The Pennsylvania State University. The Graduate School. Department of Mechanical and Nuclear Engineering

Transcription

1 The Pennsylvania State University The Graduate School Department of Mechanical and Nuclear Engineering CHARACTERIZATION OF INTERFACIAL STRUCTURE IN PEFCS: WATER STORAGE AND CONTACT RESISTANCE MODEL A Thesis in Mechanical Engineering by Tushar Swamy 2009 Tushar Swamy Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science May 2010

2 The thesis of Tushar Swamy was reviewed and approved* by the following: Matthew M. Mench Associate Professor of Mechanical Engineering Thesis Advisor Emin C. Kumbur Thesis Coordinator Assistant Professor of Mechanical Engineering Drexel University, PA Liming Chang Professor of Mechanical Engineering Thesis Reviewer Karen A. Thole Professor of Mechanical Engineering Head of the Department of Mechanical Engineering *Signatures are on file in the Graduate School

3 iii ABSTRACT In this work, an analytical model of the micro porous layer (MPL) and the catalyst layer (CL) interface under elastic compression is developed to investigate the effects of the MPL CL interfacial morphology on the ohmic and mass transport losses at the MPL CL interface in a polymer electrolyte fuel cell (PEFC). The model utilizes experimentally measured surface profile data as input. Results indicate that the uncompressed surface morphology of mating materials, elasticity of PEFC components and local compression pressure are the key parameters that influence the characteristics of the MPL and CL contact. The model predicts that a 50% drop in the MPL and CL surface roughness may result in nearly a 40% drop in the MPL CL contact resistance. The model also shows that the void space along the MPL CL interface can potentially store significant amount of liquid water (0.9 to 3.1 mg/cm 2 ), which could result in a performance loss and reduced durability. A 50% drop in the MPL and CL surface roughness is expected to yield nearly a 50% drop in the water storage capacity of the MPL CL interface. The results of this work provide key insights that enhance understanding regarding the complex relation between MPL CL interfacial structure and cell performance. Additionally, an upgraded (fractal) model is formulated to simulate the bi-polar plate (BP) diffusion media (DM) interface. The fractal model can potentially provide a better estimate of the aforementioned results when applied to the MPL CL interface. Either model is capable of digitally reconstructing the MPL CL interfacial morphology via control volume allocation, which can be incorporated into a macroscopic fuel cell model to facilitate a more accurate prediction of PEFC performance.

4 iv TABLE OF CONTENTS LIST OF FIGURES... v LIST OF TABLES... vii NOMENCLATURE... viii ACKNOWLEDGEMENTS... xi Chapter 1: INTRODUCTION History of Fuel Cells Operating Principles of a PEFC Components of a PEFC Background Interfacial Contact Modeling in PEFCs Interfacial Contact Modeling in Tribology Objectives of this Study Chapter 2: MICRO POROUS LAYER CATALYST LAYER INTERFACIAL CONTACT MODEL Introduction Method of Approach Experimental Model Formulation Surface Profile Characterization Contact Model for Smooth and Rough Surface Contact Model for Two Rough Surfaces Results and Discussion Chapter 3: BI-POLAR PLATE DIFFUSION MEDIA INTERFACIAL CONTACT MODEL Introduction Model Formulation Surface Characterization Fractal Contact Model Elastic-Plastic Regime of Contact Spots Surface Load and Separation Size Distribution of Contact Spots Chapter 4: SUMMARY AND CONCLUSIONS Chapter 5: FUTURE WORK REFERENCES... 52

5 v LIST OF FIGURES Figure 1-1. Operating principle of a fuel cell [2] Figure 1-2. A typical fuel cell polarization curve [3] Figure 1-3. Components of a fuel cell [4] Figure D schematic of the MPL CL interfacial contact Figure 2-1. Contact geometry at a single summit on a rough surface with a smooth surface Figure 2-2. Verification plot of area of contact (AC) and dimensionless separation (DS) versus the applied load, comparing current model results with the data reported in literature [40] Figure 2-3. Predicted MPL CL contact resistance (CR) versus applied compression pressure Figure 2-4. A typical MPL CL interface cross-section Figure 2-5. Predicted MPL CL contact resistance versus compression pressure for different degrees of MPL and CL roughness Figure 2-6. Effect of the Young's modulus of the backing DM layer on the predicted MPL CL contact resistance for homogeneous compression pressure of 1.5 MPa (under a typical land) Figure 2-7. Predicted MPL CL contact resistance versus the summit density on the MPL surface Figure 2-8. Predicted MPL CL contact resistance (CR) as a function of the distance (x) under one set of land (L) and channel (C) affected due to inhomogeneous compression Figure 2-9. Effect of the compression pressure (CP) on the maximum water content in the MPL CL interfacial gaps Figure Quantification and location of liquid water in a PEFC (Figure adapted from [92]) Figure Impact of the Young's modulus of DM on the maximum liquid water content in the MPL CL interfacial gaps Figure Effect of the variation in MPL and CL surface roughness on the maximum water content in the MPL CL interfacial voids for a range of applied compression pressures

6 vi Figure 3-1. Smooth and rough surface contact Figure 3-2. Geometry of a contact spot of length scale l

7 vii LIST OF TABLES Table 2-1. Measured surface roughness data of MPL and CL samples Table 2-2. Properties of various materials

