Pore Network Modeling and Synchrotron Imaging of Liquid ... · 3 Unstructured Pore Network Modeling...

Pore Network Modeling and Synchrotron Imaging of Liquid Water in the Gas Diffusion Layer of Polymer Electrolyte

Membrane Fuel Cells

by

James Thomas Hinebaugh

A thesis submitted in conformity with the requirements

for the degree of Doctor of Philosophy

Department of Mechanical and Industrial Engineering

University of Toronto

© Copyright by James Hinebaugh (2015)

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Pore Network Modeling and Synchrotron Imaging of Liquid Water in

the Gas Diffusion Layer of Polymer Electrolyte Membrane Fuel Cells

James Thomas Hinebaugh

Doctor of Philosophy

Department of Mechanical and Industrial Engineering

University of Toronto

2015

Abstract

Polymer electrolyte membrane (PEM) fuel cells operate at levels of high humidity, leading to

condensation throughout the cell components. The porous gas diffusion layer (GDL) must not

become over-saturated with liquid water, due to its responsibility in providing diffusion

pathways to and from the embedded catalyst sites. Due to the opaque and microscale nature of

the GDL, a current challenge of the fuel cell industry is to identify the characteristics that make

the GDL more or less robust against flooding. Modeling the system as a pore network is an

attractive investigative strategy; however, for flooding simulations to provide meaningful

material comparisons, accurate GDL topology and condensation distributions must be provided.

The focus of this research is to provide the foundational tools with which to capture both of these

requirements. The method of pore network modeling on topologically representative pore

networks is demonstrated to describe flooding phenomena within GDL materials. A stochastic

modeling algorithm is then developed to create pore spaces with the relevant features of GDL

materials. Then, synchrotron based X-ray visualization experiments are developed and conducted

to provide insight into condensation conditions.

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It was found that through-plane porosity distributions have significant effects on the GDL

saturation levels. Some GDL manufacturing processes result in high porosity regions which are

predicted to become heavily saturated with water if they are positioned between the condensation

sites and the exhaust channels. Additionally, it was found that fiber diameter and the volume

fraction of binding material applied to the GDL have significant impacts on the GDL

heterogeneity and pore size distribution. Representative stochastic models must accurately

describe these three material characteristics. In situ, dynamic liquid water behavior was

visualized at the Canadian Light source, Inc. synchrotron using imaging and image processing

techniques developed for this work. Liquid water primarily originated beneath the flow field

landings, sometimes spreading laterally into the less compressed regions of the GDL beneath the

flow field channels. Independent water clusters were tightly packed within the GDL, rarely

occupying more than 1 mm2 of planar area. These tools and observations provide the capability

to predictively design high performance GDL materials.

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Acknowledgments

I would like to sincerely thank those who have contributed to this project. Firstly, Dr. Aimy

Bazylak, my supervisor, has provided me with superb resources and guidance to do this work.

She has given me the freedom to work on a great range of projects, the experiences of which

have given me great depth as a research scientist. I would like to thank her for the trust she has

always had in me to do quality work. I would also like to thank the team at the Biomedical

Imaging and Therapy line at the Canadian Light Source. Beam scientist George Belev spent

dozens of hours at our side during our group’s first visit in 2010 to transfer his expertise onto our

team. Thanks also to Adam, Denise, Tomasz, and Dean for taking us into your facility to do great

science. Next, I would like to thank my lab mates for sharing their research with me, and for

allowing me to share my work with them. The collaborative atmosphere in our lab has been

remarkable, and has made the days go by enjoyably. I have never worked with a group of people

so concerned for each other’s sanity. While all of my lab mates have supported me in this

endeavor, I’d like to particularly thank Zachary Fishman, Jon Ellis, Ronnie Yip, Pradyumna

Challa, Jongmin Lee, Steven Bothello, and Nan Ge for the long discussions we’ve had about this

work over the years. There is likely not a paragraph of this thesis that was not somehow

influenced by your bright minds. I am sincerely grateful to the many sources of funding that have

made this research possible. Canada is blessed to have local businesses such as Hatch, the

Automotive Fuel Cell Cooperation, and Hydrogenics that actively encourage alternative energy

research. I am particularly grateful to Dr. Bert Wasmund of Hatch, who has made it a personal

mission to facilitate graduate research of renewables. Of course, I wouldn’t be writing these

words had it not been for my large, loving family that ensured that I was provided with every

tool required to achieve. They have been there for me my entire life, and their unwavering

support has given me the confidence to tackle this PhD. Finally, and most importantly, I would

like to thank my beautiful wife, whose love and sacrifice have kept me afloat these six years.

You are my guardian angel, Zeynep. I will be forever grateful of the wife you have been.

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Table of Contents

Acknowledgments................................................................................................................... iv Table of Contents ..................................................................................................................... v List of Tables .......................................................................................................................... ix

List of Figures.......................................................................................................................... x List of Appendices .................................................................................................................xix 1 Introduction......................................................................................................................... 1

1.1 Background and Motivation .......................................................................................... 1

1.2 PEM Fuel Cell Background........................................................................................... 2 1.3 Modeling Two Phase Phenomena within the GDL ......................................................... 4 1.4 Stochastic Modeling of the GDL ................................................................................... 5 1.5 In Situ Visualizations of Liquid Water in the GDL ......................................................... 6

1.6 Primary Assumptions .................................................................................................... 9 1.6.1 Invasion algorithms ........................................................................................... 9 1.6.2 Visualized liquid water .................................................................................... 10

1.7 Contributions.............................................................................................................. 10

1.8 Organization of the Thesis .......................................................................................... 12 1.9 Co-Authorship ............................................................................................................ 13

2 Pore Network Modeling of Two-Phase Transport in PEM Fuel Cells ................................... 14 2.1 Abstract...................................................................................................................... 14

2.2 Introduction ................................................................................................................ 14 2.3 Invasion Algorithm ..................................................................................................... 18 2.4 Modeling Assumptions ............................................................................................... 21

2.4.1 Inlet Assumptions............................................................................................ 21

2.4.2 Pore and throat shape ....................................................................................... 22 2.4.3 Wettability ...................................................................................................... 22 2.4.4 Steady state ..................................................................................................... 23 2.4.5 Network size ................................................................................................... 24

2.4.6 Trapping ......................................................................................................... 24 2.5 Representative Highlights ........................................................................................... 24

2.5.1 Inlet assumptions ............................................................................................. 24 2.5.2 Pore-space assumptions ................................................................................... 26

2.5.3 Capillary fingering .......................................................................................... 27 2.5.4 Diffusion ......................................................................................................... 28

2.6 Conclusion ................................................................................................................. 29 3 Unstructured Pore Network Modeling with Heterogeneous PEM Fuel Cell GDL Porosity

Distributions...................................................................................................................... 30 3.1 Abstract...................................................................................................................... 30 3.2 Introduction ................................................................................................................ 30 3.3 Pore Network Model................................................................................................... 33

3.4 Results and Discussion................................................................................................ 36 3.4.1 Network size sensitivity ................................................................................... 36 3.4.2 Measured heterogeneous porosity distributions ................................................. 37

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3.4.3 Uniform, sine-, and square-wave porosity distributions ..................................... 41 3.4.4 Theoretical surface treatments.......................................................................... 43

3.5 Conclusions ................................................................................................................ 46

4 Stochastic Modeling of PEM Fuel Cell GDLs II. Physical Characterization ......................... 48 4.1 Abstract...................................................................................................................... 48 4.2 Introduction ................................................................................................................ 48

4.2.1 Fiber count in stochastic models ....................................................................... 50

4.2.2 MPL modeling ................................................................................................ 52 4.3 Methods ..................................................................................................................... 53

4.3.1 Fiber diameter ................................................................................................. 53 4.3.2 Fiber pitch ....................................................................................................... 55

4.3.3 Fiber co-alignment .......................................................................................... 57 4.3.4 Additive materials ........................................................................................... 57 4.3.5 MPL cracks ..................................................................................................... 58

4.4 Results and Discussion................................................................................................ 59

4.4.1 Fiber diameter ................................................................................................. 59 4.4.2 Fiber pitch ....................................................................................................... 60 4.4.3 Fiber co-alignment .......................................................................................... 61 4.4.4 Additive materials ........................................................................................... 61

4.4.5 MPL cracks ..................................................................................................... 62 4.5 Conclusions ................................................................................................................ 63

5 Stochastic Modeling of PEM Fuel Cell GDLs II. A Comprehensive Substrate Model with Pore Size Distribution and Heterogeneity Effects ................................................................ 64

5.1 Abstract...................................................................................................................... 64 5.2 Introduction ................................................................................................................ 64 5.3 Model Development ................................................................................................... 66

5.3.1 Model overview .............................................................................................. 67

5.3.2 Individual fiber placement ............................................................................... 67 5.3.3 Fiber count ...................................................................................................... 68 5.3.4 Generated fiber volume.................................................................................... 69 5.3.5 Through-plane material distribution ................................................................. 72

5.3.6 Fiber co-alignment .......................................................................................... 72 5.3.7 Fiber overlap ................................................................................................... 72 5.3.8 Binder placement............................................................................................. 72

5.4 Pore-space Characterization ........................................................................................ 73

5.4.1 Porosity heterogeneity ..................................................................................... 73 5.4.2 Mercury intrusion porosimetry simulations ....................................................... 74

5.5 Results and Discussion................................................................................................ 76 5.5.1 Stochastic model of Toray TGP-H 090 ............................................................. 76

5.5.2 Porosity heterogeneity ..................................................................................... 79 5.5.3 Mercury intrusion porosimetry simulations ....................................................... 81

5.6 Conclusions ................................................................................................................ 85 6 Visualizing Liquid Water Evolution in a PEM Fuel Cell Using Synchrotron X-ray

Radiography ...................................................................................................................... 87 6.1 Abstract...................................................................................................................... 87 6.2 Introduction ................................................................................................................ 87 6.3 Experimental Setup..................................................................................................... 89

6.3.1 Fuel cell assembly ........................................................................................... 89

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6.3.2 Imaging setup .................................................................................................. 90 6.3.3 Fuel cell operating conditions .......................................................................... 91 6.3.4 Liquid water quantification .............................................................................. 91

6.4 Results: Behavior of Visualized Water ........................................................................ 93 6.5 Future Design Considerations...................................................................................... 95

6.5.1 Membrane thickness ........................................................................................ 95 6.6 Uneven Attenuation .................................................................................................... 96

6.6.1 Channel alignment........................................................................................... 97 6.7 Pre-Monochromator Filters ......................................................................................... 98 6.8 Conclusions ................................................................................................................ 98

7 Accounting for Low Frequency Synchrotron X-ray Beam Position Fluctuations for

Dynamic Visualizations ....................................................................................................100 7.1 Abstract.....................................................................................................................100 7.2 Introduction ...............................................................................................................100 7.3 Imaging Setup ...........................................................................................................101

7.4 Experiments ..............................................................................................................102 7.5 Beer-Lambert Image Analysis ....................................................................................104 7.6 Ring Current Decay ...................................................................................................105 7.7 Beam Position Movement ..........................................................................................105

7.8 Image Analysis with Beam Position Pairing................................................................109 7.9 Image Processing Routine ..........................................................................................111 7.10 Conclusions ...............................................................................................................114

8 Quantifying Percolation Events in PEM Fuel Cell Using Synchrotron Radiography ............115

8.1 Abstract.....................................................................................................................115 8.2 Introduction ...............................................................................................................115 8.3 Method......................................................................................................................118

8.3.1 Fuel cell materials and assembly .....................................................................118

8.3.2 GDL materials................................................................................................119 8.3.3 Fuel cell control sequence ...............................................................................120 8.3.4 Beamline controls...........................................................................................121 8.3.5 Data collection ...............................................................................................122

8.3.6 Image normalization .......................................................................................123 8.3.7 Surface and edge breakthrough quantification..................................................124

8.4 Results ......................................................................................................................125 8.4.1 Visualized liquid water ...................................................................................125

8.4.2 Breakthrough density......................................................................................126 8.5 Discussion .................................................................................................................127

8.5.1 Water cluster size limits ..................................................................................127 8.5.2 Temperature effects ........................................................................................129

8.5.3 Anode flow rate ..............................................................................................129 8.6 Conclusions ...............................................................................................................130

9 Conclusions and Recommendations ..................................................................................131 9.1 Conclusions and Contributions ...................................................................................131

9.2 Future Work ..............................................................................................................134 References ............................................................................................................................135 Appendix A ..........................................................................................................................143 Appendix B ..........................................................................................................................144

B.1 Dark Current Correction .............................................................................................144

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B.2 Linear Intensity Correction .........................................................................................144 B.3 Beam Position Correction ...........................................................................................145 B.4 Flat Field Normalization .............................................................................................145

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List of Tables

Table 3.1 Summary of the GDL material properties obtained by tomography and breakthrough

saturation levels obtained through pore network simulations. ................................................... 41

Table 4.1 Material characteristics measured or calculated in this study. .................................... 61

Table 5.1 Parameters employed to create materials for this study. Underlined parameters are

assumed to best represent Toray TGP-H 090. .......................................................................... 77

Table 5.2 Mean pore diameter values for each studied combination of fiber diameter and binder

fraction .................................................................................................................................. 85

Table 5.3 Pore diameter ranges for each studied combination of fiber diameter and binder

fraction. ................................................................................................................................. 85

Table 8.1 GDLs chosen for water visualization study. Each letter represents a single cell build,

where the subscript denotes the number of data sets collected with that cell, at the specified

temperature. ..........................................................................................................................120

Table 8.2 Breakthrough (BT) density data for each data set. Cells are shaded according to their

relative breakthrough densities. .............................................................................................127

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List of Figures

Figure 1.1 A 3D model of a GDL. PTFE (grey) coated fibers (black) with an MPL (green) coated

on one side. While this model was created to scale of actual GDL features and represents a

realistic GDL thickness, it only represents a 250 µm × 250 µm sample of a GDL, which typically

are on the order of 100 cm2 in area............................................................................................ 1

Figure 1.2. An illustration of standard configuration of PEM fuel cell. The CCM has a catalyst

layer (black) coated on both anode and cathode sides of the membrane (pink). The cathode flow

field has flow channels that cannot be seen in this orientation. Not to scale. ............................... 3

Figure 1.3 Node and bond (a) pore network representation of pore space (white) with

corresponding sphere and tube geometries (b) for pores and throats, respectively. ...................... 5

Figure 1.4 Exploded view of the PEM fuel cell components with through-plane and in-plane X-

ray beam orientations illustrated. .............................................................................................. 7

Figure 1.5 In-plane X-ray orientation, providing through-plane view of water distribution. Raw

absorption image (a) and imaged properly normalized for liquid water visualization (b). See

Chapter 6 for more details. ....................................................................................................... 8

Figure 1.6 Through-plane X-ray orientation, providing in-plane view of water distribution. A

circular viewing hole was drilled through the metallic components of the fuel cell to provide

“viewing” windows. The positions of 3 cathode channels are marked. For scale, each channel is

1 mm wide. See Chapter 8 for more details. .............................................................................. 8

Figure 2.1 Illustration of node/bond network representative of a pore space. Nodes are

considered to be locations of large void spaces (pores) in a porous material. Bonds illustrate the

connections (throats) present between pores. ........................................................................... 15

Figure 2.2 Illustration of pore network depicting pore space and key features of network ......... 15

Figure 2.3 Structured network (cubic). .................................................................................... 17

Figure 2.4 Unstructured pore network created around 2D material locations............................. 18

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Figure 2.5 Illustration of a non-wetting phase invading a pore space of variable diameter from

left to right. Seven interface locations are drawn in grey. ......................................................... 23

Figure 2.6 Predicted saturation levels at positions across the depth of the network, demonstrating

the effect of saturation in a 2D pore network model when a nucleation site is introduced at

various fractional distances (xns) from the inlet, within the domain [37]. ................................... 25

Figure 2.7 Steady state water saturation patterns predicted for networks generated with

prescribed porosity distributions by Hinebaugh et al. [38]. Water (blue) invades the pore space

(white) from the bottom face of this 2D pore network. (These figures are presented and described

in detail in Chapter 3)............................................................................................................. 26

Figure 2.8 Predicted saturation levels (blue) for networks generated with prescribed porosity

distributions (red) demonstrating the effect of porosity distribution on saturation profile in 2D

pore networks by Hinebaugh et al. [38]. (These figures are presented and described in detail in

Chapter 3).............................................................................................................................. 27

Figure 3.1 A through-plane cross section of Toray TGP-H-060 obtained through micro-computed

tomography (SkyScan 1172, 2.44 μm/pixel) illustrating through-plane pore structure. .............. 31

Figure 3.2 A 2D (600 μm x 200 μm) unstructured pore space generated by the random placement

of 7μm wide fibers (solid black disks) until the desired porosity of 0.80 is reached. As seen in the

magnified image (b), circular pores (hollow circles) are centered at the nodes of the overlaid

Voronoi diagram, connected to adjacent pores by throats which are represented by the bonds of

the Voronoi diagram. Each polygon of the Voronoi diagram is created by lines equidistant from

disks. ..................................................................................................................................... 34

Figure 3.3 Porosity and material fraction data, f, for a Toray TGP-H-060 GDL. Blue diamonds

represent the measured porosity distribution obtained from micro-computed tomography

visualizations [54] . The black line represents the calculated material fraction from interpolated

porosity data. The red line represents the resultant average porosity of 100 networks generated

with the calculated material fraction........................................................................................ 36

Figure 3.4 Aspect ratio and network size sensitivity study with invasion percolation simulations

run on stochastic networks created with Toray TGP-H-060 porosity data. a) Mean saturation

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levels generated using a constant network thickness of 200 μm. b) Comparison of three network

thicknesses. One standard deviation is displayed with each data point. ..................................... 37

Figure 3.5 Example saturation patterns (distinct realizations) using tomography derived porosity

distributions. The following materials are represented: a) Toray TGP-H-030, b) Toray TGP-H-

060, c) Toray TGP-H-090, d) Toray TGP-H-120, e) SGL Sigracet 10AA, and f) Freudenberg

H2315. .................................................................................................................................. 39

Figure 3.6 The heterogeneous porosity and breakthrough saturation profiles associated with six

commercially available GDL materials. Interpolated porosity values are shown in red. The

average saturation level for each pixel column is shown in blue. The following materials are

represented: a) Toray TGP-H-030, b) Toray TGP-H-060, c) Toray TGP-H-090, d) Toray TGP-H-

120, e) SGL Sigracet 10AA, and f) Freudenberg H2315. ......................................................... 40

Figure 3.7 The porosity and breakthrough saturation curves associated with three theoretical

GDL materials. Theoretical porosity values are shown in red. The average saturation level for

each pixel column (vertical slice) is shown in blue. Network thicknesses are set to 200 μm, and

an aspect ratio of 5 is maintained. ........................................................................................... 43

Figure 3.8 The porosity and breakthrough saturation curves associated with six commercially

available GDL materials with an inlet-side surface treatment. Interpolated porosity values are

shown in red. The average saturation level for each pixel column is shown in blue. Thin red and

blue lines represent the original porosity and saturation profiles respectively. The following

materials are represented: a) Toray TGP-H-030, b) Toray TGP-H-060, c) Toray TGP-H-090, d)

Toray TGP-H-120, e) SGL Sigracet 10AA, and f) Freudenberg H2315. ................................... 45

Figure 4.1 2D stochastic models demonstrating the similar pore-space effects caused by the

modeling assumptions: I fiber diameter, II fiber bundling, III and binder fraction. Pore space is

represented as white. Fibers, either 7 µm or 10 µm, are represented as black. Binder is

represented as grey. Each 100 µm × 100 µm model is created to be 65% porous, with randomly

distributed, non-overlapping fibers.......................................................................................... 51

Figure 4.2 3D stochastic model of the PEM fuel cell GDL. There is no scale for reference as this

model could have been made with any fiber diameter. ............................................................. 52

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Figure 4.3 Edge of hand-torn GDL (a) with region of interest highlighted. Intensity profile (b) of

region of interest in direction perpendicular to fiber. The dotted line displays the value at 50% of

the average background intensity, defining the edge of the fiber............................................... 54

Figure 4.4 Visualized nano-CT dataset of Toray TGP-H 090 0 wt % PTFE. (a) Through-plane

cross sectional slice. (b) Planar cross-sectional slice. (c) 3D view with slice positions highlighted.

The blue reference cube has an edge length of 50 µm. ............................................................. 55

Figure 4.5 Through-plane cross sectional nano-CT slices of Toray TGP-H 090 0 wt % PTFE

with arrows indicating highlighted fiber positions. Slice (a) is separated from (b) by 50 µm in the

direction normal to the slices. ................................................................................................. 56

Figure 4.6 Imaged 35 µm thick sheets of nano-CT dataset of Toray TGP-H 090 0 wt % PTFE

with clearly bundled fibers painted in red, and clearly individual fibers highlighted in light blue.

.............................................................................................................................................. 57

Figure 4.7 Scanning electron micrographs of the MPL surfaces of (a) SGL Sigracet 25BC, and

(b) Freudenberg H2315 I3 C1, with annotated cracks. ............................................................. 59

Figure 4.8 Fiber diameter distributions for (a) Toray TGP-H 090 0 wt % PTFE, (b) SGL Sigracet

25AA, (c) Freudenberg H2315. .............................................................................................. 60

Figure 4.9 Fiber pitch distribution of 30 fibers measured from nano-CT image of Toray TGP-H

090 0 wt % PTFE. .................................................................................................................. 60

Figure 4.10 MPL cracks of GDL types. (a,b) SGL Sigracet 25BC, (c) Freudenberg H2315 I3 C1,

and (d) Freudenberg H2315 with custom PTFE and MPL treatments. ...................................... 62

Figure 5.1 Size comparison between a relatively small GDL sample area (5 cm × 5 cm) and a

relatively large stochastic model (1 mm × 1 mm). ................................................................... 66

Figure 5.2 Stochastic model of Toray TGP-H 090 GDL substrate and enlargement for detailed

view. Fibers (black) have diameter of 8 µm, binder (yellow) has binder fraction of 0.4. Sample

has dimensions 990 µm × 990 µm × 260 µm ........................................................................... 67

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Figure 5.3 Fiber placed into a stochastic modeling domain. x, y, and z offsets, as well as angles φ,

and θ (pitch) were assigned based on an assumed probability distribution of possible values.

Portions of fibers extending beyond the domain were made to reappear at the opposite face of

domain. ................................................................................................................................. 68

Figure 5.4 Comparison of mean fiber volume, Vf,gen, and input diameter, dinput, for cylinder

generation algorithm. The ideal case of V = π l (dinput/2)2 is displayed as a dashed line. The

calculated equivalent diameter, deq, based on cylinders with volume = Vf,gen, is also displayed. . 71

Figure 5.5 Permitted resolution values, R, over the dinput values tested, for five hypothetical fiber

diameters, dexp. ....................................................................................................................... 71

Figure 5.6 Demonstration of a porosity heterogeneity analysis of a 2D example (a) with white

material on black void. The blue and red dashed regions each represent a randomly placed 502

pixel2 sample. After a sufficient number of similar random samples were examined, a

representative histogram of measured porosities (b) was obtained. Note: in the 3D models

characterized in this study, the random samples were 503 µm3 cubes........................................ 74

Figure 5.7 MIO demonstration on pore space shown in Figure 5.6a. The pore space coloring (a)

corresponds to the diameter of the largest circular structuring element (SE) that was accessible

from the top or bottom of the domain. The pore size distribution and saturation curves (b) were

calculated from the volume of each color shown in (a). Note: in the 3D models characterized

later in this study, the probing structuring element was spherical. ............................................ 75

Figure 5.8 Comparison between cross sectional slices of a µCT data set of Toray TGP-H 090 (a)

and a stochastically generated material generated with representative input parameters and a

binder fraction of 0.4 (b). Material (white) represents both fibers and binder material. .............. 77

Figure 5.9 Comparison between the µCT derived through-plane porosity distribution used as a

weighting function to stochastic fiber placement, and the porosity distribution of a single,

stochastically generated material............................................................................................. 78

Figure 5.10 Comparison between SEM micrographs (a) of top-down (xy plane) and edge (xz

plane) views of Toray TGP-H 090 material and similar views of stochastically generated, digital

materials (b). The scale bar in (a) applies to all images. ........................................................... 79

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Figure 5.11 Porosity heterogeneity comparison showing the relationship between binder fraction

and heterogeneity for fiber diameters: (a) 7 µm, (b) 8 µm, (c) 9 µm, (d) 10 µm, (e) 11 µm. Each

colored field is bound by two standard deviations above and below the mean value from 10

samples. The reference line in each figure corresponds to the mean value of materials generated

with 8 µm-diameter fibers and a binder fraction of 0.4. ............................................................ 80

Figure 5.12 MIO saturation curve comparison showing the relationship between binder fraction

and saturation curves for fiber diameters: (a) 7 µm, (b) 8 µm, (c) 9 µm, (d) 10 µm, (e) 11 µm.

Each colored region is bound by two standard deviations above and below the mean value

obtained from 10 samples. The reference line in each figure corresponds to the mean value of

materials generated with 8 µm-diameter fibers and a binder fraction of 0.4. ............................. 82

Figure 5.13 MIO pore size distribution comparison showing the relationship between binder

fraction and pore size distribution for fiber diameters: (a) 7 µm, (b) 8 µm, (c) 9 µm, (d) 10 µm,

(e) 11 µm. Each colored region is bound by two standard deviations above and below the mean

value obtained from 10 samples. The reference line in each figure corresponds to the mean value

of materials generated with 8 µm-diameter fibers and a binder fraction of 0.4. ......................... 83

Figure 5.14 An example distribution of mercury from a simulation of mercury intrusion

porosimetry with a spherical SE of diameter of 30 µm in a 1 mm × 1 mm × 263 µm modeled

material with a fiber diameter of 9 µm and a binder fraction of 0.2. Fibers were intentionally

hidden in this representation for clarity. .................................................................................. 84

Figure 6.1 Schematic illustrating the components of the PEM fuel cell assembly. After assembly,

GDL and gasket reside in the same plane. ............................................................................... 90

Figure 6.2 Synchrotron X-ray radiographs showing the cross-sectional view of an operating PEM

fuel cell: (a) raw (b) processed images. The white dashed selection represents the selection

shown in Figures 6.4 and 6.5. The grayscale calibration bar is in units of cm of liquid water.

Scale bars represent 1 mm. ..................................................................................................... 92

Figure 6.3 Current density and potential response of fuel cell when current density is increased

from 0.30 A/cm2 at a rate of 2 mA/cm2/s. Regions (a - d) represent the 17 seconds of combined

exposure for each of the four frames displayed in Figure 6.4. ................................................... 93

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Figure 6.4 Liquid water evolution over 4 minutes. Liquid water forms near the catalyst layer

under the cathodic flow field landings (b,c) and appears to spread laterally through the bulk of

the GDL to the region under the channel (d). Black lines outline the location of the flow field

landings. Negative values represent artifacts caused by material relocation during membrane

hydration. The grayscale calibration bar is in units of cm of liquid water. Scale bars represent 0.5

mm. ....................................................................................................................................... 94

Figure 6.5 Radiograph taken at OCV normalized to the dry-state image used in this study (0.30

A/cm2) (inverted for consistency with Figures 6.4 and 6.5). Bright regions represent a net gain of

material between OCV and 0.30 A/cm2, while dark regions represent a net loss. Black lines

outline the location of the flow field landings. The scale bar represents 0.5 mm. ...................... 96

Figure 6.6 Single cross sectional slice of 3D computed tomograph taken of PTFE-coated

fiberglass gasket material. Brightness values represent X-ray attenuation. The fiberglass bundles

in the composite significantly attenuate the signal when compared to the PTFE influence. The

scale bar represents 0.25 mm. ................................................................................................. 97

Figure 7.1 Exploded view of fuel cell components and relative beam direction for in situ

experiment (a). Example radiograph of in situ experiment (b). ................................................102

Figure 7.2 Exploded view of injection apparatus components and relative beam direction for ex

situ experiment (a). Example radiograph of ex situ experiment (b). .........................................103

Figure 7.3 Radiographs normalized to the first dry-state image in the sequence demonstrating the

presence of high levels of artifacts appearing at some points in time (a), and little to no artifacts

are present at others (b). ........................................................................................................107

Figure 7.4 Raw radiograph (a) with two regions (highlighted) selected on either side of the

vertical hotspot position where the mean intensity value is to be calculated. Mean intensity

values for regions 1 and 2 over time (b). ................................................................................107

Figure 7.5 Raw radiograph (a) with two regions (highlighted) selected on either side of the

horizontal hotspot position where the mean intensity value is to be calculated. Mean intensity

values for regions 1 and 2 over time (b). ................................................................................108

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Figure 7.6 Raw radiograph (a) with solid graphite block region (highlighted) used to find the

vertical beam intensity profile. Vertical beam intensity profile (black) with eighth-order

polynomial fit overlaid in red (b). Calculated vertical position of the beam hotspot over 3 min

(c). Vertical hotspot position versus time (d) for an extended period (gray), with the linear trend

overlaid in black. ..................................................................................................................109

Figure 7.7 Three regions of a normalized radiograph (a) displaying significant false water

artifacts. Region 1 is entirely within the solid graphite block. Region 2 samples a heterogeneous

region of the radiograph, including rib, channel and GDL. Region 3 samples a region of the

radiograph well below the vertical position of the hotspot. The mean water thickness values for

each of the three regions (solid lines), with a linear fit (dashed lines) at a single point in time (b).

