Quantifying Transport, Geometrical, and Morphological Parameters in

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Quantifying Transport, Geometrical and Morphological Parameters in Li-ion Cathode Phases using X-ray Microtomography Thushananth Rajendra, Aashutosh N. Mistry, Prehit Patel, Logan Ausderau, Xianghui Xiao, Partha P. Mukherjee, and George Nelson ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.8b22758 • Publication Date (Web): 08 May 2019 Downloaded from http://pubs.acs.org on May 8, 2019

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ACS Applied Materials & Interfaces

Quantifying Transport, Geometrical and Morphological Parameters in Li-ion Cathode Phases using X-ray Microtomography Thushananth Rajendra1, Aashutosh N. Mistry2,a, Prehit Patel1, Logan J. Ausderau1, Xianghui Xiao3,†, Partha P. Mukherjee2,b,*, George J. Nelson1,c,* 1Department

2School

of Mechanical & Aerospace Engineering, The University of Alabama in Huntsville, Huntsville, AL 35899, USA of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA

3Advanced †Current

Photon Source, Argonne National Laboratory, Lemont, IL 60439, USA

Affiliation: National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, NY 11973, USA

Keywords: NMC Cathode; Binder/Conductive Additives; X-ray microtomography; Microstructural characterization; Electrode processing; Transport phenomena

COI Disclosure Note: The authors declare no competing financial interest. a

ORCID: 0000 – 0002 – 4359 – 4975 ORCID: 0000 – 0001 – 7900 – 7261 c ORCID: 0000 – 0002 – 1170 – 245X * Corresponding authors: [email protected] (GJN), [email protected] (PPM)

b

ACS Paragon Plus Environment

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ACS Applied Materials & Interfaces 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Abstract The charge/discharge capabilities of Li-ion cathodes are influenced by the meso-scale geometry, transport properties and morphological parameters of the constituent phases in the cathode: active material, binder, conductive additive and pore. Electrode processing influences the structure and attendant properties of these constituents. Thus, performance of the battery can be enhanced by correlating various electrode processing techniques with the charge/discharge behavior in the Lithium-ion cathodes. X-ray microtomography was used to image samples obtained from pristine Li(Ni1/3Mn1/3Co1/3)O2 (NMC) cathodes subjected to distinct processing approaches. Two sample preparation approaches were applied to the samples prior to microtomography. Casting the samples in epoxy yielded only an cathode active material domain. Encapsulating the sample with Kapton tape yielded phase contrast data that permitted segmentation of the active material, combined carbon/binder and pore regions. Geometrical and morphological details of the active material and the secondary phases were characterized and compared between the varied processing approaches. Calendered and ball-milled samples exhibited distinct differences in both geometry and morphology. Drying modes demonstrated variation in the distribution of the secondary and pore phases. Applying phase contrast capabilities, the processing-morphology relationship can be better understood to enhance overall battery performance across multiple scales.

1. Introduction The lithium-ion battery (LIB) is a leading candidate for energy storage applications due to its high energy density, high specific power and long cycle life compared to other energy storage devices1–3. The optimization of LIBs is a challenging problem, due to the combined effects of electrochemical, transport, mechanical, morphological and thermal characteristics on the ability


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of the battery, its components, and their constituent materials to deliver and store energy for increasingly demanding applications4–6. Electrochemical operation of a battery electrode relies on multiple transport processes in discrete phases and electrochemical reactions at the active material-electrolyte interface7–9. These phases and their specific geometrical arrangement dictate the overall electrochemical response8,10,11. Numerous properties of the components that make up the battery–the electrolyte, cathode, anode and separator, along with the constituent materials should be scrutinized. Understanding the impact of these components and materials, as well as their discrete and aggregate properties is necessary to maximize the performance and lifetime of LIBs systems. The common LIB can be defined as a domain with two electrodes, cathode and anode, typically separated by a polymer film in which the electrodes and separator film are porous and contain a liquid electrolyte. The cathode enables the storage of lithium ions (Li+) by forming ion complexes within the active material, usually a lithium transition metal oxide. Electrochemical reactions and the storage and transport of lithium (Li) in the active material are influenced by the particle morphology and geometry. A secondary phase8, an agglomerate of carbon black conductive additive and polymer binder, is interspersed with the active material. The conductive additive increases the electrical conductivity, and the secondary phase keeps the active material attached to the different phases present in the porous electrode 12. Multiscale porous regions are formed during electrode preparation. The morphology of these regions significantly influences the movement of Li+ within the electrodes. The behavior of LIBs can be studied through a combination of experiment and mathematical modeling to assess physical and electrochemical processes occurring within the battery. The influence of electrode specifications such as thickness and porosity 13–15, the composition ratio of


