Acta Mechanica Sinica

, Volume 29, Issue 5, pp 682–698 | Cite as

A micromechanical model for effective conductivity in granular electrode structures

  • Julia Ott
  • Benjamin Völker
  • Yixiang Gan
  • Robert M. McMeeking
  • Marc Kamlah
Research Paper

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.

Keywords

Granular electrode structures Effective conductivity Percolation 

Nomenclature

c0

initial Li+ concentration

cx

momentary Li+ concentration

cmax

maximum Li+ concentration

D

diffusivity

fn

normal force

ft

tangential force

I

flux respectively current

K

conductivity matrix

kbulk,l

conductivity of bulk material

keff,l

effective conductivity of granular structure

L

box length

ni

normal unit vector

Pl

percolation probability

PF

packing factor

R

resistance between 2 particles

Rmax

resistance of a cylinder with rp and δ

r0

initial particle radius

rc

contact radius

rx

momentary particle radius

T

temperature

t

time

tj

tangential unit vector

u

displacement

V

voltage

xi

position of particle i

Z0

overall coordination number

Zl,l

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

Greek symbols

δ

distance between two particles

porosity

ɛ

strain

ν

Poisson’s ratio

σ

stress

ϕl

volume fraction

φ

potential

Ω

partial molar volume

Subscripts

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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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Julia Ott
    • 1
  • Benjamin Völker
    • 2
  • Yixiang Gan
    • 3
  • Robert M. McMeeking
    • 2
    • 4
    • 5
    • 6
  • Marc Kamlah
    • 1
  1. 1.Institute of Applied MaterialsKarlsruhe Institute of TechnologyKarlsruheGermany
  2. 2.Department of Mechanical EngineeringUniversity of CaliforniaSanta BarbaraUSA
  3. 3.School of Civil EngineeringThe University of SydneySydneyAustralia
  4. 4.Materials DepartmentUniversity of CaliforniaSanta BarbaraUSA
  5. 5.School of EngineeringUniversity of Aberdeen, King’s College, AberdeenScotlandUK
  6. 6.INM — Leibniz Institute for New MaterialsSaarbr⩊kenGermany

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