On the mechanisms of electrochemical transport in Polymer Electrolyte Fuel Cells

Transcription

1 Loughborough Unversty Insttutonal Repostory On the mechansms of electrochemcal transport n Polymer Electrolyte Fuel Cells Ths tem was submtted to Loughborough Unversty's Insttutonal Repostory by the/an author. Addtonal Informaton: A Doctoral Thess. Submtted n partal fulfllment of the requrements for the award of Doctor of Phlosophy of Loughborough Unversty. Metadata Record: Publsher: c Pratap Rama Please cte the publshed verson.

2 Ths tem was submtted to Loughborough s Insttutonal Repostory ( by the author and s made avalable under the followng Creatve Commons Lcence condtons. For the full text of ths lcence, please go to:

3 On the Mechansms of Electrochemcal Transport n Polymer Electrolyte Fuel Cells by Pratap Rama A Doctoral Thess submtted n partal fulflment of the requrements for the award of Degree of Doctor of Phlosophy of Loughborough Unversty 15 th February 2010 by Pratap Rama 2010

4 Abstract The Polymer Electrolyte Fuel Cell (PEFC) s well-posed to play a key role n the portfolo of future energy technologes for cvl and mltary applcatons. Prncpally, the PEFC converts part of the chemcal energy released durng hydrogenoxdaton and oxygen-reducton nto electrcal energy, generatng water a b-product. It s potentally a zero-emssons technology whch can operate slently due to the absence of any movng parts, has quck start-up characterstcs and can acheve hgh thermodynamc effcency. In order to ensure that the PEFC emerges as a vable opton for all applcatons, t s necessary to ensure that the technology s relable, capable of delverng performance and cost-effectve throughout ts lfe-cycle. To acheve these objectves, a better fundamental understandng of the mechansms of electrochemcal transport n the PEFC s requred than s presently avalable. The lterature dentfes that mult-component electrochemcal transport wthn the PEFC plays a central role n fuel cell operaton and longevty. Water transport s one of these. It s well-understood that excessve amounts of water wthn the porous electrodes of the cell can cause floodng, whch mpedes the supply of reactant gases. It s also well-understood that nsuffcent water can cause the polymer electrolyte membrane (PEM) to dehydrate, thereby reducng ts proton conductvty. Both of these processes can undermne cell performance. Repettve hydraton cycles are also known to precptate degradaton mechansms whch can undermne relablty. However, the mechansms of mult-component and potentally two-phase transport across the PEFC as a mult-layered assembly whch ncludes the porous electrodes and the PEM are not understood as well: the mechansms of contamnant transport, fuel crossover and lqud water nfltraton partcularly through the PEM are mportant examples. The modellng lterature demonstrates that electrochemcal transport n the PEFC s treated ether through the use of dlute soluton theory or concentrated soluton theory. The modellng lterature also demonstrates a wde spectrum n the applcaton of modellng assumptons and the formulaton of electrochemcal equatons to smulate transport n the dfferent layers of the PEFC. Ths thess

5 Abstract descrbes research amed at reconclng the dfferent modellng approaches and phlosophes n the lterature by developng and applyng a unfed mechanstc electrochemcal treatment to descrbe mult-component, two-phase transport across the layers of the PEFC. The approach adopted here s frst to construct a mult-component zerodmensonal model for mult-component nput gases whch s merged wth a multlayer PEFC model to correctly predct the boundary condtons n the gas channels based on the cross-flow of components through the cell. The model s valdated usng data from the open lterature and appled to understand contamnant crossover from anode to cathode. The second step s to develop a unfed mechanstc electrochemcal treatment to descrbe mult-component transport across the layers of the PEFC: the general transport equaton. Ths s central to the contrbuton of ths thess. It s theoretcally valdated by dervng the key transport equatons used n the benchmark fuel cell modellng lterature. It s then mplemented wth the mult-component nput model developed prevously and valdated usng data from the open lterature. The model s subsequently appled to understand fuel crossover characterstcs n the cell. The thrd and fnal step s to further-develop the applcaton of the general transport equaton to account for two-phase transport across the layers of the PEFC. The resultng model s valdated aganst three dfferent sets of data from the open lterature and subsequently appled to understand the effects of PEM thckness, anode gas humdfcaton, cell compresson and PEM structural renforcement on lqud nfltraton and two-phase transport across the PEM. It s demonstrated that the general transport equaton developed n ths thess establshes a backbone understandng of the modellng and smulaton of transport across the layers of the PEFC. The study successfully reconcles the dfferent modellng phlosophes n the fuel cell lterature. The progressve valdaton and applcaton of the general transport equaton demonstrates the potental to enhance the scentfc understandng of factors affectng PEFC performance and demonstrates ts value as a tool for computatonally-based cell desgn, optmsaton and dagnostcs.

6 Acknowledgements The author wshes to express hs profound ndebtedness frst and foremost to Prof. Ru Chen for the opportunty to carry out the research presented here and for the tremendous amount of tme, gudance, knd moral support and nvaluable advce gven wholeheartedly over the years. The author s also grateful to Prof. Rob Thrng and Prof. John Andrews for support and to Dr. Xao L for helpng wth techncal matters n chapter 8. The author also wshes to acknowledge hs fellow researchers for nsprng hm through ther own abltes and for makng these past few years a dotng lfelong memory. As ths manuscrpt represents the culmnaton of educatonal endeavours from chldhood, the author wshes to thank all of hs teachers and lecturers from Catherne Infants School, Catherne Junors School, Rushey Mead Secondary School, Wyggeston and Queen Elzabeth I College, and fnally Loughborough Unversty for nurturng the means to learn and understand. Thanks are also pad to Harpal Rajput and Pratk Patel for ther frendshp and laughter throughout these years. The author would also lke to express hs gratefulness to hs lovng, vrtuous parents and sster Dvya for ther selfless patence and unequvocal support throughout; for hs fellow researcher and now dear wfe Dovlė, the author wshes to express a husband s grattude for nourshng hs lfe wth endurng love, peace and resolve. Ths thess would not have been possble wthout ther help. The author s partcularly grateful for and humbled by the graceful vrtues of hs parents and grandparents, some of whom wll never get to see ths. For the hardshps that they have endured, and for the adverstes that they have overcome for the sake of ther chldren, ths thess s dedcated to them.

7 TO Shr. Munja Vnja & Smt. Manjula Munja Rama Late Shr. Vnja Rama & Smt. Jas Vnja Odedra Late Shr. Narbad Karsan & Late Smt. Nath Narbad Ranavaya

8 Contents 1 Introducton Basc Prncples Objectves of the Current Research Outlne of Thess References The Polymer Electrolyte Fuel Cell Components of the PEFC Cell Performance The Thermodynamc Equlbrum Potental Thermodynamc Effcency Irreversble Voltage Losses Polarsaton Curve References A Revew of Practcal Factors Governng the Performance of Polymer Electrolyte Fuel Cells Introducton Actvaton Losses Platnum Agglomeraton Platnum Mgraton Exposure to Sub-Zero Operatng Condtons Atmospherc Contamnants Fuel Contamnants Carbon Corroson Chemcal Degradaton of Slcone Seals Mass Transportaton Losses Cell Floodng Hydrophobcty of Porous Layers Ionomer Loadng n Catalyst Layer Impedance to Transportaton due to Ice Formaton

9 Contents v Effects of Compacton on the GDL Ohmc Losses Resstance to Electron Transfer n the B-Polar Plate Resstance to proton transfer n the Polymer Electrolyte Membrane Effcency Losses and Catastrophc Cell Falure Mechancal Attack Chemcal Attack Summary Conclusons References Mathematcal Modellng of a PEFC Mass Transport Concentrated Soluton Theory Dlute Soluton Theory Knudsen Fluxes Electro-Osmotc Drag Dscussons on Mass Transport Processes across the PEM Ohmc Resstance Resstance to the Flow of Electrons Resstance to the Flow of Protons Dscussons on Modellng Resstance to the Flow of Protons PEM across the PEM Electrode Knetcs Thn Interface Model The Macro-Homogeneous Model The Agglomerate Model Dscussons on Fundamental Models for Electrode Knetcs References

10 Contents v 5 A Polymer Electrolyte Fuel Cell Model wth Mult- Component Input Introducton The Basc PEFC Model Thermodynamc Equlbrum Potental and Irreversble Losses Membrane Water Transport Model The Mult-Component Transportaton Model Molar Flux of Oxdsed, Reduced and Produced Speces Channel Flows Gas Transportaton n the Electrode Dffuson Layer Gas Transportaton n the Membrane Sem-emprcal Carbon Monoxde Degradaton Effect Results and Dscussons Overvoltage Mult-Component Dffuson CO Crossover and Contamnaton Conclusons References A Unversal Modellng Framework from Fundamental Theory Introducton Theoretcal Study Drvng Force Equaton Molecular and Thermal Dffuson Equaton The General Transport Equaton Theoretcal Valdaton Dlute Solutons Concentrated Solutons Model Development Governng Equatons Soluton Procedure Results and Dscussons Model Valdaton

11 Contents v Hydrogen Crossover: 4-Speces System Conclusons References A Unversal Approach to Mult-Layer Two-Phase Modellng through the General Transport Equaton Introducton Theoretcal Equatons for Two-Phase Transport n Porous and Electrolytc Quas-Porous Meda The General Transport Equaton Theoretcal Equatons for Two-Phase Transport n Porous Meda Theoretcal equatons for two-phase flow n quas-porous meda Sub-Models for the Physcal Propertes of PEFC Meda and Infltratng Fluds Sub-models for the Inlet and Channel Regons Sub-models for the Porous Layers Sub-models for the Quas-Porous Layers Modellng Structure for a One-Dmensonal Two-Phase PEFC Model Expermental Valdaton Net water transport per proton Ohmc Resstance across the PEM Water Content across the PEM Conclusons References Water Transport Studes Introducton Non-Renforced Membranes PEM Thckness Anode Humdfcaton PEM Constrant

12 Contents x Parameter Effects on PEM Resstance Structurally-Renforced Membranes Expermental Results and Dscusson Conclusons References Conclusons and Future Work Conclusons Future Work Mcroscopc Modellng Macroscopc Modellng References A Appendces A.1 Sub-models for the Inlet and Channel Regons of a PEFC A.2 Key equatons for the effects of cell compresson on the water uptake and thckness of the quas-porous PEM A.3 References B Lst of Publcatons

13 Lst of Fgures 1-1 Prncple reducton-oxdaton processes of a hydrogen-fuelled polymer electrolyte fuel cell The key regons and flows of a PEFC sngle-cell An llustraton of a PEFC stack showng the b-polar plate and membrane electrode assembles of a two-cell PEFC stack Maxmum thermal effcency of a hydrogen-fuelled low temperature PEFC and the Carnot lmt of a heat engne wth an exhaust temperature of 45 C Basc polarsaton curve of a PEFC Thermodynamc effcency of a PEFC as a functon of electrcal load and cell voltage Fve regons of the polymer electrolyte fuel cell Thrd-order polynomal dependence of Θ on current densty Fourth-order polynomal dependence of Θ on current densty Smulated and measured fuel cell performance at 70 C Effect of varyng oxygen composton on the fuel cell performance Effects of varyng temperature on the fuel cell performance; 55 C (328 K), 70 C (343 K) and 85 C (358 K) Interfacal oxygen mole fractons wth 50% and 100% saturaton at 85 C (358 K) Actvaton overvoltage wth 50% and 100% of saturaton at 85 C (358 K) Effect of oxygen mole fracton on the fuel cell voltage Effects of varyng hydrogen composton on the fuel cell performance Interfacal ar consttuent mole fractons at cathode-membrane nterface CO crossover effects on cathode potental CO to H 2 flux rato for nlet fuel feed CO concentratons of 10 ppm, 50 ppm and 100 ppm Smulaton Flowchart Smulated membrane water content from the general transport equaton (6-14), and Sprnger et al

14 Lst of Fgures x 6-3 Crossover dependence on dry membrane thckness at 1 atm H 2 Crossover dependence on dry membrane thckness at 3 atm at 80 C (353 K) and 110 C (383 K) H 2 Crossover as functon of current densty for PEM thcknesses of 50, 100 and 175 µm PEFC cell structure for the one-dmensonal two-phase model Smulaton flowchart for the object-orentated sngle-cell, two-phase mult-layer one-dmensonal PEFC model Comparson of smulated and expermental values of net water flux per proton for the 18 test cases Specfc resstance and water content profles across the PEM for smulated and measured results Smulated and measured water content profles as a functon of nondmensonal PEM thckness for three levels of supply gas relatve humdty; 92%, 80% and 40% Expanded membrane thckness and percentage change n thckness as a functon of the orgnal thckness for fve smulated PEM thcknesses Water content profle as a functon of non-dmensonal poston along the expanded PEM thckness for the fve dfferent PEM thcknesses Lqud ntruson profles for fve dfferent PEM thcknesses as a functon of non-dmensonal poston along the expanded PEM thckness Depth of lqud water penetraton from cathodc PEM boundary for fve PEM thcknesses Net water transport per proton and average vapour and lqud phase components for fve PEM thcknesses Water flux per proton as a functon of non-dmensonal poston along PEM thckness Vapour and lqud phase components of net water transport as a functon of poston along PEM thckness for the 25.4 µm PEM case PEM water content profle as a functon of the non-dmensonal membrane poston for fve PEM thcknesses Lqud ntruson profles for fve dfferent PEM thcknesses as a functon of nondmensonal poston along the expanded PEM thckness Net water transport per proton and average vapour and lqud phase

15 Lst of Fgures x components for fve PEM thcknesses Vapour and lqud phase components of net water transport as a functon of poston along PEM thckness wth both fuel supples fully humdfed Change n PEM thckness as a functon of degree of constrant Effect of PEM constrant on PEM water content and lqud nfltraton Resstance maps for dfferent levels of constrant and PEM thcknesses Appled anode and cathode flow rates n standard ltres per mnute Membrane resstance and tuned dffusvty scalng factor as a functon of current densty Smulated thckness-averaged water content as a functon of current densty for case 1 and case 2 as a functon of current densty Electro-osmotc drag and dffusve components of net water flux across the PEM as a functon of current densty Smulated change n PEM thckness as a functon of current densty Sngle phase mult-component lattce Boltzmann smulaton of oxygen permeaton through a carbon paper GDL Mult-Scale PEFC Modellng Smulated pressure drops wthn a 25-cell stack usng the Hardy-Cross method and the sngle-phase electrochemcal transport model

16 Lst of Tables 2-1 Changes n free energy and entropy at standard temperature and pressure for hydrogen, oxygen and water Constants for equaton Grades of stanless steel accordng to composton by weght percentage Summary of factors affectng actvaton, Ohmc and mass transportaton losses Summary of factors affectng effcency losses and catastrophc cell falure Governng equatons for channel model based on the mult-component nput model n chapter Governng equatons for electrode model Governng equatons for membrane model Propertes for base case 3-speces (water, electrolyte membrane, protons) concentrated soluton membrane system Addtonal propertes for 4-speces (water, electrolyte membrane, protons, hydrogen) concentrated soluton membrane system Expermental and smulated hydrogen permeablty coeffcents for a 50 µm polymer electrolyte membrane Key equatons for the porous regons of the PEFC Key equatons for the quas-porous regon of the PEFC Test cases for model valdaton Base operatng condtons & materal propertes used n the PEFC model for the water transport studes

17 Nomenclature a b C actvty coeffcent for compressve stran compressve pressure (bar, 0.1MPa) c concentraton of speces (mol/cm 3 ) d D j T D erf E E EW f F I j molecular drvng force (g/molecule-j) dffuson coeffcent of speces n speces j (cm 2 /s) thermal dffuson coeffcent of speces (cm 2 /s) error functon potental (V) Young s modulus (MPa) equvalent weght (g/equv) volume fracton of water n the PEM Faraday constant (96484 C/equv.) molar flux of water produced at the cathode (mol/cm 2 -s) current (A) J exchange current densty (A/cm 2 ) 0 J current densty (A/cm 2 ) J ( s) Leverett J-functon k k J Boltzmann constant (J/K) relatve permeablty pre-factor for phase J F free energy of actvaton (kj/mol) G bulk modulus (MPa) G change n free energy (kj/mol) H crossover-loss gradent (per ppm) H molar change n enthalpy (kj/mol) m M n molecular mass (g/molecule) molar mass of speces (g/mol) number of electrons

18 Nomenclature xv n molecular concentraton of speces (molecules/cm 3 ) n& N & N A p R molar flux of speces (mol/cm 2 -s) molar flow of speces, (mol/s) Avagadro number ( molecules/mol) pressure (Pa) unversal gas constant ( J/mol-K) nternal R nternal resstance (Ω) proton r area-specfc resstance to proton transfer (Ω-cm 2 ) s porous layer saturaton s expanded pore fracton n the quas-porous layer epf s S S t T v V x X X z z molar entropy of speces (J/mol-K) molar entropy (J/mol-K) molecular entropy of speces (J/molecule-K) membrane thckness (µm) temperature (K) volumetrc flow rate of speces (cm 3 /s) molar volume of speces (cm 3 /mol) PEM expanson coeffcent general molecular force for speces, (J/cm-molecule) general molar force for speces (J/cm-mol) transverse cell co-ordnate valence of speces Greek α α E β rato of net water flux to hydrogen flux due to electro-reducton charge transfer coeffcent for electrode E rato of net water flux to proton flux due to overall redox reacton β parametrc coeffcent X for electrode E n the thn-nterface treatment X,E γ ε surface tenson of water (N/m) porosty

19 Nomenclature xv ε η θ Θ compressve stran overvoltage (V) contact angle, degrees CO-nduced degradaton factor κ absolute permeablty, cm 2 p κ electroknetc permeablty, cm 2 φ λ Λ moles of water per mole of charge ste dffusve flux affnty for speces (J/g-cm) µ molecular electrochemcal potental of speces (J/molecule) µ molar electrochemcal potental of speces I (J/mol) µ vscosty of flud n phase J (Pa-s) J υ ν ξ stochometry of speces Posson rato electro-osmotc drag rato of speces ρ densty (g/cm 3 ) ρ specfc resstance (Ω-cm) perm ψ permeablty coeffcent of speces (mol/cm-atm-s, 1/ mol/cm-pa-s) σ τ φ Φ 1 proton conductvty (S/cm) tortuosty electrc potental (V) dffusve coeffcent n the two-phase quas-porous general transport equaton Φ protonc coeffcent n the two-phase quas-porous general transport 2,J equaton Φ convectve coeffcent n the two-phase quas-porous general transport 3,J χ equaton degree of constrant

20 Nomenclature xv Subscrpts and superscrpts 0 superscrpt: standard state pressure (1 bar, 0.1MPa) cap comp cons crt epf subscrpt: standard temperature (25 C, K) capllary compressed constraned crtcal property fracton of expanded pores E 1,2 nterface 1 or 2 of electrode E fs gas + H j J l lq free-swellng property gaseous hydrogen on speces speces j phase J lmtng value lqud m mode max mem Ox Red sat T Th exponent for the relatve permeablty pre-factor mode of water flux across PEM (.e., dffusve, convectve or protonc) maxmum value membrane oxdaton process reducton process saturated property total value thermal property u / c uncompressed property vap w vaporous water

21 1 Introducton 1.1 Basc Prncples The Polymer Electrolyte Fuel Cell (PEFC) s an energy converson devce. It operates under the prncple that a proporton of the chemcal energy released by oxdsng hydrogen and reducng oxygen to produce water can be harnessed as electrcal energy. Because the release of electrcal energy n a fuel cell s not dependant upon ntermedate processes of thermal or mechancal energy converson, t has the potental to acheve effcences n excess of the nternal combuston engne. The PEFC s comprsed of two non-consumable electrodes and a separatng protonconductng polymer electrolyte membrane (PEM). The fuel hydrogen s suppled to the anode where t s oxdsed to produce electrons and protons. The protons are conducted to the cathode through the PEM, whle an external electrcal crcut whch connects the two electrodes conducts electrons to the cathode. The reductant oxygen s suppled smultaneously to the cathode where t s reduced to water by combnng wth the electrons and protons. The anode and cathode both contan catalysts to drve the oxdaton and reducton processes respectvely. Due to rreversble losses n the PEFC, a proporton of the chemcal energy released from the reducton-oxdaton (redox) reactons cannot be harnessed to do useful work. Irreversble losses occur manly due to the slowness of reactons n the electrodes, lmtatons n the mass transport of reactant gases and due to fnte resstances to onc and protonc transport n the electron and proton conductng materals of the cell. The remander of the chemcal energy release s carred by the electrons n the external electrcal crcut. The amount of energy carred by one mole of electrons gves rse to a cell voltage, whle the rate at whch the energy carrers move around the electrcal crcut gves rse to an electrcal current. The product of the cell voltage and the electrcal current defnes the useful amount of energy released per unt tme n electrcal form. For a hydrogen-fuelled PEFC, the overall reacton s;

22 1 Introducton 2 H O H O (1-1) The hydrogen-oxdaton reacton (HOR) that occurs n the anode s; H H + e (1-2) The oxygen reducton reacton (ORR) that occurs n the cathode s; + 1 2H + 2e + O2 H 2O 2 (1-3) The prncple processes are llustrated n Fgure 1-1. Fgure 1-1 Prncple reducton-oxdaton processes of a hydrogen-fuelled polymer electrolyte fuel cell The merts, lmtatons and applcatons of PEFC technology have been wdely dscussed n the lterature [1,2,3]. In spte of tremendous scentfc and engneerng progress over the past couple of decades, fuel cell research remans hghly geared towards dentfyng materal desgns, confguratons and operatng strateges for better performance, cost reducton and longevty. Due to the small length scales of a PEFC and the mcro and nanoscale features of ts nternal components, n-stu measurement can be formdable. As such, t can be advantageous to employ numercal models that can predct the nternal

23 1 Introducton 3 electrochemcal state of a PEFC n detal and the speces dstrbutons wthn t based on cell confguraton, materal composton and operatng condtons. In order to do so, t s necessary to have a structured understandng of mult-speces, mult-phase electrochemcal transport. The purpose of ths thess s to draw attenton to the mechansms of electrochemcal transport n a PEFC. As wll be dscussed, the lterature demonstrates a sgnfcant degree of dversty n the selecton, manpulaton and applcaton of electrochemcal theory to model transport wthn a PEFC, ncludng ts multple layers. Ths can compound fuel cell development because t does not demonstrate clarty or consstency n the understandng of the nternal transport. In order to truly understand nternal electrochemcal transport n a PEFC, ts relatonshp wth the physcal propertes of the fuel cell materals, nfltratng fluds and the thermodynamc condtons that the cell operates under, t s necessary to structure, demonstrate and apply a unfyng mechanstc electrochemcal theory. 1.2 Objectves of the Current Research The am of the current research s to develop a unversal electrochemcal theory to descrbe the mechansms of electrochemcal transport n PEFCs whch reconcles the benchmark modellng phlosophes n the lterature and demonstrably predcts sngle-phase and two-phase mult-component transport characterstcs of a sngle-cell. The objectves of the current research are as follow: 1. to establsh an understandng of the exstng theores and modellng phlosophes for the PEFC as an electrochemcal system; 2. to formulate, numercally valdate and apply a mult-component nput model for the boundary condtons of a PEFC; 3. to formulate and theoretcally valdate a unversal treatment for mult-component electrochemcal transport through the PEFC; 4. to merge, numercally valdate and apply (2) and (3) to study factors affectng snglephase mult-component electrochemcal transport through the PEFC va mult-layer smulatons;

24 1 Introducton 4 5. to formulate and numercally valdate a unversal treatment for two-phase multcomponent electrochemcal transport through the PEFC based on (3) and merged wth (2); 6. to apply the above to study factors affectng two-phase water transport through the PEM va mult-layer PEFC smulatons. It s antcpated that the knowledge generated from ths research wll mprove the understandng of the dfferent approaches to modellng transport across the PEFC, how they are fundamentally related and how they can be reconcled under a unversal electrochemcal theory whch can be appled to potentally all layers of the PEFC. It s antcpated that the applcaton of the unversal theory developed n ths thess wll progressvely uncover the phenomenologcal processes that affect the transport mechansms wthn the layers of the PEFC whch are formdable to measure n-stu, as dscussed, and not rgorously captured through exstng modellng approaches. All numercal work for the current study wll be carred out n the one-dmensonal doman through the thckness of the cell where temperature gradents wll be consdered as havng a neglgble nfluence on transport [4]. In addton, the current study can be lmted to non-reactve transport. However t s antcpated that the lmtatons of the numercal models developed n ths research can be addressed n future work by nterfacng the electrochemcal model formulated n the current work wth other hghly-developed numercal tools such as computatonal flud dynamcs and lattce-boltzmann modellng. 1.3 Outlne of Thess Chapter 1: Introducton The frst chapter of the thess has provded a bref ntroducton to PEFC technology and dscussed the ams, objectves and outlne of ths thess. Chapter 2: The Polymer Electrolyte Fuel Cell The second chapter wll provde a dscusson on the ndvdual components of the PEFC and wll dscuss mportant aspects n respect to the performance of the PEFC. In dong so,

25 1 Introducton 5 fundamental concepts of fuel cell thermodynamcs and rreversble voltage losses wll be covered. Chapter 3: A Revew of Practcal Factors Governng the Performance of Polymer Electrolyte Fuel Cells The thrd chapter wll provde an n-depth revew of the factors that affect fuel cell performance and longevty and wll provde an account of state-of-the-art technologcal developments that are enhancng the readness of hydrogen-fuelled PEFCs for market adopton. Chapter 4: Mathematcal Modellng of a Polymer Electrolyte Fuel Cell The fourth chapter wll present and dscuss the exstng theores for molecular transport and electrode knetcs n the PEFC as an electrochemcal system. Chapter 5: A Polymer Electrolyte Fuel Cell Model wth Mult-Component Input The ffth chapter wll provde a complete sngle-phase model of the PEFC n one-dmenson whch fully accounts for mult-component nput gases. The results obtaned wll be valdated aganst data obtaned from the open lterature. The model wll also be appled to smulate contamnant transport and ts affect on cell performance. Chapter 6: A Unversal Transport Equaton from Fundamental Theory The sxth chapter wll dscuss the dervaton of a sngle general transport equaton (GTE) to descrbe electrochemcal molecular transport through the layers of the PEFC. The electrochemcal theory developed n ths chapter wll be theoretcally valdated by dervng all benchmark molecular transport equatons employed n the PEFC modellng lterature. The theory wll then be translated nto a sngle-phase one-dmensonal mult-component model and numercally valdated aganst data from the open lterature. The model wll also be appled to elucdate the operatonal factors that affect hydrogen crossover. Chapter 7: A Unversal Approach to Mult-Layer Two-Phase Modellng through the General Transport Equaton The seventh chapter wll further-develop the unversal theory developed n the prevous chapter to model two-phase flow through the layers of the PEFC. The chapter wll provde a descrpton of how lqud water nfltraton through porous and quas-porous layers can be

26 1 Introducton 6 modelled usng the GTE as well as the effects of cell compresson. The developed model wll be translated nto an object-orented two-phase one-dmensonal model and valdated aganst data from the open lterature. Chapter 8: Water Transport Studes The eghth chapter wll present a parametrc study to nvestgate the desgn and operatonal factors that can affect lqud water transport through the cell, the b-modal water content of the PEM, and therefore PEFC performance. Factors consdered nclude PEM thckness, anode humdfcaton, PEM constrant and structural renforcement. Chapter 9: Conclusons and Future Work The fnal chapter wll outlne the achevements and conclusons of ths thess and wll provde suggestons for further work. 1.4 References 1 Sammes NM. Fuel Cell Technology: reachng towards commercalzaton, 2005 (Sprnger-Verlag, London) 2 Bengt S. Transport phenomena n fuel cells, 2005 (WIT Press, Southampton) 3 Barbr F. PEM fuel cells: theory and practce, 2005 (Elsever Inc., Burlngton) 4 Rowe A, L X. Mathematcal Modellng of Proton Exchange Membrane Fuel Cells. J. Power Sources, 2001, 102, 82-96

27 2 The Polymer Electrolyte Fuel Cell The prncpal components that form the PEFC are two electrodes (anode and cathode) and a polymer electrolyte membrane (PEM). The electrodes typcally contan at least two parts; a relatvely thck (~ 250 µm) porous carbon-fbre based gas dffuson layer (GDL), whch acts to dstrbute reactant gases and product water n and out of the cell whle provdng conductve pathways for the movement of electrons, and a relatvely thn (~ 10 µm) carbon-agglomerate based porous catalyst layer (CL) whch serves as the reacton bed for the oxygen-reducton or hydrogen-oxdaton processes. 2.1 Components of the PEFC Fgures 2-1 provdes a descrpton of the physcal components of the cell and the potental confguraton of a PEFC. A seven-layer assembly s shown whch ncludes anode and cathode GDLs, CLs and a PEM. As commercal products, fuel cell layers can be suppled n a varety of pre-fabrcated combnatons. The catalyst coated membrane (CCM) s essentally a PEM coated wth anode and cathode CLs. A two-layer gas dffuson electrode (GDE) s a GDL wth a CL coatng on one surface. A three-layer GDE contans an MPL between the GDL and CL. The membrane electrode assembly (MEA) s often a fve-layer assembly consstng of anode and cathode GDLs, CLs and a PEM. A seven-layer MEA assembly contans both anode and cathode mcro-porous layers (MPL). The MPL s used selectvely to control hydraton wthn the cell and therefore does not appear unversally n all PEFCs. Fgure 2-2 shows a PEFC wth repeatng components of a sngle-cell arranged n seres.