8 viii NOMENCLATURE z Z Height of asperity (mm) Analytical representation of the surface profile data j Complex number, ( 1 ) p P d θ R E i Compression pressure (MPa) Compression load (kg) Surface mean plane separation (mm) Probability Radius (mm) Young s Modulus, (i = 1, 2) (MPa) ν i Poisson s ratio, (i = 1, 2) ρ i σ Resistivity, (i = 1, 2) (Ω.mm) Standard deviation or surface height (mm) D Density of summits on the surface (mm -2 ) g Conductance (mω -1.cm -2 ) r Resistance (mω.cm 2 ) f υ Gaussian distribution Normal distribution m Spectral moment, (i = 0,2,4) (mm (i-2) ) α λ Bandwidth parameter Roughness (μm) a Area of contact spot (m 2 ) F Fractal dimension of surface profile

9 ix G K l L n(a) δ σ y Fractal roughness parameter (m) Factor relating hardness to yield strength Length scale of an asperity or contact spot (m) Characteristic length of a surface profile (m) Size distribution of contact spots of area a Amplitude of deformation of an asperity (m) Yield strength of softer surface (Pa) ϕ Material property, σ y /E γ Scaling parameter for the W-M function S Power of the profile spectrum (m 3 ) ω Frequency or reciprocal of length scale (m -1 ) Subscripts eq o sum m q t a c f h l Equivalent Contact (single) Summit Average Root mean square Maximum height of the surface Apparent or nominal critical fraction Higher cut-off Lower cut-off

10 x p r s Plastic Real Smallest spot Superscripts * Non-dimensional form Acronyms PEFC MPL CL BP DM Polymer electrolyte fuel cell Micro porous layer Catalyst layer Bi-polar plate Diffusion media

11 xi ACKNOWLEDGEMENTS I would like to thank my advisor Dr. Matthew Mench for his time and patience. I greatly appreciate the opportunity to work on an interdisciplinary project involving plentiful learning as well as peer interaction. This project has provided me with knowledge and experience that will help me achieve my career goals, for which I am grateful. Dr. E. C. Kumbur, was a crucial part of this project s success. He was involved in all steps of this study, including planning, advising, and most importantly, mentoring me through times of hardship and success. I would like to thank Dr. Liming Chang, Professor of Mechanical Engineering at The Pennsylvania State University for providing useful insight and support in developing the interface model. I also greatly appreciate his time in reviewing this study. I would also like to thank Dr. Manish Khandelwal for his guidance and support during the initial stages of this project. My sincere appreciation goes out to my lab mates Erinç Hizir, Hemant Bajpai, and Michael Manahan for their unabated help and support, and most of all for the countless productive discussions that we have had during the course of the project. I am grateful indeed.

12 Chapter 1 INTRODUCTION This chapter discusses the history, operating principles and components of a polymer electrolyte fuel cell (PEFC). This chapter also explains the purpose of the study, and provides the necessary background required for a clear understanding of the underlying concepts herein. 1.1 History of Fuel Cells A fuel cell is an electrochemical cell that converts a source fuel into an electrical current and water. It generates electricity inside a cell through reactions between a fuel and an oxidant, triggered in the presence of an electrolyte. The reactants flow into the cell, and the reaction products flow out of it, while the electrolyte remains within it. Fuel cells can operate virtually continuously as long as the necessary flows are maintained. Fuel cells are different from conventional electrochemical cell batteries in that they consume reactant from an external source, which must be replenished a thermodynamically open system. Hydrogen (H 2 ), the most typically used fuel in proton exchange membrane fuel cells (PEFCs), is the most abundant element in the universe, and therefore is considered to be a potential long-term energy source for the fuel cell engines. As an efficient conversion technology, fuel cells have great potential to contribute to addressing energy challenges that the world faces today. They will have a significant role to play in a number of energy end-use sectors, from electric vehicles to power plants. With the potential for high power density and efficiency, fuel cells hold the most promise for powering future portable, automotive and stationary.

13 2 Only in the recent past has the fuel cell technology been put into practical use. The fuel cell was first demonstrated, however, in February 1839 by a Welsh scientist and barrister Sir William Robert Grove [1]. In 1955, W. Thomas Grubb, a chemist working for the General Electric Company (GE), further modified the original fuel cell design by using a sulphonated polystyrene ion-exchange membrane as the electrolyte. Three years later another GE chemist, Leonard Niedrach, devised a way of depositing platinum onto the membrane, which served as catalyst for the necessary hydrogen oxidation and oxygen reduction reactions. GE went on to develop this technology with NASA and McDonnell Aircraft, leading to its use during Project Gemini [1]. This was the first commercial use of a fuel cell. In the middle 1980s, research on PEFCs became active again because of breakthroughs in electrolyte material and catalyst technology. Developments of proton exchange membranes based on stable sulphonated fluoropolymers greatly lengthened the lifetime of PEFCs. In the early 1990s, the carbon supported platinum catalyst was invented by a group at Los Alamos National Laboratory [1]. These improvements provided an impetus to PEFC research, which were further fuelled with the intention of developing highly efficient PEFC systems for various terrestrial applications. Today, the PEFC is considered to be the primary alternative to the internal-combustion engine in future automotive applications. Additionally, PEFC systems are fast proving their worth as stationary power plants as well. 1.2 Operating Principles of a PEFC A fuel cell operates much like a commercial battery. A fuel cell has an anode side and a cathode side, as shown in Fig The difference in activity of the reactants creates a potential difference across the two electrodes, namely the anode and cathode. In a PEFC, hydrogen gas or fuel is supplied to the anode side as fuel through the flow channels, while an oxidizer such as oxygen or air enters the cathode side in the same manner. The flow channel is open to the

