Improvement of Electrocatalyst Performance in Hydrogen Fuel Cells by Multiscale Modelling

Transcription

1 Improvement of Electrocatalyst Performance in Hydrogen Fuel Cells by Multiscale Modelling A thesis submitted to the University of Manchester for the degree of Doctor of Philosophy in the Faculty of Engineering and Physical Sciences 2012 SUTIDA MARTHOSA School of Chemical Engineering and Analytical Science

2 Contents Abstract 14 Declaration 15 Copyright statement 16 Dedication 17 Acknowledgements Introduction Background of research Motivation Scope Thesis outline Fuel cells and polymer electrolyte membrane fuel cells Fuel cell development history Operating principles Components Bipolar plates End plates Membrane electrode assembly Gas diffusion layer Catalyst layer Membrane Types and applications Technology comparison of fuel cells and heat engines Advantages of fuel cells

3 Disadvantages of fuel cells Fuel cell performance Reversible thermodynamics operation: the Gibbs free energy Non-standard conditions: the Nernst equation Irreversible voltage losses Activation loss Mass transport loss Ohmic loss Internal current loss or fuel crossover loss Cell voltage Efficiency Thermodynamic efficiency Operational efficiency Summary Literature review for catalyst layer modelling Introduction Development of fuel cell modelling Electrocatalyst Catalyst layer structure Internal structure of agglomerates Non-embedded electrolyte concept Embedded electrolyte concept Common characteristics used in catalyst layer modelling Catalyst layer modelling Interface models Single-pore models Porous-electrode models Agglomerate models Summary Interface model Introduction Model development Model description Assumptions

4 Composition of the inlet gases Gas transport in the gas diffusion layer Gas transport in the anode gas diffusion layer Gas transport in the cathode gas diffusion layer Membrane properties Water content Water transportation in membrane Electro-osmosis Diffusion Convection Protonic conductivity in the membrane Fuel cell performance Voltage losses in fuel cell Voltage loss in the anode (η a ) Voltage loss in the cathode (η c ) Voltage loss in electrolyte (η Ω ) Computational procedure Assumption analysis and model validation Assumption analysis Model validation Anode Cathode Membrane Summary Porous-electrode model Introduction Model development Model description Assumptions Diffusion and conservation of oxygen in the catalyst layer Electrochemical reaction in the cathode Computational procedure Model validation Assumption analysis Model validation

5 5.5. Results and discussion Summary Agglomerate model Introduction Model development Model description Assumptions Diffusion and reaction kinetics Computational procedure Overall procedure Procedure for determination of the current density in the electrolyte phase Model validation Assumption analysis Validation of the numerical method Model validation Parametric and statistical sensitivity analysis Parametric analysis Sensitivity analysis Results and discussion Overpotential and kinetics parameters Effects of the thickness of electrolyte film and the agglomerate size The concentration profile and the limiting mechanism in fuel cell operation The effect of agglomerate shapes Assumptions Comparison at a constant platinum loading (L pt ) Comparison at a constant platinum loading (L pt ) and a constant characteristic length (ζ) Comparison at a constant platinum loading (L pt ) and a constant characteristic length (ζ) without assuming the semi-finite structure Selection of the suitable shape analysis method Effect of the agglomerate shapes on the reaction kinetics

6 6.8. Benefits and potential applications of the agglomerate model Summary Conclusions and future work Conclusions Interface model Porous-electrode model Agglomerate model Summary Future work Bibliography 202 A. Derivations in the interface model 213 A.1. Material balance at anode inlet A.2. Material balance at cathode inlet A.3. Multicomponent diffusion in cathode gas diffusion layer A.3.1. Diffusion of oxygen A.3.2. Diffusion of water A.4. Fourth order Runga-Kutta method B. Solution for differential equation in the porous-electrode model 222 C. Ranges and sources of parameters from literatures 224 D. List of presentations 225 E. Visual Basic Code 226 Total word count 59,457 6

7 List of Figures 2.1. Schematic diagram illustrating the operating principles of a hydrogen/oxygen PEM fuel cell Typical MEA and hydrogen/oxygen PEM fuel cell stack configuration Schematic diagram of a cross-section in fuel cell MEA components Transport of protons, electrons, water and oxygen in the cathode catalyst layer Example of Nafion R structure Typical polarisation curve for a PEM fuel cells Change in the reactant partial pressure on electrode surface when the current density varies from no current to the limiting current density Thermodynamic efficiency of hydrogen/oxygen fuel cell at standard pressure and of heat engine (Carnot limit) with exhaust temperature of 50 C. Redrawn from Larminie and Dicks (2000) Variation of modelling features in PEM fuel cells (a) SEM image of the electrode membrane interface, (b) SEM image showing agglomerate particles, (c) SEM image at higher magnification and (d) SEM image at higher resolution (HR-SEM) shows carbon and platinum particles forming the agglomerates (Middelman, 2002) TEM images for platinum deposition on the electrode, with permission from Moore (2009) Schematic diagram of catalyst layer structure according to the twophase zone concept SEM image of an MEA for a hydrogen PEM fuel cell showing the anode at the top, the cathode at the bottom and the thin catalyst layer between the electrodes and membrane (Chen et al., 2006)

8 3.6. Crossectional view of a MEA cut using a glass knife showing an electrode with impregnated catalyst layer next to a Nafion R 117 layer (Broka and Ekdunge, 1997a) Schematic diagram of the catalyst layer structure assumed in single pore models where the cylinders were assumed to be filled with (a) the electrolyte and the catalyst aggregates and (b) the reactant gas Schematic diagram of catalyst layer in a complex single-pore model, based on Bultel et al. (1999) Schematic diagram of catalyst layer in an agglomerate model Schematic diagram of hydrogen/air fuel cell in the interface model Water content in membrane as a function of water activities at 80 C Polarisation curves from the interface model and the experiment data from Du (2010) Mole fraction profiles of hydrogen at each interfaces as function of current density Mole fraction profiles of oxygen at each interfaces as function of current density Mole fraction profiles of water at each interfaces as function of current density (a) Membrane water content and (b) protonic conductivity in the membrane from the anode to the cathode interfaces Ratio of water flux at the anode (interface 2) to the rate of water generated at the cathode as a function of current density in a PEM fuel cell operating at 65 C Schematic diagram of fuel cell cathode in the porous-electrode model Three dimensional view shows current flow in the catalyst layer The cathode activation and ohmic losses as a function of the current density in PEM fuel cell operation The predicted polarisation curve and the experimental results of PEM fuel cell operating at 65 C Polarisation curves of fuel cell at different values of the catalyst layer porosity of 0.2, 0.3 and Polarisation curves of fuel cell at different values of the exchange current density of 0.5, 2 and 20 A m

9 5.7. Oxygen concentration profile in dimensionless forms of concentration and thickness of the catalyst layer Schematic diagram of catalyst layer structure in agglomerate model Schematic structure of a catalyst agglomerate in the agglomerate model Schematic diagram shows an agglomerate with radius R ag Diagram for the calculation procedure for determination of the current density in the electrolyte phase Comparison of polarisation curves generated by agglomerate model using different numbers of elements in the numerical method Polarisation curves of the experimental data and the simulation results at the standard simulating conditions Fuel cell (a) voltages and (b) power density as function of current density when the cathodic exchange current density is 7, 10 and 13 A m Fuel cell (a) voltages and (b) power density as function of current density when the agglomerate radius is 0.8, 1.2 and 2.0 µm Fuel cell (a) voltages and (b) power density as function of current density when the agglomerate porosity is 0.1, 0.25 and Fuel cell (a) voltages and (b) power density as function of current density when the electrolyte film thickness is 0.1, 0.13 and 0.15 µm Fuel cell (a) voltages and (b) power density as function of current density when the specific surface area is , and m Fuel cell (a) voltages and (b) power density as function of current density when the volume fraction of electrolyte in agglomerate is 0.15, 0.20 and Percentage difference in fuel cell peak power density as a function of the percentage difference in the parameters Map of the results and discussion section (a) The cell voltage losses in the anode, cathode and membrane, (b) the average intrinsic rate constant, (c) the Thiele modulus and (d) the catalyst utilisation effectiveness as function of the current density based on the reference parameters

10 6.16. Fuel cell polarisation curve as a function of current density for various values of (a) the thin film thickness (with t f = 0.1, 0.13 and 0.15 µm) and (b) the agglomerate radius (with R ag = 0.8, 1.2 and 2.0 µm) Intrinsic rate constant as a function of current density for various values of (a) the thin film thickness (with t f = 0.1, 0.13 and 0.15 µm) and (b) the agglomerate radius (with R ag = 0.8, 1.2 and 2.0 µm) The Thiele modulus as a function of current density for various values of (a) the thin film thickness (with t f = 0.1, 0.13 and 0.15 µm) and (b) the agglomerate radius (with R ag = 0.8, 1.2 and 2.0 µm) Catalyst utilisation effectiveness as a function of current density for various values of (a) the thin film thickness (with t f = 0.1, 0.13 and 0.15 µm) and (b) the agglomerate radius (with R ag = 0.8, 1.2 and 2.0 µm) Cathodic activation loss as a function of current density for various values of (a) the thin film thickness (with t f = 0.1, 0.13 and 0.15 µm) and (b) the agglomerate radius (with R ag = 0.8, 1.2 and 2.0 µm) Log-log plot of the effectiveness and the Thiele modulus of three agglomerate radii Individual spherical agglomerate structure Concentration profile in a spherical agglomerate with a radius of 1.2 µm at various values of Thiele modulus Concentration profile in spherical agglomerate with radius of 0.8 and 1.2 µm The characteristic length and semi-finite structure of spherical, cylindrical and slab-like agglomerates Geometric structure of the studied agglomerates Power density as a function of current density in fuel cells with agglomerate shape of (a) cylinder (b) slab (c) all shapes and (d) Power density profile of selected fuel cells with cylindrical (α=10) and slab-like (α=2, α 1 =2) agglomerates Fuel cell (a) voltage and (b) power density as a function of current density when different agglomerate shapes were used Comparison of fuel cell (a) voltage, (b) power density of the hydrogen fuel cells with different agglomerate shapes as functions of the current density

11 6.30. Relation of peak power density of each shape to SSA and 1/ζ The catalyst utilisation effectiveness as function of the current density for spherical, cylindrical and slab-like agglomerates Cathodic activation overpotential (η act ) as a function of current density of fuel cells with different agglomerate shapes Log-log plot of utilisation effectiveness versus Thiele modulus for each agglomerate shape Percentage improvement in fuel cell using (a) slab-like agglomerates and (b) cylindrical agglomerates, in the utilisation effectiveness and the power density as a function of current density Platinum paticle size as function of temperature after cycling from V for 1500 cycles (Borup et al., 2006) SEM images shows thicknesses of layers in MEA after a number of cycle (Chen et al., 2006) A.1. Schematic diagram of fuel cell in the model

12 List of Tables 2.1. Types of fuel cells Typical dimensions in a catalyst layer of a hydrogen PEM fuel cell Single-pore catalyst layer modelling Porous-electrode catalyst layer modelling Agglomerate catalyst layer modelling Values of parameters used in the model (O Hayre et al., 2006; Springer et al., 1991; Washburn, 1934) Interface model calculation matrix Simulation parameters in the interface model Fuel cell operating conditions in Du (2010) Simulation parameters in the porous-electrode model Dimensionless forms of parameters, their derivatives and the boundary conditions %difference in fuel cell voltage between simulations with 100, 500, 1000 and 1500 elements in the numerical method Simulation parameters in the agglomerate model The additional parameters used in the agglomerate model PEM fuel cell parameters and their levels used in the statistical sensitivity analysis The matrix of cases and the levels of each parameters in each case Statistical sensitivity analysis of the PEM fuel cell performance Geometries of agglomerate in different shapes at fixed ζ and L pt Specific surface area of each agglomerate shape

13 6.10. The length of slab, the specific surface area and the peak power density of fuel cell with slab-like agglomerate, determined without assuming the semi-finite structure in the analysis Comparison of the peak power density in fuel cells with different agglomerate shapes, from three methods C.1. Values of the simulation parameters and their sources

14 Abstract The work in this thesis addresses the improvement of electrocatalyst performance in hydrogen PEM fuel cells. An agglomerate model for a catalyst layer was coupled with a one dimensional macroscale model in order to investigate the fuel cell performance. The model focuses on the agglomerate scale and the characteristic length in this study was 0.4 µm. The model was validated successfully with the experimental data. Based on the analysis of variance method at a 99% confidence level, the variation in the average fuel cell voltage was significantly sensitive to that in the volume fraction of electrolyte in an agglomerate. The effect of changing electrolyte film thickness was observed to have a significant impact only in the mass transport limited region, whereas the effect of changing agglomerate radius was found over the entire range of current density. An analysis comparing the effect of agglomerate shape at a constant platinum loading, a constant characteristic length and assuming the semi-finite structure was suitable for this study. Sphere, cylinder and slab agglomerate geometries were considered. The behaviour of the utilisation effectiveness was discovered to be strongly affected by the agglomerate shape. The improvement in the utilisation effectiveness was non-linear with current density. The advantage of the slab geometry in distributing reactant through the agglomerate volume was reduced and consequently the increase in utilisation effectiveness for slab-like agglomerates diminishes in the high current density region. At 0.85 A cm 2, the maximum improvement of the catalyst utilisation effectiveness in slab was 27.8 % based on the performance in sphere. The improvement in fuel cell maximum power density achieved using slab-like agglomerate was limited to around 3%. The improvement in the overall fuel cell performance by changing the agglomerate shape was not significant. To achieve significant improvements in fuel cell performance will require changes to other features of the catalyst layer. Sutida Marthosa, Improvement of Electrocatalyst Performance in Hydrogen Fuel Cells by Multiscale Modelling, Degree of Doctor of Philosophy, The University of Manchester, July

15 Declaration I declare that no portion of the work referred to in the thesis has been submitted in support of an application for another degree or qualification of this or any other university or other institute of learning. Sutida Marthosa July

16 Copyright statement i. The author of this thesis (including any appendices and/or schedules to this thesis) owns certain copyright or related rights in it (the "Copyright") and s/he has given The University of Manchester certain rights to use such Copyright, including for administrative purposes. ii. Copies of this thesis, either in full or in extracts and whether in hard or electronic copy, may be made only in accordance with the Copyright, Designs and Patents Act 1988 (as amended) and regulations issued under it or, where appropriate, in accordance with licensing agreements which the University has from time to time. This page must form part of any such copies made. iii. The ownership of certain Copyright, patents, designs, trade marks and other intellectual property (the "Intellectual Property") and any reproductions of copyright works in the thesis, for example graphs and tables ("Reproductions"), which may be described in this thesis, may not be owned by the author and may be owned by third parties. Such Intellectual Property and Reproductions cannot and must not be made available for use without the prior written permission of the owner(s) of the relevant Intellectual Property and/or Reproductions. iv. Further information on the conditions under which disclosure, publication and commercialisation of this thesis, the Copyright and any Intellectual Property and/or Reproductions described in it may take place is available in the University IP Policy (see 487), in any relevant Thesis restriction declarations deposited in the University Library, The University Library s regulations (see library/aboutus/regulations) and in The University s policy on Presentation of Theses 16

17 Dedication To the love, encouragement and patience of my beloved parents, families and friends. 17

18 Acknowledgements First of all, I would like to thank my supervisor, Dr. Edward Roberts. Thank you so much for offering me the opportunity to work as your PhD student, for your help and guidance throughout my study. Above all, I would like to thank you for your understanding and support during my difficult time. I would also like to thank my co-supervisor, Dr. Stuart Holmes, for all of his suggestions and comments during my study. I would like to thank you Dr. Shangfeng Du from the Centre of Hydrogen and Fuel Cell Research, School of Chemical Engineering, University of Birmingham for his collaboration on the experimental data and all of his suggestions. Thank you to all of the members and staff of CEAS who have helped me out on different matters during these years and made it possible for me to complete the study without too much struggle. I am very grateful to all of the friends that I have made here, especially Nuria, Chaiwat, Ashley, Craig, Geraint, Chatkaew, and my other E-floor friends. Thanks to Martin for helping me with using Latex editor. Thank you all for friendship and support during my study. My great gratitude goes to The Royal Thai Government for the financial support and staffs at the Office of Educational Affairs (OEA), London, UK for their support in all matters. Finally, special thanks to my families and friends in Thailand for their endless love, support and encouragement. To my mom and dad for keeping me going and helping me get this far. To my sisters and brother for looking after our parents. None of this would have been possible without your support. 18

19 Glossary A surface area, m 2. A c cross-sectional area, m 2. C concentration, mol m 3. D λ water diffusivity in membrane, m 2 s 1. D ij binary diffusivity between i and j, m 2 s 1. D o oxygen diffusivity, m 2 s 1. E catalyst utilisation effectiveness. E a activation energy. E ca cathode potential, V. E e reversible cell potential, V. E m potential in electrolyte phase, V. E so potential in solid phase, V. E v cell potential, V. E w membrane equivalent weight. F Faraday s constant, C mol 1. 19

20 G Gibbs free energy, J. H Henry s constant, mol Pa 1 l 1. H sl slab thickness, m. L pt platinum loading, mg cm 2. M molecular weight, g mol 1. P pressure, Pa. P power density, W m 2. P c critical pressure, Pa. Q molar flux, mol m 2 s 1. R universal gas constant, J mol 1 K 1. R ag agglomerate radius, m. T absolute temperature, K. T c critical temperarure, K. V volume, m 3. W molar flow rate per unit volume, mol m 3 s 1. W sl slab width, m. ℵ number of agglomerate. α charge transfer coefficient. Ā average surface area, m 2. v volume fraction. 20

21 β ratio of water flux through anode GDL to the generated water flux. ɛ porosity. η voltage loss, V. γ specific ionic conductivity, S m 1. κ hydraulic permeability, m. λ membrane water content. µ water viscosity, Pa s 1. ν ratio of the inlet flux to the required flux of gases. φ Thiele modulus. ρ density, kg m 3. σ protonic conductivity of membrane, S m 1. θ roughness factor. ς efficiency. ϑ specific fuel rate, mol cm 2 s 1. ζ characteristic length (volume per surface area) of the agglomerate,m. a interfacial specific surface area, m 1. a ag geometric specific surface area, m 1. a w water vapour activity. b Tafel s coefficient. j current density, A m 2. 21

22 j 0 exchange current density, A m 2. j i,j transfer current for the electron transfer reaction between i and j, A m 2. j l limiting current density, A m 2. j m current density in electrolyte phase, A m 2. j so current density in solid phase, A m 2. k an intrinsic rate constant. l length, m. m mass, g. n e number of electrons involved in the reaction. p partial pressure, Pa. q molar flow, mol s 1. r radius, m. t thickness, m. u velocity, m s 1. x mole fraction. z position in direction from anode to membrane. z position in direction from cathode to membrane. 22

23 Subscript act activation. ag agglomerate. a anode. b bulk. C carbon. Carnot Carnot cycle. c cathode. cl catalyst layer. co convection. cy cylinder. d diffusion. ef f effective. el electrolyte. e electro-osmotic drag. 23

24 f film. 4 interface 4. F fuel. h hydrogen. 1/2 half cell. i species i. no resistance. inkc carbon ink. inkp t Pt catalyst ink. j species j. j species j. h higher. l lower. max maximum. m mid. m membrane. n nitrogen. Nf Nafion. 24

25 o oxygen. Ω Ohmic. od dry gas. 1 interface 1. P t platinum. P t/c Pt/C catalyst powder. ref reference. r reaction. sl slab. so solid phase. sp sphere. s surface. thermo thermodynamic. 3 interface 3. 2 interface 2. v voltage. w water. wc water in cathode GDL. 25

26 Superscript I inlet. L outlet. sat saturated. 26

27 1. Introduction The study of electrocatalyst performance in hydrogen polymer electrolyte membrane fuel cell by multiscale modelling is presented in this thesis. In this chapter, the research background, motivation for the study, the scope and thesis s outline are exhibited Background of research The fossil fuel combustion has been widely used for power generating. However there are two main problems caused by the technology. Firstly, the combustion products such as CO 2 contribute significantly to the problem of global warming. Secondly, global supply of fossil fuels is diminishing and may not be sufficient for our future energy demands. Therefore, an alternative sustainable power generation technology is needed. Hydrogen fuel cells using a sustainable fuel may become the main energy delivery devices of the 21 st century. Fuel cells combine fuel with an oxidant in electrochemical reactions. Hydrogen fuel cells produce electricity, water and some waste heat without producing CO 2 in the product (Barbir, 2005), therefore it offers a solution to the first problem of the combustion engine. An example of a sustainable fuel source (possibly as a solution to the second problem) is hydrogen produced from the electrolysis of water which could be powered by electricity from solar cells or wind turbines. A fuel cell consists of two electronically separated electrodes; a negatively charged anode and a positively charged cathode. Fuel (e.g. hydrogen) and oxidant (usually oxygen in air) are supplied to the anode and cathode, respectively. An external circuit connects the two electrodes and an electrolyte membrane allows the conducting ions 27

28 1. Introduction to be transported between them. Although there are many types of fuel cell, polymer electrolyte membrane (PEM) fuel cells have received the most attention for automotive and small stationary applications. Fuel cell technology has been developed since 1839 (Larminie and Dicks, 2000). Between 1959 and 1982, the General Electric Company developed PEM fuel cells for NASA s Gemini space flights. Until the 1990 s, the PEM fuel cell was an expensive technology due to its high loading of platinum catalyst. In the 1990s, there were many technological breakthroughs in PEM fuel cell development and the costs were significantly reduced, enabling their development for other applications. Recently, PEM fuel cells are largely employed in zero CO 2 emission automobiles. However, commercialisation of PEM fuel cells has not been achieved at a large industrial scale due to significant drawbacks in the current technology. To achieve commercially viable PEM fuel cells for automotive applications, cost reduction and improvements in volumetric power density, fuel cell performance and durability must be attained (Stumper and Stone, 2008). Wang et al. (2011) also emphasised that fundamental research, improving our understanding of the fuel cell operation principles, can potentially generate the knowledge required to overcome barriers to commercialisation related to the cost and durability of fuel cell components Motivation The research carried out in this project has used multiscale modelling as a research tool to gain understanding of the phenomena occurring in the cathodic catalyst layer and the influence of its design and structure on fuel cell performance. Multiscale modelling was selected as it provides an in-depth understanding of the most crucial component of a PEM fuel cell: the electrocatalyst. Modelling of fuel cells will provide fundamental understanding and identify optimum catalyst layer designs at a reduced cost, and shortening the development time greatly in comparison to experiment-only approaches. The electrocatalyst has been selected as the focus for the research for two reasons. Firstly, the electrochemical reactions take place at the triple phase boundary of 28

29 1. Introduction the electronically conducting carbon, the protonically conducting Nafion R and the reactant gas in the catalyst layer. The electrocatalyst layer greatly influences the reaction rate and fuel cell performance, thus understanding the phenomena in the electrocatalyst layer is crucial for further fuel cell development. Secondly, PEM fuel cells generally use platinum which is an expensive catalyst, thus searching for a catalyst layer structure which maximises the catalyst utilisation can reduce the fuel cell cost. The breakdown of the costs of a PEM fuel cell provided by Papageorgopoulos (2010) showed that the catalyst is the main cost of the membrane electrode assembly (MEA). The US department of energy (DOE) announced a target for the reduction of the catalyst cost from $4.5 per kw in 2010 to $2.70 per kw by 2015 (Papageorgopoulos, 2010). This research is thus consistent with the DOE guidelines indicating that it is up to date and its contribution to the field of knowledge is important Scope Multiscale modelling is a technique which used in this study to achieve the research objectives. A macro-scale model which is a model focusing on the overall mass transport in PEM fuel cell and two of the meso-scale models, focussing on catalyst layer, are developed and integrated into the macro-scale model. By using the multiscale modelling technique, the influence of catalyst layer structure in the mesoscale can be observed in the overall scale of PEM fuel cell operation. The macro-scale model is an isothermal one-dimensional model based on the balancing of the fluxes of hydrogen, oxygen, water, protons and electrons through the gas diffusion layers and membrane. An interface catalyst layer model, which considers the catalyst layer as an interface between the gas diffusion layer and the membrane, was used in the macro-scale model. Two of the alternative approaches to the modelling of the meso-scale catalyst layer have been considered. Each catalyst layer model has been integrated into the macroscale model to illustrate the effects of catalyst layer structure on fuel cell performance. In this study, the meso-scale model has only been applied to the cathode. The main 29

30 1. Introduction objectives of this research project were: To develop a macro-scale model of the fuel cell performance. To review meso-scale catalyst modelling approaches, develop and integrate them into the macro-scale model. To analyse results from various catalyst layer models in order to select a suitable approach for this study. To determine the effect of the electrocatalyst structure on the fuel cell performance Thesis outline The thesis is divided into 7 chapters as follows: Chapter 1: introduction. The current chapter outlines the background to the research, the research motivation and scope of this thesis. Chapter 2: fuel cells and polymer electrolyte membrane fuel cells. It provides an overview of fuel cell technology including the history, principles of operation and types of fuel cell. The PEM fuel cell is discussed in further detail including a review of PEM fuel cell components. Chapter 3: literature review for catalyst layer modelling. The modelling methods reported in the literature for modelling the catalyst layer are summarised. The structure of the catalyst layer, the electrochemical mechanisms and common characteristics used in catalyst layer modelling are presented before the various catalyst layer models are discussed. Chapter 4: interface model. An overview of the macroscale PEM fuel cell model is provided. Despite the simplicity of the interface catalyst layer model used, this model takes into account many interrelated and complex phenomena in the fuel cell such as mass transfer, electrochemical reactions, and ionic and electronic transport. The 30

31 1. Introduction modelling procedure and the results obtained from the interface model are discussed. Chapter 5: porous-electrode model. The mesoscale model for the catalyst layer is presented. An overview of the model, its development, the computational procedure and its integration into the macroscale model (described in chapter 4) is presented. The model is validated and the results is discussed. Chapter 6: agglomerate model. An agglomerate model is a mesoscale model. The model development, the computational procedure, the model validation, the parametric study and the sensitivity analysis are described. The effect of the electrocatalyst structure such as the catalyst agglomerate shape on the fuel cell performance is evaluated. Chapter 7: conclusions and future work. The findings are reviewed with respect to the objectives of the project. The general conclusions and recommendations for future work are presented. 31

32 2. Fuel cells and polymer electrolyte membrane fuel cells In this chapter, fuel cell development history, operating principles and components of fuel cells are presented. Special attention is given to the polymer electrolyte membrane fuel cell. This chapter also introduces different types of fuel cells, and methods for characterisation of fuel cell performance which are commonly used for benchmarking developments in fuel cell research Fuel cell development history In 1839, Sir William Grove was the first to demonstrate a simple fuel cell operation by using oxygen (oxidant), hydrogen (fuel), platinum (catalyst) and sulphuric acid (electrolyte) (Hoogers, 2003). There were four cells connected in series and each cell had two strips of platinum, submerged in dilute sulphuric acid. Initially the experiment was carried out by using power supply to electrolyse water; as a result, hydrogen and oxygen were produced. The gas tubes were inverted and lowered over each platinum strips, the electrolyte was replaced by the gas products. The second part of the experiment was to reverse the electrolysis reaction by replacing the power supply with an ammeter. Current was generated in the second half of the experiment (Srinivasan, 2006). Although the generated current was low, the fuel cell operating principles were demonstrated for the first time. During , Christian Friedrich Schönbein reported that the current produced by the fuel cell was not entirely a result of contact between hydrogen and oxygen but was due to the chemical combination of oxygen and hydrogen in the presence of 32

33 2. Fuel cells and polymer electrolyte membrane fuel cells platinum (Larminie and Dicks, 2000). In 1889, L.Mond and C.Langer developed a prototype of fuel cell using platinum foil and platinum black electrodes with high surface area. They used a sulphuric acid electrolyte in a porous diaphram (plaster or earthenware) and their fuel cell produced approximately A cm 2 (Hoffman, 2001). In 1967, a new and promising polymer membrane, called Nafion R, was developed (Warshay and Prokopius, 1990). Nafion R has polytetrafluoroethylene (PTFE) as the backbone polymer and its side chains are ended with sulphonic sites (SO 3.) Nafion R yielded higher chemical stability and improved proton conductivity over other alternative known materials at the time. During , the first PEM fuel cell stack of 1 kw, operating in the temperature range C, was installed as the power source in the Gemini space craft. The fuel cells demonstrated the use of unsupported platinum electrocatalyst and polystyrene sulfonic acid (PSS) membrane (Srinivasan, 2006). It produced A cm 2 at a cell voltage of 0.65 V with a high catalyst loading of 5 mg cm 2 (Warshay and Prokopius, 1990; Kalhammer, 2000). The next milestone in fuel cell development came from Wilson and Gottesfeld (1992), who separately prepared the catalyst layer and gas diffusion layer and hot pressed them into a Membrane Electrode Assembly (MEA). This novel structure effectively improved the accessibility of reactant gas to the catalyst. This new approach led to an increase in catalyst utilisation of approximately ten folds between (Kalhammer, 2000). The interest in PEM fuel cell research was sluggish until the early 1990 s, when Ballard Power Systems (Canada) and Los Alamos National Laboratory (USA) advanced the technology in many aspects. Examples of their achievement included the modification of fuel cell hardware to work effectively with air rather than with pure oxygen and the determination of maximum acceptable hydrogen fuel impurity. It was established that hydrogen fuel with 25% CO 2 impurity did not affect fuel cell performance significantly, while contamination with CO was found to adversely affect the fuel cell performance at a concentration of 0.3%. The research group also reduced the fuel cell cost by lowering platinum loadings from 8 to 0.4 mg cm 2 while maintaining 33