28 2 The Polymer Electrolyte Fuel Cell 8 Fgure 2-1 The key regons and flows of a PEFC sngle-cell Fgure 2-2 An llustraton of a PEFC stack showng the b-polar plate (BPP) and membrane electrode assembles of a two-cell PEFC stack [1]. 2.2 Cell Performance The performance of a PEFC s ndcated by a polarsaton curve. Conventonally, ths shows the output cell voltage of a sngle cell as a functon of current densty, n Amps per square centmetre. Current densty s obtaned by normalsng the total current drawn from the cell to the total footprnt area of a cell. Ths allows the performance of dfferent cells to be compared smultaneously wthout havng to consder the actual footprnt area of the cells. Multplyng current densty wth cell voltage yelds power densty, n W/cm 2. What s

29 2 The Polymer Electrolyte Fuel Cell 9 mportant s the nature of the cell voltage vs. current densty relatonshp. In general, the output cell voltage devates from a theoretcal maxmum potental as current densty ncreases. The purpose of ths secton s to dscuss the deal output of the cell, the thermodynamc effcency of a cell and the rreversble losses that typcally characterse the polarsaton curve The Thermodynamc Equlbrum Potental Consder the followng general reversble reacton, whch takes place under a state of thermal, chemcal and mechancal equlbrum; aa + bb mm + nn (2-1) The change n free energy of the forward reacton s gven by the Van t Hoff sotherm [2]; G = RT ln K + RT ln m [ M ] [ N ] [ A] a [ B] b n (2-2) where R K = unversal gas constant = equlbrum constant of the reacton at temperature T [ ] x X = actvty of speces X The maxmum electrcal work W el, max that can be obtaned from the cell s equal to the change n free energy at temperature T and can be related to the electromotve force of the reacton E by; G = Wel, max = nfe (2-3) where n F = number of moles of electrons = Faraday constant

30 2 The Polymer Electrolyte Fuel Cell 10 Because by defnton the reacton gven by equaton 2-1 occurs under a state of thermodynamc equlbrum, the electromotve force of the reacton E s more commonly termed the thermodynamc equlbrum potental. At standard state (1 bar), the change n free energy can be defned as a functon of the equlbrum constant K as follows [3]; 0 G = RT ln K (2-4) The change n free energy at standard state 0 G can also be defned n terms of the electromotve force at standard-state, also known as the standard-state potental, 0 E ; 0 0 G = nfe (2-5) Substtutng equatons 2-3 to 2-5 nto 2-2 yelds the general form of the Nernst Equaton; E = E 0 + RT nf ln a b [ A] [ B] [ M ] m [ N] n (2-6) Therefore, for a gven system where the reversble reacton gven by equaton 2-1 occurs under a state of thermodynamc equlbrum, t s possble to determne the thermodynamc equlbrum potental of the forward reacton f the temperature of the system s known, f the actvtes of the reactants and products are known and f the standard-state potental s known. The thermodynamc equlbrum potental s establshed when the forward chemcal process occurs at the same rate as the reverse reacton and therefore when there s no net charge beng drawn from the cell. As such, the thermodynamc equlbrum potental s also commonly known as the open crcut potental,.e., the electromotve force measured from a cell at zero current. The standard-state potental can be defned by revstng the change n free energy of the forward reacton at standard-state. The change n free energy can be defned n terms of the change n enthalpy 0 H and entropy 0 G vares accordng to temperature T ; 0 S durng the reacton at standard-state, such that

31 2 The Polymer Electrolyte Fuel Cell G = nfe = H T S (2-7) The standard-state potental s defned usng the standard temperature T 0 (25 C) as [2]; E 0 0 S0 G0 S ( T T ) + ( T T ) nf 0 0 E nf nf 0 0 (2-8) Here, 0 E 0, 0 G 0 and 0 S 0 are the standard-state potental, free energy change and change n entropy for the forward reacton gven n equaton 2-1 at standard temperature. condton s known as standard temperature and pressure (STP). Substtutng equaton 2-8 nto 2-6 yelds; Ths G E = nf ( T T ) 0 0 S0 nf + RT nf ln a b [ A] [ B] [ M ] m [ N] n (2-9) For a hydrogen-fuelled PEFC, the overall reacton nvolves 2 electrons, hence n = 2. The change n free energy and entropy at STP can be calculated usng the fgures provded n Table G 0 0 S 0 kj/mol kj/mol-k Gaseous Hydrogen (H 2 ) Gaseous Oxygen (O 2 ) Lqud Water (H 2 O) Table 2-1 Changes n free energy and entropy at standard temperature and pressure for hydrogen, oxygen and water [2,4] Assumng that the overall forward reacton of the PEFC can be gven as H O H O, the change n free energy at STP can be calculated as; G 0 = G0 G (2-10) 0 products reactants G = G0 = water kj/mol

32 2 The Polymer Electrolyte Fuel Cell 12 The cell potental at STP s therefore calculated as; E G = nf = = 1.229V Smlarly, the change n entropy at STP can be calculated as; S 0 = S0 S (2-11) 0 products reactants S = = kj/mol- K such that S nf = = V/K (2-12) Assumng that the actvty of product water s equal to unty, that partal pressures can be defned n bar,.e., a p p = 0 where 0 X X p s the standard pressure, and by substtutng equatons 2-11 and 2-12 nto 2-9 the followng form of the Nernst equaton can be obtaned; E 2 [ p ] 1/ H p 0 5 = E T ln (2-13a) 2 O2 where ( T ) 0 3 E = (2-13b) Thermodynamc Effcency The effcency of an energy converson devce s generally defned as the rato between the energy delvered by the system and the energy put nto the system. In the context

33 2 The Polymer Electrolyte Fuel Cell 13 of heat engnes, t s usually defned n thermodynamc terms,.e., the mechancal work done by the system dvded by the heat energy nput to the system. The heat nput corresponds to the heat energy released due to the exothermc reactons durng combuston and commonly known as the calorfc value or the enthalpy of formaton, H f. The Carnot lmt shows that the maxmum thermal effcency of a heat engne s dependant solely on the temperatures of the hgh and low temperature zones and drectly proportonal to the temperature of the low temperature zone. η W mech Carnot, therm = = 1 H f T T C H (2-14) where W mech = mechancal work done H f = enthalpy of formaton T C T H = temperature of the low temperature zone = temperature of the hgh temperature zone For a PEFC, the effcency s usually defned smlarly n thermodynamc terms. The energy delvered by the PEFC s defned by the electrcal energy output W elec whle the energy put nto the system agan corresponds to the heat energy that can be released f the fuel s combusted wth an oxdant. Ths defnton allows a relatvely straghtforward comparson of the PEFC wth a heat engne because both effcences are defned relatve to the amount of heat energy that s released when the fuel s burnt. η PEFC, therm W = H elec f (2-15) When hydrogen s burnt below 100 C, there s a release of what s known as the latent heat of condensaton,.e., the heat released when water vapour s converted nto lqud water wthout a reducton n ts temperature. As such, the hgher heatng value s commonly used for PEFC effcency calculatons, as they typcally operate below 100 C. For the burnng of hydrogen, the HHV s kj/mol. Usng equatons 2-13a and 2-7 t s

34 2 The Polymer Electrolyte Fuel Cell 14 possble to determne the standard-state potental and the change n free energy of the PEFC for a range of temperatures. Usng equaton 2-15 t s then possble to determne the maxmum thermodynamc effcency of the PEFC over ths range. Correspondngly, Fgure 2-5 compares the maxmum thermodynamc effcency of a PEFC usng the HHV aganst the Carnot lmt of a heat engne where the exhaust temperature s 45 C. Generally speakng, Fgure 2-5 demonstrates that the maxmum thermodynamc effcency of a heat engne accordng to the Carnot lmt approaches that of a low-temperature PEFC (<100 C) when the hgh temperature zone exceeds 200 C (473 K). It s noteworthy from Fgure 2-3 that the maxmum thermal effcency of the Carnot lmt can exceed the thermal effcency of a PEFC. Therefore, the PEFC does not always have a hgher thermal effcency than the Carnot lmt. In addton, whle Fgure 2-3 suggests that operatng at low temperatures can ncrease the maxmum thermodynamc effcency of the PEFC, two other ssues have to be consdered. Frst of all, t has to be noted that t can be more advantages to operate at hgher temperatures as the waste heat s more useful (f the product water takes lqud form, t has already released the latent heat of condensaton whereas water vapour contans more heat energy as t retans the latent heat of vaporsaton). Second, t has to be noted that the voltage losses that occur when current s drawn from the cell can be greater at low temperatures and therefore t can be more practcal to operate at hgher temperatures Irreversble Voltage Losses The useful amount of work, the electrcal energy, s obtaned from the PEFC only when a reasonably large current s drawn. Under such condtons, the cell potental decreases from ts thermodynamc equlbrum potental because of rreversble losses. These losses are often referred to as polarsatons, overpotentals or overvoltages. The cause of these losses

35 2 The Polymer Electrolyte Fuel Cell 15 Fgure 2-3 Maxmum thermal effcency of a hydrogen-fuelled low temperature PEFC and the Carnot lmt of a heat engne wth an exhaust temperature of 45 C. nclude slow electrode knetcs, Ohmc resstances of the electrolyte, electrodes and leads, and mass transport lmtatons. Actvaton Losses At low current denstes (1 100 ma/cm 2 ) the actvaton losses manly account for the rreversble voltage loss of a PEFC. Actvaton losses are attrbuted to the slowness of reactons occurrng n the fuel cell electrodes,.e., the catalyst layers. The anode knetcs are generally much faster than the cathode knetcs and therefore the cathode knetcs largely contrbuted to the overall actvaton loss. Actvaton losses can be reduced by ncreasng the temperature of the cell, ncreasng the electrochemcal actvty of the electrode wth sutable catalysts and by ncreasng the electrochemcally actve surface area (EASA) of the electrodes. Actvaton losses can ncrease durng the course of operaton f the EASA reduces n the fuel cell catalyst layers. Other factors sgnfcantly affectng performance n the catalyst layers nclude ts materal composton and dstrbuton, ts geometrc structure and the mpurty content of the reactant feeds. Assumng that the anode overvoltage s small compared to that of the cathode, the actvaton loss can be descrbed as follows usng the general form of the Tafel equaton:

36 2 The Polymer Electrolyte Fuel Cell 16 η = act RT α nf c J ln J 0 (2-16) where J α c = current densty = cathodc charge transfer coeffcent The exchange current densty J 0 corresponds to the rate at whch hydrogen s oxdsed and oxygen s reduced accordng to reversble reacton gven by equaton 2-1. Ohmc Losses At ntermedate current denstes ( mA/cm 2 ), the rreversble losses are domnated by Ohmc losses n the cell. Ohmc losses can be attrbuted to the on conductng propertes of the dfferent elements of the cell. The PEM s the central proton conductng part of the cell, whch connects the dsperson of electrolyte n the two catalyst layers. Resstance to the flow of protons n the PEM can sgnfcantly contrbute towards the Ohmc loss of a cell. Resstance to the flow of electrons also contrbutes towards the Ohmc loss. The electron conductng parts of the PEFC have fnte resstances that are dependant upon cell operatng temperature and the compacton force appled to a cell. Charge transfer resstances at the anode and cathode electrode, as well as resstance contrbutons from any other components n a fuel cell, such as current collectors, all contrbute to Ohmc losses. Ohmc losses can be expressed n terms of Ohms law: η Jr (2-17) ohmc = where r s the total Ohmc resstance to charge transfer. Proton conductvty can be mproved by mprovng the hydraton of the membrane durng operaton, by decreasng the thckness of the membrane and mprovng the onc conductvty of the membrane. Electrcal conductvty can be mproved by

37 2 The Polymer Electrolyte Fuel Cell 17 selectng/desgnng components wth materals that have hgh bulk electrcal conductvtes, and ensurng mnmal surface corroson and mantanng good electrcal contact between electron-conductng components of the PEFC. Mass Transport (Concentraton) Losses At hgh current denstes (> 1000mA/cm 2 ), mass transportaton domnates the rreversble losses. Mass transport losses occur when there s a change n the concentraton of a reactant gas on the surface of an electrode, whch occurs at hgh current denstes where the hydrogen oxdaton and oxygen reducton rates correspondngly hasten. In order to mantan a current for a gven potental, the supply of reactng speces to the electrode surface has to be sustaned. Ths sustans the electrolytc current due to the movement of ons through the membrane and therefore balances the electrc current flowng n the external crcut. Ths movement cannot be ncreased ndefntely and a pont must be reached where speces react at the electrode as fast as they reach t. The amount of current obtaned under such a crcumstance s known as the lmtng current. Mass transport losses can be caused by the slow dffuson of the gas phase through the porous regons, soluton/dssoluton of the reactants/products nto/out of the electrolyte membrane, or dffuson of reactants/products nto/out of the electrolyte to/from the electrochemcal reacton ste. Mass transportaton losses can be estmated as; η conc RT J ln 1 nf J = l (2-18) where J l s the lmtng current densty. The product water generated nsde the PEFC forms at the cathode sde and some of t s retaned by the PEM, thereby enhancng ts proton conductvty. Excess water has to be expelled from the cathode n order to prevent lqud water formaton and accumulaton, whch can subsequently mpede pathways for the transport of oxygen to the catalyst stes. At hgh current denstes, the producton of water correspondngly hastens. It can become dffcult to remove the water from the cathode and can therefore begn to saturate the porous

38 2 The Polymer Electrolyte Fuel Cell 18 electrodes. Ths can slow down the oxygen dffuson, causng a sharp drop n the oxygen concentraton resultng n a drastc ncrease n the mass transport loss. Fuel Effcency Losses As hydrogen passes through the anode GDL and enters the anode catalyst layer, t s possble for some of the hydrogen to permeate straght through the PEM, forgong the electro-oxdaton process. Consequently, t reacts drectly wth oxygen n the cathode catalyst layer and amounts to a proporton of spent fuel that does not contrbute towards the electrcal energy harnessed from the cell. Ths s descrbed as an effcency loss. Oxygen can also permeate the polymer membrane from the opposte drecton through enlarged pores and drectly react wth hydrogen n the anode catalyst layer. Fuel effcency losses are hghlydependant on the structure and mechancal state of the PEM; thn PEMs and the formaton of pnholes can cause hgh rates of fuel crossover Polarsaton Curve The overall cell output s gven by subtractng three of the losses dscussed n the precedng secton from the open crcut potental of the cell: RT J RT J V = E Jr ln ln 1 α cnf J 0 nf J l (2-19) Typcal parameters for the constants n equaton 2-19 are gven n Table 2-2. Fgure 2-6 demonstrates the typcal form of a polarsaton curve based on the parameters n Table 2-2. The thermodynamc effcency of the PEFC when current s drawn from the cell can be calculated by assumng that the electrcal work done by the cell can be equated to the free energy actually delvered by the cell based on the actual cell voltage; W = G nfv (2-20) elec act =

39 2 The Polymer Electrolyte Fuel Cell 19 Equaton 2-20 can be appled to 2-15 to determne the thermodynamc effcency as a functon of power densty, as shown n Fgure 2-7. It s noteworthy that the thermodynamc effcency ncreases wth decreasng load, unlke the nternal combuston engne (ICE). Generally speakng, the PEFC mantans thermodynamc effcency n the 40% ± 10% band, compared to an average of around 42% and 35% for state-of-the-art desel and gasolne ICEs respectvely. Parameter Unts Value Cell Potental at STP 0 E V Open Crcut Potental E V 0.95 Cell Temperature T K 343 Total area-specfc cell Resstance r Ohm-cm Cell Footprnt Area A cm Cathodc Charge Transfer Coeffcent α c Exchange Current densty J ma/cm Lmtng Current Densty J A/cm l Unversal Gas Constant R J/mol-K Faraday Constant F C/mol Table 2-2 Constants for equaton 2-19 Fgure 2-4 Basc polarsaton curve of a PEFC

40 2 The Polymer Electrolyte Fuel Cell 20 Fgure 2-5 Thermodynamc effcency of a PEFC as a functon of electrcal load and cell voltage. 2.3 References 1 Greenwood PS. Internal communcatons, Loughborough Unversty, Berger C. Handbook of Fuel Cell Technology, 1968 (Prentce-Hall, Englewood Clffs) 3 Bard AJ, Faulkner LR. Electrochemcal Methods, 2001 (John Wley & Sons, New York) 4 Hamman CH, Hamnett A, Velstch W. Electrochemstry, 1998, (Wley-VCH, New York)

41 3 A Revew of Practcal Factors Governng the Performance of Polymer Electrolyte Fuel Cells Ths chapter presents a comprehensve revew that ams to provde a structured understandng of the practcal factors that govern the performance of hydrogen-fuelled PEFCs by consderng the underlyng phenomenologcal mechansms that can degrade cell performance and cause falure. As dscussed n the precedng chapter, the performance of a PEFC s charactersed by one of four loss mechansms; (1) actvaton losses; (2) Ohmc losses; (3) mass transportaton losses and; (4) fuel effcency losses. Degradaton mechansms can contrbute towards multple loss mechansms and can also lead on to the fnal form of user-detectable loss; (5) catastrophc cell falure. 3.1 Introducton Research and development n PEFC technology to date has resulted n a vast array of materals, desgns, manufacturng technques and consderatons for the dfferent components of the cell [1,2,3]. These varatons reflect the fact that there are a multtude of factors that govern the performance of the PEFC, all of whch have some element of physcal desgn or operaton assocated to t that can be altered to mprove an aspect of cell performance. Dfferences n operatng modes and general cell desgn accordng to applcaton means that the mpact of certan performance degradaton and falure mechansms are also lkely to be dfferent from applcaton to applcaton. Automotve fuel cells, for example, are lkely to operate wth neat hydrogen under load-followng or load-levelled modes and be expected to wthstand varatons n envronmental condtons, partcularly n terms of temperature, pressure and atmospherc composton. In addton, they are also requred to survve over the course of ther expected operatonal lfetmes.e., around 5,500 hrs, whle undergong as many as 30,000 startup/shutdown cycles [4]. PEFCs for statonary applcatons would not be subjected to as many startup/shutdown cycles, however, would be expected to survve 10,000-40,000 hrs of operaton whlst mantanng a tolerance to fuel mpurtes n the reformate feed. The current revew dscusses factors that are potentally relevant to all types of applcatons, and covers all major hardware components n the PEFC.

42 3 Revew of Practcal Factors Governng PEFC Performance Actvaton Losses Platnum Agglomeraton In order to maxmse the electrochemcally actve surface area (EASA) n the anodc and cathodc catalyst layers, the catalyst s appled as fne and wdely dspersed nanopartcles on the surface of a supportng partcle [5]. Typcally, the catalyst s platnum or platnum alloyed wth ruthenum or chromum for example, and the larger supportng partcle s carbon-based. Recent studes have shown that wthn 2000 hrs of operaton, t s possble for the metal catalyst to undergo morphologcal change n the form of catalytc agglomeraton and/or rpenng [6]. Ths leads on to a gradual decrease n the EASA. Whle ths phenomenon s observed for both anode and cathode catalyst layers, t s usually the cathodc partcles that undergo more extensve agglomeraton. Ths s because the cathode can contan suffcent lqud water to facltate prmary corroson [7]. Repettve on/off load cycles for PEFCs can also cause platnum snterng; resdual hydrogen can nduce a hgh voltage equvalent to open-crcut voltage to the cathode, causng the snterng to occur [8]. Ths can be mtgated by purgng the anode channel wth ar. Loss of EASA due to agglomeraton has also been observed for un-humdfed PEFCs operatng at a hgher temperature of 150 C n polybenzmdazole (PBI) membranes [9] Platnum Mgraton Another mechansm for the loss of EASA could be attrbuted to the movement of platnum. When the PEFC s operated through hydrogen-ar open crcut to ar-ar open crcut, platnum can become soluble and could therefore nfltrate adjacent layers [10]. The correspondng loss of platnum can also compromse the EASA. Such phenomenon can also be accompaned by an apparent mgraton of platnum. Mgraton of metal catalyst partcles n both the anode and cathode catalyst layers n PEFCs has been observed, movng towards the nterface between the catalyst layer and the membrane [7]. Platnum mgraton from the cathode catalyst layer to the anode has also been observed n phosphorc acd fuel cells (PAFC) [11].

43 3 Revew of Practcal Factors Governng PEFC Performance Exposure to Sub-Zero Operatng Condtons Exposure to sub-zero operatng envronments are also known to compromse the EASA. The repettve freezng and meltng of water n the catalyst layer s lkely to deform the structure of the catalyst layers by ncreasng the pore sze and reducng the EASA [12] Atmospherc Contamnants The effects of reactant contamnaton and the leachng of contamnants can also sgnfcantly contrbute towards ncreases n actvaton losses at the anode and the cathode; catalytc contamnaton can occur due to both ar pollutants and fuel mpurtes. The presence of excess lqud water exacerbates the effects of contamnaton, whch can act to transport leached mpurtes wthn the cell [13]. Impurtes are thereby deposted on the catalyst stes, compromsng the EASA on ether electrode. Ar mpurtes such as ntrogen doxde (NO 2 ), sulphur doxde (SO 2 ) and hydrogen sulfne (H 2 S) have been found to have a negatve mpact on cell performance due to ther adsorpton on platnum catalyst stes [14]. It has been reported that wth low concentratons of NO 2 and SO 2,.e., 0.4 and 0.5 ppm respectvely, the effects of contamnaton on cell performance can be reversed f the cathode s subsequently fed wth neat ar [15]. For hgher concentratons,.e., 1-5ppm of ether NO 2 or SO 2, cyclc voltammetry s requred to fully recover the cathode [14,16]. Exposure to SO 2 and H 2 S appear to lead on to the formaton of two sulphur speces, one of whch adsorbs strongly on the platnum stes. In ether case, cyclc voltammetry s requred to oxdse the sulphur adsorbed [14] Fuel Contamnants Operatng PEFCs on a hydrocarbon reformate could expose the anode catalyst layer to CO n the concentraton range of ppm [17]. Reformaton of methane (CH 4 ) for example, can yeld a hydrogen-rch fuel feed wth 80% H 2 and 20% carbon doxde and carbon monoxde n the mentoned concentratons [18]. The carbon doxde can lead on to the formaton of addtonal carbn monoxde n the anode catalyst layer ether through a

44 3 Revew of Practcal Factors Governng PEFC Performance 24 reverse water-gas shft reacton or through the electro-reducton of carbon doxde [18]. Carbon monoxde s problematc because t can adsorb onto platnum more strongly than hydrogen, whch thereby compromses the EASA for hydrogen oxdaton. The carbon monoxde n the fuel feed can also cross-over through the membrane to the cathode catalyst layer [19] and can also be present n ar. Carbon monoxde contamnaton can therefore also compromse the EASA for oxygen reducton n the cathode catalyst layer, reducng cathode performance. Carbon monoxde coverage can be reduced f the platnum catalyst s alloyed wth ruthenum (Ru) and tn (Sn) to gve PtRu and Pt 3 Sn [20]. Other methods nclude ensurng that the saturated vapour pressure of the fuel feed s mantaned durng operaton, by reducng the thckness of the catalyst layer [21], and by elevatng the cell temperature from 80 C to around 120 C, whch mproves the actvty of the catalyst layer for hydrogen oxdaton [22]. Accordng to another method, oxygen could be bled nto the hydrogen feed n order to oxdse carbon monoxde to carbon doxde before t reaches the anode catalyst layer [23]. A more recent method ncludes the use of a reconfguraton anode, where a catalytc materal whch uses cobalt, ron and copper s appled to the gas-facng sde of the anode gas dffuson layer to oxdse the carbon monoxde n the fuel feed before t permeates nto the anode catalyst layer [24]. A comprehensve revew of artcles dscussng PEFC contamnaton has been carred out by Cheng et al. [25] Carbon Corroson Alterng the structural composton and materal use can mprove the performance and stablty of the catalyst layers. Nafon and catalyst dstrbutons can be appled nonunformly to favourably maxmse the proton transport and porosty n the opposng regons of greatest on flux and gaseous flux respectvely [26,27,28,29]. Catalytc supports can be favourably chosen for mnmsed oxdaton rates. Carbon corroson s a sgnfcant ssue for fuel cells and can occur durng fuel starvaton, when there s only partal coverage of hydrogen on the catalyst stes and durng localsed floodng [30,31]. Such condtons can be nduced or exacerbated durng cyclc operaton. If a sngle cell has nsuffcent fuel to support the current drawn, carbon can corrode to support the current above that provded by the fuel [30]. The standard potental for the corroson of carbon s 0.207V. When the anode potental s below 0.207V, fuel s consumed to drve the current. When the anode potental rses above 0.207V, carbon corroson n the anode catalyst layer occurs to supply protons to support the