Normalized values of the three regions’ gradients over 3 min compared with the calculated

vertical hotspot position for the same image sequence (c). ......................................................111

Figure 7.8 A comparison between radiographs normalized to the dry-state radiograph at t=0 and

the same radiographs normalized to the dry-state radiographs with matching false water

thickness gradient values. The pairs of radiographs at the top and bottom provide two examples

of this comparison. ................................................................................................................113

Figure 8.1 Images of modified 25 cm2 Fuel Cell Technologies PEM fuel cell. Note: Although

three viewing holes are present, only the lowermost hole was employed in this study. .............118

Figure 8.2 Calculated pressures under flow-field landings with respect to bolt torque for Toray

TGP-H 090 10 wt% PTFE. ....................................................................................................119

Figure 8.3 Voltage response to current and flow rate set-points for an example cell build (SGL

Sigracet 25BC, 60 ºC). Δ’s denote points used for time-synchronization with the image

collection process..................................................................................................................122

Figure 8.4 Illustration of possible configurations of imaging setup. Sequences of images were

taken in Configurations I, III, and IV for the processing steps highlighted in Section 2.6. ........123

Figure 8.5 An illustration of a fuel cell cross section (a) with droplets of water forming on the

surface of the GDL and at the edge of the gas channels, and a corresponding illustration of

xviii

visualized water (b) with “edge” and “surface” breakthrough locations annotated. Note that the

anode flow field channels are offset from the cathode. ............................................................125

Figure 8.6 Six frames from the final stage (λA=2.8, λC=1.4) of an example experiment (GDL:

Toray TGP-H 090 with 10 wt % PTFE1 and proprietary MPL. Cell temperature: 75 ºC).

Greyscale values correspond to thickness levels of liquid water, scaled between -0.2 mm and 0.6

mm. The positions of three cathode channels are highlighted on the left. For scale, each channel

width is 1 mm. ......................................................................................................................126

xix

List of Appendices

Appendix A ......................................................................................................................... 143

Appendix B ......................................................................................................................... 144

1

1 Introduction

1.1 Background and Motivation

The polymer electrolyte membrane (PEM) fuel cell is an energy conversion device that

facilitates the use of hydrogen gas as an energy carrier, an important step towards a future with

renewable energy. The key challenges currently impeding widespread PEM fuel cell

commercialization are their high costs and limited hydrogen availability [1,2]. Since fuel cell

material costs scale with active area, Srinivasan et al. [3] explained that a key to driving down

costs is to enable greater power densities from PEM fuel cells, so that smaller fuel cell

configurations can handle greater power ranges. However, as power densities increase, heat

transfer and gas diffusion rates become limiting factors to performance, and both of these factors

are heavily influenced by the porous transport layer often referred to as the gas diffusion layer

(GDL) [4,5].

Figure 1.1 A 3D model of a GDL. PTFE (grey) coated fibers (black) with an MPL (green) coated on one side. While this model was created to scale of actual GDL features and represents a realistic GDL thickness, it only

represents a 250 µm × 250 µm sample of a GDL, which typically are on the order of 100 cm2 in area.

The GDL is a highly porous, paper-like material, sandwiched between the catalyst layer and the

flow field and is typically built upon a carbon fiber substrate. A scale model of a section of GDL

is shown in Figure 1.1. Often, these fibers are immobilized with the use of a carbonized binder

2

material [6]. To mitigate the wet environment often found within the PEMFC, this substrate is

coated with a wet-proofing agent (usually polytetrafluoroethylene (PTFE)) to create hydrophobic

surfaces. Additionally, a fine-grained, hydrophobic, microporous layer (MPL) is often applied to

one face of the substrate for durability and water management purposes [6]. The primary

function of the GDL is to maintain abundant, distributed, low resistance transport pathways for

electrons, heat, water molecules, and reactant gases.

The GDL is a thin hydrophobic porous material with a mix of homogeneous and heterogeneous

pore spaces. The pore sizes in the heterogeneous regions are on a similar order of magnitude

with the GDL thickness. Due to the dominating capillary forces of the domain, liquid water can

be expected to become trapped in the largest of these pores, creating major discontinuous

obstacles to oxygen transport. Because different GDL types have been observed to have

drastically different effects on water transport and fuel cell performance [7], the question that

needs to be answered from a design point of view is, "How do the many decisions of GDL

manufacturing affect the tendency for these water clusters to cause dramatic changes in GDL

diffusivity?" To answer this question, we need a model of the GDL capable of capturing the

subtle differences in pore morphology caused by different GDL "recipes", and we need reliable

information with which to calibrate this model. I propose that pore network models extracted

from stochastically generated digital GDL materials are uniquely suited to handle the first

criteria, while synchrotron based in situ liquid water visualization provides a viable means of

validation for such a model.

1.2 PEM Fuel Cell Background

Hydrogen fuel cells electrochemically react hydrogen gas and oxygen. The hydrogen fuel cell

configuration most widely applied in consumer applications is the polymer electrolyte membrane

(PEM) fuel cell. This fuel cell utilizes an ionically conductive polymer to create a thin membrane

separating hydrogen and oxygen, across which hydrogen ions can travel. Two attractive

characteristics of this configuration are the low operating temperatures (< 100 °C) and zero-local

greenhouse gas emissions. With proper hydrogen and electrical safety measures, PEM fuel cell

systems can be extremely safe for both industrial and consumer applications.

3

Electrochemical reactions take place on each side of the PEM fuel cell membrane. The hydrogen

molecule is ionized on the anode side:

𝐻2 → 2 𝐻+ + 2 𝑒−, 1.1

and its product species are recombined with an oxygen atom to produce a water molecule on the

cathode side:

2 𝐻+ + 2 𝑒− +1

2 𝑂2 → 𝐻2𝑂. 1.2

The hydrogen ions reach the cathode half-cell reaction by traveling through the ionomer

membrane; however, the electrons are routed around an external circuit, providing useful

electricity. A precious metal catalyst coating on each side of the membrane allows these half-cell

reactions to occur at low temperatures.

Figure 1.2. An illustration of standard configuration of PEM fuel cell. The CCM has a catalyst layer (black) coated on both anode and cathode sides of the membrane (pink). The cathode flow field has flow channels

that cannot be seen in this orientation. Not to scale.

4

Individual cathode catalyst sites are only active if there are pathways connecting them to the

sources of each of the three reactant species: hydrogen ions, electrons, and oxygen gas. Because

the applied catalyst layer is a poor conductor of electrons, an electrically conductive, yet highly

porous material called the GDL is positioned adjacent to the catalyst coated membrane (CCM) to

supply catalyst sites with electrons while allowing oxygen to diffuse freely. Similarly, a GDL is

also placed adjacent to the anodic face of the CCM. This assembly is compressed between a pair

of conductive end-plates containing flow channels for reactant distribution. What results is the

standard configuration of a PEM fuel cell shown in Figure 1.

One of the challenges of the PEM fuel cell is that the ionomer is only ionically conductive when

humidified. In addition to electrical energy, water and heat are produced by the combined half-

cell reactions, producing complicated, three dimensional temperature and humidity gradients

throughout the cell that give rise to regions of condensation. This condensed water poses a

problem when it accumulates in the pore space of the catalyst layer and GDL, blocking gaseous

reactant pathways. This problem is often most severe in the cathode, primarily because O2 is less

mobile than H2, but also because the anode-cathode water balance almost always yields more

water in the cathode [6].

Water flooding in both the catalyst layer and in the GDL can negatively affect the fuel cell

performance. This thesis focuses specifically on the GDL.

1.3 Modeling Two Phase Phenomena within the GDL

Liquid water in the GDL has been observed to form discrete patches of saturation throughout the

GDL [8]. Because of the large pore length scales involved, it is not feasible to explicitly capture

this discontinuous behavior and their effects on oxygen diffusion with a continuum model of the

GDL. Pore network models have been proposed to offer a solution to this problem, providing

rich simulation environments in which basic assumptions can be explored, such as the

distribution and footprint of condensation sites [9]. An illustration of a pore network

representation of a porous material is provided in Figure 1.3.

A detailed analysis of the applicability of pore network modeling for GDL research is provided

in Chapter 2. To summarize: the insights gained from pore network modeling studies with

5

respect to the key factors that influence liquid water distributions within the GDL have been

profound. We have seen that geometrical inlet assumptions (the footprint and distribution of

condensation induced water clusters) can have dramatic effects on overall saturation [9,10].

Also, the pore topology factors (coordination number and pore size distribution) are

demonstrated to impact predicted saturations [9].

Figure 1.3 Node and bond (a) pore network representation of pore space (white) with corresponding sphere and tube geometries (b) for pores and throats, respectively.

Until recently, pore network models of GDL have primarily assigned pore locations to a rigid,

cubic lattice structure [9-18]. While experimentally derived pore size distributions can be applied

onto such a structured network [12], other topological features, such as pore connectivity and

pore size correlations can be harder to experimentally measure. However, with the development

of pore network extraction algorithms, it is now possible to generate topologically representative

pore networks based on a 3D image of the porous material, resulting in an unstructured network,

intrinsically capturing the topology with an accuracy only limited to the resolution of the image.

Luo et al. [19] demonstrated how this approach can be used to generate a two phase phenomena-

based comparison of two imagined materials, from their images alone.

1.4 Stochastic Modeling of the GDL

Microscale computed tomography (µCT) provides the capability to generate 3D images of the

GDL with sufficient resolution from which to extract accurate pore networks [20,21]; however,

very few facilities in the world are equipped to provide such high resolution tomograms. Instead,

researchers have set out to develop 3D stochastic models of the fibrous GDL (e.g. Figure 1.1),

with pore network modeling being just one of a variety of modeling applications [22-27]. The

6

relative ease of stochastic model generation makes it an attractive option for GDL research.

While most stochastic models of the GDL are generated with an existing material in mind, the

technique can also be used to search for idealized material configurations.

With the abundance of stochastic modeling of GDLs in the PEM fuel cell literature, it is

surprising that many of the fundamental modeling parameters have not been thoroughly

investigated. Fiber diameter, for example, is often only casually listed with little justification as

if it has little bearing on the final product, even though its impact has yet to be demonstrated.

Before truly representative pore spaces can be generated with stochastic models of the GDL,

comprehensive parametric studies must be performed, and relevant material properties must be

experimentally obtained.

1.5 In Situ Visualizations of Liquid Water in the GDL

Due to the strong capillary forces within the GDL, percolating water clusters will follow

predictable pathways [28]. This means that within a representative pore network, reliable water

distributions can be simulated, as long as appropriate inlet conditions can be determined.

Unfortunately, the condensation of liquid water in and around the GDL is a highly complex

phenomenon, which is difficult to predict, and equally difficult to directly observe due to the

opacity and microscale nature of the GDL. However, the resultant water clusters, can be directly

observed with the use of synchrotron radiography, as has been demonstrated by [8,29]. With the

deterministic nature of the water growth, it should be possible to work backwards from a known

water distribution to gain a more fundamental understanding of the condensation phenomena

expected in PEM fuel cells.

Dynamic liquid water behavior can be visualized in situ with synchrotron X-ray radiography due

to the high spatial and temporal resolutions associated with the technique [30]. Depending on

how the fuel cell is oriented with respect to the X-ray beam (Figure 1.4), one of two types of

images can be realized. With in-plane X-rays, the through-plane distributions of liquid water can

be obtained (Figure 1.5). In this orientation, however, the attenuation of water clusters along the

beam direction is combined, and only an average distribution can be obtained. This is still a

powerful tool with which to validate inlet assumptions, as averaged simulation results can

duplicate this effect. With a through-plane beam orientation, individual clusters of water can be

7

differentiated (Figure 1.6), while their through-plane positions must be inferred. A combination

of in-plane and through-plane imagining is proposed to provide a sufficient amount of data from

which to determine realistic inlet assumptions for pore network models.

Figure 1.4 Exploded view of the PEM fuel cell components with through-plane and in-plane X-ray beam orientations illustrated.

8

Figure 1.5 In-plane X-ray orientation, providing through-plane view of water distribution. Raw absorption image (a) and imaged properly normalized for liquid water visualization (b). See Chapter 6 for more details.

Figure 1.6 Through-plane X-ray orientation, providing in-plane view of water distribution. A circular viewing hole was drilled through the metallic components of the fuel cell to provide “viewing” windows. The

positions of 3 cathode channels are marked. For scale, each channel is 1 mm wide. See Chapter 8 for more details.

9

These imaging techniques have been demonstrated by a number of research groups [8,29,31];

however, there are a limited number of synchrotron facilities globally, each with highly

competitive beam time. Canada is fortunate to have the Canadian Light Source, Inc. in

Saskatoon, SK with a beamline capable of such experiments; however, before the work

associated with this thesis, no PEM fuel cell studies had been performed at that specific facility.

1.6 Primary Assumptions

The models of the PEM fuel cell employed in this work relied on a number of assumptions.

When simulating liquid water percolating through the GDL, the assumption that capillary forces

dominated the pore filling sequence allowed for a computationally inexpensive simulation

technique to be used, named invasion percolation (see Chapter 2). Also, during the image

processing steps involved with quantifying liquid water from X-ray radiographs, several

assumptions of imaging stability are made, and small artifacts are caused when the subject or the

illumination source are unstable (see Chapters 6-7).

1.6.1 Invasion algorithms

Capillary forces are assumed to dominate over gravitational, inertial, and viscous forces when

liquid water clusters are growing within the pore space of the GDL. This is a reasonable

assumption in the GDL substrate when the length and time scales of the percolation process are

taken into account. Water clusters can be assumed to occupy a 1 mm2 or less footprint (Chapter

8), while pore and throat diameters can be expected to fall between 18 µm and 48 µm (Chapter

5). Additionally, fuel cells produce water at a rate of 0.0934 mg s-1 for each ampere of current

produced. Should 100% of that water condense before reaching the flow field, a cell running at

an extremely high current density, 5 A cm-2, can be expected to generate only 4.7 nL s-1 per water

cluster. In Chapter 2, a list of non-dimensional numbers characterizing the ratios of the relevant

forces is presented. With the scales presented above, those non-dimensional numbers point to a

strongly capillary force dominated system.

This assumption may not hold if water clusters are connected under large delaminated regions

between the GDL and the catalyst layer. In this case, both the gravitational and the viscous forces

could generate substantial pressure gradients influencing the percolation process. Additionally, if

10

liquid water was assumed to percolate through the nanoscale pores of the MPL, the viscous

forces should be reconsidered.

1.6.2 Visualized liquid water

In Appendix B, a step by step procedure is provided for normalizing an X-ray radiograph of a

PEM fuel cell with a similar radiograph taken during a dry condition. A primary assumption

associated with this is that the solid fuel cell components remain fixed in position, relative to

both the X-ray beam and the imaging apparatus. Should any one of these three entities change in

position, the normalization process will produce inaccurate water thickness calculations. In

Chapter 7, artifacts due to beam position instabilities were demonstrated, and a modification to

the normalization algorithm was presented to account for this. In Chapter 6, major water

thickness artifacts were seen to be generated by fuel cell material movement. This is a problem

that can be partially corrected for with a more rigid fuel cell design. However, the thermal

expansion of the fuel cell apparatus and the sample stage may cause the entire cell to translate

relative to the beam and detector. Even 1 µm of movement can generate substantial artifacts

along the planes where fuel cell materials meet. Therefore, it is recommended that additional

image processing techniques should be developed to account for such movement.

It is assumed that the high capillary pressure water clusters within the GDL do not damage or

reorient the carbon fibers of the GDL. This assumption appears to be valid in that the

radiographs of a dried fuel cell acquired before and after water generation are indistinguishable

from each other.

In addition to position, the X-ray beam is assumed to maintain a steady, or predictable intensity

profile throughout the experiment. There has been no indication in the way of unexplained

imaging artifacts that would indicate that this assumption is unwarranted.

1.7 Contributions

My thesis is focused on the development of the tools with which to model two phase behavior in

PEM fuel cell GDLs. This includes developing a representative stochastic model of the GDL as

well as developing synchrotron based visualization tools with which to validate water inlet

assumptions employed in pore networks. As one of the two original graduate students of my

11

research group, I am pleased to see a large number of our new group members using the tools

that I helped develop.

My contributions are as follows:

Provided review of the state-of-the-art pore network modeling studies of liquid water in

the GDL.

Published as: Hinebaugh J, Bazylak A, Mukherjee PP. Multi-scale modeling of two-phase

transport in polymer electrolyte membrane fuel cells. In: Hartnig C, Roth C, editors. Polymer electrolyte membrane and direct methanol fuel cell technology. Cambridge, UK: Woodhead Publishing; 2012, p. 254.

Demonstrated the non-negligible impact that through-plane porosity distributions have on

liquid water originating from the catalyst layer.

Published as: Hinebaugh J, Fishman Z, Bazylak A. Unstructured pore network modeling with heterogeneous PEMFC GDL porosity distributions. Journal of the Electrochemical Society 2010; 157(11):B1651-7.

Provided in-depth characterization of GDL fiber properties (diameter, pitch, co-

alignment) as well as MPL properties (areal volume, crack size, crack distribution)

specifically relevant to stochastic modeling.

Submitted as: Hinebaugh J, Bazylak A. Stochastic Modeling of PEMFC GDLs I. Physical

Characterization. Journal of Power Sources (Submitted November 2014).

Developed stochastic model of GDL fibrous substrate incorporating measured fiber pitch,

co-alignment, and diameter. Demonstrated the impact of fiber diameter and binder

fraction on pore space.

Submitted as: Hinebaugh J, Bazylak A. Stochastic Modeling of PEMFC GDLs II. A Comprehensive Substrate Model with Pore Size Distribution and Heterogeneity Effects. Journal of Power Sources (Submitted November 2014).

Led the first investigations of PEM fuel cell water dynamics at the Canadian Light

Source, Inc. synchrotron (CLS). Co-developed methods for both in-plane and through-

plane imaging.

Published as: Hinebaugh J, Lee J, Bazylak A. Visualizing Liquid Water Evolution in a PEM Fuel

Cell Using Synchrotron X-ray Radiography. Journal of the Electrochemical Society 2012; 159(12):F826.

and: Lee J, Hinebaugh J, Bazylak A. Synchrotron X-ray radiographic investigations of liquid water transport behavior in a PEMFC with MPL-coated GDLs. Journal of Power Sources 2013; 227(0):123-30.

Identified and developed post-processing correction for vertical beam instabilities at the

CLS.

12

Published as: Hinebaugh J, Challa PR, Bazylak A. Accounting for low frequency synchrotron x-ray beam position fluctuations for dynamic visualizations. J. Synchrotron Rad. 2012; 19:994.

Quantified distribution of visualized individual water clusters in the GDL based on

synchrotron imaging.

Currently being prepared for submission to the Journal of Power Sources.

The link between the experimental and numerical contributions can be summarized as follows.

The primary motivation behind this work is the need to predict the distribution of liquid water in

various GDL morphologies. For that, both realistic domains and realistic boundary conditions

(i.e. condensation assumptions) are needed. Realistic domains can be obtained from a rigorous

study of GDL morphologies. The precise nature of condensing water in the GDL and catalyst

layer, however, is a non-trivial process and extremely difficult to model. That being said, in a

capillary force dominated system, the final water distribution has much less to do with

condensation rates, as it has with the physical distribution and density of active condensation

sites. Therefore, instead of explicitly modeling condensation, condensation information is

gathered from resultant water accumulations, visualized in situ with synchrotron based

radiography. In Chapter 8, the lower bounds of the number of condensation sites is determined.

In Chapter 6, through-plane distributions of liquid water are identified, which can be compared

with simulated results in order to calibrate the assumed distribution of condensation sites.

1.8 Organization of the Thesis

This thesis is organized into nine chapters. The background and motivations are presented in

Chapter 1, along with an overview of the contributions of the thesis. A review of pore network

modeling of two phase phenomena in PEM fuel cell GDLs is provided in Chapter 2. Chapter 3

provides a demonstration of the usefulness of pore network modeling as a tool for predicting the

discrete distributions of liquid water in the GDL, with a specific emphasis on the effects that a

non-uniform through-plane porosity can have on the predicted distributions. Chapter 4 provides a

detailed study of a variety of commercial GDLs such that stochastic modeling parameters of the

materials can be obtained. Chapter 5 describes an algorithm for stochastic model generation of

GDL. A demonstration of synchrotron based, in-plane oriented, in situ imaging of liquid water in

the GDL is provided in Chapter 6, with an overview of best practices for experimental setup.

Vertical beam position movement is addressed in Chapter 7, and a technique for post-processing

13

is developed and demonstrated that corrects for this movement. Chapter 8 employs through-

plane oriented synchrotron-based imaging to quantify the distribution and size of liquid water

clusters within the GDL. Conclusions and a road map for future work are provided in Chapter 9.

1.9 Co-Authorship

Chapter 2 was previously published as the first half of a book chapter. Dr. Partha Mukherjee was

a co-author on the Chapter, but his contribution was limited to the second half, concerning lattice

Boltzmann modeling, which was not included in this thesis.

Chapters 3, 6, and 7 were previously published in journals. Chapters 4 and 5 have been

submitted to the Journal of Power Sources. Chapter 8 is being prepared for submission to the

Journal of Power Sources. Prof. Aimy Bazylak, my supervisor, was a co-author on all journal

articles book chapters and manuscripts prepared for publication.

Zachary Fishman was a co-author to the publication resulting from Chapter 3. Zachary led the

porosity distribution analysis, and aided in the development of the 2D stochastic model of the

GDL.

Prof. Jeffery Gostick from McGill University was a co-author on the submitted manuscript

resulting from Chapter 5. Prof. Gostick provided the morphological image opening algorithm

employed to simulate mercury intrusion porosimetry.

Jongmin Lee was a co-author on publication and manuscript associated with Chapters 6 and 8,

respectively. Jongmin led the design of the fuel cell modifications and helped run the 24-hr/day

experimental schedule required of this facility.

Pradyumna Challa was a co-author on the publication resulting in Chapter 7. While I produced

the research, Pradyumna, a user of the correction algorithm, wrote a first draft of this chapter and

contributed to the final written product.

All image processing in Chapter 8 was performed by an undergraduate summer research

assistant, Craig Mascarenhas.

14

2 Pore Network Modeling of Two-Phase Transport in PEM Fuel Cells

2.1 Abstract

The accumulation and distribution of liquid water in the polymer electrolyte membrane fuel cell

(PEM) fuel cell is highly dependent on the porous gas diffusion layer (GDL). Oftentimes, the

accumulation of liquid water is simply reduced to a relationship between liquid water saturation

and capillary pressure; however, recent experimental studies have provided valuable insight that

the microstructure of the GDL as well as the dynamic behavior of liquid play important roles in

how water will be distributed in a PEM fuel cell. Due to the importance of the GDL

microstructure, there have been recent efforts to provide predictive modeling of two-phase

transport in PEM fuel cells including pore network modeling and lattice Boltzmann modeling.

2.2 Introduction

Pore network modeling is a method of reducing a complex pore space into a node/bond network.

Nodes, called pores, represent large void regions within the material. Bonds, called throats,

represent the constrictions which connect the pores. Transport calculations can then be

generalized for pore-to-pore interactions, governed by pore and throat characteristics. Figure 2.1

is an illustration of a pore space, with the pores (dark points) connected by throats (straight

lines). A planar pore space can be represented with a two-dimensional (2D) pore network, as

shown in Figure 2.2. In Figure 2.2, the pores, throats, pore radii, and throat radii are illustrated.

Intrinsically, a pore network contains the pore space’s connectivity data, where the term

“coordination number” represents the number of throat connections at each pore. In addition to

this topological information, the size and shape of each element can be incorporated. A pore

network model can be tuned to have the necessary level of detail required to achieve one’s

specific modeling goals. Additional information might be added to each element by specifying

values such as shape factor, temperature, and wettability.

15

Figure 2.1 Illustration of node/bond network representative of a pore space. Nodes are considered to be

locations of large void spaces (pores) in a porous material. Bonds illustrate the connections (throats) present between pores.

Figure 2.2 Illustration of pore network depicting pore space and key features of network

Recently, pore network modeling has been applied to simulate the accumulation of liquid water

saturation within the porous electrodes of PEM fuel cells. The impetus for this effort is the

understanding that liquid water must reside in what would otherwise be reactant diffusion

pathways. It therefore becomes important to be able to describe the effect that saturation levels

have on reactant diffusion. Equally important is the understanding of how the properties of

porous materials affect local saturation levels. This requirement is in contrast to most continuum

modeling of the PEM fuel cell, where porous materials are treated with volume averaged

16

properties. For example, the relationship between bulk liquid saturation and capillary pressures

found through packed sand and other soil studies are often employed in continuum models [32].

Experimental and numerical studies of diffusion properties of dry GDL materials are available,

as described in [33]. However, due to the presence of liquid water in the PEM fuel cell

electrodes, these relationships must be modified to accurately describe PEM fuel cell

performance. Measuring diffusion rates under saturated conditions is difficult; however, pore

network modeling can be used to provide this information conveniently through numerical

simulations. Similar modeling techniques that may also provide this information include Lattice

Boltzmann modeling and pore morphology modeling.

Pore network modeling has the advantage of requiring a minimized number of modeling

elements while maintaining an equivalent topology; therefore, it is generally regarded as a

computationally inexpensive technique. Often, pore network definitions representing GDL

materials are stochastically generated, and the model can provide valuable statistical transport

data [9-11,14,16-18,34-38]. Additionally, modeled phenomena in individual pore networks

(deterministic simulations) have also been studied to provide detailed insight into the

consequences of a particular set of assumptions [12,13,19,39].

The geometric and transport assumptions of pore network models built to study GDL invasion

often vary. A primary distinction is in how the pore space is defined. For visual purposes, it is

useful to illustrate two-phase flow behavior using a planar, 2D network [34,35,37-40]; however,

a three-dimensional (3D) network is required to achieve a realistic network topology.

Additionally, many pore network models created to study GDL invasion, such as [9-18,34-

37,40], can be classified as structured networks, where pores are positioned along a rigid lattice

(Figure 2.3). In such a model, pore and throat sizes can be randomly generated from distributions

of pore and throat sizes. The majority of structured networks are based on a cubic lattice [9-

18,36], where the coordination number can be adjusted by either adding to or deleting bonds

from the original lattice. For better or for worse, each of these models except for [9,18] have

maintained a coordination number of 6. Along with the coordination number, a structured

network allows the direct assignment of pore and throat size distributions, spatial correlation, and

anisotropy. Demonstrated in Gostick et al. [12], this flexibility can be employed to calibrate a

model to experimental mercury intrusion porosimetry data.

17

Figure 2.3 Structured network (cubic).

Unstructured networks, where nodal positions are not predetermined, can either be made by

randomly placing nodes and applying a Voronoi/Delaunay tessellation to determine connectivity

as in [41], or by analyzing an available pore space. The former method has been proposed

specifically for fibrous materials [41]; however only the latter method has been applied to study

two-phase flow in GDLs [19,38,39]. To characterize a GDL pore space, micro- or nano-scale

computed tomography (CT) images of GDL materials can be acquired and reconstructed into 3D

binary images. While this technique could be applied to generate pore networks, many

researchers alternately use stochastic modeling to characterize the GDL pore space [19,38,39].

The use of stochastic models avoids any resolution or sample size limitations associated with CT

images. Chapuis et al. [39] and Hinebaugh et al. [38] applied 2D stochastic models of randomly

placed material disks to create pore spaces (Figure 2.4), while Luo et al. [19] developed

algorithms for the random placement of cylinders to create a 3D pore space. Pore networks that

are found through an available pore space have the advantage of having pore and throat size

distributions and coordination numbers that are intrinsically appropriate to the physical pore

space of the actual GDL. This reduces the number of tunable parameters in a model, with the

expectation of improved predictability.

18

Figure 2.4 Unstructured pore network created around 2D material locations.

Once a pore space is known, a pore network can be created through a variety of methods.

Methods that reduce the pore space into a topologically equivalent skeleton involve either a

thinning algorithm [42] or, in the case of the 2D models [38,39], a Voronoi diagram around the

material locations. An alternative method to determine the representative pore network for a pore

space is the maximal ball method [21], which is a computationally inexpensive technique that

has been demonstrated for GDL-like structures in [19].