34 2. Fuel cells and polymer electrolyte membrane fuel cells similar performance. A Dow membrane was used which increased the fuel cell performance four fold. The research group also redesigned the fuel cell stack to reduce the peripheral material cost. These improvements allowed the research group to commercialise their fuel cells for both private and government sectors (Kalhammer, 2000) and revived interest in fuel cell research Operating principles A fuel cell with hydrogen/oxygen electrodes in an acid electrolyte is used here to demonstrate the fuel cell operating principle and the chemical reactions in the fuel cell. A fuel cell consists of two electronically separated electrodes immersed in an electrolyte. Fuel (hydrogen) is supplied to the negative electrodes, oxidant (usually oxygen in air) is supplied to the positive electrode and there is an external electrical circuit connecting the electrodes as shown in Figure 2.1. H 2 H + e - O 2 O 2- H 2 O H 2,in O 2,in Catalyst layer H 2 O,out Anode Membrane Cathode Figure 2.1.: Schematic diagram illustrating the operating principles of a hydrogen/oxygen PEM fuel cell. 34

35 2. Fuel cells and polymer electrolyte membrane fuel cells The anode reaction is: H 2 2H + + 2e (2.1) Gaseous hydrogen diffuses through the porous gas diffusion layer and is oxidised to hydrogen ions and electrons at the anodic catalyst. One molecule of hydrogen releases two electrons as seen in the reaction 2.1. Hydrogen ions are transported through the acid electrolyte membrane, which does not conduct electrons. Electrons are forced to travel through the external circuit and the electron flow is measured as current flow. The cathode reaction is: 2e O 2 + 2H + H 2 O (2.2) The inlet oxygen diffuses through the porous cathodic gas diffusion layer and is reduced in the cathodic catalyst layer. The electrons and hydrogen ions from the anode react with the oxygen, producing water. Water management is required to keep the anode and the membrane electrolyte hydrated, to remove water from the active catalyst layer and to free up platinum surface area for further reactant. Fuel and oxidant react in electrochemical reactions simultaneously and the overall reaction is: H O 2 H 2 O + electricity + heat (2.3) 2.3. Components Understanding the operating principle leads to suitable designs of fuel cell components. A PEM fuel cell has a polymer membrane sandwiched between two catalyst layers which are then covered by gas diffusion layers on each side of the membrane. The cells are then connected by bipolar plates to form a fuel cell stack. A typical fuel cell can produce a small amount of power output so a number of fuel cells are stacked together in series (see Figure 2.2), with a bipolar plate between the adjacent MEAs, to offer practical power output. A fuel cell prepared using a commercial MEA produces approximately 0.4 W cm 2, furthermore, a power density of 0.8 W cm 2 generated by a low temperature hydrogen PEM fuel cell have been achieved (Du, 2010; Wilson et al., 1995). PEM fuel cell stacks need to produce kw for automotive and 35

36 2. Fuel cells and polymer electrolyte membrane fuel cells combined heat and power generation systems (Hoogers, 2003). The bipolar plates and end plates are discussed in this section. The structure of the MEA will be discussed in more detail in section 2.4. Electrolyte Gasket Anode Endplate MEA O 2 Gas channels Cathode Membrane electrode assembly (MEA) H 2 H 2 Bipolar plate O 2 Figure 2.2.: Typical MEA and hydrogen/oxygen PEM fuel cell stack configuration Bipolar plates A bipolar plate is a flat piece of composite material with carefully manufactured grooves providing the gas flow channels on both sides of the plate; hence they are sometimes called flow field plates. Bipolar plates are used to separate MEAs in fuel cell stacks and to transfer electrons between MEAs connected in series. Other functions of bipolar plates include giving the mechanical support for the cells, providing the gas flow channels for hydrogen and oxygen and facilitating the water removal. In a stack, bipolar plates are also often used for cooling, with cooling water circulated within an internal circuit. A suitable bipolar plate should remove water at an effective rate to avoid flooding 36

37 2. Fuel cells and polymer electrolyte membrane fuel cells problems (when water blocks gas flow in the fuel cell) and membrane dehydration (the polymer electrolyte membrane must be fully hydrated to effectively transfer the mobile proton from anode to cathode). In summary, the desirable characteristics of bipolar plates are good thermal conductivity, high electrical conductivity, impermeability to gases, light weight, high corrosion resistance and ease of manufacture (Sadiq Al-Baghdadi, 2007) End plates A fuel cell system employs bipolar plates has to use end plate at each end of stack (see Figure 2.2). The end plates have the electrical connection points to the external circuit; give mechanical strength and support the stack Membrane electrode assembly A Membrane Electrode Assembly (MEA) is thinner than the biplates and the end plates. One MEA is comprised of two gas diffusion layers (GDL), two catalyst layers and one polymer electrolyte membrane as shown in Figure 2.3. The components are fabricated separately, and then hot pressed into one thin assembly. Two simple preparation techniques of an MEA after separately preparing an anode, a cathode and a membrane are varied based on the way that the catalyst layers are deposited. One technique is to deposit the catalyst layer on one side of each electrode then hot press the electrodes with the membrane, ensuring that the sides containing catalyst are in contact with the membrane. Another technique is to deposit the catalyst layer on both sides of the membrane then hot press the anode, the membrane and the cathode to form an MEA. The catalyst layers can be deposited to either the gas diffusion layers or to both sides of the membrane before the electrodes and the membrane are hot pressed to form an MEA. 37

38 2. Fuel cells and polymer electrolyte membrane fuel cells Anode 365 µm MEA Membrane 50 µm Cathode 365 µm GDL 350 µm Catalyst layer 15µm Figure 2.3.: Schematic diagram of a cross-section in fuel cell MEA components Gas diffusion layer An electrode consists of two distinctive layers which are the gas diffusion layer (GDL) and the catalyst layer (see Figure 2.3). A gas diffusion layer is a carbon layer coated with hydrophilic polytetrafluoroethylene (PTFE). It is usually prepared by coating a mixture of carbon powder and polytetrafluoroethylene (PTFE) onto carbon paper or cloth. Polytetrafluoroethylene, which is used to make Teflon, is hydrophobic so the application of the PTFE coated carbon can prevent water flooding in the fuel cell, ensuring the reactant gas can be transported through the GDL (Bradley, 2008; Prater, 1990). There are three distinguishable pore size regions in the GDL. Macropores which are µm in diameter and mainly coated with the hydrophobic PTFE. This sub layer is in contact with the bipolar wall and functions as gas passages for the inner sub layer. Mesopores with µm in diameter consisting of both PTFE and non PTFE coated pores, so this region has both hydrophobic and hydrophilic features. Lastly, micropores with diameters less than 0.1 µm, formed by carbon powders. The vapour water can easily condensed into liquid water in these small pores so this region acts as a liquid water passage (Bradley, 2008; Karvonen et al., 2008). The important roles of the gas diffusion layer are to provide gas and water transport 38

39 2. Fuel cells and polymer electrolyte membrane fuel cells mechanisms. The reactant gas flow from the gas channels to the active site in the catalyst layer. Additionally, the gas diffusion layers must conduct electrons, allow water to flow to the membrane for hydration and give mechanical support to the catalyst layer (Prater, 1990; Kalhammer, 2000). Note that the gas diffusion layer must perform all of these tasks simultaneously (Karvonen et al., 2008) Catalyst layer The second component of a fuel cell electrode is the catalyst layer. This layer is about 10 µm in thickness (Wang et al., 2011) but it is a crucial component in the MEA because the electrochemical reactions take place here. The redox reactions in both electrodes are accelerated by use of platinum in the catalyst layer. At the cathode, electrochemical reaction only occurs when the three key components are found at the catalyst: protons, electrons, and oxygen. Protons (H + ) must be transported from the anode through the polymer electrolyte membrane to the cathodic catalyst layer. Electrons (e ) produced during hydrogen oxidation at the anode must be transported through the bipolar plate and the cathodic GDL to the catalyst layer. Reactant gas (O 2 ) is transported from the gas channel to the catalyst layer via the gas diffusion layer as shown in Figure 2.4. Proton conducting media, Nafion Carbon supported catalyst, Pt/C Electrically conductive carbon layer H 2 O e - H + O 2 Membrane Catalyst layer Gas diffusion layer Figure 2.4.: Transport of protons, electrons, water and oxygen in the cathode catalyst layer. The catalyst layer has to be in close proximity to the polymer electrolyte membrane 39

40 2. Fuel cells and polymer electrolyte membrane fuel cells to reduce resistance for proton transfer from the membrane to the catalyst surface. The anodic catalyst loading is usually less than that at the cathode because the hydrogen oxidation at the anode is kinetically more favourable than the oxygen reduction at the cathode. In early PEM fuel cells, a practical Pt loading was 28 mg cm 2 which was reduced to 8 mg cm 2 during the 1990 s. Recently, typical values of platinum loading have decreased to 0.2 mg cm 2 while maintaining fuel cell performance (Larminie and Dicks, 2000; Warshay and Prokopius, 1990). The platinum loading s influence has been investigated by Bradley (2008), Prater (1990) and Litster and McLean (2004). They have shown that an excess amount of platinum is likely to form clusters which can block the gas passage and reduce the specific surface area of the catalyst. On the other hand, an insufficient amount of platinum will greatly reduce the fuel cell performance due to the limited catalyst surface area available Membrane The development of Nafion R by Dupont during the 1960 s was the first technological breakthrough to address the difficulty of water management in fuel cells (Hoogers, 2003). In 1998, the Dow Chemical Company successfully improved the membrane conductivity by reducing the side chain in the Nafion R structure and this new membrane increased the fuel cell performance drastically. Its production rights were later transferred to Dupont (Passalacqua et al., 2001a). Nafion R has been used since then and it is still the preferred membrane in many PEM fuel cell systems today. However, there are alternative membranes available such as Aciplex-S R and Flemion R which are commercialised by Asahi Chemical and Asahi Glass Company, respectively. Nafion R is a sulfonated polytetrafluoroethylene. Its production starts from perfluorination of polyethylene to substitute hydrogen with fluorine making polytetrafluoroethylene (also known as PTFE or Teflon). PTFE is a useful polymer for PEM fuel cell applications as its C-F bonding is very strong, providing a high resistance to chemical attack. The C-F bonding has a very strong hydrophobic character so using PTFE as the backbone chain for Nafion R makes the membrane strongly hydrophobic. The next step is to sulphonate the basic PTFE polymer by adding a side chain 40

41 2. Fuel cells and polymer electrolyte membrane fuel cells terminated with sulphonic acid (HSO 3 ) (Warshay and Prokopius, 1990; Thompson et al., 2001). The side chain structure is flexible and one example of the side chain in Nafion R is shown in Figure 2.5. hydrophobic Side chain hydrophilic Water collects around the clusters of hydrophilic sulphonate side chains in Nafion Water molecule Figure 2.5.: Example of Nafion R structure. A Teflon-like, fluorocarbon backbone is connected to side-chain and the ionic clusters consisting of sulfonic acid ions is located at the end of the side chains. The negative SO 3 ions are permanently attached to the side chain and are immobile. On the other hand, in a fully hydrated membrane, the hydrogen ions combine with water molecules to form hydronium ions which are relatively mobile. Hydronium ions hop from one SO 3 to another within the membrane, thus, the protons diffuse in the hydrated Nafion R. The proton from the anode can only be transported in hydrated Nafion R, thus it is important to hydrate and pre-treat Nafion R before use. The proton (H + ) in HSO 3 is covalently bonded to the side chain and this bond is hydrophilic. The ionic bonds of the side chain are relatively weak so the H + is relatively mobile, the ion is easily bonded with the other side chains ends. The side chains form clusters of hydrophilic groups to transport the mobile ions within a structure of the backbone polymer which is hydrophobic. The combined existence of 41

42 2. Fuel cells and polymer electrolyte membrane fuel cells hydrophilic and hydrophobic groups is also displayed diagrammatically in Figure 2.5. The Nafion R membrane works effectively in an acid environment (Slade et al., 2002). Its proton conductivity depends on the level of hydration, electrolyte environment, cell temperature and operating load. The proton conductivity of the membrane strongly depends on the membrane environment, such as whether the membrane is submerged in water or located above water vapour and depends on the fuel cell operating temperature. Slade et al. (2002) has summarized the membrane conductivity values for different Nafion R materials in various environments and operating temperatures. Generally, the fuel cell power output is increased by reducing the membrane thickness. With a thin membrane, a greater proportion of the membrane is fully hydrated in comparison to a thicker membrane, thus thin membranes have higher overall proton conductivity (Srinivasan, 2006). It is important to note that reducing the membrane thickness increases the possibility of fuel crossover, reduces the mechanical strength and thus makes it more difficult to handle MEAs. Alternative solution to increase the specific conductivity is to chemically modify the membrane structure. Nafion R s role in a PEM fuel cell includes (Warshay and Prokopius, 1990; Larminie and Dicks, 2000; Cha and Lee, 1999): electrolyte: allows inter-electrode proton transport. gas barrier: separates the hydrogen and oxygen gases, avoiding a direct chemical combination of hydrogen fuel and oxygen gases. electronic insulator: forces electrons through the external circuit. ionic connection between the membrane and the catalyst: bridges protons from membrane to the interior active surface in catalyst layer (see Figure 2.4). Nafion R polymer can be integrated into the catalyst layer using various methods. The electrocatalyst layer is typically prepared by mixing Nafion R solution with platinum before spraying the mixture on the carbon support layer. An excessive loading of Nafion R in the catalyst layer will unfavourably isolate 42

43 2. Fuel cells and polymer electrolyte membrane fuel cells platinum from the gas phase (Litster and McLean, 2004; Ioroi et al., 2003); hence, reducing reaction rate. Too little Nafion R will not provide sufficient ionic connection for protons travelling to the catalyst particles. Litster and McLean (2004) suggested that the optimum Nafion R content in the catalyst layer is 33 wt% Types and applications The fuel cell operating principle has remained the same since its first development, although there have been improvements in the technology. Fuel cells can be grouped based on their operating temperature (e.g. low and high temperature fuel cells), the type of fuel (e.g. hydrogen, methanol) and the electrolyte used (e.g. alkali, phosphoric acid). The most common classification is based on the electrolyte used. According to Hoogers (2003) and Larminie and Dicks (2000), there are six main types of viable fuel cell technology at present. Key features of the different types of fuel cell are summarized in Table

44 44 Type Direct methanol (DMFC) Polymer electrolyte membrane(pemfc) Alkaline (AFC) Phosphoric acid (PAFC) Molten carbonate (MCFC) Solid oxide (SOFC) Electrolyte and state Solid polymer (e.g. Nafion R ), Solid Solid polymer (e.g. Nafion R ), Solid Potassium hydroxide, Liquid Phosphoric acid, Liquid Lithium and potassium carbonate, Liquid Solid oxide electrolyte (e.g. zicronium oxide), Solid Mobile ion Operating temperature Fuel/Oxidant Application H C Methanol/ O 2 or air Portable low power electronic system H C Pure H 2 (tolerate CO 2 )/O 2 Vehicle and low power CHP system OH C Pure H 2 /O 2 Space vehicle H C Pure H 2 (tolerate 1% CO 2 )/O 2 200kW CHP CO C H 2, CO, CH 4 (tolerate CO 2 )/O 2 or air O C H 2, CO, CH 4 (tolerate CO 2 )/O 2 or air Table 2.1.: Types of fuel cells. Medium to large scale CHP of MW power 2kW to multi-mw CHP 2. Fuel cells and polymer electrolyte membrane fuel cells

45 2. Fuel cells and polymer electrolyte membrane fuel cells Polymer electrolyte membrane fuel cells PEM fuel cells operate at relatively low temperature (<100 C) so can be started up quickly and is suitable for automobile applications such as cars or buses. The fuel cell employs a thin polymer membrane as the electrolyte. Direct methanol fuel cell The DMFC was developed to take advantage of using methanol (CH 3 OH) directly as a fuel and avoid the pure hydrogen supply problem. DMFCs obtain the proton mobile ions directly from liquid methanol and they also operate in a low temperature regime. Unfortunately DMFCs have low power output so it is only a viable system for slow and steady power consumption applications, for example in portable electronic devices. Alkaline fuel cell Another low operating temperature fuel cell is the alkaline fuel cell (AFC) which operates at slightly higher temperature ( C) and uses hydroxide as the mobile ion. AFCs were used in the Apollo missions and the slow reaction rate was overcome by using highly porous electrodes. The fuel cells require carbon dioxide (CO 2 ) free air. Phosphoric acid fuel cell The technology has been successfully commercialized for stationary power supply applications and is widely used in the USA and Europe. PAFC systems are reliable and require very low maintenance. They operate at approximately 220 C and use platinum catalyst to achieve practical reaction rates. Typically PAFC systems use reformer to produce hydrogen from natural gas, which adds the cost, complexity and size of the system. Solid oxide fuel cell and molten carbonate fuel cell Unlike PAFC, SOFC and MCFC can use natural gas directly, without the need for an external reformer. SOFCs are attractive for stationary power applications because they are highly efficient and fuel flexible. They use thin ceramic membranes as the electrolyte, which can withstand the harsh environment and can function at the high operating temperatures (approximately 600 C) but their fabrication can be difficult and expensive. The SOFC system requires an air and fuel pre heater and a complex cooling unit to complete the system. MCFC systems also operate at high 45

46 2. Fuel cells and polymer electrolyte membrane fuel cells temperature (approximately 650 C), providing a good reaction rate, and can use inexpensive catalyst such as nickel Technology comparison of fuel cells and heat engines Both fuel cells and heat engines are suitable for automotive applications. It is useful to discuss the strengths and weaknesses of fuel cell technology for this application. Understanding of the technology s competitiveness can help to guide the research Advantages of fuel cells Fuel cells can produce electricity as long as fuel is supplied, as in combustion engine system. Fuel cells are more efficient than heat engines as they convert chemical energy directly to electrical energy. Section has shown that at temperature lower than 700 C, fuel cell has higher thermodynamic efficiency than a heat engine. Additionally, fuel cell systems have no moving parts (hence it is a silent system), so it is mechanically more reliable and longer lasting compared with heat engines with moving parts, such as a combustion engine. PEM fuel cells have higher thermal efficiency than combustion engines (50% cf. 30%) (Srinivasan, 2006). The power density of fuel cells ( kw l 1 ) is similar to that of the internal combustion engines (> 1000 kw l 1 ) (Srinivasan, 2006). In terms of environmental impacts, hydrogen PEM fuel cells do not produce undesirable side-products such as NOx, SOx, COx, and there is zero emissions of toxic gases at the point of use. The fuel cell system allows easy independent scaling between power (determined by number of the fuel cells) and capacity (determined by the fuel reservoir size). Fuel cell systems can scale well a few watts (e.g. for a mobile phone) to megawatts for power plant applications (O Hayre et al., 2006; McDougall, 1976). 46

47 2. Fuel cells and polymer electrolyte membrane fuel cells Disadvantages of fuel cells The main disadvantage of fuel cell system is the high cost. Fuel cells are currently only economically competitive to other power system for some applications such as space travel. In automotive application, the projected capital cost of H 2 PEM fuel cells is $100 per kw which is much higher than that of an internal combustion engine with a capital cost of $20-50 per kw (Srinivasan, 2006). Hydrogen storage on board a vehicle is also a major issue for the PEM fuel cell. Fuel cell systems, particularly the low temperature fuel cells, are vulnerable to catalyst poisoning by CO in fuel supply thus pure hydrogen fuel is needed: this effectively increases the cost of the hydrogen PEM fuel cell system. Systems for hydrogen supply, storage and distribution are not yet fully established, whereas, the fossil fuel distribution for heat engines is well in place Fuel cell performance The fuel cell performance is usually presented in a polarisation curve, which is typically generated by measuring the cell voltage at a range of different current loads. An example of a polarisation curve is shown in Figure

48 2. Fuel cells and polymer electrolyte membrane fuel cells Reversible cell voltage of 1.2 V Rapid initial fall in voltage Cell voltage [V] Slow and fairly linear fall in voltage Rapid fall in voltage at higher current density Current density [A cm -2 ] Figure 2.6.: Typical polarisation curve for a PEM fuel cells. An open circuit voltage (OCV) is defined as the cell voltage at equilibrium where no current is drawn. In a fuel cell, the OCV is lower than the theoretical value (see section 2.7.2) due to the irreversibility of the electrochemical reaction in the cell, the non-equilibrium condition and the non-zero current flow. The equilibrium concentrations at the operating conditions can not be practically achieved due to the possible flows of chemical species and electron through the membrane electrolyte (Srinivasan, 2006). A small fuel crossover reduces the actual fuel concentration from its equilibrium value at a given condition thus the cell voltage is less than the expected theoritical value. A small amount of electron flow in the membrane causes some internal current which can not be measured in the external circuit, as a consequence, the no current flow condition could not be practically obtained. Furthermore, when the cell is connected to an external circuit, at a zero reading shown in the connected voltmeter/ampmeter, there is a small amount of current flows through the connected circuit thus the no current condition for OCV measurement can not be gained. The voltage continuously decreases from the theoretical cell voltage when the current density increases. This section discusses the reversible thermodynamics of the reaction which gives rise to the theoretical cell voltage shown in Figure 2.6, the effects of 48

49 2. Fuel cells and polymer electrolyte membrane fuel cells non-standard operating conditions and the sources of voltage loss in an operating fuel cell Reversible thermodynamics operation: the Gibbs free energy The standard reversible cell voltage is the thermodynamic potential for a fuel cell at standard conditions, corresponding to a temperature of 25 C, a pressure of kpa and unit activity of reactants. This standard reversible cell voltage ( E 0 ) for a hydrogen/air fuel cell is based on the chemical potential of hydrogen in the oxidation reaction and oxygen in the reduction reaction. The reversible cell potential of a system can be determined by the sum of the potentials (E 0 ) in the system (Larminie and Dicks, 2000): E 0 cell = E1/2 0 (2.4) where E1/2 0 is the reversible cell potential for each electrode. The reversible potential can be determined from the change in the standard Gibbs free energy ( G 0 ) of reaction: E 0 1/2 = G0 n e F (2.5) The Gibbs free energy can indicate the spontaneous nature of the reaction. Only reactions with a negative G 0 occur spontaneously (Larminie and Dicks, 2000). In a PEM fuel cell, H 2 fuel is catalytically oxidized into electrons and protons in the anodic catalyst layer, O 2 is reduced with the transported electrons through the external circuit and the protons conducted through the membrane electrolyte in the cathodic catalyst layer. The standard potentials for the half cell reactions in the H 2 /O 2 PEM fuel cell (O Hayre et al., 2006) are: Anode : H 2 2H + + 2e E 0 a = 0V Cathode : 2e O 2 + 2H + H 2 O E 0 c = 1.229V Cell : H O 2 H 2 O + electricity E 0 cell = 1.229V As there is no change in the Gibbs free energy in the hydrogen formation reaction at standard state, the reversible cell potential of the H 2 reduction is zero (O Hayre et al., 2006). The standard cell potential of the O 2 reduction based on the higher heating value (HHV) is V. The higher heating value (HHV) assumes production of 49

50 2. Fuel cells and polymer electrolyte membrane fuel cells liquid water in the reaction (Larminie and Dicks, 2000). According to Equation 2.4, the standard reversible cell potential (Ecell) 0 in a H 2 PEM fuel cell is V (Zhang, 2008; O Hayre et al., 2006). Ecell 0 is presented as a dash line in Figure 2.6. However, the cell voltage obtained in an operating fuel cell is typically very different from the theoretical reversible cell voltage. One source of discrepancy is that fuel cells do not usually operate at the thermodynamic standard states of 25 C, kpa and unit activity of reactants (Larminie and Dicks, 2000; O Hayre et al., 2006; Barbir, 2005). The practical temperature range of PEM fuel cell is C (Srinivasan, 2006) which is significantly higher than the standard state. The other reasons are associated with the irreversibility of the electrochemical reactions and the voltage losses that occur during the fuel cell operation. These phenomena effectively lower the thermodynamic values of Ecell 0 to the cell voltage (Hoogers, 2003). The commonly obtained polarisation curve is shown as the solid line in Figure Non-standard conditions: the Nernst equation The Nernst equation is used to account for the non-standard operating conditions (Zhang, 2008). The equilibrium potential at non-standard conditions, E e, can be calculated using the Nernst equation (Larminie and Dicks, 2000; Speigel, 2008): E e = G0 n e F + RT ( n e F ln ph p 0.5 ) o p w (2.6) where G 0 cell is the change in Gibbs energy (G) of the overall reaction. p h, p o and p w are the partial pressures of hydrogen (at the anode), oxygen (at the cathode) and water (at the cathode), respectively. R is the universal gas constant, T is the absolute temperature, F is Faraday s constant, and n e is the number of electrons transferred for each molecule of reactant, which is 2 for H 2 and 4 for O 2. The equilibrium potential (E e ) in Equation 2.6 takes into account effects of the actual operating pressure and temperature, but does not include irreversible voltage losses which are significant in operating fuel cells. 50

51 2. Fuel cells and polymer electrolyte membrane fuel cells Irreversible voltage losses The irreversible voltage losses are reduction in potential of a fuel cell from the theoretical value. It is classified into four groups: activation loss, mass transport or concentration loss, ohmic loss and internal current loss or fuel crossover loss. In a PEM fuel cell, the internal current loss is relatively small in comparison to the others, so the polarisation curve in Figure 2.6 can be split into three distinct regions. Firstly, the low current density range is dominated by the activation loss. Secondly, the medium range current density, the effect of ohmic loss is evident. Lastly, at high current density the sudden drop of voltage is associated with the mass transport losses (Barbir, 2005). Activation loss The activation loss is related to the ability of electrode to transfer electrons between an electrode and a chemical species in solution. It is the extent of variation of the potential, across the electrode/electrolyte interface (at which this reaction occurs), from the reversible potential at each current density (Srinivasan, 2006). This loss is associated with the reaction kinetics which can be visualised as an energy barrier that the reaction has to overcome before it can release the usable energy to the external environment. The activation loss (η act ) increases nonlinearly with current density. It causes a significant voltage drop in the low current density region (see Figure 2.6). The theoretical Butler-Volmer equation relates the current density (j) to the exchange current density (O Hayre et al., 2006; Barbir, 2005): [ ] [ ]) αrd F (E e E) αox F (E e E) j = j 0 (exp exp (2.7) RT RT where j 0 is the exchange current density, (E e E) or η act is the potential difference between the reversible or equilibrium potential (E e ) and the reaction potential (E), α is the charge transfer coefficient, n e is the number of electron transferred per molecule of reactant, F is Faraday s constant, R is the ideal gas constant and T is absolute temperature (O Hayre et al., 2006; Larminie and Dicks, 2000). The Butler-Volmer equation can be used for both the anode and cathode. A simplified 51

52 2. Fuel cells and polymer electrolyte membrane fuel cells form of the Butler-Volmer equation is known as the Tafel equation which neglects one of the exponential terms in Equation 2.7, depending on the activation overpotential (η act ) of the electrode (Barbir, 2005). Anode The equilibrium potential (E e ) at anode for the hydrogen oxidation is 0 volt by definition, and to drive the oxidation, the overpotential term is negative with E e < E a. At significant overpotential, the first exponential term in Equation 2.7 is negligible. The oxidation current is dominant and the Tafel equation for the anode is simplified to: Cathode j a = j 0,a exp [ ] αox n e F (E e E a ) RT (2.8) At the cathode, the activation overpotential (E e E c ) is positive to drive the reduction reaction, consequently, the second term in Equation 2.7 is negligible. The cathodic current density can be simplified to: j c = j 0,c exp [ ] αrd n e F (E e E c ) RT (2.9) The exchange current density is current at which the forward and reverse reactions proceed at the same rate. The exchange current density and the charge transfer coefficient are kinetic parameters of the reactions at each of the electrode, and are indication of catalytic activity. Mass transport loss In a hydrogen/air PEM fuel cell, the reactant gases are used in the reaction and their partial pressures at the electrodes decrease when the current is increased. The extent of the reduction in the partial pressure is related to the current and the electrode physical characteristics which influence the rate of transport of reactant. The decrease in reactant partial pressure leads to an increase in the voltage loss at the electrode (Harvey et al., 2008). This increase in voltage loss is called the mass transport loss. 52

53 2. Fuel cells and polymer electrolyte membrane fuel cells j=0, p= p o j=j, p= p s p o Inlet reactant partial pressure supplied to electrode j=j l, p=0 Electrode surface p=reactant partial pressure at electrode surface Figure 2.7.: Change in the reactant partial pressure on electrode surface when the current density varies from no current to the limiting current density. Figure 2.7 shows the change in reactant partial pressure on electrode surface at different values of current density. Let p o be the reactant partial pressure when no current is drawn (j = 0). As the current is increased to a current density j, the reactant partial pressure at the electrode surface is reduced to p s. As the current approaches the limiting current density (j l ), the reactant partial pressure at the electrode approaches 0 (p = 0). The limiting current density is the maximum possible current density at an electrode. This limiting current density corresponds to a situation where the reactants are supplied to the electrode at the maximum possible rate. The reactant partial pressure at the electrode is assumed to decrease linearly with current density between zero and j l. The reactant partial pressure at any current load (p s ) is thus linearly interpolated between p o and zero. p o p s p o 0 = j j l (2.10) Thus: ) p s = (1 jjl p o (2.11) The Nernst equation describes the effect of reactant partial pressure on the equilibrium 53

54 2. Fuel cells and polymer electrolyte membrane fuel cells voltage at the electrode (Larminie and Dicks, 2000), which gives: η mass = RT n e F ln ( ) ps p o (2.12) The pressure ratio p s /p o in the electrode (Equation 2.11) is substituted in Equation 2.12, giving: η mass = RT ) (1 n e F ln jjl (2.13) Ohmic loss There are two main sources of ohmic loss in PEM fuel cells; loss in the fuel cell components and loss in the electrolyte (Pukrushpan et al., 2004). The loss in fuel cell components such as the electrodes and their interconnections is caused by the material s resistance to the electron flow. The loss in the electrolyte is due to the membrane conductivity which depends on membrane condition and chemical structure. Typically the ohmic loss in the fuel cell s components is negligible and only the loss in electrolyte is accounted for. η Ω = jr m (2.14) where η Ω is the ohmic potential loss and R m is the specific area resistance of the electrolyte. Internal current loss or fuel crossover loss Internal current loss occurs when electrons travel through the membrane to combine with O 2 and create a direct current flow between the electrodes within the fuel cell (Larminie and Dicks, 2000). Fuel crossover loss refers to a situation where fuel permeates through the membrane and combines with O 2 at the cathodic catalyst layer, reducing the cell potential. These losses are generally negligible because the membrane in PEM fuel cells has a very low permeability for the reactants and has negligible electronic conductivity. 54