45 3 Revew of Practcal Factors Governng PEFC Performance 25 current [30]. Platnum agglomeraton can also be nstgated as a consequence of a loss of catalytc support durng carbon corroson [32]. The chemcal equaton for carbon corroson s as follows [30]; C + 4e + 2H 2 O = CO2 + 4H + (3-1) It has been shown, for example, that whle XC72 carbon black reacts more slowly than Black Pearls (BP) 2000, they both become less stable supports under humdfed fuel cell operatng condtons n comparson to dry condtons [33]. Whlst humdfcaton s necessary for most PEFC desgns to reduce the resstance to proton transfer n the polymer membrane, humdfyng the cathodc reactant supply up to 60% wll also mprove catalytc actvty due to ts mpact on the rate-determnng step of the oxygen reducton reacton [34]. For low-temperature automotve PEFC stacks, for example, some level of humdfcaton can be unavodable. Graphtzaton of carbon supports s suggested as one method to mprove thermal stablty under such condtons f a hgh surface area for the supports can be mantaned [33]. Operatng under fxed current denstes and flow rates can also avod carbon corroson [31]. One alternatve to carbon-black supported platnum catalysts are mult-walled carbon nanotube supported platnum (Pt/CNT) catalysts, whch through accelerated durablty tests have shown that they are more resstant to platnum snterng. Ths s due to the stablty of CNTs, whch possess a hgher resstance to electrochemcal oxdaton than carbon black [35] Chemcal Degradaton of Slcone Seals Another reported form of catalytc contamnaton can be caused by the chemcal degradaton of sealng materal used n the fuel cell stack. Typcally, seals n fuel cell stacks are made of slcone and serve to avod mxng of hydrogen and oxygen. The acdc character of the polymer electrolyte membrane along wth the thermal stressng of the slcone seal can cause t to degrade chemcally but wthout compromsng ts mechancal functonalty [36]. The process s marked by yellow colouraton. The products of the slcone reacton occur at both the anode and cathode sde, but mgrate towards the cathode due to the electrc feld. PFSA membranes have been found to be mpermeable to the products, and so cause the products to accumulate n the catalyst layers. Schulze et al. reported that n the cathode

46 3 Revew of Practcal Factors Governng PEFC Performance 26 catalyst layer the decomposton products react wth catalyst to form partcles contanng slcone, oxygen and platnum [36]. 3.3 Mass Transportaton Losses Cell Floodng Impedance to the transport of reactants to the catalyst stes results n an ncrease of mass transportaton losses. Impedance to reactant transport can manfest tself n several dfferent ways, but compromse the porous network for gas permeaton through the porous layers of the cell. The foremost contrbutor to the mpedance to reactant transport occurs n the cathode sde of the cell, due to the formaton of lqud water whch restrcts the transport of oxygen. Ths compromses the partal pressure hence the local oxygen concentraton on the cathode catalyst stes. It propagates from the cathode catalyst layer and can lead to floodng n the GDL and parts of the cathode reactant supply channel. Water management has therefore been the focus of a sgnfcant number of research groups and has resulted n a multtude of desgns and operatng strateges amed at mtgatng mass transportaton losses. Lqud water n the flow felds can be carred away f the channel flow rates are suffcently hgh. Pressure drops along straght sectons and partcularly around flow feld bends however can lead to water accumulaton, subsequently leadng to the cloggng-up of channels and therefore potentally cell shut-down [37]. Pressure drops along a sngle channel are governed by the physcal characterstcs of the channel and the physcal characterstcs of the flud. The most relevant physcal characterstcs of the channel nclude the length and cross-sectonal geometry of the channel, the number, closeness, abruptness and geometry of channel bends and the hydrophobcty of the BPP surface. The characterstcs of the flud are reflected by the Reynolds number (Re) [38,39]. Flows that have low Reynolds numbers (Re < 50) are manly domnated by vscous forces and thereby susceptble to pressure losses nduced by skn frcton. Flows wth hgher Reynolds numbers,.e., Re > 200, are susceptble to flow separaton partcularly when ts drecton s abruptly changed. Flow separaton n the vcnty of sharp corners of flow feld bends leads on to the formaton of vortces, whch also results n pressure losses. Vortces

47 3 Revew of Practcal Factors Governng PEFC Performance 27 can also form n the same manner n the vcnty of nlet manfolds [40]. The ntroducton of fnte curvature ratos for 90 bends can assst n mantanng lamnar flow [39]. In addton, n order to allow separatng flows to become lamnar agan, t s necessary to optmse the length of the straght secton mmedately downstream of the bend. In the general case, pressure losses along sngle channels can be mnmsed f the overall flow feld path length s kept short and f the number and abruptness of bends are mnmsed. Recent studes have hghlghted that unform flows wth typcally small pressure drops can be establshed partcularly for flow felds wth straght, parallel channels [41] and for serpentne channels that have shorter path lengths and larger numbers of multple channels rather than longer path lengths and fewer channels wthn the same cell area [42]. Such measures can ensure that the channels reman pressursed along ther entre lengths and reduce the chance of floodng whereby hgh upstream pressures and low downstream pressures are establshed causng lqud water to be pushed down and accumulate n downstream regons of the flow felds [43]. In general, lqud water has a tendency to accumulate n regons where the gas-phase flow becomes stagnant, partcularly n abrupt 180 bends often seen n serpentne flow felds [44,45,46]. Interdgtated flow felds could be used over conventonal gas dstrbutors to mprove oxygen dstrbuton to the cathode catalyst layer and water removal by addng forced convecton to gas dffuson to drve transport n the porous layers [47]. Forced convecton s nduced by decouplng the drect path between nlet and ext flow felds on one or both sdes of the b-polar plate desgn. Under certan condtons, nterdgtated flow felds can also yeld reductons n fuel consumpton rates wthout loss n performance compared to conventonal flow feld desgns [48]. In the context of PEFC stacks, nterdgtated flow felds can also nduce unbalanced pressure drops between cells. The concept s stll undergong development [49,50,51,52,53,54,55, 56,57,58,59, 60,61]. Counterflow confguratons have shown that orentng the reactant flows to pass through opposte-sded nlets can allow for better nternal humdfcaton of the cell [62,63]. The hgh water content n the anode nlet feed can be used to humdfy the membrane when water molecules are electro-osmotcally dragged from the anode to the dry cathode by mgratng protons, whereas the cathode nlet s adjacent to the drer anode ext feed whch allows for membrane hydraton through dffuson and convecton, drven from the cathode

48 3 Revew of Practcal Factors Governng PEFC Performance 28 sde. Counterflow confguratons appear n automotve fuel cell stacks [64] and dependng upon the operatng strategy t can be possble to delay the onset of floodng. If water can be generated wthn the membrane for humdfcaton, t could be possble to reduce the extent to whch the nlet reactant gases need to be humdfed. Ths could naturally suppress the onset of two-phase flow and cell floodng, and could assst n smplfyng the system desgn. As such, the dsperson of platnum partcles wthn the membrane has been explored [65,66]. Here, water would be generated wthn the membrane by vrtue of the recombnaton of hydrogen and oxygen on catalyst stes. The concept therefore reles upon the permeaton of hydrogen and oxygen through the membrane regon. The lmtaton of ths method s that the platnum dspersons are susceptble to formng electron-conductng networks that could cause short crcuts [67]. Recent re-developments have focused on membranes consstng of one mddle layer of Nafon contanng dspersons of Pt/CNT wth two outer layers of Nafon [67]. The entre membrane assembly can be as thn as 25 mcrons. Reported results show that up to 90% of the performance obtaned wth humdfed reactants can be obtaned by such self-humdfyng membranes wth dry reactants [67]. Another example s of slcone oxde-supported platnum catalyst dspersed wthn protected three-layer sulfonated poly(ether ether ketone) (SPEEK)/PTFE/Nafon matrx membranes [68]. At present, though, self-humdfcaton s not a standard concept. Along wth the lterature reported above on the varous means of mtgatng mass transportaton losses, numerous patents have been fled related to mproved water management schemes [69,70,71,72,73,74] Hydrophobcty of Porous Layers Lqud water transportaton and removal can be facltated by treatng porous layers wth hydrophobc materal, commonly polytetrafluoroethylene (PTFE) or fluornated ethylene propylene (FEP). The hydrophobcty of a surface s reflected through the contact angle that a water droplet makes on the surface of the materal; a contact angle less than 90 reflects a hydrophlc surface, whle that greater than 90 reflects a hydrophobc surface.

49 3 Revew of Practcal Factors Governng PEFC Performance 29 Water transport can be managed through the use of the MPL. Because t s hghly hydrophobc, t can act to transport lqud water away from the cathode GDL n the drecton of the anode va the membrane, thereby delayng floodng effects n the cathode and smultaneously hydratng the membrane layer [75,76,77,78,79]. The use of an MPL also lessens the senstvty of the catalyst layer to floodng, allowng thnner catalyst layers to be used [80]. A b-functonal hydrophobc and hydrophlc porous structure can smultaneously facltate both gas-phase and lqud-phase transport respectvely. Such pore structures can be acheved wth composte carbon black loaded to around 0.5mg/cm 2 wth a PTFE content of 30 wt.% [81]. The GDL s also usually treated wth PTFE. A hgher PTFE content can also help to preserve the porous structure of the GDL by ncreasng the materal rgdty [82], however t can also compromse the electrcal conductvty of the GDL [83] and excessve coatng can lead to hgh levels of floodng [80]. Also, t has been shown that for GDLs that are made up of graphte fbres, the hydrophobc polymer tends to localse on the surface regons on treatment; large numbers of surface pores made by ntersectng fbres wll be blocked by thn polymer flms, renderng the bulk of the nteror less hydrophobc [84]. It has also been shown that the contact angle of treated GDLs can reduce wth temperature [84]. Mechancal and electrochemcal degradaton of PTFE n GDLs has also been reported [84,85]. Operatng condtons that nduce thermal cycles n the fuel cell stack whch result n a loss of hydrophobcty can therefore make water removal more dffcult. It can also cause the polymer to delamnate, thereby deteroratng the hydrophobc property of the GDL and compromsng the ablty to remove water wth respect to operatonal lfe. It s arguable that the MPL, whch has a comparable materal composton to the GDL and s also porous n nature, s susceptble to the same degradaton mechansms. Damage to PTFE coatngs can also be nduced when GDLs are exposed to sub-zero operatng condtons [86] Ionomer Loadng n Catalyst Layer The PFSA onomer loadng n the catalyst layer can also have an effect on the transport of reactants to actve stes n the catalyst layer. The materal s placed n the anode and cathode catalyst layers n order to provde pathways for proton transport [87,88]. Water

50 3 Revew of Practcal Factors Governng PEFC Performance 30 uptake n the polymer electrolyte materal could cause t to correspondngly expand, thereby reducng the pore szes n the catalyst layer [89] whch mpedes reactant supply. The effect s usually reversble snce the polymer electrolyte materal wll also contract when the cell s not n operaton, or when lqud water producton reduces at lower operatng cell current denstes for example. Excessve onomer loadng for a gven platnum loadng wll also nherently mpede reactant supply; hgher mass transportaton losses have been reported due to the mpedance to oxygen transportaton n the catalyst layer [90]. Ionomer skns can also form on the outer surface of the catalyst layer of the completed MEA, however ths can be lmted to certan fabrcaton technques [91]. In general, the fabrcaton processes for the catalyst layer such as sprayng, pantng rollng and screen prntng all possess a lmted degree of precson and ultmately therefore the degree of control over the composte structure of the fabrcated MEA [92]. Navessn et al. reported that decreasng the on exchange capacty (IEC) of the onomer, whch s the equvalent to ncreasng the equvalent weght (EW), results n an ncrease n hydropobcty, decrease n water content, ncrease n oxygen solublty and an ncrease n the ORR current. The EW reflects the rato of the atomc weght of an element to the valence t assumes n a chemcal compound. A low IEC (or hgh EW) could mprove the cell performance by facltatng water management Impedance to Transportaton due to Ice Formaton The effects of sub-zero operatng condtons sgnfcantly nfluence mass transportaton losses. The operatng temperature of the cell has to be brought up to above freezng before ce formaton completely flls the pores of the cathode catalyst layer [93]. The nstantaneous effect of ce formaton s to mpede oxygen transport to the catalyst stes and can render entre cells nactve. Freezng condtons are known to weaken the MPL structurally to an extent that renders t prone to materal loss from ar flow through the GDL [94]. In practce, ce formaton can occur n any regon of the fuel cell where water resdes and so t s mportant to remove excess water from the cell pror to start-up, and to operate the cell on start-up such that water generated n the cathode catalyst layer s not allowed to freeze. Gas-purgng has been dentfed as a mechansm by whch excess water can be removed [95]. In one reported method, gas-purgng s done before the cell temperature falls below 0 C usng dry gases such as ntrogen and oxygen for the anode and cathode respectvely, optonally usng 30% methanol or 35% ethylene glycol as antfreeze addtves

51 3 Revew of Practcal Factors Governng PEFC Performance 31 [96]. Another reported method nvolves purgng usng gases wth a lmted degree of relatve humdty to ensure that the provson of adequate water content n the proton conductng membrane s not completely compromsed [97] Effects of Compacton on the GDL The porous structure and thckness of the GDL also nfluences two-phase water and reactant transport [98]. Reactant transport can be enhanced when the GDL porosty s n the regon of around [99,100] and lqud water removal to the gas channel can be enhanced wth a lnearly-graded porosty [99]. The use of thnner GDLs can also mprove performance by allowng for greater lqud water mass transfer under steady-state condtons [99,101] and greater reactant mass transfer towards the catalyst layer [100]. The permeablty of a GDL s another relevant parameter, whch vares accordng to the carbon type [82]; woven and non-woven GDLs have exhbted slghtly hgher permeablty than carbon fbre paper GDLs wth smlar sold volume fractons [102]. A fuel cell stack s held together by compactng together sngle cells. The correspondng compresson can result a non-unform pressure dstrbuton across the actve area of the cell, whch can affect the structural propertes of the GDL. Over-compresson s argued to be a common occurrence n most fuel cells [103] whch causes pores n the GDL to collapse, thereby reducng the porosty, ncreasng floodng [104] and reducng gas permeablty [105]. The deformng over-compresson can be less sgnfcant under channel regons and occurs manly between matng surfaces that transmt compacton forces, for example land areas n the b-polar plates and under rb areas where the cell s sealed wth gasket materal [105,106,107]. It has been observed that ncreased compresson ntally mproves the performance of the cell by reducng the nterfacal resstance between the bpolar plate and the GDL up to an optmal threshold, whereas further compresson thereafter narrows the dffuson path for mass transfer from the gas channels to the catalyst layers [108,109]. The effects of stress due to over-compresson are more pronounced at hgh current and low pressure [110]. Chang et al. [109] dentfed the threshold clampng pressure to be n the regon of 0.5MPa. The damage to GDLs s manfested through a break-up of fbres and a deteroraton of hydrophbc coatng, thereby compromsng the ablty to remove water from the cell [111].

52 3 Revew of Practcal Factors Governng PEFC Performance Ohmc Losses Resstance to Electron Transfer n the B-Polar Plate Both resstance to electron transfer and proton transfer contrbute towards the overall Ohmc losses ncurred n PEFCs. Elements of the cell where electron transfer occurs ncludes the carbon support n the catalyst layers, the GDL and the BPP. Proton transfer occurs n the polymer electrolyte matrx dspersed n the catalyst layers and the PEM. Whle the bpolar plate provdes the bulk of the mechancal strength of the stack, t also serves as a current collector, as a thermally conductve medum to remove excess heat energy from sngle cells, and as a devce to supply reactants and to remove water va flow felds on both faces of the plate. However, they must wthstand the acdc and humd condtons wthn the stack. Corroson s a sgnfcant ssue for BPPs, whch leads on to the loss of electrcal conductvty. Whle the BPP must have hgh mechancal strength, low susceptblty to materal dssoluton, low susceptblty to the release of metal ons and hgh corroson resstance, the bulk electrcal conductvty must be hgh and the nterfacal contact resstance (ICR) must be kept low [112]. As an ndcaton, targets set for mechancal strength and electrcal conductvty are MPa and 100 S/cm respectvely [113]. These attrbutes have to be acheved wth materals and processes that are compatble wth the concept of low cost and hgh volume manufacturablty. As such, an array of dfferent chemcal compostons and synthessng processes have been nvestgated to dentfy how these requrements can be smultaneously met. Graphtc B-Polar Plates Graphte s conventonally regarded as the standard materal for BPPs because of ts hgh conductvty (300 S/cm) [113] and hgh corroson resstance [114]. However, graphte BPPs are susceptble to fracturng due to shock and mechancal vbraton, are permeable to gases and can be costly to machne n hgh volumes [112].

53 3 Revew of Practcal Factors Governng PEFC Performance 33 Stanless-Steel B-Polar Plates Whle corroson-resstant metals have better mechancal propertes and are cheaper to machne n hgh volumes than graphte plates, the chemcal process that provdes corroson resstance can also compromse ts electrcal conductvty. Stanless steel (SS), for example, develops a chromum (III) oxde (Cr 2 O 3 ) passvatng layer on the surface whch prevents the bulk metal from corroson. Ths thn flm however mpedes electron transfer and therefore rases the ICR. The consequent Ohmc heatng thereby compromses the electrcal energy that can be harnessed from sngle cells. The bulk resstvty s however nsgnfcant n relaton to the surface resstance due to ths flm [115]. Stanless steel s the standard alloy for metallc BPPs, and has the major consttuents of ron (Fe), chromum (Cr) and nckel (N). There are manly sx relevant grades of SS for BPPs, dstngushable by ther chemcal compostons. These are provded n table 3-1. Chromum (Cr) Nckel (N) SS316L SS317L SS904L SS349 TM SS AISI Table 3-1 Grades of stanless steel accordng to composton by weght percentage [115] [116] [117] The conductvty of SS316 s, for example, around 51 S/cm [113]. It has been shown that those grades of SS wth a hgher content of chromum and nckel, SS904L for example, result n the formaton of thnner passve oxde flms wth low ICR. Rasng chromum content alone, however, can mprove corroson resstance and t s possble to attan a low ICR f a clean, stable and ntegral surface s developed [115,116,117,118,119]. The effect of chromum content on corroson resstance s also evdent n amorphous ron-based alloys such as Fe 50 Cr 18 Mo 8 Al 2 Y 2 C 14 B 6 [120]. Amorphous alloys ntrnscally possess hgh corroson resstance and hgh strength (around 2GPa) due to the absence of defects such as gran boundares and dslocatons [120]. In addton, surface treatment of SS n the form of a selectve dssoluton processes can mprove the metallurgcal surface structure, ensurng that

54 3 Revew of Practcal Factors Governng PEFC Performance 34 t s defect-free, sold and ntegral [118]. Smoother surfaces can also result n reduced nterfacal contact resstances. Coatng of Stanless-Steel Substrate Corroson resstance can be mproved f stanless steel s coated as a substrate. When coated wth ttanum ntrde (TN), f coatng defects such as mcro-cracks and pnholes can be mnmsed, a hgher corroson resstance and electrcal conductvty for SS316 can be acheved [121]. Stanless steel can also be coated wth conductng polymers such as polypyrrole (PPY) and polyanlne (PANI) [122,123,124]. The nterfacal contact resstance however s fve tmes that of graphte at a compacton force of 200N/cm 2, and reduced to one-two tmes that of graphte at 400N/cm 2 [122]. The number of deposton cycles that the substrate s subjected to durng the electro-polymersaton process dctates the thckness of the polymer flm; the coatng s known to degenerate wth tme, and coatng compostons need to be modfed n order to mantan the protectve propertes of the polymer surface [124]. SS304 coated wth ntrde layers usng the physcal vapour deposton (PVD) method has also been reported, whch results n nterfacal contact resstances less than that of uncoated SS904L [125]. Coatng does generally however add to the cost of the fnal product [113]. Other forms of metallc bpolar plates nclude copper alloys such as C copperberyllum, whch form electrcally conductve oxdes [126] and nckel-based alloys wth lower amounts of [Fe + Cr], resultng n oxdes wth reduced ICR [125]. Moulded B-Polar Plates Injecton and compresson mouldng as low-cost, hgh-volume manufacturng processes could arguably mtgate the hgh producton costs assocated wth machned graphte and stanless steel bpolar plates. The process requres the synthess of a mouldable compound. In general, polymer-based compounds can be susceptble to shrnkage after the mouldng process and could warp wth tme. Also, nhomogeneous pre-mxng of the carbonpolymer compound can gve rse to the formaton of polymer-rch boundares n the mould,

55 3 Revew of Practcal Factors Governng PEFC Performance 35 compromsng the electrcal conductvty closer to the surface. Two reported compounds nclude carbon polymer [127], for example graphte powder (80-60 wt.%) wth vnyl ester (20-40 wt.%) [128], and Nylon-6 wth SS316L alloy fbres [129]. The bulk conductvtes of the resultng materals are S/cm and 60 S/cm for the carbon-polymer [127] and Nylon- 6 SS316L compounds respectvely. Commercally avalable carbon-based b-polar plates and b-polar plate materals nclude those based on phenolc resn and other polymers such as polyvnyldene dfluorde (PVDF) and polypropylene (PP) [130,131,132,133]. The conductvty of these materals range from around 30 S/cm to 200 S/cm wth flexural strength n the regon of MPa. Other compounds consttutng of vnyl ester resn, graphte powder wth organoclay have been reported wth bulk conductvtes n the regon of S/cm [134]. The organoclay s prepared by onc exchange of montmorllonte (MMT) wth poly(oxypropylene)-backboned damne ntercalatng agents. Hgher MMT content mproves flexural strength, mpact strength and antcorrosve protecton, but slghtly reduces the electrcal conductvty Resstance to proton transfer n the Polymer Electrolyte Membrane Impurty Ions Resstance to proton transfer n the polymer electrolyte materal s charactersed by the nterplay between absorbed water, catons and fxed charge onc clusters of the membrane electrolyte. Catons n the form of foregn mpurty ons can dsplace protons and enter the electrolyte membrane, decreasng the proton conductvty n proporton to the onc charge of the caton [13]. Foregn ons reported n lterature nclude the alkal metals L +, Na +, K +, Rb + and Cs + [135,136,137,138,139,140,141], the alkalne earths Mg 2+, Ca 2+, Sr 2+ and Ba 2+ [142,143,145], the transton elements Ag +, N 2+, Mn 2+, Cu 2+, Zn 2+, Cr 3+, Fe 3+ [144,145,146,147], rare earths La 3+ [145] and Al 3+ [147], and ammonum dervatves R n NH 4 n + (where R = H, CH 3, C 2 H 5, C 3 H 7, C 4 H 9 and n = 1 to 4) [148,149]. Sources of mpurty ons nclude mpure gas feeds, corroded materals n the fuel cell stack or reactant supply system,.e., transton metal on contamnants such as Cu 2+, N 2+ and Fe 3+ [144], fttngs, tubng or ndeed ons n the water or coolant supply [141].

56 3 Revew of Practcal Factors Governng PEFC Performance 36 As dscussed, compromsng the hydrated state of the membrane results n the loss of proton conductvty. Water transport through the cell governs how well the membrane s hydrated, and water transport tself s charactersed by ts dffusvty and ts transfer coeffcent n the dfferent regons of the cell. For the general case of operaton under uncontamnated condtons, the water content of the membrane decreases non-lnearly through the membrane thckness towards the anode wth ncreasng current densty, thereby resultng n an decrease n proton conductvty. Ths reflects the rse n electro-osmotc drag wth ncreasng current densty, resultng n a comparably large amount of water movng away from the anode to the cathode n relaton to that dffusng through the PFSA-based membrane from the cathode to the anode [17]. Membrane contamnaton can ncrease the non-unformty n water content and decrease the overall water content profle. The lterature reports that the penetraton of mpurty ons nto the membrane nduces; (1) a decrease n the dffuson coeffcent of water, and; (2) an ncrease n the water-transfer coeffcent [13]. The lterature suggests that water can resde n the membrane n the form of one of three possble populaton groups [137]; (1) Henry or Flory-Huggns type populatons where water molecules are sorbed by an ordnary dssoluton mechansm; (2) Langmur type populatons where water molecules resde n a hydraton layer around catons and sulfonc charge groups due to the strong nteractons caused by hydrogen bonds, and; (3) water cluster populatons. Water clusters can be dstngushed from Langmur-type populatons and are known to become domnant populatons when the water actvty n the membrane s greater than around 0.6. Clusterng can change dependng upon the type of caton penetratng the membrane; t s known to ncrease n the order of Cs + > L + > H +. Legras et al. reported that the water clusters compromse the moblty of water overall whch correspondngly results n a decrease n water dffusvty [137]. Sh et al. reported that the replacement of protons by mpurty ons can nduce electro-statc cross-lnkng of onc domans or the formaton of sulfonate salts, causng the membrane to contract and expel water [145]. Ths can also result n the loss of water dffusvty [13]. Kundu et al. reported that physcal cross-lnkng of onc domans alters the mechancal propertes of the membrane, causng an ncrease n membrane stffness [141]. Young s Modulus s shown to ncrease by one order of magntude wth ncreasng onc radus, n the order N 2+ > Cu 2+ > Na + > K +. The transport of protons through the polymer electrolyte from the anode to the cathode s known to nduce the aforementoned electro-osmotc drag flux [150]. For other

57 3 Revew of Practcal Factors Governng PEFC Performance 37 ons, the magntude of each contrbutory transport mode depends upon the exstence of hydrophlc and hydrophobc parts of the on. Through the nvestgaton of ammonum dervatves, Xe et al. reported that such ons wth hydrophobc skeletons tended not to have perpherally bound water molecules and nstead cause hydrodynamc pumpng [149]. Other catons, ncludng fully hydrophlc catons, wth a hgh charge densty and a hgh enthalpy of hydraton tend to carry more water molecules durng transport by the electro-osmotc drag, whch ncreases wth water content [142,149,151]. Overall ths llustrates that whle the transfer of protons across the polymer electrolyte materal nduces an electro-osmotc drag, overall water transfer can ndeed be unfavourably magnfed as water nteracts wth mpurty ons. The duraton over whch the degradaton s prolonged depends upon the concentraton of the mpurty ons [138] and the length of tme that the mpurty ons resde wthn the polymer electrolyte membrane. Impurtes wth large dameters can penetrate the membrane and nduce a pluggng effect, compromsng hydraton and thus proton conductvty [149]. Therefore n general, water transport due to the presence of mpurty ons can ndeed hasten membrane dehydraton, and the adverse effect on membrane performance s exacerbated when the mpurty ons are concentrated closer to the anode and cathode catalyst layers [152,153]. Ansotropc Expanson The swellng phenomenon experenced n fuel cells that use PFSA-based materals due to the uptake of water can lead on to ansotropc expanson. Cascola et al. reported that through-plane conductvty could decay when such swellng occurs, precptated by hgh operatng temperatures (120 C) and hgh relatve humdty (>90%) [154]. Membrane expanson could be restraned by the compacton of the cell. However, t has already been argued that the stresses actually experenced n operatng fuel cells are lkely to be less than those requred to suffcently constran the membrane [155]. Renforcng the membrane structurally however provdes a more robust method. Methods nclude dspersng PTFE fbrls wthn membranes (fbrl content of 2.7 wt.%) [156], dspersng carbon nanotubes wthn Nafon membranes (CNT content of 1 wt.%) [157] and the use of porous, expanded PTFE sheets that are bonded wth membrane resns on both sdes [158,159,160]. A 50 mcron thck membrane made of recast Nafon has a tensle strength of

58 3 Revew of Practcal Factors Governng PEFC Performance MPa. Dspersng 1 wt.% CNT wthn the membrane can ncrease ths by 68.8% [157]. The use of a PTFE porous sheet for renforcement can ncrease the tensle strength by 87.5% [157]. The dmensonal change for recast Nafon n water at 80 C s 25% [159]. For Nafon renforced wth dspersed CNT, the dmensonal change s decreased to 12.4% [157] and for PTFE renforced Nafon ths s decreased to 10% [159]. At 90% RH, expanded PTFE renforcement can suppress n-plane dmensonal change from 12% down to 2.5% [161]. 3.5 Effcency Losses and Catastrophc Cell Falure Loss of effcency and catastrophc cell falure can be nduced when the strength and stablty of the fuel cell materals are degraded rreversbly by mechancal or chemcal attack. Rgd elements such as the bpolar plate are susceptble to crackng under mechancal stress and vbraton. Seals are susceptble to oxdaton [162], whch compromses ts functonalty and can therefore rupture. The electrolyte materal has to survve under varous cyclc loads and through chemcally-nduced structural degradaton whlst servng ts prmary role as a proton conductor. Effcency losses n the electrolyte membrane can result as an nherent consequence of employng thn membranes [163] or by n-stu membrane thnnng, allowng hydrogen to dffuse through the electrolyte from anode to cathode. Membrane thnnng largely reflects a loss of chemcal structure, prmarly nduced by peroxde radcal attack. Pnhole formaton s a precursor to catastrophc cell falure, propagatng from localsed regons where temperature extremes exst whch mechancally degrade the fuel cell materals. Ths ncludes regons exposed to thermal hot-spots or ce formaton. The purpose of ths secton s to dscuss the rreversble degradaton mechansms caused by mechancal and chemcal attack Mechancal attack The mpedance to transport n the porous layers of the cell due to ce formaton was dscussed prevously. It has also been reported that ce formaton caused as a consequence of operaton at sub-zero condtons down to -20 C can cause the catalyst layer to delamnate

59 3 Revew of Practcal Factors Governng PEFC Performance 39 from both the membrane and the gas dffuson layer [86]. The surface of the electrolyte membrane has also been observed to become rough at sub-zero condtons, leadng to the formaton of cracks and eventual pnholes [86]. The formaton of thermal hot-spots has also been reported n the lterature, as nstgated through dfferent mechansms [164,165]. Hottnen et al. reported that a sgnfcant porton of the heat generated under the channel sectons of the bpolar plate has to flow n the n-plane drecton [165]. Ths could result n the formaton of hot-spots below the channel. The begnnng of rb areas where current enters the GDL from the bpolar plate could also be regons of hgh Ohmc heatng, gvng rse to other hot-spots, and the effect of heat transfer can be magnfed when supermposed wth nhomogeneous compresson. Stanc et al. [164] reported evdence of the formaton of pnholes n regons where carbon fbres at the MEA- GDL nterface created spots of hgh compresson, acceleratng membrane creep. Hgh reacton rates n the vcnty of hghly compressed membrane regons can rase the amount of heat energy generated, and therefore the local temperature. Overall, the local strength of the membrane at these hgher-temperature, hgh-compresson hot-spots can reduce and so can cause the electrolyte membrane to collapse. Membrane durablty s also affected by repeated swellng and contracton nduced by varatons n relatve humdty (RH) [166]. Kusolgu et al. [167] nvestgated n-plane stresses caused by n-plane membrane swellng and found that swellng as a phenomenon can have a more domnant mpact on fatgue stresses than clampng condtons or the membrane thckness. Thermal hotspots can also develop n regons where hydrogen and oxygen combne exothermcally on platnum catalyst stes, causng a cycle of ncreasng crossover and contnual propagaton of pnholes [168]. In general, hygro-thermal stressng can sgnfcantly affect the durablty of PFSA-based membranes [161, 169, 170, 171]. However dmensonal change due to hygro-thermal stressng can be restraned by renforcng PFSA membranes wth expandable PTFE, as dscussed [161]. It s possble that rregulartes n the electrolyte membrane or MEA could be nduced durng manufacture. Ensurng the absence of contamnants and unformty n the thckness of membrane batches depends upon qualty control durng the manufacturng process. Curtn et al. reported DuPont s manufacturng technques for PFSA membranes, whch ncludes two nspecton ponts for membrane flm thckness and one nspecton pont for defects [172].