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binder to conductive additive 12,16 and the particle size 17 on the different capabilities of the battery (energy density, lifecycle, charging rate and rate capability) have been studied both experimentally and computationally. Recently, due to advancement in 3D imaging methods, microstructures in the composite electrodes can be readily discerned and used as computational domains in simulations to complement experimental observations 12,18. 3D images have the capability of providing quantitative data that can help identify percolation, connectivity and other aspects of phase networks to better understand how microstructure impacts electrode performance. Focused Ion beam/Scanning electron microscope (FIB/SEM) is capable of resolving structures in great detail but destroys the imaged sample. FIB/SEM has been applied extensively for the study of 3D microstructures in Li-ion batteries5,19,20. On the other hand, X-ray tomography is a non-destructive imaging technique that has been applied to the study of Li-ion battery components at multiple scales18,21,22. In the present work, cathodes based on the symmetric layered compound Li(Ni1/3Mn1/3Co1/3)O2 (NMC) are studied. Synchrotron-based X-ray microtomography (µCT) was applied to extract the 3D microstructure of NMC cathodes to assess the impact of production methods on the overall behavior of the electrode. The extracted microstructural information includes the NMC active material (AM), secondary phases (conductive additives/PVDF) and macropore regions for thin electrodes. The FIB-SEM technique is known to distinguish the different phases 19 while X-ray tomography has shown limitations in that aspect because the secondary phases have very low attenuation coefficients and may not be readily distinguishable from the pore space 21. Zernike phase contrast imaging has been implemented for to yield a sparse, heterogenous secondary phase of conductive additive and polymeric binder 23. For synchrotron-based microtomography


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carbonaceous materials, silicon particles and void spaces have been segmented in Si laminated electrodes through a quantitative phase-contrast imaging technique24. Despite advances in discerning secondary phases in Li-ion cathodes 19,25, there has been a limitation in understanding the influence of these phases on cathode transport parameters and their attendant influence on performance. To further this understanding, an approach similar to the quantitative phase-contrast imaging technique26 was implemented in the present work. X-ray microtomography measurements yielded phase contrast information on the secondary phases and the porous regions of Li(Ni1/3Mn1/3Co1/3)O2 cathode samples. Image processing techniques were exploited to extract the subtle differences between the active material, secondary phases and the pore space within the electrode domain. Due to the lower instrument resolution of the µCT measurements, the secondary phases were defined as an agglomerate of sub-resolution AM particles, microscale porous regions, carbon conductive additive and binder. Nevertheless, statistically significant variations in mesoscale morphology were found between the processing approaches. Effective transport parameters were determined based on microstructural data to evaluate the diffusion time of Li within the active material and Li+ ions through the pore phase. Consequently, diffusion times are correlated with capacity estimates obtained using a pseudodirect numerical simulation (DNS) battery model. The present work demonstrates the capability of X-ray microtomography to image multiple cathode phases. In combining this experimental characterization with numerical studies the impact of processing on microstructural morphology, cathode transport behavior, and battery performance is further uncovered.


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2. Experiment 2.1. Electrode Preparation The purpose of this study was to investigate how processing variants impact the structure and transport characteristics of lithium ion cathodes. The imaged electrode samples were from the same set analyzed by Nelson et al.22. The electrode processing method followed in this work was described in detail by Stein et al.27. For the electrodes studied LiNi1/3Mn1/3Co1/3O2 was obtained from Targray, Kynar Flex 2801 PVDF was obtained from Arkema, and 1.0M LiPF6 was purchased from BASF. Super C-65 (carbon black) was obtained from TIMCAL. The NMC, Super C-5 and the NMP were mixed together for about 15 minutes; this process was followed by the addition of 10% by weight of PVDF/NMP solution. The suspension was then mixed for another 5 minutes in total prior to casting on a foil current collector. The current study investigates four different manufacturing methods (variants) that affect the morphology and transport characteristics of the electrode. In the first variant, the cast slurry was dried rapidly in a single drying step at 70 °C. In the second variant, the cast slurry was dried gradually with an initial drying stage at 25 °C for 16 hours followed by a second drying step at 70 °C for 1 hour. In the third variant, an electrode subjected to the gradual (2-step) drying process was calendered with 2 MPa calendering pressure. In the fourth variant, the as-received NMC powder was ball milled followed by the rapid (1-step) drying process. These variants are designated as cathodes 1-4, as summarized in Table 1. 2.2.

X-ray Microtomography Measurements

Two approaches were applied in preparing samples for the µCT measurements: casting in epoxy and encapsulating in Kapton tape. These approaches are described further in the Supporting


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Information. The microstructural characteristics of the NMC active material phase were assessed for samples prepared with both methods. No effect of sample preparation was seen on the NMC active material phase. The samples prepared by encapsulation in Kapton tape yielded phase contrast information that permitted segmentation and analysis of the pore and carbon/binder regions. The sample set is summarized in Table 1. The term sample region in Table 1 refers to regions covering a consistent electrode area of 175.5 µm x 422.5 µm that were extracted from the tomographic data for segmentation and analysis. Synchrotron-based P8 was performed on samples extracted from the composite electrodes at a resolution of 1.30 P' (0.65 P' pixel size) using beamline 2-BM-A at the Argonne National Laboratory Advanced Photon Source (APS). The P8 scans were performed in white beam mode with an exposure time of 50 ms per projection image. The white beam energy applied at 2BM-A extends up to 100 keV. However, there is phase contrast in the projection images due to a partially coherent X-ray beam that allows for phase retrieval in the tomographic reconstructions. Each tomographic scan contained 1500 projection images equally spaced over 180o of rotation. Table 1. Overview of sample set and sample regions extracted for analysis Treatment

Cathode 1

Cathode 2

Cathode 3

Cathode 4

Drying

Rapid

Gradual

Gradual

Rapid

Calendering

No

No

Yes

No

Ball Milling

No

No

No

Yes

Epoxy Cast Samples

2

2

2

2

Kapton Encapsulated Samples

3

3

4

4

Total Sample Regions

5

5

6

6

Sample Regions with Phase Contrast

3

3

4

4


7


2.3.