55 2. Fuel cells and polymer electrolyte membrane fuel cells These losses can be reduced by increasing membrane thickness at the expense of greater ohmic loss. Thus a thorough analysis of this trade off is recommended (Sadiq Al-Baghdadi, 2007). For Nafion R membrane, the internal current loss is relatively small compared to the other voltage losses in H 2 /O 2 PEM fuel cells, and it is usually ignored in fuel cell simulations (Speigel, 2008; O Hayre et al., 2006) Cell voltage The negative change in the Gibbs free energy ( G 0 cell) of the overall H 2 /O 2 fuel cell reaction indicates the spontaneous nature of the reaction. G 0 is used to determine the standard state electrochemical potential of a PEM fuel cell (see Equation 2.5). The Nernst equation takes into account the non-standard operating conditions of the fuel cell. The reversibility and other voltage losses also occur as discussed above. The practical cell voltage (E v ) in an operating fuel cell is given by the reversible cell voltage (E e ) less the total voltage loss (η): E v = E e η act η mass η Ω η internal (2.15) 2.8. Efficiency The efficiency of different energy system can be used to compare their performance. PEM fuel cells have high potential for automotive application. The competing technology in this field is the internal combustion engines which operate on the heat engine principle (Sammes, 2006). The efficiency of these two systems is discussed and compared in this section Thermodynamic efficiency Thermodynamic efficiency (ς) is the maximum possible efficiency of the energy conversion process at a thermodynamically reversible state. Fuel cell 55

56 2. Fuel cells and polymer electrolyte membrane fuel cells Chemical energy is converted to electrical energy in PEM fuel cell: H O 2 H 2 O and the thermodynamic efficiency is: ς thermo = Energy available to produce work Energy available in the system (2.16) = G0 H 0 (2.17) where G 0 and H 0 are the Gibbs free energy ( kj mol 1 ) and the enthalpy of formations for the reaction at the standard state. The enthalpy of formation of liquid water is kj mol 1 (higher heating value; HHV) and of water vapour is kj mol 1 (lower heating value; LHV). The difference between HHV and LHV is the molar enthalpy of vaporisation of water which is kj mol 1. The HHV value for liquid water formation is commonly used because PEM fuel cells are generally operated at < 100 C (Speigel, 2008) in which water takes the liquid form. The HHV reversible thermodynamic efficiency (ς thermo ) of the H 2 /O 2 PEM fuel cells is approximately 83%. Conventional heat engine In an internal combustion engine, heat is converted to mechanical work and the maximum theoretical efficiency is limited by the Carnot cycle, for which the maximum efficiency is given by (Larminie and Dicks, 2000): ς Carnot = T hot T cold T hot (2.18) Compared to the maximum theoretical efficiency of PEM fuel cell, found that fuel cells have higher thermodynamic efficiency than the Carnot efficiency for T hot < 700 C and exhaust gas temperature of 50 C (Larminie and Dicks, 2000). The maximum theoretical efficiencies of a hydrogen/oxygen PEM fuel cell and of a heat engine are compared in Figure 2.8. The thermodynamic efficiency of fuel cell operating lower and higher than 100 C are calculated using HHV and LHV, respectively. The Carnot limit of heat engine is calculated for an exhaust gas temperature of 50 C (323 K). 56

57 2. Fuel cells and polymer electrolyte membrane fuel cells Efficiency limit [%] Fuel cell, liquid product Carnot limit Fuel cell, steam product Temperature [Celsius] Figure 2.8.: Thermodynamic efficiency of hydrogen/oxygen fuel cell at standard pressure and of heat engine (Carnot limit) with exhaust temperature of 50 C. Redrawn from Larminie and Dicks (2000). The thermodynamic efficiency of a fuel cell decreases as the operating temperature increases, whereas the Carnot limit of a heat engine increases with an increasing temperature. Fuel cells operate with higher efficiency than heat engines at temperature less than 750 C. The PEM fuel cell technology is not designed for the operation temperature far above 80 C thus in a practical temperature of the application, PEM fuel cells have higher thermodynamic efficiency than heat engines Operational efficiency In practice, the reversible thermodynamic efficiency of fuel cell can not be attained because, firstly, not all of the supplied fuel participates in the reaction; some fuel may be used in side reactions, be un-reacted or permeate through the membrane. Secondly, the voltage losses in fuel cell operation (as discussed in section 2.7.3) reduce the cell potential. These inefficiencies are included in the operational efficiency. The fuel efficiency (ς F ) is the ratio of the fuel used in the reaction to the total amount of fuel supplied (Barbir, 2005). The voltage efficiency (ς v ) is the ratio of the 57

58 2. Fuel cells and polymer electrolyte membrane fuel cells cell voltage (E v ) to the thermodynamic reversible potential (E e ) at the operating conditions (Zhang, 2008; Larminie and Dicks, 2000). ς F = 1 ν (2.19) ς v = E v E e (2.20) where ν is the fuel stoichiometric ratio, which is the ratio of the amount of fuel supplied to the amount utilised in a complete reaction. The thermodynamics, fuel and voltage efficiencies are combined to give the overall operational efficiency of a fuel cell: ς = G0 E v 1 H 0 E e ν (2.21) For a system which is not operated at a fixed fuel stoichiometric ratio, the fuel efficiency is determined by; ς F = j/(n e F ) ϑ (2.22) where ϑ is the specific fuel supply rate, therefore, the overall operational efficiency of fuel cell is; ς = G0 E v j/(n e F ) H 0 E e ϑ (2.23) 2.9. Summary The PEM fuel cells oxidise hydrogen fuel by using oxygen in the presence of platinum catalysts and the electrodes are electronically separated by a polymer electrolyte membrane, Nafion R being the most commonly used. A combined unit of anode, electrolyte membrane and cathode is called a MEA; many MEAs are aligned forming a fuel cell stack. Within the stack, bipolar plates separate the adjacent MEAs. At each end of stack, end plates are used to connect the stack to the external electrical circuit. The Nernst equation is used to determine the non-standard reversible cell potentials. However, practically this cell potential is reduced further due to irreversibility, including the effects of: the activation loss; the mass transport loss; the ohmic loss; and the internal current loss. 58

59 2. Fuel cells and polymer electrolyte membrane fuel cells Generally, PEM fuel cells are being developed for automotive application, due to the sustainable fuel and high efficiency. The high cost of the fuel cell system is one of the commercialisation barriers. The catalyst layer is known to be the most expensive component of the MEA. Thus, this study is set to model the effects of catalyst layer structure on the fuel cell performance, in order to gain a deeper understanding of this layer and improves its utilisation effectiveness. In the next chapter, a literature review of PEM fuel cell catalyst layer modelling is presented. 59

60 3. Literature review for catalyst layer modelling This chapter provides an overview of the development of PEM fuel cell modelling, the significance of the electrocatalyst to fuel cell performance, the importance of the catalyst layer structure and the common characteristics used in fuel cell modelling. Furthermore, the characteristics of various modelling approaches for the PEM fuel cell catalyst layer are discussed and a description of multiscale modelling is included at the end of chapter Introduction Significant obstacles to commercialisation of PEM fuel cells are related to the high cost of platinum catalysts, the large overvoltage of the cathodic reaction and the low catalyst utilisation and effectiveness (Papageorgopoulos, 2010; Srinivasan, 2006). In order to address these limitations, models have been developed to find the optimal fuel cell design and to investigate the effect of catalyst layer structure on the PEM fuel cell performance. The optimisation process involves controlling many parameters and can vary depending on the optimisation targets, such as the cell voltage, cost or durability Development of fuel cell modelling The modelling of PEM fuel cells shares the same origins as models for the phosphoric acid fuel cells, due to their similarities in using porous electrodes; with only the 60

61 3. Literature review for catalyst layer modelling electrolyte being different; i.e. a polymer electrolyte membrane in PEM fuel cells and a liquid electrolyte in phosphoric acid fuel cells (Weber and Newman, 2004b). The PEM fuel cell models developed by Springer et al. (1991) and Bernardi and Verbrugge (1992) presented the two main fundamental concepts of PEM fuel cell modelling (Wang, 2004; Speigel, 2008). The model of Springer et al. (1991) focused on water transport through a membrane and applied a flux-balanced method to describe mass transport phenomena in the hydrogen/air fuel cell with a partially hydrated membrane. The relationship between the membrane conductivity and the water content in the membrane was empirically determined. The catalyst layer was modelled as an interface between the membrane and the gas diffusion layer, whereas the model of Bernardi and Verbrugge (1992) used the Stefan-Maxwell gas diffusion equations to describe the material transport in the PEM fuel cell, and assumed a fully hydrated membrane. The catalyst layer was assumed to be filled with electrolyte and the reactant gas thus dissolved into the polymer phase and diffused through the electrolyte filled media to reach the reaction sites. Both models were one dimensional and set the framework for future PEM fuel cell modelling development. With the increasing computational ability of computers, more detailed simulations have been achieved through a finite element framework. These models are called Computational Fluid Dynamics (CFD) models and they are increasingly available through commercial packages (Wang, 2004). PEM fuel cell modelling has evolved in terms of complexity and variation in the field. Some of the models features are shown in Figure

62 3. Literature review for catalyst layer modelling Half-cell Membrane Catalyst layer Gas diffusion layer Vapour and Liquid Vapour Complete cell Stack Scope Modelling complexity Water phase Electrocatalyst performance 1D Dimension Focus Membrane properties 2D 3D Material transport Thermal effect Water management Flowfield effect Figure 3.1.: Variation of modelling features in PEM fuel cells. Four main features of PEM fuel cell modelling are presented in Figure 3.1. They are the modelling scope, phase of water, focus or objective of the model and dimension being considered in the model. The highlighted terms in Figure 3.1 are characters of the developed model in this study. The model in this study is a one-dimensional model considering variations of chemical species and ions in the direction perpendicular to the MEA surface. The modelling scope is a complete cell, including processes in membrane and both electrodes. Water is considered only in a single phase of vapour and the model focuses on studying the impact of electrocatalyst structure on the PEM fuel cell performance. The highlighted terms in Figure 3.1 are characters of the models developed in this study. The model was initially developed as a simple macro-scale model, and then the complexity was increased until the final model is a one dimensional, single phase and isothermal fuel cell operating at a steady state. The model includes one complete fuel cell of anode, cathode and membrane. It focuses on the influence of the structure of the electrocatalyst components on the fuel cell performance. 62

63 Electrocatalyst 3. Literature review for catalyst layer modelling The electrocatalyst refers to catalysts that participates in the electrochemical reaction (Zhang, 2008). Electrocatalysis is similar to normal catalysis but only refers to catalysis with a net transfer of electrons across the interface of either gas solid or solid liquid (Srinivasan, 2006). Catalysts accelerate reaction rate but not being consumed in the reaction. The electrode plays a catalytic role of either accepting electrons from the anodic reaction or producing electrons for the cathodic reaction. In PEM fuel cell, platinum is a suitable catalyst for both oxygen reduction and hydrogen oxidation in the acidic environment (Bultel et al., 1999; Eikerling et al., 2001). The electrocatalysis at cathode is discussed in detailed in this work. The cathodic electrochemical reaction occurs on the platinum surface, where H +, O 2 and e co-exist and are chemically combined in the presence of the liquid electrolyte as shown previously in Figure 2.4. The active sites are sometimes referred to as the three-phase zone of; oxygen (gas phase), electrons on the platinum/carbon surface (solid phase) and electrolyte (liquid phase). A two-phase zone concept for the active sites has been proposed and Weber and Newman (2004b) recommend that the two-phase zone concept is well supported by experimental results. In the two-phase zone concept, there are only liquid and solid phases at the reacting site. Oxygen gas is assumed to dissolve in Nafion R and the dissolved oxygen diffuses through the electrolyte network to react with protons and electrons on the platinum surface. The two-phase zone is selected to describe the reaction mechanism in this study Catalyst layer structure In catalyst layer modelling, a description of the catalyst layer structure must be clear so the processes occurring in the layer can be properly described. Microscopic techniques such as scanning electron microscopy (SEM) and transmission electron microscopy (TEM) are commonly used to show the catalyst layer morphology. Typical images of platinum in the catalyst layer of a PEM fuel cell were presented by Middelman (2002). 63

64 3. Literature review for catalyst layer modelling (a) (b) (c) (d) Figure 3.2.: (a) SEM image of the electrode membrane interface, (b) SEM image showing agglomerate particles, (c) SEM image at higher magnification and (d) SEM image at higher resolution (HR-SEM) shows carbon and platinum particles forming the agglomerates (Middelman, 2002). The SEM images in Figure 3.2 shows the catalyst layer structure in PEM fuel cell and the randomly distributed catalyst clusters and pores were observed in Figure 3.2(a) and 3.2(b). At the higher magnification, Figure 3.2(c) shows that the particles were agglomerates of much smaller particles which were coated. Middelman (2002) used HR-SEM to give the catalyst morphology in Figure 3.2(d). Platinum particles were observed as bright spots and randomly deposited on the supporting carbon surface. The TEM image by Moore (2009) in Figure 3.3 provides a higher magnification images of the platinum deposit on the supporting carbon. It shows platinum particles as black spot, the platinum particles randomly distributed on the carbon surface and small clusters of platinums were observed. The majority of data supports the 64

65 3. Literature review for catalyst layer modelling Figure 3.3.: TEM images for platinum deposition on the electrode, with permission from Moore (2009). existence of agglomerates based on TEM images and porosimetry (Siegel et al., 2003; Uchida et al., 1995). The typical dimensions of components in catalyst layer are summarised in Table 3.1. Items Dimension Source Catalyst layer thickness 1-20 µm Chan and Tun (2001) Ridge et al. (1989) Platinum diameter 2-5 nm Koper (2009) Uchida et al. (1996) Carbon size nm Koper (2009) Uchida et al. (1996) Porosity of catalyst layer 0.4 Zhang and Jia (2009) Table 3.1.: Typical dimensions in a catalyst layer of a hydrogen PEM fuel cell. The thin catalyst layer of 1-20 µm is sandwiched between the gas diffusion layer and the electrolyte from the membrane; therefore the agglomerates are partially exposed to the electrolyte whilst also in contact with the electrode. The deposited Pt/C particles on the backing layer coalesce and form clusters of catalyst whose size depends on the deposition technique. The supporting carbon particles are about 10 times larger than the platinum particles. Based on the images shown in Figure 3.2, the platinum and carbon particles form agglomerates with a random network of agglomerates in the catalyst layer. The typical catalyst layer porosity is 0.4 (Zhang and Jia, 2009) and the void space in the layer facilitates reactant flow. Information 65

66 3. Literature review for catalyst layer modelling on the morphology can be used to develop the schematic catalyst layer structure in the PEM fuel cell, as shown in Figure 3.4. Meso/micropores (20-40 nm) Catalyst agglomerate Carbon fiber Pt particle (2-3 nm) Electrolyte Oxygen diffusion path Supporting carbon (20-40 nm) R ag t f Macropores ( nm) R ag is agglomerate radius t f is electrolyte film thickness Membrane layer Catalyst layer GDL Figure 3.4.: Schematic diagram of catalyst layer structure according to the two-phase zone concept. According to this diagram of the catalyst layer structure, the model assumes that the reactant gas diffuses through the gas diffusion layer to the inner catalyst layer as shown in Figure 3.4. The gas dissolves into the electrolyte at the agglomerate surface before it diffuses to and reacts at the platinum surface. Ideally, all of the catalyst agglomerate within the catalyst layer is in close proximity to the membrane to reduce the proton transfer resistance across the catalyst layer. In Figure 3.4, agglomerates are evenly distributed in the catalyst layer, whereas in practice there is probably a mixture of carbon clusters with carbon fibre which are interconnected by tendrils of the membrane (Larminie and Dicks, 2000; Weber and Newman, 2004b) Internal structure of agglomerates Networks of electrolyte must cover the catalyst agglomerates to transport protons from the conducting gas diffusion layer through the electrolyte to the catalyst surface. 66

67 3. Literature review for catalyst layer modelling The agglomerates are in general difficult to characterise precisely. Despite the widely accepted concept of agglomerate formation in the catalyst layer of PEM fuel cells, the internal agglomerate structure turns out to be a controversial issue (Zhang, 2008). There are two concepts being circulated about the internal structure of the agglomerates: one which assumes that the electrolyte covers and does not exist within the agglomerates. The other assumes that electrolyte is embedded in agglomerates. Both concepts assume that platinum particles are smoothly deposited on the supporting porous carbons. Non-embedded electrolyte concept According to the size consideration, it seems impossible that ionomer fibrils of electrolyte can penetrate the nanometer size pores and become embedded within the agglomerates. Therefore, hydrophilic pores must occupy volume in the agglomerates and these are filled with water during fuel cell operation (Wang et al., 2004). This model is also known as the water-filled agglomerate model. These models generally use Nernst-Planck equations to describe the flux of dissolved species in the membrane and catalyst layer (Eikerling and Kornyshev, 1998). Examples of models which are derived from this concept include those presented by Sadiq Al-Baghdadi (2007), Eikerling and Kornyshev (1998) and Uchida et al. (1996). Embedded electrolyte concept This concept is known as the ionomer-filled agglomerate concept in which the electrolyte is assumed to penetrate and co-exist with the Pt/C cluster within the agglomerates. The typical method of dispersion of Pt/C in a mixture of ionomer and solvent solution during preparation of the catalyst ink, prior to its deposition on a backing layer, ensures homogeneity of the Pt/C with ionomer to the point that the ionomer becomes embedded within the agglomerate structure. Examples of models which were developed from this concept are given by Siegel et al. (2003), Weber and Newman (2004b) and Harvey et al. (2008). Note that the penetration of the electrolyte into the agglomerates depends upon, for example, the MEA fabrication technique, the size of carbon particles and the 67

68 3. Literature review for catalyst layer modelling electrolyte concentration used (Zhang, 2008). In this research, the embedded electrolyte model is selected to represent the catalyst structure. The catalyst layer is a porous layer with voidage and solid phase regions of carbon, Pt and Nafion R and a network of spherical catalyst agglomerates, as shown in Figure 3.4. Modelling of this structure commonly involves the catalyst utilisation effectiveness which is derived from the well known Thiele modulus (Bird et al., 2007). Regardless of the differences between these two methods, both concepts yield a model taking into account the most important mechanisms of fuel cell operation and consider how the catalyst layer composition affects the overall fuel cell performance Common characteristics used in catalyst layer modelling Most research studies using catalyst layer modelling aim to maximise the catalyst dispersion and to enhance electrochemical utilization of the catalyst. Commonly used characteristics includes Nafion R loading, platinum loading, platinum surface area, particle size and platinum to carbon ratio. It is very useful to understand these terms and their effect on the fuel cell performance. Nafion R loading Nafion R electrolyte serves as an ionic connection between the membrane and the catalyst. An insufficient Nafion R loading cannot provide sufficient ionic connection for proton transport to the cathodic catalyst layer; however, an excessive amount of Nafion R is also not desirable. According to the three-phase zone concept, an excessive loading of Nafion R can potentially isolate platinum from reactant gas and, therefore, reduces the reaction rate. In the two-phase zone concept, an excessive Nafion R loading increases diffusion resistance for the transport of dissolved gas from the agglomerate surface to the platinum catalyst particles. Passalacqua et al. (2001a) suggests that the optimum Nafion R content in the catalyst layer of low temperature PEM fuel cell is around 33 % by weight. Platinum loading Platinum is relatively expensive compared to other available catalysts, therefore it should be utilised at the highest possible efficiency. An excessive amount of platinum favours particle agglomeration and the clusters can potentially reduce the passage of 68

69 3. Literature review for catalyst layer modelling oxygen in the catalyst layer. On the other hand, an insufficient amount of platinum will greatly reduce the fuel cell performance due to lack of the available active surface area. In the early 1990 s the practical platinum loading was as high as 8 mg cm 2, recently, the typical platinum loading has decreased to 0.2 mg cm 2 while similar fuel cell performance has been maintained (Larminie and Dicks, 2000). Many research groups in this field focus on increasing platinum utilization in the fuel cells. For example, Cha and Lee (1999) used a novel sputtering method to achieve reasonable PEM fuel cell performance with platinum loadings as low as mg cm 2. Platinum surface area and particle size In order to achieve an acceptable reaction rate, the catalyst surface area must be much larger than the geometric area of the electrode. The total surface area of the dispersed catalyst is inversely proportional to the particle size: and thus smaller particles are expected to give better performance. Ralph and Hogarth (2002) recommended that it is economical and effective to have platinum particles with diameter of 4 nm or smaller. Koper (2009) suggested that there is a diminishing return of the active surface area when the catalyst particle size is below 2 nm, and that a 1 mg cm 2 loading of platinum with a particle size of 2-5 nm could generate an active electrode surface area of cm 2 per Pt cm 2. The catalyst-support material is commonly carbon powder with a high mesoporous area (>75 m 2 g 1 ). The carbon powder must provide sufficient void and surface area for gas transport channels and catalyst deposition respectively. Examples of the commercially available carbon powders are Ketjen Black, Vulcan XC72R and Black Pearls BP2000 (Speigel, 2008; Uchida et al., 1996). Platinum to carbon ratio The ratio of platinum to carbon (Pt/C) in the catalyst layer by weight is commonly stated in catalyst powder supply. An optimum ratio of platinum to carbon is needed to achieve the required mobility of the electrons, protons and gases. A Pt/C ratio of greater than 40 % by weight is usually used (Speigel, 2008). 69

70 3. Literature review for catalyst layer modelling 3.2. Catalyst layer modelling Catalyst layer models can be grouped into four main types (Speigel, 2008; Weber and Newman, 2004b). The simplest type of model of the catalyst layer is the interface model. The second type is the single-pore model, which is a direct derivative of the models developed for phosphoric acid fuel cells. It uses a detailed structure of the catalyst layer and it is sometimes referred to as the microstructure model. The other two models are the porous-electrode model and the agglomerate model. Both models are macro-homogeneous models, based on the average properties of an effectively homogeneous catalyst layer. The catalyst layer is seen as a continuum with prescribed transport properties for ions, electrons and molecules. The microscopic details of the catalyst layer are neglected in these models. The distinct difference of these two models is the length scale studied; the porous-electrode model considers the whole catalyst layer, whereas the agglomerate model focuses on the agglomerate scale (Weber and Newman, 2004b; Kulikovsky, 2010). The characteristic length in the porous-electrode model is in the range of µm (Grujicic and Chittajallu, 2004; Chan and Tun, 2001). The characteristic length in the agglomerate model is in the range of µm (Broka and Ekdunge, 1997a). Ohm s law is used to describe the proton transfer and the theoretical Butler-Volmer equation is used to describe the reaction kinetics in the models. 70

71 Interface models 3. Literature review for catalyst layer modelling Figure 3.5.: SEM image of an MEA for a hydrogen PEM fuel cell showing the anode at the top, the cathode at the bottom and the thin catalyst layer between the electrodes and membrane (Chen et al., 2006). Electrode Membrane Figure 3.6.: Crossectional view of a MEA cut using a glass knife showing an electrode with impregnated catalyst layer next to a Nafion R 117 layer (Broka and Ekdunge, 1997a). 71

72 3. Literature review for catalyst layer modelling The typical thickness of the gas diffusion layer is 350 µm, of the catalyst layer is 10 µmand of membrane electrolyte is 50 µm as illustrated in Figure 3.5 and 3.6 (Wang et al., 2011; Chen et al., 2006). The catalyst layer is relatively thin compared to other components in a PEM fuel cell so the interface models assume the thin layer has negligible thickness for modelling purposes (Weber and Newman, 2004b). All of the relevant variables are assumed to be uniform across the layer and independent of the structure. The macro-scale modelling of the fuel cell discussed in chapter 4 uses this approach. A study of the catalyst layer structure on the fuel cell performance cannot be achieved by an interface model. This is because the treatment of the catalyst layer in the interface model does not account for the chemical species concentration gradients within the catalyst layer (Weber and Newman, 2004b) Single-pore models The single-pore model is a microscopic model which requires information on the microstructure of the layer and does not use average parameters such as the effective diffusivity or conductivity of the catalyst layer. It was originally used for phosphoric acid fuel cell modelling. Cylinders filled with electrolyte and catalyst aggregates Cylinders filled with reactant gas Nafion Carbon support Pt Nafion Carbon support Pt membrane Catalyst layer GDL membrane Catalyst layer GDL (a) (b) Figure 3.7.: Schematic diagram of the catalyst layer structure assumed in single pore models where the cylinders were assumed to be filled with (a) the electrolyte and the catalyst aggregates and (b) the reactant gas. 72

73 3. Literature review for catalyst layer modelling The single-pore model describes the catalyst layer as a porous layer consisting of straight cylinders with defined radius. The cylinders can be filled with either the composition of electrolyte and catalyst agglomerates or the reactant gas. Figure 3.7(a) shows a schematic diagram of the catalyst layer structure that had its cylinders filled with the electrolyte and the catalyst agglomerate composition (Viitanen and Lampinen, 1990; Yang et al., 1990). In this case, the voidage in the catalyst layer was filled with oxygen. The oxygen must dissolve in the electrolyte and diffuses to the active catalyst surface to react. The oxygen reduction reaction took place in the cylinder region (Yang et al., 1990). Figure 3.7(b) shows an alternative structure of the catalyst layer in a single-pore model. Based on Grens et al. (1964), the cylinders were filled with oxygen, whereas the electrolyte and catalyst particles were distributed in the voidage region. The electrochemical reaction occurred on the surface of the gas-filled cylinders. In a more complex single-pore model, Bultel et al. (1999) combined the single-pore model with the agglomerate model (see section 3.2.4) to account for the discrete distribution of catalyst particles. The spherical catalyst agglomerates were assumed to be in a 3D hexagonal array (see Figure 3.8), the particles were arranged in cylindrical displacement and the electrolyte filled the space between the agglomerates. These models from Bultel et al. are grouped into the single-pore models category because a detailed catalyst layer structure (the agglomerate displacement within the catalyst layer) was assumed. Consequently, these single-pore models showed the localised reactant concentration distribution and the effect of agglomerate particle displacement in the catalyst layer. 73

74 3. Literature review for catalyst layer modelling Top view Side view Cylindrical symmetry Spherical catalyst particles Symmetric axis Electrolyte (a) (b) GDL Catalyst Membrane Figure 3.8.: Schematic diagram of catalyst layer in a complex single-pore model, based on Bultel et al. (1999). Characters Dimension 1D 1D 2D 1D 1D 1D Polarisation x x x - x x Mass transport in the following components were considered: Anode GDL Membrane Cathode GDL - x - - x - Catalyst layer modelling was applied to: Anode - - x Cathode x x x x x x Source of structure parameters Literature x x x x x x Microscopic study Reaction occurs On surface of gas cylinder x - - In electrolyte-filled cylinder x x x - x x Table 3.2.: Single-pore catalyst layer modelling where, 74

75 3. Literature review for catalyst layer modelling 1 Giner and Hunter (1969) 2 Ridge et al. (1989) 3 Bultel et al. (1999) 4 Grens et al. (1964) 5 Viitanen and Lampinen (1990) 6 Yang et al. (1990) Some features of single-pore models found in the literature are summarised in Table 3.2. Most of these models focused on the cathode performance and used parameters from other studies of the catalyst layer structure. Most of the models assumed the reaction to occur in the non-gas region. Although the catalyst agglomerate concept has been indirectly integrated into the model such as models from Bultel et al. (1999), the single-pore model is not suitable for PEM fuel cell use. It is suitable for a certain structure catalyst layer only whereas the pores in PEM fuel cell catalyst layer are randomly distributed and they are tortuous rather than straight. Additionally, the PEM fuel cell electrolyte does not necessarily penetrate the pore space as assumed in the single-pore model. The observed catalyst structure in PEM fuel cell is more agglomerate-like, therefore this modelling approach is not ideal for the purpose of this study Porous-electrode models Porous-electrode models assume that all phases exist at all points in the interested volume with non-uniform concentrations and potentials. The model is concerned with the overall reaction distribution in the catalyst layer and uses representative values of properties such as volume fraction and surface area per volume to describe the layer. The exact geometric details of the catalyst layer are not considered. The characteristic length scale of the porous-electrode model is the catalyst layer thickness. The models apply mass transfer theory and electrochemical reaction kinetics to simulate fuel cell performance. A porous-electrode model from Bernardi and Verbrugge (1992), which considered a finite catalyst layer thickness and a fully hydrated membrane, is seen as the origin of the approach. Most of the models are designed to determine the fuel cell voltage by including the potential loss in the catalyst layer such as the model reported by Kulikovsky et al. (1999). 75

76 3. Literature review for catalyst layer modelling Both three-phase and two-phase zone concepts have been applied in models in literature. Kulikovsky (2001) and Bernardi and Verbrugge (1992) used a three-phase zone concept, which uses the Stefen-Maxwell equation to describe gas diffusion in the catalyst layer. Kulikovsky (2001) simplified the calculation by assuming a uniform gas concentration existed throughout the layer whereas Gurau et al. (1998) assumed a concentration gradient in the layer. On the other hand, Wang and Savinell (1992) used a two-phase zone concept and assumed that reactant gas dissolves in the electrolyte and diffuses to the catalyst in the layer. The reactant gas concentration in the electrolyte was assumed to be in equilibrium with the gas phase partial pressure. Some features of the reviewed porous-electrode models are presented in Table 3.3. Characters Dimension 1D 1D 1D 2D 1D 1D 3D 2D 1D 1D Polarisation x x x x x x x x x x Mass transport in the following component was considered: Anodic GDL x x Membrane x - - x - x x Cathodic GDL x x - x x x x Catalyst layer modelling was applied to: Anode x - x x x x Cathode x x x x x x x x x x Source of structure parameters Literature x x x x x x x x x x Microscopic study - x Table 3.3.: Porous-electrode catalyst layer modelling. where, 1: Stonehart and Ross (1976) 2: Broka and Ekdunge (1997a) 3: Bultel et al. (1999) 4: Gurau et al. (1998) 5: Marr and Li (1999) 6: Chan and Tun (2001) 7: Harvey et al. (2008) 8: Kulikovsky et al. (1999) 9: Bernardi and Verbrugge (1992) 10: Wang and Savinell (1992) Some models include the mass transport effects in the gas diffusion layer and membrane, where others focus only on the catalyst layer. The cathodic catalyst layer 76

