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Determination of Key Structural
Parameters of Fuel Cell Materials through
Microstructure Quantification
9th ASME International Conference on Fuel Cell Science,
Engineering and Technology – Washington, D.C.
Monday, 8th August 2011
A. Cecen, E. A. Wargo, A. C. Hanna, D. Turner,
S. R. Kalidindi and E. C. Kumbur
Electrochemical Energy Systems Laboratory
Mechanics of Microstructures Group
Department of Mechanical Engineering
Drexel University, Philadelphia PA
www.mem.drexel.edu/energy
Motivation and Objective
Due to complex nature of fuel cell materials, experimental quantification of
the key properties of these materials can be expensive and quite difficult to
conduct.
Develop advanced microstructure analysis tools for direct
quantification of the key structure-related transport properties
of porous fuel cell materials that are difficult to measure.
Materials Internal
Structure
Key Transport
Properties
Performance and
Durability of Fuel Cells
Objective
Method of Approach
Microporous layer of SGL 10BC gas diffusion layer is selected.
Measurement via FIB-SEM
ReconstructionMicrostructure Analysis Virtual Microstructure
Adapted from: Iwai et al., J. of P. Sources, 2010
Platinum coating
Imaged surface
Target volume
Gradient Removal
Raw Gradient Result
Segmentation
Raw Threshold Result
Data Processing
~ 150 Slices
Pore Volume
Total VolumePorosity =Solid
Pore
0
1
Pixelated Structure
• Two phase: pore and solid phase
for MPL
• Label pixels for each phase
Internal Surface Area :
A
A
Hypothetical StructurePore Voxel
Counted Surface
Total Surface Area
Total VolumeSA =
Standard Metrics Calculation
Standard Metrics Calculation
Pore Volume
Total VolumePorosity =Solid
Pore
0
1
Pixelated Structure
• Two phase: pore and solid phase
for MPL
• Label pixels for each phase
Connectivity
Hypothetical Structure Pore Voxel
Not Connected
Connected Network
Pixel Tracking
Algorithm
Connected Pore Volume
Total Pore VolumeC =
Tortuosity Distribution
o Computes tortuosity distribution rather
than giving a single value
o Direct method applicable to 3D datasets
o Uses two surfaces as boundaries and finds
tortuous paths from one surface to another.
1
2 3
... …
... N
Pore Pixels
(Starting Points)
N Tortuous Paths
Start SurfaceStart Surface
End Surface
Ch
ara
cte
ristic D
ista
nce
Shortest Flow Path
The tortuosity is typically determined indirectly via use of effective medium
approximation or some semi-empirical correlations
Method Highlights
Tortuosity Distribution
Hypothetical Structure
Connection
Graph Representation
Connection
Step 1 - Transform 3D Dataset into 2D Graph for Path Search Algorithm
Step 2 – Apply Breadth Search Algorithm to 2D Graph
C B
A
C B
AB
A
CA
AAA
5 3
6
4
1
2
7
Defined Start
End Point
Defined Start
End Point
Hypothetical Graph Computed Tortuous Path
Tortuosity – Method Validation
*** Hypothetical 3D Structure
Computed Shortest PathsEnd Surface
Start Surface
Solid
Obstruction
Step 3 – Test the approach on 3D dummy structures
*** Simulation Results
Chord Length Distribution (Pore Size Distribution)
o Defining “an individual pore and a single shape”
is not realistic in complex fuel cell materials
MPL Microstructure
Chord Length Distribution - An alternative
conceptualization for pore-size distribution.
C=Chord
Chord is defined as a line segment:
• Lies completely within a single phase
• Connects two phase boundaries
• With a specific orientation
Pore Material
Idealized pore geometry
approximation yields
unreliable results
r
Chord Length Distribution (Pore Size Distribution)
Pore
Material
ChordOrientation
Orientation0
(O0)
C1 C2
CN
C3
C4
O1
O2
O3
ON
Chords can be drawn and measured for the pore phase in any orientation
within the 3D microstructure to determine the pore shape and size
distribution
Structural Diffusivity Coefficient
Diffusion of species differs for each material due to the difference
in the microstructure of the material
Structural Diffusivity Coefficient
Finite Volume Discretization and Solving for K
Flux
Boundary Conditions Overall Flux Profile
Concentration A
Concentration B
JA=JB
K1 K2
Body Voxels
Net Flux = 0
Flux In (JA)
Flux Out (JB)
• Agrees well with literature, porosity = 0.4 – 0.6
Results - Standard Metrics
Full Dataset
80 Random
Volumes
Select sets of
random volumes
(each 1x1x1 µm)
. . . .
. . . .
. . . .
Vol 1
Vol 2
Vol 80
Vol 1
Vol 2
Vol 100
Vol 1
Vol 2
Vol 200
. . . .