60 3 Revew of Practcal Factors Governng PEFC Performance 40 In general, greater control over manufacturng qualty could be granted by adoptng manufacturng processes and qualty control practces that have become hghly-developed n smlar ndustres. Relevant examples nclude the recodng meda, semconductor, battery and photovoltac ndustres [173] and well-establshed standards for manufacture and test [174,175,176] Chemcal Attack Chemcal attack n PFSA-based membrane can occur due to the presence of defects n the polymer group. The defects exst as groups n the polymer that can nteract wth actve radcals, resultng n the chemcal degeneraton of the PFSA-based materal. The PFSA polymer s synthessed from a copolymer of tetraflouroethylene (TFE) and perfluoro(4-methyl-3,6-doxa-7-octene-1-sulfonyl fluorde) by chemcally convertng the pendant SO 2 F sulfonyl fluorde groups to sulfonc acd SO 3 H [172,177]. The SO 3 H s oncally bonded such that the end of the sde chan contans an SO 3 and an H + on [5]. Formaton of Defectve End Groups End group defects can be generated durng polymer synthess as a consequence of chemcal or mechancal processes; ntators, transfer agents, solvents or contamnants could nduce defects durng chemcal processng, whle ageng, heatng or extruson could also nduce defects durng the handlng of the polymer [178]. Panca et al. [178] dentfed the followng end groups; carboxylc acd ( CF 2 COOH), amde ( CF 2 CONH 2 ), perfluorovnyl ( CF 2 CF=CF 2 ), acyl fluorde ( CF 2 COF), dfluoromethyl ( CF 2 CF 2 H) and ethyl ( CF 2 CH 2 CH 3 ). Alentev et al. [179] dentfed other end groups ncludng CF 2 CF=O and CF 2 CF=O and resdual C H bonds n the man chan such as R f CFH-R f. It s prmarly the H contanng end groups that are of partcular nterest for PFSA membranes n fuel cell envronments, whch can undergo aggressve chemcal attack n the presence of peroxde radcals at low relatve humdty condtons and temperatures n excess of 90 C [172].

61 3 Revew of Practcal Factors Governng PEFC Performance 41 Formaton of Hydrogen Peroxde Hydrogen peroxde can be formed through three reported processes. The frst occurs as a consequence of oxygen reducton at the cathode [180]; O H e H O 2 2 (3-2) The second occurs as a consequence of oxygen crossover from the cathode to the anode, or when ar s bleed to the anode sde [180,181,182]; Pt H2 PtH (3-3) * 2H + O2 H 2O2 (3-4) La Cont et al. dentfed the ntermedate formaton of hydroperoxy (HO 2 ) [183]; H 2H (on Pt or Pt - alloy catalyst) (3-5) 2 + O 2 HO2 H (3-6) HO H H 2O2 (3-7) The thrd occurs due to the crossover of hydrogen from the anode to the cathode, makng t possble for hydrogen peroxde to form n the cathode catalyst layer [184,185]. It has been reported that hydrogen peroxde formaton can be hastened by the presence of chlorde ons whch act as ste-blockng speces, reducng the number of actve stes for the ORR and reducng the number of pars of platnum stes requred to break the O-O bond [186]. Chlorde anons can orgnate from the fuel cell catalyst synthessng process and can be present as a water contamnant n the humdfed reactant supples. Formaton of Peroxde Radcals Hghly-oxdatve peroxde radcals can subsequently form from the decomposton of hydrogen peroxde and as actve speces can decompose PFSA-based membranes [177]. Transton metals such as Cu 2+ and Fe 2+ are known to be catalysts for the decomposton of

62 3 Revew of Practcal Factors Governng PEFC Performance 42 hydrogen peroxde [177] and can orgnatng from ppng tubes and tanks of fuel cell systems. The Haber-Wess mechansm detals the formaton of reactve oxygen hydroxyl (HO ) and hydroperoxyl radcals for Fe 2+ [177]; H 2O2 + Fe HO + OH + Fe (3-8) Fe + HO Fe + OH (3-9) H 2 O2 + HO HO2 + H 2O (3-10) HO2 Fe + HO2 Fe (3-11) Fe + HO2 Fe + H + O 2 (3-12) Steps (3-8) and (3-10) result n the formaton of hydroxyl and hydroperoxyl radcals, respectvely. For bvalent transton metals n general (M 2+ ), radcal formaton can be generalsed by the followng mechansm [183]; H (3-13) O2 + M HO + OH + M H 2 O2 + HO HO2 + H 2O (3-14) Mechansm of Peroxde Attack on Defectve End Groups Peroxde radcals n the presence of defectve polymer end groups proceed to decompose the polymer structure. Curtn et al. detal the followng three-step mechansm whereby hydroxyl radcals attack carboxylc acd end groups [172]; Step 1: Abstracton of hydrogen from an acd end group R CF COOH + HO R CF + CO H O (3-15) f 2 f Step 2: Reacton of perfluorocarbon radcal wth hydroxyl radcal R CF2 + HO Rf CF2OH R f COF HF (3-16) f +

63 3 Revew of Practcal Factors Governng PEFC Performance 43 Step 3: Hydrolyss of acd fluorde R COF + H 2 O R COOH HF (3-17) f f + The release of fluorde therefore reflects the decomposton of the PFSA membrane. Fluorde emsson rates (FER) can be determned by samplng the fluorde content of water n the anode and cathode exhaust [187]. Assumng a zero-order reacton for the producton of fluorde ons, t s possble to postulate the followng relatonshp to determne the rate at whch Nafon decomposed [188]; r d = M M F F Nafon t (3-18) where s the change n the amount of F released n µmol, M F Nafon s the total amount M F of F n the Nafon and t s the tmestep n hours. The lterature demonstrates that the FER technque s beng ncreasngly appled to determne onomer degradaton [181,187,188,189]. Effect of Membrane Degradaton due to Peroxde Attack The effect of peroxde attack s to alter the membrane structure and the chemcal propertes of the PFSA membrane. Loss of sulfonc end groups results n the loss of proton conductvty, thereby ncreasng the Ohmc resstance. Contnual membrane degradaton due to peroxde radcal attack and subsequent fluorde release results n membrane thnnng. Ths ncreases the dffuson of oxygen and hydrogen n opposng drectons from the cathode and anode respectvely. Prmarly, t s the crossover of hydrogen that ncreases because of the hgh effectve dffusvty of hydrogen molecules [6]. 3.6 Summary The performance degradaton, falure modes and the assocated causes dscussed n the above are summarsed n Tables 3-2 and 3-3. Faults are lsted accordng to the physcal component of the PEFC assembly where they orgnate or resde. The nformaton presented

64 3 Revew of Practcal Factors Governng PEFC Performance 44 n these tables have been used to construct a systematc set of fault trees for the PEFC, whch has been reported elsewhere [190]. 3.7 Conclusons The revew gven n ths chapter provdes a qualtatve account of performance degradaton and falure n hydrogen-fuelled PEFCs and dscusses some of the state-of-the-art concepts amed at overcomng these lmtatons. The purpose of the revew s to establsh a backbone understandng of the phenomenologcal processes that occur wthn the PEFC, how they are nfluenced through elements of desgn, manufacturng and operaton and ultmately how they can affect the performance of the PEFC. The conclusons from ths chapter are as follows; Performance degradaton or falure can occur as a consequence of gradual processes, where certan operatng condtons or operatng routnes cause a systematc degradaton of structural and electroknetc propertes of PEFC components. Latent flaws n component desgn and manufacture can also lead to performance degradaton or falure. The dentfed phenomenologcal processes that lead on to performance degradaton can be organsed n terms of potentally rreversble ncreases n actvaton losses, Ohmc losses, mass transportaton losses and effcency losses The performance degradaton and falure modes dentfed through the lterature pertan to the followng PEFC components: o PFSA-based membrane o Catalyst layer Carbon support PFSA-based onomer matrx Catalyst partcles Porous structure of the catalyst layer o Gas dffuson meda Hydrophobc treatment materal n the GDL Porous structure of the GDL o Bpolar Plate Stanless Steel BPPs

65 3 Revew of Practcal Factors Governng PEFC Performance 45 Polymer-based BPPs o Sealng materal Slcone-based seals In revewng the performance degradaton and falure modes, twenty-two common faults can be dentfed The twenty-two common faults are nduced by forty-eght general causes. As mentoned, the revew also dscusses newer aspects of fuel cell desgn, manufacture and operaton as remedal measures that lmt performance degradaton and falure. In terms of MEA development, there s emphass on attanng hgh mechancal strength, dmensonal stablty and an understandng of the mechansms that govern nternal transport and water management. For BPP and GDL development there s emphass on mprovng the homogenety of mult-phase flows through channels and porous meda and on establshng materals, materal preparaton, materal treatment and fabrcaton processes for hgh mechancal strength, hgh electrcal conductvty and low susceptblty to chemcal attack. Manufacturng and qualty control are also crtcal areas for PEFC development whch depend on the adopton of scalable manufacturng processes and practces from smlar establshed ndustres, establshng repeatable precson processes and by adoptng qualty control practces. The revew demonstrates that nternal electrochemcal transport and water management n partcular s a key phenomenologcal process that affects performance and longevty, and therefore cost. Understandng the mechansms of electrochemcal transport and how they can be theoretcally smulated s therefore fundamental to fuel cell research and development.

66 3 Revew of Practcal Factors Governng PEFC Performance 46 Performance Loss Mechansm Increase of Actvaton Losses Increase of Mass Transportaton Losses Fuel Cell Component Fault/Process Cause Platnum catalyst (1) Platnum agglomeraton causng loss of EASA (1) Repettve on/off load cyclng (2) Hgh voltage nduce at cathode equvalent to OCV due to resdual hydrogen (3) Loss of carbon support (2) Platnum mgraton causng loss of catalyst materal (4) Solublty of platnum when cell s operated through hydrogen-ar open crcut to ar-ar open crcut (3) Adsorpton of atmospherc contamnants on platnum (5) Ar mpurtes such as NO 2, SO 2 and H 2S causng loss of EASA (4) Adsorpton of fuel mpurtes on platnum causng (6) Fuel mpurtes such as CO and CO 2 loss of EASA (5) Loss of catalyst due to chemcal attack and formaton of slcone/oxygen/platnum partcles (7) Chemcal degradaton of slcone sealant Geometrc structure of the catalyst layer Carbon support n catalyst layer Porous and vod regons of the cell; catalyst layers, GDLs, BPP flow felds Geometrc structure of catalyst layer GDL (6) Deformaton of catalyst structure by freezng and (8) Resdual water n catalyst layers meltng water, resultng n ncreased pore sze and reduced EASA (7) Corroson of carbon to support the current above that (9) Fuel starvaton provded by the fuel when the cell s suppled wth (10) Partal coverage of hydrogen on catalyst stes nsuffcent fuel to support the current drawn (11) Localsed floodng (8) Floodng caused by the accumulaton and (12) Low flow rate of channel gases condensaton of water vapour to nduce two-phase flow (13) Low pressure n gas flow channels (14) Flow-feld geometry (15) Degradaton of polymer electrolyte n catalyst layer due to mpurty ons (9) Loss of hydrophobcty n porous regons of the cell (16) Loss of materal/materal propertes due to repeated thermal cyclng / hgh treated wth hydrophobc materal operatng temperature (17) Delamnaton caused by repeated thermal cyclng (18) Damage to materal caused by exposure to sub-zero condtons (19) Cell over-compresson, mpactng the GDL (10) Impedance to transport attrbutable to presence of (20) Ionomer expanson on water uptake causng pores to collapse onomer (21) Excessve onomer loadng (22) Formaton of onomer skns on catalyst layers (23) Lack of control durng MEA processng (11) Impedance to transport attrbutable to ce formaton (24) Presence of resdual water from prevous shut-down (12) Loss of porosty, ncreased floodng and reduced gas permeablty Table 3-2 Summary of factors affectng actvaton, Ohmc and mass transportaton losses (25) Operaton at sub-zero temperatures (26) Over-compresson and nhomogeneous compresson, nduced durng cell assembly or by warpng of moulded BPPs

67 3 Revew of Practcal Factors Governng PEFC Performance 47 Performance Loss Mechansm Increase of Ohmc Losses Increase of Effcency Loss, potentally leadng to Catastrophc Cell Falure Catastrophc Cell Falure Fuel Cell Component Fault/Process Cause Stanless-steel BPP (13) Loss of surface electrcal conductvty (27) Impedance to electron transfer due to passvatng layer on SS surface Coated stanless-steel BPP (-) Loss of surface electrcal conductvty (28) Coatng defects such as pnholes and mcro-cracks when coated wth TN (29) Degradaton of conductve coatng (30) Degradaton of conductve polymer coatng Injecton-moulded BPP (14) Low electrcal conductvty (31) Formaton of polymer-rch boundary durng njecton-mouldng process Polymer Electrolyte Membrane (15) Loss of proton conductvty (32) Loss of membrane hydraton (33) Replacement of protons by mpurty ons causng decrease n the water dffuson coeffcent and ncrease n water transfer coeffcent (34) Ansotropc swellng of membrane causng the water dffuson coeffcent to decrease Polymer electrolyte membrane (16) Formaton of cracks and pnholes (35) Increased roughness of electrolyte membrane surface, nducng by sub-zero operatng condtons (36) Mechancal stresses nduced by thermal hotspots n regons of strong electrcal contact (.e., GDL and BPP shoulder), hgh compresson, and hgh reacton rates (37) Defects durng the manufacturng process (38) Peroxde and peroxde radcal attack of polymer end groups (39 Repettve swellng/contracton due to hygro-thermal stresses (40) Excessve pressure dfferental between anode and cathode gas supply GDL/catalyst layer/membrane (17) Delamnaton of layers (41)Thermal cyclng ncludng exposure to sub-zero condtons Catalyst layer (18) Excessve adsorpton of atmospherc and fuel mpurtes (42) Loss of tolerance to contamnants BPP (19) Crackng (43) Inhomogeneous compresson (44) Mechancal shock/vbraton (45) Irregulartes n cell/stack constructon (20) Warpng (46) Low ntal rgdty of polymer matrx Seal (21) Gas leakage (47) Oxdaton of seals Polymer electrolyte membrane (22) Short crcut (48) Formaton of electrcal network due to mal-dstrbuton of platnum wthn (self-humdfyng) membrane Table 3-3 Summary of factors affectng effcency losses and catastrophc cell falure

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79 4 Mathematcal Modellng of a PEFC In ths chapter, the electrochemcal theory that descrbes the processes of the PEFC are dscussed n greater detal. The dscusson s presented n three parts, frst focusng on the central topc of mass transport, followed by Ohmc losses and fnally electrode knetcs. 4.1 Mass Transport Molecular transport s a key process that drectly affects the rreversble losses n an operatng fuel cell at practcal operatng current denstes. Mass transport losses occur when the concentraton of oxygen at the cathode catalyst ste falls, partcularly at hgh current denstes. Ohmc losses occur when the water content of the PEM s below a matrx threshold, whch causes the resstance to proton transport across t to ncrease. A clearer nsght nto the mechancs of phenomenologcal cell processes and therefore rreversble voltage losses can be obtaned by consderng and applyng the theory of molecular transport n electrochemcal systems. Mass transport can be broken down nto two fundamental components: the thermofludc and electrochemcal state wthn a confned system and the transport that occurs as a consequence. The two most rudmentary thermo-fludc condtons that can nduce transport are spatal pressure gradents and temperature gradents. As an electrochemcal system, transport n the PEFC can also be nduced by spatal concentraton gradents and by an electrc feld. Molecular Dffuson The molecules of a gven speces wthn a defned enclosed system wll dstrbute through random moton from a regon of hgh concentraton to a regon of low concentraton. Ths process s known as molecular dffuson, or smply dffuson. The dffusve flux can be defned as the net molecular flux of the speces from the regon of hgh concentraton to the regon of low concentraton. For an open system, a reference volume can be taken whch

80 4 Mathematcal Modellng of a PEFC 60 travels at a reference velocty. Wthn ths volume, f there s a concentraton gradent of a consttuent speces, then there wll be a net molecular flux of that speces from the regon of hgh concentraton to the regon of low concentraton. If the velocty of the speces s dfferent to the reference velocty, then the molecules of the speces are sad to be dffusng and the dffuson velocty can be defned as the average velocty of the speces wth respect to the reference velocty. Convecton In convectve or vscous flux, the molecules surroundng a wall partcle loose ther ntal relatvely hgh velocty, causng them to slow down. Ths leads to a dampenng effect that contnues untl the boundary layer reaches the same velocty as the wall partcle. The convectve flux tself corresponds to that porton of flow that occurs n the lamnar regme, whch s drven by a pressure gradent. Convectve flow can occur n gas-phases and lqudphases. Snce convecton s a form of bulk flow, t does not have a tendency to separate consttuent speces of lke-phase mxtures and so a mxture of dfferent consttuents n a sngle phase can be treated as a sngle phase. Knudsen Flux The Knudsen regme descrbes a type of flow that occurs when the lkelhood of molecule-molecule collsons s low n relaton to molecule-wall collsons. As such, molecules colldng off walls do not collde wth other molecules. Therefore, the mean dstance between two molecular collsons s much greater than the average dstance between two neghbourng partcles. Thermal Dffuson Thermal dffuson (also known as the Soret Effect) s the tendency of a mxture of two or more components of a flud to separate as a result of a spatal temperature gradent. It s possble for the mxture to partally separate nto components wth the heaver larger

81 4 Mathematcal Modellng of a PEFC 61 molecules concentratng at the lower temperature and lghter smaller molecules at the hgher temperature as a result of thermal dffuson. The spatal temperature gradents that develop nsde a workng PEFC are usually not consdered to be suffcently large to nduce molecular separaton amongst the components of the fluds that nfltrate the cell. Thermal dffuson s therefore not explctly consdered n the current work. Electro-Osmotc Drag In a PEFC, electro-osmotc drag s the process by whch water molecules are forcbly moved under an electrc feld through the polymer electrolyte. The process can be attrbuted to the nteracton between the protons that mgrate from the anode catalyst layer through to the cathode va the PEM and the water (a polar lqud) that nfltrates the sold polymer electrolyte. The nteracton s commonly descrbed as a drag process; a number of water molecules are sad to be dragged per proton that mgrates due to the electrc feld Concentrated Soluton Theory Concentrated soluton theory can often be traced as the fundamental startng pont for many of the key transport equatons n the fuel cell modellng lterature. For a multcomponent electrochemcal system, t can be assumed that ntermolecular transport s drven by a spatal gradent n electrochemcal potental. The gradent n electrochemcal potental tself reflects a spatal gradent of electrc potental and chemcal concentraton. The flux equaton for ths type of system can be expressed as [1]: j j ( v v ) c µ = K (4-1) j where c = concentraton of speces µ = gradent n electrochemcal potental of speces K j = frctonal coeffcent of speces par,j

82 4 Mathematcal Modellng of a PEFC 62 v = velocty of speces The frctonal coeffcent accounts for the local concentratons of pars of consttuent speces and the dffuson coeffcent of the speces par; K = j RTc c c T D j j (4-2) Substtutng equaton 4-2 nto 4-1 yelds c µ RT = n j c c c T j D j ( v v ) j (4-3) The molar flux of a gven speces can be defned n terms of ts concentraton and velocty as: n& = c ( v v ) ref (4-4) where the reference velocty accounts for the bulk flud moton. Substtutng equaton 4-4 nto the flux equaton 4-3 yelds; c µ = RT n j c n& c n& j c T D j j (4-5) Ths s the common form of the flux equaton for concentrated soluton theory and forms the bass of a number of PEFC models [2,3,4,5]. It has been appled to model transport across the PEM by treatng t as a ternary system composed of water, electrolyte and protons. In dong so, the electrochemcal potental gradent can be expressed as; c µ = z F φ + RT c (4-6)

83 4 Mathematcal Modellng of a PEFC 63 The Stefan-Maxwell Equaton For mult-component transport that does not nvolve speces whch have a postve or negatve valance ( z = 0 ), the electrochemcal potental gradent can be expressed as: µ = RT c c (4-7) Substtutng nto the flux equaton yelds c = n j c n& c n& j c T D j j (4-8) By the deal gas law c T = p RT (4-9) Substtutng equaton 4-9 nto 4-8 yelds what s more commonly known as the Stefan- Maxwell equaton: c = n j RT pd j ( c n& c n& ) j j (4-10a) Usng the dentty terms of mole fractons as: c = y c and assumng that c = 0, equaton 4-10a can be rewrtten n T T y = n j RT pd j ( y n& y n& ) j j (4-10b) The Stefan-Maxwell equaton can be appled to smulate mult-component dffuson n a chemcal system. When dffuson occurs n a porous medum such as the GDL or MPL, the bnary dffuson coeffcent of speces par j has to be adjusted to account for ts

84 4 Mathematcal Modellng of a PEFC 64 tortuosty, porosty and pore saturaton, partcularly f lqud water can nfltrate ts porous network. Generally speakng, therefore, D j s replaced wth a recalculated value eff D j such that D < D. The effectve dffusvty can be calculated as: eff j j D eff j ε = Dj 1 τ ( s) m (4-11) In the context of PEFC modellng, the Stefan-Maxwell equaton can be appled to determne the dstrbuton of oxygen through the cathodc porous layers (GDL, MPL) and through the pores of the cathodc catalyst layer. The Stefan-Maxwell equaton can be appled to calculate the change n the concentraton of a reactant through a porous medum as a functon of thckness when the reactant s a part of a mult-component system and the flux rate of each speces through the medum s known. Therefore, the Stefan-Maxwell equaton s crtcal n charactersng the effects of mass transport lmtatons Dlute Soluton Theory Dlute soluton theory can be derved from concentrated soluton theory. The fundamental dfference between the two approaches s that t s assumed that for a dlute system, the concentraton of the solvent s much greater than the concentraton of the solutes. Consequently, each solvent speces can be consdered n relaton to the solvent and not n relaton to each other because solvent nteractons are assumed to be nsgnfcant. If the solute speces s j then c << c j and c j ct. Hence, equaton 4-5 can be expressed as & c µ n = Dj + RT c v j (4-12) Ths s sometmes known as the dffuson equaton n fuel cell modellng. Equaton 4-12 can be appled to smulate the transport of water across the PEM. In ths case, the velocty of the polymer electrolyte s zero ( = 0) v and so equaton 4-12 reduces to j

85 4 Mathematcal Modellng of a PEFC 65 n& c µ = D RT j (4-13) where D j becomes the dffuson coeffcent of water n the polymer electrolyte and should take nto account the fact that t can swell durng water uptake. The Nernst-Planck Equaton For the transport of a charged speces through a solute accordng to dlute soluton theory, equaton 4-6 can be substtuted nto equaton 4-12 to yeld: Dj n & = z Fc φ Dj c + cv RT j (4-14) The moblty of the speces can be defned as; u = D j RT (4-15) whch can be substtuted nto equaton 4-14 to yeld the Nernst-Planck equaton: n & = z u Fc φ D c + c v (4-16) j j The Nernst-Planck equaton therefore descrbes the transport of a solute speces n a solvent speces j due to: mgraton due to a gradent n electrc potental dffuson due to a gradent n the chemcal concentraton of speces convecton (due to a pressure gradent) Convecton s not mplctly lnked to a pressure gradent n equaton Bernard and Verbrugge [6] apply equaton 4-16 to model the transport of protons across the PEM by treatng t as a lqud water and electrolyte membrane composte solvent. They assume that the electrolyte s unformly hydrated, whch as a general assumpton could be plausble for

86 4 Mathematcal Modellng of a PEFC 66 very thn membranes (<50 mcrons n ths case). The convectve flux becomes the superfcal pore-water flux n the membrane that s drven by a hydraulc pressure gradent. Generally, ths can be gven by Darcy s law: v j κ p = p µ (4-17) However f t s assumed that the pore water velocty s also affected by the gradent n electrc potental, then Darcy s law has to be modfed nto a form that s known as Schlogl s velocty equaton [6]: v j κ φ κ p = z jc j Fj φ p µ µ (4-18) Fck s Law For the transport of a speces that has no net charge, substtuton of equaton 4-7 nto 4-13 yelds Fck s law of dffuson: n& = D c j (4-19) Here, D j becomes the dffuson coeffcent of speces n the solute j, both of whch by defnton should be electro-neutral substances. Fck s law s often used nstead of the Stefan- Maxwell equaton for smplcty to descrbe mult-component transport across the GDL and the MPL; Fcks law forgoes the need to consder cross-speces nteractons. When applyng Fcks law to model transport across a materal that has a tortuous, porous network, the same consderatons dscussed prevously regardng the use of eff D j nstead of D j would apply Knudsen Fluxes Typcally, Knudsen fluxes occur as free-molecular transport n porous structures where the characterstc pore rad are less than 10nm. As such, ths type of flow can occur n

87 4 Mathematcal Modellng of a PEFC 67 the catalyst layers of a PEFC. The Knudsen flux for a gven speces s calculated as a functon of ts concentraton gradent, such that: n& K = D K c (4-20) The effectve Knudsen dffusvty K D accounts for the molar mass of the speces and the geometry of the pore n whch the Knudsen flux occurs. It can be calculated as [7]: D = r K K RT M (4-21) where r K M = the Knudsen radus = the molar mass of speces The total Knudsen flux for a mult-component system s calculated as: n K tot = n& K (4-22) Although Knudsen flux s a form of dffusve flux, t does not explctly appear n concentrated soluton theory or dlute soluton theory and s therefore often appended on to the relevant flux equaton for a gven speces Electro-Osmotc Drag The electro-osmotc drag flux ndcates n molar terms the rate at whch water molecules are dragged by protons that mgrate due to an electrc feld from the anode catalyst layer through the PEM to the cathode catalyst layer. For water t can be defned as: n& w, drag = J F ξ w (4-23)

88 4 Mathematcal Modellng of a PEFC 68 where ξ w = electro-osmotc drag coeffcent of water The electro-osmotc drag coeffcent vares accordng to the local hydraton of the PEM and temperature, and usually determned by expermental means [8,9]. For Nafon, the drag coeffcent s typcally between 1.5 to 2.8 [9]. Water flux due to electro-osmotc drag can be accommodated for by appendng equaton 4-23 on to the end of the flux equaton from ether concentrated or dlute soluton theory. In ther standard forms as gven above, nether concentrated or dlute soluton theory explctly account for electro-osmotc drag when appled to descrbe the transport of water n sold polymer electrolytes Dscussons on Mass Transport Processes across the PEM The dscussons above hghlght the standard electrochemcal equatons to mechanstcally descrbe the dfferent types of transport that occur n the PEFC. Dffuson and convecton can potentally occur n all layers of the PEFC. Knudsen flux s lkely to develop n structures where the characterstc pore rad are n the order of 10 nm, for example, the catalyst layers. Electro-osmotc drag occurs through electrolytc regons of the cell, whch therefore ncludes the catalyst layer and PEM. The dscusson demonstrates that there are largely two treatments that can be used to descrbng molecular transport n electrochemcal systems; concentrated soluton theory and dlute soluton theory. As shown, the second can be obtaned from the frst f t s assumed that the concentraton of the solute s much less than that of the solvent,.e., the dlute soluton assumpton. For a mult-component concentrated system, concentrated soluton theory can be appled. If t s assumed that cross-component nteractons can be neglected accordng to the dlute soluton assumpton, dlute soluton theory can be appled. In order to capture convecton, Knudsen flux and electro-osmotc drag, t s necessary to ntroduce equatons 4-17 or 4-18, 4-20 and 4-23 respectvely nto both concentrated and dlute soluton theory.