77 3. Literature review for catalyst layer modelling is more widely investigated in comparison to the anodic catalyst layer. Most of the reviewed porous-electrode models use literature as a source for data parameters. It has been demonstrated by Chan and Tun (2001) that the porous-electrode approach is suitable for modelling the anode which has a highly non-uniform reaction distribution. In conclusion, the porous-electrode modelling method assumes that the main mechanisms effecting fuel cell performance are not occurring within the agglomerates. The agglomerate structure has not been accounted for. So clearly the model could not be used to study the impact of the catalyst layer structure at the agglomerate scale, unlike the agglomerate model which is discussed below Agglomerate models The agglomerate model is also a homogeneous model similar to the porous-electrode model but its characteristic length is a function of agglomerate radius instead of the catalyst layer thickness (Harvey et al., 2008). This type of model was developed mainly to study the impact of the catalyst layer structure on the fuel cell performance; such as the cell voltage, the power output and the catalyst utilisation effectiveness (Harvey et al., 2008). Catalyst agglomerates Nafion Carbon support Pt GDL Catalyst layer membrane Gas flow through macro/meso pores via in the catalyst layer Figure 3.9.: Schematic diagram of catalyst layer in an agglomerate model. 77

78 3. Literature review for catalyst layer modelling The agglomerates are assumed to be identical in shape and size. At the agglomerate boundary, gases (and ions) diffuse through the electrolyte layer covering the carbon agglomerates to the platinum surface where the electrochemical reaction takes place. Within the agglomerates a gas concentration gradient is expected (Weber and Newman, 2004b). Agglomeration of catalyst particles and the electrolyte concept was introduced by Giner and Hunter (1969) amongst one of the first publications to present the agglomerate concept. The concept was later adopted widely for fuel cell modelling for example by Stonehart and Ross (1976) and Ridge et al. (1989) and Broka and Ekdunge (1997a). Although these models use the agglomerate concept, they are not categorized as agglomerate models here because either their characteristic length scale was not the agglomerate radius or the agglomerates were assumed to occupy a discrete configuration as in the single-pore models. The application of the agglomerate model was not limited to a particular type of fuel cell, for example, Fuller et al. (1995) studied the impact of catalyst loading on phosphoric acid fuel cell performance using an agglomerate model. They used the agglomerate model to predict and compare the performance of the fuel cell. However, this review focuses on the application of the agglomerate approach in PEM fuel cells only. Effects of catalyst parameters such as optimum catalyst loading and agglomerate size have been studied using the agglomerate concept. Secanell et al. (2007) considered effects of agglomerate radius and electrolyte thickness on the agglomerate on the fuel cell performance in a 2D model. The catalyst agglomerates were commonly assumed to be spherical in agglomerate modelling (Obut and Alper, 2011; Rao and Rengaswamy, 2006). Furthermore, microscopic study has also been used to improve the agglomerate model accuracy. Broka and Ekdunge (1997a) presented microscopic analysis of the catalyst layer and showed that the catalyst layer is made up of clumps of Pt/C catalysts surrounded by a thin film layer of electrolyte and that these clumps are separated by gas filled pores. The results attained in this study support the use of the agglomerate concept for catalyst layer modelling. Siegel et al. (2003) prepared the electrode for microscopic study by freezing a commercially obtained MEA in liquid nitrogen and then cutting the sample at room temperature with a razor (freeze fracture). The microscopic data such as the catalyst layer thickness, agglomerate size and the layer porosity were used in a 2D agglomerate model of the catalyst layer. The model s accuracy was good and they planned to develop a 3D model in 78

79 3. Literature review for catalyst layer modelling the future. Characters Dimension 1D 1D 3D 1D 2D 2D 1D 2D 3D 1D Polarisation x x x x x x x x x x Mass transport in the following component was studied: Anodic GDL x Membrane x x - Cathodic GDL x - - x x - Catalyst layer modelling was applied to: Anode - - x - x x Cathode x x x x x x x x x x Source of structure parameters Literature x x x x x x x x x x Microscopic study x x Table 3.4.: Agglomerate catalyst layer modelling. where, 1: Broka and Ekdunge (1997a) 2: Eikerling and Kornyshev (1998) 3: Obut and Alper (2011) 4: Chan and Tun (2001) 5: Siegel et al. (2003) 6: Grujicic and Chittajallu (2004) 7: Farhat (2004) 8: Secanell et al. (2007) 9: Harvey et al. (2008) 10: Rao and Rengaswamy (2006) Some common features of the reviewed models are presented in Table 3.4. There is a variation of model dimension from 1D to 3D. Most models focus on cathodic catalyst layer modelling without including the transport phenomena in the gas diffusion layer and membrane, and use structure parameters from the literature to describe the electrode structure. However, Siegel et al. (2003) presented a detailed 2D model which used a microscopic study to determine the model s parameters. Nevertheless, none of these models studies the effect of agglomerate shape on the overall fuel cell performance. Most of the models focused on the cathode catalyst layer. Cathodic electrocatalyst modelling is generally more complicated than anode electrocatalyst modelling. This 79

80 3. Literature review for catalyst layer modelling is due to the water generation and slow reaction in the cathode. The slow reaction kinetics of the cathode reaction involves a four electron-transfer reaction which is much slower than the reaction at the anode which involves two electrons transferring per mole of reactant (Bultel et al., 1999). Also, cathode modelling is complicated because the water generated at the cathode impedes oxygen transport Summary The interface models consider the mass transport mechanisms in fuel cell without including the structure of the catalyst layer. The single-pore models consider a certain catalyst layer structure but the catalyst layer in PEM fuel cell consisting of randomly distributed catalyst agglomerate, thus the single-pore models are not ideal for this study. The porous-electrode model and agglomerate model are the most relevant models for the scope of this study, based on the literature review presented. Both models use a macro-homogeneous approach with different characteristic length scales: the catalyst layer thickness and the agglomerate radius, respectively. The interface, the porous-electrode and the agglomerate models are presented in the following three chapters. 80

81 4. Interface model This chapter will provide an overview of the transport mechanisms of the chemical species, ions and electrons in hydrogen PEM fuel cells. The model derivation development, the simulation procedure and results are also presented Introduction The interface model is considered as the model for the macro-scale because it views the catalyst layer as a boundary between gas diffusion layer and membrane. The interface model assumes the thin layer is negligible for modelling purpose. The relevant parameters are independent of the catalyst layer structure. The development of the interface model gives an overall understanding of the transport mechanisms of the chemical species in the fuel cell Model development This section discusses the gas composition, gas transport in the gas diffusion layers, water transport in the membrane, sources of voltage loss and the power density output of the fuel cell. Also included is the calculation procedure for the model.the model was developed following the approach described in Springer et al. (1991). 81

82 4. Interface model Model description The system to be modelled is a low temperature hydrogen/air PEM fuel cell fed with saturated pure hydrogen at the anode and saturated air at the cathode. The PEM fuel cell is divided into five domains with four interfaces as shown in Figure 4.1. The catalyst layer is assumed to be at the interface between the electrode and the membrane. The boundaries of each domain are identified by the numbers 1 to 4 as shown in Figure 4.1. H 2, H 2 O In O 2, H 2 O, N 2 In Out Out O 2, H 2 O, N 2 H 2, H 2 O Gas channels Anode GDL Membrane Cathode GDL Gas channels Z = 0 Z = 0 Figure 4.1.: Schematic diagram of hydrogen/air fuel cell in the interface model Assumptions The following assumptions were made in the model: 1. The model is one dimensional, so it assumes that all variables only vary in the z direction, and are constant in all other directions. 2. Uniform temperature is assumed throughout the cell. 3. The cathode and anode feed streams are assumed to be saturated with water vapour at the humidifier temperature and the gases are assumed to be ideal. 4. The water is treated as existing only in the vapour phase. 82

83 4. Interface model 5. The model considers the concentration gradient, while the pressures are assumed to be constant in the electrodes. 6. The electronically conducting fuel cell components are assumed to have negligible ohmic resistance. 7. It is assumed that no hydrogen or oxygen permeated through the membrane so the fuel crossover voltage loss is insignificant. 8. The ohmic voltage loss in the cell is assumed to be due to the membrane resistance only. 9. The reactions at the anode and cathode are both assumed to be first order reactions so that the reaction rates are proportional to the reactant concentrations in each electrode. 10. The inlet gases are assumed to be saturated with water. 11. Water convection due to pressure gradients in membrane swelling is assumed to be negligible. 12. Hydrogen and oxygen fluxes are negligible in the membrane Composition of the inlet gases This section describes how the continuity equation is used to determine the composition of the chemical species between interfaces 1 and 4. Hydrogen, oxygen, water and nitrogen are denoted as subscripts h, o, w and n, respectively. The anode, cathode and interfaces 1 to 4 are denoted as subscripts a, c, 1, 2, 3 and 4, respectively. The inlet and outlet streams are denoted as superscripts I and L. The electrochemical reactions in a hydrogen/air PEM fuel cell are: 83

84 4. Interface model Anode H 2 2H + + 2e (4.1) Cathode 2e O 2 + 2H + H 2 O (4.2) Overall H O 2 H 2 O + electricity + heat (4.3) The total molar fluxes at anode (Q a ) and cathode (Q c ) are: Q a = Q h + Q w (4.4) Q c = Q o + Q n + Q w (4.5) At a current density of j (A m 2 ), the corresponding hydrogen molar flux (Q h ) at the anode is derived from the stoichiometry of the hydrogen oxidation. Q h = j 2F (4.6) where F is Faraday s constant of C mol -1. Similarly for oxygen, its molar flux (Q o ) is: Q o = j 4F (4.7) At steady state, due to the continuity equation and the stoichiometry of the electrochemical reaction, Q h can be expressed in terms of the other molar fluxes in the fuel cell: Q h = j 2F = Q h1 = 2Q o4 = Q wa β = Q wc 1 + β (4.8) where Q h1 is the hydrogen flux at interface 1, Q o4 is the oxygen flux at interface 4, Q wa is the water flux through interface 2, Q wc is the water flux from the cathode into the cathode gas diffusion layer (GDL) and β is the ratio of the water flux through interface 2 in anode to the water flux generated by the electrochemical reaction. Note that the water flux through interface 2 is the same as that through interface 1 and that the generated water flux is the same as the hydrogen flux through interface 1, hence: β = Q wa j/2f = Q w1 Q h1 (4.9) 84

85 4. Interface model Water mole fractions in the inlets can be calculated from the ratio of the saturated water vapour pressure to the corresponding electrode pressure because the inlet gases were assumed to be saturated with water. The saturated vapour pressure of water in the stream is calculated using the Antoine equation: ( ) P sat B = exp A T C (4.10) where P sat (kpa) is the saturated water vapour pressure, T (K) is the operating temperature and the constants A of , B of and C of are obtained from Smith et al. (2003). Thus the inlet water mole fractions at the anode and cathode, x I wa and x I wc respectively, are given by: x I wa = P wa sat (4.11) P a x I wc = P wc sat (4.12) P c Composition at interface 1 Referring to Figure 4.1, the difference between the fluxes of the inlet water with the saturated hydrogen (Q I wa) and the exit water (Q L wa) gives the water flux crossing interface 1 (Q w1 ). Q I wa Q L wa = Q w1 (4.13) Q I wa = ν hq h1 x I wa 1 x I wa (4.14) Q L wa = (ν h 1)x w1 Q h1 1 x w1 (4.15) The hydrogen stoichiometric coefficient (ν h ) is the ratio of the inlet hydrogen flux to the required hydrogen flux in the electrochemical reaction (ν h = Q I ha/q h1 ). Details of the derivations are given in Appendix A. These equations are rearranged to give the expression for the water mole fraction crossing interface 1 (x w1 ). x w1 = ν h x I wa β(1 x I wa) x I wa β(1 x I wa) + ν h 1 (4.16) 85

86 4. Interface model The hydrogen mole fraction at interface 1 is given by: x h1 = 1 x w1 (4.17) Composition at interface 4 The cathode is fed with saturated air, and the Antoine equation (Equation 4.10) was used to find the saturated water vapor pressure. The inlet water mole fraction (x I wc) can be obtained. The dry gas mole fraction of oxygen is defined as x od, therefore the inlet oxygen mole fraction (x I o) can be written as: x I o = x od (1 x I wc) (4.18) The inlet fluxes of inlet water at cathode (Q I wc), inlet oxygen (Q I o) and inlet nitrogen (Q I n) can be related to Q h1 as follows: Q I wc = xi wcν o Q h1 2(1 x I wc)x od (4.19) Q I o = ν oq h1 2 where ν o is the oxygen stoichiometric coefficient. (4.20) Q I n = ν oq h1 (1 x od ) 2x od (4.21) The outlet gas fluxes are related to Q h1 through the following equations: Q L wc = Q I wc + (1 + β)q h1 (4.22) Q L o = (ν o 1)Q h1 2 Derivations of these equations are given in Appendix A. (4.23) Q L n = ν oq h1 (1 x od ) 2x od (4.24) For each species, the difference between the cathode inlet and outlet fluxes is the gas flux crossing interface 4. Since the mole fraction is the ratio of the individual fluxes to the total flux crossing interface 4, the water and oxygen mole fractions at 86

87 4. Interface model interface 4 (x w4, x o4 ) can be shown to be equal to: x w4 = ν ox I wc + 2(1 + β)(1 x I wc)x od ν o + (2β + 1)(1 x I wc)x od (4.25) x o4 = (ν o 1)(1 x I wc)x od ν o + (2β + 1)(1 x I wc)x od (4.26) In conclusion, the gas mole fractions at interface 1 and 4 are derived from the continuity equation and are connected to the measurable inlet gas conditions and water flux ratio (β). The mass transport behaviour in the porous gas diffusion layer is used to determine the gas compositions at interfaces 2 and 3 from the initial conditions at interfaces 1 and 4, respectively, as discussed in the following section Gas transport in the gas diffusion layer The gas diffusion layer is composed of a porous carbon layer of either carbon cloth or carbon paper. It is a porous medium and as such there are four main modes of gas transport through it (Weber and Newman, 2004b; Speigel, 2008): Knudsen flow: This mode of transport represents the molecule-pore wall interaction. With a decreasing pore size, molecules collide more often with walls than with each other. According to the order-of-magnitude analysis between the average pore size in the gas diffusion layer and the mean-free path of reactant molecule, Knudsen flow has a significant impact when the average pore size is less than 0.5 µm (Weber and Newman, 2004b). Viscous/bulk flow: This mode is driven by the pressure gradient. The viscous flow is significant in a fuel cell operating with different pressures of anode and cathode. Continuum diffusion: This gas diffusion mode is caused by a concentration gradient. Surface flow: This mechanism occurs when there is a movement of the solid 87

88 4. Interface model materials through which the gas flows, causing gas to move with the solid particles. For example the movement of catalyst in a moving bed reactor can significantly affect the gas flow rate, so the surface flow must be considered in such a moving bed reactor but not in a gas diffusion layer that has no significant solid movement. The pore radius in a typical gas diffusion layer (GDL) is in the range of µm. The rate of Knudsen diffusion can therefore be shown to be insignificant in the GDL (Passalacqua et al., 2001b; Kong et al., 2002). There is no significant solid movement causing surface flow in GDL. The diffusion mechanism is taken into account. Gas transport in the anode gas diffusion layer Between interfaces 1 and 2 the total gas flux in the anode GDL (Q a ) is the sum of hydrogen and water fluxes, therefore Fick s law, a binary diffusion model, can be used (O Hayre et al., 2006). The diffusion flux of species i (Q i ) in a mixture of species i and j depends on its concentration gradient (dc i /dz) and the binary diffusivity (D ij ). The concentration gradient can be replaced by the mole fraction gradient for each component using the universal gas law, i.e. C i = P x i /(RT ), where x i is mole fraction of species i, P is the pressure, T is the temperature and R is the universal gas constant. dc i Q i = D ij dz = D ij RT P dx i dz (4.27) The binary diffusivity coefficient (D ij ) in a low operating temperature range can be calculated from (Bird et al., 2007): P D ij = a ij T Tci T ji b ij (P cip cj) 1 3 (Tci T cj ) 5 12 ( 1 M i + 1 M j ) 1 2 ɛ 3 2 (4.28) where D ij is the binary diffusion coefficient of i and j, P is the total pressure, T c is the critical temperature, P c is the critical pressure, M is the molecular weight and ɛ is the GDL porosity. Table 4.1 shows the values of the constants and the gas properties used in this model. 88

89 4. Interface model Parameters Values Parameters Values a w,o,a w,n, a w,h b w,o,b w,n, b w,h a n,o b n,o P c,w bars T c,w K P c,o bars T c,o K P c,n bars T c,n K P c,h bars T c,h K Table 4.1.: Values of parameters used in the model (O Hayre et al., 2006; Springer et al., 1991; Washburn, 1934). Natural convection makes a contribution to the gas flux in the anode GDL. The naturally convected flux is equal to uc i, where u is the velocity in direction of gas diffusion and C is the concentration. Since C i = x i /V where V is the molar volume, the naturally convected flux can also be written as ux i /V. Combination of the gas diffusion and convection equations allows the total water flux in anode GDL to be expressed as: Q wa = u x w V D whp a dx w RT dz = β j 2F Q a = (1 + β) j 2F = u V (4.29) (4.30) Equation 4.29 and 4.30 are rearranged to express the water mole fraction gradient: dx w dz = RT P a D wh [ (1 + β) j 2F x w βj 2F ] (4.31) Equation 4.31 is analytically integrated over the anode GDL thickness from z = 0, x w = x w1 to z = t a, x w = x w2. Integration of Equation 4.31 gives the water mole fraction profile in the anode GDL. The mole fraction expression is: x w (z) = ( x w1 β ) [ exp (1 + β) 1 + β RT P a D wh ] j 2F z + β 1 + β (4.32) 89

90 4. Interface model Gas transport in the cathode gas diffusion layer A mixture of nitrogen, oxygen and water vapour is transported from interface 4 to interface 3 and this multi-component diffusion is described using the Stefan-Maxwell equation. The gradient mole fraction given by Stefen-Maxwell equation is expressed as (Springer et al., 1991): dx i dz = RT j x i Q j x j Q i P D ij for i j (4.33) From Equation 4.33, the differential equations for oxygen and water transport across the cathode GDL are written as: dx o dz = RT P c j 2F [ xo (1 + β) 0.5x wc 0.5(1 x ] wc x o ) D ow D on (4.34) dx wc dz = RT P c j 2F [ (1 xwc x o )(1 + β) + 0.5x ] wc + x o (1 + β) D wn D wo (4.35) To determine x o3 and x w3, equations 4.34 and 4.35 were integrated numerically in the direction from interface 4 to interface 3 with the initial conditions of x o4 and x w4, respectively. The numerical solutions were obtained using fourth order Runge-Kutta integration. Detailed derivations of Equation 4.34, 4.35 and the fourth order Runge-Kutta integration are shown in Appendix A. While the electrodes are certainly important parts in the function of a fuel cell, the processes taking place in the membrane also have a significant impact on fuel cell behaviour. These processes include membrane properties such as water content and water diffusivity, which are discussed in the following section Membrane properties Nafion R is a copolymer with polytetrafluoroethylene (PTFE) as the backbone polymer. Nafion R has a fixed number of sulphonic sites (SO 3 ) in it. Nafion R 117 is a proton-conducting membrane which has been well characterized in a fuel cell 90

91 4. Interface model operating environment by much research over many years (Weber and Newman, 2004a). Recently, Nafion R 212 has been more commonly used in hydrogen PEM fuel cell application. Nafion R 212 is a non-reinforced dispersion-cast film and it has the same equivalent weight (EW), defined as the weight of Nafion R (in grams) per mole of sulfonic acid group, as Nafion R 117 of 1100 (Xu et al., 2011; Basura et al., 1998). The average membrane thicknesses of Nafion R 212 and 117 are 50.8 µm and 177 µm, respectively (Xu et al., 2011). The thinner membrane introduces less ohmic loss and this is one of reasons that recent hydrogen fuel cell applications have adopted Nafion R 212. Both membranes are manufactured from the same polymer but vary in thicknesses, therefore, their water and proton transport properties are expected to be the same. It has been assumed that the properties of Nafion R 212 are the same as Nafion R 117, the only difference being the thickness of the membranes. The model assumes the membrane to be a homogeneous mixture of three main components: membrane, water and protons. The membrane conducts protons when it is hydrated and its proton conductivity (σ) depends strongly on the water content (λ) in the membrane, which in turn depends on the water vapour activity (a w ) (Springer et al., 1991). The water vapour activity is determined by: a w = x wp P sat (4.36) where x w is the water mole fraction, P is the pressure and P sat is the saturated water vapour pressure. Water content The membrane water content (λ) is the ratio between the number of moles of water and the number of moles of SO 3, and it depends on the water vapour activity (a w ). The water content of Nafion R 117 has been measured at various temperatures. For instance, Zawodzinski et al. (1993b) measured λ of Nafion R 117 at 30 C, Hinatsu et al. (1994) at 80 C and Morris and Sun (1993) conducted a similar experiment at 91

92 4. Interface model 50 C and 100 C. All of the results show a similar outcome: the water content varies proportionally to the water activity but decreases at higher operating temperatures (Broka and Ekdunge, 1997b). Discrepancies in published results are related to differences in the measuring techniques and their accuracies (Weber and Newman, 2004b). An empirical equation for water content at 80 C has been used in this study because the fuel cell operating temperature is typically in this range. According to Hinatsu et al. (1994), a Nafion R 117 membrane in saturated air (a w = 1) has a water content at 80 C of In unsaturated air (a w < 1) and temperature of 80 C, the experimentally determined relationship between the water content (λ) and the water activity (a w ) is (Hinatsu et al., 1994): λ = a w 15.4a 2 w a 3 w (4.37) In contrast, Springer et al. (1991) reported that at 80 C, the water content of Nafion R 117 in equilibrium with liquid water reached as high as This latter water content is higher than the result from Hinatsu et al. (1994) even though both experiments were carried out at the same temperature. Springer et al. (1991) suggested that the membrane water content depends on the phase of the water (liquid or vapour) as well as the temperature. The operating range of the membrane in this model was extended to cover membrane supersaturation up to a w = 3 with a water content of Since liquid water is not considered in this study, it is possible for the calculated water activity to be greater than one i.e. x w P > P sat. The water content is assumed to increase linearly with water activity in the supersaturation region (Springer et al., 1991). For 1 a w 3: λ = (a w 1) (4.38) The membrane water content in this study has a profile as shown in Figure

93 4. Interface model Water content (λ) Water activity (a w ) Figure 4.2.: Water content in membrane as a function of water activities at 80 C. The minimum water content in the membrane is 1, which means that there is at least one mole of water per mole of SO 3. Data on the Nafion R 117 water content at 65 C was not available, thus, the profile of water content at 80 C in Figure 4.2 was assumed to be applicable to the temperature range in this study, 65 C Water transportation in membrane Water transportation in the electrolyte membrane is caused by three processes (Rowe and Li, 2001). Firstly, electro-osmotic drag is induced by proton movement from the anode to the cathode as a result of the electric potential gradient between the electrodes. Secondly, water diffusion occurs due to a gradient in water content. The content is higher at the cathode than the anode, so diffusion occurs in the opposite direction to the proton flow, hence it is termed back diffusion. The final process is convection. In this study, convection is assumed to occur only due to the pressure gradient between the electrodes is considered; convection due to pressure gradients that arise from membrane swelling are assumed to be negligible. Note that hydrogen and oxygen fluxes in the membrane are assumed to be zero and they do not influence the water and proton transport. 93

94 4. Interface model Electro-osmosis The electro-osmotic coefficient is defined as the number of water molecules accompanying the movement of each proton in the membrane. Zawodzinski et al. (1993a) measured the number of water molecules dragged per proton in Nafion R 117 by applying an electric field through a fully hydrated membrane at 30 C in equilibrium with liquid water. The coefficient was measured to be 2.5 H 2 O/H + in a fully hydrated membrane with water content of 22 (Zawodzinski et al., 1993a). Based on La Conti et al (1977), the water drag coefficient is assumed to be linearly related to the membrane water content, therefore the water flux caused by the electro-osmotic drag (Q w,e ) can be calculated from: Q w,e = 2 j 2F 2.5 λ 22 (4.39) where j is the current density, F is Faraday s constant and λ is the water content in the membrane. Diffusion Due to the electro-osmotic transport, water builds up at the cathode side so the water concentration near the cathode is higher than that near the anode. This water concentration gradient effectively causes back diffusion of water (Q w,d ) from the cathode to the anode (Springer et al., 1991). Q w,d = ρ m dλ D λ M m dz (4.40) where ρ m is the dry membrane density, M m is the membrane equivalent molecular weight, D λ is the water diffusivity in membrane, λ is the water content and z is the position along the membrane thickness in the direction from anode to cathode. Convection In a fuel cell operating with different electrode pressures on each side of the membrane, water convection takes place. The pressure gradient across the membrane is assumed 94

95 4. Interface model to be linear and the convected water flux (Q w,co ) is given by (Bernardi and Verbrugge, 1992): Q w,co = κ p µ λ ρ m M m P c P a t m (4.41) where κ p is the hydraulic permeability of water in the membrane, µ is the water viscosity, P c and P a are the cathode and anode pressures, respectively. The pressure gradient is assumed to be constant throughout the membrane. In summary, the total water flux in the membrane is determined considering electroosmosis, diffusion and convection, is expressed as: Q w,m = Q w,e + Q w,d + Q w,co (4.42) β j 2F = 2 j 2F 2.5 λ 22 ρ m M m D λ dλ dz κ p µ λ ρ m M m P c P a t m (4.43) Equation 4.43 is rearranged for the water content gradient: [ dλ dz = λ M m 2.5 j 11ρ m D λ 2F κ ] p P c P a M m µd λ t m ρ m D λ j 2F β (4.44) Equation 4.44 is numerically solved by using Runge-Kutta method Protonic conductivity in the membrane The proton conductivity depends on the level of hydration of the membrane. Conductivity increases approximately linearly with membrane water content and exponentially with temperature (O Hayre et al., 2006; Zawodzinski et al., 1993b). The conductivity of a Nafion R 117 membrane at 30 C with a water content of less than 1 is assumed to have a constant value of S cm 1 (Springer et al., 1991; Zawodzinski et al., 1993b). The conductivity of Nafion R 117 (in S cm 1 ) has been found to obey the following 95

96 4. Interface model relationship with λ (mole H 2 O / mole SO 3 ) and T (K) (Zawodzinski et al., 1993b): [ ( 1 σ(λ, T ) = (0.5193λ 0.326) exp )] T (4.45) Fuel cell performance Fuel cell performance is usually presented in the form of polarisation curve, which is a plot of cell voltage versus current density. The standard reversible cell voltage for a hydrogen/air fuel cell can be predicted using the Gibbs free energy change( G) of the reaction. The Nernst equation is used to account for the operating conditions which are different from the standard thermodynamic conditions (25 C at 1 atm). The theoretical electrical potential of the electrochemical reaction (E e ) can be calculated from the Nernst equation described in Equation 2.6 (Larminie and Dicks, 2000; Speigel, 2008). Alternatively, the reversible cell voltage (E e ) can be empirically predicted based on voltage - current models. For example, Xia and Chan (2007) and Amphlett et al. (1995) suggested an empirical equation in form of: E e = (T ) + 2 RT 4F ln ( ) p h p 0.5 o (4.46) where E e is in volt, pressures are in atm and temperature is in K. Assuming the gases are ideal, the partial pressure (p) of oxygen and hydrogen can be related to their mole fractions of hydrogen and oxygen, thus the reversible cell voltage (E e ) can also be expressed accordingly: E e = (T ) + 2 RT 4F log ( ) P a Pc 0.5 x h x 0.5 o (4.47) The practical cell voltage (E v ) is the remainder once the voltage losses caused by irreversibility have been subtracted from the reversible voltage, (E e ). E v = E e η a η c η Ω (4.48) where η a is the anode voltage loss, η c is the cathode voltage loss and η Ω is the ohmic loss. Furthermore, the output power density (P ) at a given current density (j) can 96

97 4. Interface model be determined from: P = E v j (4.49) Voltage losses in fuel cell There are four key voltage losses in each electrode of an operating fuel cell: activation loss, mass transport loss, ohmic loss and internal current loss (see section 2.7.3). The voltage losses in anode, cathode and electrolyte membrane are summarised in this section. Voltage loss in the anode (η a ) At the anode, the activation loss and the mass transport loss are accounted for. The activation loss is calculated using the Tafel equation and the concentration loss is calculated from the gas concentrations: η a = b a ln( j j 0,a ) + b a ln( x h1 x h2 ) (4.50) The exchange current density (j 0 ) is an indication of the kinetics of the electrochemical reaction. The value of j 0 depends on temperature, catalyst loading and available catalyst specific surface area. The Tafel coefficient (b a ) in Equation 4.50 can be calculated from (Larminie and Dicks, 2000): b a = RT n e α h F (4.51) where n e is the number of electrons transferred in the electrochemical reaction per mole of reactant, equal to 2 in the hydrogen oxidation reaction and α h is the hydrogen charge transfer coefficient which has a value between 0 and 1. 97

98 4. Interface model Voltage loss in the cathode (η c ) Oxygen is supplied to the cathode as air which means that at a high current density access of oxygen to the reaction sites may be limited by mass transport. activation and mass transport losses are included for the total voltage loss in cathode. The expression is: and The η c = b c ln( j j 0,c ) + b c ln( x o4 x o3 ) (4.52) b c = RT n e α c F (4.53) where b c is the cathode Tafel coefficient, F is Faraday s constant, x o3 is the water mole fraction at the cathode membrane interface, t c is the cathode GDL thickness and x o4 is oxygen mole fraction in the cathode inlet. Voltage loss in electrolyte (η Ω ) The major source of voltage loss in the membrane electrolyte is the resistance opposing proton movement, known as the area specific resistance (ASR). The model used in this study assumes that the ohmic voltage loss in the fuel cell is caused by the membrane resistance only. The method used for calculating the protonic conductivity profile over the membrane thickness was described in section Integration of the conductivity over the membrane thickness yields the total membrane resistance. The product of the total resistance and the current density is the ohmic loss at the current density, thus: η Ω = j tm 0 1 dz (4.54) σ(λ) 4.3. Computational procedure The equations described in the previous sections were used to determine the fuel cell performance. The calculation approach was to balance chemical species and ions through the cross-section of a MEA by using water to relate the fluxes because water exists in anode, membrane and cathode. For a specific current density, there 98