14 3 Diffusion Media (DM), so the reactant gas can diffuse to the catalyst electrode surfaces (active electrochemical sites) through the DM in both electrodes to meet with the platinum (Pt) particles, which act as a catalyst for the electrochemical reaction [1]. Figure 1-1. Operating principle of a fuel cell [2]. At the anode, hydrogen is split by an electrochemical oxidation reaction into hydrogen ions, H +, and electrons, e -. The semi-permeable polymer membrane is conductive to H + ions, but it does not allow electrons to pass through. The electrons must flow through an external circuit, producing useful current. The electrons passing through the external circuit reunite with H + ions and O 2 molecules to participate in the electrochemical reduction reaction at the cathode catalyst layer. As a result, water and waste heat are generated at the end of overall reaction. The electrochemical reactions that occur at the respective electrodes are as follows [1]: Anode Reaction: Cathode Reaction: 2H 2 4H + + 4e [1-1]

15 O 2 + 4H + + 4e 2H 2 O [1-2] 4 Overall Reaction: H O 2 H 2 O [1-3] The typical performance curve of a PEFC and the current density regions, where each loss dominates are as shown in Fig The performance of a PEFC is characterized by three main kinds of polarization losses, which are [1]: i. Activation polarization ii. iii. Ohmic polarization Concentration polarization iv. Cross-over polarization Figure 1-2. A typical fuel cell polarization curve [3]. The activation polarization represents the rate of an electrochemical reaction controlled by sluggish electrode kinetics in the low current density region. Similar to chemical reactions,

16 5 electrochemical reactions in fuel cells also involve an activation energy that must be overcome by the reacting species. This energy loss due activation energy requirements manifests itself as a drop in the electrode potential which is termed as activation polarization [1]. Ohmic polarization is caused by the limited ionic conductivity of the membrane, the electrical resistance of the DM, the micro porous layer (MPL), the catalyst layer (CL) and the current collector plates (bi-polar plates). In addition, due to the small length scales of fuel cell components, the inherent contact resistance at the various component interfaces in a PEFC also contributes to the ohmic polarization [1]. Concentration polarization represents the mass transport limitations of the reactant gases to the reaction sites at high current densities. At high current density operations, the amount of generated water vapor increases. Due to the low operating temperature (~80 C) and humidification of reactant gases, the generated water condenses, and blocks the available pores of the DM. As a result, the transport of reactant gas species to the active reaction sites in the catalyst layer is mitigated. This diffusive limitation in the DM results in a concentration difference between the catalyst surface and the DM, and subsequently causes a reduced electrode potential [1]. The final type of loss that occurs in a PEFC is the fuel cross-over loss. Since hydrogen can be easily transferred from anode to cathode through the membrane due to the high concentration gradient across the electrodes, such crossed-over fuel does not release its electrons, which normally go through the external circuit, but instead reacts with oxygen at the cathode catalyst layer directly. This leads to a reduction in electrochemical reaction rate, therefore decreasing the cell voltage and efficiency [1].

17 6 1.3 Components of a PEFC A polymer electrolyte fuel cell consists of a polymer based electrolyte, catalyst layers, bipolar plates (BP), and anode/cathode materials which consist of a porous DM coated with a micro porous layer. Figure 1-3 shows the typical components of a PEFC. An ion conducting solid polymer membrane (Polyperfluorosulfonic acid membrane) is typically used as the electrolyte in PEFC systems [1]. The DM is a thin layer of carbon cloth or paper with a thickness ranging from 180 μm to 450 μm. The DM serves to transport the reactants from the flow channels to the catalyst sites. The DM also assists in removing the reaction products from the reaction sites to the flow channels. Additionally, it conducts the electrons from the catalyst layer to the current collecting land, while mechanically supporting the electrolyte. Often, to enhance water transport, a highly hydrophobic coating called the micro porous layer is applied to the DM, resting between the DM and the CL. This layer has an average pore size somewhere between that of the CL and the DM [1]. Figure 1-3. Components of a fuel cell [4].

18 7 The catalyst layer consists of a platinum powder (~2 nm in diameter) usually supported by larger carbon particles with a diameter of 45 to 90 nm. An average loading of mg/cm 2 of platinum catalyst is used on both anode and cathode for enhancing the electrochemical reaction [1]. Pt particles are heterogeneously coated on the surface to increase the active surface area required for electrochemical reactions. The membrane, the DM and the CL assembly is often referred to as the membrane electrode assembly (MEA). The bi-polar plate includes gas flow channels, which are machined through one side of the bi-polar plate. The bi-polar plates are made of an electrically conductive material, usually graphite or coated metal with an average thickness of 2 mm, and they serve to distribute the reactants through the overall assembly and transport the electrons from anode to cathode, while providing robustness and support for the overall cell assembly [1]. 1.4 Background Knowledge and comprehension of the existing literature in the field of the proposed work is an essential part of the research study, prior to its implementation. Therefore, a thorough literature survey was performed and is summarized in the following sub-sections Interfacial Contact Modeling in PEFCs Owing to the potential for high power density, high efficiency, and relatively emission free operation, there has been an increased interest in the usage of polymer electrolyte fuel cells (PEFCs) as a power source for various applications, as mentioned earlier. However, certain performance limiting aspects of the technology are yet to be fully explained and optimized. In particular, ohmic and mass transport losses can originate at the various interfaces that exist between the fuel cell components, which include the micro porous layer and the catalyst layer (MPL CL) interface, the micro porous layer and the diffusion media (MPL DM) interface, and