89 4 Mathematcal Modellng of a PEFC Ohmc Resstance Resstance to the Flow of Electrons The total Ohmc resstance of a sngle cell s composed of two components; a resstance to the flow of electrons and a resstance to the flow of protons. Resstance to the flow of electrons s manfested n the electron-conductng parts of the cell, such as the catalyst layers, the carbon substrates of the GDL and MPL, and the bpolar plate. The compacton force appled to a PEFC assembly can force carbon fbrls wthn the GDL closer together, whch can reduce the nternal resstance to electron flow. Cell compacton can also decrease the contact resstance n the nterface between electron-conductng layers (.e., between the GDL and BPP, the MPL and the CL or the GDL and CL). Overall resstance to electron flow can be measured drectly ex-stu as a functon of compacton force for compressble layers and usually do not change n-stu accordng to the operatng condtons of the cell. Ths s because the electron-conductng propertes of the relevant materals such as carbon are unaffected by thermo-fludc varables such as temperature, pressure and mass transport under fuel cell operatng condtons Resstance to the Flow of Protons The resstance to proton flow n the cell s charactersed by two components; most sgnfcantly that whch occurs across the proton-conductng PEM but also that whch occurs n the polymer electrolyte n the catalyst layers. As such, the resstance to proton flow depends manly upon the concentraton of water across the PEM and can be calculated as r proton = t mem 0 1. dz σ (4-24) where σ = proton conductvty of the PEM t mem = thckness of the PEM

90 4 Mathematcal Modellng of a PEFC 70 It s possble to determne the proton conductvty of the PEM through ex-stu expermental tests based upon the uptake of water over a range of temperatures. As such, the expermental expresson can be substtuted drectly nto equaton 4-24 where the proton conductvty becomes σ ( λ,t ) and λ s the water content per sulphonc sde chan. A mechanstc descrpton of resstance to the flow of protons across the PEM nvokes a more detaled understandng of the dffusvty, concentraton and convectve velocty of protons. The movement of protons across the PEM s governed by Ohms law: J = σ φ (4-25) Substtutng 4-25 nto 4-24 yelds: r proton t m = φ. dz J 0 (4-26) The rght hand sde of equaton 4-26 can be determned by recallng the form of the Nernst- Planck equaton as gven by 4-14 and applyng t to determne the transport of protons across the PEM: n& D + H = z + Fc + φ D H H RT c H H H c + H v (4-27) where v = the pore water velocty D + = the dffuson coeffcent of protons n the PEM H If the flow of electrolytc charge across the membrane s related to the current densty, then the current densty can be gven by: J = Fz & n + + H H (4-28) Substtutng equaton 4-27 nto 4-28 yelds:

91 4 Mathematcal Modellng of a PEFC 71 J 2 2 F = z D + c + φ z + FD + c + + z 2 H H H H H RT H + + H H c Fv (4-29) Gven that z + H =1, equaton 4-29 can be rearranged to gve: JRT φ = D c F H H RT Fc + H c + H + RT FD + H v (4-30) Substtutng 4-30 nto 4-26 and ntegratng yelds: r proton = RT 2 F tm tm tm 1 1 dc (4-31) + H dz + dz D + c + JF c + dz JF D + 0 H H RT 0 H RT 0 v H dz Dscussons on Modellng Resstance to the Flow of Protons across the PEM Because the PEM s at least a ternary system, the nteracton of mgraton, dffuson and convecton processes can have an overall affect on water content and dstrbuton. The challenge n employng equaton 4-31 s that t s does not capture how the three proton transport processes nteract wth the varous forms of water transport n the membrane. Therefore, equaton 4-24 s commonly appled wth expermental expressons for conductvty determned from ex-stu tests nstead,.e., σ ( λ,t ). The nteracton between protons due to mgraton and water n the PEM can be smply accounted for by consderng the electro-osmotc drag flux, whch s a functon of the expermental electro-osmotc drag coeffcent and the dstrbuton of water across the PEM smulated through dlute or concentrated soluton theory. 4.3 Electrode Knetcs Actvaton losses occur n the anode and the cathode catalyst layers. Ths secton consders three technques by whch the catalyst layer can be modelled to estmate the actvaton losses. The frst method calculates the overall actvaton overvoltage of both

92 4 Mathematcal Modellng of a PEFC 72 catalyst layers combned, treatng each as a thn nterface. The two methods that subsequently follow, namely the macro-homogeneous and agglomerate methods, are macroscopc treatments where the catalyst layer s treated as a regon of fnte thckness Thn Interface Model Butler-Volmer Knetcs Consder the followng reacton whch descrbes the reducton and oxdaton processes for a reacton; Red Ox + e (4-32) The rate of a reacton s the rate constant multpled by the concentraton of reactants rased to the orders of reacton, whch s usually frst order [10]. Therefore, the rates of the reducton and oxdaton processes can be expressed n terms of an Arhennus equaton such that; υ Red = K Red G RT Red [ c ] exp Red (4-33) υ Ox = K Ox G RT Ox [ c ] exp Ox (4-34) where the subscrpts Red and Ox refer to the reducton and oxdaton processes respectvely, K Red and Ox K are the correspondng rate constants, [ c ] and [ ] concentratons of the reactant molecule and ons, and Red c are the GRed and GOx are the actvaton energy change for the reducton and oxdaton reactons respectvely. In an rreversble system, there s no perceptble reacton at equlbrum. Current s generated only by the applcaton of extra potental, the overpotental η. Therefore, the magntude of G Ox become Ox GRed and

93 4 Mathematcal Modellng of a PEFC 73 0 ( G ) αnfη G Red = Red + (4-35) 0 ( G ) ( α ) nfη GOx = Ox 1 (4-36) The overpotental serves two purposes; a proporton of t (a fracton gven by α ) asssts n the reducton process whle the remanng slows down the oxdaton process. The parameter α n the theory of electrode knetcs s known as the charge transfer coeffcent and ranges between 0 and 1. The rates of the reducton and oxdaton processes now become; υred = K Red Red exp G αnfη RT Red [ c ] (4-37) υ Ox = K Ox [ c ] Ox G exp Ox ( 1 α ) + RT nf η (4-38) These can also be expressed n terms of the reducton and oxdaton current denstes as follows usng Faradays law: υ = J Red Red nf (4-39) υ = Ox J Ox nf (4-40) Therefore, J Red = nfk Red [ c ] Red ( G ) exp RT Red 0 αnfη exp RT (4-41) J Ox = nfk Ox [ c ] Ox 0 ( G ) ( 1 α ) Ox exp RT nf exp RT η (4-42) The forms of equatons 4-41 and 4-42 can be smplfed to;

94 4 Mathematcal Modellng of a PEFC 74 J Red αnfη = J 0 exp RT (4-43) J Ox = J 0 ( 1 α ) nf exp RT η (4-44) were the J 0 s the exchange current densty. The net current densty J = J Red J s gven Ox by: J ( αnfη ) αnfη 1 = J o exp exp RT RT (4-45) The above equaton s known as the Butler-Volmer equaton. Because t s thought that only one electron can be transferred at a tme, the expresson strctly holds n the above form for processes nvolvng a sngle electron. Reactons that nvolve multple electron transfers, therefore, should be expressed as a number of one-electron reactons. Under such a crcumstance, t s more rgorous to replace α wth because α + α 1 except for when n = 1; Red Ox α and to replace ( α ) Red 1 wth α Ox J ( α nfη ) α = Red nfη Ox J o exp exp RT RT (4-46) The Tafel Equaton In fuel cell modellng the overpotental at the anode electron s often neglected because t s usually at least an order of magntude smaller than that of the overpotental at the cathode electrode. Amphlett et al. [11] suggest that the actvaton overvoltage for hydrogen oxdaton at K and at a current densty of 0.11 A/cm 2 s V compared to 0.35 V for oxygen reducton. In addton, when consderng the overpotental at the cathode electrode, the second term on the rght hand sde of equaton 4-46 s nsgnfcant compared to the frst term. Therefore, the net current densty produced by the cell can be

95 4 Mathematcal Modellng of a PEFC 75 obtaned from the followng reduced Butler-Volmer equaton, where the subscrpt c refers to the reducton process at the cathode, J α nf = J c η 0 exp RT (4-47) Based on the reduced Bulter-Volmer equaton, the dependence of cathodc current densty on overpotental s gven by; ln J = ln J 0 α c nfη RT (4-48) For a large overpotental to the cathodc reacton, η can be expressed by η RT = ln J 0 α nf act, cathodc c α c RT ln J nf (4-49) Conversely, for a large overpotental to the anodc reacton, only the second term of equaton 4-49 s of sgnfcance, and η RT = ln J 0 α nf act, anodc a α a RT ln J nf (4-50) The two equatons above are known as the Tafel equaton, whch can be generally expressed n the form η = d + e log J (4-51) In general terms, therefore, the actvaton overvoltage can be gven as follows; η = act RT αnf J ln J 0 (4-52)

96 4 Mathematcal Modellng of a PEFC 76 The Thn Interface Treatment The thn nterface treatment consders the actvaton overvoltage separately at both electrodes n terms of the exchange current densty. The total actvaton overvoltage s then determned as the sum of the two components. The analyss starts by defnng the exchange current densty of the oxygen reducton process at the cathode usng surface concentratons [12]; J 0 b ( ) ( 1 α ) ( ) ( ) ( ) ( ) c 1 α c αc c + c c = nfk (4-53) H O2 H 2O where K b k BTS Fe = exp ++ hγ RT ++ (4-54) and where k B S h = Boltzmann constant = standard state of surface concentraton = Planck constant ++ γ = transfer coeffcent at the transton state ++ F e = standard state free energy of actvaton from gong drectly from gas-state and actve electrode ste to the actvaton complex of onsaton The transton state refers to a poston from the electrode surface where an electrolyte speces can become assocated wth ether the electrolyte soluton by ganng a postve charge to become surface to become M. Substtutng + M or can just as easly become assocated wth the metal of the electrode K B nto the exchange current densty yelds: J k F RT * ( ) ( 1 α ) ( ) ( ) ( ) ( ) c * 1 α c * αc c + c c ++ B e 0 = nf exp ++ H O2 H 2O hγ TS (4-55) Substtutng the cathodc exchange current densty nto the Tafel equaton for the cathode actvaton overpotental yelds:

97 4 Mathematcal Modellng of a PEFC 77 η RT k BTS Fe = ln nf exp + α nf c hγ RT ++ * ( ) ( 1 α ) ( ) ( ) ( ) ( ) c * 1 α c * α c c c c O H O ln H 2 act, cathodc + J + 2 (4-56) The law of electroneutralty requres that: m m + z c = z c 0 (4-57) where z c s the total charge on the PEM and m m z c s the total charge on moble speces n the PEM. When there are no onc contamnants permeatng the PEM, protons are the only onc speces and the sulfonc end groups are the only charged membrane speces. Gven that z m and z are both constants, beng -1 and +1 respectvely, yelds c = c. m It can be assumed that the part of the PEM that s n closest contact wth the cathode wll have an approxmately constant concentraton of water and protons. It s as also assumed that all other terms wll be constant apart from the surface concentraton of oxygen at the catalyst layer, the current and the temperature.. Therefore, the constants n equaton 4-56 can be grouped together and the cathodc actvaton overvoltage can be expressed n parametrc form as; * ( c ) ln( J ) η act, cathodc = β1, c + β 2, ct + β3, ct ln O + β (4-58) 2 4, c where β 1, c β β Fe = α cnf ++ R kbts = ln nf + αcnf hγ * ( ) ( 1 α ) ( ) ( ) c * αc c c 2, c + + H H2O 3, c R = 1 α nf c ( α ) c β 4, c R = α nf c

98 4 Mathematcal Modellng of a PEFC 78 For the anode, t s suggested that the process that controls the reacton rate s the chemsorpton of hydrogen [12],.e., the process whereby a valence bond s formed between a molecule of hydrogen and the surface of the catalyst-loaded anode. The exchange current densty for strong chemsorpton at the anode can be defned as: J 0 = nfk a exp ( 1 γ ) F RT c (4-59) where K a kbt = hγ * ( ) ( F γ F c ch exp ) 2 RT (4-60) and where γ = 1 α a ++ F = standard-state free energy of actvaton for chemsorpton F c = standard-state free energy of chemsorpton from gas state per mole of H 2 The exchange current densty can therefore be expressed as J k BT = nf hγ * ( c ) 0 ++ H2 exp ++ ( F γ F ) ( 1 γ ) RT c exp F RT c (4-61) Substtutng the anodc exchange current densty nto the Tafel equaton for the anodc overvoltage yelds: η RT k BT = ln nf + α cnf hγ * ( c ) exp ++ ( F γ F ) ( 1 γ ) exp F RT ln c c act, cathodc J + H 2 RT (4-62) Because hydrogen s usually suppled neat to a PEFC or through a hydrogen-rch reformate feed wth a mole fracton n excess of 0.7, t can be assumed that the varaton n ts

99 4 Mathematcal Modellng of a PEFC 79 concentraton for most low-pressure fuel cell applcatons s lkely to be neglgble. Therefore, the hydrogen concentraton at the reacton stes for the above equaton can be approxmated as a constant, along wth all other terms apart from temperature and current. In parametrc form, therefore, the above equaton can be expressed as ( J ) η act, anodc = β1, a + β 2, at + β 4, a ln (4-63) where β 1, a F = α nf a ++ β β R * ( c ) B 2, a = ln nf H 2 anf + + α hγ 4, a R = α nf a k The total actvaton overvoltage s gven by η = + (4-64) act ηact, cathodc ηact, anodc such that * ( c ) ln( J ) η act = β1 + β 2T + β 3T ln O + β (4-65) 2 4 where β = + 1 β1, c β1,a β = + 2 β 2, c β 2,a β 3 = β 3,c β = + 4 β 4, c β 4,a Therefore, by usng the thn nterface treatment, t s possble to defne the total actvaton overvoltage of a PEFC n parametrc form. The parametrc constants can be statstcally evaluated from emprcal analyss and appled to estmate the actvaton

100 4 Mathematcal Modellng of a PEFC 80 overvoltage at a gven current, temperature and predetermned oxygen concentraton at the catalyst stes The Macro-Homogeneous Model Fundamentally, macroscopc models such as the macro-homogeneous and agglomerate models consder the catalyst layer to be a matrx structure that contans three prncpal components; a porous network for the supply of oxygen to the reacton stes and the removal of excess water; a sold nterconnected carbon-phase whch serves as a network for the supply of electrons; an electrolytc phase whch provdes a network for the supply of protons. The macro-homogeneous (MH) model consders the catalyst later to be a homogeneous phase and calculates ts performance accordng to the bulk propertes of the catalyst layer structure [13,14]. It s possble for molecular dffuson, convecton and Knudsen dffuson to occur wthn the catalyst layer. Two-phase flow can also propagate through the catalyst layer, partcularly n the cathode catalyst layer due to the product water beng formed there. For the current dscusson, the smplest case s taken, where Fck s law of dffuson s appled to descrbe materal balance of oxygen; dc O J 2 dz J = nfd ( z) eff O2 (4-66) where J ( z ) s the local current densty. Ohms law can be used to defne the ncrease n phase potental n the sold and the electrolyte wth respect to channel depth [13]: dη (4-67) = I J ( z) eff eff eff dx + κ s κ m κ s

101 4 Mathematcal Modellng of a PEFC 81 The total actvaton overvoltage of the cathode catalyst layer can then be calculated wth known boundary condtons The Agglomerate Model The agglomerate model assumes that the catalyst layer can be approxmately modelled as a collecton of carbon-supported catalyst agglomerates that are coated by a thn layer of polymer electrolyte [15,16,17,18]. The agglomerates are all assumed to be dentcal n geometry and organsed n an artfcal manner. The agglomerate model was ntally used by Iczkowsk and Cutlp to determne the performance of the cathode catalyst layer n a PAFC [19]. In general, lke the macrohomogeneous model, t s assumed that oxygen s reduced as t dffuses through the catalyst layer; dn o2 dz ( z) = n R (4-68) where n o 2 = dffusve flux of oxygen past any pont n the catalyst layer (kmol/m 2 -s) n R = rate of reacton of oxygen per m 3 of electrode at a gven pont (kmol/m 3 -s) Frst, oxygen dffuses nto the catalyst layer, where t permeates through the porous network. The oxygen then dssolves n the outer layer of the flm of electrolyte whch covers the agglomerates. The dssolved oxygen then dffuses across the flm and dffuses nto the pores of the agglomerates. The rate of reacton per unt volume n the catalyst layer s calculated as n R = ad O2, mem p O2 0 ( z) c c ( r, z) O2 δ O2 a (4-69) where a = the area of the flm per unt volume of the electrode

102 4 Mathematcal Modellng of a PEFC 82 D O, mem 2 = the dffuson coeffcent of oxygen n the electrolyte p O2 ( z) = the partal pressure of oxygen n the gas pores 0 c O 2 = the solublty of oxygen n the electrolyte δ r a = the thckness of the flm = the radus of the agglomerate Usng denttes for the concentraton of dssolved oxygen at the surface of the agglomerate c ( r z) O a, 2, the above equatons can be equated and rearranged to yeld an expresson for the change n oxygen flux rate across the catalyst layer: dn O2 dz = δ ad p c O2 ( z) 1 + ς K c 0 0 O2, mem O2 c e O2 (4-70) where the effectveness factor for the dffuson and reacton of oxygen ς c can generally be defned as the actual reacton rate for a gven quantty of catalytc agglomerates to the reacton rate f the oxygen concentraton throughout t was the same as at the surface [20]. The rate constant can be defned n terms of the current densty assumng that the only source of voltage loss s actvaton, J T ( E) : K = e J ( E) T 4 0 Fz O p 2 O2, gasc O 2 (4-71) where z O 2 = thckness of the catalyst layer p O, gas 2 = partal pressure of oxygen n the gas stream Fnally, J T ( E) can be related to potental through the equaton; E Ref ( E) = J ( E ) exp J Ref 10 E T s (4-72)

103 4 Mathematcal Modellng of a PEFC Dscussons on the Fundamental Models for Electrode Knetcs The three types of models dscussed above clearly have dfferent applcatons and n terms of fuel cell modellng. The most pertnent dfference between the thn nterface and two macroscopc treatments s that former deals wth the reacton knetcs n great detal but does not afford any consderaton to structural aspects of the catalyst layer. Therefore, n terms of generatng polarsaton curves consderng the dependence of actvaton overvoltage on parameters that are controllable from an operatonal pont of vew (.e., cell temperature, ar/oxygen supply pressure and composton, current densty), the thn nterface model can suffce. However, n order to elucdate certan effects of catalyst layer desgn on the reactve flow through t, macroscopc treatments would appear to be more relevant. Rdge et al. [21] took the same fundamental approach descrbed for the agglomerate model descrbed above, but also consdered the transport of protons through the electrolyte phase by consderng the Nernst-Planck equaton and determned that proton transport lmtatons can have a large effect on electrode performance. It was also found that electrode performance can be mproved by mnmsng the agglomerate rad. For a gven catalytc loadng, smaller agglomerates would have the effect of ncreasng the accessble surface area of the actve stes. Broka and Ekdunge [22] found that the macro-homogeneous model can predct that thcker catalyst layers can nduce hgher overpotentals due to a correspondng ncrease n the barrer to mass transport and lmted proton conductvty, whle the agglomerate model predcts that the lmtng current densty s proportonal to the total accessble surface area of the actve stes, such that ncreasng the thckness of the later ncreases the lmtng current. It s argued n the same work that the macro-homogeneous model does not smulate the polarsaton as well as the agglomerate model n relaton to expermental data. It s evdent that the two dfferent macroscopc modellng treatments can generate conflctng results, though the predctons of the agglomerate treatment do appear to follow predcted polarsaton data more closely than the macro-homogeneous treatment. However, t has to be acknowledged that not all of the requste constants for ether of the macroscopc treatments can be readly determned, and that nether nherently reflects the true

104 4 Mathematcal Modellng of a PEFC 84 heterogeneous nature of catalyst layer structures, whch can nfluence the actual performance of the catalyst layer. For the purposes of the current research, the thn nterface model s appled when requred to determne the actvaton overvoltage of the cell. Reactve flow across the catalyst layer s not treated rgorously n the present work. It s assumed that the polymer electrolyte whch penetrates the catalyst layer acts as an nfntely thn contnuum to the PEM and therefore has the same water content n the electrolytc phase throughout ts thckness as the PEM at the catalyst layer/pem nterface. In realty the total thckness of the catalyst layers could contrbute towards 5% of the total thckness of a complete seven-layer assembly assumng that the total thckness of the assembly s ~ 500 µm (agdl/ampl/acl/pem/ccl/cmpl/cgdl). It s acknowledged that reactve flow smulaton n electrochemcal systems s a separate branch of fuel cell modellng and smulaton that requres dedcated focus, whch s beyond the scope of the current thess. However, usng the fundamental electrochemcal theory dscussed n ths chapter, t s possble to construct the foundatons of a smple fuel cell model that handles multcomponent nlet gases to the anode and cathode. 4.4 References 1 Newman J. Electrochemcal Systems, 1991 (Prentce Hall, Englewood Clffs) 2 Fuller TF, Newman J. A Concentrated Soluton Theory Model of Transport n Sold-Polymer- Electrolyte Fuel Cells. The Electrochemcal Socety Proceedngs Seres, 1989, PV 89-14, Fuller TF, Newman J. Water and Thermal Management n Sold-Polymer-Electrolyte Fuel Cells. J. Electrochem. Soc., 1993, 140(5), Weber AZ, Newman J. Transport n Polymer-Electrolyte Membranes, II Mathematcal Model. J. Electrochem. Soc., 2004, 151(2),A311-A325 5 Janssen GJM. A Phenomenologcal Model of Water Transport n a Proton Exchange Membrane Fuel Cell. J. Electrochem. Soc., 2001, 148(12),A1313-A Bernard DM, Verbrugge MW. A Mathematcal model of the Sold-Polymer-Electrolyte Fuel Cell. J. Electrochem. Soc., 1992, 139, Cunnngham RE, Wllams RJJ. Dffuson n Gases and Porous Meda, 1980 (Plenum Press., New York) 8 Fuller TF, Newman J. Expermental Determnaton of the Transport Number of Water n Nafon 117 Membranes. J. Electrochem. Soc., 1992, 139(5), A1332-A1337

