran et al., Lithium intercalation/deintercalation behavior of basal and edge planes of highly

(1995) 221-224

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oriented pyrolytic graphite and graphite powder, Journal of Electroanalytical Chemistry 386

[37] N. Zhang, Dissecting anode swelling in commercial lithium-ion batteries, Journal of Power

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Sources 218 (2012) 52-55

[38] D. Auerbach, The Role Of Surface Films on Electrodes in Li-Ion Batteries, in: Advances in Lith-

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ium-Ion Batteries, Kluwer Academic/Plenum Publishers, 2002 [39] A.M. Colclasure et al., Modeling detailed chemistry and transport for solid-electrolyte-interface (SEI) films in Li–ion batteries, Electrochimica Acta 58 (2011) 33– 43

[40] L. Liu et al., A thermal-electrochemical model that gives spatial-dependent growth of solid electrolyte interphase in a Li-ion battery, Journal of Power Sources 268 (2014) 482e490

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Table 1 Parameterization of half-cell model.

n/a n/a OCP = 0 V n/a 0.038 S/cm

reaction rate constant

0.2 (A/cm²)/(mol/cm³)1.5

Li concentration: maximum initial OCP relation

31368·10-6 mol/cm³ 20076·10-6 mol/cm³ f(SOC)

Li diffusion coefficient

3.9⋅10-10 cm²/s

electron conductivity

1 S/cm

reaction rate constant

0.2 (A/cm²)/(mol/cm³)1.5

initial salt concentration activity term

1000⋅10-6 mol/cm³

ion conductivity

f(c)

Li diffusion coefficient

7.5⋅10-6 cm²/s

transference number

0.363

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separator

ion conductivity Li diffusion coefficient initial salt concentration activity term transference number

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reference

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electrolyte

value

Error! Reference source not found. Error! Reference source not found.

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positive electrode

parameter Li concentration: maximum initial OCP relation Li diffusion coefficient electron conductivity

theoretical number technically representative Error! Reference source not found. Error! Reference source not found. Error! Reference source not found. Error! Reference source not found. technically representative

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domain negative electrode

1

electrolyte reduced by factor of 0.281 as electrolyte

simplification (not distinctively sensitive) Error! Reference source not found. Error! Reference source not found. Error! Reference source not found. reduction factor as determined in this publication

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Figure captions for manuscript “Multiscale Process for Simulation of Composite Battery Electrodes” Christian Wiesera, Torben Prillb, Katja Schladitzb a) Adam Opel AG, IPC S1-01, 65423 Rüsselsheim, Germany, [email protected], (corresponding author: phone +49-6142/7-65773, fax +49-6142/7-78165)

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b) Fraunhofer Institut für Techno- und Wirtschaftsmathematik ITWM, Fraunhofer-Platz 1, 67663 Kaiserslautern, Germany ([email protected], [email protected])

Figure 1 Comprehensive, predictive and interconnected process “from material to module/battery”.

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Figure 2 SEM image of electrode coating surface showing large active material particles connected and partially coated with additive layer.

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Figure 3 Virtual material design process

Figure 4 Schematic of serial sectioning and imaging by FIB/SEM.

Figure 5 Representative SEM image obtained by FIB serial sectioning. The large particle at the bottom left is part of the active material while the porous area represents the additive. Figure 6 Exemplary slice of the reconstructed SR-CT imaging data set of the active material coating (size: 287×287 µm², resolution 0.28 µm).

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Figure 7 Flow chart of the segmentation procedure used for the additive.

Figure 8 Volume rendering of the segmented active particles from SR-CT. Figure 9 Proposed procedure to evaluate impact of nano-scale additive in µ-scale active material on cell performance by consolidating scales through homogenization.

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Figure 10 Volume rendering of final image-processed voxel mesh of nano-porous additive.

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Figure 11 Computational domain for the electrochemical battery simulation reflecting the composite battery negative electrode comprised of the large active particles and the distributed small-scale additive. Figure 12 Detail of meshed porous negative electrode in Figure 11 showing the regions for the transport regimes as well as the interface situation; note that the interface reaction is implemented also at the solid/additive interface. Figure 13 Virtual half-cell used as arrangement in this study. Figure 14 Impact of consideration of additional transport resistance introduced by additive at low and high discharge current. Figure 15 Through-plane distribution of slice-averaged Li-ion flux and maximum Li-ion fluxes in respective slices.

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Macrohomogeneous Physicochemical Battery Cell Performance Model

Electro-Thermal Battery Module & Pack CFD Model

Equivalent Circuit Battery Cell Performance Model

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Microheterogeneous Physicochemical Battery Cell Performance Model

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experimental customer

modeling/simulation

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imaging and image processing need to provide “as correct as possible” structure grid

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experimental

material fabrication and model validation homogenized properties for simulation of material in application

modeling/simulation customer and supplier

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material imaging on pore scale

simulation of relevant mass structure-resolving and heat transport computational grid virtual mechanisms design from imaging or on pore scale cycle virtual structure to derive macromodel scopic, effective performance

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Preprocessing

Thresholding

Constrained Watershed

Minima of z-Profiles

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Preliminary Segmentation

Half Gradient of z-Profiles

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Thresholding

Thresholding

Result

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Input Image

Morphological Gradient

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execute battery simulation of active material only

active material scale: 1..10 µm method of choice: x-ray CT, SR-CT

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compare global battery performance and local effects

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process steps: 1. determine effective transport properties by pore-scale simulation 2. virtually infiltrate active material through morphological closing 3. consider additive by its homogenized, effective properties here: assign electrolyte effective diffusivity and conductivity

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additive scale: 10 nm method of choice: FIB/SEM

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“free” transport in electrolyte in open pore

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transport in solid active material

effective transport in electrolyte in porous additive

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solid positive electrode (Li foil)

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separator area (bulk electrolyte properties assumed)

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porous composite negative electrode

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30

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-0,4

40 voltage discrepancy [mV]

5C, no additive 5C, with additive discrepancy 5C no/with additive

-0,8

20

1E-08

2E-08 3E-08 4E-08 transferred charge [Ah]

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half-cell voltage [V]

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5E-08

10

0 6E-08

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4,0E-06

ave. flux, no additive

ave. flux, with additive

max. flux, no additive

max. flux, with additive

RI PT

3,0E-06

2,0E-06

1,0E-06

0,0E+00

0,00

0,20

0,40

SC

Li ion flux magnitude [mol/s]

5,0E-06

0,60

0,80

AC C

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TE

D

M AN U

normalized through-plane position in electrode [-]

1,00

ACCEPTED MANUSCRIPT

Highlights

EP

TE D

M AN U

SC

RI PT

A multiscale, multiphysics simulation process for Li-ion batteries is demonstrated. 3D imaging and image-processing of porous battery materials is included. Computational grid resolves electrode morphology. Simulation case comprises both nano- and micro-scale electrode materials. Results indicate simulation relevance of nanoporous additive.

AC C

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