2.3 Invasion Algorithm

Pore network models have been frequently employed to simulate the invasion of a dry GDL by a

liquid water phase [9-19,34-40]. A convenient attribute of the modeling subject is that capillary

and viscous forces are expected to dominate forces from gravity and inertia due to the

corresponding Bond and Reynolds numbers of this system. The Bond number is defined as

𝐵𝑜 =𝑔∆𝜌𝐿2

𝜎 , 2.1

where 𝑔 is the acceleration of gravity, 𝜌 is the density difference between the fluids, 𝐿 is the

characteristic length, and 𝜎 is the interfacial surface tension. The Reynolds number is defined as

𝑅𝑒 = 𝜌𝑉𝐿

𝜇, 2.2

where V is the mean velocity of the fluid, and µ is the dynamic viscosity of the fluid.

19

Having both Bond and Reynolds numbers much less than 1 suggests that capillary and viscous

forces dominate gravity and inertial forces, respectively. With pore sizes less than 100 μm, Bond

numbers of droplets within the GDL can be assumed to be below 5×10-3 and Reynolds numbers

can be assumed to be less than 1×10-3. Similarly, many researchers [9,10,12,14,16,17,19,36,39]

state that the system’s associated capillary number suggests that viscous forces are also

negligible during an invasion process of GDL, where the capillary number can be defined as:

𝐶𝑎 =𝜇𝑉

𝜎, 2.3

where μ is the viscosity of liquid water, v is the mean velocity of liquid water, and σ is the

surface tension of the fluid/fluid interface. The mean velocity considered in the equation for

capillary number is often an average velocity across the inlet face of the modeled domain

[15,39]. While the average velocity in this situation is very small, this representation does not

capture the velocities experienced in individual throats, especially at the invading front, where

the associated flow is divided between a handful of throats. Therefore, a macroscopically

determined capillary number may not be well suited to solely determine the ratio of forces

present in microscopic throats and pores.

With the above said about the use of capillary number, the assumption that viscous forces can be

neglected allows for a highly simplified simulation of GDL invasion. For each throat of a pore

network, an associated entry pressure can be calculated, where entry pressure is typically

proportional to cos(θcontact)/rthroat, where θcontact is the contact angle that the interface makes

against the material, and rthroat is the radius of the throat. Then, a brief algorithm, as outlined

below, can be conducted to simulate the growth of a water cluster:

1. Assign a list of pores that are initially filled with liquid water.

2. Identify interfacial throats (between fully unsaturated pores and fully saturated pores).

3. Identify the interfacial throat, thmin, with lowest entry pressure.

4. Invade thmin and any air-filled pore adjacent to thmin with liquid water.

5. Repeat steps 2-4 until percolation or predefined stopping point.

The above algorithm is commonly referred to as “invasion percolation” as defined by Wilkinson

and Willemsen [43] and has been employed by Bazylak and coworkers [34,35,38], Prat and

coworkers [14,36,39], and Zhu and coworkers [9,17,18] to simulate the quasi-static growth of

20

liquid water clusters in PEFMC GDLs. In invasion percolation, the rate of accumulation of liquid

water in the system is assumed constant or limited, and the liquid pressure can freely fluctuate,

but will maintain the lowest value possible. The physical mechanism at work is that, if the entire

liquid water cluster can be assumed to be at a uniform pressure, as liquid water accumulates in

the system, its fluid pressure will increase until the smallest entry pressure is reached, and the

associated throat will no longer contain a “stable” (static) interface.

When the assumption of negligible viscous forces is not made, researchers have modified the

invasion percolation algorithm to incorporate a flow-induced pressure drop within the invading

cluster in a variety of ways [10,11,15,37] typically following a “dynamic invasion” algorithm,

such as the following:

1. Assign a list of pores that are initially filled with liquid water.

2. Identify interfacial throats.

3. Identify any interfacial throats at which the pressure difference across the interface

exceeds the entry pressure of the throat, label as thunstable.

4. Invade thunstable, and begin filling any air-filled pore adjacent to thunstable with liquid water.

5. Calculate the flow induced pressure distribution within the water cluster.

6. Advance the simulation clock by Δt.

7. Repeat steps 2-6 until percolation or predefined stopping point.

As was described by Lenormand and Touboul [44], this algorithm requires a convergence step

due to the fact that the list of unstable throats can only be determined after a pressure distribution

is calculated, while the pressure distribution is determined based on a flow pattern, including

flow through any unstable throats. A convergent pressure distribution is typically found by

iterating steps 2-5. Due to the non-linear nature of this problem, some researchers have employed

a relaxation process to solve the pressure distribution [10,44]. Hinebaugh and Bazylak [37]

achieved relatively fast convergence when a combination of invasion percolation and dynamic

invasion was used, where, during each time step, the throat with the lowest entry pressure was

assumed to be unstable regardless of the network pressure distribution; however, other throats

could also be simultaneously invaded according to the pressure distribution. An alternative

approach involves simulation time steps that are small compared to the filling time of a pore,

while assuming that the saturation level of pores containing liquid water is a function of pressure.

21

This strategy has been employed for GDL invasion in [11,40] and allows the calculation of flow

patterns even when pressures do not predict throat instability.

2.4 Modeling Assumptions

Once the structure and invasion algorithm are defined, current pore network models of GDL

invasion differ due to the following assumptions.

2.4.1 Inlet Assumptions

A pore network model of GDL invasion must include assumptions of the mechanisms which

produce liquid water within the GDL. Two mechanisms have been employed thus far in

literature: liquid water enters at the GDL/catalyst layer interface due to pressure buildup of

condensed liquid water in the catalyst layer [9-19,34-40], or liquid water enters within the bulk

of the GDL due to a condensation mechanism [13,37]. These mechanisms can be explained

respectively by the high humidity levels near the catalyst layer driving the diffusive flux of

water-vapor to the gas channel and by the relatively low temperatures near the ribs of the flow

field. A third mechanism has yet to be applied: liquid water entering the GDL at the GDL/gas

channel interface due to upstream accumulation.

When the inlet assumptions state that water is entering the GDL at its interface with the catalyst

layer, further clarification must be made between what has been called the uniform flux

assumption or the uniform pressure assumption [10]. The uniform flux assumption includes an

individual source of liquid water for every inlet throat along the GDL/catalyst layer interface,

where the uniform pressure assumption includes only a single source of liquid water that is

connected to each inlet throat along the GDL/catalyst layer interface. Physically, the uniform

pressure assumption assumes that there is a water cluster outside the GDL with negligible

hydraulic resistance from one side to another. Due to the microstructure of the catalyst layer, this

scenario would approximate reality only if a pocket of liquid water could form between the

catalyst layer and the GDL. Conversely, the uniform flux assumption assumes no hydraulic

connectivity outside of the GDL between inlet locations. A compromise between these two

assumptions was made by Hinebaugh and Bazylak [37] in a 2D structured pore network model

of GDL invasion, where the first row of pores and throats within the GDL is initialized as fully

22

saturated. Similar to the uniform flux assumption, a liquid water source was added to each such

pore, but similar to the uniform pressure assumption, these sources were hydraulically connected

by their adjoining throats.

Further specification of catalyst layer inlet assumptions can be made through the fraction of

GDL/catalyst layer interfacial throats that are assumed to be in contact with an inlet. While most

pore network models of GDL invasion assume that 100% of such throats are potential inlets,

several models have been created to study the effects of this assumption [10,14,36].

2.4.2 Pore and throat shape

Typically, pore network models of GDLs assume cubic or spherical pores and square or

cylindrical throats. Conveniently, these pore geometries require standard calculations of volume,

and these throat geometries are assumed to facilitate Poiseuille-like flow. Furthermore, the

hydraulic conductance is a simple function of throat size, length, and fluid viscosity. An

alternative to this method, when creating a pore network from a predefined pore space, is to

incorporate a shape factor for each pore and throat, which is then incorporated into the

conservation and flow equations. Luo et al. [19] demonstrate this method by choosing a shape

factor based on the surface to volume ratio of the physical elements that were converted into pore

network elements.

2.4.3 Wettability

For simplicity, many pore network models of GDL invasion assume that the GDL surfaces are

uniformly hydrophobic, where a single value of contact angle is assumed, often within the range

of 100-120º [10,11,14-16,37,40]. However, manufactured GDLs are typically treated with a

hydrophobic coating; therefore, uniform wettability assumes a uniform application of this

coating. There is little evidence to support this assumption due to the fact that it is extremely

difficult to visualize the coating on individual fibers as well as the liquid water/air contact angle

at the fiber-scale. Sinha and Wang [16] model a non-uniform GDL by allowing a fraction of

pores and throats to be hydrophilic (θcontact < 90) with a specified spatial distribution.

23

Figure 2.5 Illustration of a non-wetting phase invading a pore space of variable diameter from left to right.

Seven interface locations are drawn in grey.

2.4.4 Steady state

Often, a pore network simulation of GDL invasion ends once a steady state condition is reached.

This condition requires assumptions to be made of the mechanism of water transport from the

GDL into the gas channel. Because the associated capillary pressure within the ~1 mm gas

channel is dramatically less than the capillary pressures associated with the ~0.02 mm pores and

throats within the GDL, the “breakthrough” event, where liquid water enters the gas channel, is

given special significance. Often researchers assume that a simulation reaches steady state at

breakthrough, as it is assumed to be impossible for the pressure of the cluster to reach the entry

pressures associated with throats within the GDL [13,14,36,40]. Justification for this assumption

is shown in Figure 2.5, where a non-wetting phase invades a pore space, reaching a relatively

low pressure at breakthrough. However, several researchers allow the simulation to continue

after breakthrough, either by assigning a relatively high associated capillary pressure within the

channel [15,16], or by simply not considering flow into the channel until all GDL/channel

interfacial throats are invaded [34].

24

2.4.5 Network size

The assumption of a representative sample size becomes especially consequential when only a

single water cluster is considered and the initial breakthrough is assumed to be at steady state. In

this case, breakthrough density, the number of breakthrough locations per unit area, will become

solely dependent on the sample size and no other parameter.

2.4.6 Trapping

The invasion algorithm can be further modified with trapping assumptions. Trapping is a

phenomenon described as a portion of one phase becoming hydraulically disconnected from its

source [43]. In the case of GDL invasion, where the invading phase, liquid water, might trap the

defending phase, air, there must be absolutely no thin film of air connecting the trapped cluster to

the primary cluster of air in the system. Researchers [16] often cite the geometrical finding of

Concus and Finn [45] that states that thin films of a wetting fluid can only persist in cracks

crevices that have an angle smaller than θcontact - 90.

2.5 Representative Highlights

The following is an account of some influential conclusions reached about GDL invasion after

pore network investigations.

2.5.1 Inlet assumptions

The mechanism with which liquid water enters the pore network has been demonstrated to

heavily influence the resulting steady state saturation levels within the material

[9,10,13,14,36,37]. From work conducted by Lee et al. [10], a striking difference can be seen

between the uniform pressure and uniform flux inlet conditions described above. The uniform

flux inlet generated a breakthrough saturation roughly twice as large as that produced with a

uniform pressure boundary condition. Rebai and Prat [14] demonstrated a dramatic result when a

uniform pressure boundary condition was compared with a single throat inlet. The relatively low

saturation levels generated from the single throat inlet condition was shown to be a strong

function of the network dimensions, and in all cases has a very different concavity from the other

boundary conditions.

25

Wu et al. [9] investigated a new inlet condition where liquid water was assumed to agglomerate

in finite sized droplets between the catalyst layer and gas diffusion media. In this study, a bi-

layer gas diffusion media was assumed, where liquid water must first percolate the MPL before

reaching the fibrous substrate. Similar to the distinction between uniform pressure and uniform

flux, when many small droplets are assumed to coat the inlet, a high overall saturation is

observed, and when only a few large droplets are considered, saturation levels are minimized in

both materials.

Figure 2.6 Predicted saturation levels at positions across the depth of the network, demonstrating the effect of saturation in a 2D pore network model when a nucleation site is introduced at various fractional distances

(xns) from the inlet, within the domain [37].

Finally, when researchers assume liquid water enters the network due to bulk GDL condensation,

saturation profiles are even further distinct [13,37]. As seen in Figure 2.6, Hinebaugh and

Bazylak [37] demonstrated that a peak in the saturation profile tends to line up with the through-

plane position of water cluster nucleation.

26

2.5.2 Pore-space assumptions

Several researchers have shown that the assumed geometry of the GDL pore space can have an

impact on modeled transport [12,35,38]. Gostick et al. [12] found that the anisotropic

permeability observed in GDLs could be recreated in a pore network by correlating pore and

throat sizes in directions of higher permeability. Bazylak et al. [35] demonstrated that saturation

can be directed by imposing spatial biasing to the throat sizes of a network. A similar study was

conducted by Hinebaugh et al. [38], where experimentally derived through-plane porosity

gradients are imposed onto an unstructured pore network. As can be seen in Figures 2.7 and 2.8,

Hinebaugh et al. [38] found that liquid water tends to accumulate in pockets of high porosity

when they exist between the inlet and outlet of the GDL.

Figure 2.7 Steady state water saturation patterns predicted for networks generated with prescribed porosity

distributions by Hinebaugh et al. [38]. Water (blue) invades the pore space (white) from the bottom face of this 2D pore network. (These figures are presented and described in detail in Chapter 3)

(a)

(b)

(c)

(d)

(e)

(f)

27

Figure 2.8 Predicted saturation levels (blue) for networks generated with prescribed porosity distributions (red) demonstrating the effect of porosity distribution on saturation profile in 2D pore networks by

Hinebaugh et al. [38]. (These figures are presented and described in detail in Chapter 3)

2.5.3 Capillary fingering

The characteristic breakthrough saturation pattern in capillary dominated systems is capillary

fingering, where the invading phase follows the path of least resistance, with no notion of

directionality. Such invasion has been characterized by Wilkinson and Willemsen [43], where

breakthrough saturation levels are strong functions of network size, connectivity and

dimensionality. In pore network models that include viscous forces, researchers [11,15,37] have

found that capillary fingering has breakthrough saturations that are low to moderate compared to

those observed when the liquid water’s viscous forces dominate. Employing these models, the

(a) (b)

(c) (d)

(e) (f)

28

researchers found that, simulating the possible operating conditions of a PEM fuel cell, viscous

forces had no effect on the breakthrough saturation patterns. However, two unrelated pore

network studies provided evidence that high saturations can occur in intermediately wet, or

mixed wet GDLs without viscous forces playing a role [16,39]. Chapuis et al. [39] demonstrated

that due to an increased likelihood of coalescence of neighboring invading fronts at lower contact

angles, a nearly fully saturated breakthrough condition could be reached even without

consideration of viscous forces. By assuming that there is a minimum capillary pressure required

for the invading cluster to break through the outlet, Sinha and Wang [16] also neglected viscous

forces but were able to obtain high saturated conditions in mixed wet pore networks.

2.5.4 Diffusion

Few pore network models of GDL materials have been applied to calculate the material’s relative

diffusivity after an invasion process. This could be due to the fact that most models apply inlet

conditions such as uniform pressure or uniform flux, where it is assumed that liquid water is

present at each throat at the catalyst layer GDL interface. However, with a uniform pressure

boundary condition, Gostick et al. [12] modeled diffusion at various stages of saturation and

calculated the limiting current density due to reactant transport across the GDL. They were able

to do this for two reasons. First, they did not consider the effect of the inlet reservoir on reactant

transport. Therefore, reactants could diffuse through inlet throats as long as they had not yet been

invaded by water. Secondly, they investigated a scenario where there was thin film of air in

liquid saturated pores and throats through which reactants could diffuse.

In subsequent work, Gostick et al. [13] again modeled diffusion through gas diffusion media, this

time incorporating an MPL and water generated through condensation near the flow field ribs.

With the calculated limiting current densities, the group concluded that gas diffusion media alone

could not account for the mass transport losses experienced in PEM fuel cells.

Wu et al. [18] also modeled effective diffusivities of oxygen in a saturated GDL after an invasion

process. A uniform pressure boundary condition was assumed; however, the group avoided

having the flooded catalyst layer by only sampling the central 50% of the network thickness. The

group calculated the effective diffusivities with respect to a large number of modeling

parameters, finding that diffusion rates after saturation are most affected by the network’s

29

through plane coordination number and through plane throat sizes. They determined that

diffusion through an unsaturated network is also highly influenced by these two modeling

parameters.

2.6 Conclusion

Within less than a decade, pore network modeling has gained momentum as a promising method

of studying the liquid water saturation in the PEM fuel cell GDL as a function of key parameters,

such as capillary pressure, diffusion, and permeability. Several key challenges for this technique

still remain, such as how to accurately represent the GDL pore space in order to produce

predictive results on a stochastic scale, and how to accurately represent the dominating forces

that govern the multiphase transport at the microscale for the fibrous substrate and nanoscale for

the MPL.

30

3 Unstructured Pore Network Modeling with

Heterogeneous PEM Fuel Cell GDL Porosity Distributions

3.1 Abstract

This is the first investigation of liquid water saturation profile dependence on empirically

determined heterogeneous polymer electrolyte membrane cell (PEM) fuel cell gas diffusion layer

(GDL) porosity distributions. An unstructured, two-dimensional pore network model using

invasion percolation is presented. Random fiber placements are based on the heterogeneous

porosity distributions of six commercially available GDL materials recently obtained through X-

ray computed tomography visualizations. The pore space is characterized with a Voronoi

diagram, and simulations are performed with a single inlet liquid water cluster. Saturation

profiles are also computed for GDLs with uniform, sinusoidal, and square-wave porosity

distributions. It is shown that liquid water tends to accumulate in regions of high porosity due to

the associated lower capillary pressures. The results of this work suggest that GDLs tailored to

have smooth porosity distributions will have fewer pockets of high saturation levels within the

bulk of the material. Finally, a study on theoretical surface modifications demonstrates that low

porosity surface treatments at the catalyst layer | GDL interface result in greatly reduced overall

saturation levels of the material.

3.2 Introduction

Water is introduced into the cathode of the PEM fuel cell at the catalyst layer (CL) as both a

product of the electrochemical reaction and via electroosmotic drag through the polymer

electrolyte membrane. Water is also introduced at the flow field (FF) inlet from humidified

oxidant streams. In studies [46,47], saturated relative humidity levels have been predicted at the

GDL|CL boundary, indicating that liquid water streams within the cathode may originate near

the GDL|CL boundary under specific operating conditions.

Pore network models have been employed to describe the liquid water saturation patterns

generated from the invasion of hydrophobic, porous materials [10,11,13-16,34-36,39,48], where

31

heterogeneity is often provided by randomizing pore and throat radii on pore networks structured

upon a square or cubic lattice. Two phase flow for GDL materials has recently been modeled

within three-dimensional pore spaces found from either micro-computed tomography [49] or

stochastic geometry generation [50-52]. The modeling techniques employed were the Lattice-

Boltzmann method [25,53] and pore morphology modeling [25,49]. While pore space

heterogeneity is obtained intrinsically with these methods, the detailed, three dimensional images

are required for all simulations and transport calculations, which can result in high computational

costs. More recently, a topologically equivalent pore network model by Luo et al. [19] has been

developed for three-dimensional stochastic models of GDL materials, which applies the maximal

ball method [21] to reduce the pore space into an unstructured pore network. The work published

by Luo et al. [19] demonstrates the utility of a pore network for efficient invasion simulations in

GDL-like microstructures and for modeling single- and multi-phase flows.

Figure 3.1 A through-plane cross section of Toray TGP-H-060 obtained through micro-computed

tomography (SkyScan 1172, 2.44 μm/pixel) illustrating through-plane pore structure.

Recently, our group has characterized the through-plane dependence of porosity for various

commercial GDL materials [54]. Using micro-computed tomography, Fishman et al. [54]

measured heterogeneous through-plane porosity distributions for seven commercially available

GDL materials. Our measured distribution of Toray TGP-H-060 was similar to the single

porosity distribution published by Büchi et al [20]. A single through-plane slice of commercial

220 μm

32

GDL material (Toray TGP-H-060) obtained through micro-computed tomography is displayed in

Figure 3.1.

The concept of non-uniform GDL porosity has appeared in only a few PEM fuel cell models in

recent years [55-57]. However, these models exhibit non-uniform porosities due to the

obstruction of GDL pores with liquid water, rather than due to the heterogeneity of the GDL

itself. Gurau et al. [55] and Chu et al. [56] model the PEM fuel cell cathode with a porosity

gradient that increases from the catalyst layer to the flow channel, in order to simulate the effects

of water saturation. Roshandel et al. [57] build on this work with the addition of rib compression

effects on the porosity gradient. However, Roashandel et al. [57] assume that there is a uniform

GDL porosity distribution prior to compression and water saturation. Zhan et al. [58] employ a

one dimensional model to further investigate the difference between a GDL with a uniform

porosity and a gradient porosity, recommending a linear porosity gradient of 0.4x +0.4, where x

is the fractional GDL thickness. While the work presented by Zhan et al. [58] provides

interesting insight into new GDL designs, it is necessary to understand the effects of

heterogeneous porosity distributions that are already present in the GDL. Previous studies [55-

58] have all concluded that GDLs with high porosities achieve larger current densities by

facilitating improved reactant transport and product water removal; however, further

investigation is vital for understanding the effect that GDL heterogeneity has on liquid water

transport, which will in turn, affect PEM fuel cell performance.

In this work, an unstructured, two-dimensional pore network model is described and employed to

characterize the liquid water invasion of six GDL materials that exhibit heterogeneous porosity

distributions. Details of the micro-computed tomography visualizations employed to evaluate the

heterogeneity of these GDL materials are presented in [54]. A network size sensitivity analysis is

performed, and a comparison between porosity distributions and breakthrough saturation profiles

will provide insight into the passive water management qualities of several GDL morphologies.

Finally, a theoretical surface treatment is proposed as a strategy to reduce the breakthrough

saturation levels in GDL materials

33

3.3 Pore Network Model

Unstructured two-dimensional pore networks were generated for this work by randomly placing

circular disks, representing carbon fibers, into the network domain until a desired porosity was

achieved, where porosity was defined as the ratio of non-material area to total area. To place the

disk centers according to a specific distribution, each pixel (0.5µm/pixel) of the network domain

was given a probability of being randomly selected. Matching the approximate diameter of the

carbon fibers in typical gas diffusion layers [6], the randomly placed disks were each 7 μm in

diameter. During placement, disk overlap was not permitted by repeatedly shifting an

overlapping disk a random distance in the in-plane direction away from the original location until

overlap is avoided. Similar to the pore network model created by Chapuis et al. [39], pore space

was described with a Voronoi diagram, as shown in Figure 3.2, where circular pores are outlined.

Pores were centered at the nodes of the Voronoi diagram and connected to adjacent pores at the

bonds of the diagram. Pore radii were calculated as the distance from the pore center to any of

the three bordering disks. Throat radii were calculated as the distance between the adjacent disks.

For this and all similar diagrams in this paper, the GDL|CL interface is oriented along the left

hand side, and the GDL|FF interface is oriented along the right hand side of the figure.

The application of Voronoi diagrams in this paper was different than that of Thompson [59],

who established a method of generating three-dimensional pore network models for

stochastically generated fibrous models. In Thompson’s work, fibrous materials were represented

as the bonds of Voronoi diagrams formed around pre-defined pore locations, whereas in this

work, it was the material location that was pre-defined, and the Voronoi diagram described the

pore and throat locations as stated above.

To simulate the slow evolution of liquid water clusters within the PEM fuel cell GDL, an

invasion percolation algorithm was employed. The liquid water inlet boundary condition was

defined by a single water cluster, which was in contact with each throat at the GDL|CL interface.

Invasion percolation, as described by Wilkinson and Willemsen [43], assumes that an advancing

fluid interface follows the path of least resistance, such that the invading phase maintains the

lowest possible pressure at each simulation step. When the invading phase is non-wetting, such

as water in a hydrophobically-treated GDL, and the viscous forces within the fluid clusters can

be assumed to be negligible, the path of least resistance during invasion is determined by the

34

throat size with the lowest barrier capillary pressure [43][60]. Throat capillary pressure, 𝑃𝑐 ,

defined as the pressure difference between the invading and defending fluids, can be

approximated with a form of the Young-Laplace equation:

𝑃𝑐 = −2 𝜎 cos(𝜃)

𝑟, (3.1)

where 𝜎 is the interfacial surface tension, 𝜃 is the contact angle of the interface, and is the radius

of the throat. Surface tension and contact angle were assumed to be uniform throughout the

network. Water was therefore assumed to invade the largest available throat at each simulation

step, and no pressure calculations were required.

Figure 3.2 A 2D (600 μm x 200 μm) unstructured pore space generated by the random placement of 7μm wide fibers (solid black disks) until the desired porosity of 0.80 is reached. As seen in the magnified image (b),

circular pores (hollow circles) are centered at the nodes of the overlaid Voronoi diagram, connected to adjacent pores by throats which are represented by the bonds of the Voronoi diagram. Each polygon of the

Voronoi diagram is created by lines equidistant from disks.

With respect to breakthrough saturation levels, pore network models of GDL invasion

considering viscous forces have thus far demonstrated no noticeable effects of such consideration

at water generation rates associated with PEM fuel cell operation [11,15,37]. Viscous forces

within the fluid clusters are therefore not considered in this study.

200μm

600μ

m

(b)(a)

35

The invasion percolation algorithm employed in this investigation includes the following

assumptions:

1. The system was isothermal.

2. The gas phase could not become completely trapped by the liquid and solid phases.

3. Viscous forces within the liquid water clusters at the GDL|CL interface and within the

GDL were negligible.

4. The GDL was uniformly hydrophobic; therefore the capillary pressures associated with

pore entry were only inversely proportional to throat width.

5. A steady state condition was reached once the cluster invades a throat at the GDL|FF

interface, an event labelled breakthrough. At breakthrough, the water cluster ceased to

grow within the GDL due to the low capillary pressures associated with a water droplet

either in the channel or in contact with a relatively hydrophilic rib.

6. The GDL was initially dry. Liquid water at the gas channel was not considered.

While uneven distributions of PTFE within GDL materials have been reported [6], it is unclear if

the hydrophobicity of the GDL is heterogeneous as a result. A thin film of PTFE on fiber

surfaces combined with large PTFE agglomerates throughout the material could produce this

effect while maintaining a uniform contact angle.

The pore network model was developed in MATLAB. Simulations were run on a single

workstation with 8 GB of RAM and dual 2.33 GHz CPUs. Individual simulations required

between 5 and 30 s to reach breakthrough, depending on the network size. A total of 1500 such

simulations were run for this study.

As was described by Fishman et al. [54], three dimensional X-ray tomographic reconstructions

were used to characterize the porosity distributions of various commercially available GDL

materials. The bulk porosities and thicknesses of these materials are summarized in Table 1. A

porosity distribution was defined as the porosity of each thin, in-plane slice of the material with

respect to its through-plane position. As described in [54], each slice represented a 5000 μm ×

5000 μm × 2.44 μm slice of the material oriented parallel to the plane of the material. It is

important to note that the porosities of various materials are strong functions of the through-

plane position. Also, the six materials chosen for use in this study were untreated and

uncompressed.

36

To apply the experimentally found porosity distributions to the disk distributions of two-

dimensional pore networks, porosity levels were first linearly interpolated between data points to

attain a resolution of 0.5 μm. Then, to provide the proper weight to the probability distribution

for disk placement, the interpolated porosity distribution, 𝜀(𝑥), was converted into a material

fraction distribution, 𝑓(𝑥), as follows:

𝑓(𝑥) = 1 − 𝜀(𝑥), 3.1

where x is the through-plane distance through the material. Using Toray TGP-H-060 as an

example, Figure 3.3 presents the porosity distribution, material fraction distribution, and the

average resultant porosity distribution from 100 generated networks with a thickness of 220 μm

and length of 1100 μm.

Figure 3.3 Porosity and material fraction data, f, for a Toray TGP-H-060 GDL. Blue diamonds represent the

measured porosity distribution obtained from micro-computed tomography visualizations [54] . The black

line represents the calculated material fraction from interpolated porosity data. The red line represents the resultant average porosity of 100 networks generated with the calculated material fraction.

3.4 Results and Discussion

3.4.1 Network size sensitivity

To compare GDL materials of a range of thicknesses, we began by determining the pore network

model’s sensitivity to network aspect ratio. In this study, dimensions were chosen such that the

network length was greater than the network thickness. The aspect ratio was increased from 2 to

11 by varying network length, while a constant network thickness (200 μm) and f(x) for Toray

TGP-H-060 were employed. For each aspect ratio, 100 random network definitions were

generated for invasion percolation simulations. The breakthrough saturation of each simulation

37

was calculated as the ratio of water filled pore space to total pore space. The mean breakthrough

saturation value for each ratio was displayed in Figure 3.4a. Saturation levels were most sensitive

to low aspect ratios (below 5). To determine whether saturation levels were more affected by the

aspect ratio or overall network size, a similar sensitivity study was performed with aspect ratios

of 3, 5, and 7 with network thicknesses 120 μm, 220 μm, and 320 μm. As seen in Figure 3.4b,

the network size had little influence on breakthrough saturation levels as long as a single aspect

ratio was maintained. Therefore, an aspect ratio of 5 was chosen and employed for all subsequent

simulations discussed in this paper.