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Image Reconstruction

Once the measurements were taken the transmission images were reconstructed using a filtered back projection algorithm available in TomoPy28. The general reconstruction process is illustrated in Figure 1.a. The first step in the reconstruction process was to iteratively find the rotational center28. Following identification of the center phase retrieval and reconstruction were completed. The imaged samples had some slight tilt from the vertical axis. While this tilt was not found to impact the quality of the reconstruction, it did present an initial challenge in defining the full electrode domain, without excess open regions, over the reconstructed image stack. Therefore, the images were realigned as a final step prior to segmentation. Additional details of the reconstruction are provided in the Supporting Information. 2.4.

Segmentation of Cathode Phases

To obtain geometrical and morphological details from the cathode samples the distinct phases were segmented. Segmentation and analysis were performed on sample regions extracted from the larger tomographic data sets. These sample regions covered a consistent electrode area of 175.5 µm x 422.5 µm. Different methods of segmentation have been applied on tomographic data in the past. Ebner et al. combined a watershed technique with distance transform to segment NMC particles in cathode samples; shared surface area and proximity of the particles’ volume centers were used as a criterion to lower the over-segmentation of the particles29. Hutzenlaub et al. used histogram characteristics with a thresholding algorithm to segment the different phases in a porous electrode 19. In the present work, two different segmentation techniques were followed to distinguish between the active material, carbon/binder and the pore. The application of the two segmentation methods corresponds to the different sample preparation approaches: casting in epoxy and encapsulating with Kapton tape.


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The first segmentation technique, referred to as the watershed method, strictly segmented the active material alone from the sample regions. This segmentation approach applied a minimum operation, initial thresholding and a watershed segmentation to convert the gray scale image to a binary image of distinct AM particles as illustrated in Figure 1.b (i-viii). Corresponding details are given in the Supporting Information. Given the difference in attenuation between the NMC active material and the other phases, the active material could be readily segmented from the less attenuating phases. The watershed method was applied to all of the electrode sample regions, indicated by the total sample region count in Table 1. Active material characteristics were segmented for 22 sample regions across the processing variants. No effect of sample preparation was seen on the characterization data for NMC active material phase. The latter segmentation method separates the phases present in the porous electrode using phase contrast data. This segmentation technique was applied to only the samples that were encapsulated in Kapton tape. In these samples, elimination of the epoxy from porous regions provided sufficient phase contrast data for segmentation of multiple phases. In Table 1, these samples are referred to as sample regions with phase contrast. Microstructural characteristics were segmented for 14 sample regions across the processing variants. Three distinct electrode phases were classified as the active material, macropore and the carbon/binder domain (CBD). Note, the phase herein referred to as the carbon/binder domain is composed of binder, conductive additive, and a sub-resolution microporous phase containing CBD and active material. The brightness and contrast adjustment function in ImageJ was used to vary the observable contrast between the electrode phases. A binary mask of the AM from the watershed method was used to isolate the less attenuating phases. Once isolated, the CBD and macropore regions were


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Phase segmentation was implemented on the cathode samples that yielded three distinct regions: active material, macropore, and combined carbon/binder domain. It is expected that the last of these three regions includes micropores and sub-resolution active material particles. These regions are shown in Figure 1.d. As seen in the plots, a significant difference is not observed in the morphology of the NMC active material between cathode 1 (Figure 1.d.i) and cathode 2 (Figure 1.d.ii). The processing methods for these cathodes differ in terms of the drying methods applied, where cathode 1 was dried rapidly and cathode 2 was dried gradually. Different rates of drying play a role in the distribution of the solid phases particularly due to solvent evaporation 30. The distribution of the conductive additive and binder can have major influences on the effective electronic and ionic transport properties of the electrode27. No significant difference was seen in the thickness of the electrodes between cathode 1 and cathode 2. This invariance suggests that drying has limited effect on the macroscopic volume changes of the binder/pore regions. However, a slight difference is qualitatively observed in the distribution of the macropore and CBD regions between these cathodes. In cathode 1, subjected to rapid drying, the macropore and CBD regions were found to be distributed non-uniformly throughout the electrode domain. This non-uniform distribution may arise because fast drying did not allow enough time for the binder to distribute throughout the domain to create more uniform pore regions. In cathode 2, the gradual drying provides adequate time for the binder to distribute throughout the domain, creating more uniform pore and CBD regions. Although this observation is strictly qualitative in the present work, it supports the observations of Stein et al. regarding the effects of drying protocol on cathode structure. For cathodes produced by the same methods, Stein et al. found that a slower two-stage drying process led to a more uniform distribution of pore and CBD regions compared to a faster single-stage drying process 27.


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The 3D plots of cathode 3 and cathode 4 do not provide a clear qualitative illustration of how the morphological details of the secondary phases differ between these two processing variants. However, morphology of the NMC active material significantly changes when the electrode is subjected to calendering (Figure 1.d.iii) and ball-milling processes (Figure 1.d.iv). Samples of cathode 3 were subjected to gradual drying followed by calendering, and Figure 1.d.iii shows that the particles are more compacted. This compaction gives an appearance of a continuous active material phase in the 3D rendering. However, cross-sections of cathode 3, such as those shown in Figure 1.c reveal that the active material regions are primarily discrete particles joined by thin CBD regions. Some of the particles can be distinctly seen as irregular spheres. This is supported by the measured geometric parameters, specifically a lower value of sphericity compared to cathodes 1 and 2, as shown in Table 2. The electrode thickness is also reduced for cathode 3 compared to cathodes 1 and 2 due to calendering. The reduction of electrode thickness is attributed to the compaction of CBD domain as the pore domain remains intact. These observations are shown quantitatively in Table 2, where the CBD radius for cathode 3 decreases considerably relatively to other cathode samples, and the pore radius for cathode 3 remains comparable to other cathode samples. Cathode 4 contains AM subjected to ball-milling and was dried in a rapid one step drying process. As seen in Figure 1.d.iv, the particles in cathode 4 have more distinct morphological and geometrical differences compared to the calendered sample, mainly due to the absence of the secondary phases during the process of ball-milling prior to the electrode processing 22. The morphological differences are seen in terms of particle granularity, surface area and sizes. During ball-milling the particles fracture and disintegrate into smaller, irregular grains. This is seen in cathode 4 as the electrode consists of coarser grain particles with much lower particle sizes. These observations are supported in the geometric parameters