19 8 lastly, the diffusion media and the bipolar plate (DM BP) interface. Due to the inherent roughness of the surfaces that form these interfaces, the contact between the materials under compression is imperfect, which results in a loss of contact area and the formation of interfacial gaps between the surfaces, as shown in Fig The improper contact not only give rise to an electronic contact resistance, but can also lead to liquid water pooling in the interfacial void space. This water pooling effect, or film formation, is important as it could play a pivotal role in blocking the reactant gas transport, promoting mass transport losses. Therefore, it is necessary to investigate the impact of the ohmic and liquid water transport losses at the various interfaces to better understand water management and performance loss distribution in PEFCs. Surface 1 d Contact regions Mean plane of Surface 1 Mean plane of Surface 2 Surface 2 Figure D schematic of the MPL CL interfacial contact. There are many modeling studies in the literature that investigate the impact of the BP [5-9], CL [10-14], DM [15-18], and MPL [18-24] on ohmic and mass transport losses in a PEFC; however, these studies do not consider a distinct interfacial regions, modeled using a separate set of control volumes. They apply numerical boundary conditions, such as flux and concentration matching, at the bordering control volumes in the two layers that form the interface. By preventing the independent treatment of the various interfaces that exist in a PEFC, the unique physical characteristics of the interfacial regions are neglected. There exist a few experimental studies that have focused on interfacial losses [25-30], however, only a couple of studies have

20 9 dealt with the MPL CL interface in particular [29, 30]. Although a few numerical studies have attempted to incorporate the DM CL interface (DM without MPL) into the modeling framework [31,32], these models neglect the geometry of the DM and CL surfaces; instead they consider a lumped/macro representation of the resulting interface. A few studies have attempted to model the DM BP interfacial contact resistance in a PEFC [28, 33-36], some of which take the average morphology of the mating surfaces into consideration as well [28, 35, 36]. However, to the best of the authors knowledge, there is no study reported in the literature that utilizes the actual MPL CL interface morphological structure to estimate the contact losses and associated performance drop due to the resulting imperfect contact. Additionally, even though the BP DM interface has been dealt in the existing literature, there exists no study that strives to determine the effect of BP DM interfacial morphology on PEFC performance Interfacial Contact Modeling in Tribology As mentioned earlier, despite the importance of these contact interfaces in dictating PEFC performance, little is understood or yet published in PEFC literature regarding the interfacial characteristics, such as the role of the interfacial morphology, compression, and material properties on the specified interfacial regions. However, interfacial modeling has been extensively studied in the field of tribology and electrical contact mechanics. At the outset, H. Hertz pioneered the theory of elastic contact between spheres under load in Thereafter, several attempts were made to understand the nature of rough surface contact, but the fundamental theories to explain the interfacial phenomena between two rough surfaces in contact were first developed by Holm (1958) in the field of electrical contact mechanics [34], and by Bowden & Tabor (1954, 1964) in the related subject of friction [38]. These theories suggested that even if the applied load is in the elastic region, the local stresses at the interfacial contacts would be so high that the asperities would deform plastically. However, in 1957, Archard [39]

21 10 objected to the aforementioned argument, and suggested that although it is reasonable to assume plastic flow in the early stages of compression, but after sufficient operation time, a steady state must be reached, in which the load is supported elastically. Archard s theory [39] implied that in most cases, asperities deform elastically, and plasticity sets in subsequently if extremely rough surfaces are compressed under high load. Thereafter, in 1966, Archard s concept was utilized by Greenwood and Williamson [40], who pioneered an approach (GW model) to model the elastic contact between two rough surfaces to span the entire mating area, which is still widely used today. The GW model is based on the Hertzian theory of isolated contact and probabilistic modeling techniques to account for the stochastic nature of the mating surface profiles. However, one major drawback of the GW model is that it does not provide an approach to evaluate all of the input parameters for the contact model. The resolution of this drawback occurred in 1971, when Nayak [41] recognized the applicability of the pioneering work in statistical geometry by the oceanographer Longuet- Higgins [42], and facilitated a method to evaluate the required input parameters for the GW model. Nayak s statistical approach [41], when combined with the GW model, provides a useful tool to simulate the contact between rough surfaces with known surface profile information. Many numerical studies utilize the GW approach [43-49]. However, these models require the contacting surfaces to be isotropic, and are valid only in the region of elastic contact. As an added approximation, the models consider the contacting asperities on the surfaces to be largely separated, neglecting the interaction between them. Although most interfaces with small real area of contact reasonably satisfy these approximations, further development of the basic model was necessary to simulate the contact between anisotropic surfaces, and the interfaces that contained both elastic and plastic deformation.