99 4. Interface model is a value of β (ratio of water flux being transported through interface 2 to the flux generated in the reaction) that satisfies the overall material balance. The water content of membrane at the interface between membrane and cathode was calculated from two procedures. One procedure was to determine the membrane water content (λ 3m ) resulted from mechanisms in anode and membrane electrolyte. Another procedure based on the mechanisms in cathode (λ 3 ). The discrepancy between λ 3m and λ 3 was calculated and the solution (suitable value of β) was accepted when the discrepancy was less than the convergence criteria of The discrepancy (δ) between λ 3 and λ 3m was determined by: δ = λ 3 λ 3m (λ 3 + λ 3m )/2 (4.55) After the material balance was solved, the potential losses in anode, membrane electrolyte and cathode were determined in order to find the fuel cell potential and power density. The computational steps used in the model are presented in Table 4.2. The computational procedure was written and simulated in Visual Basic for Microsoft Excel. 99

100 4. Interface model Step Action Anode Membrane Cathode Overall 1 Set j x h1 (eq 4.17) x w1 (eq 4.16) D ij (eq 4.28) Set β x w2 (eq 4.32) λ 2 (eq 4.37, ) λ 3m (eq 4.44) x o4 (eq 4.26) x w4 (eq 4.26) D ij (eq 4.28) x o3 (eq 4.34) x w3 (eq 4.35) λ 3 (eq 4.37, ) 15 Set convergence criteria for the difference in the values of water content at interface 3 determined from the cathode GDL (λ 3 ) and water transportation in the membrane(λ 3m ). 16 Determine discrepancy between λ 3 and λ 3m. 17 β was adjusted based on the bisection method, until the convergence criteria was satisfied E e (eq 4.47) 19 - η a (eq 4.50) η Ω (eq 4.54) η c (eq 4.52) E v (eq 4.48) P (eq 4.49) Table 4.2.: Interface model calculation matrix Assumption analysis and model validation This section analyses the assumptions which used in the interface model and validates the model against experimental data. 100

101 Assumption analysis 4. Interface model The one-dimensional nature of the model implies that there is no variation in the lateral distribution of gases along the gas channels. In reality, gas concentrations along the channels will vary due to diffusive and convective transport as well as the kinetics in the catalyst layer. These distributions will depend on the gas-medium properties and also on the reaction rates, which are also a function of the gas concentrations. The model does not focus on the concentration distribution in the gas channel, thus the constant concentration assumption is acceptable for the purpose of the study at this stage. The concentration distribution along the gas channels can not be studied in a 1D model and so 2D modelling is recommended to study the effect and improve model accuracy (Gurau et al., 1998). The assumption of a single phase of water vapour is generally acceptable. A twophase flow model is necessary when modelling the effects of liquid water, fuel cells with unsaturated gas feed or when studying flooding (Siegel et al., 2003). Isothermal operation was assumed in the model. The electrochemical reaction in a hydrogen PEM fuel cell is an exothermic reaction while ionic resistance can also cause ohmic heating in the cell (Siegel et al., 2003). These processes raise the gas temperature from the gas inlet toward the catalyst layer, affecting the density and diffusion coefficients of the gas components across the domain. However, the density-diffusivity product that characterises the gas transport varies less than 4% for practical temperatures in hydrogen PEM fuel cells, provided that the inlet air is saturated (Gurau et al., 2000). The isothermal assumption is therefore acceptable for the operating conditions studied. Hydrogen oxidation is a first order reaction (Larminie and Dicks, 2000) but oxygen reduction at platinum is a complex multistep reaction, depending on the overpotential, pressure and temperature, might follow several reaction paths. There is still some debate concerning the appropriate values of Tafel slopes and charge transfer coefficients in different operating condition regimes. Charge transfer coefficient is the ratio of the change in the energy of the transition state to the change in the energy of the reactant when the potential is changed. It represents how the reaction rate constants are affected by the applied potential (Bard and Faulkner, 1980). It is between 0 and 1 and the typical value is 0.5 (Srinivasan, 2006; Larminie and 101

102 4. Interface model Dicks, 2000). Due to the large dependence of the Tafel slopes and charge transfer coefficients on the operating conditions, the charge transfer coefficient has been used as a variable parameter (Eikerling and Kornyshev, 1998) Model validation The interface model was used to simulate the polarisation curve of a fuel cell. The set of parameters used in the model is shown in table 4.3 and the experiment conditions are shown in Table 4.4. Parameters Values Sources Anode transfer coefficient (α a ) 0.5 Larminie and Dicks (2000) Cathode transfer coefficient (α c ) 0.5 Larminie and Dicks (2000) Anode GDL thickness (t a ) 350 µm Speigel (2008) Cathode GDL thickness (t c ) 350 µm Speigel (2008) Anode GDL porosity (ɛ a ) 0.4 Zhang and Jia (2009) Cathode GDL porosity (ɛ c ) 0.4 Zhang and Jia (2009) Anode exchange current density (j 0,a ) 2000 A m 2 Larminie and Dicks (2000) Water diffusivity in membrane (D λ ) cm 2 s 1 Speigel (2008) Hydraulic permeability (κ) at 80 C m Bernardi and Verbrugge (1992) Water viscosity (µ) at 65 C Pa s Perry et al. (1998) Nafion R 117 dry density (ρ m ) 2000 kg m 3 Weber and Newman (2004a) Nafion R 117 equivalent weight (M m ) kg mol 1 Basura et al. (1998) Table 4.3.: Simulation parameters in the interface model. The cathode exchange current density (j 0,c ) shows a large variation in the literature. The range was found to be A m 2 (Lin et al., 2004; Zhang and Jia, 2009). The exchange current density is strongly related to the kinetics of the electrochemical reaction of the electrode, thus, the value of j 0 depends on catalyst loading and available catalyst specific surface area (Larminie and Dicks, 2000). The value of j 0,c = 1 A m 2 resulted the best fit of the interface model to the experimental data from Du (2010). This value was used in the model validation section. The parameter ranges found in literature are shown in the Appendix C. The fuel cell experiments of Du (2010) used the E-TEK ELAT R GDE LT120EW (Pt loading 0.5 mg cm 2 ) as both electrodes and a Nafion R NRE-212 membrane. The 102

103 4. Interface model experimental conditions are given in Table 4.4. Parameters Values Anode pressure (P a ) 2.5 atm Cathode pressure (P c ) 2.5 atm Hydrogen stoichiometric flow (ν h ) 1.5 Oxygen stoichiometric flow (ν o ) 2.0 Cell operating temperature (T ) 65 C Membrane Nafion R 212 thickness (t m ) 50.8 µm Table 4.4.: Fuel cell operating conditions in Du (2010). Results from the data set were compared with the experimental data for the hydrogen PEM fuel cell (see Figure 4.3.) Cell voltage [V] Experiment Interface power exp power model Current density [A cm -2 ] Power density[w cm -2 ] Figure 4.3.: Polarisation curves from the interface model and the experiment data from Du (2010). The simulation result was relatively accurate at a very low current density, however as the current density increased the interface model significantly overestimated the fuel cell performance (Figure 4.3). At 0.1 A cm 2, the model overestimated the cell voltage by 4% from the experimental data, whereas at 0.5 A cm 2, the over-estimation increased to 17.5%. This overestimation was expected because the interface model does not include effect of mass transport resistance in the catalyst layer. Although, the model could not simulate the fuel cell performance accurately as shown 103

104 4. Interface model in Figure 4.3, it shows the mass transfer mechanism in each domains of the fuel cell. The water and gases compositions in anode, cathode and membrane are discussed later Anode At the anode inlet, H 2 and H 2 O diffused from the anode inlet (interface 1) to the anode GDL membrane interface (interface 2), where H 2 O was transported through the membrane and, according to the mass conservation equation, the mole fraction of H 2 was raised slightly at the anode catalyst layer as shown in Figure 4.4. Hydrogen mole fraction Series1 Anode inlet (x h1 ) Series2 Anode GDL membrane (x h2 ) Current density [A cm -2 ] Figure 4.4.: Mole fraction profiles of hydrogen at each interfaces as function of current density. As the current load was increased in the model, the flux of H 2 O through the membrane increased because there was a greater molar flux of H +. The diffusion of H 2 O from anode to cathode was accelerated due to the higher current density and the hydrogen stream began to dry faster. Thus water mole fraction decreases and hydrogen mole fraction increases with the increasing current density. 104

105 4. Interface model Cathode Oxygen mole fraction Series1 Membrane cathode GDL (x o3 ) Cathode inlet (x Series2 o4 ) Current density [A cm -2 ] Figure 4.5.: Mole fraction profiles of oxygen at each interfaces as function of current density. In the feed of saturated air to the cathode, O 2, N 2 and H 2 O were present in the inlet stream. The difference in flux between the outlet and inlet was assumed to enter interface 4 and diffuse through the cathodic gas diffusion layer to the cathodic catalyst layer (interface 3). At interface 3, O 2 was used and H 2 O was generated in the reaction thus x o,4 > x o,3 and x w,4 < x w,3. At higher current densities, more H 2 O was generated and more O 2 was used than those at low current densities, thus an increase in the concentration of H 2 O and a decrease in the concentration of O 2 with respect to current density (j) were observed, as in Figure 4.5. Note that a high value of x w can potentially cause flooding and effectively reduce the catalyst surface area in the fuel cell. Comparison of Figures 4.4 and 4.5 shows that the O 2 concentration in the cathodic GDL changed faster than the H 2 concentration in the anodic GDL with respect to a change in current density. The steeper mole fraction gradient in the cathode indicated its higher gas diffusion resistance than in the anode. The author believes that the additional resistance was due to the water produced in oxygen reduction. 105

106 4. Interface model Membrane Water mole fraction Series1 Series2 Series3 Series4 Anode inlet (x w1 ) Anode GDL membrane (x w2 ) Membrane cathode GDL (x w3 ) Cathode inlet (x w4 ) Current density [A cm -2 ] Figure 4.6.: Mole fraction profiles of water at each interfaces as function of current density. Figure 4.6 shows mole fractions of water at the anode inlet, at interface of the anode GDL to the membrane, at interface of the membrane to the cathode GDL and at the cathode inlet as function of current density. The water mole fractions at anode (x w1 ) decreased while that at cathode (x w4 ) increased with the increasing current density. Across the thickness of membrane, the net water flux moves from anode to cathode because the water mole fraction increased from the anode (x w2 ) to the cathode (x w3 ) sides. Furthermore, the difference in mole fractions between interfaces expanded with the increasing current density, the observation indicates a significant variation in the membrane hydration level from anode to cathode sides in a high current density operation. Nafion R conducts protons most effectively when it is hydrated (Larminie and Dicks, 2000). As can be seen in Figure 4.6, the water mole fraction increased with current density, this was due to the increasing rate of electro-osmosis. H 2 O was transported 106

107 4. Interface model by electro-osmosis from the anode through the membrane to the cathode, thus x w,2 < x w, Membrane water content ( λ) increasing j increasing j Protonic conductivity [S m -1 ] increasing j increasing j %membrane thickness from anode interface %membrane thickness from anode interface (a) (b) Figure 4.7.: (a) Membrane water content and (b) protonic conductivity in the membrane from the anode to the cathode interfaces. In Figure 4.7, the water content profile and conductivity profile have the same trend as the water mole fraction at interfaces 2 and 3 in Figure 4.6. The water content at the anode side (interface 2) was in the range of 6-10 mole H 2 O/ mol SO 3 and it increased to the higher range of mole H 2 O/ mol SO 3 at the cathode side (interface 3). Protonic conductivity at the anode side (interface 2) varied from 4-8 S m 1, and increased across the membrane to 8-12 S m 1 at the cathode side (interface 3) beta (β) Current density [A cm -2 ] Figure 4.8.: Ratio of water flux at the anode (interface 2) to the rate of water generated at the cathode as a function of current density in a PEM fuel cell operating at 65 C. 107

108 4. Interface model The material balance in the interface model was achieved by varying the ratio of the water flux at interface 2 to the generated water (β). The obtained profile of β as a function of j is shown in Figure 4.8. At the standard simulation conditions of 65 C, which was used to represent the experimental conditions in Du (2010), β increased steeply in the region of 0 to 0.4 A cm 2, then remained constant at approximately 0.19 for current densities greater than 0.4 A cm 2. Half of the ratio, which is 0.5β, is a ratio of the net flux of water per proton transported through membrane electolyte that can give an indication of the electro-osmotic diffusion of water in membrane at the operating conditions Summary A flux balance-based method was used to determine the amount of chemical species in the reaction according to the fuel cell operating conditions. The continuity equation was used to complete the material balance and suitable governing equations for each domain were applied. Diffusion was the main transport mechanism in both the electrodes and the membrane, although in the membrane water transport was influenced by membrane specific effects such as protonic conductivity. The chemical composition at the interfaces and the potential losses in the fuel cell were determined. The interface model overestimated the fuel cell performance and at the high current density range, the over-estimation was significant. The model could not capture the mass transport effects in the catalyst layer, which dominantly occurs at high current density operation. To improve the simulation accuracy, a catalyst layer model should be integrated into the macro-scale model. 108

109 5. Porous-electrode model In this chapter, a porous-electrode model for the cathodic catalyst layer in a low temperature hydrogen PEM fuel cell is described and developed. The model has been applied to the cathode only and the anode has been treated as an interface between the gas diffusion layer and the membrane using the interface model (Chapter 4). The computational procedure for the catalyst layer model is explained. The model is then integrated into the interface model to simulate the overall fuel cell performance. The simulation and experiment results are compared in order to validate the model Introduction The porous-electrode model assumes a homogeneous composition of media in the catalyst layer. The model is based on mass transfer principles and describes the catalyst layer using average/overall values of properties such as volume fraction (Harvey et al., 2008). It considered the overall reaction distribution in the catalyst layer without including the exact details of the catalyst structure Model development The description of the catalyst layer in the porous-electrode model is shown schematically in Figure 5.1. The conservation of oxygen in the layer, involving the diffusion and electrochemical reaction, is used to develop the governing equation for the model. The model was developed following similar approach exhibited in Marr and Li (1999); Chan and Tun (2001). 109

110 Model description 5. Porous-electrode model The cathodic catalyst layer is modelled as a porous material, that has its pores filled with liquid electrolyte. The catalyst agglomerates are uniformly distributed in the layer. The reactant gas dissolves in the electrolyte and moves by diffusion and reaction. Bulk properties in the catalyst layer are used in this model. O 2, H 2 O, N 2 In Out Membrane Cathode GDL Gas channels O 2, H 2 O, N 2 Z = t cat,c Z = 0 Figure 5.1.: Schematic diagram of fuel cell cathode in the porous-electrode model. Material transportation is considered from the gas inlet towards the membrane covering the catalyst layer thickness, that is from z = 0 to z = t cat,c as shown in Figure 5.1. The model focuses on the overall reaction distribution in the catalyst layer, consequently, the characteristic length scale in this model is the catalyst layer thickness: ζ = t cat,c (5.1) where ζ is the characteristic length and t cat,c is the thickness of catalyst layer in the cathode Assumptions The following assumptions were made in the porous-electrode model development: 1. The model is assumed to be one dimensional, so reactant concentrations and 110

111 5. Porous-electrode model other variables only change in the z direction. 2. The fuel cell is assumed to operate at a steady state and isothermal. 3. Double-layer charging in the catalyst layer is assumed insignificant and can be neglected. 4. The porous material in the catalyst layer is uniform and homogeneous. 5. Ohmic loss in the electrolyte phase of catalyst layer is assumed negligible. 6. Diffusion of the dissolved oxygen in the electrolyte phase of the catalyst layer can be described by Fick s law Diffusion and conservation of oxygen in the catalyst layer Oxygen diffuses from the cathode gas diffusion layer to the catalyst layer and dissolves in the electrolyte phase in the catalyst layer. According to Henry s law of gas solubility, the solubility is directly proportional to the partial pressure (Atkins and Jones, 1940). Oxygen concentration at the electrolyte surface is calculated from the oxygen partial pressure: (C o ) z =0 = H op o (5.2) where C o is the concentration of dissolved oxygen in the electrolyte, H o is the Henry s constant and p o is the partial pressure of oxygen. Furthermore, Henry s constant is a temperature dependent variable: H o = H o,ref exp [ 1700 ( 1 T 1 )] T ref (5.3) The dissolved oxygen is transported in the catalyst layer by diffusion. Fick s law is used to describe the binary diffusion of oxygen and water in the layer: Q o = D o,cl dc o dz (5.4) where Q o is the molar flux of oxygen and D o,cl is the effective diffusivity of oxygen in the catalyst layer. The effective is used to indicate the transport coefficient applied 111

112 5. Porous-electrode model to a porous material, as distinguished from a homogeneous region. The tortuous, random, and interconnected arrangement of the porous region makes the length of the diffusion path unknown (Smith, 1974). The effective diffusivity in the catalyst layer is evaluated by the Bruggemann relation (De La Rue and Tobias, 1959; Chan and Tun, 2001), where: D o,cl = D o,el (ɛ cl ) 1.5 (5.5) where D o,el is the diffusivity of oxygen in the electrolyte and ɛ cl is the porosity of the catalyst layer. Differentiating equation 5.4 gives: dq o dz = D o,cl d 2 C o dz 2 (5.6) In terms of the electrochemical reaction, the diffused oxygen is reduced at the platinum surface to produce current. The oxygen reduction reaction is: 2e + 1O H + H 2 O Thus one mole of oxygen reacts with four moles of protons: Q o = j 4F (5.7) where Q o is oxygen molar flux, j is the ionic current density flowing in the catalyst layer and F is Faraday s constant. The oxygen molar flux is balanced by the proton conduction in the catalyst layer, due to the electrochemical reaction thus: dq o dz = 1 4F dj dz (5.8) At steady state, the flux due to diffusion (equation 5.6) and the rate of consumption in the electrochemical reaction (equation 5.8) are balanced: D o,cl d 2 C o dz 2 = 1 4F dj dz (5.9) The current density gradient expression in equation 5.9 is integrated over the catalyst 112

113 5. Porous-electrode model layer thickness to find the total current generated in the catalyst layer: j = = tcat,c 0 tcat,c 0 dj dz dz 4F D o,cl d 2 C o dz 2 dz = 4F D o,cl [ dco dz z =t cat,c dc o dz z =0 ] (5.10) The expression for the oxygen concentration gradient in the catalyst layer will be determined in the next section Electrochemical reaction in the cathode Electron transfer, generating current, occurs in the catalyst agglomerates, which are assumed to be distributed randomly in the catalyst layer. The change in current density (j) of a small element of catalyst layer of thickness dz is illustrated in Figure 5.2. j z +dz A j z d z Figure 5.2.: Three dimensional view shows current flow in the catalyst layer. The amount of current transferred from the electrolyte in dz is given by: (j z +dz j z )(A) (5.11) 113

114 5. Porous-electrode model where A is the cross-sectional area of the catalyst layer. Current is transferred from all of the active agglomerates, thus, the current is expressed as function of the catalyst layer geometry: Total current = j ag av cl (5.12) where j ag is the current density at the agglomerate surface, a is the surface area of agglomerates per unit volume of catalyst layer (i.e. the specific surface area), and V cl is the volume of the catalyst layer. Thus: Total current = ( P o j 0,c Po ref [ ] αc n e F ) exp η act (a)(a dz ) (5.13) RT where j 0,c is the exchange current density, P o is the oxygen pressure, Po ref is a reference oxygen pressure, α c is the charge transfer coefficient of oxygen reduction, n e is the number of electrons involved in the reaction, F is Faraday s constant, R is the gas constant, T is the absolute temperature and η act is the activation overpotential. The expression for current density gradient in the catalyst layer is obtained by combining equation 5.11 and 5.13: j = aj 0,c P o Po ref [ ] αc n e F exp η act RT (5.14) According to the ideal gas law, the pressure ratio can also be expressed as a concentration ratio: Therefore: j = aj 0,c P o P ref o C o Co ref = C o C ref o [ ] αc n e F exp η act RT This equation can be simplified for the one dimensional model: dj dz = a j 0,c C o C ref o [ ] αc n e F exp η act RT (5.15) (5.16) (5.17) Equation 5.17 is substituted into equation 5.9 and the second order differential 114

115 5. Porous-electrode model equation for oxygen and current balance in the porous catalyst layer is: d 2 C o D o,cl dz = a j 0,c 2 4F C o C ref o [ αc 4F exp RT η act ] (5.18) The analysis is carried out using dimensionless terms by normalising the variables to reference values. Let C and Z be the dimensionless concentration and dimensionless thickness: C = C o C ref o and Z = z t cat,c (5.19) where t cat,c is the catalyst layer thickness and Co ref is the reference oxygen concentration on which j o,c is based. Thus equation 5.18 can be written as: d 2 C dz 2 = a j 0,c t 2 cat,c D o,cl 4F C ref o [ αc 4F exp RT η act ] C (5.20) Equation 5.20 can be integrated analytically (see Appendix B) to give: C = e hz + e hz e h + e h (5.21) where h = ( a j0,c t 2 cat,c D o,cl 4F C ref o [ αc 4F exp RT η act ] ) 0.5 (5.22) Rewriting the dimensionless variables of C and Z to their original variables: C o = [ Cref o e h + e h e h z t cat,c + e h z t cat,c ] (5.23) The derivative of equation 5.23 gives the oxygen concentration gradient in the catalyst layer, which is: dc o = Cref o dz e h + e h h t cat,c [ e h z t cat,c e h z t cat,c ] (5.24) 115

116 5. Porous-electrode model The concentration gradients are substituted into equation 5.10, giving: where: j = 4F D o,cl C ref o e h + e h j = 4F D o,cl h Cref o t cat,c h 2 = a j 0,c t 2 cat,c D o,cl 4F C ref o h t cat,c (e h e h ) e h e h e h + e h (5.25) [ αc 4F exp RT η act ] (5.26) Equation 5.25 is the governing equation for the porous-electrode model. It takes into account the mass transport and electrochemical reaction kinetics in the cathodic catalyst layer Computational procedure The calculation was carried out for each specific current density of j, and a bisection method was used to numerically determine the solution for the differential equation in The concentration of the dissolved oxygen at the interface between the catalyst layer and the gas diffusion layer was used as the boundary condition for the porous-electrode model. 1. The oxygen mole fraction at interface between the gas diffusion layer and the catalyst layer (x o3 ) was determined in the interface model, and the corresponding partial pressure and equivalent concentration at the operating temperature were calculated using equations 5.2 and The estimates of the lower end (η act,l ), the higher end (η act,h ) and the mid point value (η act,m ) of the activation loss were used in equation 5.26 and 5.25 to give their corresponding current density of j l, j h and j m, respectively. 3. The required current density (j) was compared to the current density at the mid point (j m ). The discrepancy between j m and j was calculated from equation 5.27: δ = j m j (j m + j)/2 (5.27) 116

117 5. Porous-electrode model If the discrepancy was less than or equal to the convergence criteria, which was 0.01, the activation loss at the mid point (η m ) was accepted as the solution for the specified current density. 4. On the other hand, if the criteria was not met, the sub-interval, which is half of the activation loss interval in the step 2, that contained the required current density was identified. 5. Based on the new interval, step 2,3 and 4 were repeated, until the convergence criteria was satisfied. 6. To integrate the porous-electrode model of catalyst layer into the macro-scale model of the fuel cell in Chapter 4, the cathodic activation loss (η act,c ), the first term in equation 4.52 was substituted by the activation loss found in this model. 7. The rest of the computational procedure was carried out as shown in Table 4.2 in Chapter Model validation Some of the key assumptions applied to the porous-electrode model are discussed in this section and the simulation results have been compared with the experimental results from Du (2010) to validate the model Assumption analysis Fick s law was used to describe the diffusion of the dissolved oxygen in the electrolyte. The diffusion law should be valid for a steady state operation with low solubility oxygen in the electrolyte of a thin catalyst layer. The double layer effect at the pore surfaces in the electrolyte phase causes microscopic variation of the electrolyte potential in a direction perpendicular to the z direction. 117

118 5. Porous-electrode model This microscopic variation was suggested to be averaged out in the macroscopic model and the double layer effect was assumed negligible (Eikerling and Kornyshev, 1998). The catalyst layer was assumed to be filled with electrolyte and uniformly distributed agglomerates. The proton resistance in the electrolyte phase introduces ohmic loss and the reaction in the agglomerates indicates the presence of activation loss in the layer. The ohmic loss in the catalyst layer, which is proportional to the electrolyte conductivity and electrolyte thickness, was compared to the loss in the membrane layer. The conductivities were expected to be the same because the electrolyte in both domains were in similar environments. The electrolyte membrane was 4 times thicker than the total catalyst layer thus the related ohmic loss in the membrane was expected to be around 4 times higher than that in the catalyst layer. Furthermore, the ohmic loss in the membrane was much less than the activation loss in the catalyst layer (see Figure 5.3). 0.3 Ohmic ohmic loss in membrane Cathodic act,c activation loss Voltage loss [V] Current density [A cm -2 ] Figure 5.3.: The cathode activation and ohmic losses as a function of the current density in PEM fuel cell operation. Figure 5.3 illustrates that the ohmic loss in Nafion R membrane was much less than the activation loss in the cathode. Combination of this information with the previous discussion regarding the relative scales of ohmic losses in the membrane and in the catalyst layer, presented a conclusion that it was valid to assume a negligible ohmic loss in the catalyst layer in comparison to the activation loss in the same domain. 118

119 Model validation 5. Porous-electrode model The model was used to simulate the polarisation curve of a fuel cell at the experimental conditions shown in Table 4.4. The set of parameters used in the model is shown in Table 5.1. The parameter were taken from literature data for hydrogen PEM fuel cells operating at similar conditions to the conditions considered in this study. Parameters Values Source Cathode transfer coefficient (α c ) 0.5 Larminie and Dicks (2000) O Hayre et al. (2006) Jeng et al. (2004) Henry s constant for oxygen in mol Pa 1 l 1 Secanell et al. (2007) Nafion R (H o ) at 298 K Catalyst layer thickness (t cat,c ) 13 µm Average of values from Grujicic and Chittajallu (2004) and Chan and Tun (2001) Catalyst layer porosity (ɛ cl ) 0.30 Average of values from Gurau et al. (2000) and Zhang and Jia (2009) Diffusivity of oxygen in the electrolyte m 2 s 1 Siegel et al. (2003) (D o,el ) Specific surface area of the catalyst layer (a) m 1 Zhang and Jia (2009) Table 5.1.: Simulation parameters in the porous-electrode model. The exchange current density (j 0,c ) shows a large range of variation in literature, A m 2, indicating that there is a strong catalytic effect on the parameters (Larminie and Dicks, 2000). The value was adjusted within the range of literature, and j 0,c = 2 A m 2 was used to give the polarisation curve for the model validation. Ranges of parameters from literatures can be found in Appendix C. The polarisation curve is shown in Figure

120 5. Porous-electrode model Cell voltage [V] x Porous-electrode model Experiment Current density [A cm -2 ] Power density [W cm -2 ] Figure 5.4.: The predicted polarisation curve and the experimental results of PEM fuel cell operating at 65 C. The porous-electrode model simulated the fuel cell operation in the low current density region better than in the high current density (see Figure 5.4). As the current density was increased: the accuracy declined. At 0.5 A cm 2, the model overestimated the cell voltage by 11% and at 1.0 A cm 2, the over-estimation increased to 26%. To reduce the discrepancy, the simulated loss in the high current density region must increase more significantly with current density Results and discussion According to Figure 5.3, the cathode activation loss increased sharply from V when the current density was increased from A cm 2. The activation loss increased in smaller gradient at the higher current density i.e. it increased from V when the current density raised from A cm 2. At higher current density, the activation loss gradually increased and reached a value of 0.20 V at 0.8 A cm

121 5. Porous-electrode model Voltage [V] Catalyst layer porosity increasing catalyst layer porosity Current density [A cm -2 ] Figure 5.5.: Polarisation curves of fuel cell at different values of the catalyst layer porosity of 0.2, 0.3 and 0.4. A parametric study was carried out to study the effects of the porosity in the catalyst layer and the exchange current density on the cell voltage. Figure 5.5 shows that changing the catalyst layer porosity from had a positive impact on the fuel cell voltage. The catalyst layer was assumed to have its pores filled with the electrolyte for the proton conduction thus increasing the porosity improves the effective proton conductivity in the catalyst layer, hence increases the fuel cell voltage. Voltage [V] Exchange current density [A m -2 ] increasing j 0,c Current density [A cm -2 ] Figure 5.6.: Polarisation curves of fuel cell at different values of the exchange current density of 0.5, 2 and 20 A m 2. Increasing the exchange current density also had a positive impact on the fuel cell 121

122 5. Porous-electrode model voltage, as shown in Figure 5.6. Increasing the value of j 0,c had the effect of raising the cell voltage by a constant amount at most current density. A fuel cell using an electrode with a high degree of surface roughness has a higher value of the exchange current density because the electrode roughness increases the real surface area of each nominal 1 cm 2 (Larminie and Dicks, 2000). Dimensionless concentration increasing current density Membrane Dimensionless thickness GDL Figure 5.7.: Oxygen concentration profile in dimensionless forms of concentration and thickness of the catalyst layer The data set in the model validation was used to give the oxygen concentration profile in Figure 5.7. The dimensionless thickness of 0 and 1 correspond to the interfaces of the catalyst layer to the cathodic gas diffusion layer and the membrane electrolyte layer, respectively. Oxygen concentration decreased from the gas diffusion layer interface to the membrane interface as expected. The concentration reduced faster in the higher current density; oxygen was reduced mainly in the catalyst layer located near the gas diffusion layer interface. At a high current density, catalyst particles which are located away from the interface between the catalyst layer and the gas diffusion layer may not be utilised due to the poor oxygen distribution in the catalyst layer as shown in Figure 5.7. A catalyst deposition technique that can locate more catalyst near the interface with the gas diffusion layer, essentially reduces the non-utilised amount of the catalyst at a high current density: gives higher cell voltage at the same catalyst loading. Referring to the over-estimated cell voltage in Figure 5.4, the underestimation of the 122