Figure 3.4 Aspect ratio and network size sensitivity study with invasion percolation simulations run on stochastic networks created with Toray TGP-H-060 porosity data. a) Mean saturation levels generated using a constant network thickness of 200 μm. b) Comparison of three network thicknesses. One standard deviation

is displayed with each data point.

3.4.2 Measured heterogeneous porosity distributions

Invasion percolation simulations were run until the breakthrough condition was reached for 100

random networks for each material. Pore networks associated with different GDL materials were

distinct in that they are generated with specific input thicknesses and porosity distributions, while

other properties such as fiber size and network aspect ratios were held constant for the entire

study. Thickness and bulk porosity data were obtained from X-ray tomography visualizations

[54] (Table 3.1). Example breakthrough saturation patterns are displayed in Figure 3.5. The

resulting average saturation profiles are displayed in Figure 3.6, and the mean saturation levels

are listed in Table 3.1. Saturation profiles were defined as the ratio of liquid filled pore space to

all pore space for each vertical slice (0.5 μm thick) across the network thickness. It should be

(a) (b)

38

noted that the pore space used in saturation calculations did not include the void space contained

uniquely in throats and around the perimeter of the domain.

Furthermore, because GDL samples were uncompressed when the X-ray tomography data was

attained, local porosity values and pore and throat sizes of the resultant pore networks near the

GDL|CL and GDL|FF interfaces were expected to be larger than would otherwise be expected in

the compressed environment of a PEM fuel cell. Due to the increased throat sizes at the GDL|CL

interface, these throats were nearly always invaded by the end of the simulation. As can be seen

from Figure 3.5, this fact led to a prediction of fully saturated conditions at the GDL|CL

interface.

To account for the lack of symmetry of porosity distributions, a second set of 100 random

simulations were run for each distribution, beginning the invasion from the opposite face. As

seen in Table 1, the mean saturation levels of a specific material varied by as much as 0.09,

depending on the orientation. Saturation profiles presented in Figure 3.6 were the results of

orientations with the lowest corresponding saturation level.

The saturation profiles displayed in Figure 3.6 were highly correlated with the applied porosity

distributions. This was most apparent with the simulation results of Toray TGP-H materials 060,

090, and 120, where the porosity distributions contained multiple local minimums. The local

porosity distribution minimums correlated well with the local saturation profile minimums.

Similarly, it can be seen in Figures 3.5 and 3.6 that pairs of dense regions of disks (local

minimums in porosity) could create “water traps” causing spikes in the saturation profile. As

shown in Table 3.1, breakthrough saturation levels varied only from 0.29 to 0.37 for one

orientation of each commercial GDL material; however, the breakthrough saturation levels of the

Toray TGP-H-060 simulations exhibited the widest range of saturation, with a standard deviation

of 0.09.

Toray TGP-H GDL materials are classified as “papers”, and the thicknesses of these papers were

generated by bonding thin layers together [6]. The results displayed in Figures 3.5 and 3.6

indicate that this manufacturing process had a large impact on the breakthrough saturation

profiles, as the layering process used to create thicker Toray papers led to highly heterogeneous

porosity distributions, with well-defined peaks and valleys [54]. The SGL Sigracet 10AA, and

Freudenberg H2315 materials are both classified as “felts” where carbon fibers were hydro-

39

entangled during the manufacturing process [6]. In contrast to Toray paper GDLs, felt porosity

distributions did not result in saturation profiles with the same degree of heterogeneity as seen

for paper.

Figure 3.5 Example saturation patterns (distinct realizations) using tomography derived porosity distributions. The following materials are represented: a) Toray TGP-H-030, b) Toray TGP-H-060, c) Toray

TGP-H-090, d) Toray TGP-H-120, e) SGL Sigracet 10AA, and f) Freudenberg H2315.

(a) (b) (c) (d) (e) (f)

40

Figure 3.6 The heterogeneous porosity and breakthrough saturation profiles associated with six commercially

available GDL materials. Interpolated porosity values are shown in red. The average saturation level for each pixel column is shown in blue. The following materials are represented: a) Toray TGP-H-030, b) Toray TGP-

H-060, c) Toray TGP-H-090, d) Toray TGP-H-120, e) SGL Sigracet 10AA, and f) Freudenberg H2315.

(a) (b)

(c) (d)

(e) (f)

41

Table 3.1 Summary of the GDL material properties obtained by tomography and breakthrough saturation levels obtained through pore network simulations.

GDL Type Thickness a

(μm) Bulk

Porositya

Orientation 1 Breakthrough

Saturation Levelb

Orientation 2 Breakthrough

Saturation Levelb

Surface Treatment on Orientation 1 Saturation Levelb

Toray TGP-H-030 117 0.829 0.37 ± 0.04 0.45 ± 0.06 0.15 ± 0.04

Toray TGP-H-060 220 0.821 0.31 ± 0.08 0.35± 0.09 0.13 ± 0.05

Toray TGP-H-090 298 0.826 0.29 ± 0.05 0.31 ± 0.07 0.11 ± 0.04

Toray TGP-H-120 359 0.787 0.36 ± 0.07 0.38 ± 0.06 0.15 ± 0.06

SGL Sigracet 10AA 344 0.847 0.33 ± 0.04 0.39 ± 0.05 0.08 ± 0.02

Freudenberg H2315 290 0.802 0.34 ± 0.04 0.41 ± 0.05 0.10 ± 0.03

Uniform 200 0.800 0.27 ± 0.08 - -

Sine Wave 200 0.800 0.27 ± 0.11 - -

Square Wave 200 0.800 0.30 ± 0.11 - -

a Calculated from micro-computed tomography visualizations [54]. b The average result and standard deviation of 100 simulations performed on random networks.

Pore network models of PEM fuel cell GDL invasion generally produced saturation profiles

containing one local maximum (at the CL) and one local minimum (at the FF) [11,12,15,34].

When the inlet condition was modified to allow fewer entry throats at the CL, the single local

maximum was seen to shift slightly into the bulk [10,14,36]. Peaks in saturation within the GDL

bulk were predicted by a pore network model that included bulk generation of liquid water due to

condensation [13,37]. Bulk saturation extrema were also witnessed when a wettability gradient is

imposed on a mixed-wettability pore network model [16]. The model presented in our paper

provided an additional explanation to the peaks in saturation within the bulk of the GDL to those

which have been reported in [29,61,62], where water tends to accumulate between areas of low

porosity.

3.4.3 Uniform, sine-, and square-wave porosity distributions

To verify the impact that heterogeneous porosity distributions have on saturation profiles,

invasion simulations with networks generated from theoretical porosity distributions were also

performed. Three distributions were generated to have an average porosity value of 0.80:

uniform porosity, sine-wave porosity, and square-wave porosity. Both the sine- and square-wave

porosity distributions were comprised of 3 periods, which oscillate between porosity values of

0.75 to 0.85, as shown in Figure 3.7 (red). Each porosity distribution was applied to 100

stochastic networks of thickness 200 μm and aspect ratio 5. The resultant average breakthrough

saturation profiles are displayed in Figure 3.7 (blue), and mean saturation levels are summarized

42

in Table 1. As shown in Figure 3.7, and in agreement with Figure 3.6, there was a strong

correlation between the heterogeneous porosity distributions and resultant average saturation

profiles. In fact, the correlation is even more apparent in Figure 3.7 than in Figure 3.6. Peaks in

saturation profiles generated from sine- and square-wave porosity inputs were directly beneath

peaks in the original porosity distributions. Also, the flat top of the square-wave porosity input is

carried over to the resultant saturation profile.

In contrast to the results generated from measured material porosities, where the first 10-20% of

the network adjacent to the CL was fully saturated with liquid water, the breakthrough saturation

profiles for uniform, sine-wave, and square-wave porosity each had sharp, negative initial slopes

of saturation near the CL. This difference can be explained by the relatively high porosities at the

CL|GDL interfaces from measured materials (Figure 3.6), which led to large throats being

flooded at the inlet. This effect was diminished by the average or below average porosity levels

near the inlet in networks generated from the three theoretical porosity distributions discussed

here (uniform, sine-wave, and square-wave). The results of these simulations provide insight into

the influence of near-surface porosities on near-surface and overall material saturation levels.

43

Figure 3.7 The porosity and breakthrough saturation curves associated with three theoretical GDL materials. Theoretical porosity values are shown in red. The average saturation level for each pixel column (vertical

slice) is shown in blue. Network thicknesses are set to 200 μm, and an aspect ratio of 5 is maintained.

3.4.4 Theoretical surface treatments

To further investigate the influence of near-surface porosities on breakthrough saturation,

theoretical surface treatments were explored. Here, simulations were performed on 100

additional random networks for each commercial GDL material studied, where the originally

obtained porosity distributions were adjusted to create a linear transition from a porosity of 0.60

(a)

(b)

(c)

44

at the GDL|CL interface to the first local minima of the original porosity distribution. The choice

of this surface modification was intended to represent the application of a lower porosity material

to the GDL, where the resultant composite would transition from the low porosity material into

purely GDL material. This modification was inspired by current micro-porous layer (MPL)

treatments. Ostadi et al. [63] reported a local MPL porosity of 0.40 in a region without cracks or

large defects using focused ion beam/scanning electron microscopy. To account for the presence

of cracks and defects, a porosity value of 0.60 was chosen for this study. The modified porosity

distributions and resultant breakthrough saturation profiles are shown in Figure 3.8. The mean

saturation levels are summarized in Table 1.

Figure 3.8 provides a direct comparison between the saturation profiles generated from porosity

distributions with and without the surface treatment. This figure indicates the highly beneficial

impact that such a treatment would have to GDL materials in terms of liquid water management.

The saturation levels at the CL|GDL interface were significantly reduced with the addition of the

surface treatment. This was attributed to the presence of much smaller throats near the inlet

region, which are associated with significantly higher capillary pressures than the bulk of the

material. The positive slope at the inlet side of the porosity distribution created a situation where

associated average capillary pressures decreased as the liquid|gas interface advances into the

bulk of the network. Although this treatment has lowered the average saturation levels by 58-

76% (Table 3.1), saturation profiles remained correlated to the porosity distributions used to

generate their pore networks, where visible local maxima in porosity distributions of Toray TGP-

H 060, 090, and 120 were still reflected in the resultant saturation profiles.

45

Figure 3.8 The porosity and breakthrough saturation curves associated with six commercially available GDL

materials with an inlet-side surface treatment. Interpolated porosity values are shown in red. The average saturation level for each pixel column is shown in blue. Thin red and blue lines represent the original porosity

and saturation profiles respectively. The following materials are represented: a) Toray TGP-H-030, b) Toray TGP-H-060, c) Toray TGP-H-090, d) Toray TGP-H-120, e) SGL Sigracet 10AA, and f) Freudenberg H2315.

(a) (b)

(c) (d)

(e) (f)

46

3.5 Conclusions

This was the first investigation of liquid water saturation profile dependence on empirically

determined heterogeneous GDL porosity distributions. A two-dimensional unstructured pore

network model for simulating the liquid water invasion percolation in a PEM fuel cell GDL was

presented. With this model, we demonstrated a powerful method of applying porosity

distributions to the definition of pore networks. By randomly placing circular fibers (disks) in a

defined two-dimensional area, with disk placement probabilities weighted by a given porosity

distribution, X-ray computed tomography data become an input to the definition of each

generated pore network.

Aspect ratio and network size sensitivity studies were performed, and an aspect ratio of 5 was

employed for all investigations. Based on simulation results, it was found that local saturation

levels have a high correlation to the local porosity levels in the through-plane direction. The

peaks and valleys present in the porosity distributions of thick carbon fiber papers created highly

saturated regions in the bulk of the GDL, with peaks in porosity distributions corresponding to

highly saturated regions. It is recommended that GDLs are created to have porosity distributions

with few local minimums.

A comparison between the shape of saturation profiles generated from uniform, sine-wave, and

square-wave porosity distributions revealed that, not only did the amplitude and frequency of

through-plane porosity fluctuations impact saturation levels, but also the shape of the

fluctuations was reflected in the shape of the saturation profile.

Finally, an inlet-side surface treatment was theoretically applied to the experimentally derived

porosity distributions of GDL materials, where a lower porosity was applied to the inlet and was

linearly transitioned to the first local minimum in porosity. Simulation results suggested that this

treatment can reduce saturation due to percolation by 58-76%, and drastically decrease saturation

levels near the catalyst layer.

It should be noted that based on the boundary condition of a single liquid water cluster at the

CL|GDL interface, the assumption that viscous forces were negligible, and the assumption that

liquid water transport would reach steady state once breakthrough is achieved, only one

breakthrough point would ever be expected in an operational fuel cell cathode. However, in-situ

47

experiments have shown this not to be the case [8]; therefore, further investigations are required

to determine the influence of viscous forces and water cluster connectivity within the CL and

GDL on liquid water transport in the PEM fuel cell.

48

4 Stochastic Modeling of PEM Fuel Cell GDLs II. Physical Characterization

4.1 Abstract

Stochastic modeling of GDL structures requires a detailed characterization of the constituent

elements of the material. In this work, a variety of imaging methods, including optical

microscopy, microscale computed tomography, and scanning electron microscopy, were used to

characterize seven commercially available gas diffusion layers (GDLs). The result is a catalogue

of the following geometrical characteristics: fiber diameter, fiber pitch and co-alignment, areal

weight and volume, and microporous layer (MPL) crack size and frequency. This catalogue,

when combined with previous GDL characterizations is expected to provide enough information

to create representative, predictive, stochastic models of the GDL.

4.2 Introduction

GDL materials have been extensively characterized using standard porous material analysis

techniques to determine bulk average properties such as permeability [64-66], effective

diffusivity [67,68], and the relationship between capillary pressure and saturation by a non-

wetting fluid [69-71]; however, there are many decisions that go into GDL manufacturing, some

of which have already been shown to impact these bulk properties [23,24,67,70,72]. These

decisions include GDL thickness, carbon fiber diameter, binder quantity, PTFE quantity, PTFE

distribution, MPL quantity, and MPL composition [6]. With so many variables involved, there is

a need for sophisticated, predictive models of transport within the GDL, able to capture the

effects of each of these decisions. With such a tool, GDL types can be compared theoretically,

and idealized materials can be envisioned.

One modeling method available involves the generation of digital, stochastic representations of

the microscopic GDL geometry, on which transport phenomena can be directly modeled with

various computational fluid dynamic modeling techniques [23,27,28,53,73] or indirectly

modeled with pore network modeling techniques [19]. Such stochastic representations of the

GDL microstructure are labelled “stochastic models”. Stochastic models require, as input

49

parameters, characteristics of the common repeating elements (fibers) and additive materials

(binder, PTFE, and MPL) used in GDL manufacturing. Representative models of currently

available materials must make reasonable approximations of these values. Mathais et al. [6] gave

a thorough description of GDL manufacturing techniques that provides useful insight into how

the GDL constituents are arranged. Additionally, Fishman and coworkers provided a catalog of

characteristic through-plane distributions of material porosity [54,74,75], while other researchers

[6,73,76] studied the through-plane distribution of PTFE. This body of work is extremely

important for building pore-scale models that aim to resolve the microscale features of the GDL;

however, key characteristics that are necessary to accurately resolve the GDL are missing,

namely: characteristic distributions of fiber diameter and orientation, volume fraction estimates

of the constituent elements, and the water transport related characteristics of the microporous

layer (MPL), namely its crack distributions.

Fiber pitch is defined as the angle the fiber makes with the plane of the material. Carbon fibers

have been observed to be in orientations largely coplanar to the GDL [54]. Therefore, many

stochastic models apply zero pitch to individual fibers [24,26,77,78]. Other models, in order to

fine-tune material anisotropy, have applied distributions of small pitch values [22,25]. However,

due to recent advances in computed tomography resolutions, the 3D orientation of fibers can

now be measured directly and used as an input to stochastic models.

While manufactures typically only state the PTFE weight (wt) % of their GDLs, estimates of the

quantities of the other additive materials can be made through a comparison of similar GDLs

with respect to their areal weight, defined as the area-specific mass of the GDL. While this

specification is often available from the GDL manufacturer, conducting the measurement of a

batch-specific value is a relatively simple procedure. These measurements can also provide an

understanding of the batch-to-batch variability of the manufacturing process.

A material property analogous to areal weight is areal volume, defined as the solid volume per

unit area. A known areal volume of a material regulates the proportion of a stochastic modeling

domain that must be solid. Furthermore, a comparison of the areal volumes of similar materials

can indicate the volume fractions of constituent elements of the GDL, which allows stochastic

models to more properly represent these elements.

50

Using lattice Boltzmann modeling, Nabovati and coworkers have demonstrated that both fiber

diameter and the assumed solid fractions of binder and PTFE, have strong positive correlations

with calculated permeability when porosity was held constant [23,24]. Interestingly, they found

that additive material fraction also has a positive correlation with tortuosity [24]. GDL fiber

diameters have been reported to fall within the range of 7 to 10 µm [6,79,80]; however, a

statistical analysis of fiber diameters has not been presented in the literature. As will be described

next, fiber diameter, binder and PTFE fractions, and fiber orientation can all be expected to have

similar effects on the pore space of the GDL and therefore should all be characterized.

4.2.1 Fiber count in stochastic models

Stochastic models, as defined above, are generated by the repeated random placement of solid

objects into an originally empty domain. In the case of GDLs, these repeating objects are most

often cylindrical fibers. Each additional fiber that is placed can cut through the existing pore

space, further dividing it into smaller pores. Dividing the pore space by a number of independent

fibers is useful for understanding the commonality between fiber diameter, fiber co-alignment,

and additive materials (binder and PTFE). After the final material porosity and fiber length are

chosen, the number of independent fibers which divide the pore space is fully defined.

Figure 4.1 contains four simplified representations of GDL materials made from 2D stochastic

modeling. Each material is of equal porosity, where three comparisons can be made. In

comparison I, we see that the smaller 7 µm-diameter fibers divide the pore space into smaller

“pores” than are created from the larger 10 µm-diameter fibers. In comparison II, we see that if

fibers are bundled together, each bundle acts as a single larger fiber and creates fewer, larger

pores than are created if the fibers are independent of each other. In comparison III, 50% of the

fibers are replaced with modeled binder, which can be safely assumed to reside in the tight

spaces between fibers [22,24,77]. This binder leaves the large pore spaces untouched, and again

results in fewer, larger pores than seen in the original material. The common theme is that the

fewer independent fibers there are in the substrate, the fewer pores can be expected, and the more

open the material should be.

51

Figure 4.1 2D stochastic models demonstrating the similar pore-space effects caused by the modeling assumptions: I fiber diameter, II fiber bundling, III and binder fraction. Pore space is represented as white.

Fibers, either 7 µm or 10 µm, are represented as black. Binder is represented as grey. Each 100 µm × 100 µm model is created to be 65% porous, with randomly distributed, non-overlapping fibers.

The effect of independent fibers on the pore size distribution is most clearly demonstrated with

further consideration of comparison I. In Figure 4.2, we see a section of a 3D stochastically

modeled GDL with a porosity of 75%. However, without a scale bar, there is no indication that

the structure displayed in Figure 4.2 is made with smaller or larger fibers. If this material was

made up of 7 µm-diameter fibers, the domain would represent a (100 µm)3 cube. On the other

hand, if the fiber diameters were set to 10 µm, the domain would represent a (142 µm)3 cube,

which is nearly 3 times the volume of a (100 µm)3 cube. While the domain volumes depend on

fiber size, the number of resulting pores would be unaffected. In fact, a material made with larger

fibers would be, by nature, more heterogeneous than a similar porosity material made with

smaller fibers, since a larger volume of the larger fiber material is necessary to obtain a

geometrically similar pore size distribution to the smaller fiber material. It is the authors’

hypothesis that pore size distribution and heterogeneity are affected similarly by fiber bundling

and presence of additives (binder and PTFE).

52

Figure 4.2 3D stochastic model of the PEM fuel cell GDL. There is no scale for reference as this model could

have been made with any fiber diameter.

In this discussion, manufacturing parameters such as fiber length, ply thickness in paper-made

materials, or water-jet separation in hydro-entangled felts are not accounted for. However, a

simplified geometrical representation of the GDL structure is a necessary tool for investigating

the fundamental effects of fiber diameter, fiber orientation, and additive materials.

4.2.2 MPL modeling

The MPL provides two theoretical services to the GDL [6,81]. First, it is hydrophobically

treated, making the micropores particularly difficult to become flooded by local accumulations

of liquid water. Second, when compared to the fibrous substrate, the relatively smooth surface of

the MPL can more evenly distribute the applied assembly forces to the catalyst coated

membrane, reducing local contact resistances while protecting the membrane from punctures.

However, researchers have proposed that the transport characteristics of the MPL differ

significantly from that of the fibrous substrate [82]. Therefore, a stochastic model of the GDL

would be incomplete without including the salient features of the MPL.

The MPL is composed of sub-micron carbon black particles held together by PTFE, yielding

reported porosities between 0.35 and 0.62 [83-85]. While nanoscale stochastic models of the

MPL have been created [84], the difference in length-scales between the MPL and the substrate

make it difficult to explicitly model both materials concurrently, while including a representative

volume of the substrate. However, stochastic modeling could follow the example of Gostick et

al. [13], who employed a pore network representation of the GDL. In that work, the pores of the

53

substrate were explicitly modeled, while bulk-averaged transport properties were applied to

regions designated as the MPL. An analogous stochastic model would explicitly describe

substrate geometrical features, but only describe the larger geometrical features of the MPL.

Each voxel designated as MPL would then represent a porous material with effective transport

properties.

The pore sizes of the MPL are typically described with a bimodal distribution [75] with micron

to sub-micron pores homogeneously distributed throughout the bulk of the material, while cracks

or pockets of gas trapped in the manufacturing process can also be present [75]. The cracks in the

MPL have been postulated as relatively low capillary pressure conduits for excess liquid water to

pass through the MPL from the catalyst layer to the porous substrate [86], and evidence for this

has been shown with in-situ X-ray imaging [87,88]. It is therefore of interest to characterize

MPL treatments with respect to the size and frequency of these cracks for more accurate

stochastic models of the MPL.

In this paper, we address a set of gaps in our understanding of the GDL which each impact

critical input parameters of 3D stochastic models [19,23,24,26,27,53,73]. An assortment of

commercially available GDL materials is studied, and detailed characterizations are provided of

the following properties: fiber diameter, fiber pitch, fiber co-alignment, areal weight, areal

volume, MPL crack frequency, and MPL crack diameter. This information, when combined with

previously reported properties, can sufficiently define the GDL for the purposes of stochastic

modeling.

4.3 Methods

4.3.1 Fiber diameter

A technique employed to perform fiber diameter measurements was developed for this study.

Measurements were obtained from the intensity profiles across isolated silhouettes of individual

fibers. To accomplish this, GDLs were torn to create frayed edges. Digital images of silhouetted

fibers were obtained from a back-lit, compound microscope with a 2 megapixel monochrome

charge coupled device (CCD) camera (PCO 1600). The back lighting was adjusted so that the

background intensity reached 10x the intensity measured at the center of a fiber silhouette in

54

focus. An example field of view is shown in Figure 4.3a, and the mean greyscale profile of a

single fiber is shown in Figure 4.3b. The fiber edge location was defined as the point where the

greyscale profile reached 50% of the background intensity.

The above technique was developed using a 559 µm-diameter graphite cylinder as a reference.

The cylinder was measured at multiple positions with a micrometer and then imaged at a

magnification scaled to match the pixel-to-cylinder diameter size ratio available for carbon fiber

imaging. The technique produced precise diameter measurements, with a confidence interval of

3%. On the length scale of a carbon fiber, this represents a maximum error of 0.3 µm per

measurement.

Figure 4.3 Edge of hand-torn GDL (a) with region of interest highlighted. Intensity profile (b) of region of

interest in direction perpendicular to fiber. The dotted line displays the value at 50% of the average background intensity, defining the edge of the fiber.

55

Figure 4.4 Visualized nano-CT dataset of Toray TGP-H 090 0 wt % PTFE. (a) Through-plane cross sectional

slice. (b) Planar cross-sectional slice. (c) 3D view with slice positions highlighted. The blue reference cube has an edge length of 50 µm.

4.3.2 Fiber pitch

A nanoscale computed tomography (nano-CT) dataset (courtesy of Skyscan 2011, Belgium) of

Toray TGP-H 090 with a voxel-resolution of 390 nm was analyzed to provide a first look at fiber

orientation statistics. Figure 4.4 displays this nano-CT data-set, with through-plane and in-plane

cross-sections and a 3D representation.

56

Figure 4.5 Through-plane cross sectional nano-CT slices of Toray TGP-H 090 0 wt % PTFE with arrows indicating highlighted fiber positions. Slice (a) is separated from (b) by 50 µm in the direction normal to the

slices.

To measure fiber pitch, the nano-CT domain shown in Figure 4 was first segmented into solid

(white) and void (black). Then, 30 easily identifiable fibers were traced for 50-100 µm of their

lengths. Their pitch, θ, was calculated as:

𝜃 = sin−1(|∆𝑧| 𝐿)⁄ , 4.1

where |∆𝑧| is the absolute difference in the fiber center position, with respect to the direction

normal to the plane of the material, and 𝐿 is the traced distance.

In Figure 4.5, this tracing is demonstrated on four fibers. Figure 4.5a shows the segmented, cross

sectional view of the GDL. Four identified fibers are highlighted in four unique colors. Figure

4.5b shows a cross sectional slice at a position of 50 µm from the first slice. Colored arrows

highlight original and final fiber positions. The three dimensional vector was recorded, and the

fiber pitch was calculated.

57

4.3.3 Fiber co-alignment

The nano-CT data set can also provide insight on the frequency of fiber co-alignment. To obtain

an estimate of this bundling phenomenon, the nano-CT data set was visualized through the

observation of 35 µm-thick, planar sheets. Then, as shown in Figure 4.6, the aligned fibers were

highlighted in red, while the individual fibers were highlighted in light blue.

Figure 4.6 Imaged 35 µm thick sheets of nano-CT dataset of Toray TGP-H 090 0 wt % PTFE with clearly

bundled fibers painted in red, and clearly individual fibers highlighted in light blue.

4.3.4 Additive materials

Measuring the mass of a GDL sample with a known planar area produces an areal weight

measurement. For the measurements provided in this paper, material images were compared to a

calibration standard to attain a precise area measurement, and mass was measured with an

analytical balance. The image resolution combined with the precision of the balance yielded

areal weight measurements with a maximum error of 1 g m-2.

To calculate areal volume from areal weight, knowledge of the material makeup of the GDL is

required, including its constituent elements, relative proportions, and densities. This relationship

is as follows:

𝐴𝑉 = 𝐴𝑊 ∑𝑊𝛼

𝜌𝛼𝛼 , 4.2

where 𝐴𝑉 is the areal volume, 𝐴𝑊 is the measured areal weight, and 𝑊𝛼 and 𝜌𝛼 are the

approximated weight fraction and density of component 𝛼, respectively. Graphitized carbon

fibers are expected to have densities ranging from 1.9-2.0 g cm-3 [6]. Binder material can be

expected to consist of amorphous carbon with a density of approximately 1.65 g cm-3 [6].

Unfortunately, the volume fractions of fibers and binder were not supplied by manufacturers, but

58

from qualitative image analysis this fraction appeared to be consistently less than 0.5. For the

purposes of this study, this volume fraction was assumed to be 0.5, yielding an average density

of 1.8 g/cm3 for the solid matrix of the untreated carbon fiber substrates. The carbon black in the

MPL was assumed to have a density of 1.8 g cm-3 [89,90], and the PTFE within the MPL and

coating the substrate, was assumed to have a density of 2.25 g cm-3 [91]. Because manufactures

have not published the detailed composition of the MPL, the weight fraction of the MPL was

found as:

𝑊𝑀𝑃𝐿 =𝐴𝑊,𝐺𝐷𝐿1−𝐴𝑊,𝐺𝐷𝐿2

𝐴𝑊,𝐺𝐷𝐿1+𝐴𝑊,𝐺𝐷𝐿2 , 4.3

where 𝐴𝑊,𝐺𝐷𝐿1 is the areal weight of a GDL with an MPL present, and 𝐴𝑊,𝐺𝐷𝐿2 is the areal

weight of the same GDL type without an MPL. Additionally, the MPL was assumed to be 20 wt.

% PTFE [92], leading to a combined solid density of 1.88 g cm-3.