22 11 Not all engineering surfaces are isotropic in nature; therefore, some models [50-52] were developed in order to simulate the contact between anisotropic rough surfaces. Yet, these studies limit themselves to the elastic contact region, whereas in reality, in addition to elastic contact, there may be some plastic deformation in the contacting asperities as well. Thereafter, numerous numerical studies [53-62] have attempted to simulate contact interfaces which contain elasticplastic deformation regions. Even though these models exhibit higher accuracy compared to the previous models, yet, they failed to address the interaction between neighboring asperities on a surface via which, agglomerates are formed out of growing number of contacts adjacent to each other. Although this phenomenon was included in a few numerical studies [63-67], nonetheless, complete justification of experimental evidence has yet to be provided. A comparison of some of the widely used contact models, based on Greenwood and Williamson s approach [40], is given in [68]. The GW model is based on roughness characteristics of the contacting surface profiles, and it is argued in [69, 70], that these roughness metrics are sensitive to the adopted sampling interval of the measuring instrument. This issue has brought some concern to the researchers in this field, and prompted the development of alternate models to simulate rough surface contact. It is argued in several numerical studies [70-79] that the surface profiles of most engineering surfaces is fractal (property of self-similarity) in nature, and hence, they utilize fractal geometry modeling techniques to simulate the contact interface. These models are not based on the roughness of the surface profiles and hence, are independent of the sampling interval of the measuring instrument. Majumdar et. al. [71, 72] has developed a fractal interfacial model which accounts for the elastic-plastic nature of contact and also considers the influence of neighboring asperities on each other. A corresponding contact resistance model based on fractal contact theory has been developed by Majumdar et. al. [73]. However, besides being complicated compared to

23 the GW model, results of the fractal geometry based contact models may not show a significant improvement in accuracy relative to the GW model. 12 Another class of contact models, based on the finite element technique [80-83], was developed to model the interfacial contact. Although, the existence of finite element software makes the development of these models favorable, however, similar to the case of fractal geometry based simulations, the accuracy of these models is questionable. Essentially, the suitability of a contact model for a particular simulation is decided based the desired level of accuracy, acceptable levels of complexity, the applied load, and the nature of the materials in contact. 1.5 Objectives of this Study This study is motivated by the need to gain a better understanding of interfacial contact characteristics in a PEFC via considering the actual mating surface morphology and contact characteristics. The specific objectives of this study are the following: 1. To develop and implement an analytical model that can predict the MPL CL contact resistance losses and the potential water accumulation capacity of the MPL CL interface for different set of materials under compression. 2. To formulate an upgraded analytical model to simulate the BP DM (or the MPL CL) interface in order to better estimate the corresponding contact resistance losses and water accumulation capacity under compression. 3. Either model must be capable of digitally reconstructing the MPL CL interfacial morphology via control volume allocation, which can be incorporated into a macroscopic fuel cell model to facilitate a more accurate prediction of PEFC performance.

24 13 Chapter 2 MICRO POROUS LAYER CATALYST LAYER INTERFACIAL CONTACT MODEL This chapter presents the implementation details of the MPL CL interfacial contact model. Model results and discussion on contact resistance and water storage implications due to the MPL CL interface are also discussed in this chapter. 2.1 Introduction As mentioned earlier, the contact between the MPL and CL surfaces is often imperfect due to the inherent roughness of the surfaces. This results in a loss of contact area and the formation of interfacial gaps between these two surfaces. The improper contact not only give rise to an electronic contact resistance, but can also lead to liquid water pooling in the interfacial void space. This water pooling effect is important as it could play a pivotal role in blocking the reactant gas transport to the active sites in the CL, promoting mass transport losses. Therefore, it is necessary to investigate the impact of the MPL CL interface to better understand water management. Clearly, out of the existing interfaces, the MPL CL interface carries especially high importance due to its direct influence on the electrode structure and performance. Since little is understood or yet published regarding the MPL CL interfacial characteristics, major emphasis in this study was placed on understanding the role of the interfacial morphology, compression, and material properties on this MPL CL interfacial region. In order to model the MPL CL interface, the GW model [40, 41] is adopted to simulate the resulting contact. An application of the aforementioned models to simulate the current scenario is possible since these models depend only on the surface profile characteristics and

25 material properties. However, it is necessary to obtain reliable surface profile statistics prior to model implementation Method of Approach The MPL CL interface model presented herein requires three key input parameters, which are a function of the MPL and CL surface profile characteristics [40]. These parameters can be statistically evaluated if the discrete surface profile data of the two surfaces are known [41]. For this purpose, optical profilometry was used to obtain the MPL and CL surface profile data [85]. Detailed information regarding the optical profilometry measurements can be found in [85], however, for the sake of continuity, a brief description of the measurement technique and the corresponding results are given below within the context of the interface model formulation presented in this study Experimental The surfaces of catalyst layers from membrane electrode assemblies and MPL of carbon paper type diffusion media (SGL 10BB) were investigated separately to generate the corresponding surface profile characteristics. Optical profilometry was used to quantify the surface roughness and morphology of these samples. The key advantage of this imaging technique is that it can perform high vertical resolution, quantitative and damage-free measurements of broad areas without any direct contact with the surface of interest. Details of this technique and measurement procedures are provided in [85]. Prior to making measurements using optical profilometry, it is necessary to select an appropriate sampling interval to obtain accurate surface profile data. A detailed analysis given in [84] discusses the issue concerning the choice of a suitable sampling interval required to accurately measure the roughness of a given surface. It is argued in