123 5. Porous-electrode model losses suggests that there is an additional oxygen transport resistance in the catalyst layer which has not been included in the porous-electrode model. The diffusion resistance on the dissolved oxygen in the electrolyte has been taken into consideration but the further step accounting for the transport of oxygen inside the porous agglomerates has not been included within the model scope. This must be the additional mass-transfer resistance needed to accurately simulate the fuel cell performance Summary The porous-electrode model has shown the positive impacts of the catalyst layer porosity and the exchange current density on the cell voltage. The distribution of oxygen concentration in the catalyst layer in each current density was also illustrated. The model simulated the fuel cell performance at low current density more accurate than in the high current density range. The fuel cell performance in high current density region is known to be dominated by the mass-transfer resistance, but the porous-electrode model could not capture the mass transfer effect sufficiently. The lack of accuracy at high current load suggests that the catalyst layer structure must be considered. The next chapter investigates the effect of the catalyst layer structure, considered at a smaller scale than that in the porous-electrode model. 123

124 6. Agglomerate model This chapter uses the agglomerate model to describe the phenomena in the catalyst layer of a hydrogen PEM fuel cell. The chapter outlines the model descriptions, the catalyst layer structure and the model development. The computational procedure is listed in detail, the model is validated with experimental results and used to study the effects of the catalyst layer structure on the hydrogen PEM fuel cell performance Introduction The agglomerate model is a homogeneous catalyst layer model developed to study the impact of the catalyst layer structure on the performance of a hydrogen PEM fuel cell. It considers processes occurring in the catalyst layer including the reactant transport in the catalyst agglomerate, the reaction kinetics and the catalyst utilisation. These processes take place inside the agglomerate, where the electrochemical reaction occurs, and have a large influence on the overall fuel cell performance. The model focuses on the agglomerate scale and thus the characteristic length is a function of the agglomerate radius. The model is applied to the cathode only, the anode is described using an interface model between the gas diffusion layer and the membrane (see Chapter 4). Results from this model are integrated to the macro-scale model in Chapter 4, to evaluate the overall fuel cell performance. 124

125 6.2. Model development 6. Agglomerate model The physical structure which is to be modelled is shown in Figure 6.1 and providing the basis for the model development. The process begins with the introduction of the catalyst layer structure, to which mass conservation of species and charge is applied, relating mass transport processes to the electrochemical reactions, arriving finally at the governing equations for the model. The model in this study was developed following the analysis of mass transport in porous catalyst presented in Fogler (1992); Bird et al. (2007) and Rawlings and Ekerdt (2002). The modelling approach for the electrochemical reaction in the catalyst layer based on the concept shown in Eikerling and Kornyshev (1998) Model description Meso/micropores (20-40 nm) Catalyst agglomerate Carbon fiber Pt particle (2-3 nm) Electrolyte Oxygen diffusion path Supporting carbon (20-40 nm) R ag t f Macropores ( nm) R ag is agglomerate radius t f is electrolyte film thickness Membrane layer Catalyst layer GDL Figure 6.1.: Schematic diagram of catalyst layer structure in agglomerate model. The catalyst layer is thin and located between the gas diffusion layer and the membrane, as shown in Figure 6.1. The catalyst layer porosity (ɛ cl ) refers to the 125

126 6. Agglomerate model macro/meso pores, which provides oxygen transport in the catalyst layer. The layer is assumed to contain identical catalyst agglomerates distributed uniformly throughout the layer. Each agglomerate is covered by a thin film of electrolyte (t f ). The surrounding gaseous oxygen at the outer surface of the thin film of electrolyte must dissolve and permeate through the film layer into the catalyst inside the agglomerate. The agglomerate is a porous structure with porosity of ɛ ag. The non-porous volume is composed of the Pt/C with volume fraction, v so, and the electrolyte with volume fraction, v el. The characteristic length (ζ) of the agglomerate model is the ratio of the volume to the surface area of the agglomerate. The model assumes a spherical agglomerate and thus the characteristic length is: ζ sp = V A = R ag/3 (6.1) where V, A and R ag are volume, surface area and radius of the agglomerate (Weber and Newman, 2004b). The defined characteristic length is an inverse of the specific surface area of agglomerate. A specific surface area is an important characteristic of catalyst regarding the diffusion of reactant which can limit the electrocatalyst performance. Due to the relation of the characterisric length and the specific surface area, it can be concluded that the defined characteristic length is suitable for the electrocatalyst performance study Assumptions 1. The model assumes the catalyst layer is one dimensional and homogeneous with uniformly distributed agglomerates in direction perpendicular to the MEA surface. 2. The fuel cell is assumed to be operating at steady state and isothermally. 3. All of the agglomerates are assumed to be exposed to the same gas phase concentration of oxygen in the catalyst layer. The macro-pores are relatively large so the reactant concentration is assumed to be constant in the pores 126

127 6. Agglomerate model throughout the catalyst layer. 4. The ohmic drop in the solid phase is assumed to be negligible due to its high conductivity in comparison to that of the electrolyte phase. 5. Oxygen reduction is assumed to take place as a first order reaction. 6. The model assumes that the gas concentration in the electrolyte at the surface of the electrolyte film is in equilibrium with the gas pressure in the catalyst layer. 7. It is assumed that diffusion of the dissolved gas in the electrolyte can be described using Fick s law. 8. The diffusivity of the dissolved oxygen in the electrolyte is assumed to be constant. 9. The gas space in the agglomerate is assumed to be isolated from the macro/meso pores surrounding the agglomerate and the gas space does not provide the path way for oxygen transport in the agglomerate Diffusion and reaction kinetics Supporting carbon Platinum catalyst C o (r = 0) Oxygen diffusion path C o,s C o,b Electrolyte t f r = 0 r = R ag Figure 6.2.: Schematic structure of a catalyst agglomerate in the agglomerate model. 127

128 6. Agglomerate model The gaseous oxygen dissolves in the electrolyte at r = R ag + t f to give the bulk concentration concentration (C o,b ) then diffuses through the electrolyte thickness (t f ) to give the surface concentration (C o,s ) at r = R ag. The diffusion of the dissolved oxygen in the electrolyte can be described by the binary diffusion process which will be discussed in the context of the agglomerate. The reaction kinetic will be explained in terms of a reaction rate (r o ), an intrinsic rate constant (k), a Thiele modulus (φ) and a catalyst utilisation effectiveness (E). These terms will be briefly explained here. The oxygen reduction rate (r o ) is proportional to the current load and is also a function of the intrinsic rate constant and the oxygen concentration (Fogler, 1992). The oxygen concentration in the agglomerate depends on the radial position inside the agglomerate and the intrinsic rate constant is also expected to vary with location. This intrinsic rate constant is not the true reaction rate constant of the oxygen reduction reaction. Instead it is dependent on factors including, but not limited to, the conversion factor, catalyst density, catalyst area and the overpotential (Bird et al., 2007). To measure the relative influence of the chemical reaction rate and the mass transport rate in the agglomerate, the Thiele modulus (φ) is employed. It is a dimensionless parameter expressing a ratio of the constants of the reaction rate to that of the diffusion rate. When the Thiele modulus is large, the internal diffusion usually limits the overall reaction rate; when the Thiele modulus is small, the surface reaction is usually rate-limiting (Fogler, 1992). Catalyst located near the outer surface of an agglomerate will be exposed to a higher oxygen concentration, while those closer to the centre of an agglomerate experiences a lower concentration. Catalyst that oxygen cannot access is not being utilised. The amount of active catalyst strongly depends on the agglomerate structure, reaction rate, diffusion rate and current load. The catalyst utilisation effectiveness (E) is used to characterise the active fraction of the catalyst (Gurau et al., 2000). It is defined as the ratio of the actual reaction rate at a point to the rate of reaction that would occur if the entire catalyst agglomerate was exposed to the oxygen concentration prevailing at the surface of the agglomerate (C o,s ). 128

129 6. Agglomerate model Diffusion of oxygen in the electrolyte film The gaseous oxygen in the macro/meso pores dissolves at the electrolyte interface to an extent usually described by Henry s law, which states that the concentration is directly proportional to the pressure (Treybal, 1981). The model assumes that the oxygen concentration in the agglomerate (C o,b ) is in equilibrium with the gas pressure (p o ), therefore: C o,b = p o H o (6.2) where H o is Henry s constant for oxygen in the electrolyte membrane. As oxygen diffuses through the electrolyte film covering the agglomerate surface, Fick s law was used to determine the oxygen molar flux (Q o ) across the electrolyte thickness of t f (in Figure 6.2), giving: ( ) Co,b C o,s Q o = D o,el t f (6.3) where D o,el is the effective oxygen diffusivity in the electrolyte, C o,b is the oxygen concentration in equilibrium with the gaseous oxygen in the macro/meso pores of the catalyst layer, C o,s is the oxygen concentration at r = R ag and t f is the thickness of the electrolyte film covering the agglomerate. In a volume of catalyst agglomerate with a specific surface area of a, the diffusion rate of oxygen in mol m 3 s 1 ( Q o ) is: ( ) Co,b C o,s Q o = ad o,el t f (6.4) Intrinsic rate constant (k) The oxygen reduction reaction is assumed to be a first order reaction. For an agglomerate with oxygen concentration (C o ) throughout its volume, the reaction rate (r o ) is expressed as: Q o = r o = kc o (6.5) when k is the intrinsic reaction rate constant (Bird et al., 2007). The oxygen depletion rate is balanced by the change in the cathodic current density 129

130 6. Agglomerate model ( j) which can be described by Faraday s law: Q o = j 4F (6.6) therefore: j = 4F kc o (6.7) The current density gradient ( j) can be theoretically related to the kinetics of the reaction and the operating conditions using the modified Butler-Volmer equation. The derivation of the modified Butler-Volmer equation for the cathode is presented in Chapter 5. The current density gradient in agglomerate with the active specific surface area,a, is: j = aj 0,c C o Co ref [ ] αc n e F exp η act RT (6.8) where j 0,c is the exchange current density, C o is the oxygen concentration and C ref o is the reference oxygen concentration. Substitution of Equation 6.8 in Equation 6.7. The intrinsic rate constant can be written as: k = aj 0,c 4F C ref o [ ] αc n e F exp η act RT (6.9) The activation potential loss (η act ) is defined as the deviation of the operating cathode voltage (E ca ) from the reversible cathode voltage (E e ). η act also relates to the potential in the solid electrode phase (E so ) and the potential in the electrolyte phase (E m ) as follow: η act = E ca E e (6.10) = E m E so (6.11) The model assumes that the electronic conductivity of the solid phase is high, so that there is no potential gradient in the solid phase of the catalyst layer. On the other hand, a potential gradient in the electrolyte phase is expected. The reversible cathode voltage in the catalyst layer (E e,cl ) is the remainder once the mass transport overpotential (η mass ) has been subtracted from the reversible cathode voltage (E e ). Both η mass and E e have been discussed in Chapter

131 6. Agglomerate model Thiele modulus (φ) The diffusion inside the porous agglomerate with radius R ag is considered between two points (A and B) within the agglomerate as shown in Figure 6.3. B A r r=0 r=r ag Figure 6.3.: Schematic diagram shows an agglomerate with radius R ag The mass balance for oxygen between point A and B can be described as: Q o,a 4πr 2 = Q o,b 4π(r + r) 2 r o 4π(r 2 ) r (6.12) where Q o,a and Q o,b are the oxygen molar flux at point A and B, respectively. r o is the oxygen reduction rate and r is the radial difference between points A and B. The term r o 4π(r 2 ) r is the approximate molar rate of oxygen involved in the chemical reaction between the points. Using the definition of the first derivative to represent the mass balance equation in Equation 6.12: d dr (r2 Q o,ag ) = r 2 r o (6.13) The oxygen flux in the agglomerate is denoted as Q o,ag for clarity. The mass transport of the dissolved oxygen in the agglomerate can be described by the binary diffusion of Fick s law. Q o,ag = D o,ag dc o dr (6.14) 131

132 6. Agglomerate model where D o,ag is the effective diffusivity of oxygen in the electrolyte of the porous agglomerate and dc o /dr is oxygen concentration gradient. The Bruggemann relation is commonly used to describe the effective diffusion in porous media (Song et al., 2004). The effective diffusivity of oxygen in the electrolyte of the porous agglomerate (D o,ag ) can be determined in terms of the oxygen diffusivity in the bulk electrolyte (D o,el ), the agglomerate porosity (ɛ ag ), the volume fraction of electrolyte in the non-porous volume of the agglomerate ( v el ), as follow: D o,ag = D o,el ((1 ɛ ag ) v el ) 1.5 (6.15) Equation 6.14 is substituted in Equation 6.13: ( 1 d D o,ag r 2 dc ) o = r r 2 o (6.16) dr dr At steady state, the oxygen depletion rate can be expressed as r o Equation 6.16 can be written as: = kc o, thus ( 1 d D o,ag r 2 dc ) o = kc r 2 o (6.17) dr dr The differential equation is converted to the dimensionless parameters and solved with the following boundary conditions; at r = R ag : C o = C o,s and at r = 0: dc o /dr = 0. The dimensionless form of concentration is C, where C = C o /C o,s, and of radial position is r, where r = r/ζ. The expressions, their derivatives and the used boundary conditions used are presented in their dimensional and dimensionless forms in Table 6.1 below. The dimensionless form of Equation 6.17 is: ( 1 d r 2 dc ) kζ2 C 2 = 0 (6.18) r 2 d r d r D o,ag 132

133 6. Agglomerate model Normal form Dimensionless form Parameters C o C = C o /C o,s r r = r/ζ Derivative of the parameters dc o dc = dc o /C o,s dr d r = dr/ζ Boundary condition of the parameters C o = C o,s at r = R ag C = 1 at r = 1 dc o /dr = 0 at r = 0 dc/d r = 0 at r = 0 Table 6.1.: Dimensionless forms of parameters, their derivatives and the boundary conditions. Defining the Thiele modulus φ as (Bird et al., 2007): φ = ζ k (6.19) D o,ag the dimensionless terms in Equation 6.18 can be rewritten as follows: ( 1 d r 2 dc ) φ 2 C 2 = 0 (6.20) r 2 d r d r The solution to this differential equation (DE) has been derived by Bird et al. (2007) who has shown that, in terms of the dimensionless parameters, the concentration can be written as: C( r) = 3 r sinh( rφ) sinh(3φ) (6.21) This expression gives the dimensionless concentration as a function of the dimensionless radius inside an agglomerate. The concentration expression in the normal form is: C o = R ( ) ag sinh(rφ) C o,s r sinh(r ag φ) (6.22) Catalyst utilisation effectiveness (E) The catalyst utilisation effectiveness is a measure of the amount by which the reaction rate is lowered due to the mass transport resistance in the electrolyte. The effectiveness can be used to indicate how accessible the catalyst is to the reactant in the agglomerate. 133

134 6. Agglomerate model The factor is a ratio of the oxygen molar flow when influenced by mass transport (q o ) to that without the transport resistance (q o, ). The symbol is used to indicate no mass transport resistance, i.e. the situation in which the active surfaces are all exposed to the oxygen concentration at r = R ag, thus: E = The oxygen molar flow in the agglomerate with r = R ag is: q o q o, (6.23) q o = 4πR 2 agq o,ag = 4πR 2 agd o,ag dc o dr (6.24) The oxygen concentration expression in Equation 6.22 is substituted in Equation 6.24 to give the molar rate of oxygen (q o ) in the agglomerate (Bird et al., 2007). If all of the catalytically active surfaces were all exposed to the oxygen concentration at the agglomerate surface, the molar rate would be given by: q o, = 4 3 πr3 ag(kc o,s ) (6.25) Taking the ratio of the two molar rates of q o and q o,, to give the catalyst utilisation effectiveness (Bird et al., 2007): E = 1 ( 1 φ tanh(3φ) 1 ) 3φ (6.26) When E = 1, reaction occurs at the same rate throughout the agglomerate, as if there is no concentration gradient. Continuity equation The oxygen transport rate in the catalyst layer is: Q o = kec o,s (6.27) Under steady state conditions, the oxygen which diffuses into the catalyst volume is consumed in the oxygen reduction reaction. Combining Equation 6.4 and 6.27: C o,s = C o,b Q o t f D o,el a = Q o ke (6.28) 134

135 6. Agglomerate model Eliminating C o,s, we can obtain an expression for the oxygen consumption rate ( Q o ): Q o = C o,b / ( 1 ke + t f ad o,el ) (6.29) Faraday s law is used to find the equivalent current density for the reacted oxygen: Q o = 1 4F j (6.30) The reaction kinetics on the catalyst surface can be theoretically related to the current density gradient by using the Butler-Volmer equation (see Equation 6.8), thus Equation 6.29 becomes: j = 4F C o,b / [ tf + 1 ] ad o,el ke (6.31) Charge conservation Charge conservation in the catalyst layer gives: j = j so + j m (6.32) where j is the local current density, j so is the current density in the solid electrode phase and j m is the current density in the electrolyte phase. The solid electrode phase is considered to have a constant potential (Broka and Ekdunge, 1997a) because the conductivity of the solid phase (carbon and platinum) is much higher than that of the electrolyte phase. The conductivity in the solid phase (Pt/C) is 1000 S m 1 (Grujicic and Chittajallu, 2004), where the conductivity in the electrolyte phase is determined to be in the range of S m 1 (refer to the calculation in section 4.2.7, Equation 4.45), respectively. The change in the electrolyte potential can be described by Ohm s law. The potential change depends on the current density (j m ) and the ionic conductivity (σ). The Bruggemann relation is used to account for the porosity and the tortuosity in the catalyst layer (Chan and Tun, 2001). de m dz = j m ((1 ɛ cl ) v el,cl ) 1.5 σ (6.33) 135

136 6. Agglomerate model where E m is the potential in the electrolyte, z is the distance from the interface with the GDL, j m is the current density in the electrolyte phase, σ is the conductivity of the electrolyte, ɛ cl is the catalyst layer porosity and v el,cl is the volume fraction of the electrolyte in the non-porous volume of the catalyst layer. At steady state, the electrode has a constant potential and thus the current gradient in the electronically conducting solid (Pt and carbon) is balanced by that in the ionically conducting electrolyte phase (Weber and Newman, 2004b). The kinetic expression for the charge balance between them is: j m = j so (6.34) where j so and j m represent the current density gradients in the solid phase and in the electrolyte phase of catalyst layer Computational procedure The procedure is presented in two sets, the first one being the overall procedure and the second one being the procedure for the determination of the current density in the electrolyte phase (j m ) Overall procedure For a specific current density (j), there is a value of the electrolyte potential at the catalyst layer GDL interface (E m at z = 0) that satisfies the following boundary conditions. Conditions at the interfaces between the catalyst layer and the membrane and between the catalyst layer and the cathode GDL are used as the boundary conditions in this study: At the catalyst GDL interface (z thus, j m = 0 and j = j so. = 0), no protons leave the catalyst layer, At the membrane catalyst interface (z j so = 0 and j = j m. = t cat,c ), current is conserved, thus, 136

137 6. Agglomerate model The bisection method was used to find a numerical solution in this procedure. 1. Estimates of the lower end (E m (0) l ) and higher end (E m (0) h ) of the potential in electrolyte at the catalyst GDL interface were established. 2. The average of the estimated values of the potential in electrolyte (E m (0) m ) was calculated. 3. The second procedure (determination of j m ) was carried out to find the current density in the electrolyte phase for each value of E m (0) to give the corresponding current density at the lower end (j m,l ), the higher end (j m,h ) and the mid point value (j m,m ). 4. The required current density (j) was compared to the current density in electrolyte phase at the mid-point (j m,m ) given by E m (0) m. The discrepancy (δ) between j and j m,m was calculated from Equation 6.35, where: δ = j m,m j (j m,m + j)/2 (6.35) If the discrepancy was less than or equal to the convergence criteria, which was 0.01, the activation loss at the mid point (E m (0) m ) was accepted as the solution for the specified current density. 5. On the other hand, if the criteria was not met then the sub-interval, which is half of the E m (0) interval in step 1, that contained the required current density was identified. E m (0) l and E m (0) h were reset based on the new interval. 6. Steps 1-5 were repeated, using the selected interval in step 5, until the convergence criteria was satisfied. 7. Equation 6.11 was used to calculate the activation loss (η act,c ) corresponding to the converged value of E m (0). 8. To integrate the agglomerate model of the catalyst layer into the macro-scale model of the fuel cell in Chapter 4, the cathodic activation loss (η act,c ), which is the first term in Equation 4.52 was substituted with the activation loss found in this model. 137

138 6. Agglomerate model 9. The rest of the computational procedure was carried out as shown in Table 4.2 in Chapter Procedure for determination of the current density in the electrolyte phase The cathodic catalyst layer was divided into 1000 elements of equal thickness. The validation of numerical method in section shows that the numerical method gave sufficiently accurate solution when using 1000 elements representing the catalyst layer. The calculation began at i = 0, which was the interface between the catalyst layer and GDL, and moved step-wise to i = 1000 which was the interface between the catalyst layer and membrane. A diagram of the calculation step is shown in Figure 6.4 and a description of the procedure follows it. j = j m E m (i+1) x Stepping by Euler s method x E m (i) j = j so x E m (0) i= i+1 i 2 1 i=0 z =t cat,c Membrane Catalyst layer z =0 Catalyst layer GDL Figure 6.4.: Diagram for the calculation procedure for determination of the current density in the electrolyte phase. 1. An estimate was made for the electrolyte potential at the catalyst layer GDL interface (E m (i = 0)). 2. j m (i) was established. The boundary condition sets j m (i = 0) to be 0 because there are no protons leaving the catalyst layer at this position 138

139 6. Agglomerate model 3. j so (i) can be calculated from Equation 6.32 and the activation overpotential can be calculated from Equation The electrolyte potential gradient (de m /dz ) between adjacent positions of (i) and (i + 1) was determined by using Equation Euler s method can be used as a stepping technique to find E m (i + 1) from the obtained gradient, thus: E m (i + 1) = E m (i) + z de m dz (6.36) 6. The characteristic length of the agglomerate (ζ), the dissolved oxygen concentration in the electrolyte film (C o,b ), the intrinsic rate constant (k), the Thiele modulus (φ) and the catalyst utilisation effectiveness (E) were determined from equations 6.1, 6.2, 6.9, 6.19 and 6.26, respectively. 7. The current density gradient can be determined from Equation 6.31 and it was used to calculate the current density in the solid phase (j so (i + 1)) at the next position in the catalyst layer. 8. The current density gradient in the electrolyte phase ( j m ) was calculated from Equation j m (i + 1) was determined by Euler s method. 10. Using j m (i + 1), steps 2 through to 9 were repeated to calculate j m (i + 2). 11. The calculation was repeated from step 3 until the current density in the electrolyte phase (j m ) at z = t cat,c was obtained Model validation This section discusses some of the assumptions used in the model and validates the simulation with experimental data. 139

140 Assumption analysis 6. Agglomerate model The oxygen partial pressure in the macro/meso pores throughout the catalyst layer was assumed to be constant. This assumption may affect the accuracy at a high current density where mass transport is the dominant mechanism for voltage loss. The agglomerates were assumed to be the same size in order to simplify the model, the effect of agglomerate radius will be investigated and in reality, a catalyst layer is expected to have a spectrum of agglomerate radii. The study assumed that Fick s law of diffusion can sufficiently represent the diffusion process of oxygen at steady state operation, this should be valid due to the low solubility of oxygen in Nafion R. To account for the porous agglomerate, the effective diffusivity was used, based on the Bruggemann relation for porosity and tortuosity. Similarity, an effective value for catalyst layer conductivity was used because the layer contains many phases: liquid, gas, solids(platinum and carbon) and membrane (Weber and Newman, 2004b). The electrolyte conductivity was assumed to be constant in the catalyst layer. The protonic conductivity depends on water content which is influenced by electro-osmotic effects. The cathode was assumed to be saturated with water, and the conductivity was assumed to be constant (Eikerling and Kornyshev, 1998) Validation of the numerical method The accuracy of the numerical method in the simulations reaches the accuracy limit when the cell voltage does not depend significantly on the number of elements in the numerical method. The polarisation curve generated by the agglomerate models using 100, 500, 1000 and 1500 elements of equal thickness in the catalyst layer are compared in Figure

141 6. Agglomerate model Voltage [V] Number of elements Current density [A cm -2 ] Figure 6.5.: Comparison of polarisation curves generated by agglomerate model using different numbers of elements in the numerical method. It was found that the fuel cell voltage in the simulation using 500, 1000 and 1500 elements were almost the same. In terms of numerical method accuracy, the simulation using 1500 elements was regarded as having the most accurate results, thus its result was used as the standard for accuracy comparison with the other groups of results in Table 6.2. j[a cm 2 ] % V in each simulation Table 6.2.: %difference in fuel cell voltage between simulations with 100, 500, 1000 and 1500 elements in the numerical method. The deviation in cell voltages from the standard voltage (1500 elements) increased with the increasing current density. The maximum difference in cell voltage between the simulations with 1000 and 1500 elements was 0.07% at 1.2 A cm 2. This small difference was acceptable in this study and the number of elements used in the numerical method for the remaining work was This reduces the simulation time while not significantly affecting the accuracy. 141

142 Model validation 6. Agglomerate model The model was used to simulate the polarisation curve of a fuel cell under the experimental conditions shown in Table 4.4. The set of parameters used in the model is shown in Table 6.3 and 6.4 Parameters Values Sources Cathode transfer coefficient (α c ) 0.5 Larminie and Dicks (2000) Cathode GDL thickness (t c ) 350 µm Speigel (2008) Cathode GDL porosity (ɛ c ) 0.4 Zhang and Jia (2009) Water diffusivity in membrane (D λ ) cm 2 s 1 Speigel (2008) Cathode catalyst layer thickness (t cat,c ) 13 µm Average of values from Grujicic and Chittajallu (2004) and Chan and Tun (2001) Catalyst layer porosity (ɛ cl ) 0.30 Average of values from Gurau et al. (2000) and Zhang and Jia (2009) Volume fraction of electrolyte in catalyst layer ( v el,cl ) 0.20 Grujicic and Chittajallu (2004) Agglomerate porosity (ɛ ag ) 0.25 Ridge et al. (1989) Volume fraction of electrolyte in agglomerate ( v el,ag ) 0.20 Grujicic and Chittajallu (2004) Oxygen diffusivity in Nafion R (D o,el ) m 2 s 1 Siegel et al. (2003) Henry s constant for oxygen in Nafion R at 298 K (H o ) mol Pa 1 l 1 Secanell et al. (2007) Table 6.3.: Simulation parameters in the agglomerate model. There were other parameters which were fitted, within their ranges in literature, to the experimental data. The fitting was carried out manually based on the leastsquares fitting method. The objective function was the cell potential in a current density range of A cm 2. The set is presented in Table 6.4. Sources of the literature values are listed in Appendix C. Parameters Values used in model Range in literature validation Cathode exchange current density (j 0,c ) 10 A m A m 2 Electrolyte film thickness (t f ) 0.13 µm µm Agglomerate specific surface area (a) m m 1 Agglomerate radius (R ag ) 1.2 µm µm Table 6.4.: The additional parameters used in the agglomerate model. 142

143 6. Agglomerate model The model was validated by comparing the polarisation curve obtained with the experimental data from Du (2010). The polarisation curve simulated by the agglomerate model and the experiment data are shown in Figure 6.6. Cell voltage [V] Experiment Agglomerate exp agg Power density[w cm -2 ] Current density [A cm -2 ] 0 Figure 6.6.: Polarisation curves of the experimental data and the simulation results at the standard simulating conditions. The gradient of the polarisation curve decreased at low current density and increased at high current density. The model slightly overestimated the cell voltage in the activation loss dominated zone (low current density region) but underestimated the cell voltage in the mass transport loss dominated zone (high current density region). The average % difference between the experiment and simulated cell voltage was 1.5%. The assumption of constant oxygen partial pressure in the macro/meso pores of catalyst layer is expected to contribute to the overestimation of cell voltage in the mass transport loss dominated zone. The assumption neglected any mass transport resistance in the catalyst layer, which could potentially reduce the cell voltage. Overall, the simulation results were in good agreement with the experimental result from Du (2010). The parameters used in the validated simulation will be referred to as the reference values in the following studies. 143

144 6. Agglomerate model 6.5. Parametric and statistical sensitivity analysis The influence of a few key parameters on the fuel cell performance is discussed in detail and they will be analysed to compare their effect on the fuel cell Parametric analysis Six key parameters in the model have been studied: the cathodic exchange current density (j 0,c ), the specific surface area in the catalyst layer (a), the agglomerate radius (R ag ), the agglomerate porosity (ɛ ag ), the thickness of the electrolyte layer covering the agglomerate surface (t f ) and the volume fraction of the electrolyte in the agglomerate ( v el,ag ). These parameters are commonly used to characterise a catalyst layer in the agglomerate model. Note that the relationship between the agglomerate radius and the specific surface area of the catalyst layer was not considered in the parametric analysis because their individual influences on the fuel cell performance was the purpose of this study. Cathodic exchange current densities (j 0,c ) The exchange current density characterises the kinetics of the cathode reaction on the catalyst which is affected by the catalyst type, its preparation and catalyst network. This current density is high in a more active electrode and it is critical in controlling the fuel cell performance. The value should be as high as possible in a fuel cell (Larminie and Dicks, 2000). 144