Vol 1
Vol 2
Vol 300
100 Random
Volumes
200 Random
Volumes
300 Random
Volumes
Apply Metric Algorithms to Each Volume
Metric Number of Random Volumes Units
80 100 200 300
Porosity 0.41±0.04 0.41±0.04 0.41±0.04 0.42±0.04 fraction
Total
Surface Area 23.94±2.70 24.13±2.80 24.08±2.46 24.21±2.64 (µm2/µm3)
Pore
Connectivity 0.99±0.003 0.99±0.003 0.99±0.003 0.99±0.003 fraction
5x8x2 µm
Tortuosity Analysis on a Random Volume
End Surface
Direction o
f A
naly
sis
Tortuosity Analysis
Start SurfaceMaterial
Pore
Computed tortuous pathways in
the measured microstructure
1 1.2 1.4 1.6 1.8 20
0.5
1
1.5
2
2.5
3
Tortuosity
Pro
babili
ty D
ensity
τeff = τavg = 1.33
Mode = 1.27
Tortuosity,τ
Pro
babili
ty D
ensity
1 1.2 1.4 1.6 1.8 2 2.20
0.5
1
1.5
2
2.5
3
3.5
Pro
babili
ty D
ensity
Tortuosity
τeff = τavg = 1.42
Mode = 0.37
Pro
babili
ty D
ensity
Tortuosity,τ1 1.1 1.2 1.3 1.4 1.5 1.6
0
1
2
3
4
5
6
7
Effective Tortuosity
Pro
babili
ty D
ensity
τeff, avg = 1.33
St. Dev. = 0.08
Effective Tortuosity, τeff
Pro
babili
ty D
ensity
Tortuosity analysis on the 300 random volumes
Tortuosity Distribution of Full Dataset
. . . .
τeff, 1 τeff, 2 τeff, 300
. . . .
τDistribution, 1 τDistribution 2 τDistribution, 300
Tortuosity distribution gives a more comprehensive
representation of tortuous structure than a single effective value.
0 200 400 600 800 10000
0.001
0.002
0.003
0.004
0.005
Chord Length (nm)
Pro
babili
ty D
ensity
Through-plane (x)
In-plane (y)
In-plane (z)
Average
O2
O1
Chord length analysis (pore size
distribution) on the full dataset,
along the x, y, and z axes
Full Dataset
5x8x2 µm
Orientation 1 (O1)
O2
Chord Length, c (nm)
Pro
babili
ty D
ensity
Chord Length Distribution (Pore Size Distribution)
• Large percentage of
chords (pores) below
300 nm
• High mass transport
resistance in the MPL
Knudsen Number Distribution
The chord length distribution can be utilized to determine the mode of
transport within the MPL microstructure.P
robabili
ty D
ensity
Knudsen Number, Kn
Pd
TkB
22path freeMean
LKn cL length, Chord
Chords represent the characteristic
length scale of the structureKnudsen Number
10-3
10-2
10-1
100
101
102
0
0.001
0.002
0.003
0.004
0.005
0.006
Knudsen Number
Pro
babili
ty D
ensity
H
H2O
O
Transition
Region
Knudsen
Dominant
Fickian
Dominant
H2
O2
H2O(g)
Structural Diffusivity Coefficient
Diffusivity analysis on the 300 random volumes of tested MPL.
Structural Diffusivity Coefficient
. . . .
K1 K2 K300
0.1 0.15 0.2 0.25 0.3 0.35 0.40
2
4
6
8
10
12
Structural Diffusivity Coefficient
Pro
babili
ty D
ensity
Keff = Kavg = 0.23
St. Dev. = 0.045
Structural Diffusivity Coefficient, K
Pro
babili
ty D
ensity
Large variation in K
indicates strong spatial
heterogeneity within the
MPL microstructure.
(each volume is 1x1x1 µm)
K = 0.22
Empirical Relations:
Theoretical Relation:
Structural Diffusivity Coefficient
(from diffusion simulation)
Comparison with Empirical Relations
0
0.4
0.3
0.2
0.1
0.1 0.2 0.3 0.4
K (
fro
m d
iffu
sio
n s
imula
tion)
absoluteeffective DKD
2
K
2
2
K
Mean error = 8%
Best approximation for
the tested MPL dataset
Density
Error(ε ,τ from metrics analysis)
5.1K Mean error = 15%
K Mean error = 27%
• Novel microstructure analysis tools were developed for the
estimation of key structure-related metrics of fuel cell materials
Summary & Conclusions
• A direct approach for quantifying tortuous paths is developed
• Tortuosity distribution gives a more comprehensive
representation of tortuous structure than a single effective value
• Chord length distribution is introduced as an alternative concept
for describing the pore size distribution
– More accurate analysis of irregular pore geometries
– Determination of dominant diffusion mode within the microstructure
• Effective medium approximations for diffusion where compared
against the metrics analysis results of the MPL data
– Significant error exists
20
Acknowledgements
Future Work
• Dr. Craig L. Johnson (Centralized Research Facilities, Drexel)
• NSF Grant #1066623
• NSF Grant #DMR-0722845
• ED Award #P200A100145
• Characterization of GDL and catalyst layer of PEM fuel cells
• Development of key structure-transport correlations for fuel
cell materials
21
THANK YOU!