26 15 [84] that a much larger value of sampling interval compared to the root mean square (RMS) roughness of the surface indicates excessive smoothening of the surface, which is undesirable. Furthermore, a much smaller value of the sampling interval relative to the RMS roughness of the surface indicates that sufficient short-wavelength content is not filtered, resulting in sharp local peaks on the captured profile. This inclusion is unnecessary, since the plastic deformation of these localized peaks does not impact the overall characteristics of the elastic contact morphology [84]. Therefore, for relatively accurate surface roughness measurements, it was suggested that the measurement sampling interval should be proportional to the nominal RMS roughness of the surface [84]. Contextually, for the MPL and CL samples tested in [85], the average RMS roughness of the MPL and CL surfaces was determined to be 7.39 µm and 3.63 µm respectively via using a profiling instrument with a sampling interval of 0.82 µm in the x-direction and 0.95 µm in the y-direction along the surface [85]. These results indicate that the sampling interval of the profiling instrument and the roughness of the MPL and CL surfaces obtained are within an order of magnitude apart, suggesting a reasonably accurate and appropriate surface roughness measurement. Measurements show that both MPL and CL exhibit rough surface characteristics, having irregularities such as large valleys and deep cracks. However, the MPL surface is found to be rougher in nature compared to the CL surface [85]. The difference between cracks or deep cuts in the CL and MPL surfaces should be distinguished from interfacial voids, which can occur as a result of surface roughness, regardless of the presence of cracks. It is important that the various surface characteristics of the sample be quantitatively distinguishable and isolated, therefore, surface profile information of a cracked CL was obtained. The cracked CL consists of intentionally widened and/or deepened cracks, relative to the existing cracks on the regular CL. This exacerbation of crack width/depth may be accomplished either by accelerated coating of the CL slurry, or by excessive heat treatment to remove the volatile components in the slurry. The

27 16 thickness of the MPL and CL were determined to be 80 μm and 30 μm, respectively. Table 2-1 lists the MPL and cracked CL surface roughness metrics that were measured for the tested samples via optical profilometry. Table 2-1. Measured surface roughness data of MPL and CL samples. (Arithmetic mean values ± standard deviation of measurements [85]) Average RMS Crest-Trough Sample Roughness, λ a Roughness, λ q Roughness, λ t (µm) (µm) (µm) MPL 5.35± ± ±19.95 Cracked CL 2.19± ± ± Model Formulation The discrete surface data from optical profilometry measurements were first converted to a continuous representation, which is fed into the model to evaluate certain characteristic surface parameters of the MPL and CL. These MPL and CL surface parameters are then combined to obtain the three key parameters required as input to the MPL CL interface model. The model formulation is divided into the following steps: a) Surface profile characterization. b) Contact model for smooth and rough surface. c) Contact model for two rough surfaces. These steps in the modeling procedure are explained in detail in the following sections.

28 Surface Profile Characterization In order to obtain the required interfacial morphology input parameters for the MPL CL contact, a continuous mathematical representation of the discrete surface profile data of the two surfaces is necessary. For this purpose, the Discrete Fourier Transform (DFT) algorithm was utilized to represent the discrete measured data as a sum of sine and cosine series. Since the DFT algorithm is a commonly adopted procedure, details of the algorithm have been omitted from this text. A comprehensive description of the DFT algorithm can be found in [86]. Representative cross-sections of the measured MPL and CL discrete surface profile data were chosen from [85], and fed into the DFT algorithm as input. Consequently, continuous representations of the MPL and CL surface profiles, Z MPL (x) and Z CL (x), respectively, are obtained as output Contact Model for Smooth and Rough Surface Figure 2 represents the contact between a smooth surface and a single summit on a rough surface, showing the undeformed summit and its deformed shape when a load, F, is applied. In order to apply the GW model to the present case, the porosity of the contacting media at the MPL CL interface is neglected, since the pore sizes are significantly less than the morphological features observed. Additionally, all MPL CL contacts are approximated to be elastic, and the contact points are largely separated so that the interaction between them can be neglected.

29 18 Load (P) Non-deformed shape (z-d) Deformed Shape R o R z d Smooth surface Mean summit plane of the rough surface z height of asperity d surface mean plane separation R radius of summit R o contact radius Figure 2-1. Contact geometry at a single summit on a rough surface with a smooth surface. The MPL and CL surfaces are inherently rough with asperities distributed more or less randomly over the entire surface. According to the Hertzian theory of elastic contact [40-41, 47, 68], the load, P, on a single summit (Fig. 2-1) of height, z, and radius, R, can be evaluated as: P = 4 3 E eq R 1 2(z d) 3 2 z > d [2-1] and E eq = 1 υ υ 2 2 E 1 E 2 1 [2-2] where R is the radius of the summit before deformation, d is the surface mean plane separation, υ i and E i (i = 1, 2) are the Poisson s ratio and Young s modulus of the two materials in contact, respectively. Equation (2) represents the effective Young s modulus as E eq. Approximating the current flow across the interface to be independent due to the relatively large separation between asperities; the electrical contact conductance for a single contact can be defined as [37]:

