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A micromechanical model for effective conductivity in granular electrode structures

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Abstract

Optimization of composition and microstructure is important to enhance performance of solid oxide fuel cells (SOFC) and lithium-ion batteries (LIB). For this, the porous electrode structures of both SOFC and LIB are modeled as a binary mixture of electronic and ionic conducting particles to estimate effective transport properties. Particle packings of 10 000 spherical, binary sized and randomly positioned particles are created numerically and densified considering the different manufacturing processes in SOFC and LIB: the sintering of SOFC electrodes is approximated geometrically, whereas the calendering process and volume change due to intercalation in LIB are modeled physically by a discrete element approach. A combination of a tracking algorithm and a resistor network approach is developed to predict the connectivity and effective conductivity for the various densified structures. For SOFC, a systematic study of the influence of morphology on connectivity and conductivity is performed on a large number of assemblies with different compositions and particle size ratios between 1 and 10. In comparison to percolation theory, an enlarged percolation area is found, especially for large size ratios. It is shown that in contrast to former studies the percolation threshold correlates to varying coordination numbers. The effective conductivity shows not only an increase with volume fraction as expected but also with size ratio. For LIB, a general increase of conductivity during the intercalation process was observed in correlation with increasing contact forces. The positive influence of calendering on the percolation threshold and the effective conductivity of carbon black is shown. The anisotropy caused by the calendering process does not influence the carbon black phase.

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Abbreviations

c 0 :

initial Li+ concentration

c x :

momentary Li+ concentration

c max :

maximum Li+ concentration

D :

diffusivity

f n :

normal force

f t :

tangential force

I :

flux respectively current

K :

conductivity matrix

k bulk,l :

conductivity of bulk material

k eff,l :

effective conductivity of granular structure

L :

box length

n i :

normal unit vector

P l :

percolation probability

PF :

packing factor

R :

resistance between 2 particles

R max :

resistance of a cylinder with r p and δ

r 0 :

initial particle radius

r c :

contact radius

r x :

momentary particle radius

T :

temperature

t :

time

t j :

tangential unit vector

u :

displacement

V :

voltage

x i :

position of particle i

Z 0 :

overall coordination number

Z l,l :

number of contacts of a l-particle to other l-particles

δ :

distance between two particles

:

porosity

ɛ :

strain

ν :

Poisson’s ratio

σ :

stress

ϕ l :

volume fraction

φ :

potential

Ω :

partial molar volume

AM:

active material

bulk:

bulk property

CB:

carbon black

eff:

effective property

i :

particle label

l :

species

max:

maximum

SP:

small particles

x :

momentary state

0:

initial state

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Correspondence to Julia Ott.

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Ott, J., Völker, B., Gan, Y. et al. A micromechanical model for effective conductivity in granular electrode structures. Acta Mech Sin 29, 682–698 (2013). https://doi.org/10.1007/s10409-013-0070-x

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  • DOI: https://doi.org/10.1007/s10409-013-0070-x

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