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(volume, surface area, sphericity, and radius) given in Table 2. Due to the significant reduction of particle sizes as a result of ball-milling, the thickness of the processed electrode is lower compared to the other cathode samples. Figure 2 (right corner inset) shows the volume fraction occupied by each phase within the electrode domain. The effect of compaction can be seen on the active material volume fraction for the calendered sample (cathode 3). Because of reduced thickness, the AM particles occupy a greater portion of the representative volume of interest. The increase in AM volume fraction corresponds to a reduction in the secondary phase volume fraction. This reduction is significantly higher in the CBD domain over the pore domain suggesting that the binder and conductive additives compact during the process while the pore space retains, or regains, its volume after compression. This observation is also supported by the continuous size distribution (CSD) data for these two phases, CBD and Macropore (Figure 2.b and 2.c). The other samples do not show a significant variation in the volume fraction for the porous domain or the carbon/binder domain. Table 2. Mean values for the geometric characteristics and transport parameters for the porous NMC cathodes subject to varied electrode processing methods. Metric

Cathode 1

Cathode 2

Cathode 3

Cathode 4

Particle Count

516

493

310

304

Median AM Radius (CSD) [ m]

3.22

3.17

3.00

2.50

Mean AM Radius (3Lc) [ m]

3.15

3.14

3.04

2.80

Mean AM Surface Area [ m2]

314.45

276.28

326.58

238.07

1.03

1.03

1.06

1.13

401.05

354.03

392.00

252.67

Mean AM Characteristic Length [ m]

1.05

1.05

1.01

0.93

Mean AM Sphericity

0.812

0.836

0.790

0.795

Median CBD Radius (CSD) [ m]

2.06

2.22

1.52

1.86

Median Pore Radius (CSD)

3.01

2.81

2.96

2.81

Mean Specific Surface Area [ m

1

]

Mean AM Volume [ m3]

m]


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Mean Cathode Thickness [ m]

24.45

24.22

18.73

16.76

Mean Cathode Porosity [%]

38.4

36.5

36.2

35

Mean Cathode Tortuosity

1.12

1.10

1.15

1.09

Mean AM Diffusion Time (CSD) [s]

210

203

182

125

Mean AM Diffusion Time (3Lc) [s]

198

197

185

157

Mean Pore Diffusion Time (CSD) [s]

532

591

591

386


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Cathode 2 - Cathode 1

1


0.8

Cathode 3 - Cathode 2 Cathode 4 - Cathode 2

0.6 Cathode 4 - Cathode 3 -1.25

-1.00

-0.75

0.4

-0.50

-0.25

0.00

0.25

0.50

60

Cathode 1

Phase Volume %

Continuous Phase Size Distribution (Active Material)


Cathode 2 Cathode 3

0.2

Cathode 4

a)

XNT-Calendered

50 40 30 20 10 0

0 0

1

2

3

4

5

6

Discharge rate(s)1 Cathode 2 - Cathode

7

8

9


0.8


0.6 Cathode 4 - Cathode 3 -1.00

-0.75

-0.50

-0.25

0.00

0.25

0.50

60

0.4 Phase Volume %

Continuous Phase Size Distribution (Carbon/Binder)

1

0.2

b)

50 40 30 20 10 0

0 0

1

2

3

4

5

6

7

8

9


1


0.8


0.6

Cathode 4 - Cathode 3 -1.0

-0.5

0.4

0.0

0.5

1.0

60

Phase Volume %

Continuous Phase Size Distribution (Macropore)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.2

c)

50 40 30 20 10 0

0 0

1

2

3

4

5

6

7

8

9

Phase radius (-m)

Figure 2. Continuous size distribution (CSD) of the different phases in the imaged cathode samples. ANOVA applied on the median values of each cathode sample is shown at top inset. If


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the confidence interval includes zero, then there is no significant difference between the distinct samples. The volume fractions of each phase are shown in the bottom right corner inset. The error bars are defined as T of the datasets. a) CSD of the active material, b) CSD of the carbon/binder domain (Kapton tape samples) c) CSD of the macropore domain (Kapton tape samples)