30 g c = 19 4R o ρ 1 + ρ 2 [2-3] and R o = R z d [2-4] where R o is the deformed contact radius of the summit and ρ i (i = 1, 2) is the electrical resistivity of the materials in contact, as shown in Fig Since Eq. (2-1) and (2-3) are derived for a single asperity in contact, it is necessary to extend the theory to the entire surface encompassing all the asperities. As described, three key statistical parameters that characterize the rough surface must be evaluated and incorporated into Eq. (2-1) and (2-3), which are then integrated over the whole surface. The randomly distributed asperities on the given rough surface are approximated to be spherical in shape with a constant radius, R, and with a Gaussian probability distribution that can be defined as [40, 68]: 1 f z = ς sum 2π e z 2 2ς 2 sum [2-5] where σ sum represents the standard deviation of summits. The probability, θ, that a randomly selected summit has a height in excess of the surface separation, d, can be expressed as: θ z > d = f z dz d [2-6] It is clear that the load, P, is a function of the random variable z. The average value of a function of a random variable is obtained by integrating the product of the function and the probability density of the random variable over the domain of the random variable. Therefore, averaging the load, P, over the entire surface area and evaluating the compression pressure, p, by multiplying the resulting expression with the density of summits on the surface, D sum, gives: p = d 4 E 3 eq D sum R 1 2 z d 3 2f z dz [2-7]

31 20 Note that the average compression pressure is approximated to be uniform over the MPL CL contact interface being simulated. Similarly, integrating the electrical contact conductance in Eq. (2-3) over the entire contacting surface gives: g = 4 D ρ 1 + ρ sum R 1 2 z d 1 2f z dz 2 d [2-8] Now, consider the normal probability distribution function, υ(x), which can be written as: φ x = 1 x 2 2π e 2 [2-9] To simplify the integration in Eq. (2-7) and (2-8), the equations are written in terms of the normal probability distribution function, υ(x). Additionally, the height variables are scaled for numerical convenience using σ sum. After some mathematical manipulation, the following equations are obtained: p = 4 3 E eq D sum R 1 2ς sum 3 2F3 2 d ς s [2-10] 4 g = D ρ 1 + ρ sum R 1 2ς sum 2 1 2F1 2 d ς s [2-11] r = 1 g [12] where r is the contact resistance, and: F n t = t x t n φ x dx [13] where the function in Eq. (2-13) is evaluated by expressing it in terms of the parabolic cylinder functions, U(a,t) [87], as:

32 21 F n t = n! 2π U(n + 1 2, t) e t 2 4 [2-14] It is clear from Eq. (2-10), (2-11) and (2-12) that the compression pressure, p, and the contact resistance, r, are a function of the material properties (E eq and ρ i ), and the three main statistical properties of the mating surfaces (D sum, R and σ sum ). The material (electrical) properties of the MPL and CL are given in Table 2-2. In order to establish the choice of a suitable value of Young s modulus as an input to the model, attention must be diverted to the classic problem of bearing contact in tribology, to which the current model was originally applied [40-41, 47, 68]. In reality, it is known that no surface is perfectly clean. All material surfaces have a coating of particles (lubrication material, oxide material, dust etc.), and therefore, there always exists a layer of finite thickness on the base material. Even though the Hertzian relations are derived for the materials in direct contact (the thin layer coatings), contact between bearing surfaces has been modeled using the current formulation with reasonable success, while neglecting the existence of the layer coatings. The key to this modeling triumph lies in the concept of relative dimensions, where it is argued, that if the layer coating is relatively thin compared to the thickness of the bearing material, bulk of the total deformation occurs in the bearing material. Therefore, the mechanical properties (Young s modulus) of the layer coating may have little impact on the mechanical contact characteristics (such as interfacial separation, d) of the interface under load (although the electrical interfacial characteristics still depend on the layers in direct contact). Drawing a parallel between the MPL/CL interfacial contact and the bearing contact, it is argued that the MPL/CL is relatively thin compared to the DM. Therefore, as an approximation, the Young s modulus of the DM is chosen as an input to the model. The severity of the approximation depends on the relative dimensions and the relative Young s modulus of the DM, when compared to the MPL/CL. Since the relative dimensions are known to be relatively small,

33 22 attention must be focused on the relative Young s modulus of the DM. For a given compression pressure, a smaller Young s modulus of the DM, relative to that of the MPL/CL, would imply a much larger relative strain (which equates to larger relative deformation) in the DM. Therefore, the approximation of selecting the Young s modulus of the DM as input may result in a smaller error, if the Young s modulus of the DM is smaller relative to that of the MPL/CL. As an added approximation, the Young s modulus of TGP-H-060 is used as model input (Table 2-2), since the Young s modulus of SGL 10BB has not been reported in literature. Although the manufacturing process of the two DMs are different, both TGP-H-060 and SGL 10BB are carbon paper type DMs, and essentially consist of a similar fused carbon fiber matrix [88, 89]. Both DMs also have similar porosities (~0.8), contain a similar weight percentage of Teflon material (~ 5% wt.) [88, 89], and therefore, it is argued that the Young s modulus of the two materials may lie within an order of magnitude apart. The error in the approximation will depend on factors influencing the manufacturing process, such as heat treatment etc. A parametric study on the Young s modulus of the DM is performed in order to determine its impact on the MPL CL contact resistance. Table 2-2. Properties of various materials. Properties Material Value Units Young s Modulus [90] DM 10,000 MPa Electrical conductivity [91] (through plane) MPL 300 S.m -1 Electrical conductivity [91] (through plane) CL 200 S.m -1 Hereafter, since the material properties have been chosen, evaluation of these main statistical parameters (D sum, R and σ sum ) is necessary to solve the model equations. In order to