4.3.5 MPL cracks

For each GDL type containing an MPL, SEM micrographs were acquired with a pixel resolution

of 2 µm and a field of view large enough to contain at least 4 mm2 of MPL surface area. Figure

4.7 displays two example micrographs with crack locations annotated. Crack density is defined

as the number of cracks observed, divided by the visualized area. Crack diameter is defined as

the diameter of the largest circle that could fit within the crack. Crack diameters were measured

with an open source imaging software (distance tool in FIJI1). Visible cracks were counted and

their diameters were measured. Two such micrographs were characterized for each material type,

yielding a total area of 8 mm2 per material type. It should be noted that the pixel resolution

yielded an error of up to 4 µm per diameter measurement. This resolution was chosen to

facilitate a large field of view, as the accuracy of crack density measurements was deemed more

valuable for stochastic models than that of the crack diameters.

1 http://fiji.sc/

59

Figure 4.7 Scanning electron micrographs of the MPL surfaces of (a) SGL Sigracet 25BC, and (b) Freudenberg H2315 I3 C1, with annotated cracks.


4.4.1 Fiber diameter

The diameters of 30 fibers for each of three substrate types were measured. Histograms of the

individual measurements are displayed in Figure 4.8. The distributions of fiber diameter are seen

to be tight around the mean, with standard deviation values of 0.8 µm, 0.6 µm, and 0.9 µm for

the materials Toray TGP-H 090, SGL Sigracet 25AA, and Freudenberg H2315, respectively. The

mean fiber diameter values appear on Table 1.

60

Figure 4.8 Fiber diameter distributions for (a) Toray TGP-H 090 0 wt % PTFE, (b) SGL Sigracet 25AA, (c) Freudenberg H2315.

When creating stochastic models of GDL materials, voxel-sizes are often approximately (2 µm)3

[24-26] and rarely smaller than (1 µm)3 due to the computational challenges of manipulating

larger images. Therefore, it may be impossible to recreate the fine details of such tight

distributions of fiber diameters, as are shown in Figure 8. In these cases, uniform fibers of the

mean diameters reported in Table 1 may be employed.

4.4.2 Fiber pitch

Figure 9 shows the absolute pitch distribution of the 30 untreated Toray TGP-H 090 fibers

measured. The mean absolute pitch was 2.44° and individual values never exceeded 7°.

Figure 4.9 Fiber pitch distribution of 30 fibers measured from nano-CT image of Toray TGP-H 090 0 wt %

PTFE.

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Also from the nano-CT dataset of untreated Toray TGP-H 090, a total of 54 fibers were clearly

aligned with others, while 95 fibers were clearly not aligned with others. As described in Section

4.2.1, fiber bundling is expected to have a non-negligible effect on the pore size distribution and

tortuosity of the pore space. Therefore, 36% of fibers should be co-aligned in stochastic models

of paper-made GDLs.

4.4.4 Additive materials

The areal weight was measured for seven materials, yielding values ranging from 35 g m-2 to 156

g m-2 (Table 4.1). Estimates of constituent component weight fractions can be made by

comparing like materials from the same manufacturer, as in the SGL Sigracet 25 series or the

Freudenberg H2315 series. SGL Sigracet 25 AA had no PTFE or MPL, whereas both the

substrates of the SGDL 25 BA and SGL 25 BC materials had a common PTFE coating, and the

SGL 25 BC material had an MPL coating. The SGL 25 BA material had a weight of 37 g m-2,

which was 2 g m-2 greater than the untreated SGL 25 AA material. This indicates that PTFE

represented roughly 5.4 wt % of the SGL 25 BA material. This compared well with the specified

5 wt % PTFE provided by the manufacturer. Similarly, approximately 59% of mass of SGL 25

BC was calculated to be the MPL.

Table 4.1 Material characteristics measured or calculated in this study.

Material

Areal Weighta (g m-2)

Areal Volume

(cm3 m-2)

Mean Fiber Diameter

(µm)

Mean Fiber Pitch

(degrees)

MPL Crack Density (mm-2)

MPL Crack Radius

(µm)

Toray TGP-H 090 131 (157) 72.8 7.7 2.44 - -

SGL Sigracet 25 AA 35 19.4 7.6 - - -

SGL Sigracet 25 BA 37 (40) 20.1 - - - -

SGL Sigracet 25 BC 90 (86) 48.3 - - 8.33 6.26

Freudenberg H2315 96 53.3 10.8 - - -

Freudenberg H2315 I6 119 (115) 63.6 - - - -

Freudenberg H2315 I3C1 156 (145) 83.2 - - 6.26 3.38

a Values in parentheses represent manufacturers specifications.

It is worth noting that many of the areal weight values measured varied from the GDL

specifications, indicating that some degree of variability in GDLs can be expected. The authors

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recommend a focused study on areal weight variability due to batch-to-batch inconsistencies,

and/or macro-scale material heterogeneity.

The areal volume values reported in Table 4.1 can be directly applied to stochastic modeling.

Similar to the comparisons of areal weights, the areal volumes of similar materials can also be

compared to get an approximation of relative fractions of constituent elements. For example,

SGL Sigracet 25 BC had an areal volume of 48.3 cm3 m-2. A stochastic model of a 1 mm × 1 mm

planar section of this material with (1 µm)3 cubic voxels contained 19.4 cm3 m-2 × 10-6 m2 / 10-12

cm3 = 1.94 × 107 solid voxels representing the fibrous substrate, since the areal volume of the

untreated fibrous substrate (SGL Sigracet 25 AA) was 19.4 cm3 m-2. From the comparison of

SGL 25 BA and SGL 25 AA areal volumes, SGL 25 BC required 7 × 105 voxels (0.7 cm3 m-2) of

PTFE coating. Similarly, through a comparison of the areal volume values of SGL 25 BC and

SGL 25 BA materials, this SGL 25 BC required 2.82 × 107 (28.2 cm3 m-2) voxels of solid MPL.

It should be noted that stochastic models of MPL may not contain sufficient resolution to

properly describe the sub-micron pores, and therefore the MPL voxel count may need to be

adapted to account for the nano-scale porosity of the MPL voxels.

Figure 4.10 MPL cracks of GDL types. (a,b) SGL Sigracet 25BC, (c) Freudenberg H2315 I3 C1, and (d) Freudenberg H2315 with custom PTFE and MPL treatments.

4.4.5 MPL cracks

The MPL crack characteristics were determined for two materials: SGL Sigracet 25 BC and

Freudenberg H2315 I3 C1 (Table 4.1). Cracks were 100% more frequent and, on average, were

33% larger in the SGL material compared to the Freudenberg material. The MPL of the

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Freudenberg material would therefore present a stronger capillary barrier than that of the SGL

material. Distributions of crack diameters of each material type are presented in Figure 4.10.

While few millimeter-scale stochastic models of MPL are already available in the literature, the

above characterizations of MPL cracks will be highly valuable for the eventual stochastic models

that are built for studies of two-phase phenomena.

4.5 Conclusions

In this chapter, a number of important, but previously uncharacterized GDL properties were

identified and measured. These properties were each shown to be specifically relevant to pore-

scale stochastic models of the GDL. A novel technique was developed to measure fiber

diameters with a backlit, optical microscope. Measurements of fiber diameters were seen to vary

based on GDL manufacturer, yet tight distributions around their individual means were observed.

To the authors’ knowledge, this paper provides the first reported measurements of GDL fiber

pitch, which was seen to be minimal (2.44°) in Toray TGP-H 090. While fiber pitch may not

have a strong impact on pore size distributions, it will impact solid phase transport processes,

such as electron and thermal transport, which must follow the paths defined by the fiber network

[27,93]. From the analysis of nano-CT images of Toray TGP-H 090, 36% of fibers were

observed to be bundled together. This co-alignment of fibers is expected to have a large impact

on models of both the pore space and the solid matrix. Areal weight values were measured and

found to be in agreement with manufacturers. Areal volumes were calculated based on material

densities. These values, or similarly derived areal volumes should be used when creating

stochastic models to ensure that the proper proportions of constituent elements. Finally, MPL

cracks were counted and measured from high-resolution SEM micrographs. These characteristics

are expected to prove essential in the creation of representative stochastic models of the GDL.

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5 Stochastic Modeling of PEM Fuel Cell GDLs II.

A Comprehensive Substrate Model with Pore Size Distribution and Heterogeneity Effects

5.1 Abstract

A stochastic modeling algorithm was developed that accounts for porosity distribution, fiber

diameter, fiber co-alignment, fiber pitch, and binder and/or polytetrafluoroethylene fractions.

Materials representative of a commercially available gas diffusion layer (GDL) (Toray TGP-H

090) were digitally generated based on empirical measurements of these various properties.

Materials made with varying fiber diameters and binder/fiber volume ratios were compared with

a generated reference material through porosity heterogeneity calculations and mercury intrusion

porosimetry simulations. Fiber diameters and binder/fiber ratios were found to be key modeling

parameters that exhibited non-negligible impacts on the pore space. These key parameters were

found to positively correlate with heterogeneity and mean pore diameter and exhibit a

complementary relationship in their impact on the pore space. Because both parameters directly

impacted the number of fibers added to the domain, modeling techniques and parameters

pertaining to fiber count must be considered carefully.

5.2 Introduction

Performance models of polymer electrolyte membrane (PEM) fuel cells have typically relied on

assumptions about the bulk transport properties of the GDL [32]. The presence of liquid water in

the GDL can dramatically alter the pore-space available for reactant diffusion, and therefore,

dramatically alter the bulk-transport properties of the GDL. Current PEM fuel cell performance

models would benefit from accurately defined relationships between GDL structure, GDL

flooding, and resultant gas transport. In order to gain insight into microscale heat and mass

transport through these materials, researchers are now performing numerical simulations directly

on images of the microstructure obtained through X-ray tomography or stochastic fiber

placement algorithms [22,23,27,94,95]. Simulating the invasion of water into these images

enables the determination of valuable multiphase transport parameters that can otherwise be

challenging and expensive to measure experimentally [19,25,28,53,96]. However, in order to

65

rely on the results of invasion simulations into artificially generated images, the generation

algorithm must be accurate. Becker et al. [94] applied voxel-based solvers on X-ray tomography

images and was able to match experimentally measured diffusivity, permeability, and

conductivity. However, in the same study they employed state-of-the-art stochastic modeling

techniques to create a virtual material image, but could not reconcile many numerical results

between the stochastic model and the tomography-based model. Permeability values calculated

in the stochastic domain were higher than expected, and all three properties had

uncharacteristically low levels of anisotropy. They attributed these discrepancies to a lack of

sufficient heterogeneity in the generated material [94].

Most stochastic models of the GDL involve cylindrical representations of carbon fibers. The

groups at the Fraunhofer Institute (Kaiserslautern) and the Institute of Stochastics (Ulm) were

instrumental contributors to the development and use of such GDL models in the fuel cell

community [25,26,42,73,94,97,98]. In some studies, cylinder orientations were randomized, and

orientation distributions were controlled to prescribe material anisotropy [25,94]. As was first

demonstrated in our previous work [38,99], the random placement of cylinders (fibers) can be

spatially constrained to replicate porosity distributions that have been observed to exist in most

GDL materials [54,74,75]. Binder and PTFE are often assumed to attach to the fibers as highly

wetting fluids and thus recede into the smaller pores of the material upon drying, sintering or

carbonization. Therefore, in stochastic models it is common practice to approximate binder

and/or PTFE addition with the morphological opening of the fibrous pore space

[22,24,77,94,100].

Several groups have provided valuable characterizations of stochastic modeling parameters.

Nabovati et al. [23] discussed material permeability dependence on fiber diameter. When

modeling binder with the morphological opening of the pore space, Didari et al. [22] found that

anisotropic permeability values could be arrived by employing a 2D disc shaped, co-planar

structuring element. Nabovati et al. [24] found that enforcing experimentally obtained, through-

plane porosity distributions on the stochastic fiber placement also increased the anisotropic

permeability when compared to uniformly distributed fibers. They also found that the degree of

anisotropy in the permeability was dependent on the assumed volume fraction of binder [24].

Inoue et al. [78] studied the impacts of bulk porosity and fiber diameter on the generated pore

space of stochastically generated GDLs. By comparing in-plane porosity distributions, they

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determined that heterogeneity was strongly related to fiber diameter, while heterogeneity did not

have a noticeable relationship with the bulk porosity. Their heterogeneity comparison involved

porosity calculations of through-plane columns of voxels; therefore, through-plane sources of

heterogeneity (such as a through-plane porosity distribution [54,74,75]) were not resolved.

In this work, a methodology for stochastically generating fibrous substrates is presented. These

stochastic models of fibrous substrates are created to match the reported properties of one of the

materials reported in Part 1 of this study [101], and the resultant materials are characterized in

terms of heterogeneity and pore size distributions. The impact of fiber diameter and binder

fraction (volumetric solid fraction of binder material) are each demonstrated to dramatically alter

the heterogeneity and pore size distribution of generated materials.

Figure 5.1 Size comparison between a relatively small GDL sample area (5 cm × 5 cm) and a relatively large stochastic model (1 mm × 1 mm).

5.3 Model Development

In this work, a detailed exploration of GDL generation parameters and techniques was performed

to create a valid and representative virtual structure. Figure 5.1 shows a typical realization of a 1

mm2 domain, and its size relative to a full scale GDL sample. The stochastic modeling algorithm

employed in this work was based on the algorithm developed previously [24], and was enhanced

to incorporate the fiber pitch and fiber co-alignment frequency observed in Part 1 of this study

[101]. The algorithm requires the following inputs: domain dimensions, fiber diameter, fiber

length, areal volume, fiber pitch distribution, through-plane porosity distribution, binder fraction,

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and voxel resolution. Binder fraction, fb, was defined as the desired fraction of the solid volume

occupied by binder, as opposed to fiber. From these inputs, the algorithm returned a stochastic

model of the substrate, an example of which is displayed in Figure 5.2.

Figure 5.2 Stochastic model of Toray TGP-H 090 GDL substrate and enlargement for detailed view. Fibers (black) have diameter of 8 µm, binder (yellow) has binder fraction of 0.4. Sample has dimensions 990 µm ×

990 µm × 260 µm

5.3.1 Model overview

Fibers of uniform length and diameter were placed into the domain based on an experimentally

measured, through-plane porosity distribution. The fiber center was given random xy-

coordinates, as well as a random planar angle, φ. Fibers were also given random z-coordinates;

however, those coordinates were chosen from an experimentally measured through-plane

material distribution. Fibers were assigned a random pitch, θ, which was chosen from the

experimentally measured distribution described in [101]. All coordinates were converted from

standard units to units of voxels.

5.3.2 Individual fiber placement

A novel feature of this model is that any portion of a placed fiber extending beyond a side-wall

domain boundary reappears at the opposite boundary, as shown in Figure 5.3. This was done to

68

ensure isotropic in-plane porosity distributions, while creating materials that are intrinsically

well-suited for numerical transport simulations with periodic side-wall boundary conditions.

Figure 5.3 Fiber placed into a stochastic modeling domain. x, y, and z offsets, as well as angles φ, and θ (pitch)

were assigned based on an assumed probability distribution of possible values. Portions of fibers extending beyond the domain were made to reappear at the opposite face of domain.

5.3.3 Fiber count

The number of fibers traversing the domain are expected to have a critical impact on the pore

size distribution and heterogeneity of the pore space. It is therefore important to carefully

determine the appropriate number of fibers to add to the domain. Due to the voxelated nature of

the present reconstructions, this determination turns out to be surprisingly non-trivial. For

instance, even if the experimentally measured fiber diameter, dexp, is well known, one is forced to

round this quantity to the nearest voxel. The voxelized fiber volume is also prone to error due to

the voxelated fiber cross-section. To circumvent these issues, the fiber count, nf, was determined

by first calculating the idealized volume, Vf,ideal, of a cylinder with length, l, and experimentally

derived diameter, dexp:

𝑉𝑓,𝑖𝑑𝑒𝑎𝑙 = 𝜋 𝑙 (𝑑𝑒𝑥𝑝/2)2 . 5.1

Then, the total volume of all fibers required was calculated as:

69

𝑉𝑓,𝑡𝑜𝑡𝑎𝑙 = 𝑉𝑑𝑜𝑚𝑎𝑖𝑛 × (1 − 𝑓𝑏), 5.2

where Vdomain is the total volume of the domain. Finally fiber count was calculated as:

𝑛𝑓 = 𝑉𝑓,𝑡𝑜𝑡𝑎𝑙/ 𝑉𝑓,𝑖𝑑𝑒𝑎𝑙. 5.3

By forcing nf to be calculated by idealized cylindrical volumes instead of the voxelized volumes

of generated fibers, a more realistic pore space is ensured.

This volume-based approach is necessary for placing the correct number of fibers. Consider an

alternative approach, where, for example, two voxelated fibers of 1000 voxels each added to a

domain. If they overlap in 100 voxels, then the total voxel volume added would be 1900 voxels,

not 2000. This effect can become quite insidious if many fibers overlap each other in many

places, resulting in far too many fibers added to the domain. The volume-based approach

outlined above avoids this by counting the volume before it is added to the domain, thus

overlapping does not impact the final fiber count. Another subtle but vital benefit to using this

approach is that fiber intersections are properly accounted for. This is discussed in detail below

in section 5.3.7.

5.3.4 Generated fiber volume

Although nf is independent of the voxelized volume of generated fibers, it remains important to

closely match generated fiber volumes with ideal fiber volumes. In the final step of the material

generation, binder material is placed to reach the correct bulk porosity, and if an appropriate

number of fibers are placed, but with inappropriate volumes, the result would be an inappropriate

amount of binder placed in the domain.

Fibers were generated with the use of a cylinder generation sub-function obtained from the

MATLAB File Exchange2. The sub-function accepted the following parameters in units of

voxels: an input diameter, dinput, and input endpoint coordinates. Voxels were assigned to a

2 https://www.mathworks.com/matlabcentral/fileexchange/21758-cylinder-surface-connecting-2-points

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nearby fiber if they were within a radial distance of dinput/2 of the line segment formed by the

fiber endpoints.

A voxel resolution, R, with units of µm/voxel, was required in order to dimensionalize voxel-

based lengths. The dimensional input diameter, dinput × R, was not matched to the experimentally

derived dexp. This is because, due to the voxelized nature of the system, generated fibers volumes,

Vf,gen, were limited to discrete numbers of voxels which rarely precisely coincided with Vf,ideal/R3.

Compounding this problem, was the fact that fibers of different orientations would have different

volumes, depending on their alignment with the voxel orientation. As a result, complementary

dinput and R values had to be found such that �̅�𝑓,𝑔𝑒𝑛 ≈ 𝑉𝑓,𝑖𝑑𝑒𝑎𝑙/𝑅3, where �̅�𝑓,𝑔𝑒𝑛 is the average

generated fiber volume.

To determine complementary dinput and R values for a given dexp and corresponding Vf,ideal, a short

study was conducted. First, 200 individual, randomly oriented fibers were generated for each of a

range of dinput values between 1 voxel to 20 voxels. For each fiber, a summation of the associated

voxels was determined, and the mean volume of each group of 200 cylinders was found (Vf,mean).

The relationship between dinput and �̅�𝑓,𝑔𝑒𝑛 is shown in Figure 5.4 along with the ideal case of V =

π l (dinput/2)2. It can be seen that �̅�𝑓,𝑔𝑒𝑛 contains only discrete values which are consistently

higher than the ideal case. Equivalent diameters of generated fibers were found as:

𝑑𝑒𝑞 = 2 (𝑉𝑓,𝑔𝑒𝑛 𝑅

𝜋 𝑙)

0.5

, 5.4

which represent the diameter of an idealized cylinder with volume, �̅�𝑓,𝑔𝑒𝑛 and dimensionless

length l/R. Finally, voxel resolutions for any dinput were found as:

𝑅 = 𝑑𝑒𝑥𝑝/𝑑𝑒𝑞, 5.5

where dexp is measured in µm and deq is measured in voxels. Figure 5.5 illustrates the possible

voxel resolutions that result from the dexp values discussed in this work.

To check that this results in reasonable generated fiber volumes, equations 5.1 and 5.5 were first

combined to yield:

𝑉𝑓,𝑖𝑑𝑒𝑎𝑙 = 𝜋 𝑙 (𝑑𝑒𝑞 𝑅 2⁄ )2, 5.6

71

which can then be combined with equation 5.4, resulting in the following desired relationship:

�̅�𝑓,𝑔𝑒𝑛 = 𝑉𝑓 ,𝑖𝑑𝑒𝑎𝑙 𝑅3⁄ . 5.7

Figure 5.4 Comparison of mean fiber volume, �̅�𝒇,𝒈𝒆𝒏, and input diameter, dinput, for cylinder generation

algorithm. The ideal case of V = π l (dinput/2)2 is displayed as a dashed line. The calculated equivalent diameter,

deq, based on cylinders with volume = �̅�𝒇,𝒈𝒆𝒏, is also displayed.

Figure 5.5 Permitted resolution values, R, over the dinput values tested, for five hypothetical fiber diameters, dexp.

72

5.3.5 Through-plane material distribution

Substrate models were prescribed porosity profiles by randomly choosing through-plane fiber

positions from a known through-plane material distribution. This distribution can be found as the

complement of a µCT derived through-plane porosity distribution [38].


Each placed fiber was assigned a probability of being co-aligned (paired) with the most recently

placed fiber in the system. If the fiber was selected for co-alignment, its xy-position was offset

from that of the previous fiber by a distance of one fiber diameter in the direction normal to that

fiber. Its z-position, φ, and θ values were identical to those of the previous fiber.

5.3.7 Fiber overlap

When placing fibers it is not reasonable to avoid fiber intersections. As outlined above, the

volume of fibers involved in an intersection was fully accounted for, resulting in the correct

number of fibers added to the domain. However, these intersections resulted in a slight inflation

of neighboring pore sizes. The addition of binder to the image offered one way to qualitatively

correct for this, as binder coalesces in the corners and crevices precisely at fiber intersection

points. In this work, binder was added to the sample until the known porosity of the material

was reached. By bulking up the regions near the intersections, this step had the effect of

mimicking the displacement and bending of fibers at these point locations.

5.3.8 Binder placement

After nf fibers were placed into the domain, the application of binder was simulated with the

morphological opening of the pore space with a structuring element (SE) [100]. The SE

employed in this case was spherical, with a diameter determined through a half-interval search

algorithm, which resulted in the SE diameter providing the best match to the desired final

material porosity. As the SE was also voxelized, the accuracy of this process was limited by the

resolution chosen. With a resolution of 0.99 µm/voxel, the bulk porosity value for each material

was observed to fall within 1.4 % of the desired value. To avoid edge effects associated with

morphological opening, the domain dimensions were temporarily increased before this step; each

73

sidewall was padded with the first 25 voxel planes from the opposite sidewall; first the

corresponding xz-planes, and then the corresponding yz-planes were added.

5.4 Pore-space Characterization

Two characterization methods are presented to explore the effects of input parameters on the

resultant pore space of stochastically modeled GDLs. The first method was used to characterize

the heterogeneity of the material based on local porosity calculations. The second method was

used to characterize the pore size distributions of the generated materials by simulating mercury

intrusion porosimetry curves.

5.4.1 Porosity heterogeneity

The goal of the porosity-based heterogeneity test was to evaluate material uniformity. Numerous

subdomains were selected from the main domain and the porosity in each was calculated. The

size of these sub-domains (50 µm × 50 µm × 50 µm) was chosen to be sufficiently large such

that single fibers did not dominate the porosity value and sufficiently small to capture localized

regions of high and low porosities (porosity heterogeneity) throughout the GDL. 100,000 such

measurements were made of cubic sub-domains randomly selected from throughout the material.

If a sub-domain position was chosen near the edge of the domain, such that a portion of the cube

would be outside the primary domain, that portion of the cube was extended into the opposite

face of the domain, taking advantage of the fact that fibers were placed using periodic rules at the

side walls. A 2D example of this process is shown in Figure 5.6a, where two random samples are

outlined in dashed lines. The region outlined in blue did not overlap with the primary boundary

and had a local porosity of 78%. The region outlined in red happened to be placed near a corner,

and therefore this sub-domain extended into the opposite faces of the domain. Figure 5.6b shows

the distribution of local porosity of 150 random samples in the example 2D domain. If the

domain had been more heterogeneous, the distribution would be more widely spread. If the

domain was perfectly homogeneous, the porosity distribution width would approach zero with a

peak at a single value.

74

Figure 5.6 Demonstration of a porosity heterogeneity analysis of a 2D example (a) with white material on

black void. The blue and red dashed regions each represent a randomly placed 502 pixel2 sample. After a sufficient number of similar random samples were examined, a representative histogram of measured

porosities (b) was obtained. Note: in the 3D models characterized in this study, the random samples were 503

µm3 cubes.

5.4.2 Mercury intrusion porosimetry simulations

Mercury intrusion porosimetry (MIP) is widely used experimental tool for characterizing the

pore size distributions of porous materials [102,103]. In MIP studies an evacuated porous

material is invaded with mercury in a controlled step-wise manner, yielding a so-called capillary

pressure curve relating mercury saturation to capillary pressure. As the capillary pressure is

incrementally increased, the mercury penetrates pores of decreasing size. With knowledge of the

surface tensions involved, capillary pressures can be used to approximate pore sizes, resulting in

a pore size distribution [102,103].

Gostick [104] described a simple morphology-based simulation of two-phase invasion, built on

the work of Hilpert and Miller [105], entitled a morphological image opening (MIO) algorithm.

The MIO algorithm was used to determine the saturation of the invading phase as a function of

the capillary pressure of the invading fluid. This algorithm was employed in the present work to

characterize the pore size distributions of the generated materials. In traditional MIP, the

invading mercury has access to pores along all surfaces of the sample, and due to the sample size

requirements of a GDL sample, the contribution of side-wall invasion is expected to be

negligible. For example, the side-walls compose only 5% of the total surface area of a 1 cm × 1

cm sample of Toray TGP-H-090. However, for a typical numerically generated GDL of

75

dimensions 1 mm × 1 mm, the side-walls compose 33% of the sample, and sidewall invasion

could be expected to contribute to the resultant pore size distribution. To mitigate unrealistic

sidewall effects while characterizing the 0.99 mm × 0.99 mm materials generated in this work,

the MIO algorithm was implemented such that the invading fluid had access to both planar faces

of the material, but not the sidewalls.

The progression of the MIO technique is explained with the 2D demonstration illustrated in

Figure 5.7. Figure 5.7a shows a visualization of the pore space, where decreasing pore diameters

were accessible by the invading fluid with incrementally increasing capillary pressure. Figure 7b

displays the calculated saturation levels for each simulation step and the corresponding pore size

distribution that was obtained from the saturation data. It should be noted that since the primary

output of the MIO algorithm is a saturation vs. pore size curve, corresponding capillary pressures

need not be calculated.

Figure 5.7 MIO demonstration on pore space shown in Figure 5.6a. The pore space coloring (a) corresponds

to the diameter of the largest circular structuring element (SE) that was accessible from the top or bottom of the domain. The pore size distribution and saturation curves (b) were calculated from the volume of each

color shown in (a). Note: in the 3D models characterized later in this study, the probing structuring element

was spherical.

The saturation curve (e.g. Figure 5.7b, blue) was used to provide the following statistical

information of the pore space. The mean (volumetric) pore size was defined as the diameter

representing a saturation of 0.50. Similarly, arbitrary limits to the pore size distribution were set

as those that contain 90% of the pore volume. Minimum and maximum pore sizes were set to

diameters corresponding to saturation values of 0.95 and 0.05, respectively. In the 2D example

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shown in Figure 5.7, the mean pore size was 7.4 pixels, and the pore size range was [3.3, 30.5]

pixels.

In the 2D example (Figure 5.7) described above, a majority of the internal pore space was

inaccessible to the invading fluid until higher pressures were reached. This was due to an

effective barrier of smaller pores near each surface. Therefore all pores in the interior of the

domain were categorized as small pores. Such mislabeling of pore sizes is a known limitation of

the MIP technique [49]; however, it remains a conventionally utilized tool for porous media

characterization and, as such, was an important experiment to numerically simulate.


5.5.1 Stochastic model of Toray TGP-H 090

The modeling algorithm described in Section 5.3 was employed with input parameters specific to

Toray TGP-H 090 without MPL or PTFE treatments. According to [101], this material is best

described by 7.7 µm-diameter fibers, a mean fiber pitch of 2.44º, an areal volume of 72.8 cm3

m-2, and a fiber co-alignment probability of 36%. Aside from fiber diameter, these parameters

were perfectly matched, including the full fiber pitch distribution reported in [101]. Fiber

diameters were varied in increments of 1 µm, and a diameter of 8 µm was assumed to be the

most representative of Toray TGP-H 090.

Voxel resolutions were based on their discretized relationship with input diameter (Section

5.3.4). A single voxel resolution of 0.99 µm/voxel was found to accommodate the integer dexp

values of 7 µm, 8 µm, 9 µm, 10 µm, and 11 µm, where respective dinput values were chosen

according to Figure 5.5.

Stochastically generated materials were generated with a domain size of 0.99 mm × 0.99 mm ×

0.26 mm. Cylindrical fibers were prescribed a length 0.99 mm. Modeling parameters are listed in

Table 1. A total of 20 parametric combinations were possible with 5 diameter values and 4

binder fraction values shown.