1.1 Geometrical Features of Porous Electrodes 1.1.1

Phase and Particle Size Distributions

The geometric characteristics of the active material including radius, volume, surface area and sphericity were analyzed using particle size distribution methods developed by Münch and Holzer 31. Different electrode preparation methods change the cathode structure. To better determine the impact of these methods, variance of the properties between the different cathode samples was investigated using analysis of variance (ANOVA). The statistical test applied was a one-way layout F-test that follows the Tukey-multiple comparison method. A confidence interval of 95% was used in this study, corresponding to approximately twice the standard deviation C TD of the data. A total of 20 distinct samples were used in the active material analysis. Each cathode processing variant had 5 distinct samples for these comparisons. This set of samples included both epoxy-cast and Kapton tape encapsulated samples. No significant influence of sample preparation approach was seen for the active material phase. The results of the Tukey test are shown in the upper right insets of the plots in Figures 2a-c. If the dotted line on these plots falls within confidence interval of 95%, then there is no significant difference between the cathode samples indicated. The p-value of these results is the basis for defining significant variations between manufacturing approaches (Table 3). Particles having characteristic length below the pixel size of the microtomography measurements (0.65 m) were removed from consideration. As a result of this procedure, particles with an


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equivalent radius less than 1.95 m (3Lc) were eliminated from the dataset. This cleaning procedure highlights a significant limitation in terms of imaging microstructures since most of the smaller particles ranging in the nano-scale are eliminated during this process. This procedure also explains why the particle count parameter obtained from the X-ray nanotomography (XNT) analysis22 differs from the current study. The mean geometrical parameters for each sample were obtained (Table 2), and a one-way layout ANOVA was applied on the tomographic data to highlight significant differences in the geometrical parameters (Table 3). Based on the ANOVA results, there are no significant differences seen on the geometrical parameters between cathodes influenced by the drying process (cathode 1 and cathode 2).

Table 3. ANOVA results in the form of p-values for the geometric and morphological characteristics of NMC cathodes subject to varied preparation method. A p-value of p < 0.05 indicates a significant difference between processing variants for a given parameter. Cathode 1 vs. 2

Cathode 1 vs. 3

Cathode 1 vs. 4

Cathode 2 vs. 3

Cathode 2 vs. 4

Cathode 3 vs. 4

AM Radius (CSD)

0.986

0.410

0.000

0.603

0.001

0.012

AM Radius (3Lc)

0.992

0.300

0.000

0.439

0.000

0.007

AM Surface Area

0.480

0.934

0.055

0.754

0.085

0.020

AM Volume

0.620

0.724

0.003

0.949

0.105

0.018

AM Specific Surface Area

1.000

0.603

0.001

0.650

0.001

0.008

AM Characteristic Length

0.992

0.300

0.000

0.439

0.000

0.007

AM Sphericity

0.850

0.573

0.433

0.001

0.002

0.090

AM Diffusion Time (CSD)

0.973

0.362

0.001

0.600

0.001

0.018

AM Diffusion Time (3Lc)

0.994

0.340

0.024

0.471

0.039

0.017

CBD Radius (CSD)

0.382

0.002

0.245

0.000

0.023

0.033

Parameter


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A discrepancy is seen as particle count decreases significantly between cathodes influenced by manufacturing process and drying process (cathode 1 and 2 vs. cathode 3 and 4). There are two reasons that account for this discrepancy. First, during post-processing of the particle size distribution data, most of the particles with radius and characteristic length below the given instrument resolutions were eliminated. Particles located at the edge of the electrode domain were also removed. These processes significantly reduced the particle count. Second, during calendering, some of the particles fracture and disintegrate into sub-resolution particles that could not be resolved through microtomography measurements. The ball-milled sample has a significant number of sub-resolution particles that could not be resolved as well. Based on higher resolution imaging, the ball-milled sample should have the highest particle count followed by the calendered sample 22. However, since the ball-milling process significantly reduces the particle size compared to the calendering process, the decrease in particle count between cathode 3 and cathode 4 is likely attributed to the lower instrument resolution. Particle sizes defined by volume and specific area show a significant variation between the cathode samples influenced by the manufacturing methods. The ball-milled sample produced particles with lower volume and a higher specific surface area. The calendered sample shows the highest surface area among other cathodes likely due to the effect of compaction; the volume of the particles increases relative to cathode 2 due to the fact that the particles expand within the same representative volume of interest. Münch and Holzer describe the technique of continuous pore size distribution (CSD) 32; this technique was used to evaluate the CSD of the different phases observed in the tomographic data. This technique was implemented on the cathodes having only the active material segmented and the cathodes with multiple phases segmented, as shown in Table 1. The median


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value of radii obtained from the CSD was used as the equivalent radius in estimating diffusion times. To investigate the variance between the different cathode samples, ANOVA was applied on the median values of the CSD for each cathode sample. As noted, the statistical test applied was a one-way layout F-test that follows the Tukey-multiple comparison method. A confidence interval of 95% was used. A total of 20 distinct samples were used in the active material analysis, 5 distinct samples for each processing variant. For the macropore and carbon/binder domain analysis a total of 12 distinct samples were used in statistical analysis, 3 distinct samples for each processing variant. The different phases characterized using this approach were the active material (Figure 2.a), carbon/binder domain (Figure 2.b) and macropore domain (Figure 2.c). The active material shows size variation for the ball milled samples. The macropore regions show smaller size variation for the different production variants. The CBD regions for the calendered samples show a significant size reduction. Relative phase size distributions could be used to analyze the morphological differences in the secondary phases. Secondary and macropore phase distributions can significantly impact the transport of Li+ ions and electrons especially due to its dependence on the tortuosity which influences the movement of Li+ between the electrodes through the electrolyte. Figure 2.a shows the CSD for the active material. The CSD obtained from XNT measurements for the calendered sample 22 is plotted to show the discrepancy in phase sizes brought up by the instrument resolution. In the microtomography datasets the regions corresponding to radii of less than 1.30

are not resolved. However, in the nanotomography dataset, the sample did not

exhibit radii higher than ~1.50

. This discrepancy highlights the importance of imaging the

microstructures at multiple scales. For the microtomography dataset, ball-milled samples


