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RESEARCH PAPERS: Special Issue on Time-Dependent Behaviors of Polymer Matrix Composites and Polymers

# Compression of Packed Particulate Systems: Simulations and Experiments in Graphitic $Li$-ion Anodes

[+] Author and Article Information
Y.-B. Yi, C.-W. Wang

Department of Mechanical Engineering, College of Engineering, University of Michigan, Ann Arbor, MI 48109

A. M. Sastry1

Department of Mechanical Engineering, College of Engineering, University of Michigan, Ann Arbor, MI 48109 and Department of Biomedical Engineering, College of Engineering, University of Michigan, Ann Arbor, MI 48109

1

Corresponding author; email: amsastry@umich.edu

J. Eng. Mater. Technol 128(1), 73-80 (Mar 17, 2005) (8 pages) doi:10.1115/1.2130733 History: Received October 12, 2004; Revised March 17, 2005

## Abstract

Increased thermal conductivity, electronic conductivity, and reversible capacity (i.e., reduced irreversible capacity loss, or ICL) have been demonstrably achievable by compression of anodes into higher volume fraction plates, though excessive compression can impair $Li$-ion battery performance. In our previous study, we correlated conductivity and compression of these materials. Here, we further investigated the effects of friction and deformability of particles on the compressibility of model carbons of $Li$-ion anodes. First, we implemented a statistically unbiased technique for generating a range of random particulate systems, from permeable to impermeable arrangements, along with a contact model for randomly arranged triaxial ellipsoidal particles, suitable for implementation in finite element analysis of compression of a random, porous system. We then quantified the relationship between interfacial friction and jamming fraction in spherical to ellipsoidal systems and applied these models to correlate maximum stresses and different frictional coefficients, with morphology (obtained by image analysis) of graphite particles in $Li$-ion anodes. The simulated results were compared with the experiments, showing that the friction coefficient in the system is close to 0.1 and that the applied pressure above $200kg∕cm2$$(200MPa)$ can damage the materials in SL-20 electrodes. We also conclude that use of maximum jamming fractions to assess likely configuration of mixtures is unrealistic, at best, in real manufacturing processes. Particles change both their overall shapes and relative orientations during deformation sufficient to alter the composite properties: indeed, it is alteration of properties that motivates post-processing at all. Thus, consideration of material properties, or their estimation post facto, using inverse techniques, is clearly merited in composites having volume fractions of particles near percolation onset.

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## Figures

Figure 1

SEM images of SL-20 anode materials under a pressure of 100kg∕cm2, including (a) a top view and (b) a cross-sectional view

Figure 2

Schematics of particle compression simulations (a) before compression and (b) after compression

Figure 3

A schematic showing the reconstruction of ellipsoidal particle geometry using AFM. (a) The scanning range covers only a portion of the upper surface, (b) geometrical relations among the measured parameters.

Figure 4

AFM image on a SL-20 natural graphite particle

Figure 5

Reactive force on the pressing plate as a function of volume fraction, for systems of spherical and ellipsoidal particles

Figure 6

Close-up picture of Fig. 5 for ellipsoids without friction, for demonstrating the transition between pre-jamming and post-jamming stages during compression

Figure 7

Reactive force applied on the pressing plate as a function of volume fraction, for systems of ellipsoidal particles, under different friction coefficient ranging from 0 to 10.0

Figure 8

Jamming fraction as a function of friction coefficient for ellipsoidal particles

Figure 9

Maximum internal Von Mises stresses versus volume fraction, for systems of ellipsoidal particles. The stress is normalized against the elastic modulus.

Figure 10

Von Mises stress distribution in a system of 1000 ellipsoids at friction coefficient 0.5

Figure 11

Severe local deformation of ellipsoids can be observed at volume fraction 90%. Friction coefficient 0.5.

Figure 12

Computer generation of a polydisperse particulate system comprised of impermeable ellipsoids (a) with varied aspect ratio and no coating and (b) with varied aspect ratio and coating layers. Note in (b) that the coating layers are exaggerated: their thickness is 40% of the mean diameter of the hard cores.

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