GDLs were stochastically generated with a range of binder fractions so that the best (most

realistic) binder fraction could be identified. The cross-sectional images of these GDLs were

77

visually compared to microscale computed tomography (µCT) cross-sections of Toray TGP-H

090. At a constant porosity and fiber diameter, stochastic materials generated to have higher

binder fractions required fewer fibers. Materials made with a binder fraction of 0.4 appeared to

have an appropriate number of fibers present. An example comparison between the cross

sections of the µCT dataset and a stochastic model is provided in Figure 5.8.

Figure 5.8 Comparison between cross sectional slices of a µCT data set of Toray TGP-H 090 (a) and a

stochastically generated material generated with representative input parameters and a binder fraction of 0.4 (b). Material (white) represents both fibers and binder material.

Table 5.1 Parameters employed to create materials for this study. Underlined parameters are assumed to best represent Toray TGP-H 090.

Property Name Symbol Unit Value

Area µm2 990 × 990

Thickness µm 263

Fiber diameter dexp µm 7, 8, 9, 10, 11

Fiber length l µm 990

Bulk porosity 0.72

Mean fiber pitch θmean ° 2.44

Binder fraction fb 0.0, 0.2, 0.4, 0.6

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The through-plane porosity distribution of generated materials was prescribed with that of a 1

mm × 1 mm region of a µCT image of untreated Toray TGP-H 090 under minimal compression.

A comparison between the µCT image-based porosity distribution (model input) and the porosity

distribution of a single stochastically generated model (output) is displayed in Figure 5.9. Using

a sufficiently large domain (experimental and numerical) enabled a close agreement between the

input and output distributions. This was an improvement to our previous work, where smaller

domains were employed [24,38].

Figure 5.9 Comparison between the µCT derived through-plane porosity distribution used as a weighting function to stochastic fiber placement, and the porosity distribution of a single, stochastically generated

material.

Using the image processing software FIJI3, stochastic models were rendered in a fashion similar

to scanning electron microscopy (SEM). As can be seen in Figure 5.10, the stochastically

modeled material bears a reasonable resemblance to the top-down view from SEM. The edge

views (xz-plane) exhibit fewer similarities, where large pores are shown in Figure 5.10a that do

not appear in Figure 5.10b. This can be attributed to the existence of carbon fibers near the

sample edges that were broken during sample preparation to distort the depth perception. Such

large pore sizes were not as prominent in the µCT through-plane cross sections (Figure 5.8a).

For each possible combination of parameters in Table 5.1, 10 materials were stochastically

generated. It was assumed that the materials generated with a fiber diameter of 8 µm and binder

3 http://fiji.sc/

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fraction of 0.4 most closely resembled Toray TGP-H 090. All materials were created to match

the µCT-derived through-plane porosity distribution displayed in Figure 5.9.

Figure 5.10 Comparison between SEM micrographs (a) of top-down (xy plane) and edge (xz plane) views of

Toray TGP-H 090 material and similar views of stochastically generated, digital materials (b). The scale bar in (a) applies to all images.

5.5.2 Porosity heterogeneity

Figure 5.11 displays the local porosity distributions for evaluating porosity heterogeneity for all

20 combinations of fiber diameter and binder fraction. Each shaded region in Figure 5.11

represents two standard deviations (2σ) about the mean distribution values. The 2σ fields contain

approximately 95.5% of the individual distribution values. To provide a frame of reference, the

mean values for the 8 µm diameter materials with a binder fraction of 0.4 were shown in each

subfigure.

This characterization method produced a distinct trend in the profiles for the various parametric

combinations. Highly heterogeneous materials (e.g. Figure 5.11e, blue) produced wide

distributions of porosity, and narrower distributions were realized with less heterogeneous

materials (e.g. Figure 5.11a, grey). The 2σ fields were seen to be situated tightly around the mean

curves. Also, upon examination of the curves in general, a change in binder fraction of 0.2

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consistently resulted in a more dramatic change in heterogeneity than a 1 µm change in fiber

diameter. However, both parameters exhibited strong positive correlations to heterogeneity.

To determine the effects of fiber count, two materials with a similar number of fibers were

compared. Though not shown, it was found that the materials with 7 µm-diameter fibers and a

Figure 5.11 Porosity heterogeneity comparison showing the relationship

between binder fraction and heterogeneity for fiber diameters: (a) 7 µm, (b) 8 µm, (c) 9 µm, (d) 10 µm, (e) 11

µm. Each colored field is bound by two standard deviations above and below the mean value from 10 samples. The

reference line in each figure corresponds to the mean value of materials generated

with 8 µm-diameter fibers and a binder fraction of 0.4.

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binder fraction of 0.6 (Figure 5.11a, blue) were generated with almost exactly the same number

of fibers as those generated with 10 µm-diameter fibers and a binder fraction of 0.2 (Figure

5.11d, red). However, the 7 µm-diameter material was more heterogeneous (wider local porosity

distribution) than the 10 µm-diameter material. Therefore, it can be said that, while parameters

that decrease fiber count can be expected to have a positive correlation with heterogeneity, fiber

count alone cannot be used to predict material heterogeneity when a combination of parameters

have been altered.

Three parameter combinations produce materials with local porosity distributions that are nearly

matching to the reference case. Materials made with 9 µm-diameter fibers and a binder fraction

of 0.4 (Figure 5.11c, green), 10 µm-diameter fibers and a binder fraction of 0.2 (Figure 5.11d,

red), and 11 µm-diameter fibers and a binder fraction of 0.2 (Figure 5.11e, red) produced similar

local porosity distributions. This demonstrates the complementary effect that the two parameters

have on material heterogeneity.

From these results, the authors recommended paying close attention to both fiber diameter and

assumed binder fraction when attempting to generate realistic material heterogeneities. Due to its

similar impact on effective fiber count [101], the inclusion of fiber bundling was expected to

generate a non-negligible impact on heterogeneity.

5.5.3 Mercury intrusion porosimetry simulations

The simulations of mercury intrusion porosimetry provided a quantitative measure of the effects

of fiber diameter and binder fraction on the pore space of the material.

The saturation curves and pore size distributions corresponding to each of the 20 possible

combinations of fiber diameter and binder fraction are displayed in Figure 5.12 and Figure 5.13,

respectively. Additionally, a visualized mercury distribution is shown in Figure 5.14,

representative of a typical early stage in a simulation (saturation = 0.16). Similar to porosity

heterogeneity distributions, MIO-based saturation curves were distinct for each of the material

types, and 0.99 mm × 0.99 mm samples appeared to be sufficiently large to provide domain size

independence.

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Figure 5.12 MIO saturation curve

comparison showing the relationship between binder fraction and saturation curves for fiber diameters: (a) 7 µm, (b) 8

µm, (c) 9 µm, (d) 10 µm, (e) 11 µm. Each colored region is bound by two standard

deviations above and below the mean value obtained from 10 samples. The reference line in each figure corresponds

to the mean value of materials generated with 8 µm-diameter fibers and a binder fraction of 0.4.

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Figure 5.13 MIO pore size distribution comparison showing the relationship between binder fraction and pore size

distribution for fiber diameters: (a) 7 µm, (b) 8 µm, (c) 9 µm, (d) 10 µm, (e) 11 µm. Each colored region is bound by two

standard deviations above and below the mean value obtained from 10 samples.

The reference line in each figure corresponds to the mean value of materials generated with 8 µm-diameter

fibers and a binder fraction of 0.4.

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Figure 5.14 An example distribution of mercury from a simulation of mercury intrusion porosimetry with a spherical SE of diameter of 30 µm in a 1 mm × 1 mm × 263 µm modeled material with a fiber diameter of 9

µm and a binder fraction of 0.2. Fibers were intentionally hidden in this representation for clarity.

Unlike in the porosity heterogeneity comparison, only one other parameter combination, i.e. 10

µm-diameter fibers and a binder fraction of 0.2 (Figure 5.12d, red), resembled the reference

combination of 8 µm-diameter fibers and a binder fraction of 0.4. This result indicated that

porosity heterogeneity could not fully describe each material type and emphasized the

importance of implementing multiple characterization methods when generating representative

materials.

The mean pore diameters, as well as the pore diameter ranges are displayed for all material types

in Table 5.2 and Table 5.3, respectively. As shown in Tables 5.2 and 5.3, fiber diameter and

binder fraction exhibit a strong positive correlation to the minimum, mean, and maximum pore

sizes of the materials. An increase in binder fraction from 0 to 0.6 leads to the doubling of the

mean pore size, while an increase in fiber diameter from 7 µm to 11 µm leads to an increase in

the mean pore size by over 50%. On the log scale provided in Figure 5.13, it can be seen that the

width of the pore size distribution remains relatively constant throughout the range of parameter

combinations.

From these results, the authors recommend matching pore size distributions of stochastically

modeled materials to experimentally derived values, as each parametric combination of fiber

diameter and binder fraction resulted in distinct pore size distributions.

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Table 5.2 Mean pore diameter values for each studied combination of fiber diameter and binder fraction

Mean Pore Diameter (µm)

Binder Fraction

0.00 0.20 0.40 0.60

Fiber

Diameter

(µm)

7 16 18 23 30

8 18 21 26 34

9 20 24 29 39

10 22 26 33 43

11 24 29 36 48

Table 5.3 Pore diameter ranges for each studied combination of fiber diameter and binder fraction.

Pore Diameter Range,

90th percentile [min, max] (µm)

Binder Fraction

0.00 0.20 0.40 0.60

Fiber

Diameter

(µm)

7 [8, 27] [12, 33] [16, 41] [22, 53]

8 [10, 32] [13, 38] [18, 48] [25, 60

9 [11, 36] [15, 43] [20, 54] [28, 67]

10 [12, 40] [17, 48] [23, 59] [31, 72]

11 [13, 45] [18, 53] [25, 62] [35, 77]

5.6 Conclusions

A methodology was presented for the stochastic generation of the carbon fiber substrates of PEM

fuel cell GDLs. This methodology was unique in that it incorporated experimentally derived

values for fiber diameter, fiber pitch, through-plane porosity distribution, and fiber bundling.

Also, particular emphasis was given to generating the correct number and volume of fibers,

which involved careful treatment of these experimentally derived parameters. A parametric study

was conducted on assumed fiber diameter and fiber/binder ratio (binder fraction). For each

parametric combination, 10 stochastic materials were generated and compared with a reference

material. It was found that each parameter had strong effects on both the material heterogeneity

and the pore size distributions derived from mercury simulations. Material heterogeneity and

pore size distribution were shown to be useful methods when characterizing the pore space of the

material, in that each parametric combination generated distinct, consistent profiles

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corresponding to each method. Similar effects on the pore space can be achieved by either

increasing the fiber diameter or by increasing the binder fraction, in that nearly indistinguishable

materials can be generated with complementary adjustments of these two parameters. The

authors recommend that future studies involving stochastic models of the GDL substrate employ

carefully chosen values for these parameters. Additionally, when experimental data is available,

materials should demonstrate realistic porosity heterogeneity and pore size distribution.

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6 Visualizing Liquid Water Evolution in a PEM Fuel Cell Using Synchrotron X-ray Radiography

6.1 Abstract

Synchrotron X-ray radiography was utilized to study the time evolution of liquid water in an

operating polymer electrolyte membrane (PEM) fuel cell. A high aspect ratio fuel cell designed

with offset anode and cathode flow field channels was operated at conditions that produced

critical water management issues. The X-ray beam was directed along the plane of the fuel cell,

and was therefore employed to elucidate the through-plane distribution of liquid water in the

porous materials. Due to the offset between the anode and cathode gas channels, the membrane

electrode assembly exhibited sinusoidal warping, and liquid water accumulated in possible areas

of delamination. Liquid water first appeared near the cathode catalyst layer, and then traveled

laterally within the porous gas diffusion layer. The experiment provides a basis for future design

considerations, including membrane thickness and attenuation estimates.

6.2 Introduction

Due to the micrometer scale of the GDL and the coupled relationship between local temperature

and phase change, it can be challenging to create realistic ex situ experiments of liquid water

forming in and around the GDL. Several groups have conducted invasion experiments to mimic

fuel cell conditions, where liquid water is assumed to enter the system from the interface

between the GDL and the catalyst layer and percolate to the opposite face [69,80,106,107]. Other

groups have utilized environmental scanning electron microscopy (ESEM) to visualize

condensation on the surface fibers of the GDL [108,109]. Each of these techniques involves

assumptions about the impact of the concentration and temperature gradients present in the GDL

material during fuel cell operation. The assumptions for these ex situ experiments must be better

informed to increase their applicability to the operating PEM fuel cell.

In situ experiments that give insight into the behavior of liquid water in PEM fuel cell materials

almost always require some means of visualizing the liquid water [8,29,30,110-118]. Optically

transparent flow fields have been employed by [110,111] to visualize liquid emerging from the

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surface of the GDL and condensing on the channel walls. The drawback of this technique is that

the difference between the thermal properties of the transparent flow field and those of a metallic

or graphite material may significantly alter the in situ temperature distributions within the GDL

and induce unrealistic condensation behavior.

The theory behind using neutron and synchrotron X-ray radiography to visualize in situ liquid

water in PEM fuel cells is described in detail in [30], and several researchers have demonstrated

the usefulness of these [8,29,114-116,119]. The two techniques are similar in that they both

involve detecting changes in beam attenuation of an irradiated sample, with those changes being

directly related to the accumulation of liquid water in the system. Neutron radiography has the

advantage of facilitating few fuel cell modifications, due to the near transparency of metals and

graphite to a neutron beam and the high attenuation from water molecules. Recently, synchrotron

based X-ray radiography has been demonstrated to reach resolutions of less than 1 μm, compared

to a limit of ~20 μm in neutron radiography [30]. A very recent neutron radiography study [112]

reported a resolution of 13 μm, however a total of 60 minutes of images were averaged for noise

reduction. Because thick metals can be opaque to X-ray light, some fuel cell modifications are

sometimes performed to create viewing windows [8] for the system. These modifications are

seen to be less invasive than the use of a transparent flow field for optical visualizations.

Therefore, synchrotron X-ray radiography has emerged as a promising technology for the study

of liquid water within the porous materials of the PEM fuel cell.

A growing number of synchrotron facilities are beginning to conduct studies of liquid water in

PEM fuel cell materials [8,29,116,117], which results in many individuals participating in the

same learning curve regarding experimental design. This method of employing synchrotron X-

ray radiography to PEM fuel cell investigations could be further advanced with the development

of a best practices approach. In this study, we collected a time-series of radiographs at the

Canadian Light Source (CLS) in Saskatoon, Canada with the goal of learning best practices for

designing synchrotron-based experiments for investigating liquid water transport in an operating

PEM fuel cell.

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6.3 Experimental Setup

The fuel cell utilized in this study was designed for synchrotron X-ray based visualization of in

situ liquid water while the plane of the cell is oriented in the direction of the X-ray beam. Similar

to the study performed by Hartnig et al. [29], the fuel cell employed here was designed for in-

plane imaging to produce cross-sectional information about the evolution of liquid water

transport. Additionally the cell was constructed such that channel and landing regions of each

membrane electrode assembly (MEA) could be distinguished in radiographs.

6.3.1 Fuel cell assembly

A 5 cm2 active area cell (Figure 6.1) was constructed with a high aspect-ratio in order to reduce

the amount of material (including gaskets) that the beam traversed before reaching the detector.

Single-serpentine flow-fields were machined into a graphite composite, with 1 mm landings and

channels and 25 turns over the active area. While the fuel cell is in a co-flow configuration, the

anode flow-field pattern was offset by 1 mm compared to the cathode pattern, such that the

cathode channels aligned with the anode landings. While this may induce additional sheer forces

and misalignments of the MEA components, the offset was necessary to mimic the configuration

of a concurrent visualization study [7]. The catalyst coated membrane (CCM) employed was

custom ordered from IonPower, Inc. (Delaware, US). A Nafion 115 membrane (dry thickness of

127 μm) was coated with a catalyst layer (thickness of 12 μm) with a Pt loading of 0.3 mg/cm2.

Toray TGP-H 090 GDLs (thickness of 280 μm) were used, treated with 10% wt.

polytetrafluoroethylene (PTFE), with no microporous layer. Surrounding the active area was a 5

mm width of 254 μm-thick PTFE coated fiberglass gasket material.

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Figure 6.1 Schematic illustrating the components of the PEM fuel cell assembly. After assembly, GDL and gasket reside in the same plane.

6.3.2 Imaging setup

The experiment was performed at the BioMedical Imaging and Therapy Bending Magnet (05B1-

1) beamline at the Canadian Light Source (CLS) synchrotron (Saskatoon, Canada).

Monochromatic X-ray light provided at 25 keV was used to obtain absorption radiographs with a

Hamamatsu C9300-124 (12bit, 10 Megapixel) charged coupled device (CCD) camera placed 30

cm from the sample. The pixel resolution was 4.27 μm, and the spatial resolution of the optical

setup was 10 μm. Radiographs were obtained every 0.9 s. To reduce the effects of noise from the

CCD camera and the thermal instability of the monochromator [113], 19 consecutive images

were averaged, reducing the temporal resolution of the each frame to 17 seconds. Due to the

orientation of the fuel cell in this study, where the 1 cm width of the active area was aligned to

the beam path, individual pore-scale water accumulation events were overlapped by many

similar and simultaneous events along the width of the cell. Therefore, high temporal resolutions

were not necessary, as these combined events had much larger time scales than the individual

events.

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6.3.3 Fuel cell operating conditions

A Scribner 850e Fuel Cell Test Station (Scribner Associates Inc., Southern Pines NC) was

utilized to regulate load, cell temperature, reactant flow rates, and reactant relative humidity

(RH). Prior to the experiment, the fuel cell was conditioned with 4 hours of load cycling. At the

time of the experiment, the fuel cell was operated at 65C, with a constant flow rate of 0.5 lpm

air at the cathode and 0.3 lpm hydrogen at the anode. Both reactants were humidified to 80%

RH, and the outlet pressure was atmospheric.

The initially dry cell was held at open circuit voltage (OCV) for 5 minutes. The cell was then

brought up to a current density of 0.30 A cm-2 at a rate of 2 mA cm-2 s-1. The cell was held at this

current for 15 min. Finally, the cell current density was increased at a rate of 2 mA cm-2 s-1 until

the cell potential fell below 0.1 V, which occurred at a current density of ~0.7 A cm-2.

See Appendix A for a detailed schematic of the fuel cell testing equipment.

6.3.4 Liquid water quantification

To quantify liquid water in the cell, each averaged radiograph in the “wet-state” must be

normalized to a “dry-state” radiograph obtained before the accumulation of liquid water. The

normalization process involved the Beer-Lambert law of attenuation as described in detail in

[113] (also see Appendix B for an improved methodology). The dry-state radiographs used for

normalization were the average of one hundred “dry-state” radiographs, each exposed for 0.9 s.

Due to membrane swelling, dry-state radiographs were chosen from the period of time where the

cell was held at 0.30 A/cm2. Since some water is expected to be in the system at 0.30 A/cm2, the

normalization may lead to undetected water. However, this dry-state condition was chosen to

prevent the majority of swelling-related artifacts. As will be discussed in the section titled

“Future Design Considerations,” this problem may be mitigated with careful membrane

selection.

Figure 6.2a displays a radiograph before normalization, showing the location of the fuel cell

components. The flow field channels and landings are seen as light and dark rectangles,

respectively, on both sides of the MEA. The 127 μm-thick membrane is seen as a thin, lighter

grey region, oriented along the center of the image (top-down). Finally, the GDL materials are

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seen within the darkest regions, situated between the flow fields and the catalyst coated

membrane (CCM). Figure 6.2b displays this same image as Figure 6.2a, after normalization to a

dry-state radiograph, where liquid water and any other material movement become pronounced.

Figure 6.2 Synchrotron X-ray radiographs showing the cross-sectional view of an operating PEM fuel cell: (a) raw (b) processed images. The white dashed selection represents the selection shown in Figures 6.4 and 6.5.

The grayscale calibration bar is in units of cm of liquid water. Scale bars represent 1 mm.

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6.4 Results: Behavior of Visualized Water

The following results describe the fuel cell performance and liquid water generation from a

comparatively dry state to a critically wet state, caused by a steady increase of 2 mA/cm2/s.

Figure 6.3 shows the voltage response while the cell is taken from 0.30 A/cm2 to ~0.7 A/cm2.

Four regions of this timeline, marked (a-d), are highlighted in Figure 6.3, representing the four,

17 s frames displayed in Figure 6.4. Region (d) is located near the point where mass transport

becomes a dominating factor in the over-potential of this cell.

Figure 6.3 Current density and potential response of fuel cell when current density is increased from 0.30 A/cm2 at a rate of 2 mA/cm2/s. Regions (a - d) represent the 17 seconds of combined exposure for each of the

four frames displayed in Figure 6.4.

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Figure 6.4 Liquid water evolution over 4 minutes. Liquid water forms near the catalyst layer under the cathodic flow field landings (b,c) and appears to spread laterally through the bulk of the GDL to the region

under the channel (d). Black lines outline the location of the flow field landings. Negative values represent artifacts caused by material relocation during membrane hydration. The grayscale calibration bar is in units

of cm of liquid water. Scale bars represent 0.5 mm.

Figure 6.4 shows the time-evolution of water in the cathode GDL region at 4 points of the steady

ramp up from a current density of 0.30 A/cm2 to ~0.7 A/cm2. Figure 6.4a represents the state of

the cell 30 s before the beginning of the ramp, while the current density was maintained at 0.30

A/cm2. Figure 6.4b represents the state of the cell at 35 s into the ramp where the current density

is 0.37 A/cm2. Each subsequent image in the sequence represents a step of 60 s and 0.12 A/cm2.

Liquid water first appeared (Figure 6.4b) at the interface of the GDL and the catalyst layer, in

locations centered under the landings. At 95 s into the ramp, at a current density of 0.49 A/cm2,

Figure 6.4c shows that water continued to accumulate at these locations, with no invasion into

other regions of the GDL. Finally, by a current density of 0.61 A/cm2, liquid water had spread

laterally within the bulk of the GDL, into the less compressed region under the flow field

channel (Figure 6.4d).

A reasonable explanation for this observed behavior is that liquid water condensed in or near the

catalyst layer, under the cathode landings. The liquid water maintained a low capillary pressure

by only invading the large pores formed at the interface of the GDL and the catalyst layer. Then,

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when a current density of 0.61 A/cm2 was reached, the volume of liquid water had occupied all

available low-capillary pressure locations, and was forced to reach pressures associated with

entering the bulk of the hydrophobic GDL (Figure 6.4d).

It is important to reiterate that the visualized liquid water is the combined water along the entire

1 cm-width of the active area (integrated in the in-plane direction) and may not be representative

of each individual growing water cluster in the system. The maximum value of quantified liquid

water thickness in the region of interest is 0.125 cm. This can be interpreted that 12.5% of the

total width of the active area is occupied with liquid water at these locations. With an estimated

70% porosity within the GDL under compression, this can be translated into a peak saturation

value of 18%.

6.5 Future Design Considerations

Several aspects of the fuel cell design and experimental design were shown to have a high impact

on the clarity of the experimental results. In order of importance, these design elements were:

membrane thickness, uneven attenuation, channel alignment, and pre-monochromator filtering.

The impacts of each design were made evident through a careful study of both the raw and

normalized radiographs, and will be described in detail below.

6.5.1 Membrane thickness

Nafion membrane materials have been reported to swell by as much as 50% as a result of current

density induced humidification [119]. In a fuel cell assembly, this tendency to swell can affect

the position of the catalyst layer and the GDL. The membrane used in this study was 127 μm

thick in its dry-state, which would correspond to a thickness change of 63 μm, when fully

humidified. Such swelling could lead to displaced positions of the anodic and cathodic GDLs

towards the flow fields. A comparison of the two membrane states is displayed in Figure 6.5,

where an image captured during open circuit voltage (OCV) was normalized to an average of

100 frames taken while the cell was held at 0.30 A/cm2. The water generated at this low current

density was enough to humidify the visualized region of the membrane and cause severe artifacts

in the normalized image due to the resulting shift of material position. In this case, little evidence

of liquid water was present in the comparison between these two states, so the 0.30 A/cm2 image

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can be assumed to be in a dry-state as well. In fact, all normalized images presented in the

previous section were normalized to the cell at the 0.3 A/cm2 state. However, it was decided that

all future studies would be performed with 25 μm-thick membranes, to mitigate such artifacts,

and ensure zero water in the dry-state images. It is primarily for the reason of material movement

that the grayscale range was mapped to both negative and positive water thickness

measurements.

Figure 6.5 Radiograph taken at OCV normalized to the dry-state image used in this study (0.30 A/cm2) (inverted for consistency with Figures 6.4 and 6.5). Bright regions represent a net gain of material between OCV and 0.30 A/cm2, while dark regions represent a net loss. Black lines outline the location of the flow field

landings. The scale bar represents 0.5 mm.

6.6 Uneven Attenuation

While imaging the fuel cell, the raw radiographs must have sufficient signal in the regions of

interest so that any slight attenuation due to the presence of liquid water can be distinguished

from the noise of the CCD camera. Increased beam intensity addresses this problem; however, if

the beam intensity is too high, the image may become over saturated, such that the CCD pixels in

other regions (such as at the flow field channels) reach their maximum value or higher.

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Therefore, it is important to ensure that all regions of interest will attenuate the synchrotron light

to roughly the same degree.

As can be seen in Figure 6.2a, the region with the highest level of attenuation, and therefore the

darkest region of the radiograph, is that of the GDL. The Beer-Lambert law states that the

intensity, I, of the attenuated beam can be solved as:

𝐼 = 𝐼0 𝑒− ∑𝜇𝑖𝑋𝑖 ,

where I0 is the incident beam intensity, Xi is the thickness of material, i, in the beam path, and µi

is the attenuation coefficient of that material. With this cell configuration, the GDL and gasket

materials reside in the same plane, and due to the alignment of the cell with the beam, they both

contribute to the attenuation in this region. While attenuation due to the GDL itself is

unavoidable, careful gasket material selection can reduce the attenuation to facilitate a stronger

signal in this primary region of interest. A micro-computed tomography image (Figure 6.6) of

the gasket material employed in this study reveals that the fiberglass fibers strongly attenuate X-

ray light, compared to their PTFE coating, and therefore it is recommended that in future studies,

pure PTFE gaskets are used in lieu of PTFE-coated fiberglass. Once the gasket material is chosen

and the associated beam attenuation can be estimated, the flow field plates can be designed so

that attenuation in the channel regions of the radiograph is comparable.

Figure 6.6 Single cross sectional slice of 3D computed tomograph taken of PTFE-coated fiberglass gasket

material. Brightness values represent X-ray attenuation. The fiberglass bundles in the composite significantly attenuate the signal when compared to the PTFE influence. The scale bar represents 0.25 mm.

6.6.1 Channel alignment

As can be seen from Figure 6.2a, the entire membrane electrode assembly takes on a sinusoidal

shape. This can be explained by the offset between anode and cathode channels. The stress that

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the landings of the flow fields apply to each GDL translates into a displacement of the membrane

from the vertical center plane of the cell. The authors expect that this would not be the case if the

anode and cathode landings were aligned. It is unknown whether this misalignment promotes or

discourages delamination of the GDL from the catalyst layer. Should delamination be caused by

this configuration, the accumulation of liquid water at the interface may be exaggerated due to

the increased volume of low-capillary pressure pore space in the region. In future studies, both

this configuration and the symmetric flow field configuration will be compared.

6.7 Pre-Monochromator Filters

The 05B1-1 beamline consists of a bending magnet source followed by masks, collimators,

shutters, slits, filters and a double crystal Bragg monochromator at 13 m from the source (see

[120,121] for beamline details). The filtering system consists of sheets of aluminum and copper

at various thicknesses that can be placed between the source and the monochromator. While the

filters reduce the intensity of the entire spectrum of the signal, they have a stronger effect on

low-energy light, as attenuation coefficients, in general, decrease with photon energy level. The

filters can improve image quality by decreasing the intensity of the beam that reaches the silicon

crystals of the monochromator. This, in turn, reduces the associated thermal artifacts from the

monochromator, such as the beam position movement reported in [113]. However, the intensity

of the desired photon energy will also diminish with increased levels of filtering. This may lead

to the need for longer exposure times, which can have a negative impact on the signal-to-noise-

ratio of the CCD camera. In future studies, a variety of filter settings will be employed for

finding the proper balance between monochromator related artifacts and CCD noise levels.