19


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(cathode 4) show a significant decrease in the AM radius compared to the other samples. This difference is also supported by the decrease in mean radius as shown in Table 2. Figure 2.b shows the CSD for the carbon/binder domain. Cathode 3 has the lowest phase radius compared to the other cathodes because calendering compresses and reduces the size of the secondary phases present in the electrode; this observation was also supported previously under the discussion of the phase fractions of the electrodes (Figure 2) and in the ANOVA results (Table 3). Cathode 4 has the next lowest phase radius suggesting that the influence of smaller particles might have an effect on the sizes of the secondary phases. Cathode 1 and cathode 2 have slightly higher radii compared to the manufactured samples. However, the invariance in the ANOVA results (Table 3) suggests that these phase radii at larger scales are not influenced by the drying methods. Figure 2.c shows the CSD for the pore domain. The pore radii for the electrode processing cases do not show variance in an aggregate sense which is also supported by the ANOVA results (Table 3). Connecting back to the argument on how the pore radii remains undisturbed during the calendering process, or recovers following calendering, the argument is further supported by the plot in which the radii for cathode 2 and cathode 3 are almost equivalent. Although, cathode 1 has slightly higher radii compared to cathode 2, there is not enough confidence to suggest that the drying methods can influence changes in the pore sizes at larger scales (Table 3). However, this slight difference can be expected because of the secondary phase’s distribution during the drying process. 1.1.2

Porosity and Tortuosity


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In a composite electrode, the electrolyte occupies the pore phase. Typical electrode structure is composed of geometrical attributes over a range of length-scales, and accordingly interpretation of porosity fields varies. For example, the nanopores dispersed throughout the CBD domain affect the distribution of intercalation flux at the particle surface33, while porosity variation at larger scales define the ionic transport and in turn the spatial nature of reactions along the electrode thickness. Since the electrode fabrication step leads to a particular pore network arrangement27, here tomograms of various cathodes are studied to correlate processing with the pore network. Often calendering is introduced to reduce the porosity of a given electrode. However, it simultaneously reduces porosity as well as electrode thickness, both of which exhibit opposing effect on ionic transport. The transport resistance of a convoluted pore network not only depends on porosity (the pore volume) but also on the intrinsic connectivity which is characterized by tortuosity. Given that porosity and tortuosity are attributes of the pore network, their values are meaningful only for a large enough composite volume. This critical dimension, i.e., small enough electrode volume containing sufficient pore network information is referred to as the Representative Volume Element (RVE). Volumes smaller than RVE size do not contain statistically significant information to avail a description in terms of effective properties. The RVE identification has been discussed in authors’ earlier works8,34,35. Porosity calculations basically amount to voxel counting from the tomography data, while tortuosity estimation requires pore-scale solution of the Laplace equation (refer to Supporting Information section 8). Similar to the multiscale nature of the porosity, tortuosity at the RVE scale differs from its value at the electrode-scale, where the electrode is composed of numerous RVEs. The electrode-scale tortuosity (Figure 3.a) is related to its RVE-scale counterpart (Figure 3.b) and is calculated as such. A composite electrode


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(Figure 3.c) contains multiple phases (Figure (3.d-3.f)) to facilitate different transport processes. A steady-state concentration field was solved to estimate tortuosity of the pore and CBD regions and the resulting effective diffusion coefficient, Figure 3.e. A similar approach may be applied for the potential field in the CBD to yield an effective conductivity, Figure 3.f and 3.h.

Figure 3. An electrode is a large volume making its microstructural characterization computationally challenging. a) Reconstructed tomogram with representative volume elements (RVEs) explicitly identified. b) A reconstructed RVE has active material and other phases. c) A composite electrode structure is composed of active material, secondary solids and electrolyte filled pore network. Each of these phases is separately shown d) active material particles e) pore network and f) secondary phase, CBD network. g) The pore network is characterized by solving


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for concentration field, while h) the solid phase network is characterized by solving for potential field.

3.3. Analysis of Intercalation Dynamics The short-range interaction and the long-range interaction between structure, transport, and reaction are steered by the geometry of the active material and the surrounding secondary phase. Particle size distributions along with other geometrical properties dictate the transport behavior of Li in the active material. The diffusion time was defined for both the active material and the electrolyte influenced by the porous medium. For the active material, the diffusion time is defined as the time for Li to move a characteristic length from the center of the NMC particle. For the electrolyte, it is defined as the time taken for a Li+ to move through the electrolyte-filled porous medium characterized by both porosity and tortuosity. To define the diffusion time for the active particle, the CSD of the NMC particles was used to evaluate the radii of the particles. The radii of the particles were correlated to the Fourier number to obtain the diffusion time. The Fourier number quantifies the ratio of diffusive transport to the storage rate. Equation 1 shows the definition of the AM diffusion time,

. Here, D0 is the lithium diffusion coefficient for the

active material, r50 is the median particle radius and 50

is the Fourier number. The median radii,

obtained from the pore size distribution were equated to the characteristic length in Equation

1. The lithium ion diffusion coefficient of 5 × 10

14

m2s

1

material and a Fourier number of 1

was used for this study; these were obtained from previous literature 22. =

2 50

[1]

To corroborate the diffusion time in the active material, another equivalent radius is defined as a ratio of the particle volume and particle surface area36 as shown in Equation 2. These parameters


23


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were obtained by calculating the particle size distribution31 of the segmented active material. The mean volume and surface area for each distinct sample was computed in order to define the diffusion time. This equivalent radius was used as the characteristic length to determine the diffusion time of Li through the active material as shown in Equation 3. The results for these calculations are given in Table 2. [2]

=3

=

2

[3]

Understanding the transport of Li+ within the electrolyte through the macropores could be vital in optimizing the porosity through varied electrode processing methods. An effective diffusion coefficient was defined to characterize the diffusion time of Li+ within the macropore. Similar to the previous method32, the macropore image data was used to obtain CSD of the pore radii. The median radius on the CSD was used to calculate the diffusion time as shown in Equation 4. The effective diffusion coefficient,

was obtained for the representative volume of interest.

