ASME2011 - Ahmetv8.pptx

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!