145 6. Agglomerate model Cell voltage [V] j 0,c 17 Am Am Am -2 Increasing j, c Power density [W cm -2 ] j 0,c 17 Am Am Am -2 Increasing j 0,c Current density [A cm -2 ] (a) Current density [A cm -2 ] (b) Figure 6.7.: Fuel cell (a) voltages and (b) power density as function of current density when the cathodic exchange current density is 7, 10 and 13 A m 2. As shown in Figure 6.7, a fuel cell with a higher cathode exchange current density produces higher cell voltage. This observation agrees with the description in Larminie and Dicks (2000). The cathode exchange current density has a significant role in the activation overpotential and its impact can be seen clearly over the entire range of current density. Catalyst agglomerate radius (R ag ) The agglomerate dimension depends on the fabrication procedure employed. Broka and Ekdunge (1997a) reported that the agglomerate radius was in the range of µm based on SEM images. Siegel et al. (2003) analysed SEM data and obtained a mean agglomerate radius of 3 µm. Other studies such as Chan and Tun (2001) used a value of 1 µm. The agglomerate radius that gives the best fit with experimental data in section is 1.2 µm. The value is well in the range of values in the literature. The value of the agglomerate radius was extended to higher and lower values than the reference value: 0.8 and 2.0 µm. The responding polarisation curves are shown in Figure

146 6. Agglomerate model Cell voltage [V] R ag µm µm µm Increasing R ag Power density [W cm -2 ] R ag µm 21.2 µm 32.0 µm Increasing R ag Current density [A cm -2 ] (a) Current density [A cm -2 ] (b) Figure 6.8.: Fuel cell (a) voltages and (b) power density as function of current density when the agglomerate radius is 0.8, 1.2 and 2.0 µm. Figure 6.8 shows the effect of agglomerate radius on the fuel cell voltage and power density. A hydrogen PEM fuel cell prepared with small agglomerates can produce higher voltage than one prepared with large agglomerates. The decreased performance with the larger agglomerates was due to the increasing diffusional path for oxygen within the large agglomerates, and reduced utilisation of catalyst. The effect of increased diffusional resistance can be observed clearly in the mass transport limiting (high current density) region. The analysis was carried out at a constant platinum loading per unit area of MEA. As mentioned earlier, the change in the agglomerate radius may alter the catalyst layer porosity and the specific surface area (the agglomerate radius is inversely proportional to the specific surface area of the electrode). However, these changes were assumed negligible in this parametric study. Agglomerate porosity (ɛ ag ) In the model, it was assumed that the pores in the agglomerate were partially filled with electrolyte (see Figure 6.2). The oxygen must diffuse through the electrolyte to reach the active sites. The value of porosity in the agglomerate was 0.25 in the studies by Ridge et al. (1989) and this value was also used in this model. The value was changed to 0.1 and 0.3 in the parametric study. 146

147 6. Agglomerate model Cell voltage [V] ε ag Increasing ε ag Power density [W cm -2 ] ε ag Increasing ε ag Current density [A cm -2 ] (a) Current density [A cm -2 ] (b) Figure 6.9.: Fuel cell (a) voltages and (b) power density as function of current density when the agglomerate porosity is 0.1, 0.25 and 0.3. Figure 6.9 shows the decreased cell voltage when the agglomerate porosity increased. The effect was observed mainly in the high current density region. Increasing the agglomerate porosity means a smaller amount of the electrolyte which supports diffusion of the reactant to the active sites, thus the cell voltage decreases. Electrolyte film thickness on agglomerates (t f ) In this model, the agglomerates were assumed to be covered with a thin layer of electrolyte which provides a connection between them for proton transport and oxygen diffusion into them. The thickness of this layer depends on the preparation technique, but it is commonly found to be in the range of µm. Secanell et al. (2007) used 0.08 µm, Lin et al. (2004) used 0.1 µm and Bautista et al. (2004) used 0.5 µm. In this study 0.13 µm was used as it was in the literature range and gave the best fit with the experimental data from Du (2010). The value was varied to 0.1 and 0.15 µm in the parametric analysis. 147

148 6. Agglomerate model Cell voltage [V] t f µm µm µm Increasing t f Power density [W cm -2 ] t f µm µm µm Increasing t f Current density [A cm -2 ] (a) Current density [A cm -2 ] (b) Figure 6.10.: Fuel cell (a) voltages and (b) power density as function of current density when the electrolyte film thickness is 0.1, 0.13 and 0.15 µm. Figure 6.10 shows that a fuel cell with a film thickness 0.1 µm has higher peak power density than that with 0.15 µm. Its adverse effect on power density is significant at current density higher than around 0.8 A cm 2. The electrolyte film covering agglomerates extends the diffusion path for the dissolved oxygen to reach the agglomerate surface. The thickness reduces the concentration of oxygen at the agglomerate surface (C o,s ) and consequently lowers the cell voltage. Specific surface area of catalyst layer (a) The specific surface area of the catalyst layer depends strongly on the preparation method and the value varies in the literature. A specific surface area of m 1 was used in Zhang and Jia (2009), m 1 was used in Grujicic and Chittajallu (2004), m 1 was used in Siegel et al. (2003). A value of m 1 gave the best fit to the experimental data thus it was selected for this study. For the purpose of parametric analysis, the specific surface area was changed to and m 1 and the corresponding fuel cell performance is shown in Figure

149 6. Agglomerate model Cell voltage [V] a 7x m -1 1x m x m -1 Increasing a Power density [W cm -2 ] a 7x m -1 1x m x m -1 Increasing a Current density [A cm -2 ] (a) Current density [A cm -2 ] (b) Figure 6.11.: Fuel cell (a) voltages and (b) power density as function of current density when the specific surface area is , and m 1. The fuel cell performance is strongly influenced by the specific surface area of the agglomerates in the catalyst layer. Fuel cells with a high specific surface area provide a large active area for reaction in a given volume of catalyst. Its impact is noticeable at a low current density and becomes more significant as the current density increases. The specific surface area can be increased by, for example, using small catalyst particles and promoting dispersion of the catalyst agglomerate to reduce the agglomerate size. Volume fraction of electrolyte in agglomerate ( v el,ag ) The electrolyte is the proton carrier in a hydrogen PEM fuel cell and the amount of electrolyte in the agglomerate can influence the cell performance. The volume fraction in the agglomerate was 0.2 in Grujicic and Chittajallu (2004), and this value was also used as the reference value in this study. To study the effect of the volume fraction on the fuel cell performance, the value was extended to lower and higher values than the reference value: 0.15 and The corresponding polarisation curves are shown below. 149

150 6. Agglomerate model Cell voltage [V] v el,ag Increasing v el,ag Power density [W cm -2 ] v el,ag Increasing v el,ag Current density [A cm -2 ] (a) Current density [A cm -2 ] (b) Figure 6.12.: Fuel cell (a) voltages and (b) power density as function of current density when the volume fraction of electrolyte in agglomerate is 0.15, 0.20 and As shown in Figure 6.12, a fuel cell with a higher volume fraction of electrolyte in the agglomerate gives higher fuel cell voltage. The effective proton conductivity as according to the Bruggemann relation (Secanell et al., 2007) increases when the volume fraction of electrolyte is increased. It can be concluded that the increasing volume fraction of electrolyte in the agglomerate increases the effective proton conductivity and, hence the fuel cell voltage. Comparison of parameters The parametric analysis shows the individual impact of parameters on the polarisation curve of the fuel cell and this section compares the results. This secions aims to compare the impact level of the parameters on the peak power density. The peak power density will be plotted in y-axis as a function of the %change in the value of parameters from the reference value (see Table 6.3). 150

151 6. Agglomerate model P' max j 0,c j0c Rag R tf t f a eag e vfrac v el,ag %Difference in parameter Figure 6.13.: Percentage difference in fuel cell peak power density as a function of the percentage difference in the parameters. Equations for the peak power density as function of each parameters in Figure 6.13 were derived and based on the lines of best fit generated from the Add trendlines: linear function tool in Microsoft Excel. The R 2 for all of the equations were The equations are; P max = v el,ag (6.37) P max = a (6.38) P max = j 0,c (6.39) P max = t f (6.40) P max = R ag (6.41) P max = ɛ ag (6.42) The focal point at P max = 0.44 W cm 2 in Figure 6.13 corresponds to the reference values of the parameters. The gradient in each equation reflects the changes in peak 151

152 6. Agglomerate model power density when each parameter was modified. Three parameters:t f, R ag and ɛ ag have negative gradient of , and , respectively. Increasing the values of these parameters has a negative impact on the fuel cell power density. On the other hand, v el,ag, j 0,c and a have positive gradient of , and so they should be as high as possible to improve the power density of fuel cell. Three parameters, v el,ag, a and t f, show relatively large gradients in the diagram, meaning that they have relatively large impact on the performance. The parametric analysis shows the effect of each parameters individually but does not show the effect when changes in their values are combined. The following section provides a statistical sensitivity analysis which can give an indication of how the variation of parameters in their typical ranges influences the overall fuel cell performance. The typical range of parameters is presented in Appendix C Sensitivity analysis Sensitivity analysis was used to statistically determine whether or not a parameter which influences the process output, has a significant impact on the overall performance. Usually in a fuel cell system, either the voltage or the current density can be used as an indicator of performance. Due to the model structure, where the cell voltage was determined for each specific value of current density, it was suitable to use the average voltage produced in a range from 0 to 1.2 A cm 2 as the objective function here. In terms of the influencing parameters, v el,ag, a and t f were identified in the parametric analysis. However, a and R ag are inter-related and can be combined to reflect their expected influence. A specific surface area (a) in a catalyst layer consisting of spherical agglomerate with radius R ag is (see the derivation in section 6.7.2): a = θ(1 ɛ cl ) 3 R ag (6.43) where θ is the roughness factor of the agglomerate surface, which can be determined from the reference data set, and ɛ cl is the porosity of catalyst layer in cathode. Due 152

153 6. Agglomerate model to the above relationship, the parameters of v el,ag, R ag and t f were considered in the following analysis. The sensitivity analysis tested the parameters at three levels as listed in Table 6.5. Level 2 was the reference level, which was the value from the simulation conditions listed in Table 6.3. Level 1 and 3 were the lower and upper values of the reference parameters, respectively, based on the typical range reported in literature (see Appendix C). Parameter Level 1 Level 2 Level 3 Volume fraction of electrolyte in agglomerate ( v el,ag ) Agglomerate radius(r ag ) in µm Electrolyte film thickness (t f ) in µm Table 6.5.: PEM fuel cell parameters and their levels used in the statistical sensitivity analysis. All 27 possible combinations of the parameter and their levels were denoted alphabetically from a to aa in Table 6.6. The corresponding average cell voltage (the objective function) and the square of the average voltage are also shown. 153

154 6. Agglomerate model Case v el,ag R ag t f Average Voltage 2 voltage [V] a b c d e f g h i j k l m n o p q r s t u v w x y z aa Average Table 6.6.: The matrix of cases and the levels of each parameters in each case. Case n was the reference case which gave an average voltage of V. Case i used the low end value of the volume fraction of electrolyte in agglomerate, and the high end values of the agglomerate radius and electrolyte thickness, to give the smallest average voltage of V. Case s used the high end value of the volume fraction of electrolyte in agglomerate and the low end values of the agglomerate radius and electrolyte thickness, to give the highest average of fuel cell voltage at V. The data was analysed by using the one-way analysis of variance (ANOVA) method (Ross, 1996; Grujicic and Chittajallu, 2004). ANOVA is a statistically based, objective decision making tool for detecting any differences in average of the objective function. It enables a quantitative estimate of the relative contribution each parameters makes 154

155 6. Agglomerate model to the overall response (Fowlkers and Creveling, 1995). ANOVA uses a mathematical technique known as the sum of squares to examine the effect of the deviation of the parameters v el,ag, R ag and t f in the overall response. The overall variation in the objective function is the sum of variations from the variation in each parameter, the variation in the average and an uncontrolled variation (Ross, 1996). The uncontrolled variation can not be directly identified as an effect caused by a parameter and it is called random error in this analysis. The total variation in the objective function can be represented mathematically in terms of the sum of squares (SS) (Ross, 1996; Fowlkers and Creveling, 1995): SS t = ΣSS p + SS m + SS e (6.44) where SS t is the sum of squares of all objective function values, SS m is the sum of the square of the mean of the objective function values, SS p is the sum of square due to variation in parameter each parameter and SS e is the sum of square due to the random error in the data set. Defining the objective function as x, the sum of squares terms can be calculated as follows: SS t = Σ(x 2 ) (6.45) where SS t is the sum of squares of the objective function. SS m = n( x) 2 (6.46) where SS m is sum of the square of the mean, n is the total number of cases (which is 27 in this analysis) and x is the average of the objective function. SS p = Σ l=1to3 [n (p,l) ( x (p,l) x) 2 ] (6.47) where n (p,l) is number of cases using parameter p and level l and x (p,l) is the average of the objective function in cases using parameter p and level l. SS t, SS p, SS m were determined from data set in Table 6.6 and SS e was calculated 155

156 6. Agglomerate model from Equation The degrees of freedom of each parameter (DOF p ) is the number of parameter levels minus one. DOF m is the degrees of freedom of the mean, which is 1. DOF e is the degrees of freedom of the random error which can be calculated from (Ross, 1996): DOF e = n DOF m Σ(DOF p ) (6.48) where n is the total number of cases. The variances of each parameter and the random error can be calculated from (Ross, 1996): V AR = SS DOF (6.49) The significance of the individual parameters can be quantified by comparing the variance of the parameter (VAR p ) to that of the random error (VAR e ) (Fowlkers and Creveling, 1995). This ratio of variances is also known as the F-value, which can be calculated from (Ross, 1996): F = V AR p V AR e (6.50) Details of the ANOVA analysis for the simulation data in Table 6.6 is shown below. Para- Difference from mean ( x (p,l) x ) SS % of DOF Variance F meters Level 1 Level 2 Level 3 SS v el,ag R ag t f Random error Total Table 6.7.: Statistical sensitivity analysis of the PEM fuel cell performance. To calculate the data in columns 2, 3 and 4 of Table 6.7, the mean of the objective function for each pair of parameter and level was calculated and reduced by the overall mean (0.561 V). For example, the pair of ( v el,ag, level 1) was used in 9 cases ( a to i ) in Table 6.6. The average of the objective function from these 9 cases was and the overall mean was 0.561, thus the difference from the mean in column 2 156

157 6. Agglomerate model for v el,ag, level 1 was V. Similar analyses were carried out to complete every pair of combinations. The sum of squares (SS t ) was calculated to be V 2, the sum of squares of the mean (SS m ) was calculated to be V 2 and the sum of squares for each parameter (SS p ) was calculated as according to Equation 6.47 and they are presented in Table 6.7. The degrees of freedom, the variance for each parameter and the variance-ratio (F) are presented in columns 7, 8 and 9 of Table 6.7, respectively. The F-test at a 99% confidence interval was used in this analysis. The degrees of freedom of the parameters and the random error were determined from Equations 6.48 to be 2 and 20, respectively. According to Ross (1996), the standard F-value at this condition (F 99%,2,20 ) is The F-values of the parameters in Table 6.7 were all greater than 5.85, thus it can be concluded that at a 99% confidence level, the variation in the parameters are significantly different from the variation caused by random error. This ANOVA analysis indicates the relative impacts that each parameter has on the average fuel cell voltage. According to the F-value of each parameter, the variation in volume fraction of electrolyte in the agglomerate has the most impact on the objective function. The impact of the variation in agglomerate radius has a smaller impact with a F-value of 32 and the variation in film thickness with a F-value of 10 has the smallest impact among the considered parameters Results and discussion The model was validated against the experimental data in the previous section and will now be used to investigate the effects of the electrocatalyst on the fuel cell performance. The reaction kinetics are inevitably affected by the electrocatalyst structure and the operating conditions. This section will discuss the extent of the influence by looking into the behaviour of parameters which concern the reaction kinetics. The discussion follows the structure illustrated in Figure

158 6. Agglomerate model Potential application of the model Overall performance Overpotentials Kinetic parameters No semifinite assumptions Agglomerate shape comparison Results Summary Constant ζ and L P t Constant L P t Concentration profiles Effect of t f and R ag Kinetic parameters Polarisation Overpotentials Figure 6.14.: Map of the results and discussion section Overpotential and kinetics parameters This section provides an overview of the behaviour of the overpotential and the characteristics of the reaction rate in a range of operating current densities. 158

159 6. Agglomerate model Voltage [V] Thiele modulus, φ Cathode Ohmic Anode Current density [A cm -2 ] (a) Current density [A cm -2 ] (c) Average intrinsic rate constant, k [1000 s -1 ] Catalyst utilisation effectiveness, E Current density [A cm -2 ] (b) Current density [A cm -2 ] (d) Figure 6.15.: (a) The cell voltage losses in the anode, cathode and membrane, (b) the average intrinsic rate constant, (c) the Thiele modulus and (d) the catalyst utilisation effectiveness as function of the current density based on the reference parameters. Overpotentials The kinetics of the hydrogen oxidation reaction at the anode are faster and more spontaneous than the oxygen reduction action at the cathode (Srinivasan, 2006). Thus, as observed in Figure 6.15(a), the anodic voltage loss was relatively small in comparison to that in the cathode. The ohmic voltage loss in the membrane was also very small in comparison to the cathodic loss. The losses increased with the current density. The cathode was observed to be the main source of voltage loss in a hydrogen PEM fuel cell, thus improvement of the cathode is a priority in comparison to improvement in the other components of the MEA. 159

160 6. Agglomerate model The next discussion concerns how the characteristics of the reaction rate i.e. the intrinsic reaction rate constant (k), the Thiele modulus (φ) and the catalyst utilisation effectiveness (E), change under different operating currents for a fuel cell operating with the reference parameters in Table 6.3. Intrinsic rate constant (k) The intrinsic rate constant in the agglomerate varies with the oxygen concentration at each position within the agglomerate. The average value of k at each current density is plotted in Figure 6.15(b). The average intrinsic rate constant increased with the increasing current density. Thiele modulus (φ) The modulus is a dimensionless parameter, which is a ratio of constants for the reaction and the diffusion in the catalyst agglomerate. It indicates the relative importance of these processes at each current density. A large value of φ indicates that the reaction kinetics are fast relative to the diffusion process in the agglomerate (Fogler, 1992). When the Thiele modulus is large, the internal diffusion usually limits the overall reaction rate; when the Thiele modulus is small, the reaction kinetics are usually rate-limiting (Fogler, 1992). Figure 6.15(c) shows that the Thiele modulus increased exponentially with the current density. At low current density, the Thiele modulus is of order 1, so both processes are kinetically comparable. For current densities above 0.8 A cm 2, the Thiele modulus increases rapidly and the diffusion constant became relatively much smaller than the reaction rate constant. Catalyst utilisation effectiveness (E) The catalyst utilisation effectiveness is a ratio of the observed reaction rate to the rate in the absence of the concentration gradient in the agglomerates. Figure 6.15(d) shows that E decreased from 1 to almost 0.1 when the current density was increased from 0 to 1.2 A cm 2. The reduced E reflected the lower catalyst accessibility and higher diffusion resistance occurring at higher current densities. 160

161 6. Agglomerate model Effects of the thickness of electrolyte film and the agglomerate size This section discusses effects of agglomerate radius (R ag ) and the electrolyte film thickness (t f ) on the peak power density of a hydrogen PEM fuel cell at the reference operating conditions. Both of these parameters are related to the geometry of the agglomerates; however, they each have a different impact on the fuel cell performance. Referring to Table 6.7, the F-ratio of the agglomerate radius is 32, whereas the value for the electrolyte film thickness is 10. Although these F-ratios cannot be interpreted quantitatively, they indicate the relative impacts of the parameters i.e. the variation in the agglomerate radius influences the overall performance relatively more than the electrolyte thickness does. Cell voltage [V] t f µm µm µm Increasing t f Cell voltage [V] R ag µm µm µm Increasing R ag Current density [A cm -2 ] (a) Current density [A cm -2 ] (b) Figure 6.16.: Fuel cell polarisation curve as a function of current density for various values of (a) the thin film thickness (with t f = 0.1, 0.13 and 0.15 µm) and (b) the agglomerate radius (with R ag = 0.8, 1.2 and 2.0 µm). The agglomerate radius (R ag ) was found to make a significant difference to the cell voltage over a wider range of current density than the film thickness (t f ), for which an impact was seen only in the high current density region. It is clear that the film thickness only affects the fuel cell performance in the mass transport limited region, in contrast to the agglomerate radius. To determine why the effect of the agglomerate radius is not restricted to the mass 161

162 6. Agglomerate model transport limited region (high current density operation), the variation of the intrinsic rate constant, the Thiele modulus and the effectiveness factor was studied when the agglomerate radius and film thickness were varied. Intrinsic rate constant, k [x10 7 s -1 ] t f µm µm µm Increasing t f Current density [A cm -2 ] (a) Intrinsic rate constant, k [x10 7 s -1 ] R ag µm µm µm Increasing R ag Current density [A cm -2 ] (b) Figure 6.17.: Intrinsic rate constant as a function of current density for various values of (a) the thin film thickness (with t f = 0.1, 0.13 and 0.15 µm) and (b) the agglomerate radius (with R ag = 0.8, 1.2 and 2.0 µm). Figure 6.17 shows that the intrinsic rate constant increased with the increasing film thickness and the agglomerate radius. The increase in film thickness and agglomerate radius reduce the oxygen concentration in the agglomerate and thus in order to produce the same current density as in the reference data set, the intrinsic rate constant needs to increase to compensate for the decreasing concentration caused by the increasing film thickness and the agglomerate radius. 162

163 6. Agglomerate model Thiele modulus, φ, [-] t f µm µm µm Increasing t f Current density [A cm -2 ] (a) Thiele modulus, φ, [-] R ag µm µm µm Increasing R ag Current density [A cm -2 ] (b) Figure 6.18.: The Thiele modulus as a function of current density for various values of (a) the thin film thickness (with t f = 0.1, 0.13 and 0.15 µm) and (b) the agglomerate radius (with R ag = 0.8, 1.2 and 2.0 µm). The Thiele modulus of the cathode catalyst layer with large agglomerate and thick electrolyte film were higher than that of the small agglomerate and thin electrolyte layer (Figure 6.18). As discussed in section 6.6.1, a large Thiele modulus indicates that the diffusion mechanism in the catalyst layer becomes the performance limiting mechanism. However, an increase in the film thickness only leads to an increase in the mass transport effects at high current density (greater than around 0.8 A cm 2 ), while increasing the agglomerate radius increases the Thiele modulus across the entire current density range. 163

164 6. Agglomerate model Effectiveness, E, [-] t f µm µm µm Increasing t f Effectiveness, E [-] Increasing R ag R ag 10.8 µm 21.2 µm 32.0 µm Curernt density [A cm -2 ] (a) Current density [A cm -2 ] (b) Figure 6.19.: Catalyst utilisation effectiveness as a function of current density for various values of (a) the thin film thickness (with t f = 0.1, 0.13 and 0.15 µm) and (b) the agglomerate radius (with R ag = 0.8, 1.2 and 2.0 µm). Increasing the electrolyte film thickness leads to a higher diffusion resistance in the catalyst layer, lowering the oxygen concentration at the agglomerate surface (Rengaswamy and Rao, 2006). The internal oxygen diffusion flux was therefore reduced and its effect is shown clearly in the high current density region in Figure 6.19(a). In terms of the agglomerate size, a larger agglomerate induced a larger diffusion path and the catalyst particles located away from the agglomerate surface were likely to be under-utilised in the large agglomerate. Figure 6.19(b) shows that the negative impact of a large agglomerate occurs even in the low current density region. A catalyst agglomerate with radius 0.8 µm maintained the effectiveness of for current densities up to 1.2 A cm 2. On the other hand, a larger agglomerate with radius of 2 µm showed a rapid drop in effectiveness to 0.03 at a current density of 1.2 A cm 2. This suggests that when the catalyst agglomerate has a small size, the catalyst agglomerate can prolong the high utilisation effectiveness over a wider range of current densities. 164

165 6. Agglomerate model Cathodic activation loss [V] 0.8 t f 0.10 tf1 µm 0.13 tf2 µm tf3 µm Increasing t f Current density [A cm -2 ] (a) Cathodic activation loss [V] R ag Rag1 0.8 µm Rag2 1.2 µm 0.5 Rag3 2.0 µm Increasing R ag Current density [A cm -2 ] (b) Figure 6.20.: Cathodic activation loss as a function of current density for various values of (a) the thin film thickness (with t f = 0.1, 0.13 and 0.15 µm) and (b) the agglomerate radius (with R ag = 0.8, 1.2 and 2.0 µm). Figure 6.20 shows that increasing the agglomerate radius increased the activation loss over a wider range of current densities than increasing the electrolyte film thickness. The impact due to increasing the film thickness was clearly observed in the high current density region. The effects of film thickness and agglomerate radius on the intrinsic rate constant, the Thiele modulus, the catalyst utilisation effectiveness and the cathodic activation loss have been studied. Both of these parameters have the same overall impacts on these values but the agglomerate radius has impact on the values over a wider range of current density. Impact of these parameters on the catalyst utilisation effectiveness in Figure 6.19 were clearly different. Increasing the agglomerate radius reduced the effectiveness factor significantly over the entire range of the current density. Increasing the agglomerate radius reduces the oxygen distribution inside the agglomerate and thus reduces the catalyst utilisation effectiveness at all values of the current density. On the other hand, increasing the film thickness covering the agglomerate reduces the oxygen concentration on the agglomerate (C o,s ). The reduced reactant concentration does not significantly lower the catalyst utilisation effectiveness in the reaction limited region (low current density), but there is a significant effect in the mass transport limited region (high current density). As a consequent of that, the impact 165

166 6. Agglomerate model of increasing the film thickness has been observed to be significant in the high density region The concentration profile and the limiting mechanism in fuel cell operation The two main mechanisms involved in the oxygen reduction reaction in the catalyst agglomerates are the reaction kinetics and the internal mass transfer (or the diffusion inside the agglomerate). To understand their influence, a log-log plot of the effectiveness and the Thiele modulus for all three agglomerate radii studied is plotted in Figure Catalyst utilisation effectiveness, E 0.1 R ag A 10.8 µm 21.2 µm 32.0 µm Reaction rate limiting region B Diffusion rate limiting region Thiele modulus, φ Figure 6.21.: Log-log plot of the effectiveness and the Thiele modulus of three agglomerate radii. The data analysis as presented in Figure 6.21 shows the fuel cell performance limiting mechanism in each range of current density for each given agglomerate radius. There are 2 distinct regions in Figure 6.21, A and B. Region A corresponds to high values of E, and low values of φ. In this region, the high E means that the reaction 166

167 6. Agglomerate model rate was similar to the rate without diffusion resistance. The diffusion resistance was small and did not hinder the reaction rate and consequently the reaction rate was the limiting factor in region A. Region B corresponds to low values of E and high values of φ. Low E indicates a low utilisation of catalyst due to the poor distribution of oxygen in the agglomerate. Diffusion was the limiting factor in region B. Figure 6.15(c) and 6.15(d) link data at low current densities to region A and data at high current densities to region B. Based on the combination of data from these figures, it can be concluded that for all agglomerate sizes, the reaction rate is the limiting mechanism at low current densities and that as the current is increased the diffusion mechanism becomes the limiting factor. Furthermore, Figure 6.21 shows the distribution of data from different agglomerate sizes. Data from the small agglomerates scatters in region A and the large agglomerates results are mainly in region B. In conclusion, as the agglomerate particle becomes small, the Thiele modulus decreases and the effectiveness approaches 1. In this case, the reactant diffuses thoroughly inside the agglomerate thus catalyst particles are exposed to the reactant and are utilised evenly. The electrocatalytic performance in a small agglomerate becomes limited by the reaction on the active site rather than by the diffusion process. On the other hand, when the Thiele modulus is large, the internal catalyst effectiveness is small, and the reaction is diffusion-limited within the agglomerate. This analysis is a potential design tool for catalyst selection in fuel cell design. Knowing the limiting factor for the performance of a catalyst structure (either limited by the reaction or the diffusion rates at a given range of current density) would allows us to suitably design either the operating conditions for commonly used catalysts or to improve the catalyst structure for the specified operating conditions. The concentration profile Figure 6.22 illustrates the oxygen diffusion path from the agglomerate surface through the particles in the agglomerate to the interior catalyst surface. Oxygen gas dissolves in Nafion R and diffuses from the agglomerate surface at r = R ag toward the agglomerate centre at r = 0. Oxygen depletion within a spherical agglomerate catalyst with R ag of 1.2 µm at the standard operating conditions has been studied. 167

168 6. Agglomerate model Supporting carbon Platinum catalyst C o (r = 0) Oxygen diffusion path C o,s Electrolyte r = 0 r = R ag Figure 6.22.: Individual spherical agglomerate structure. The Thiele modulus, which increases with current density, was used to calculate the dimensionless oxygen concentration as a function of the dimensionless agglomerate s radius. 1 increasing φ and j Dimensionless oxygen concentration Dimensionless radius within an agglomerate Figure 6.23.: Concentration profile in a spherical agglomerate with a radius of 1.2 µm at various values of Thiele modulus. At low current density (i.e. low Thiele modulus), oxygen could access all of the catalyst 168

169 6. Agglomerate model within the agglomerates, but as the current density increased the concentration dropped very fast and approached zero. At high current densities the dimensionless concentration approached zero at a dimensionless radius of 2 or 1/3 or radius away from the agglomerate surface. In this case, the diffused oxygen was used up before reaching the interior thus the catalysts which was deposited near the centre was not utilized. This leads to low values of the catalyst utilisation effectiveness in high current density operation. In conclusion, at low values of Thiele modulus, the reactant diffuses rapidly into the agglomerate interior. On the other hand, at large values of the Thiele modulus, the surface reaction is rapid and the reactant is consumed very close to the external agglomerate surface and very little penetrates into the interior of the agglomerate. If possible, it is advisable to deposit the catalyst in the immediate vicinity of the external surface when a large value of Thiele modulus characterises the diffusion and the reaction. At high current density, it would be a waste of the catalyst to uniformly distribute the catalyst when the internal diffusion is limiting because oxygen will be consumed near the external surface. The concentration profile of two agglomerate sizes A similar analysis was carried out to find the dimensionless concentration in an agglomerate with radius of 0.8 µm. The results are plotted in Figure 6.24, along with those from the previous section based on an agglomerate radius of 1.2 µm. 169