=

2

[4]

As noted, the CSD radius gives a more accurate definition of the characteristic length compared to the PSD radius. The intercalation time based on the CSD of the AM and the equivalent volume method is given in Figure 4.a and Table 2, respectively. The CSD as a function of intercalation time shows that the ball-milled sample (Figure 4.a) has a significantly lower diffusion time, followed by the calendered sample with a slightly lower diffusion time compared to the other dried cathode samples. The intercalation time based on the equivalent volume method (Table 2) also supports the variation observed in Figure 4.a. The fact that the ball-milled


24

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sample has significantly lower diffusion time compared to the other samples shows how the morphology of the particles can be adjusted to potentially impact battery performance. Prior XNT observations support this result and suggest that calendering may also reduce diffusion time in the AM 22. Lower diffusion time can increase the rate capability behavior of the particle and reduce the capacity of the particle. However, this process occurs contemporaneously with Li+ transport within the electrolyte-filled pore regions.


25


Continuous Phase Size Distribuution) (Active Material)

1


0.8


0.6

Cathode 4 - Cathode 2 Cathode 4 - Cathode 3 -150

0.4

-100

-50

a) 0

0

50

Cathode 1 Cathode 2 Cathode 3 Cathode 4

0.2

0 1 Continuous Phase Size Distribuution (Macropore)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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200

400

600

Difference of Means 800 1000 1200 1400 1600 Discharge Cathode 2 - Cathode 1 rate(s)

1800

2000

2200


0.8


0.6

Cathode 4 - Cathode 2 Cathode 4 - Cathode 3 -400

0.4

-300

-200

-100

0

100

200


0.2

b) 0 0

200

400

600

800 1000 1200 1400 1600 1800 2000 2200 Discharge rate (s)

Figure 4. a) Lithium diffusion time in the active material with ANOVA applied on the median values of each cathode sample (inset). b) Lithium diffusion time in the macropores with ANOVA applied on the median values of each cathode sample (inset). If the confidence interval includes zero, then there is no significant difference between the distinct samples.


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A full picture of the performance limiting transport processes within the electrode requires characterization of the secondary phases. The tortuosity of the pore network and the CBD domain stipulates the long-range transport of Li+ between the anode and cathode, as well as the transport of electrons through the electrode. Figure 4.b shows the Li+ diffusion time in the electrolyte-filled macropore regions. These pore regions are assumed to be in contact with the active material, these contact areas are visible in the segmented phase image shown in Figure 1.c.v. Lower Li+ diffusion time is observed in the ball-milled sample likely due to the lower pore radius obtained from the CSD graph for the macropores (Figure 2.c). Furthermore, the effect of reduced tortuosity values allows for faster diffusion time in the macropore. This suggests that the ball-milled sample enhances the transport of Li+ ions within the secondary phases. The drying methods (gradual vs rapid) did not significantly affect the radii of the macropores. However, a slight difference is observed in the macropore diffusion times for the differently dried cathode samples. The sample subjected to rapid drying shows a lower diffusion time in the macropore in comparison to the sample subjected to gradual drying (Figure 4.b). Gradual drying allows for uniform distribution of the macropores resulting in a lower tortuosity value for the sample. Rapid drying results in a non-uniform distribution of the macropores resulting in a slightly higher tortuosity value. By this definition, rapid drying should give a larger transport time, but this is not observed in the graph (Figure 4.b). This suggests that porosity fractions between the differently dried samples play a significant role in evaluating diffusion times in the macropore. The calendered sample (cathode 3) has a slightly higher diffusion time in the macropore in comparison to the diffusion time in the active material because of its increased tortuosity value. This analysis demonstrates that the ball-milled sample subjected to rapid drying enhances the transport time of Li+ ions in the macropore regions.


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Numerical modeling based on porous electrode theory enhances the understanding of the overall transport behavior in the cell. To further resolve the impact of the observed electrode properties on battery performance, COMSOL Multiphysics 5.2 was used to create a pseudo-DNS battery model consisting of a negative electrode (LixC6), separator, positive electrode (NMC) and a current collector. Lithium hexafluorophosphate (LiPF6) in 1:1 ethylene carbonate (EC) and Diethylene carbonate (DEC) was used as the electrolyte. Physical parameters were obtained from previous literature 17,22,37. Geometrical parameters were obtained from the tomographic data including electrode porosity, tortuosity, and particle radius, which are listed in Table 2. The governing equations and the boundary conditions used are described in the Supporting Information. A time-dependent model with discharge rates of 1C and 5C was employed to study the discharge behavior of LIB. Figure 5.a and 5.b shows the discharge curves for cathode 1 to 4 at the discharge rate of 1C and 5C. Cathode 3 provides the highest capacity at discharge followed by cathode 1, 2, and 4. The particle size, porosity, and tortuosity values change less than 5% between cathode 1, 2, and 3 whereas for cathode 4 the particle size, porosity, and tortuosity values change less than 10% when compared to cathode 1, 2, and 3. When comparing all four cathode configurations, the phase volume fraction is seen to establish the total cell capacity compared to other parameters. From Figure 2.a, cathode 3 has the highest active material percentage followed by cathode 1, 2, and 4. Particle surface area follows a comparable trend, highest for cathode 3 followed by cathodes 1, 2, and 4. This trend suggests that kinetic overpotential also influences the discharge behavior of the thin electrodes examined. These estimates help quantify the role of the shortrange interaction between kinetics at the particle surface and diffusion within the particle. As


