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Effect of particle size distribution on particle based composite anode models

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Abstract

Particle based models of composite anodes are useful tools for exploring the behavior of SOFC systems. As part of our efforts to develop models for understanding fuel cells, we have been building models of Ni-YSZ composite anodes using experimentally measured particle size distributions. The objectives of this study were to characterize the percolation threshold and conductivity of these models in comparison to simpler mono dispersed and biphasic particle size distributions from the literature. We found that the average values for the onset of percolation and the measured conductivity of the models with experimentally measured particle size distributions are similar to those for the simple distributions and the experimentally measured distributions. For all of the configurations evaluated, the onset of percolation in the Nickel phase occurred at a solid fraction of Nickel between 20% and 25%. This corresponded almost exactly to the point at which the coordination number between Nickel phase particles reached 2.2. The significant finding was that the variation in the value for the conductivity, as measured by the standard deviation of the results, was several orders of magnitude higher than for the simpler systems. We explored the validity of our assumptions, specifically the assumption of random particle placement, by building a particle model directly from FIB-SEM data. In this reconstruction, it was clear that the location of particles was not random. Particles of the same type and size had much likelihood of contact higher than would indicated by random location.

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Abbreviations

l kTPB :

TPB length between a cermet particle and the k-th neighboring particle of a different conduction type, m

α :

Acceptance ratio for determining the advancement of a Metropolis-Hasting Markov chain

\(\bar F\) :

Force acting on a particle, N

\(\bar F_D \) :

Damping force acting on particle, N

\(\bar F_N \) :

Normal force acting on particle, N

\(\bar x\) :

Vector location of a particle (x; y; z)

\(\bar x_i \) :

Vector location of particle i (x; y; z)

\(\dot \omega _{e^ - } \) :

Net rate of production of electrons at the TPB per unit length, mol/(s·m)

µ:

Mean of a probability distribution

Φ k :

Electrical potential of the k-th neighboring particle of same conduction type, V

ρ :

Standard deviation of a probability distribution

d :

Distance between two particles, m

d 0 :

Desired distance between two particles, m

d max :

Maximum distance between two particles which are in contact, m

d min :

Minimum allowed distance between two particles, m

G :

Conductance, S

G i-j :

Conductance between two particles, S

i F :

Faradaic current across a cermet particle, A

i R :

Resistive current across a cermet particle, A

i net :

Net Current across a cermet particle, A

N s :

Number of intersecting particles of the same conduction type

N TPB :

Number of intersecting particles of a different conduction type

r i :

Radius of particle i, m

R k :

Resistance between a particle and the k-th neighboring particle of the same conduction type, Ω

X :

Sample from a given distribution

X i :

i-th ample from a given distribution in a sequence

X g :

Sample from a normal distribution

x i x :

coordinate of particle i, m

y i y :

coordinate of particle i, m

Z :

Overall average coordination number

Z e :

Average coordination number for electronically conducting particles

Z i :

Average coordination number for ionically conducting particles

z i :

z-coordinate of of particle i, m

Z e-e :

Average coordination of electronically conducting particles with other electronically conducting particles

Z i-i :

Average coordination of ionically conducting particles with other ionically conducting particles

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  1. 3400 Charles Street, 031 Latrobe Hall, Baltimore, Maryland, 21218, USA

    Vaughan L. Thomas

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  1. Vaughan L. Thomas
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Correspondence to Vaughan L. Thomas.

Additional information

The project was partially supported through a MURI from the United States Office of Naval Research

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Thomas, V.L. Effect of particle size distribution on particle based composite anode models. Acta Mech Sin 29, 357–369 (2013). https://doi.org/10.1007/s10409-013-0048-8

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  • DOI: https://doi.org/10.1007/s10409-013-0048-8

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