170 6. Agglomerate model Dimensionless oxygen concentration increasing φ and j Dimensionless radius within an agglomerate R ag =1.2µm R ag =0.8µm j=0.05 Acm j=0.20 Acm j=0.40 Acm j=0.60 Acm j=0.80 Acm j=1.00 Acm j=1.20 Acm j=0.05 Acm j=0.20 Acm j=0.40 Acm j=0.60 Acm j=0.80 Acm j=1.00 Acm j=1.20 Acm -2 Figure 6.24.: Concentration profile in spherical agglomerate with radius of 0.8 and 1.2 µm. The squares and lines represent the concentration profiles in agglomerates with radii of 0.8 µm and 1.2 µm, respectively. The oxygen concentration profiles at 1.0 A cm 2 in both agglomerates are identified in Figure It can be observed that the oxygen in agglomerate with radius 1.2 µm depleted at around R ag /3 whereas oxygen in agglomerate with radius 0.8 µm distributed over entire volume of agglomerate at the same current density. In the small agglomerate, oxygen was distributed over the entire volume, thus oxygen could access the available catalyst in the agglomerate; the small agglomerate showed a high catalyst utilisation effectiveness. In contrast, for the large agglomerate oxygen was depleted closer to the surface. Catalyst near the centre of the large agglomerate would not be used effectively and this poor utilisation would affect the fuel cell performance. Rengaswamy and Rao (2006) also have illustrated the normalised concentration of oxygen in an agglomerate as a function of radial coordinate. They found that beyond a certain potential, oxygen is completely utilised at the surface of the agglomerate and there is not sufficient supply of oxygen to reach the centre of the agglomerate. This finding shows the same pattern as that discussed earlier in this section. 170

171 6. Agglomerate model This investigation was limited to a spherical agglomerate structure. Studies have been carried out to explore the possibility of improving fuel cell performance by changing catalyst layer structures such as catalyst agglomerate shapes (Sun et al., 2008). The next part of this thesis will cover the application of the agglomerate model to study the effect of agglomerate shape on the fuel cell performance and to consider whether changing the agglomerate shape can improve the fuel cell performance The effect of agglomerate shapes The previous analysis was based on spherical agglomerates. This section aims to study the effect of the agglomerate shape on the fuel cell performance by comparing the polarisation curve of fuel cell with spherical, cylindrical and slab-like agglomerates in the catalyst layer. Sphere, cylinder and slab are identified in the text by using the subscripts sp, cy and sl, respectively. The semi-finite structure was used to describe the the reactant s diffusion in different shapes of agglomerate. The semi-finite analysis considers the dimension that is most relevant to the reactant s diffusion in the agglomerates (Rawlings and Ekerdt, 2002). Diffusion through the ends and edges of agglomerate was assumed to be negligible, in comparison to the other dimensions. The considered dimension and characteristic length of each shape are shown in Figure

172 6. Agglomerate model R sp ζ = R sp /3 R cy ζ = R cy /2 L ζ = H sl /2 W sl H sl l sl Figure 6.25.: The characteristic length and semi-finite structure of spherical, cylindrical and slab-like agglomerates. The entire volume of the spherical agglomerate was considered for oxygen diffusion. The diffusion of oxygen through the ends of the cylindrical agglomerate was assumed to be negligible in comparison to the diffusion through the cylindrical wall (Rawlings and Ekerdt, 2002). The characteristic length (ζ cy ) of a cylindrical agglomerate with radius R cy and length l cy, can be calculated from: ζ cy = πr2 cyl cy = R cy 2πR cy l cy 2 (6.51) The diffusion of oxygen through the flat sides of the slab agglomerate was also assumed negligible in comparison to the flat sides, thus the characteristic length (ζ sl ) of the slab-like agglomerate with width W sl, length l sl and height H sl, can be calculated from: ζ sl = W slh sl l sl 2W sl l sl = H sl 2 (6.52) Expression for the Thiele modulus in Equation 6.19 is based on the characteristic length (ζ), thus the equation can be used for all shapes of agglomerate. However, the catalyst utilisation effectiveness has to be adjusted according to the shape s 172

173 6. Agglomerate model coordinate. Rawlings and Ekerdt (2002) have considered the mass transport in a sphere, a cylinder and a slab. Similar analyses for the catalyst utilisation effectiveness to that shown in section have been conducted to give the effectiveness factor for cylindrical and slab-like agglomerates. The expressions are: E cy = 1 I 1 (2φ) φ I 0 (2φ) (6.53) E sl = tanh(φ) φ (6.54) where E cy and E sl are the catalyst utilisation effectiveness in cylindrical and slab-like agglomerates, respectively. φ is the Thiele modulus and I 1 and I 0 are the modified Bessel functions of first and zero orders. The study was carried out using three approaches for the comparison: 1. Comparison at a constant platinum loading (L pt ). The platinum loading per area of MEA in mg cm 2 was the same in all three cases, the corresponding fuel cell performances were based on the same main cost of material. 2. Comparison at a constant platinum loading (L pt ) and a constant characteristic length (ζ). The additional constraint of a fixed characteristic length was added and the result was compared to that from the first method. 3. Comparison at a constant platinum loading (L pt ) and a constant characteristic length (ζ) without assuming semi-finite structure Assumptions The main assumptions for the three methods were: 1. The end and edge diffusion transport was negligible for cylindrical and slab-like agglomerates. 2. The agglomerates were homogeneous. 3. The agglomerates were uniformly distributed in the catalyst layer in all cases. 173

174 6. Agglomerate model 4. The catalysts were uniformly distributed in the catalyst layer, and the mass of platinum per unit volume of catalyst layer was constant. 5. Agglomerates with different shapes have a constant roughness factor, density and porosity. The results from spherical agglomerates were used as the base-line performance for the comparison Comparison at a constant platinum loading (L pt ) It is appropriate to compare the effect of the agglomerate shape on the fuel cell at a constant catalyst loading because the performance and the material cost is strongly affected by the catalyst loading (Srinivasan, 2006). The constant platinum loading in the catalyst layer and the constant agglomerate density implied that the agglomerate volume was a constant. The volume of the spherical agglomerate with a radius of 1.2 µm was taken as the base-line. For cylindrical agglomerate, a ratio of length to radius (the aspect ratio) was used to identify each case. Three aspect ratios of 2,5 and 10 were considered (see Figure 6.26). The aspect ratio was inversely proportional to the cylinder radius. To obtain the equal agglomerate volume, for a cylindrical agglomerate with aspect ratio of α and radius R cy, we have: πr 2 cy R cy α = 4 3 π R3 sp (6.55) ( ) 4 1/3 R cy = R sp (6.56) 3α For the slab-like agglomerate, the length of slab is set to equal to the length of cylinder at each aspect ratio in the cylindrical agglomerate, so the effect of shapes at the same agglomerate length can be compared. For each aspect ratio α in the 174

175 6. Agglomerate model cylinder: l sl = l cy = αr cy (6.57) To obtain the equal agglomerate volume, for a slab-like agglomerate with aspect ratio of α 1 = W sl /H sl, we have: H sl l sl α 1 H sl = 4 3 π R3 sp (6.58) substitute Equation 6.58 in Equations 6.56 and 6.57 to give: ( )1/3 ( ) 4 π 1/2 H sl = Rsp (6.59) 3α α 1 The geometry of the cylindrical and slab-like agglomerates considered are shown in Figure Sphere A R Cylinder l cy =α R cy R cy B C D α=2 α=5 α=10 Slab l sl =αr cy H sl E α=2, α 1 =2 W sl = α 1 H sl F α=5, α 1 =2 G α=10, α 1 =2 H α=2, α 1 =5 I α=5, α 1 =5 J α=10, α 1 =5 K L M α=2, α 1 =10 α=5, α 1 =10 α=10, α 1 =10 Figure 6.26.: Geometric structure of the studied agglomerates. 175

176 6. Agglomerate model Number of the agglomerates (ℵ) in the catalyst layer is given by: ℵ = (1 ɛ cl)v V ag (6.60) where ɛ cl is the catalyst layer porosity, V is volume of the catalyst layer and V ag is the geometric volume of an agglomerate. Thus the specific surface area in the catalyst layer can be calculated: ℵA ag V = (1 ɛ cl ) A ag V ag (6.61) where A ag is the geometric area of an agglomerate The left hand side term of Equation 6.61 is the specific surface area of the catalyst layer (a). The ratio of area per volume of an agglomerate (the second term on the right hand side of Equation 6.61) is the specific surface area of an agglomerate (a ag ). Thus: a = (1 ɛ cl )a ag (6.62) The actual specific surface area is higher than that of the geometric value given by Equation A roughness factor (θ) is introduced to account for the surface roughness. The roughness factor is the ratio of the actual surface area to the geometric surface area, thus: a = (1 ɛ cl )θ a ag (6.63) For a cylindrical agglomerate, it is assumed that only the cylinder walls are active, not the ends, thus: Similarly for the slab-like agglomerate: a ag,cy = 2πR cyl cy πr 2 cyl cy = 2/R cy (6.64) a ag,sl = 2W sll sl W sl l sl H sl = 2/H sl (6.65) The calculation procedure described in section 6.3 was used to calculate the fuel cell 176

177 6. Agglomerate model performance of each sample. Results and discussion Power density [W cm -2 ] increasing radius 2,2 α=2 2,5 α=5 2,10 α=10 Power density [W cm -2 ] Thicker slab α=2, 3,2,2α 1 =2 α=2, 3,2,5α 1 =5 α=2, 3,2,10 α 1 =10 α=5, 3,5,2α 1 =2 α=5, 3,5,5α 1 =5 α=5, 3,5,10 α 1 =10 α=10, 3,10,2α 1 =2 α=10, 3,10,5α 1 =5 α=10, 3,10,10 α 1 = Current density [A cm -2 ] (a) Current density [A cm -2 ] (b) Power density [W cm -2 ] Sphere Cylinder(α=10) Slab(α=10, α 1 =10) Power density [W cm -2 ] ,10 Cylinder(α=10) 3,2,2 Slab(α=2, α 1 =2) Current density [A cm -2 ] (c) Current density [A cm -2 ] (d) Figure 6.27.: Power density as a function of current density in fuel cells with agglomerate shape of (a) cylinder (b) slab (c) all shapes and (d) Power density profile of selected fuel cells with cylindrical (α=10) and slab-like (α=2, α 1 =2) agglomerates. The simulated power density profiles were compared for each agglomerate shape, with the results of the cylindrical agglomerates shown in Figure 6.27(a) and the slab-like agglomerates in 6.27(b). As one would expect, the diffusion distance decreases as the agglomerate radius and the slab thickness decrease. The case of cylinder with α=10 and slab with α=10, α 1 =10 gave the highest power density in comparison to the other aspect ratios considered. Their performances are compared in Figure 6.27(c). The slab geometry exhibited the best result, cylinder was the intermediate 177

178 6. Agglomerate model and sphere was the worst. However, the improvement was not solely a function of the agglomerate shape, the agglomerate size also influences the power density. For example, in Figure 6.27(d), the cylindrical agglomerate α=10 had higher power density than the slab-like agglomerate with α=2, α 1 =2. The improvement was related to the smaller characteristic length for the cylinder, where ζ cy (α = 10) was µm compared to the slab, where ζ sl (α = 2, α 1 = 2) was µm. Summary It has been illustrated that fuel cell performance was affected by both the agglomerate shape and the characteristic length. The power density is expected to increase as the characteristic length decreases, but the effect of shape could not be fully understood for the geometries studied. This analysis allowed one of the significant parameter, the characteristic length of agglomerate, to vary significantly from one structure to another. This issue was addressed in the following analysis Comparison at a constant platinum loading (L pt ) and a constant characteristic length (ζ) This analysis was designed to compare the effect of agglomerate shape on the hydrogen PEM fuel cell performance when the agglomerates have the same characteristic length and the catalyst layers have the same platinum loading. The constant characteristic length put restriction on geometric dimension of each shape and at the same time, the constant platinum loading criteria sets a requirement of constant agglomerate volume for each of the shapes. At a constant characteristic length, the effective diffusion distance for oxygen to travel from the agglomerate surface to catalyst is the same for all shapes. Spherical agglomerate were used to give the base-line value of the characteristic length, the agglomerate volume and the roughness factor. The reference value of the agglomerate radius in the spherical agglomerate was 1.2 µm, therefore the base-line value of characteristic length (ζ) was: ζ = 0.4µm (6.66) 178

179 6. Agglomerate model The smallest possible agglomerate would consist of a carbon particle which is nm in diameter and the platinum particles which are 2-5 nm in diameter on its surface (Koper, 2009). The smallest agglomerate radius would thus be around 30 nm and the smallest possible characteristic length would be 10 nm. The observed average characteristic length of agglomerates determined from SEM analysis of a commercial MEA has been reported to be around 1 µm (Siegel et al., 2003). Therefore, the characteristic length is expected to be in the range of 0.01 to 1 µm and the value used in the simulation ( 0.4 µm) is in this range. The characteristic length is related to the cylindrical radius (R cy ): ζ = R cy 2 = R sp 3 (6.67) The aspect ratio α can be calculated from the known agglomerate volume (V ag ) and cylindrical radius (R cy ): α = 9 (6.68) 2 Similar analysis for the slab-like agglomerates, the slab thickness (H sl ) was determined from its relation to the constant characteristic length: ζ = H sl 2 (6.69) The length of slab can be varied to any length as long as the volume of agglomerate was the same as the base-line value. For a slab with the same length as the cylinder discussed above, l sl = l cy, in this case, the slab width (W sl ) can be determined from: α 1 = π (6.70) The specific surface area for each geometry is the reciprocal of the characteristic length which was assumed to be constant in this analysis. The specific surface area was m 1. The dimensions of the agglomerate geometries are shown in Table

180 6. Agglomerate model Sphere Cylinder Slab R= m R= m H= m l= m l= m W = m Table 6.8.: Geometries of agglomerate in different shapes at fixed ζ and L pt. In terms of the computational procedure, the standard conditions were kept constant as in the previous analysis. The catalyst utilisation effectiveness (E) equation was changed according to the agglomerate shape (see Equation 6.26, 6.53 and 6.54). Results and discussion As shown in Figure 6.28, the fuel cell using slab-like catalyst agglomerates had the highest voltage and power density, the cylindrical agglomerate had a slight improvement over the spherical agglomerate Voltage [V] Sphere Cylinder Slab Power density [W cm -2 ] Sphere Cylinder Slab Current density [A cm -2 ] (a) Current density [A cm -2 ] (b) Figure 6.28.: Fuel cell (a) voltage and (b) power density as a function of current density when different agglomerate shapes were used. As the characteristic length (ζ) was constant for the three agglomerate shapes considered, any improvement in performance was due to the shape of the agglomerates. The percentage improvement in the peak power density, based on the sphere, was 0.07% for cylindrical and 3% in the slab-like agglomerate cases. Summary The slab-like agglomerates improved the fuel cell performance more than the cyl- 180

181 6. Agglomerate model indrical ones although the improvement observed was only around 3%. The improvement was expected to be due to the shape coordinate, when the other factors such as diffusion distance was controlled Comparison at a constant platinum loading (L pt ) and a constant characteristic length (ζ) without assuming the semi-finite structure. The previous analysis assumed that the agglomerate had a semi-finite structure which only considers the surface that was most relevant to the reactant diffusion into the agglomerates (Rawlings and Ekerdt, 2002). In this section, the effect of the semi-finite assumption was investigated. The characteristic length and volume of the cylinder and slab were the same as in the spherical agglomerate. The active surface was assumed to be the total surface area, including the ends of cylindrical agglomerate and the ends and sides of slab-like agglomerates. The specific surface area of each agglomerate shape are shown in Table 6.9. Shape Specific surface area [m 1 ] Sphere Cylinder Slab Table 6.9.: Specific surface area of each agglomerate shape. The polarisation curves of each fuel cell with different agglomerate shapes are compared in Figure The cell voltage and power density calculated for a fuel cell using slab-like agglomerates were the highest, cylindrical agglomerates gave the intermediate and spherical agglomerates the lowest. 181

182 6. Agglomerate model Voltage [V] Sphere Cylinder Slab Power density [W cm -2 ] Sphere Cylinder Slab Current density [A cm -2 ] (a) Current density [A cm -2 ] (b) Figure 6.29.: Comparison of fuel cell (a) voltage, (b) power density of the hydrogen fuel cells with different agglomerate shapes as functions of the current density. In this analysis, the length of slab affected the specific surface area and therefore the fuel cell performance. Results in Figure 6.29 for the slab-like agglomerates used the same length as the cylindrical case. When the length of slab was varied by 50%, the results are given in Table Parameters l sl = 0.5l cy l sl = l cy l sl = 1.5l cy α 9/4 9/2 27/4 α 1 2π π 2π/3 l sl in µm a in m P max in W cm Table 6.10.: The length of slab, the specific surface area and the peak power density of fuel cell with slab-like agglomerate, determined without assuming the semi-finite structure in the analysis. From Table 6.10, a variation of 50% in the length of slab (l sl ) increased the specific surface area (a) by +4% and +5.5% and the maximum power density (P max) by +1.36% and +1.80%. These changes in the specific surface area and consequently in the power density were small in comparison to the 50% change in the length of slab. The maximum power density depends on the change in the specific surface area more than the length of slab. 182

183 6. Agglomerate model Without assuming the semi-finite structure of the agglomerates, surfaces at all sides of the agglomerate were assumed to support the reactant diffusion, leading to the higher specific surface area as shown in Table 6.9. Thus as expected, the fuel cells in this analysis give better performances than when the semi-finite assumption was used (see the comparison of the performances in columns 3 and 4 of Table 6.11). This change in the maximum power density is due to the application of semi-finite structure assumption in the second method Selection of the suitable shape analysis method Three methods on studying the agglomerate shape effect at different conditions have been used and their results (in terms of maximum fuel cell power density, P max) are compared in Table Parameters P max [W cm 2 ] in the analysis at constant; L pt ζ and L pt ζ and L pt and semi-finite assumption no semi-finite assumption Sphere Cylinder Slab with l sl = l cy Slab with l sl = 0.5l cy Slab with l sl = 1.5l cy Table 6.11.: Comparison of the peak power density in fuel cells with different agglomerate shapes, from three methods. The results from all methods indicate that slab-like agglomerates gave the highest fuel cell peak power density, the cylinder was the intermediate and the sphere was the lowest. However, the results were different in the extent of improvement attainable. The constant platinum loading method showed a good improvement in comparison to results from the other methods. Although the method was based on a fixed catalyst cost perspective, the characteristic length was not kept constant, so that the active surface area of catalyst varied significantly. 183

184 6. Agglomerate model 1/ζ α [x10 6 m -1 ] Specific surface area, [m-1] α -1 ] 1/zeta 1/ζ [m [m-1] ] Peak power density [W cm -2 ] Peak power density [W cm -2 ] 0 E B H F A C K D I G L J M 0.0 Figure 6.30.: Relation of peak power density of each shape to SSA and 1/ζ. The 13 agglomerate shapes considered in the constant platinum loading method were labeled alphabetically as shown in Figure The data in Figure 6.30 was arranged, regardless of the shapes, from the thickest agglomerate (E) to the thinnest agglomerate (M). It was observed that the specific surface area and the power density generally improved in the thinner agglomerates. The contribution of shape could not be distinguished thus this figure illustrates the necessity of controlling the characteristic length in order to study the shape effect. In the second method, the comparison used a constant platinum loading and characteristic length. Thus the effect on fuel cell performance observed from this analysis was due to the agglomerate shape. However, the method discarded the end effects of agglomerates which in practice, the end effect may partially contribute toward the overall performance. In the third method of comparison, it assumed that all surfaces of agglomerates were utilised and, consequently, it showed higher peak power density than those in the second method. In reality, the ends and sides of agglomerates are likely to have a lower reactant transport rate than the main agglomerate surfaces. Thus the actual fuel cell performance is expected to be in between those from the second and third methods. The following discussion considers the reaction kinetics of the catalyst agglomerates for all three shapes based on the second method, so as to keep to the lower end of 184

185 6. Agglomerate model the possible improvement which may be achieved by varying the agglomerate shape Effect of the agglomerate shapes on the reaction kinetics The influence of the shape on the reaction kinetics was investigated, in an attempt to find the underlying explanation for the improvement in the fuel cell performance. The simulation results in Figure 6.28 shows that a fuel cell with slab-like agglomerates gave the highest power density, and the cylinder performance was slightly higher than the spherical. The fuel cell performance behaviour is consistent with the utilisation effectiveness of agglomerates shown in Figure 6.31: 1.0 Utilisation effectiveness, E Sphere Cylinder Slab Current density [A cm -2 ] Figure 6.31.: The catalyst utilisation effectiveness as function of the current density for spherical, cylindrical and slab-like agglomerates. The utilisation effectiveness for all three shape reduced with increasing current density. The utilisation effectiveness decreased from approximately 0.95 at 0.1 A cm 2 to 0.10 at 1.2 A cm 2. The decline in utilisation effectiveness indicates that, on average, the catalyst particles were exposed to a lower oxygen concentration at a high current density operation: oxygen was not distributed thoroughly and some of the catalyst particles did not participate in the reaction. Despite the generally poor oxygen distribution at high current density, the utilisation effectiveness in the slab geometry was significantly higher than other shapes in 185

186 6. Agglomerate model the intermediate current density range. Thus the oxygen distribution in the slab geometry was better than that for the other shapes. Figure 6.31 illustrates that slab agglomerates facilitated the reactant diffusion within agglomerates very well. High catalyst utilisation was attained and the simulation illustrated a smaller activation loss in the slab geometry in comparison to the other shapes, as shown in Figure Cathodic activation loss [V] Sphere Cylinder Slab Current density [A cm -2 ] Figure 6.32.: Cathodic activation overpotential (η act ) as a function of current density of fuel cells with different agglomerate shapes. The agglomerate model considers the mass transport of oxygen in a porous catalyst agglomerate. There are two processes governing the overall performance at any point of operation: the reaction and diffusion processes (Bird et al., 2007). These processes pose limitations on the overall performance and the extent of the limitation is not constant. A log-log plot of the catalyst utilisation effectiveness and the Thiele modulus was used to identify their range of impact (see Figure 6.33). 186

187 6. Agglomerate model Catalyst utilisation effectiveness, E Reaction limiting region data from 1 Acm -2 increasing current density Sphere Cylinder Slab Diffusion limiting region Thiele modulus, φ Figure 6.33.: Log-log plot of utilisation effectiveness versus Thiele modulus for each agglomerate shape. The performance of the three agglomerate shapes shared the same pattern as shown in Figure Slab-like agglomerates illustrated the highest utilisation effectiveness, the cylinder was intermediate and the sphere was the smallest at all values of the Thiele modulus. At the Thiele modulus was less than 0.45, the percentage difference between the utilisation effectiveness of slab-like and spherical agglomerates was less than 5.8%. This difference increased as the Thiele modulus increased up to a maximum value of 27.8% at the Thiele modulus of 2 where the current density was around 0.85 A cm 2. The current density increased with the Thiele modulus as shown by the arrow in Figure The overall reaction of all three catalyst agglomerate were reaction-limited at low current density and they were diffusion-limited within the agglomerate at high current density. Despite the same pattern, the slab-like agglomerate outperformed the others by having higher utilisation of catalyst, particularly at intermediate current densities. Based on the spherical agglomerate performance, the percentage improvements 187

188 6. Agglomerate model in utilisation effectiveness (E) and fuel cell power density (P ) for slab-like and cylindrical agglomerates is illustrated in Figure 6.34(a) and 6.34(b), respectively. % improvement in E and P' Slab-like agglomerate Effectiveness (E) Power density (P') Current density [A cm -2 ] % improvement in E and P' 30 Cylindrical agglomerate 25 Effectiveness (E) 20 Power density (P') Current density [A cm -2 ] (a) (b) Figure 6.34.: Percentage improvement in fuel cell using (a) slab-like agglomerates and (b) cylindrical agglomerates, in the utilisation effectiveness and the power density as a function of current density. According to Figure 6.34, the percentage improvement of the catalyst utilisation effectiveness was greater than that in the power density at all current densities for both shapes of agglomerate. The effect for slab-like agglomerate (Figure 6.34(a)) was larger than that for the cylindrical agglomerate (Figure 6.34(b)). At current density as low as A cm 2, Figure 6.33 shows that the reaction was the limiting mechanism. The increase in the catalyst utilisation in the slab in this current density range (Figure 6.34) could not contribute much to the improvement in the power density. From 0.2 to 1 A cm 2, the percentage improvement in both E and P increased steadily. The benefit of the slab geometry was observed at low current density range as E sl > E sp. Their matching profiles of the percentage improvement in E and P shown in Figure 6.34 indicate that the catalyst utilisation effectiveness is the factor causing the higher power density in the fuel cell. As the current density increased, the diffusion within the agglomerate became the limiting factor. The benefit of the slab geometry on the mass transport is shown by the large E in Figure 6.34(a). The slab maintained a good distribution of oxygen while the distribution in the sphere became limited. In the intermediate range of current density, the fuel cell 188

189 6. Agglomerate model operation with spherical agglomerate was closer to the diffusion limiting region than for slab-like agglomerate and the improvement in the effectiveness in the slab over the sphere was significant. When the current density was greater than 1 A cm 2, the beneficial effect of the agglomerate shape on the catalyst utilisation effectiveness diminished, and thus the improvement in the power density also decreased. There was a change in the limiting mechanism of the fuel cell performance at the high current density, causing a lower improvement in the effectiveness of slab. At high current density, or the diffusion-limiting region in Figure 6.33, the agglomerate surface reaction became rapid and oxygen was consumed near the agglomerate surface. As a consequence, the advantage of the slab-like agglomerate shape in distributing reactant was reduced as observed in the convergence of the catalyst utilisation effectiveness in this region (Figure 6.33). The data points at 1 A cm 2 of all agglomerate shapes are labeled in Figure 6.33 in order to consider the sharp drop of E observed for current densities greater than 1 A cm 2 in Figure The effect of rapid reaction near the agglomerate surface began to dominate at this point, and not much of oxygen could penetrate to the interior of the agglomerate. The effectiveness in the slab became similar to that in the sphere and benefit of the slab geometric was reduced Benefits and potential applications of the agglomerate model Apart from a direct application of an agglomerate model to predict a hydrogen PEM fuel cell performance, the other interesting benefits and potential application are: Improvement of fundamental knowledge There are interconnected and complex phenomena occurring in a fuel cell operation, these include mass/heat transfer, electrochemical reaction, and ionic transports. These phenomena govern fuel cell operation at all time and development of analytical models can show the impact of each phenomena in the considering case. The extent of these phenomena are not usually measured experimentally thus ability to understand 189

190 6. Agglomerate model the mechanism in context of operating conditions can be a very big advantage of modelling. To predict the fuel cell performance due to catalyst degradation Catalyst layer is subject to material degradation during operation, especially its catalyst components. The catalyst degradation leads to the loss of the active surface area in fuel cell and thus lowering the fuel cell performance. The degradation occurs via two different processes: (i) platinum dissolution and redeposition on carbon (Ostwald ripening), (ii) migration of soluble platinum (Pt 2+ ) species in the ionomer phase and chemical reduction of Pt 2+ by crossover H 2 molecules (Ferreira et al., 2005), and (iii) the lack of bonding between the platinum and carbon support (Borup et al., 2006). The dissolved and the loose particles either reformed on larger particles or move into electrolyte phase (Ferreira et al., 2005; Kim et al., 2008; Akita et al., 2006). Borup et al. (2006) found that platinum particles may not have been sufficiently attached to carbon supports thus they moved to ionomer portions and formed larger agglomerates during cycling from 0.1 to 0.96 V. This degradation is likely to depend on MEA preparation technique. For the technique that was considered by Borup et al. (2006), the variation of catalyst agglomerate size is shown in Figure Figure 6.35.: Platinum paticle size as function of temperature after cycling from V for 1500 cycles (Borup et al., 2006). The developed agglomerate model can be used to find the corresponding fuel cell performance due to the change in agglomerate radius by the following procedure: 190

191 6. Agglomerate model 1. Determine a parameter set that give best fit to the fuel cell polarisation curve before the start cycling the MEA. 2. Modify Equation 6.63, based on the assumption that the agglomerate surface roughness is constant to give: ( ) ( ) a a = (6.71) (1 ɛ cl )a ag (1 ɛ t=0 cl )a ag t=t where t = 0 refers to data set before the aging of MEA and t = t refers to data after the aging of MEA. a t=0, a ag,t=0 would have been obtained from step 1. a ag,t=t can be obtained from Figure 6.35, thus the only unknown is the specific surface area (a t=t ) can be calculated. 3. Use a t=t to determine the corresponding fuel cell polarisation curve. To predict the fuel cell performance due to change in catalyst thickness caused by aging of MEA SEM images of MEA in potential cycling from 0.1 to 1.2 V with 0 to cycles in Figure 6.36 shows bands of platinum particles inside membrane near the cathode side (Chen et al., 2006). The cathode thickness reduced from 17 µm at 0 cycle to 14 µm at cycles. The change in the catalyst layer thickness leading to the change in fuel cell performance, which can be determined in the developed agglomerate model if data on the layer thickness as a function of time have been identified as shown by Chen et al. (2006). 191

192 6. Agglomerate model Figure 6.36.: SEM images shows thicknesses of layers in MEA after a number of cycle (Chen et al., 2006) Summary The agglomerate model considers the reactant transport and the reaction kinetics in the catalyst agglomerate. The agglomerate structures have a large influence on the overall fuel cell performance because the electrochemical reaction occurs here. The model focuses on the agglomerate scale and thus the characteristic length is a function of the agglomerate radius. The cathode exchange current density of 10 A m 2, the electrolyte thickness on agglomerate surface of 0.13 µm, the agglomerate specific surface area of m 1 and the agglomerate radius of 1.2 µm give the best fit with experimental data from Du (2010). The negative effects of electrolyte film thickness, agglomerate radius and porosity of catalyst layer on the fuel cell voltage were observed. On the other hand, the exchange current density, the volume fraction of electrolyte in agglomerate and the agglomerate specific surface area had positive gradient with respect to the peak 192