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shown in Figure 4.a, the diffusion times are substantially lower than the time required for discharge, so surface reaction kinetics would be more likely to limit discharge behavior.

a)

4.2

Cell Voltage (V)

4 3.8 3.6 3.4


3.2 3 2.8 0

0.05

0.1

0.15

0.2

0.25

Capacity (mAh/cm2)

4.2

b)

4 Cell Voltage (V)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


3.8 3.6 3.4 Cathode 1 Cathode 2 Cathode 3 Cathode 4

3.2 3 2.8 0

0.05

0.1

0.15

0.2

0.25

Capacity (mAh/cm2) Figure 5. a) Discharge curves (1C) for the differently processed electrodes. b) Discharge curves (5C) for the differently processed electrodes.


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Short-range interactions at the particle level address a key portion of the discharge behavior, but long-range interactions across the electrode also require consideration. These interactions are influenced by the structure of the secondary phases, CBD and macropore. Charge transport resistance in the CBD and macropore regions may also contribute to increased overpotential as discharge rate increases. Diffusion within the macropore exerts less influence as there is sufficient time for the Li+ ions to move between the anode and the cathode active material. The diffusion time plots in Figure 4.b support this observation. The median diffusion time for the macropores in the cathodes varies between 600 s to 800 s, whereas the time for 5C discharge is around 720 s. More aggressive discharge may result in an increased influence. For demonstration, the discharge rate is increased from 1C and 5C to 10C and 20C in the Supporting Information, resulting in decreased capacity and cell voltage. As with lower C-rates, the active material surface area and effective conductivity of the CBD and pore regions impact the overpotential. The time required to discharge the battery is around 360 s and 180 s for 10C and 20C, respectively. This time is less than the median diffusion time for the macropores in the cathodes which highlights an increasing limitation of Li+ ions to access and completely diffuse into the active material. The short-range and long-rage structure/transport interactions manifest through variations in both local field conditions and discharge curves by influencing the concentration and electric potential. Increasing the C-rate allows an initial exploration of when long-range interactions may exert greater influence on cathode performance. These interactions arise from the influence of CBD and pore network structure on the effective conductivity and diffusivity within the cathode. Operation at higher C-rates and thicker electrodes would exhibit greater departure in realized capacity as conductivity decreases, macropore diffusion time exceeds discharge time and long-


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range interactions exert greater influence. X-ray tomography has previously yielded insight into the influence of active material structure. The phase contrast capabilities demonstrated herein provide an example of how X-ray microtomography can contribute further to the exploration of multiscale interactions within battery electrodes.

4. Conclusions Using X-ray microtomography with rapid data acquisition capabilities an extensive multiphase 3D dataset of Li-ion battery cathode structures, consisting of active material, CBD and pore regions has been assembled. Encapsulating cathode samples with Kapton tape exposed clear contrast between the NMC active material, carbon/binder, and pore regions. This capability enables segmentation and analysis of secondary phases in cathodes processed with varied methods. Different modes of drying presented variation in the distribution of the active material and secondary phases within the cathode. Calendered and ball-milled samples illustrated substantial changes in cathode morphology. Most notably, calendering exhibited a significant impact on CBD phase size, suggesting the CBD region is permanently deformed by calendering. Each processing method alters cathode microstructural characteristics which in turn impact discharge behavior, as predicted by diffusion time estimates and numerical modeling. Drying methods showed the least influence on discharge behavior. Ball-milled samples showed the lowest diffusion time in both the active material and pore regions despite having the lowest capacity. Calendered samples showed a higher diffusion time in both the phases while having the highest capacity among the processing variants. These results suggest active material content and short-range interactions governing kinetic overpotential hold greater influence on discharge capabilities for the cathodes studied.


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The present work highlights the correlation between processing methods and the mesoscale properties of lithium ion cathodes. This link is established through microstructural and numerical studies aided by X-ray microtomography sensitive to multiple cathode phases. Analysis at both particle and electrode scales demonstrate how X-ray imaging can further the exploration of multiscale interactions within battery electrodes. Acknowledgements Financial support from the National Science Foundation through a Collaborative Research Award (CBET-1438683 and CBET-1438431/1759651) and a CAREER Award (CBET-1454437) is gratefully acknowledged. This research used the resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357. Associated Content Supporting Information available: Overview of electrode preparation methods and image processing techniques; image reconstruction; extraction of active material from tomographic data (Figure S1); extraction of secondary phases (conductive additives, carbon black and pore regions) from tomographic data (Figure S2); Geometrical analysis using particle size distribution algorithm; porosity; pseudo DNS model to extract tortuosity; mathematical modeling with transport parameters (Table S1); discharge behavior at higher currents (Figure S3). References (1)

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Quantifying Transport, Geometrical, and Morphological Parameters in

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