6.8 Conclusions

In this work, a study was conducted of dynamic liquid water accumulation and transport in an

operating PEM fuel cell. The primary purpose of this study was to provide insight into the

technique of visualizing liquid water within the individual fuel cell components using

synchrotron X-ray radiography. The normalized images obtained of the high-aspect ratio fuel

cell designed for the experiment provided valuable insight into the formation and transport of

liquid water in a PEM fuel cell. While the performance of the fuel cell was generally lower than

expected, its operation still provided a means to evaluate liquid water accumulation at distinct

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through-plane locations. It was observed that liquid water can accumulate near the interface of

the GDL and catalyst layer. This water was observed to saturate some regions of that pore space

to an estimated 18%, before appearing to spread laterally through the bulk of the GDL.

Future designs of this experiment will be modified to utilize thin, 25 μm-thick membranes which

will reduce the effect of humidity driven thickness changes. In addition to this primary

modification, the flow field plates will be designed to attenuate X-ray light to a similar degree to

the combination of GDL and PTFE gasket materials.

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7 Accounting for Low Frequency Synchrotron X-

ray Beam Position Fluctuations for Dynamic Visualizations

7.1 Abstract

Synchrotron X-ray radiography on beeline 05B1-1 at the Canadian Light Source Inc. was

employed to study dynamic liquid water transport in the porous electrode materials of polymer

electrolyte membrane fuel cells. Dynamic liquid water distributions were quantified for each

radiograph in a sequence, and nonphysical liquid water measurements were obtained. It was

determined that the position of the beam oscillated vertically with an amplitude of ~25 mm at the

sample and a frequency of ~50 mHz. In addition, the mean beam position moved linearly in the

vertical direction at a rate of 0.74 mm s-1. No evidence of horizontal oscillations was detected. In

this work a technique is presented to account for the temporal and spatial dependence of

synchrotron beam intensity, which resulted in a significant reduction in false water thickness.

This work provides valuable insight into the treatment of radiographic time-series for capturing

dynamic processes from synchrotron radiation.

7.2 Introduction

Synchrotron-based X-ray radiography is advantageous for providing nearly parallel

monochromatic beams with high intensities (1011-1015 photons/s/cm2) to obtain radiographs

with high temporal (up to 0.8 s/frame) and spatial (up to 1 μm/pixel) resolutions [30]. It has been

recently employed by a number of researchers to investigate the evolution and distribution of

liquid water in the porous components of polymer electrolyte membrane (PEM) fuel cells

[8,31,61,117,119,122-124]. Readers are referred to a review provided by [125] for a thorough

overview of the various techniques that have been recently employed to visualize PEM fuel cells.

Using synchrotron radiography, the visualization of dynamic liquid water behavior in PEM fuel

cell materials can be achieved with a time-series of radiographs, where the change of liquid

water content between two radiographs can be quantified, assuming that the beam characteristics

remain constant. However, Chattopadhyay [126] reported that synchrotron generated beam

instabilities exist on time-scales ranging from 10-9 to 109 s. For synchrotron based X-ray

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radiography of liquid water in PEM fuel cell materials, where temporal resolutions are on the

order of 1 s/frame and experiments may last from several minutes to an hour, X-ray beam

instabilities with time scales between 10-1 to 104 s may cause artifacts. Such instabilities may be

the result of mechanical vibrations, ground motion, cooling water temperature fluctuations,

electric power cycles, or atmospheric temperature cycles [126]. Additionally, a diffraction-based

monochromator can be employed to select a narrow bandwidth of X-ray energies for imaging

purposes. The high intensity, polychromatic light bombarding the initial monochromator crystal

can create thermal distortions of the crystal, generating instabilities [127] and affecting the

vertical beam position [128,129]. In this paper, we report on the observed time dependent

fluctuations in the beam position that manifested in obtained radiographs of dynamic liquid

water in PEM fuel cell materials, and we present a technique that reduces the effect of these

fluctuations while enabling the quantification of water content.

7.3 Imaging Setup

The analysis presented in this paper is based on X-ray absorption radiograph sequences collected

from PEM fuel cell experiments at the BioMedical Imaging and Therapy Bending Magnet

(05B1-1) beamline at the Canadian Light Source (CLS) synchrotron. The 05B1-1beamline

consists of a bending magnet source followed by masks, collimators, shutters, slits, filters and a

double crystal Bragg monochromator at 13 m from the source [120,121]. The samples were

placed at a distance of ~ 25 m from the source. Absorption radiographs were obtained with a

Hamamatsu C9300-124 (12bit, 10 Megapixel) CCD camera at 10-50 cm from the sample. A

2010 CLS Research Report [130] listed storage ring beam stability to ~ 1 μm vertically and a few

micrometers horizontally.

The optical equipment and camera settings (exposure and gain) chosen provided an exposure

time of 0.9 s and pixel size of 4.5 μm. The photon energy was set to either 23 keV or 25 keV

depending on the experiment. The optical setup was rated to yield a spatial resolution of 10 μm;

however, positions of sharp features in the radiographs could only be determined with an

accuracy of 20 μm. Therefore, from the radiographs, it was not possible to confirm a spatial

resolution of 10 μm.

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7.4 Experiments

The experiments enabled the visualization of liquid water in the gas diffusion layer (GDL) of a

PEM fuel cell. The GDL is a planar, porous component of the PEM fuel cell that often becomes

saturated with liquid water during operation, affecting performance.

Two experiments were closely examined in this work to isolate the behavior of the synchrotron

X-ray beam: a) An in situ study of through-plane water distribution in the GDL of a PEM fuel

cell, and b) an ex situ study of through-plane water distribution in a PEM fuel cell GDL. Figure

7.1a schematically shows the in situ experimental setup and Figure 7.1b shows a typical raw

radiograph. In the ex situ study, liquid water was injected into GDLs compressed in a sample

holder. Figure 7.2a schematically shows the ex situ sample holder and Figure 7.2b a typical raw

radiograph. While both studies were oriented such that the plane of the GDL material was

parallel to the X-ray beam, the in situ study was vertically oriented while the ex situ study was

horizontal.

Figure 7.1 Exploded view of fuel cell components and relative beam direction for in situ experiment (a). Example radiograph of in situ experiment (b).

(a) (b)

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Radiographs were collected at 0.9 s/frame over a period of time to enable the visualization of

dynamic water invasion processes. Imaging was initiated while materials were in a “dry” state,

containing no liquid water, for 2 to 15 minutes. Imaging continued through the “wet” state,

where liquid water entered the GDL. Water content in the GDL was calculated by normalizing

wet-state radiographs to dry-state radiographs using the techniques described in the following

section.

Although Schneider et al. [117] observed that the performance of a fuel cell decreased after

minutes of exposure to synchrotron radiation, it has to be noted that the performance drop was

only observed when the entire active area of a fuel cell was exposed to synchrotron radiation. In

the experiments described in this paper, the entire active area of the fuel cell was not exposed to

synchrotron radiation. However, local effects on the components of the GDL and the PEM fuel

cell that were exposed to synchrotron radiation are, as of yet, unknown.

Figure 7.2 Exploded view of injection apparatus components and relative beam direction for ex situ

experiment (a). Example radiograph of ex situ experiment (b).

(a)

(b)

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7.5 Beer-Lambert Image Analysis

The Beer-Lambert law relates the attenuated intensity with the incident intensity and the

thickness of a single material in the path of an X-ray beam as [31]:

𝐼 = 𝐼0𝑒−𝜇𝑋, 7.1

where 𝐼 is the attenuated intensity, 𝐼0 is the incident intensity of the beam, 𝜇 is the attenuation

coefficient of the material with respect to the beam energy, and 𝑋 is the material thickness. The

intensity of the beam upon passing through the multi-component sample in the dry state is given

by:

𝐼𝑑𝑟𝑦 = 𝐼0 𝑒− ∑𝜇𝑖𝑋𝑖 , 7.2

where 𝜇𝑖 is the material attenuation coefficient, 𝑋𝑖 is the material thickness traversed by the

beam, and 𝑖 = 1...𝑛, where 𝑛 is the number of materials in the path of the beam. Similarly, the

intensity of the beam that passes through the sample in the wet state at time t is given by:

𝐼𝑤𝑒𝑡,𝑡 = 𝐼0 𝑒−(𝜇𝑤𝑎𝑡𝑒𝑟𝑋𝑤𝑎𝑡𝑒𝑟,𝑡+∑𝜇𝑖𝑋𝑖), 7.3

where 𝜇𝑤𝑎𝑡𝑒𝑟 is the attenuation coefficient of the water and 𝑋𝑤𝑎𝑡𝑒𝑟,𝑡 is the thickness of water

with respect to the beam direction at time 𝑡. From Equations 7.2 and 7.3, the following

expression is obtained for water thickness, 𝑋𝑤𝑎𝑡𝑒𝑟,𝑡 in the GDL with respect to dry-state and wet-

state intensity values:

𝑋𝑤𝑎𝑡𝑒𝑟,𝑡 = −[𝑙𝑜𝑔(𝐼𝑤𝑒𝑡,𝑡 /𝐼𝑑𝑟𝑦) /𝜇𝑤𝑎𝑡𝑒𝑟]. 7.4

In this manner, raw wet-state radiographs can be normalized to raw dry-state radiographs.

Equation 7.4 is employed with the assumption that 𝐼0 remains constant with respect to time,

allowing it to be removed when combining Equations 7.2 and 7.3. When the incident beam

changes intensity or position, this leads to the calculation of a non-physical addition or removal

of liquid water from the system. Likewise, false water signals can result from material movement

during an experiment, as 𝑋𝑖 is also assumed to remain constant for all materials other than water,

since the fuel cell apparatus does not contain moving parts. While material movement must be

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minimized by experimental design, the following sections discuss the steps taken to account for

variations in the intensity and position of the incident beam.

It should be noted that the image processing steps presented in this chapter have been improved

upon in the work presented in Chapter 8. Detailed, up-to-date image processing steps can be

found in Appendix B.

7.6 Ring Current Decay

Synchrotron light is an emission resulting from the radial acceleration of electrons travelling at

near-light speeds. Synchrotron facilities maintain a high speed beam of electrons in a storage

ring, and the emitted light intensity is a function of several factors, including the number of

electrons contained in the ring. The electron beam within the storage ring at a synchrotron

facility naturally decreases in current over time and must be replenished regularly. At the CLS,

this decrease in ring current and subsequent light intensity degradation can be assumed to be

linear over short time periods, causing a linear decrease in image intensity. To account for this

linear intensity decrease, subsequent images from the first captured image are corrected via the

following equation:

𝐼𝑡,𝑐𝑜𝑟𝑟 = 𝐼𝑡 (𝐶0

𝐶𝑡), 7.5

where 𝐼𝑡,𝑐𝑜𝑟𝑟 represents the corrected intensity, It is the measured intensity, and Ct represents the

ring current at time 𝑡. 𝐶0 represents the ring current at a reference time, 𝑡 = 0.

7.7 Beam Position Movement

When the obtained radiographs from both the ex situ and in situ experiments were originally

analyzed prior to our observation of beam oscillations, we observed unrealistic water thickness

values (Figure 7.3a) when using a reference dry-state radiograph at time t=0. After

normalization, non-negligible water thickness values (±350 μm) were observed in regions that

were physically constrained and had no access to liquid water, such as the solid graphite or

polycarbonate components of the apparatuses. Therefore, it was determined that either the

illumination source or the imagining system was to causing the artifacts. Most originally

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normalized radiographs in any given sequence were afflicted to some degree by these artifacts;

however, periodically, some normalized radiographs exhibited minimal artifacts (Figure 7.3b).

Such periodic artifacts could be explained with X-ray beam position oscillation.

The incident X-ray beam at the 05B1-1 line has dimensions of 240 mm (horizontal direction) by

7 mm (vertical direction) at the sample location, with the peak intensity, or “hotspot”, near the

center horizontal axis. If the beam position should rise in the vertical direction, for example, the

associated hotspot would also rise, leading to a brightening of the image above the hotspot and a

darkening of the image below the hotspot. From Figure 7.3a, it can be seen that the artifacts were

nearly uniform along the horizontal dimension but were a strong function of vertical position.

Additionally the artifact severity appeared to fluctuate over time.

To demonstrate these fluctuations, average intensity levels from the two positions outlined in

Figure 7.4a were calculated over a period of 3 min and displayed in Figure 7.4b. Regions 1 and 2

are within the graphite block (non-porous component), which was immobile and inaccessible to

liquid water. As can be seen from Figure 7.4a, these regions were located above and below the

vertical position of the hotspot. In the absence of beam position movement, the intensity should

have been constant over time. Instead, it can be seen that the intensity values fluctuated (Figure

7.4b). Region 2 exhibits an inverted intensity pattern compared to Region 1. Specifically, at time

t, when the intensity of Region 1 was increasing, the intensity of Region 2 was decreasing. This

result is consistent with the predicted behavior of vertical beam position movement described

above.

To identify the existence of significant horizontal beam position movement, the intensity data

collected during the horizontally oriented ex situ experiment was examined. As can be seen from

Figure 7.5a, Region 1 and Region 2 were located to the left and right of the horizontal position of

the hotspot. In the absence of beam position movement, the intensity should have been constant

over time. Instead, it can be seen that the intensity values fluctuate (Figure 7.5b). These regions

exhibited the same fluctuations. Specifically, at time t, when the intensity of Region 1 was

increasing, the intensity of Region 2 was also increasing. Analogous to the predicted behavior of

vertical beam position movement, horizontal beam position movement would have created

inverted intensity patterns. Since this is not the case in Figure 7.5, horizontal beam position

movement is considered negligible. It should be noted that for clarity, Region 1 was selected

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with a shorter radial distance to the hotspot compared to Region 2 in order to create an offset in

the intensity values.

Figure 7.3 Radiographs normalized to the first dry-state image in the sequence demonstrating the presence of

high levels of artifacts appearing at some points in time (a), and little to no artifacts are present at others (b).

Figure 7.4 Raw radiograph (a) with two regions (highlighted) selected on either side of the vertical hotspot position where the mean intensity value is to be calculated. Mean intensity values for regions 1 and 2 over

time (b).

(a) (b)

(a) (b)

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Figure 7.5 Raw radiograph (a) with two regions (highlighted) selected on either side of the horizontal hotspot position where the mean intensity value is to be calculated. Mean intensity values for regions 1 and 2 over

time (b).

A homogeneous section of the in situ experimental apparatus that was free of water during the

entirety of the visualization was chosen for examining the behavior of the beam hotspot position

(highlighted in Figure 7.6a). The vertical intensity profile was measured (black line in Figure

7.6b), and an 8th order polynomial was fit to the intensity profile of each frame (red line in Figure

7.6b), and the peak of the polynomial was assumed to represent the vertical position of the beam

hotspot. The peak was calculated for each frame over a period of 3 minutes and displayed in

Figure 7.6c. Oscillatory features of the peak position were present with a period of

approximately 20 s and a range of vertical positions spanning 50 μm. Over an extended period of

time (shown in Figure 7.6d) another trend was seen in the vertical hotspot position behavior,

where a linear fit of the data revealed that the average hotspot position moved vertically at a rate

of 0.74 μm/min.

No calculation has been made of the loss of spatial resolution due to beam position movement,

although such a study would indeed be of interest to the community. However, the effects of the

beam position movement can be mitigated using the techniques described in the following

sections, thereby decreasing such a loss in resolution.

(b)

(a)

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Figure 7.6 Raw radiograph (a) with solid graphite block region (highlighted) used to find the vertical beam

intensity profile. Vertical beam intensity profile (black) with eighth-order polynomial fit overlaid in red (b). Calculated vertical position of the beam hotspot over 3 min (c). Vertical hotspot position versus time (d) for

an extended period (gray), with the linear trend overlaid in black.

7.8 Image Analysis with Beam Position Pairing

Under ideal circumstances (no beam position movement), a single dry-state radiograph could be

used to normalize all subsequent wet-state radiographs. When the beam position is not constant,

one way to address the problem of false water thickness calculations is to normalize wet-state

radiographs to dry-state radiographs obtained at similar beam positions (determined through

hotspot tracking, Figure 7.6). This beam position pairing approach is possible with a sufficiently

large set of dry-state images obtained over a range of beam positions. However, this beam

(a) (b)

(c)

(d)

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position pairing approach was only possible with experiments that involved a vertically oriented

homogeneous region containing the vertical position of the hotspot, free of water during the

entirety of the visualization. When this region is not present in the radiograph, a more general

method is required to account for beam fluctuations.

A second approach to addressing the problem of false water thickness is to characterize the beam

position from the intensity of the false water thickness artifacts when all wet-state radiographs

were normalized by a single dry-state radiograph. A quantity entitled “false water gradient” was

employed to quantify the artifact intensity. To illustrate what is meant by the false water

gradient, consider again Figure 7.3a, where an overall vertical gradient is seen in the normalized

radiograph, displaying calculated water thickness.

For any subsection of a normalized radiograph, the value for the average vertical gradient of

false water thickness can be calculated. Three such subsections were chosen (outlined in Figure

7.7a), the average value of water thickness versus position was calculated (Figure 7.7b), and the

associated vertical water thickness gradient of each region as a function of time is displayed in

Figure 7.7c. The same 3 minute period analyzed in Figures 7.4b and 6c were analyzed for this

demonstration. The calculated vertical hotspot position data from Figure 7.6c was overlaid onto

Figure 7.7c to illustrate the relationship between the gradient values and the vertical hotspot

position. After all images were normalized to the first image, a net-positive change in beam

position produced as a negative vertical water thickness gradient. To illustrate the proportionality

of the vertical water thickness gradient and the beam position, the gradient values were overlaid

onto the position values in Figure 7.7c. Because there was a negative coefficient of

proportionality between these two properties, the gradient data was displayed on an inverted axis

in Figure 7.7c. Figure 7.7 also demonstrates that the region of interest (ROI) chosen for this

analysis can have been that of a highly heterogeneous portion of the radiograph, and was not

restricted to regions corresponding to homogeneous materials that was described before for the

first beam position pair approach. However, as the presence of water may distort the calculated

gradient in wet-state radiographs, it is necessary to choose a relatively dry portion of the

radiograph as the ROI for gradient calculation. Once each radiograph is characterized in terms of

gradient, dry-state radiograph and wet-state radiographs can be paired.

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Figure 7.7 Three regions of a normalized radiograph (a) displaying significant false water artifacts. Region 1 is entirely within the solid graphite block. Region 2 samples a heterogeneous region of the radiograph,

including rib, channel and GDL. Region 3 samples a region of the radiograph well below the vertical position of the hotspot. The mean water thickness values for each of the three regions (solid lines), with a linear fit

(dashed lines) at a single point in time (b). Normalized values of the three regions’ gradients over 3 min

compared with the calculated vertical hotspot position for the same image sequence (c).

7.9 Image Processing Routine

The following automated processing routine was employed:

1. Account for the effects of ring current decay on radiograph intensity using Equation 7.5

2. Characterize the beam position of each radiograph by calculating false water thickness

gradients:

a. Select an ROI for gradient calculations, preferably in the absence of liquid water.

b. Normalize this ROI sequence with the same ROI of a single, arbitrary dry-state

radiograph using the Beer-Lambert law.

c. Label each radiograph with the average vertical water thickness gradient

calculated from the associated, normalized ROI.

(a) (c)

(b)

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3. Pair each wet-state radiograph to the dry-state radiograph with the closest calculated ROI

gradient value from Step 2. Then, apply the Beer-Lambert law to each wet-state

radiograph with the paired dry-state image.

The pairing and normalizing process was automated with a routine written in MATLAB.

To reduce the noise associated with the charge coupled device (CCD) camera, the above

algorithm can be modified to pair the best n dry-state radiographs to a single wet-state

radiograph, where n is the number of dry-state radiographs with similar vertical water thickness

gradients.

Figure 7.8 displays two wet-state radiographs normalized with and without gradient pairing to

demonstrate the effectiveness of this technique. Due to the movement of the average hotspot

position, it is advisable to obtain dry images at various times throughout experiments, since the

range of dry hotspot positions should overlap the range of wet hotspot positions.

The primary difference between the processing routine used for this study and a more traditional

routine is the selection of an appropriate dry-state radiograph for each individual wet-state

radiograph for normalization. Therefore there was no expected loss of spatial or temporal

resolution due to these processing steps. In fact, the resultant spatial resolution was improved

when compared to that of a traditional processing routine, where a single dry-state radiograph

would be employed to normalize the entire sequence. In a traditional processing routine, the

beam positions associated with the majority of the wet-state radiographs would have been poorly

aligned to that of only one dry-state radiograph.

It should be noted that some experimental setups allow the capture of a “bright-field” radiograph,

where the sample is moved away from the field of view. This bright field data is then

incorporated into the normalization routine. However, for the experiments described in this

paper, the apparati were permanently fixed to the sample stage and bright-field data could not be

captured at a time near that of the experiment.

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Figure 7.8 A comparison between radiographs normalized to the dry-state radiograph at t=0 and the same radiographs normalized to the dry-state radiographs with matching false water thickness gradient values.

The pairs of radiographs at the top and bottom provide two examples of this comparison.

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7.10 Conclusions

Artifacts resulting from vertical beam position movement were observed upon processing

radiographs obtained through synchrotron X-ray radiography. Radiograph sequences, captured to

identify the dynamic behavior of liquid water in PEMFC materials were normalized, using the

Beer-Lambert law. Upon tracking the vertical beam position, it was determined that small

oscillations of beam position were present with an amplitude of ~ 25 μm and a frequency of ~ 50

mHz. In addition, the mean beam position was observed to move vertically at a speed of 0.74

μm/min. It was determined that small changes in beam position, measuring 25 μm, could result

in a “false water” signal representing up to ±350 μm of water thickness.

The vertical gradient of this false water artifact was employed to characterize the beam position

of each radiograph in the sequence. Then, instead of normalizing all wet-state radiographs

against a single dry-state radiograph, dry-state and wet-state radiographs were paired with

respect to this gradient. This technique was shown to mitigate artifacts associated with beam

position movement without causing any loss of temporal or spatial resolution, but required a

sequence of dry radiographs whose beam positions sufficiently overlap the beam positions of the

wet radiographs.

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8 Quantifying Percolation Events in PEM Fuel Cell Using Synchrotron Radiography

8.1 Abstract

The distribution of independent water clusters within the gas diffusion layer (GDL) is an

important, yet poorly understood, characteristic of polymer electrolyte membrane fuel cells. A

better understanding of these water clusters would provide ex-situ invasion experiments and two-

phase models with a set of validation criteria that is currently absent from the literature.

Synchrotron based X-ray radiography was employed visualize liquid water emerging from the

polymer electrolyte membrane fuel cell GDL. Droplet formations, entitled “breakthrough” events

originated from either the channel or landing regions of the GDL. The number of breakthrough

events in a given area (breakthrough density) provides insight into the size and number of

independent water clusters evolving within the GDL. Water clusters were found under the flow

field landings more frequently than under the gas channels. Each 1 mm2 of projected GDL area

was found to have 1-2 individual water clusters during most conditions studied, regardless of the

GDL substrate or MPL type. The existence of percolating water clusters under flow field

channels depended on the combination of GDL type and operating conditions employed.

8.2 Introduction

PEM fuel cells employ an electronically conductive porous material, commonly referred to as the

gas diffusion layer (GDL) to allow electrons, heat, and gases to travel to and from

electrochemical reaction sites. These porous materials can become partially flooded due to

condensation creating clusters of liquid water, which can continue to grow as long as the local

environment favors condensation. Using a pore network model of the GDL, Wu et al. [9]

predicted that GDL saturation distributions were highly sensitive to the number of individual

water clusters simultaneously percolating through the GDL from the catalyst layer. While the

footprint of the combined clusters fully covered the sample area, the study showed that lower

overall saturation levels could be predicted when fewer, larger individual water clusters were

assumed.

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Capillary theory suggests that once a growing water cluster reaches the large pore space within a

flow-field channel (point of breakthrough), there can be no further growth by that water cluster

throughout the hydrophobic pore-space of the GDL [9,15,37,38,48]. Additional condensed water

volume will be capillarily pumped to the channel through the breakthrough pathway. The

implication is that individual water clusters within the GDL cannot have multiple,

simultaneously active points of breakthrough into the gas channels. Simultaneously active

breakthrough locations observed by [7,8,131] must arise from multiple, disconnected water

clusters within the material.

Therefore, a concept entitled “breakthrough density” should be explored. Breakthrough density

describes the number of breakthrough locations per unit of projected surface area of the GDL in

an operating PEM fuel cell. This information is relevant when developing experiments and

models that study the expected distribution of liquid water in the GDL. Examples of such

experiments are [69,72,80,106,107,116,132-134], where syringe pumps or water columns were

employed to provide the controlled injection of liquid water into a dry GDL material. While

these ex-situ experiments provided highly valuable and novel insight into the behavior of liquid

water behavior in the GDL, ex-situ studies are prone to limitations from inlet source and sample

size.

In ex-situ liquid water invasion experiments, GDL materials are invaded from a single liquid

water source. With a single liquid water source, only a single percolating water cluster should

arise under capillary dominated flow. Also, in such ex-situ experiments, GDL sample size can

easily become constrained as a result of experimental requirements. In cases such as microscopy

[80,106,132,133] or X-ray micro-computed tomography (μCT) [116], the optical field of view

associated with the desired magnification restricted the sample size. Whereas, in other studies

[69,72,107,134], larger sample sizes were convenient for material preparation and apparatus

design. As a result of various experimental constraints, studied GDL samples have ranged from

4.9 mm2 [116] to 20 cm2 [134]. Despite this large range of sample sizes, only one breakthrough

location would be expected in these ex-situ experiments over the entire sample when a single

inlet liquid water reservoir was used. In contrast to these ex-situ experiments, high breakthrough

densities have been observed during in-situ studies. Breakthrough densities close to 1 mm-2 were

observed in visualizations provided by Ous and Arcoumanis [131] who employed an air-

breathing fuel cell with 5 mm-wide channels to allow for optical observation of gas channels.

117

Manke et al. [8] demonstrated the ability to visualize in-situ breakthrough events using

synchrotron X-ray absorption imaging. They determined that liquid water clusters underneath

flow field landings periodically gave rise to breakthrough events at the corners of

channel/landing/GDL interfaces. By applying a similar methodology, Lee et al. [7] provided a

comparison between GDL materials with and without microporous layer (MPL) coatings. Higher

breakthrough densities were observed in the cell built with MPL-coated GDLs; however, this

high breakthrough density did not appear to have a negative effect on cell performance. The

MPL was theorized as preventing water clusters near the catalyst layer from lateral spreading and

coalescing, thus allowing for more independent water clusters to percolate, while keeping the

catalyst layer accessible to oxygen diffusion.

During PEM fuel cell operation breakthrough densities are typically greater than 1 mm-2;

therefore, single inlet, ex-situ liquid water invasion experiments with GDL samples larger than 1

mm2 most likely possess unrealistic saturation levels and spatial distributions. Predictive

numerical simulations of GDL invasion that can account for arbitrary numbers and distributions

of independent water clusters are vital for understanding the nature of liquid water accumulation

at the interfaces and within the bulk of the GDL.

In this work the spatial densities of breakthrough events in 11 operational PEM fuel cells were

studied in order to gain insight into the nature of disconnected liquid water clusters within the

GDL. Synchrotron X-ray absorption was used to image liquid water droplets dynamically

emerging from the GDL. Six GDL types were studied, and their breakthrough densities are

presented. The number and sizes of water clusters under the gas channels and under the flow

field landings were estimated.

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8.3 Method

8.3.1 Fuel cell materials and assembly

The fuel cell architecture was based on standard 25 cm2 assembly produced by Fuel Cell

Technologies4. It had an active area of 5 cm × 5 cm, a triple serpentine flow field, and 1 mm-

wide channels and landings. This setup was modified by machining the anode flow field pattern

possess a 1 mm offset from the cathode flow field pattern, so that liquid water residing in the

cathode could be deciphered between liquid water residing in the anode. Additionally, 11 mm-

diameter through-holes were added to the metallic end plates and current collectors to limit

unnecessary X-ray attenuation at viewing regions (see Figure 8.1). A detailed description of the

cell architecture can be found in [7].

Figure 8.1 Images of modified 25 cm2 Fuel Cell Technologies PEM fuel cell. Note: Although three viewing holes are present, only the lowermost hole was employed in this study.

All fuel cells assembled for this study were built with catalyst coated Nafion 115 membranes

with platinum loadings of 0.3 mg cm−2 for each electrode (Ion Power, New Castle, USA5).

Silicon gaskets for sealing the MEA were 254 µm-thick and 203 µm-thick, selected to match the

thickness of the GDL used in each cell-build.

4 http://www.fuelcelltechnologies.com/

5 http://www.ion-power.com/

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The assembly pressure was calibrated for each GDL with Fujifilm Prescale pressure film placed

between the flow fields and the GDL/gasketing. During calibration, the bolt torque was

incrementally increased, and the cell was disassembled to facilitate the removal and analysis of

the film in the FPD-8010E Fujifilm Pressure Distribution Mapping System (Tekscan, USA). A

spatial distribution of applied assembly pressure was measured at each torque level. The mean

landing pressure was assumed to be twice the mean pressure for the active area, as landing

regions composed 50% of the total area. Based on repeated trials, this technique provided a

maximum error of 0.2 MPa. An example dataset is displayed in Figure 8.2. For all experiments,

1 MPa ± 0.2 MPa was applied to the GDL/landing interface.

Figure 8.2 Calculated pressures under flow-field landings with respect to bolt torque for Toray TGP-H 090 10 wt% PTFE.