105 4 Mathematcal Modellng of a PEFC 85 9 Pvovar BS. An Overvew of Electro-Osmoss n Fuel Cell Polymer Electrolytes. Polymer, 2006, 47, Hbbert DB. Introducton to Electrochemstry, 1993 (Macmllan Press, Basngstoke) 11 Amphlett JC, Baumert RM, Mann RF, Peppley BA, Roberge PR. Performance Modellng of the Ballard Mark IV Sold Polymer Fuel Cell, I. Mechanstc Model Development. J. Electrochem. Soc., 1995, 142(1), Berger C. Handbook of Fuel Cell Technology, 1968 (Prentce-Hall, Englewood Clffs) 13 Ekerlng M, Kornyshev AA. Modellng the Performance of the Cathode Catalyst Layer of Polymer Electrolyte Fuel Cells. J. Electroanal. Chem., 1998, 453, Jeng KT, Kuo CP, Lee SF. Modellng the Catalyst Layer of a PEM Fuel Cell Cathode usng a Dmensonless Approach. J. Power Sources, 2003, 128(2), Gner J, Hunter C. The Mechansm of Operaton of the Teflon-Bonded Gas Dffuson Electrode, A Mathematcal Model. J. Electrochem. Soc., 1969, 116, Vtanen M, Lampnen MJ. A Mathematcal model and optmzaton of the structure for porous ar electrodes. J. Power Sources, 1990, 32, Cutlp MB. An approxmate model for mass transfer wth reacton n porous gas dffuson electrodes. Electrochm. Acta, 1975, 20, Yang SC, Cutlp MB. Stonehart P. Smulaton and optmzaton of porous gas-dffuson electrodes used n hydrogen/oxygen phosphorc acd fuel cell - I. optmzaton to PAFC cathode development. Electrochm. Acta, 1990, 35, Iczkowsk RP, Cutlp MB. Voltage Losses n Fuel Cell Cathodes. J. Electrochem. Soc., 1980, 127(7), Wnterbottom JM, Kng MB (eds.). Reactor Desgn for Chemcal Engneers, 1999 (Stanley Thornes Ltd., Cheltenham) 21 Rdge SJ, Whte RE, Tsou Y, Beaver RN, Esman GA. Oxygen Reducton n a Proton Exchange Membrane Test Cell. J. Electrochem. Soc., 1989, 136(7), Broka K, Ekdunge P. Modellng the PEM Fuel Cell Cathode. J. Appled Electrochem., 1997, 24,

106 5 A Polymer Electrolyte Fuel Cell Model wth Mult- Component Input Many models have been successfully developed over the last couple of decades to smulate the processes of the PEFC. One of the lmtatons of these models s that typcally only two consttuent speces are consdered n the dry pre-humdfed anode and cathode nlet gases, namely oxygen and ntrogen for the cathode, and hydrogen and carbon doxde for the anode. Another lmtaton s that they do not systematcally consder the effects of cross-flow through the cell on the composton of gases n the channels as ths n turn affects the boundary condtons durng smulaton. In order to extend the potental of theoretcal studes and to brng PEFC smulaton closer towards realty, n ths chapter, a smple onedmensonal steady-state, low temperature, sothermal, sobarc PEFC model s developed whch accommodates mult-component nlet gases and accounts for the effect of cross-flow through the cell on the composton of gases n the channels. The model determnes the actual cross-flow through the cell for a gven set of cell condtons. The model s valdated and appled to nvestgate the effects of carbon monoxde nfltraton and crossover on the performance of the cathode catalyst layer. 5.1 Introducton The crtcal element of a model s the foundng theory, and for a PEFC ths encompasses electrochemstry, thermodynamcs, and flud mechancs. Whle the foundng theory for dfferent models may well be common, the manpulaton of the theory can lead to dfferent systems of equatons and dfferent assumptons as dscussed n the precedng chapter. In addton, models based largely on theory may consder the prncpal phenomenologcal processes but can also be dffcult to solve wth an abundance of parametrc constants that are not necessarly easy to defne. Alternatvely, emprcal models based upon expermental data could provde more accurate results wthn a certan operatng range for specfc cell desgns, but would not necessarly be unversal n applcablty and may not reflect a full understandng of the processes nvolved. The ntermedate soluton would therefore le n a sem-emprcal model that dentfes the key processes but uses

107 5 A PEFC Model wth Mult-Component Input 87 expermental results to assst n solvng the key equatons wthout over-computaton. There are a number of key hstorcal models that have been developed. Fuller and Newman [1] ntroduced concentrated soluton theory to descrbe speces flux n the membrane. Three speces were consdered n the model: polymer wth acd end groups, hydrogen ons, and water. Mass transportaton was consdered n 1D across the cell, whle thermal management was ntroduced n the transverse along-the-gas-channel drecton va energy balance. Each channel gas was treated as a heat removal medum, and the effects of dfferent thermal conductvtes of these gases were analysed wth respect to cell performance. It was found that the hydraton of the membrane was senstve to the rate of heat removal, such that low rates of heat removal,.e., low thermal conductvty of channel gases, would result n poor cell performance. Bernard and Verbrugge [2,3] developed a mathematcal model whch dvded the cell nto seven regons: gas flow channels, gas dffusers and catalyst layers for cathode and anode, and a membrane regon n between. Speces flux wthn these regons was descrbed usng dlute soluton theory, where the Nernst-Planck equaton was used to descrbe the flux due to mgraton, dffuson and convecton. Cell operaton was assumed to be sothermal, and gas-phase pressures were assumed to be constant due to the low gas-phase vscosty. Lqudphase pressures were assumed to be varable, and pressure gradents were ntroduced to the model va Schlogl s velocty equaton. The model assumed that the membrane was fully and unformly hydrated. Sprnger et al. [4] developed a sem-emprcal model. Dlute soluton theory was used to descrbed water flux n the membrane. The form of the flux equaton employed however coupled the flux due to mgraton and dffuson as a functon of the chemcal potental of water. The cell was assumed to be sobarc and so pressure-drven convectve fluxes were not consdered. In the PEM, snce water s produced n the cathode, the greatest concentraton of water s lkely to resde n the regon of the PEM that s the closest to the cathode catalyst layer. Dffuson therefore s lkely to occur through the PEM n the drecton of the anode. However, because water molecules nteract wth protons whch mgrate from anode to cathode, water s also electro-osmotcally dragged back to the cathode. Ths phenomenon was mathematcally smulated n the model n part usng expermental data. The fundamental argument presented by the model was that the counter-actng water fluxes caused a gradent

108 5 A PEFC Model wth Mult-Component Input 88 n water content to buld up across the membrane, such that the membrane was not always unformly hydrated. Ths gradent from anode to cathode ncreased wth respect to operatng current densty causng the membrane to loose ts proton-conductvty, whch ncreased the overall cell resstance and reduced the output cell voltage. Amphlett et al. [5] developed a dfferent sem-emprcal model usng expermental performance data from the Ballard Mark IV fuel cell. The model assumed sobarc and sothermal operaton. Electrode transport was descrbed usng the Stefan-Maxwell equaton and the actvaton and Ohmc overvotlages were defned by applyng lnear regresson to expermental data. Membrane transport was not mathematcally modelled. However, the calculated polarsaton curves correlated well wth expermental results. One of the fundamental lmtatons among these benchmark models s that only up to two consttuent speces were consdered n the dry pre-humdfed anode and cathode nlet gases. Ths lmtaton extends to other computatonal models where mult-component transport s consdered but restrcted to the ncluson of oxygen, ntrogen and water n the nlet cathode feed after humdfcaton [6,7]. Ths reflects only the deal case. Tropospherc ar would have at least ten consttuents whle reformed fuel supples would typcally contan carbon doxde and carbon monoxde. Carbon monoxde s mportant snce ts molecules wll, for example, adsorb more readly onto platnum-based catalyst stes than hydrogen. Wth ts presence, the surface fracton avalable for hydrogen chemsorpton s compromsed [8,9,10,11,12]. Correspondngly, the actvaton energy ncreases for the hydrogen oxdaton process, whch ncreases the anodc actvaton overvoltage. Although t has receved lttle attenton, carbon monoxde s known to permeate the membrane and consequently degrade the performance of the cathode catalyst [13]. In ths research, an one-dmensonal sothermal, steady-state PEFC model based on a number of key publcatons n the area has been developed. In the model, the fuel cell conssts of fve regons, as llustrated n Fgure 5-1. Gas chambers for anode and cathode transport humdfed fuel and ar respectvely and also remove unused gases and water. The catalyst s treated as an nfntely thn nterfacal layer. The model ntroduces the capablty to handle mult-component nput gases and couples ths wth the mult-component dffuson

109 5 A PEFC Model wth Mult-Component Input 89 mechansm of the Stefan-Maxwell equaton to descrbe gas transport n the electrodes. The mass transport model of the cell s completed by consderng water transport n the membrane regon. The transport processes n the two electrodes and the membrane were assumed to be smultaneous and nter-dependent. The transport of carbon monoxde across the cell from the anode nlet has been studed due to ts mpact on cell performance. The smulated overvoltages by the model are valdated aganst expermental data obtaned from the Ballard Mark IV fuel cell [5]. Fgure 5-1 Fve regons of the polymer electrolyte fuel cell 5.2 The Basc PEFC Model The current PEFC model can be dvded nto two parts; the basc model and the mult-speces mass transportaton model. The assumptons appled n developng the model are as follow: the total pressures n the channels are constant and equal both anode and cathode streams are saturated wth water vapour at ther gven gas nlet temperatures the fuel cell operates under sothermal steady-state condtons the heat conducton by channel flows s neglgble

110 5 A PEFC Model wth Mult-Component Input 90 the gas mxtures behave as deal gases the water exsts n vapour form when the local water actvty exceeds unty, the excess lqud water exsts as small droplets of neglgble volume the dffuson coeffcent of water n the membrane s a functon of the water content the water drag s a functon of the local water content there s zero crossover of hydrogen and oxygen across the membrane regon the only speces that travels through the hydrated PEM are the protons due to electrc feld, water vapour due to dffuson and electro-osmotc drag, and potentally carbon monoxde due to dffuson the concentraton of water n the membrane s much less than the electrolyte concentraton Thermodynamc Equlbrum Potental and Irreversble Losses The thermodynamc equlbrum potental can be calculated usng the Nernst equaton, as derved n chapter 2, resultng n equaton In ths chapter, t s assumed that actvaton ( η act ) and Ohmc ( η ohm ) losses decrease the cell potental from ts equlbrum potental when a reasonably large current s drawn up to a maxmum of 1.0 A/cm 2. Actvaton losses are descrbed usng the thn nterface treatment descrbed n chapter 4. The total actvaton overvoltage s calculated usng equaton It s assumed that the parametrc coeffcents n equaton 4-65 can be treated as constants for a gven fuel cell system and determned by applyng lnear regresson to measured test data. As such, the total actvaton overvoltage for the Ballard Mark IV PEFC, can be expressed as [5]; 5 C 2 [ ln( j) ] T[ ln( )] η = T T (5-1) act c O 2 The concentraton of oxygen s defned by Henry s law [5];

111 5 A PEFC Model wth Mult-Component Input 91 c C 2 po = exp T C 2 2 O2 (5-2) The total drop n the cell potental due to Ohmc resstance conssts of the combned resstance to electron and proton transport and defned by Ohm s law n the model: total eletronc protons nternal η ohmc = ηohmc + ηohmc = jr (5-3) For the purpose of ths chapter, the nternal resstance s defned n terms of cell temperature and cell current based on the actve cell area. It s assumed that ths relatonshp can be determned agan by applyng lnear regresson to test data. As such, the followng expresson determned by Amplett et al. s adopted [5]; R nternal T = + j (5-4) Water Transport Model for the PEM The actvaton overvoltage s defned by the concentraton of oxygen at the cathode to membrane nterface, whch s dependant upon the water flux n the electrodes and the membrane. Whle transport n the electrodes s dealt wth later n secton 5.3.3, consderaton s gven here to transport wthn the membrane regon. By assumng the membrane mxture to be moderately dlute, the flux of a speces can be obtaned as follows from equaton 4-12; & D RT n = c µ + v c j (5-5) The frst term explans that the gradent n chemcal potental s the drvng force behnd mgraton and dffuson. The second term represents the convecton due to the bulk moton of the solvent speces. In the case of a membrane under sobarc condtons, t reduces to [4];

112 5 A PEFC Model wth Mult-Component Input 92 & D RT n = c µ (5-6) The chemcal potental can be defned n terms of absolute actvty [14];3]; µ = RT ln a (5-7) whch leads to a defnton of water flux due to dffuson n the membrane; n& D c RT W, dff = W ( RT ln a ) W (5-8) The spatal dstrbuton of water across the PEM can often be expressed n terms of water content per charge ste. Therefore, the dffusve flux of water can be descrbed as n& W, dff = D' c W d(ln a) dλ dλ dz' (5-9) The concentraton parameter c w and laboratory coordnate z are not fxed to the membrane coordnates and need to be modfed to prevent the need to track membrane swellng. It s possble to convert from the laboratory coordnate z to the dry membrane coordnate z usng an extenson parameter x such that; z ' = (1 + xλ) z (5-10) The concentraton of water can also be defned as follows, notng that the densty of the PEM wll decrease when t s expanded; c W = λ ρ dry ( 1+ xλ) M m (5-11) Usng the followng mathematcal dentty: d( ln a) d( ln a) dλ = da da dλ = 1 da a dλ (5-12)

113 5 A PEFC Model wth Mult-Component Input 93 t s possble to redefne the dffusve flux of water across the PEM as; n& W, dff ρ M m λ D' a(1 + xλ) dry = 2 da dλ dλ dz (5-13) The term n the square bracket s the ntra-dffuson coeffcent of the water n the membrane and can be expermentally obtaned as [4]; D 2 3 ( λ λ 0. ) λ 303 T 6 λ> 4 = exp (5-14) The value of λ at the boundary of a PEM can be determned usng the local water vapour actvty. At 30 C (303 K), t has been expermental obtaned as [4], 2 3 λ 303K = a 39.85a a (5-15) n whch a s the local water actvty and s defned as the rato of the local water partal pressure to the saturaton vapour pressure. In addton to the dffusve water flux, there s a reverse water flux flowng n the membrane from anode to cathode due to electro-osmotc drag. It s therefore a functon of the local water content and the flux of hydrogen ons. It can be related to the molar flux of hydrogen to the membrane I as [4], 5λ (5-16) n& W, drag = I 22 Therefore the net water flux across the membrane s the dfference between the dffusve flux of water and the flux due to electro-osmotc drag, n& W 5λ ρ = I 22 M dry m D λ dλ dz (5-17)

114 5 A PEFC Model wth Mult-Component Input 94 To mathematcally lnk the processes of water flux across electrodes to the process of net water flux across membrane, t s necessary to ntroduce the rato of net water flux to molar hydrogen flux n the anode, A α W, nto the model. Its value s determned through teraton and s not assumed or fxed a-pror. The correct value s obtaned when the actvty of water as a functon of λ from equaton 5-18 s equal to that determned at nterface C2 from the dffuson layer model, whch wll be dscussed n secton Ths s a key feature of ths model as t drectly couples the composton and transportaton of speces n the anode and cathode sdes of the cell and can vary accordng to the smulated operatng condtons (temperature, current densty, gas pressure, humdfcaton) and desgn features of the cell (layer thcknesses, PEM equvalent weght). Rearrangng equaton 5-17 gves the water dstrbuton n the membrane; dλ M mi = dz ρ dry 1 5λ A (5-18) αw D λ The Mult-Component Input Model Mass transportaton characterses the avalablty of reactant gases at the catalyst stes and the transport of water n and out of the cell Molar Flux of Oxdsed, Reduced and Produced Speces Consder the overall fuel cell reacton H / O H O. It conssts of two electrode processes, the hydrogen oxdaton n the actve catalyst regon of the anode H H + e, and the oxygen reducton process that takes place to produce water n + catalyst regon of the cathode 1/ 2 + 2H + e H O. O2 2 2 It s assumed that hydrogen does not crossover through the membrane. Any hydrogen flux through the anode dffuser corresponds exactly to the amount of hydrogen requred to nduce a constant steady-state cell current densty J through the oxdaton process. For the anode;

115 5 A PEFC Model wth Mult-Component Input 95 & n A 1 H = I = J 2F (5-19) For the cathode, the oxygen flux also corresponds exactly to current flow wth zero crossover; n C & O = 2 1 I (5-20) E A flux rato of a speces n the electrode E denoted α s defned as the molar flux of speces over the molar flux of oxygen or hydrogen for the cathode or anode denoted as n, respectvely. α E n& = n& E E n (5-21) Ideally, the rate at whch water s generated, Gen n& W, at the cathode equals the molar flux of oxdsed hydrogen. The water flux n the cathode s the sum of the water flux from the anode and the water generated by the cell reacton. Therefore, the fluxes of oxdzed and reduced speces as well as water fluxes can be related as; I = n& C 1 A 1 C 1 Gen n& W H = 2n& O = n& W = A 1+αW (5-22) The water flux rato n the cathode can be related to that for the anode by: C W A ( α ) α = 2 1+ (5-23) W In the model, both nlet anode and cathode gas streams have been assumed to be saturated wth water vapour at a gven humdfcaton temperature. The mole fractons of water n the anode and cathode nlet gas streams are gven by;

116 5 A PEFC Model wth Mult-Component Input 96 E IN y W = p p sat E E (5-24) The saturaton vapour pressure of water s calculated as [4]; log p sat E = T T T (5-25) When the dry nlet gases each wth a speces molar fracton of o y are humdfed wth a mole fracton of water, E IN y W, the dry mole fractons of the consttuent speces change, but ther ratos relatve to hydrogen or oxygen n the anode or cathode, respectvely, reman the same, y y o o n = y y E IN E IN n (5-26) Upon humdfcaton, the new mole fractons stll add up to unty for each electrode; y E IN W n 1 E IN + + yn = 1 y E IN = 1 (5-27) Rearrangng equaton 5-27 and substtutng t nto equaton 5-26 yelds the humdfed mole fracton of a speces after the gas s humdfed s; y E IN = y 1 o E IN ( y ) W (5-28) For a humdfed gas, the rato of molar flux equals the rato of mole fractons of dfferent speces, n& n& E IN E IN n = y y E IN E IN n (5-29) The water fluxes across the electrodes can then obtaned as;

117 5 A PEFC Model wth Mult-Component Input 97 n& E IN W = n& E IN n y o n y E IN W E IN ( 1 y ) W (5-30) and for any other speces,, n& E IN = n& E IN n y y o o n (5-31) Stochometrc ratos can be defned as the rato of the oxdant or the reductant flux n the nlet to the flux of the oxdant or reductant requred to support the current densty J; ( n A IN υ = & ) I for the anode; = ( n& ) IN ( I / 2) H to the anode s, H υ for the cathode. The nlet flux of speces O C O n& A IN = Iυ H y y o o H (5-32) and to the cathode n& C IN 1 = 2 Iυ O y y o o O (5-33) Channel Flows The nlet flux of a speces to ether anode or cathode s equal to the flux of that speces through the channel and the flux of that speces through the electrode. n & = n& + n& (5-34) E IN E CH E 1 Substtutng equaton 5-21 and equatons 5-32 and 5-33 respectvely nto equaton 5-34, gves the speces flux n the anode as; n& A CH = I υ H y y o o H A α (5-35)

118 5 A PEFC Model wth Mult-Component Input 98 and n the cathode channel as; n& C CH I = υo 2 y y o o O C α (5-36) The total flux n the channel s the sum of that for all speces ncludng water, plus the flux of any addtonal speces through the PEM from the opposte electrode (OE); n& E CH T = n& E CH W + n = 1 n& E CH + n OE = 1 n& OE 1 (5-37) In the current model, f an nert speces s assumed not to permeate the membrane, the flux A C rato of ths speces can be reduced to zero,.e., α = 0 or α = 0, whch reduces the addtonal flux from the opposte. The mole fracton of a speces n the channel can be obtaned as y E CH n& = n & E CH E CH T (5-38) Gas Transportaton n the Electrode Dffuson Layer It s expected that a gradent n mole fracton across the electrode dffuson layer for all speces exsts. Dffuson n the dffuson layers s descrbed by the Stefan-Maxwell equaton n the model, dy E dz = RT y E n& E 1 j y pd j E j n& E 1 (5-39) The speces mole fracton at the electrode to membrane nterface can be obtaned by analytcally ntegratng the equaton across the electrode usng channel mole fractons. The

119 5 A PEFC Model wth Mult-Component Input 99 pressure-dffusvty term for speces par and j n the equaton can be defned usng the Slattery-Brd equaton [15], pd j = a T T c, j b 5 ( M ) 1 2 ( P ) 2 3 ( T ) 6 j c, j c, j (5-40) where M M M j j = 2 1. c, j ( Tc, Tc, j ) 2 M + M j T = and ( p p ) 1/ 2 p = are the crtcal propertes of c, j c, c, j the consttuent speces. In ths model,. the pressure-dffusvty product s modfed smply by the Bruggeman correcton factor to account for the porosty and tortuosty of the electrodes n the model [4] Gas Transportaton n the Membrane To smulate a gas speces permeatng through the membrane, t s assumed that a dffusve flux of the speces across the membrane s drven by a concentraton gradent and therefore modelled usng Fck s law of dffuson [16]. Carbon monoxde can have a serous degradaton effect on the catalyst n an electrode. Its flux s smulated n the model usng the bnary dffusvty DCO H 2O of carbon monoxde and water vapour. Applyng equaton 5-21 to Fck s law, the flux rato of carbon monoxde to hydrogen n the anode s gven as; α A CO pd = CO H O 1 2 A RT n& H 2 y CO (5-41) A The varable α CO s also refned va teraton. The correct value s obtaned when the carbon monoxde mole fracton at cathode to membrane nterface calculated from membrane sde usng equaton 5-41 equals the carbon monoxde mole fracton calculated from cathode sde usng equaton 5-39.

120 5 A PEFC Model wth Mult-Component Input Sem-emprcal Carbon Monoxde Degradaton Effect Although t has receved lttle attenton, carbon moxde s known to permeate through the membrane and to consequently degrade the performance of the cathode catalyst layer [13]. Usng the model of carbon monoxde transportaton n the membrane, the effect on cathode performance s smulated n the model by usng a carbon monoxde nduced degradaton factor, Θ defned as η η Θ = pure pos act, cath act, cath pure ηact, cath (5-42) where pure η act,cath s the cathodc actvaton overvoltage wth pure hydrogen, and actvaton overvoltage wth carbon monoxde contamnaton. pos η act,cath s the In a prevous expermental study by Q et al. [13], the cathode potental was measured usng three dfferent anode feeds; pure H 2, 70% H 2 30% CO 2 wth 10 ppm CO, and 70% H 2 30% CO 2 wth 50 ppm CO. The cathode potental reflects the sum of the thermodynamc equlbrum potental, the Ohmc overvoltage and the cathodc actvaton overvoltage. The thermodynamc equlbrum potental and the Ohmc overvoltage are not functons of carbon monoxde contamnaton. They can be calculated and taken away from the measured value to obtan the cathode actvaton overvoltage. The carbon monoxde nduced degradaton factor s assumed to be a lnear functon of the nterfacal carbon monoxde concentraton at any gven current densty. Ths s smply due to the fact that the expermental data covered two contamnated fuel feeds only. The frst tested fuel was pure H 2 and was only used to determne the cathodc actvaton overvoltage η pure act,cath. However, t cannot be used to determne the degradaton factor. Ths s because the carbon doxde contaned n the fuel feed could have some degradaton effect on cathode performance due to the water-gas shft reacton at the anode [17]. Such effect n the model s assumed to be constant for any gven current densty and ndependent of the carbon monoxde transport due to fuel feed carbon monoxde contamnaton. The relatonshp between the cathode-membrane nterfacal carbon monoxde concentraton and the degradaton factor was modelled as;

121 5 A PEFC Model wth Mult-Component Input 101 Θ = Θ 0 + Ηy C 2 CO (5-43) where Θ 0 s the water-gas shft nduced degradaton factor, y C 2 CO s the carbon monoxde concentraton at cathode to membrane nterface n ppm, and H s the gradent of the change n degradaton factor wth respect to the change n carbon monoxde nterfacal concentraton. The gradent H s obtaned from the expermental data [13]. It s found to be nonlnear wth respect to current densty as shown n Fgure 5-2. The polynomal ft of equaton 5-44 was deduced. 3 2 Η = J J J (5-44) For the straght-lne relatonshp postulated n equaton 5-43, the carbon monoxde degradaton factor attrbutable to the water-gas shft reacton Θ 0 s derved from the publshed results [13] and shown n Fgure 5-3. Agan, t s found to be non-lnear wth respect to current densty, and the polynomal ft s gven n equaton Θ = J J J J 0.11 (5-45) 0 + Fgure 5-2 Thrd-order polynomal dependence of H on current densty, J

122 5 A PEFC Model wth Mult-Component Input 102 Fgure 5-3 Fourth-order polynomal dependence of Θ 0 on current densty, J The total actvaton overvoltage gven by equaton 5-1 ncludes both anode and cathode actvaton overvoltage, and cannot be decomposed nto ndvdual contrbutons. As such, the Tafel equaton gven by equaton 5-46 was employed to solely smulate the cathode actvaton overvoltage wth a pure H 2 fuel feed, as derved n Chapter 4; pure RT J 0 η act, cath = ln αnf J (5-46) where the exchange current densty J 0 was estmated to be 0.8 ma/cm 2 for the cell from the expermental data obtaned by Q et al. [13]. For a 70% H 2 30% CO 2 pre-humdfed fuel feed wth any level of carbon monoxde contamnaton, the cathodc actvaton overvoltage s; ( ) pos pure η = η 1+ Θ (5-47) act, cath act, cath

123 5 A PEFC Model wth Mult-Component Input Results and Dscussons Overvoltage Fgure 5-4 shows a comparson of calculated cell voltage at varyng current densty wth publshed expermental results obtaned from the Ballard Mark IV [5]. The cell condtons durng test and the nputs nto the model were as follow; ar wth 21% of O 2 and 79% of N 2, pure hydrogen fuel supply, 70 C operatng temperature, and 310 kpa operaton pressure. The dffusvty correcton factor was set to 0.3 and the thckness of both electrodes were set to 250 µm. Oxygen stochometry was set to 1.75, and hydrogen stochometry set to 1.3. The membrane thckness was 180 µm, whle the dry membrane densty was assumed to be 1.98 g/cm 3, and ts equvalent weght 1100 g/mol. The actve cell area was taken to be cm 2. The results show that the model predcton agrees well wth the expermental results. There s a slght overpredcton at 0.4 and 0.5 A/cm 2 whch could be due to mass transport lmts caused by lqud water accumulaton, whch s not covered n the current model. Fgure 5-4 Smulated and measured fuel cell performance at 70 C Fgure 5-5 shows the measured and calculated effects of varyng oxygen composton from 21% to 46% and 100% on the cell voltage. The results show that the cell voltage decreases as oxygen composton reduces. Ths s because the actvaton overvoltage, whch s domnated by cell operaton temperature, current densty and oxygen concentraton at the

124 5 A PEFC Model wth Mult-Component Input 104 membrane to cathode nterface, decreases as the avalablty of oxygen n the supply ncreases. Such effect has been ncluded n equaton 5-1. Fgure 5-5 Effect of varyng oxygen composton on the fuel cell performance Fgure 5-6 shows the measured and calculated effects of dfferent cell operaton temperatures on the cell voltage as a functon of current densty. The fgure shows that the cell voltage ncreases wth temperature. The reason of such ncrease s largely due to the fact that both cell nternal electrc resstance and actvaton overvoltage are dependant on cell operaton temperature as shown n equaton 5-1 and 5-4, respectvely. As cell operaton temperature ncreases, both the nternal resstance and the actvaton overvoltage decrease. Fgure 5-6 Effects of varyng temperature on the fuel cell performance; 55 C (328 K), 70 C (343 K) and 85 C (358 K)

125 5 A PEFC Model wth Mult-Component Input 105 There s a notceable dscrepancy between smulated and measured results at the operaton temperature of 85 C; the smulated cell voltage s lower than the measured value. Ths may be due to the fact that a saturated nlet gas has been used n the model whle durng the test, the same condton may have been dffcult to mantan at the hgh humdfyng temperature [18]. The saturaton, hence the relatve humdty, has a sgnfcant nfluence towards nterfacal oxygen mole fractons and cell actvaton overvoltage. Fgure 5-7 shows the smulated nterfacal oxygen mole fractons wth 50% and 100% of saturatng vapour pressure at 85 C n the cathode nlet stream. It shows that the oxygen molar fracton at the cathode to membrane nterface ncreases as humdty decreases. Fgure 5-8 shows the calculated actvaton overvoltage as a functon of current densty wth 50% and 100% of saturaton pressure acheved at 85 C. The fgure shows that the absolute value of cell actvaton overvoltage ncreases as humdfcaton ncreases. In other words, the effect of less humdfcaton s to decrease the mpact of actvaton overvoltage on the thermodynamc cell voltage. It s consequently possble to compare the smulated cell voltage under ths condton to that obtaned from test. Fgure 5-9 shows the comparson between the measured and the recalculated overvoltage curve. Compared to the dscrepancy n the prevous result shown n Fgure 5-6, the agreement at 50% saturaton vapour pressure s notceably better. Fgure 5-7 Interfacal oxygen mole fractons wth 50% and 100% saturaton at 85 C (358 K)

126 5 A PEFC Model wth Mult-Component Input 106 Fgure 5-8 Actvaton overvoltage wth 50% and 100% of saturaton at 85 C (358 K) Fgure 5-9 Effect of oxygen mole fracton on the fuel cell voltage Fgure 5-10 shows the effects of varyng hydrogen composton, 65%, 81% and 100% on cell voltage. Smlar to the effect of oxygen varaton, the cell voltage decreases wth hydrogen composton. Ths s due to two reasons. Frst, the thermodynamc equlbrum potental s modelled as a drectly proportonal functon of the square of the hydrogen partal pressure. Correspondngly, any ncrease n the hydrogen nlet composton results n an ncrease of the thermodynamc equlbrum. Ths s because the hydrogen mole fracton gradent s postve through the electrode thckness leadng to hgher nterfacal values.

