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Morphology and electrochemical activity of SOFC composite cathodes: II. Mathematical modelling

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Abstract

This paper presents a mathematical model of mass and charge transport and electrochemical reaction in porous composite cathodes for application in solid oxide fuel cells. The model describes a porous composite cathode as a continuum, and characterises charge and mass transfer and electrochemical kinetics using effective parameters (i.e. conductivity, diffusivity, exchange current) related to morphology and material properties by percolation theory. The model accounts for the distribution of morphological properties (i.e. porosity, tortuosity, density of contacts among particles) along cathode thickness, as experimentally observed on scanning electron microscope images of LSM/YSZ cathodes of varying thickness. This feature allows the model to reproduce the dependence of polarisation resistance on thickness, as determined by impedance spectroscopy on LSM/YSZ cathodes of varying thickness. Polarisation resistance in these cathodes is almost constant for thin cathodes (up to 10 µm thickness), it sharply decreases for intermediate thickness, to reach a minimum value for about 50 µm thickness, then it slightly increases in thicker cathodes.

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Abbreviations

a :

Contact surface area (m2)

F :

Faraday constant (C mol−1)

i :

Current density (A cm−2)

j :

Current density (A (contact point)−1)

i 0 :

Exchange current (A cm−2)

j 0 :

Exchange current (A (contact point)−1)

k :

Compression factor

n V :

Density of contact points (contact point m−3)

R :

Resistance (Ω cm2)

R g :

Gas constant (J mol−1 K−1)

T :

Temperature (K)

V :

Potential (V)

X :

Volume fraction

z :

Axial coordinate (m)

α:

Transfer coefficient

δ:

Cathode thickness (m)

γ:

Relative grey level

η:

Overpotential (V)

ρ:

Resistivity (Ω m)

τ:

Tortuosity

el:

Electronic

io:

Ionic

p:

Polarisation

tot:

Total

tr:

Transfer

0:

Single-component material

cr:

Percolation threshold

eq:

Equilibrium

r :

Relative

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Authors and Affiliations

  1. Dipartimento di Ingegneria Chimica, Chimica Industriale e Scienza dei Materiali, Università di Pisa, Via Diotisalvi 2, 56100, Pisa, Italy

    Cristiano Nicolella & Antonio Bertei

  2. Istituto per l’Energetica e le Interfasi, CNR, Via De Marini, 6, 16149, Genova, Italy

    Massimo Viviani

  3. Dipartimento di Ingegneria Chimica e Processo, Università di Genova, P.le J.F. Kennedy, 16129, Genova, Italy

    Antonio Barbucci

Authors
  1. Cristiano Nicolella
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  2. Antonio Bertei
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  3. Massimo Viviani
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  4. Antonio Barbucci
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Correspondence to Cristiano Nicolella.

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Nicolella, C., Bertei, A., Viviani, M. et al. Morphology and electrochemical activity of SOFC composite cathodes: II. Mathematical modelling. J Appl Electrochem 39, 503–511 (2009). https://doi.org/10.1007/s10800-008-9691-3

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  • DOI: https://doi.org/10.1007/s10800-008-9691-3

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