8.3.2 GDL materials

Six GDL types were employed for this investigation. Two GDL types were commercially

available: SGL Sigracet 25BC and Freudenberg H2315 I3 C1. Four GDL types were supplied by

an industrial collaborator, who applied proprietary PTFE and MPL treatments to two

commercially available substrates: Toray TGP-H 090 and Freudenberg H2315. The PTFE

treatment procedure of the Toray materials was slightly altered to allow the collaborator to

compare two application methods, these are labelled as PTFE1 and PTFE2. It should be noted

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that the proprietary MPLs placed on the Toray and the Freudenberg were distinct from each

other.

From the six GDL types, eleven fuel cells (a-k) were built, and some were imaged multiple times

and at multiple temperatures, as shown on Table 8.1.

Table 8.1 GDLs chosen for water visualization study. Each letter represents a single cell

build, where the subscript denotes the number of data sets collected with that cell, at the specified temperature. Cell Temp

Property Name Code 60 ºC 75 ºC

Toray TGP-H 090 10 wt % PTFE1 with no MPL TP1 a1 b1

Toray TGP-H 090 10 wt % PTFE1 with proprietary MPL TP1M c1 d1

Toray TGP-H 090 10 wt % PTFE2 with proprietary MPL TP2M e1 f1

SGL Sigracet 25 BC SPM g1 h1 i2 g1 h1 i2

Freudenberg H2315 I3 C1 FPM1 j1 j1

Freudenberg H2315 with proprietary MPL FPM2 k1 k1

8.3.3 Fuel cell control sequence

Fuel cell operation was controlled with a Scribner 850e fuel cell test station (Scribner Associates

Inc., Southern Pines NC6).

The cell temperature was held constant by resistive heating rods embedded within the aluminum

end plates. Depending on the experiment, the cell temperature was maintained at either 60 °C or

75 °C (measured within the cathode end plate).

A single scripted routine of current density set points and reactant flow rates was developed to

initiate saturation conditions while maintaining potentials above 0.1 V. All studies were

performed after the reactants (hydrogen and air) were brought to 65% relative humidity at the

operating temperature and after the cell had been drying at open circuit voltage for 20 minutes

under high hydrogen and air flow rates (~1 lpm).

6 http://www.scribner.com/

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For the first 15 minutes of the recorded experiment, the current density was increased from 0.0 A

cm-2 to 0.6 A cm-2 in 5 minutes steps of 0.2 A cm-2. During these steps, flow rates of hydrogen

and air were maintained at 0.7 lpm and 1.2 lpm, respectively. These high flow rates were used in

order to retain dry conditions during the current steps. After 5 minutes at 0.6 A cm-2 the air flow

rate was decreased to maintain a stoichiometric ratio (λC) of 1.4 for 20 minutes, and then dropped

even further to maintain a stoichiometric ratio of 1.1 for 15 minutes. Following this step, the

hydrogen flow rate was decreased to reach an anode stoichiometry (λA) of 2.8, while the cathode

stoichiometry increased to 1.4. These conditions were chosen based on previously successful

observations of dynamic liquid water accumulation and transport [7].

A detailed schematic of the experiment is provided in Appendix A.

8.3.4 Beamline controls

All experiments described in this work were performed at the Biomedical Imaging and Therapy

Beamline (05B1-1) of the Canadian Light Source Inc. (CLS) (Saskatoon, Canada). The CLS is a

third generation 2.9 GeV synchrotron facility. The 05B1-1beamline consists of a bending magnet

source followed by masks, collimators, shutters, slits, filters and a double crystal Bragg

monochromator located 13 m from the source [120,121]. The samples were placed an additional

distance of ~ 12 m from the monochromator. Absorption radiographs were obtained with a

Hamamatsu C9300-124 (12 bit, 10 Megapixel) CCD camera combined with an AA40 imaging

unit. A10 μm-thick Gd2O2S:Tb scintillator was used. The scintillator of the imaging unit was

positioned 10 cm from the sample. This distance was minimized to reduce phase contrast related

artifacts and to improve image sharpness. This setup provided a spatial resolution of 10 µm.

Beam filter settings in this experiment were set to maximize the flux of monochromatic X-rays.

From the tested energy range of 16 keV to 35 keV, it was found that the most vivid normalized

image of water in the fuel cell was achieved with an energy level of 18 keV. Pre-monochromator

filtering was minimized (0.2 mm aluminum) to reach the most desirable image of liquid water in

the fuel cell.

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8.3.5 Data collection

8.3.5.1 Voltage data

The primary performance output of the fuel cell test station was the cell voltage, measured

continuously throughout the experiment and recorded every second. An example voltage

response to the current and flow rate set points is provided in Figure 8.3.

Figure 8.3 Voltage response to current and flow rate set-points for an example cell build (SGL Sigracet 25BC,

60 ºC). Δ’s denote points used for time-synchronization with the image collection process.

8.3.5.2 Image data

The camera and beam settings allowed for images to be acquired at a maximum rate of 1 fps;

however, this temporal resolution was not necessary for observing breakthrough events. To

decrease file size an acquisition rate of 0.3 fps was achieved by applying frame integration.

The imaging sequence was initiated, followed by the test station script. To synchronize the image

data with the test station data, frame numbers were recorded at distinct points during the

experiment. These points are denoted with a Δ on the horizontal axis of Figure 8.3.

Image normalization was performed to identify and quantify the liquid water distribution. Figure

8.4 illustrates the possible configurations of the imaging setup. With the X-ray shutters, closed

(Configuration I), a dark field image can be taken. Configuration II is often used in radiography

for flat field corrections; however in this experiment, Configuration III was employed to

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additionally account for the attenuation due to static fuel cell components. Configuration IV

represents an operational fuel cell, generating water.

Figure 8.4 Illustration of possible configurations of imaging setup. Sequences of images were taken in Configurations I, III, and IV for the processing steps highlighted in Section 2.6.

8.3.6 Image normalization

X-ray light is attenuated by any material in its path, including air. Due to the chemical

composition and density of a material, the degree to which the material attenuates can vary. A

relationship has been developed to predict the intensity of attenuated light, based on the work of

mathematicians August Beer and Johann Heinrich Lambert through the Beer-Lambert law [31].

The Beer-Lambert law relates the attenuated intensity of any light source with the thickness of a

single material in the path of the light beam as [31]:

𝐼 = 𝐼0𝑒−𝜇𝜒, 8.1

Incident light

No light

Incident light

Incident light

Attenuated light

Detector

I. For dark field correction

III. Alternative to II

II. For typical flat field

IV. Dynamic

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where 𝐼 is the attenuated intensity, 𝐼0 is the incident intensity of the beam, 𝜇 is the mass

attenuation coefficient of the material with respect to the wavelength of the light, and 𝜒 is the

material thickness. Because attenuation coefficients vary with light wavelength, it is convenient

for quantification purposes to employ monochromatic light.

Several factors had to be accounted for before the quantitative liquid water distribution was

obtained with the Beer-Lambert law. First, all CCD cameras suffer from some amount of “dark

current,” which results in a small, relatively steady signal measured in each pixel, which

becomes added to the signal produced by X-ray intensities. Second, synchrotron illumination

sources decrease with intensity over time due to the continuous escape of electrons from their

storage rings. Third, the illumination source (the X-ray beam) was observed to slowly fluctuate

in vertical position by up to 20 µm [113]. And finally, there is a distribution of signal intensity

across the raw image which masks the attenuation signal of the water. This is due to a

combination of the beam intensity distribution, local attenuation from static fuel cell

components, and the distribution of scintillator/detector sensitivity levels across the image.

A detailed description of these normalization steps can be found in Appendix B.

8.3.7 Surface and edge breakthrough quantification

Breakthrough events were classified into two types: “surface breakthrough” and “edge

breakthrough.” Surface breakthrough events are described as water emerging in the middle of the

channel forming circular droplets that are most likely the result of liquid water condensing in the

channel region of the GDL or CL. Edge breakthrough events are described as semi-circular water

droplets emerging into the channel from the triple line formed by the channel, landing, and GDL.

Edge breakthrough events could be either the result of water condensing onto the base of the

landing, within the GDL, or percolating from the GDL/CL interface. An illustration describing

the breakthrough types is provided in Figure 8.5.

The local conditions and current densities within a PEM fuel cell can vary greatly from inlet to

outlet [135]. In the following study, only 4% of the total active area was visualized, and although

the average current density was constant, the local current density was expected to fluctuate with

humidity levels and local flooding.

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Figure 8.5 An illustration of a fuel cell cross section (a) with droplets of water forming on the surface of the GDL and at the edge of the gas channels, and a corresponding illustration of visualized water (b) with “edge” and “surface” breakthrough locations annotated. Note that the anode flow field channels are offset from the

cathode.

8.4 Results

8.4.1 Visualized liquid water

Each of the 18 data sets listed in Table 8.1 corresponded to a ~1000 frame sequence of

normalized images that displayed the liquid water distributions throughout the testing procedure.

Figure 8.6 displays six water distributions of an example data set, where both surface and edge

breakthrough events were present. The greyscale values represent a range of measured water

thicknesses from -0.2 mm (black) to 0.6 mm (white). Negative values are shown to demonstrate

artifacts from the monochromator, scintillator, or cell movement.

In the data set associated with Figure 8.6, liquid water was barely visible until the final stage

(λA=2.8, λC=1.4) of the experiment, where the anode flow rate decreased. Within 90 seconds of

this operating condition (by t = 2790), new breakthrough events were visible in the centers of the

2nd and 3rd cathode channels. As can be seen in Figure 8.6, a typical observation was that

126

breakthrough events were not observed in the anode gas channels (offset from the cathode gas

channels).

Figure 8.6 Six frames from the final stage (λA=2.8, λC=1.4) of an example experiment (GDL: Toray TGP-H 090 with 10 wt % PTFE1 and proprietary MPL. Cell temperature: 75 ºC). Greyscale values correspond to

thickness levels of liquid water, scaled between -0.2 mm and 0.6 mm. The positions of three cathode channels

are highlighted on the left. For scale, each channel width is 1 mm.

8.4.2 Breakthrough density

The breakthrough densities were calculated over a 40 mm2 active area, representing 20 mm2

channel and 20 mm2 landing. The 1000+ image sequence of each experiment was carefully

inspected, and individual breakthrough locations were marked and categorized as either

“surface” or “edge”. These results are shown in Table 8.2.

1

2

3

1

2

3

t = 2700 s t = 2790 s t = 2880 s

t = 3150 st = 3060 st = 2970 s

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Table 8.2 Breakthrough (BT) density data for each data set. Cells are shaded according to their relative breakthrough densities.

Cell Build

GDL Code

Temp (C)

Surface BT

Density (mm-2)

Edge BT

Density (mm-2)

Mean BT

Density (mm-2)

BT Type Fast Anode

Flow (λa = 6.6)

BT Type Slow Anode

Flow (λa = 2.8)

a TP 75 0.8 1.4 1.1 Edge Edge + Surface

b a TP 75 0.4 2.8 1.6 Edge Edge + Surface

c TP1M 75 7.2 2.6 4.9 Edge + Surface Edge + Surface

d a TP1M 75 3.2 3.6 3.4 Edge Edge + Surface

e TP2M 75 2.4 2.2 2.3 Edge Edge + Surface

f a TP2M 75 0.2 2.0 1.1 Edge Edge + Surface

g SPM 60 1.8 3.4 2.6 Edge Edge + Surface

g SPM 75 0.0 4.0 2.0 Edge Edge

h a SPM* 60 3.2 2.8 3.0 Edge + Surface Edge + Surface

h a SPM* 75 2.4 3.2 2.8 Edge Edge + Surface

i SPM 60 2.6 3.6 3.1 Edge + Surface Surface

i SPM 75 0.0 2.6 1.3 Edge Edge

i SPM 60 2.6 2.4 2.5 Edge + Surface Edge + Surface

i SPM 75 0.0 3.4 1.7 Edge Edge

j FPM1 60 1.6 1.8 1.7 Edge + Surface Surface

j FPM1 75 0.0 2.2 1.1 Edge Edge

k FPM2 60 0.0 3.4 1.7 Edge ---

k FPM2 75 0.0 3.0 1.5 Edge ---

a cell was built in a secondary, nearly equivalent, cell assembly

8.5 Discussion

8.5.1 Water cluster size limits

The number and sizes of individual water clusters within the GDL is valuable information for

researchers attempting to recreate realistic GDL saturations, either in simulations or with ex-situ

experiments. Although the image resolution was not sufficient to confidently identify the

outlines of individual water clusters within the cathode GDL, the breakthrough density values

reported in Table 8.2 can be combined with basic principles of capillary behavior to provide

limits to the minimum number of water clusters and the maximum size of the average water

cluster. Following from the description of capillary behavior in the Introduction, the following

assumptions can be made:

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1) Any n simultaneously active breakthrough locations correspond to n isolated water

clusters.

2) Any n simultaneously active water clusters in a given area, A, should not, on average,

have individual projected areas larger than A/n, otherwise these clusters would have

likely coalesced during the percolation process.

3) A single water cluster with an active breakthrough location must be supplied by at least

one condensation source of liquid water.

4) There are at least as many active condensation “sources” in the system as there are

simultaneously active breakthrough locations.

5) Low breakthrough density could either indicate few active condensation sites, or large,

connected water clusters.

From the sequence of assumptions above, the following conclusions have been made, based on

the results shown in Table 8.2.

On average, there should be at least one isolated water cluster per square millimeter of

GDL.

In one extreme case, an average of 7.2 water clusters per millimeter were observed to

simultaneously percolate from underneath the flow field gas channels.

Clusters should not have an average footprint greater than 1mm2 and are sometimes at

least as small as 0.14 mm2.

Most observed breakthroughs appeared on the edge of the channel, indicating that most

individual water clusters resided under the landings. This can either indicate higher

condensation rates under the landings, or that there was less tendency for clusters to

coalesce under the compressed regions of the GDL.

When studying effects of GDL saturation on its effective transport properties, simple ex-situ

saturation methods are prone to misrepresent the distribution of water in the GDL due to the

challenges of producing multiple, isolated water clusters in relatively large GDL samples.

In single inlet ex-situ liquid water invasion experiments, breakthrough positions have been

observed to, on occasion, migrate over time [106,107]. Therefore, the values reported in Table

8.2 may include some double counting of single water clusters, and may not perfectly capture the

129

number of “simultaneously active” breakthrough locations per unit area. However, there may

have been breakthrough locations not captured in this analysis, if the droplets did not grow large

enough to be observed over the noise and resolution limits of the imaging setup.

8.5.2 Temperature effects

Fuel cells made with the SGL and Freudenberg materials were imaged at both 60 ºC and 75 ºC.

With one exception, surface breakthrough was not visualized during any experiments at 75 ºC.

This indicates that condensation under the channels was influenced by operating conditions. It is

interesting to note, that all fuel cells made with Toray materials were imaged at 75 ºC, and

surface breakthrough events were consistently observed in these fuel cells. In fact the highest

breakthrough density observed, 7.2 mm-2, was during a 75 ºC experiment (cell c).

Temperature did not seem to have a noticeable effect on edge breakthrough densities, and

therefore no conclusions can be made in this work about water cluster size in relation to

operating temperature.

8.5.3 Anode flow rate

As the reactant streams were only 65% humidified, faster anode flow rates allowed the anode to

more aggressively contribute to product water-removal through the back-diffusion across the

membrane.

With only one exception, surface breakthrough in cells made with Toray materials only appeared

during slow anode flow rates, while edge breakthrough events continued even with high anode

flow rates. This indicates that water clusters under landings were less affected by back diffusion

than those under gas channels. This might indicate that condensation in Toray GDLs under flow

field channels occurred in proximity to the membrane where back diffusion could play a role in

water removal. This trend was not observed in the other material types. This indicates that the

GDL type had a strong influence in the role of back diffusion in the water balance of the fuel

cell.

130

8.6 Conclusions

In this study, synchrotron based X-ray radiography was employed to visualize and quantify

liquid water percolation events, entitled “breakthrough events”, within a 40 mm2 viewing area of

a 25 cm2 PEM fuel cell. This data allows approximations to be made of water cluster sizes and

distributions within the GDL.

Breakthroughs were classified as either “surface” or “edge” depending on whether they emerged

from the GDL surface region or the edge of the cathode flow field channels, respectively.

Surface breakthroughs were assumed to result from water clusters located under the flow field

gas channels. Edge breakthroughs were assumed to result from water clusters located under the

flow field landings. With this assumption, it was determined that condensation under the

landings can be expected in practically all of the tested operating conditions and GDL types.

Condensation under the channels was also common, but seemed to be less frequent with the

Freudenberg GDLs studied and less frequent at high anode flow rates.

Because high breakthrough densities required tightly packed, independent water clusters within

the GDL, the observation of high breakthrough densities fundamentally limited water cluster

sizes. Water clusters within the GDL rarely consist of footprints larger than a square millimeter,

with a minimum size corresponding to 7 or more water clusters present in a single square

millimeter. These results should be taken into account when developing ex-situ GDL saturation

studies, as well as in two-phase, pore-scale models.

131

9 Conclusions and Recommendations

In this thesis, pore network modeling was proposed as an ideal modeling technique with which to

investigate the relationship between morphology and liquid water saturation in PEM fuel cell

GDLs. It was proposed that topologically representative pore networks extracted from

stochastically modeled GDLs would provide the best network architecture for such modeling.

Finally, it was proposed that synchrotron based in situ visualizations of dynamic liquid water

behavior would produce the best means of validating the inlet assumptions of pore network

modeling invasion algorithms. As a founding member of the research group, my research

contributions consist of developing the sophisticated tools that will be used in such a modeling

endeavor. These tools include a comprehensive 3D stochastic model of the GDL, as well as the

development of the fuel cell architectures, experimental routines, and post processing routines

necessary to visualize dynamic liquid water behavior at the Canadian Light Source, Inc.

synchrotron.

9.1 Conclusions and Contributions

Pore network modeling was identified in Chapter 2 as an ideal modeling tool for capturing the

capillary force dominated behavior of liquid water cluster percolations in the GDL. Chapter 3

provided a 2D pore network modeling study of the effects of the characteristic non-uniform

through-plane porosity distributions identified in our earlier work [54]. It was found that:

Through-plane porosity distributions can be recreated in stochastic models of the GDL.

The characteristic peaks and valleys present in the porosity distributions of thick carbon

fiber papers promote highly saturated regions at the local maxima of the porosity

distribution. This was due to the lateral invasion encouraged by the capillary barriers of

neighboring local minima.

Porosity distribution effects can be differentiated from GDL thickness effects by using a

consistent computational domain aspect ratio for all material types.

The inlet surface porosity has a drastic effect on GDL saturation, where a 58-76%

reduction in saturation results from a positive porosity gradient (in contrast to a

conventional negative gradient).

132

In Chapter 4, a number of GDL geometrical fiber and MPL properties were identified and

characterized for informing representative 3D stochastic models. It was found that:

Carbon fiber diameters of the GDL substrate vary with manufacturer, yet tight property

distributions around their mean values are observed.

Fiber pitch in Toray TGP-H 090 GDL is minimal (2.44°).

36% of fibers in Toray TGP-H 090 belong to bundles of co-aligned fibers.

Volume fractions of constituent GDL elements of known density were estimated from a

comparison of areal weight values with and without associated treatments.

The cracks formed in the MPLs of two GDL types were characterized in terms of

frequency and diameter.

The 3D stochastic modeling algorithm presented in Chapter 5 was the first of its kind to

incorporate experimentally observed through-plane porosity distributions, fiber diameters, fiber

pitch distributions, and fiber co-alignment. A necessary emphasis was given to generating the

correct number and volume of fibers. Methods for characterizing the heterogeneity and pore size

distributions of the modeled materials were presented. A parametric study of fiber diameter and

volumetric binder fraction was conducted. It was found that:

3D stochastic models of the GDL could be made to match experimentally observed

through-plane porosity distributions.

Material heterogeneity and pore size distributions were shown to be useful methods when

characterizing the pore space of the material, since each parametric combination

generated distinct, consistent profiles corresponding to each method.

Both fiber diameter and binder fraction were demonstrated to have strong effects on both

material heterogeneity and pore size distributions.

Similar effects on the pore space can be achieved by either increasing the fiber diameter

or by increasing the binder fraction, since nearly indistinguishable materials can be

generated with complementary adjustments of these two parameters.

In Chapter 6 and 7, the methodology for capturing and processing synchrotron radiography

images of dynamic, in situ liquid water behavior was presented. Some of these techniques were

133

specific to the Canadian Light Source, Inc. synchrotron, in Saskatoon SK, at which our group

conducted the first such PEM fuel cell experiments. It was found that:

The primary sources of data artifacts are: membrane swelling, un-even X-ray attenuation

by the various fuel cell components, and vertical beam position movement.

To minimize membrane swelling, thin, 25 µm-thick membranes should be used.

For in-plane oriented X-ray studies, PTFE gaskets without fiberglass reinforcement were

proposed to minimize unnecessary attenuation, while flow-field plate dimensions can be

adjusted to create similar attenuation levels in the GDL and the gas channels.

The vertical position of the X-ray beam was tracked and determined to oscillate

irregularly with amplitudes of ~ 25 µm and frequencies of ~ 50 mHz.

Vertical beam position movement was identified as creating gradient artifacts on

normalized images. The intensity of these gradient artifacts was found to directly

correlate with the vertical beam position and could therefore be used to pair appropriate

wet and dry images taken at similar beam positions.

Preliminary observations of liquid water from in-plane imaging demonstrated liquid

water accumulating near the interface of the GDL and catalyst layer. This water was

determined to represent an average local saturation value of 18%.

In Chapter 8, the size and distribution of liquid water clusters in the GDL was investigated for

the first time. Using through-plane oriented synchrotron X-ray radiography, regions of 40 mm2

of active area were imaged. Percolation events, labeled “breakthroughs” were categorized and

counted for a range of GDL types and operating conditions. It was found that:

Water clusters percolated from under the landings in nearly all of the tested operating

conditions and GDL types.

Water clusters only percolated from under the channels in certain combinations of GDL

types and operating conditions. The studied Freudenberg GDLs were less prone to

exhibiting percolation from under the channels.

It was observed that applying a high anode flow rate could frequently prevent percolation

from under the channels, indicating that back diffusion was playing a major role in the

removal of water condensing under the channels.

134

Independent water clusters were determined to be tightly distributed in regions promoting

condensation, as breakthrough densities were observed to be consistently greater than one

breakthrough per mm2 and sometimes as high as 7 per mm2.

It was concluded that ex situ invasion experiments as well as pore network models should

attempt to mimic the observations of tightly packed, independent water clusters in order

to generate realistic saturation distributions.

In summary, this thesis presents a new state-of-the-art in terms of 3D stochastic modeling of

paper GDLs, from which topologically representative pore network models can be generated.

Additionally, the Canadian Light Source, Inc. synchrotron was demonstrated to be capable of

generating high-resolution imaging of dynamic liquid water transport in the GDL. The data

collected from the visualization studies can be used to validate the inlet assumptions of future

pore network modeling simulations.

9.2 Future Work

To continue on this stream of research, it is recommended that:

Additional materials are analyzed in terms of fiber pitch and co-alignment, as high

resolution tomographs of those materials become available.

Mercury intrusion porosimetry data is collected for comparison to the simulations in

Chapter 5.

A model of the MPL that incorporates appropriate volumes and crack distributions is

developed and added to the current stochastic model developed in Chapter 5.

A pore network extraction algorithm similar to the one demonstrated in [21] is applied

and validated. This algorithm must capture pore and throat size information for capillary

simulations, pore connectivity, and the conduit (pore + throat + pore) geometrical

information relevant to single-phase transport modeling.

A pore network based investigation is conducted that isolates the possible inlet conditions

producing breakthrough densities similar to those observed in Chapter 8, while producing

through-plane liquid water distributions similar to those observed in Chapter 6. These

inlet conditions will act as the new standard for pore network based two phase

simulations.

135

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Appendix A

Fig

ure A

.1. S

chem

atic o

f the fu

el cell testin

g eq

uip

men

t used

for th

is experim

ent.

(Chap

ters 6-8

)

144

Appendix B

The image acquisition from chapters 6-8 resulted in a sequence of 16-bit images, exportable to

TIFF format, where the brightness values of each pixel in the image provide an intensity map,

denoted as 𝐼𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑[𝑥, 𝑦, 𝑡]. The following steps were taken to transform the intensity map to a

water thickness map.

B.1 Dark Current Correction

A measure of the dark current present in the CCD camera used in this study was made by

collecting a sequence of dark frame images before each set of experiments. A dark frame image

is obtained by imaging while the safety shutter is closed (Figure 8.4, configuration I), preventing

X-rays from entering the experimental room. A minimum of 20 such images are taken, and

averaged, resulting in 𝐼𝑑𝑎𝑟𝑘[𝑥,𝑦]. The values of this averaged dark field image were subtracted

from every image in the experiment to result in:

𝐼𝑛𝑒𝑡[𝑥,𝑦, 𝑡] = 𝐼𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑[𝑥, 𝑦, 𝑡] − 𝐼𝑑𝑎𝑟𝑘[𝑥,𝑦]. B.1

B.2 Linear Intensity Correction

Due to the relatively short length of each experiment, the storage ring could be assumed to lose

current linearly and the X-ray beam intensity can be expected to also decrease linearly with time.

A proportional measure of the loss in beam intensity over the course of the experiment can be

made with the average value of 𝐼𝑛𝑒𝑡[𝑥,𝑦, 𝑡] at the first and last frame (Figure 8.4, configuration

III) of the experiment. These are denoted as �̅�𝑛𝑒𝑡[𝑡0] and �̅�𝑛𝑒𝑡[𝑡𝑒𝑛𝑑], respectively.

The ratio, 𝑓𝑒𝑛𝑑 = �̅�𝑛𝑒𝑡[𝑡0]/�̅�𝑛𝑒𝑡[𝑡𝑒𝑛𝑑], represents the scaling factor that would need to be

multiplied to each pixel of 𝐼𝑛𝑒𝑡[𝑥,𝑦, 𝑡𝑒𝑛𝑑] to make the first and last frames comparable.

Additionally, the function, 𝑓[𝑡], represents this scaling factor for each time step between 𝑡0 and

𝑡𝑒𝑛𝑑, where 𝑓[𝑡𝑒𝑛𝑑] = 𝑓𝑒𝑛𝑑 and 𝑓0 = 𝑓[𝑡0] = 1. The possible water in the images keeps us from

being able to similarly calculate 𝑓[𝑡] for all the images in the series, therefore we assume a linear

transition from 𝑓0 and 𝑓𝑒𝑛𝑑, and interpolate to find 𝑓[𝑡] for all points between.

145

The intensity data of each image in the sequence is scaled to be comparable to the original

image:

𝐼𝑎𝑑𝑗𝑢𝑠𝑡𝑒𝑑[𝑥,𝑦, 𝑡] = 𝑓[𝑡] 𝐼𝑛𝑒𝑡[𝑥,𝑦, 𝑡]. B.2

B.3 Beam Position Correction

The vertical position of the X-ray beam fluctuates with time. To account for this unsteady

source, for each image of 𝐼𝑎𝑑𝑗𝑢𝑠𝑡𝑒𝑑[𝑥,𝑦, 𝑡] five dry state images were found with comparable

beam positions, using the technique described in Chapter 7. These five images were averaged,

and associated with the time stamp of their corresponding 𝐼𝑎𝑑𝑗𝑢𝑠𝑡𝑒𝑑[𝑥, 𝑦, 𝑡] image, generating a

data set denoted as 𝐼𝑎𝑑𝑗𝑢𝑠𝑡𝑒𝑑,𝑑𝑟𝑦[𝑥,𝑦, 𝑡] with the same dimensions as 𝐼𝑎𝑑𝑗𝑢𝑠𝑡𝑒𝑑[𝑥,𝑦, 𝑡].

B.4 Flat Field Normalization

The thickness of liquid water can now be quantified using the Beer-Lambert Law as:

𝜒𝑤𝑎𝑡𝑒𝑟[𝑥,𝑦, 𝑡] =

ln(𝐼𝑎𝑑𝑗𝑢𝑠𝑡𝑒𝑑[𝑥,𝑦,𝑡]

𝐼𝑎𝑑𝑗𝑢𝑠𝑡𝑒𝑑,𝑑𝑟𝑦[𝑥,𝑦,𝑡])

−𝜇𝑤𝑎𝑡𝑒𝑟, B.3

which takes into account the beam intensity distribution, fuel cell components, and the

heterogeneities in the scintillator and detector.

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