127 5 A PEFC Model wth Mult-Component Input 107 Fgure 5-10 Effects of varyng hydrogen composton on the fuel cell performance As dscussed n the precedng chapter, the total actvaton overvoltage s largely charactersed by the cathodc oxygen reducton whch s slower than the anodc hydrogen oxdaton process. The relatve nsgnfcance of the anodc actvaton overvoltage due to fast electrode knetcs verfes the assumpton of a constant anodc actvaton overvoltage, as mpled n equaton 5-1 for the current densty range of nterest n Fgure 5-8. As such, an ncrease n the nterracal hydrogen partal pressure nduces no change n calculatons from equaton Mult-Component Dffuson Expermental research on transent performance publshed by Moore et al. [20] ndcated that atmospherc concentratons of contamnant gases can degrade the cell performance. Fgure 5-11 shows the calculated cathode to membrane nterfacal mole fractons at varyng current densty when the cathode nlet s suppled wth dry atmospherc ar whch contans O 2, N 2, Ar, CO 2, Ne, He, Kr, CH 4, H 2, and N 2 O. It shows that the multcomponent dffuson model has the potental to take any number of chemcal consttuents n the atmosphere nto account smultaneously.

128 5 A PEFC Model wth Mult-Component Input 108 Fgure 5-11 Interfacal ar consttuent mole fractons at cathode-membrane nterface CO Crossover and Contamnaton Fgure 5-12 shows the calculated cathode potental for fuel feeds wth dfferent nlet carbon monoxde concentratons and the expermental results obtaned by Q et al. [13]. Both expermental and smulated results were based on a thn 25 µm PEM. The anode catalyst was a platnum-ruthenum alloy appled wth a loadng of 0.6 mg/cm 2. The cathode catalyst was pure platnum appled wth a loadng of 0.4 mg/cm 2. The smulated and measured results agree well wth pre-humdfed fuel feeds of pure H 2, H 2 mxed wth 30% CO 2 and 10 ppm CO, and 50 ppm CO. Model predctons wth hgh CO concentratons n the fuel feed are also presented n the fgure. The cathode s suppled wth pre-humdfed ar contanng 21% O 2 and 79% N 2. It shows the sgnfcant losses on the cathode potental wth fuel feeds contamnated wth hgh carbon monoxde concentratons. Fgure 5-13 shows the flux rato of CO to the H 2 across the anode and PEM and current densty. The results show that the flux rato profle ncreases for all current denstes wth ncreasng carbon monoxde content n the nlet gas. Ths ncreases the nterfacal carbon monoxde concentraton at the cathode-membrane nterface and results n the greater actvaton losses observed n Fgure In general, each curve n Fgure 5-13 shows that the CO to H 2 flux rato decreases wth ncreasng current densty.

129 5 A PEFC Model wth Mult-Component Input 109 Fgure 5-12 CO crossover effects on cathode potental; lne: smulated; ( ) 0 ppm, measured; ( ) 10 ppm, measured; ( ) 50 ppm, measured. For uncontamnated feeds, the pre-humdfed anode supply s neat H 2. For contamnated feeds, the pre-humdfed anode supply s 30% CO 2 /70% H 2. Fgure 5-13 CO to H 2 flux rato for nlet fuel feed CO concentratons of 10 ppm, 50 ppm and 100 ppm. The expermental results obtaned by Q et al. [13] showed that the anode overvoltage was lnear and relatvely small n relaton to the cathode potental. The cathode potental therefore closely characterses the cell potental. Oetjen et al. 2[18], for example, nvestgated the effect of carbon monoxde posonng on the overall cell potental wth H 2 feeds contamnated up to 250 ppm of carbon monoxde. The expermental results for an anode loaded wth platnum-ruthenum catalyst exhbted the smlar lnear current densty to

130 5 A PEFC Model wth Mult-Component Input 110 overvoltage relatonshps above 0.2 A/cm 2 as those presented n Fgure However, the overvoltages predcted by the model n Fgure 5-12 are generally lower than the expermental results of Oetjen et al. Ths may partally be attrbuted to the dfferences n catalytc loadng, fuel feed and oxdant supply. The cathode and anode catalysts loadngs were 1 mg/cm 2 of pure platnum and platnum-ruthenum, respectvely. Ths s 150% and 67% hgher than the catalyst loadngs used n the experments and cted by the model. In addton, Oetjen [2] et al. dd not use fuel feeds contanng carbon doxde, and the cathode feed was pure oxygen. Both condtons would serve to ncrease the avalablty of hydrogen and oxygen at the anode and cathode catalyst stes, and therefore reduce the actvaton overvoltages. 5.5 Conclusons A one-dmensonal steady-state, low temperature, sothermal, sobarc PEFC model has been developed and appled n ths chapter. The model accommodates mult-component dffuson n the porous electrodes and therefore offers the potental to further nvestgate effects of mult-component transport on cell performance. In ths model: channel flows were determned usng mass balance and algebrac manpulaton and derved from predefned ntal nlet condtons. electrode fluxes are determned by hydrogen oxdaton and oxygen reducton wth zero reactant crossover. gas dffuson through the electrodes s modelled usng the Stefan-Maxwell equaton. catalyst layers were consdered as fne dsperson of platnum and platnumruthenum at the cathode-membrane and anode-membrane nterfaces. electrode knetcs have been descrbed usng the Butler-Volmer equaton. It s assumed that oxygen reducton and hydrogen chemsorpton are the rate controllng steps for actvaton [15]. membrane transportaton n the model consdered the water flux n the membrane due to both dffuson and electro-osmotc drag due to proton mgraton based on the dlute soluton treatment proposed by Sprnger et al. [4]. sem-emprcal expressons for actvaton and Ohmc losses developed by Amphlett et al. [5] have been adopted n the model to smulate the overvoltages.

131 5 A PEFC Model wth Mult-Component Input 111 expermental results publshed by Q et al. [13] were used to determne the change n cathodc actvaton overvoltage wth carbon monoxde crossover across the membrane. The smulated results agree well wth expermental results of the Ballard Mark IV fuel cell obtaned by Amphlett et al. Model predctons for fuel feeds contamnated wth carbon monoxde agree well wth expermental results of Q et al. [13]. The smulated results also showed that the current mult-component PEFC model has the potental to take all chemcal consttuents n the atmosphere nto account smultaneously. The composton of the mult-component gases n each channel can be calculated based on the humdfcaton temperature and the magntude of the cross-flow that occurs wthn the cell. The theoretcal framework s at present lmted to smulatng sobarc and sothermal condtons n a fuel cell. Transport equatons based on concentrated soluton theory and dlute soluton theory are selectvely appled n order to determne the dstrbuton of speces wthn the dfferent layers of the PEFC. The next step s to focus on the fundamental modellng theory for electrochemcal transport and attempt to demonstrate a common approach to characterse mult-component flows through the dfferent layers of a PEFC. It s acknowledged that lqud water transport has not been systematcally consdered n the theoretcal treatment thus far, but wll be addressed later on n the thess. 5.6 References 1 Fuller TF, Newman J. Water and Thermal Management n Sold-Polymer-Electrolyte Fuel Cells. J. Electrochem. Soc., 1993, 140, Bernard DM, Verbrugge MW. Mathematcal Model of a Gas-Dffuson Electrode Bonded to a Polymer Electrolyte. AIChE J., 1991, 37, Bernard DM, Verbrugge MW. A Mathematcal Model of the Sold-Polymer-Electrolyte Fuel Cell. J. Electrochem. Soc., 1992, 139, Sprnger TE, Zawodznks TA, Gottesfeld S. Polymer Electrolyte Fuel Cell Model. J. Electrochem. Soc., 1991, 138, Amphlett JC, Baumert RM, Mann RF, Peppley BA, Roberge PR, Harrs TJ. Performance Modelng of the Ballard Mark IV Sold Polymer Electrolyte Fuel Cell. J. Electrochem. Soc., 1995, 142, 1-8

132 5 A PEFC Model wth Mult-Component Input Y JS, Nguyen TV. Multcomponent Transport n Porous Electrodes of Polymer electrolyte fuel cells Usng the Interdgtated Gas Dstrbutors. J. Electrochem. Soc., 1999, 146(1), Bradean R, Promslow K. Transport Phenomena n the Porous Cathode of a Polymer electrolyte fuel cell. Numer. Heat Transfer, 2002, Part A (42), Dhar HP, Chrstner LG, Kush AK, Maru HC. Performance Study of Fuel Cell Pt-on-C Anode n Presence of CO and CO2, and calculaton of Adsorpton Parameters for CO. J. Electrochem. Soc., 1986, 133(8), Vogel W, Lundqust L, Ross P, Stonehart P. The Rate Controllng Step for Electrochemcal Oxdaton of Hydrogen on Pt n Acd and Posonng of the Reacton by CO. Electrochm. Acta, 1975, 20, Wang J-T, Savnell RF. Smulaton Studes on the Fuel Electrode of a H2-O2 Electrolyte Fuel Cell. Electrochm. Acta, 1992, 37(15), Sprnger TE, Rockward T, Zawonznsk TA, Gottesfeld S. Model for polymer Electrolyte Fuel Cell Operaton on Reformate Feed. J. Electrochem. Soc., 2001, 148(1), A11-A23 12 Lu P, Logadottr A, Nørskov JK. Modellng the electro-oxdaton of CO and H2/CO on Pt, Ru, PtRu and Pt3Sn. Electrochm. Acta, 2003, 48, Q Z, He C, Kaufman A. Effect of CO n the Anode Fuel on the Performance of PEM Fuel Cell Anode. J. Power Sources, 2002, 111, Newman J. Electrochemcal Systems, 1991 (Prentce Hall, Englewood Clffs) 15 Slattery JC, Brd RB. Calculaton of the Dffuson Coeffcent of Dlute Gases and of the Self-dffuson Coeffcent of Dense Gases. AIChE J., 1958, 4, Cunnngham RE, Wllams RJJ. Dffuson n Gases and Porous Meda, 1980 (Plenum Press) 17 de Brujn FA, Papageorgopoulos DC, Stters EF, Janssen GJM. The nfluence of carbon doxde on PEM fuel cell anodes. J. Power Sources, 2002, 110, Oetjen H-F, Schmdt VM, Stmmng U, Trla F. Performance Data of a Polymer electrolyte fuel cell Usng H2/CO as Fuel Gas. J. Electrochem. Soc., 1996, 143(12), Davs M W. Development and evaluaton of a test apparatus for fuel cells. M.Sc. thess, Vrgna Polytechnc Insttute and State Unversty, Moore JM., Adcock PL., Lakeman B., Mepsted GO. The effects of battlefeld contamnants on PEMFC performance. J. Power Sources, 2000, 85,

133 6 A Unversal Modellng Framework from Fundamental Theory In ths chapter, a mathematcal mult-component modellng approach for PEFCs s presented based upon fundamental molecular theory. The am of ths chapter s to demonstrably reconcle the key transport equatons used by the hstorcally promnent PEFC models under a sngle smple unversal mechanstc equaton. The general transport equaton developed here as such descrbes transport n concentrated solutons wthout further assumptons and explctly accommodates mult-speces electro-osmotc drag. The objectve of the general transport equaton s to unversally smulate mult-speces transport across PFSA and other types of PEMs such as hgh-temperature polybenzmdazole (PBI) membranes, as well as non-reactve porous fuel cell materals such as the GDL and MPL. To test the developed theory, smulated results are generated usng wdely avalable relatons for lower-temperature PEFCs (< 120 C) n the lterature. Ths chapter s presented n fve parts. The ntroducton provdes a revew of the benchmark modellng phlosophes and how they have been appled for PEFC development. The second part presents the newly-developed general transport equaton from the theory of molecular transport. The thrd part establshes the drect lnks between the developed general transport equaton and the key transport equatons n the benchmark lterature. The fourth part merges the mult-component nput model descrbed n the prevous chapter and requste closure relatons wth the general transport equaton for mult-layer PEFC modellng. Fnally, the model s appled for numercal valdaton and to examne the phenomenon of hydrogen crossover. 6.1 Introducton The lterature dentfes three common modellng groups that can be classed accordng to the form of the transport equaton appled to model the membrane regon. Frst, we have the models based on the use of the Nernst-Planck equaton to descrbe the transport of hydrogen ons n the membrane. To recall, ths equaton descrbes the flux of a sngle

134 6 A Unversal Modellng Framework from Fundamental Theory 114 speces due to mgraton, dffuson and convecton. An early example of ths was n the model of Rdge et al. [1], although they excluded convectve fluxes. The most sgnfcant use of the Nernst-Planck equaton was made by Bernard and Verbrugge (BV) a few years later [2,3]. Bernard frst presented a relatvely smple study dentfyng the requred operatng condtons to acheve water balance [4]. Followng work frst focused on a 1D half-cell model comprsng of cathode dffuser, catalyst layer and membrane regon [2], and was subsequently extended to a complete 1D fuel cell model [3]. They also make use of the Nernst-Planck equaton to model dssolved hydrogen and oxygen transport n the membrane regon, and consder the effects of applyng back-pressure on the cathode sde to mantan water balance. Parallel two-phase flow was also consdered, wth the lqud-phase velocty n the membrane pores defned usng Schlogl s velocty equaton. In ther work however, they consder the membrane to be thn and assume t to be unformly hydrated. In realty, competng water transport mechansms would cause non-unformty n the water dstrbuton across the membrane regon lmtng the applcablty of ths type of model. Crossnteractons between speces are also neglected when usng the Nernst-Planck equaton. Incorporaton of structural parameters however allowed ther model to make sgnfcant predctons; they found that reactons across the cathode catalyst layer were lkely to be nonunform, mplyng that cost-savngs were possble by concentratng catalyst materal closer towards the cathode gas dffuser. The Nernst-Planck approach has been adopted by Psan et al. [5,6,7]. Intally they adopted the BV model and successfully mproved the model predctons at hgher current denstes [5]; the ntal BV models dd not predct the polarsatons at hgher current denstes caused by cathode floodng very well. Subsequent studes used the mproved BV model to analyse the effect of the porous structure of the catalyst layer on cell performance [6], and later work focused on optmsng the BV model for faster computaton by elmnatng non-lnear terms [7]. The NP-based BV models have also been adopted by Djlal et al. [8,9]. They developed the model to nclude the effects of heat transfer and ncluded Knudsen dffuson n the electrodes [8]. Ths research group then used the BV model to conduct a 3D computatonal analyss of a secton of the PEFC. Ther model and other such models allowed the effects of geometrc parameters of the gas dffuson layer on cell performance to be quantfed [9].

135 6 A Unversal Modellng Framework from Fundamental Theory 115 The publcaton of the half-cell BV model [2] concded wth the publcaton of another sgnfcant model presented by Sprnger et al. [10]. The Nernst-Planck equaton s a dervatve of Dlute Soluton Theory (DST) as shown n chapter 4. Another form of DST gven by equaton 4-13 was used by Sprnger et al. [10] who appled t to descrbe n part the transport of water across the membrane, assumng that the gradent n chemcal potental of water drves a dffusve flux of water across the membrane from cathode to anode. The commonalty between the Nernst-Planck based BV models and the Sprnger et al. models s the fact that ther key transport equatons both belong to DST. The dfference s that they both use the dervatves of DST to model the transport of dfferent prmary speces; hydrogen ons for BV and water for Sprnger et al. [10]. Sprnger et al. modfy the DST equaton such that the gradent n the chemcal potental of water s translated nto a gradent n water content per membrane charge ste, λ (.e., per sulphonc end group). The other sgnfcant dfference s the explct ncluson of electro-osmotc water drag n the model of Sprnger et al.; an extra term s appended to account for the drag of water by hydrogen ons across the membrane from anode to cathode, as shown n chapter 4. The net result s a counterdrectonal flux of dragged water and dffusng water n the membrane, settng up a nonunform water dstrbuton across the membrane thckness. Ths forms the bass of many dffuson models. In 1993, Van Nguyen and Whte adopted the model of Sprnger et al. to smulate heat and mass transfer n 2D [11], acknowledgng the counter-drectonal dffusve and drag fluxes of water across the membrane n 1D. They found that the back-dffuson of water across the cell from cathode to anode was nsuffcent to keep the membrane well hydrated and therefore optmally conductve, and consequently concluded that anode humdfcaton was necessary under certan operatng condtons. Smlar studes were conducted by Okada et al. [12]. In later work, the basc dffuson-based transport equaton 4-13 was modfed to account for a pressure-drven convectve water flux n the membrane [13]. By ths pont, the DST-derved dffuson term s reduced to Fck s law and the appended convectve term s smply Darcy s law. The resultng transport equaton can therefore be classed as beng semcomposte. Later modellng efforts by Van Nguyen et al. nvestgated the mprovements n cell performance when nterdgtated gas dstrbutors were used to separate gas channels nto nlet and ext channels and therefore to force flow though the porous electrodes [14]. Followng work focused more on mprovng the modellng of lqud water and consderng lqud water saturaton explctly [15]. These studes of Van Nguyen et al. have drectly

136 6 A Unversal Modellng Framework from Fundamental Theory 116 nfluenced cell desgn by dentfyng the regons of the cell where floodng s most lkely to occur frst. The water dffuson and drag-based transport equaton based on DST has commonly formed the bass of transent models [16,17,18]. Applcatons have attempted to address agan the ssues of thermal and water management [19]. The sem-composte approach has also been wdely used n the lterature [20,21,22,23,24]. Kulkovsky [21] n partcular consdered the non-lnear dffuson of water n the membrane, leadng to the dentfcaton of co-exstng dry and wet regons. Later work has been orentated around determnng cell performance under co- and counter-flow confguratons wth two-phase water, acknowledgng counter-flow confguratons allow for better nternal humdfcaton under certan condtons [22,23]. A few years followng the publcaton of the BV [2-4] and Sprnger et al. [10] models, Fuller and Newman presented an alternatve model that used Concentrated Soluton Theory (CST) to descrbe transport n the membrane [25]. Ths was based upon earler work where t was llustrated that a mult-component form of CST could be used to descrbe the transport of a three-speces system; water, hydrogen ons and electrolyte membrane [26]. Ther model assumed that temperature can change along the length of the gas channel and llustrated that the rate of heat removal from the cell was crtcal n preventng membrane dehydraton. A key aspect of ther work was the applcaton of CST to smultaneously model the transport of multple speces wthout decomposng the transport equaton nto ndependent consttuents, as done by the DST treatments of BV [2,3] and Sprnger et al. [10], and ther dervatves. Also, they llustrated that t was possble to model the membrane system wthout makng the assumpton that the system s dlute. The applcaton of CST for fuel cell modellng has been developed over several lnes. Janssen [27] used CST to model the effect of two-phase water transport n the electrodes on the electro-osmotc drag coeffcent n the membrane. More recently, two-phase water transport n the membrane was modelled by Weber and Newman, accountng for both lqud and vapour phase water boundary condtons for the membrane [28,29,30]. In both the work of Janssen [27] and Weber and Newman [28-30], the expanson of the key transport equatons yelds frctonal coeffcents whch account for nteractons between speces. These coeffcents are related to water-phase dependant transport propertes such as the electro-

137 6 A Unversal Modellng Framework from Fundamental Theory 117 osmotc drag coeffcent. Whle provng useful to predct the water flux n the membrane under two-phase condtons, the models are not able to predct H 2 or oxygen crossover usng CST wthout resortng to Fck s Law. Indeed, Weber and Newman [29] llustrated that Fck s law would be supermposed on to the CST-based two-phase water flux equatons to defne H 2 and O 2 permeaton through the membrane. Ths eludes the utlty of the mult-component nature of CST. Meyers and Newman [31,32,33] however mantaned the mult-component nature of CST to model the DMFC, for whch fuel crossover s a sgnfcant ssue. Other studes have also made use of CST. Wohr et al. [34] used t to develop a dynamc model wth energy balance. They suggested several ways to mprove membrane humdty as a result, ncludng rasng the humdfer temperature, ncreasng GDL porosty and GDL thckness, and fnally suggested the use of coolng plates to mprove heat removal. Futerko and Hsng appled forms of CST to model water transport n the membrane, focusng more on 2D effects [35,36]. They consdered the effect of humdty on membrane resstance [35], and operaton wthout reactant feed humdfcaton [36]. Thampan et al. [37] developed a model wth a smlar approach to Janssen [27] and Weber and Newman [29], concentratng on the conductvty of the membrane at dfferent operatng temperatures when the membrane s n contact wth water n ether lqud or vapour phase. Other sgnfcant models that do not strctly pertan to the categorsatons above are mentoned here. Ekerlng et al. [38] proposed a model based on the assumpton that water flux n the membrane s charactersed by convecton due to capllary pressure and electroosmotc drag. Key to ther model was the use of pore-sze dstrbuton data to determne local conductvty and permeablty. Meer et al. [39] also used the capllary pressure argument to propose a convectve flux of water n the membrane and attrbuted t to causng the nonunform dstrbuton of water across the membrane. Both these models make use of Darcys law to descrbe the convectve water flux. Baschuk and L [40] proposed a BV-based model that was orentated to defnng equvalent resstances throughout the thckness of the cell. Fnally we have the sem-emprcal based models of Amphlett et al. [41,42]. As dscussed, the actvaton and Ohmc overvoltages are defned ntally n these models on a theoretcal bass, wth characterstc constants grouped and defned usng expermental data. These models focus squarely on producng performance curves and exhbt generally good correlaton wth expermental data. These models provde quck cell performance predctons wthout applyng a systematc treatment of cell-level transport phenomenon.

138 6 A Unversal Modellng Framework from Fundamental Theory 118 The above s by no means an exhaustve lst of modellng efforts, but ams to dentfy the Nernst-Planck based BV approach [2,3], the dffuson-based approach of Sprnger et al. [10] and the CST-based approach of Newman et al. [25, 26, 28-33]. Further dscussons nto modellng approaches are gven by Weber and Newman [43] and Wang [44]. The purpose of ths work s to llustrate that all these three promnent modellng approaches can be related by a mult-speces general transport equaton, whch can be appled to the layers of the PEFC to descrbe electrochemcal transport. In ths chapter, a general transport equaton s derved and ts valdty s demonstrated by dervng all three key transport equatons n lterature (Dlute Soluton-based Nernst-Planck, Dlute Soluton-based dffuson equaton and Concentrated Soluton Theory). The general transport equaton s then appled to a smple PEFC model. Calculated water content curves obtaned usng the general transport equaton are compared to publshed data. Fnally, the mult-speces aspect of the model s used to predct hydrogen crossover through the membrane. 6.2 Theoretcal Study Drvng Force Equaton The common form of Concentrated Soluton Theory can be traced back to the work of Hrschfelder et al. [45]. The total drvng force of a general speces was defned as d n m 1 1 (6-1) = Λ p + n j X j nt kt ρ ρ j where n m n T k T = molecular concentraton of speces = molecular mass of speces = total molecular concentraton = Boltzman constant = local temperature

139 6 A Unversal Modellng Framework from Fundamental Theory 119 ρ Λ = total densty = dffusve flux affnty X j = general molecular force actng on speces j. The frst term n the bracket of equaton 6-1 reflects the flux due to dffuson; the second reflects convectve flux due to a gradent n total pressure; the fnal term reflects the nteractve flux that s nduced because of external felds actng upon the other speces n the mult-speces system. Hrschfelder et al. [45] suggested that there are three physcal contrbutors to the dffusve flux of a general speces ; a gradent n electrochemcal potental; a gradent n temperature and an addtonal general flux caused by an external feld Λ = 1 m S 1 µ + T m m X (6-2) where µ = the gradent n molecular electrochemcal potental of the general speces S = the molecular entropy of the general speces. Substtutng equaton 6-2 nto equaton 6-1 yelds d v n m m = µ + S T p X n j X nt kt ρ ρ j= 1 j (6-3) The molecular concentraton of a general speces s defned as n = N A c where c s the molar concentraton, and N A s the number of molecules per mol of substance,.e., the Avagadro Number. The total molar concentraton s defned as c = n / N and the defnton of the Boltzmann constant s k = R / N where R s the unversal gas constant. A T T A

140 6 A Unversal Modellng Framework from Fundamental Theory 120 Snce the above treatment consders partcle-level propertes, t s recast nto more convenent molar terms by usng the Avagadro number. Substtuton of these defntons nto equaton 6-3 gves the total drvng force term for a general speces ; d v c 1 M M = µ + S T p X c j X ct RT ρ ρ j= 1 j (6-4) Ths s the general drvng force equaton and accounts for the physcal condtons that drve overall ntermolecular transport ncludng effects due to a gradent n electrochemcal potental, composed of o a gradent n concentraton, and o a gradent n electrc potental an overall temperature gradent a gradent n total pressure a force nduced by an external feld Molecular and Thermal Dffuson Equaton From the same work of Hrshfelder et al. [45] t s possble to defne the general drvng force as beng the sum of the forces drvng molecular dffuson and thermal dffuson nn j nn j d = ( v j v ) + ln T 2 2 n D n D j T j j T j Th D j n jm j Th D n m (6-5) where D j v = dffuson coeffcent of speces n speces j = velocty of speces Th D = thermal dffuson coeffcent of speces.