34 23 evaluate these parameters, the following statistical manipulation is performed based on ref. [41]. Consider Z(x), which is the continuous mathematical expression that represents the surface profile. At this juncture, the MPL and CL surfaces are approximated to be isotropic. The autocorrelation function (ACF), A(x), is defined as [41]: 1 A x = lim L 2L 0 L Z x Z x + j dj [2-15] where L is the length of the profile. The power spectral density function (PSDF), Φ(k), can be defined as the Fourier transform of the ACF as [41]: φ k = 1 2π A(x)e 2πikx N dx [2-16] where k is the set of wave numbers of the spectral components that constitute the surface profile. The spectral moments, m 0, m 2 and m 4, of the PSDF are defined as [41]: m i = k i φ k dk i = 0,2,4 [2-17] The bandwidth parameter, α, which depends on the shape and the extent of the spectrum of the roughness profile, is defined as [41]: α = m 0m 4 m 2 2 [2-18] It was shown in [41] that the approximate values of the parameters R, σ sum and D sum can be expressed solely as a function of the spectral moments (m 0, m 2 and m 4 ) and the bandwidth parameter α. The corresponding relations are shown below: R = 3 8 π m [2-19]

35 ς sum = α m [2-20] D sum = 1 6π 3 m 4 m 2 [2-21] Contact Model for Two Rough Surfaces It has been shown that the contact of two rough surfaces is negligibly different from the contact of a smooth and an equivalent rough surface [43, 44]. Hence, given the values of m 0, m 2 and m 4 of the two rough surfaces in consideration i.e. the MPL and CL surfaces, the corresponding values for the equivalent rough surface can be computed in terms of their respective sums, i.e. m 0 eq = m 0 MPL + m 0 CL [2-22] m 2 eq = m 2 MPL + m 2 CL [2-23] m 4 eq = m 4 MPL + m 4 CL [2-24] and the equivalent bandwidth parameter, (α) eq, can be written as: α eq = m 0 eq m 4 eq m 2 eq 2 [2-25] Optical profilometry data from different locations on the MPL and CL samples were taken to ensure that the entire surface morphology is accurately captured [85]. The surface profile data corresponding to different cross-sections of the MPL and CL surfaces are sequentially fed into the model as input. The equivalent values of m 0, m 2, m 4 and α, are evaluated and substituted into Eq. (2-19), (2-20) and (2-21) to obtain the statistical parameters R, σ sum and D sum, which are

36 25 averaged over numerous locations on the tested samples to cover the entire surface morphology. Using the equivalent surface parameters shown above, the rough-rough surface contact problem is solved using the equations for a smooth-rough surface contact derived in the previous section. Since the compression pressure applied to the fuel cell is known, the surface separation, d, can be evaluated from Eq. (2-10). Knowing the surface separation, d, the conductance, g, and subsequently, the MPL CL interfacial resistance, r, can be evaluated from Eq. (2-11) and (2-12), respectively. 2.3 Results and Discussion Prior to conducting a parametric study of the MPL CL interface, variation of the area of contact and the dimensionless separation versus the applied load (Fig. 2-2) for a different contact problem given in [40], were simulated for verification. Figure 2-2 shows a comparison between the model results in literature and the current model predictions for the case given in [40]. The results from the model in literature and the current model show excellent agreement, indicating that the model developed in this study can successfully simulate the resulting contact interface between the two materials in consideration, as predicted by the model formulation.

37 26 Area of contact (mm 2 ) DS: Model result DS: Model result from literature [40] AC: Model result AC: Model result from literature [40] Dimensionless separation (d/ Load (kg) Figure 2-2. Verification plot of area of contact (AC) and dimensionless separation (DS) versus the applied load, comparing current model results with the data reported in literature [40]. Reverting back to the MPL CL contact, Fig. 2-3 depicts the variation of the MPL CL contact resistance as a function of the applied compression pressure in a PEFC. A comparison of the model prediction (via using actual measured cross-sections of the MPL and CL surfaces) and experimental results reported in [29] is also presented in Fig Although the DM used for the numerical simulation and the experimental data are from different manufacturers (SGL 10BB for model predictions and TGP-H-060 for the experiments [29]), a comparison between the results is reasonably justified due to the following arguments: a) Young s modulus of the TGP-H-060 is used as model input, which is also the DM used for the experiment. Therefore, the difference in the dependence of the simulation and the experimental results on the material property of the DM is eliminated.

38 27 b) The SGL 10BB comes with a pre-coated MPL by the manufacturer, whereas the TGP-H-060 was coated with an MPL for the purpose of the experiment. However, both materials having similar material properties as well as similar average roughness values of approximately 8 µm [85, 49]. It must also be mentioned that the data in [29] consist of combined MPL CL contact resistance and bulk MPL resistance. Based on a basic ohm s law calculation, the maximum bulk resistance of the MPL (under no compression) is determined to be 2.67 mω.cm 2 approximately [1]. Therefore, to enable a better comparison between the experimental and modeling results, two simulation curves, one consisting of only the MPL CL contact resistance, and the other consisting of MPL CL contact resistance and maximum bulk MPL resistance combined, are presented in Fig 2-3. Figure 2-3 clearly shows that the model predictions and the experimental results are in good agreement, indicating that the MPL CL contact resistance is significantly high at low compression, which can exist under the channel. This observation can be attributed to the fact that, as the compression pressure is reduced, a lower number of asperities located on the MPL and CL surfaces come into contact. The loss in contact points can impede the electron flow across the interface, thereby resulting in an increased MPL CL electronic (and thermal) interfacial resistance.