141 6 A Unversal Modellng Framework from Fundamental Theory 121 Equaton 6-5 s converted from molecular values to molar values usng m n ρ = and A c N n =, gvng + = j Th j Th j j j T j T D D v v D c c c d ln 2 ρ ρ (6-6) The General Transport Equaton Equaton 6-4 descrbes the physcal condtons that nduce molecular transport and equaton 6-6 reflects the transport that occurs due to the physcal drvers. Equatng the two equatons gves the general transport equaton for concentrated solutons. + = + j Th j Th j j j T j v j j j T D D v v D c c c RT X c M X p M T S c ln ρ ρ ρ ρ µ (6-7) A speces wth zero valence can be affected by an external feld, for example a feld n electrc potental set up by an electrc current can cause a speces wth zero valence to be dragged by electro-osmoss due to the flux of hydrogen ons. The molar flux of a speces, n& s defned as c n = v &. When 0 = = T P, equaton 6-7 can be smplfed and rearranged to gve; j j j j j T j j T v c X c M X c RT D c c c RT D c c n + + = ρ µ & (6-8) The frst and last terms on the rght hand sde defne dffuson and convecton. The mddle term s related to electro-osmotc drag flux. When consderng the flux of water (speces ) n the electrolytc membrane (speces j) where the electrolyte experences no drag, the electro-osmotc drag flux of water equates to

142 6 A Unversal Modellng Framework from Fundamental Theory 122 & c w T n w, drag = Dw, mem cmem RT c X w (6-9) The electro-osmotc drag rato ξ s now ntroduced whch s the number of molecules of speces dragged per hydrogen on,.e., ξ = n, drag, drag n H + c = c H + (6-10) Snce the velocty wth whch water s dragged s equal to the velocty of hydrogen ons that are transported due to the electrc feld,.e., w drag = v H +, ths gves; v, n& drag =, n& ξ w =, drag w n& H + n& H + ξ (6-11a,b) Substtuton of equaton 6-11a,b nto equaton 6-9 and rearrangng provdes the general molar force n relaton to the electro-osmotc drag rato of any speces and of water as; X = ξ n& H + RT D, mem cm c c T X w = ξ n& w H + RT D w, mem cm c c T w (6-12a,b) Generally, equaton 6-12a,b can be appled equally to a mult-speces concentrated system because; t s derved from a general concentrated soluton system the electro-osmotc drag characterstcs of speces alone n the membrane s dependant only upon ts transport propertes n the membrane (accounted for by D, mem ) and the magntude of the hydrogen on flux (accounted for by H + n& ). The overall electro-osmotc drag nduced flux for a speces ncludng nteractons wth other electro-osmotcally dragged speces s accounted for by the M ρ j c j X j term n equaton 6-7. electro-osmotc drag s assumed to occur ndependently of temperature and pressure gradents

143 6 A Unversal Modellng Framework from Fundamental Theory 123 Usng the derved expresson for X, the general transport equaton, equaton 6-7, for concentrated solutons becomes + + = + + v mem j mem j j m T m H j Th j Th j j j T j D D c c RTn T D D v v D c c c RT p M T S c,,, ln ξ ρ ρ ξ ρ ρ ρ µ & (6-13) 6.3 Theoretcal Valdaton In both key dlute soluton models [2,3,10] and key concentrated soluton model [26], 1D temperature effects across the cell were neglected ( ) = 0 T. [ ] + = + v mem j mem j j m T m H j j j T j D D c c RTn v v D c c c RT p M c,,, ξ ρ ρ ξ ρ µ & (6-14) Also, none of these explctly consder the effect of the overall pressure gradent, hence 0 = p Dlute Solutons Fundamentally for a dlute soluton the concentraton of a general mnor solute speces s assumed to be sgnfcantly lower than that of the solvent speces j, j c c << and j c T c. Also, the solvent speces experences no drag, hence 0 = j ξ. By substtutng these condtons nto the equaton 6-14 the general transport equaton can be reduced to the followng for the solute speces, j H j v n c RT D n + + = + & & ξ µ, (6-15)

144 6 A Unversal Modellng Framework from Fundamental Theory 124 Ths s the key transport equaton for dlute solutons whch ncludes flux due to electroosmotc drag. Model of Sprnger et al. Sprnger et al. [10] consder the transport of water (solute speces ) n the electrolyte membrane (solvent speces j). Snce the electrolytc membrane s statc, v = 0 and the general transport equaton 6-15 can be rearranged to yeld the net water flux across the membrane m n & w D & (6-16), RT w mem = cw µ w + ξ wnh + where the frst term on the rght hand sde descrbes dffusve flux and s consstent wth equaton 19 whch appears n the work of Sprnger et al. [10]. The second term descrbes electro-osmotc drag flux and s consstent wth equaton 18 n that work. Model of Bernard and Verbrugge In the BV models [2,3], the key transport equaton s the Nernst-Planck equaton and s appled to descrbe the transport of dssolved hydrogen ons (solute speces ) n a bulk system consstng of water and electrolytc membrane (solvent speces par j) where ξ = 0. The electrochemcal potental of a speces s defned as [46] c µ = RT + zf φ c (6-17) where F s the Faraday constant, z s the valence of speces and φ s the gradent n electrc potental (V.cm -1 ). Substtuton nto the dlute soluton transport equaton (6-15) yelds the famlar Nernst-Planck equaton

145 6 A Unversal Modellng Framework from Fundamental Theory 125 D, j n & = zfc φ D, j c + v RT j (6-18) where v j becomes the pore-water velocty n the membrane, whch s defned usng Schlogl s velocty equaton v j = κ φ κ p z jc j F φ p µ µ (6-19) Here, κ φ and κ p are the electroknetc and absolute (hydraulc) permeabltes respectvely and µ s the vscosty (g.cm -1.s -1 ), not to be confused wth the electrochemcal potental and p s specfcally the hydraulc pressure gradent Concentrated Solutons Newman stated that for a three-speces system t s more rgorous to use concentrated soluton theory to descrbe transport [46]. In the treatment of Weber and Newman [29], electro-osmotc drag s mplctly absorbed nto frctonal coeffcents whch are related to the dffuson coeffcents D j. Because of ths treatment, whch s based upon assumptons of margnal currents and margnal chemcal potental gradents for water through the membrane, the explct electro-osmotc drag terms n equaton 6-14 reduce to zero ξ = 0. Consequently substtuton nto the general transport equaton 6-14 leaves the common form of CST whch s comparable to the Stefan-Maxwell equaton c µ = RT j c c c T j D j [ v v ] j (6-20)

146 6 A Unversal Modellng Framework from Fundamental Theory Model Development Governng Equatons The valdty of the general transport equaton gven by equaton 6-14 can be examned by applyng t to model mult-speces transport n 1D across the PEFC. Ths s done n the context of an sothermal model. Equaton 6-14 s appled drectly to smulate electrochemcal transport across the PEM. It s also appled to smulate transport across the GDL wthout dervng the Stefan-Maxwell equaton. In dong so, the ξ term reduces to zero as electro-osmotc drag does not occur n the GDL (all speces have zero valence). The condtons n the channels of the cell are determned by the mult-component nput model presented n the prevous chapter. The assumptons of the new model are dfferent to the prevous model n the followng aspects; 1. the membrane regon s charactersed as a concentrated soluton system wth at least three consttuent speces; water, electrolyte membrane and protons 2. the flux of any addtonal speces can be treated as part of the concentrated soluton system, wthout supermposng an ndependent flux equaton based on Fck s law 3. the dffuson coeffcent of protons n the concentrated soluton system s charactersed solely by ts dssoluton n water dffusvty n the dry membrane s zero,.e., D 0 H +, mem dffusvty n the water contaned n a humdfed membrane s non-zero and gven by the value determned by Bernard and Verbrugge [3] 5 2 D H + w = cm / s, 4. for the four speces system ncludng hydrogen, the bnary dffuson coeffcent of the speces par of protons n hydrogen n the membrane regon s neglgble, D 0 H +, H 2 5. Capllary forces n the electrodes are assumed to be neglgble and water s assumed to exst n vapour form [47]. A summary of the key equatons for the channel, electrode and membrane regons of the cell are gven n Tables 6-1, 6-2 and 6-3 respectvely. The condtons for the base case are gven n Table 6-4. The base case reflects sobarc cell operaton at 80 C where t s assumed that both ar and H 2 feeds are fully humdfed to the same temperature, wth 3-speces n the membrane system. The addtonal case gven n Table 5 reflects a 4-speces concentrated

147 6 A Unversal Modellng Framework from Fundamental Theory 127 soluton system wth the addton of hydrogen crossover. The D, dffuson coeffcents mem should be regarded as the ntra-dffuson coeffcent of speces n the membrane. For the four component system, t s assumed that hydrogen crossover leads to the formaton of addtonal water at the cathode catalyst ste. Such reacton would produce only heat energy, and not both heat and electrcal energy. From a transport perspectve, the magntude of water and oxygen fluxes n the cathode ncreases, whch n the model s reflected by changes n the cathode flux ratos C A α ; α 2( 1+ α + α ) C = and w w H 2, X C A α O = 1+ α H 2X. Smlarly, the hydrogen flux n the anode ncreases α H = 1+ α 2 H 2X. To valdate the model aganst expermental data, calculated hydrogen permeablty coeffcents for a four-speces system are compared to calculatons based on n-stu measurements of hydrogen crossover. The H 2 permeablty coeffcents can be calculated as ψ perm H 2 = I t H 2, X mem CH A ph 2 (6-21) where the flux rate of hydrogen crossover s calculated as I H 2, X = Jα H 2, X 2F (6-22) Speces flux n channel (mol/cm 2 -s) Speces flux through electrode (mol/cm 2 -s) Total channel flux (mol/cm 2 -s) n & n & E CH E = n& E E n E IN n& E 1 = α n& anode: n& A 1 H = I n E CH E CH n& total = n& = 1 Channel mole fracton E CH E CH n& (-) y = E CH n & Channel concentraton (mol/cm 3 ) c E CH total p E CH = y - RT 1 cathode: n C & O = I 2 Table 6-1 Governng equatons for channel model based on the mult-component nput model n chapter 5

148 6 A Unversal Modellng Framework from Fundamental Theory 128 Transport Equaton Total concentraton (mol/cm 3 ) Total pressure (Pa) Pressure-Dffusvty product (Pa-cm 2 /s) M c µ p = RT ρ c T = c j 1 c D T j [ c n& c n& ] p = c RT - pd j T = a T T c, j Table 6-2 Governng equatons for electrode model b 3 / 2 ( M ) 1 2 ( P ) 2 3 ( T ) 5 6 ε j c, j j j c, j Reference Equaton [10], [48] Transport Equaton Molar Volume (cm 3 /mol) Total Concentraton (mol/cm 3 ) Partal molar volume of dry membrane (cm 3 /mol) M c µ p = RT ρ j c + RTn& c c T H + j D j c c m T [ v v ] j ξ D, m ρ ρ v ξ D j, mem j, m V = V mem + λv [29] w c V 1 - = + T c V w, mem m EW = ρ mem, dry j Reference Equaton 6-14 [29] Water content per charge ste (-) Water volume fracton n λvw membrane f v = V (-) mem + λvw Expanded membrane thckness (µm) λ = c w V - mem t mem = t mem, dry λv Vm Table 6-3 Governng equatons for membrane model w [29] [29]

149 6 A Unversal Modellng Framework from Fundamental Theory 129 Temperatures (K) PEM Equvalent Weght (mol/equv) Dry PEM densty (g/cm 3 ) Dffusvtes (cm 2 /s) sat sat TA = TC = Tcell = 353K [10] EW = 1155 [10] ρ m, dry = 1.98 D w, mem = 10 6 D w, H + = D H +, mem = 0 Electro-osmotc drag rato 2.5 (-) ξw = λ 22 = 0 Dry PEM thckness (µm) Temperature gradent (K/cm) Appled pressure gradent (Pa/cm) Channel pressures ξ m ξ H + = 0 exp T 2 3 ( λ λ λ ) 5 Reference [10] [3] - [10] t = 175 [10] m T = 0 - p = 0 - A CH C CH p = p = kPa [10] Table 6-4 Propertes for base-case 3-speces (water, electrolyte membrane, protons) concentrated soluton membrane system - - Hydrogen dffusvtes (cm 2 /s) D D D H 2, m H2, w = H2, H ( f ) exp R v T = p = 0 1 T Electro-osmotc drag rato ξ = H Channel pressures (Fg. 3) (Fg. 4, 5) Reference [29], [10] [29] - A CH C CH p = p = kPa [53] p = p = kPa A CH C CH - Table 6-5 Addtonal propertes for 4-speces (water, electrolyte membrane, protons, hydrogen) concentrated soluton membrane system

150 6 A Unversal Modellng Framework from Fundamental Theory Soluton Procedure The dagram below llustrates the soluton procedure appled to the overall model for the 4-speces concentrated soluton system n the membrane regon. In the case of the 3- speces system, the procedure s smplfed as α H does not need to be determned. Each 2 teratve step s repeated fve tmes n order to determne the correct thckness of the expanded membrane. The dfferental transport equatons n the three regons of the cell are solved usng a Runge-Kutta algorthm. Fgure 6-1 Smulaton Flowchart

151 6 A Unversal Modellng Framework from Fundamental Theory Results and Dscussons Model Valdaton Model-to-Model Valdaton: 3-Speces System The valdty of the mult-speces unversal transport equaton can be tested by comparng smulated water content curves for a 3-speces concentrated soluton to exstng publshed results. Formaton of water at the cathode sets up a concentraton gradent across the membrane, allowng for molecular transport from cathode to anode. Ths s opposed by an electro-osmotc drag flux of water from anode to cathode. Because the electro-osmotc drag flux s drectly proportonal to current densty, the water content at lower current denstes s much more unform. Ths was llustrated by Sprnger et al. [10]. Although ther work only consdered the flux of water n a dlute soluton, the mult-speces model presented here for concentrated solutons should prncpally predct the same phenomenon. Fgure 6-2 shows smulated water content curves usng equaton 6-14 for the base condton at four dfferent current denstes. The model predcts a relatvely unform water dstrbuton at 0.1 A/cm 2, wth a lnear fall n water content from 14 molecules per charge ste to 11 molecules per charge ste. At 0.8 A/cm 2, the water content profle becomes non-lnear. At ths current densty the cathode has 14.8 water molecules per charge ste whereas the anode s much drer wth less than 3 molecules per charge ste. The water content characterstcs are generally consstent wth the publshed results of Sprnger et al. [10]. The concentrated soluton theory based approach of equaton 6-14 suggests larger gradents n water content than the dluton soluton theory approach of equaton 6-15 at hgher current denstes ( > 0.2 A/cm 2 ). The dfference s due to the dlute soluton theory assumpton that the concentraton of any mnor speces s much less than that of the solute. As a consequence, a c c factor s mssng n the key equaton 6-15 for dlute j T solutons and assumed to be unty, whereas for concentrated solutons t would be less than unty. The effect s to reduce the domnance of c n the context of equaton 6-15 partcularly

152 6 A Unversal Modellng Framework from Fundamental Theory 132 at low water contents (λ < 6), thereby reducng the overall water content throughout the membrane at any poston. Overall Fgure 6-2 llustrates that the new approach correctly predcts the expected water content profles at varous current denstes. Fgure 6-2 Model-to-model valdaton: smulated membrane water content from the general transport equaton (6-14), and from the work of Sprnger et al. [10] Model-to-Measurement Valdaton: 4-Speces System The data of Cheng et al. [49] s employed n order to valdate the model aganst expermental data. They measured the hydrogen crossover rate n a 4.4 cm 2 expermental fuel cell employng a 50 µm thck PEM operated wth fully humdfed reactant supples as 80, 100 and 120 C and anode back-pressures of 2.02 atm and 3.04 atm. In ther work, the hydrogen permeablty coeffcent s calculated usng equaton 6-21 where the crossover current I x s determned drectly from the measurement. In the current work, the coeffcent s calculated usng equatons 6-21 and Ths s fundamentally smlar to that employed by Cheng et al, but modfed to be a functon of the hydrogen crossover rato, whch s determned by the smulaton. The hydrogen partal pressure can be calculated as a functon of the anode back-pressure usng; p CH A H2 p = p IN A H2 IN A total IN A ptotal + p 2 back pressure (6-23)

153 6 A Unversal Modellng Framework from Fundamental Theory 133 The data n Table 6-6 compares the calculated hydrogen permeablty coeffcents obtaned from the general transport equaton to the expermental data [49]. Hydrogen dffusvtes used n the calculaton are gven n Table 6-5. The calculated hydrogen permeablty coeffcents are generally wthn the same order of magntude as the expermentally-derved values. Table 1 demonstrates that the hydrogen permeablty coeffcent ncreases wth ncreasng humdfcaton temperature. Ths observaton can be confrmed from the work reported prevously by Weber et al. [29]; ther data ft suggests that for a PEM wth a water volume fracton of 50%, rasng the cell temperature from 80 to 120 C wll have the effect of ncreasng the hydrogen permeablty coeffcent from to mol/cm-atm-s. Humdfcaton Temperature ( C) Hydrogen Permeablty Coeffcent (mol/cm-atm-s) Anode back-pressure 3.04 atm 2.02 atm 80 Cheng et al 3.87E E-11 General Transport Equaton 1.91E E Cheng et al 6.13E E-11 General Transport Equaton 1.90E E Cheng et al 1.04E E-10 General Transport Equaton 1.36E E-10 Table 6-6 Expermental [49] and smulated hydrogen permeablty coeffcents for a 50 µm polymer electrolyte membrane Hydrogen Crossover: 4-Speces System The use of thnner membranes n fuel cells can allow for better performance because the unformty n water content s mproved at all current denstes. Ths owes to the shorter molecular transport path for water from cathode to anode and has the overall effect of ncreasng the proton conductvty of the membrane regon [10,50]. Wth better nternal humdfcaton, the need to provde external humdfcaton especally through the anode sde can be somewhat mtgated [51]. On the same prncpal however, the shorter transport path exacerbates the phenomenon of crossover across the membrane. Due to ts small molecular

154 6 A Unversal Modellng Framework from Fundamental Theory 134 dameter, hydrogen crossover s specfcally an mportant ssue n PEFCs. In general such crossover can be mpeded by usng thcker membranes [52]. The ncrease n crossover for thnner membranes amounts to unutlsed fuel and so reduces the overall cell effcency. The unused fuel corresponds to an equvalent crossover current densty, and the target for future fuel cell vehcles for ths s 5 ma/cm 2 or less at 1 atm [53]. To model crossover through the membrane, the condtons of Table 6-5 were appled n addton to the base condtons of Table 6-4 to smulate a four-component concentrated soluton system n the membrane regon. In the absence of sutable data n the lterature, t was assumed that the electro-osmotc drag of hydrogen s neglgble. Fgures 6-3 and 6-4 show the relatonshp between membrane thckness and the net flux rato of hydrogen across the membrane to oxdsed hydrogen at 1 A/cm 2 for 80 C and 110 C; 1 A/cm 2 s chosen because t s a typcal operaton pont on the performance curve, and allows for easy translaton nto an equvalent current densty and J = 2FI. Hence, A H 2 X I X A α H X I, J X = 2FI X = 2 α should be or less at 1 A/cm 2 when operated at 1 atm. Fgure 6-3 consders the crossover for dfferent thckness at 1 atm. Large stacks ( 10kW) are lkely to operate at hgher pressures, and ths s consdered n Fgures 6-4 and 6-5. Fgure 6-3 llustrates that the flux rato drops below (crossover current densty of 5 ma/cm 2 ) for membranes thcker than around 30 µm. The flux rato can be reduced further below (1 ma/cm 2 ) for membranes thcker than 175 µm. Fgure 6-4 shows the crossover for dfferent membrane thcknesses when the cell s operated at 3 atm. For a cell operated at 80 C, the results show that an ncrease n thckness from 25 µm to 50 µm yelds a 60% drop n the net hydrogen crossover flux rato and s equvalent to a reducton n the crossover current densty of 21.2 ma/cm 2. Increasng the thckness further by a factor of 3.5 from 50 µm to 175 µm yelds a 72% drop n the net hydrogen crossover flux rato, but the magntude of the drop n the crossover current densty s less, at 10.3 ma/cm 2. The results also show that for the gven base condtons, the crossover current densty only drops below 5 ma/cm 2 above 150 µm for operaton at 80 C.

155 6 A Unversal Modellng Framework from Fundamental Theory 135 Fgure 6-3 Crossover dependence on dry membrane thckness at 1 atm Rasng the operatng temperature to 110 C at the same nlet pressures of 3 atm nduces an ncrease n crossover. The ncrease s relatvely small for the thn 25 µm membrane at 7% and ncreases to 32% for a 225 µm membrane. The ncrease n crossover wth temperature can be attrbuted to the dependence of the hydrogen dffuson coeffcent on temperature. When f v = 0. 5 n the membrane regon, H mem D 2, cm / s at 80 C to cm / s at 110 C and H W D 2, ncreases from ncreases from cm 2 /s at 353K to cm 2 /s at 110 C. Due to the ncrease n H 2 crossover wth temperature, the crossover current densty only falls below 5 ma/cm 2 when the thckness exceeds 175 µm. Fgure 6-4 H 2 Crossover dependence on dry membrane thckness at 3 atm at 80 C (353 K) and 110 C (383 K)

156 6 A Unversal Modellng Framework from Fundamental Theory 136 Fgure 6-5 consders the crossover at all practcal current denstes for three typcal membrane thcknesses. In general, operaton at low current denstes nduces a hgh rate of hydrogen crossover. As current densty ncreases, the crossover rate decays for all three membrane thcknesses consdered. A smlar phenomenon was observed n the prevous chapter for carbon monoxde crossover through the membrane. The thnner membranes exhbt consstently hgher H 2 crossover wth respect to current densty. The H 2 flux rato drops below 0.05 after 80 ma/cm 2 for the 175 µm membrane, 150 ma/cm 2 for the 100 µm membrane and 300 ma/cm 2 for the 50 µm membrane. At 1 A/cm 2, the 175 µm membrane exhbts a reducton n the flux rato below The 100 µm membrane s stll allowng a hydrogen crossover rato of and the 50 µm membrane allows double that at Conclusons The lterature dentfes three promnent equatons to model electrochemcal transport across the cell; the Nernst-Planck equaton [2,3]; the dffuson equaton n terms of chemcal potental wth an appended term for electro-osmotc drag [10]; and the Stefan-Maxwell type equaton from Concentrated Soluton Theory [25,26]. The frst two pertan to Dlute Soluton Fgure 6-5 H 2 Crossover as functon of current densty for PEM thcknesses of 50, 100 and 175 µm

157 6 A Unversal Modellng Framework from Fundamental Theory 137 Theory and are generally applcable for a solute speces when ts concentraton s assumed to be much less than the solvent concentraton. The thrd drectly pertans to Concentrated Soluton Theory. Usng foundng prncpals presented by Hrschfelder et al. [45], a general transport equaton for concentrated solutons has been developed n ths work whch ncludes a term for flux due to external felds. In the context of a fuel cell membrane, t s argued that t s a feld n electrc potental whch causes electro-osmotc drag of consttuent speces wth zero valence due to the hydrogen on flux that occurs across t. Relatve to a consttuent speces wth zero valence, the feld n electrc potental s effectvely an external feld, and on ths bass s ncluded n the general transport equaton to model mult-speces electro-osmotc drag. Theoretcal valdaton has shown that the developed expresson s consstent wth all three exstng key transport equatons. Ths proves that the developed general transport equaton can be reduced to the two forms of Dlute Soluton Theory (Nernst-Planck equaton [2,3] and the dffuson equaton wth explct electro-osmotc drag [26]) for fuel cell membrane systems, and to the Stefan-Maxwell form of Concentrated Soluton Theory [25,26]. Thus, the work n ths chapter s the frst to brdge the gap that exsts between the dfferent modellng phlosophes for transport n the lterature. In the context of a smple fuel cell model, the calculated results usng the general transport equaton for a three-speces system (water, electrolyte membrane, protons) correctly predcts water content profles that are consstent wth publshed data. The calculated results predct that the water content s margnally less usng the developed general transport equaton n comparson to the results of Sprnger et al. obtaned from Dlute Soluton Theory [10]. Ths s attrbuted to the dlute soluton assumpton that cmem ct. Overall, the consstency wth the publshed data shows that the general transport equaton correctly predcts the molecular transport of water ncludng electro-osmotc drag flux. Calculated results for a smple 1D fuel cell wth a four-component concentrated soluton membrane system (water, electrolyte membrane, protons, hydrogen) gve mportant

158 6 A Unversal Modellng Framework from Fundamental Theory 138 results n relaton to the crossover of hydrogen across the PEM. The general trend shows an ncrease n crossover for thnner membranes, and for a fxed membrane thckness a hgher crossover at lower current denstes. The results show at 80 C, 1 atm and 1 A/cm 2, the nomnal membrane thckness for less than 5 ma/cm 2 equvalent crossover current densty s 30 µm. At 3 atm and 80 C, the nomnal membrane thckness for the same equvalent crossover current densty s about 150 µm, and ncreases further to 175 µm at 110 C. At 110 C, the dffuson coeffcent of hydrogen n the membrane and n water ncreases, facltatng a margnal ncrease n crossover for all membrane thcknesses. The smulaton results also show that at 3 atm and 80 C, a 60% drop n crossover can be acheved by doublng the membrane thckness from 25 µm to 50 µm at 80 C. A further 72% drop s observed when ncreasng the membrane thckness further to 175 µm at the same temperature. Thn membranes exhbt consstently hgher crossover at all practcal current denstes compared to thcker membranes. At least a 50% decrease n crossover s acheved at all practcal current denstes when the membrane thckness s doubled from 50 to 100 µm. Fnally the results for three dfferent membrane thcknesses showed a sgnfcant reducton n crossover at all practcal current denstes for thcker membranes. The calculated results suggest that from the three thcknesses consdered, the 175 µm membrane s the most lkely to offer equvalent crossover current denstes of 5 ma/cm 2 or less n the practcal operatng range. Overall, t has been shown that the general transport equaton, equaton (6-14), can be used to model mult-speces transport wthout the need to supermpose ndependent transport equatons based on dlute soluton relatons such as Fck s law. It has been shown that ths can be done n mult-component form whle beng able to accommodate electro-osmotc drag flux explctly. The next step s to apply the general transport equaton to smulate two-phase electrochemcal transport through the multple layers of the PEFC.

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161 6 A Unversal Modellng Framework from Fundamental Theory Ekerlng M, Kharkats YI, Kornyshev AA, Volfkovch YM. Phenomenologcal Theory of Electroosmotc Effect and Water Management n Polymer Electrolyte Proton-Conductng Membranes. J. Electrochem. Soc., 1998, 145, Meer F, Egnerberger G. Transport Propertes for the modellng of water transport n onomer membranes for PEM-fuel cells. Electrochm. Acta, 2004, 49, Baschuk JJ, L X. Modellng of polymer electrolyte membrane fuel cells wth varable degrees of water floodng. J. Power Sources, 2000, 86, Amphlett JC, Baumert RM, Mann RF, Peppley BA, Roberge PR. Performance Modellng of the Ballard mark IV Sold Polymer Electrolyte Fuel Cell. J. Electrochem. Soc., 1995, 142, Mann RF, Amphlett JC, Hooper MAI, Jensen HM, Peppley BA, Roberge PR. Development and applcaton of a generalsed steady-state electrochemcal model for a PEM fuel cell. J. Power Sources, 2000, 86, Weber AZ, Newman J. Modellng n Polymer-Electrolyte Fuel Cells. Chem. Rev., 2004, 104, Wang CY. Fundamental Models for Fuel Cell Engneerng. Chem. Rev., 2004, 104, Hrschfelder JO, Curtss CF, Brd RB. Molecular Theory of Gases and Lquds, 1964 (John Wley & Sons, Inc., New York) 46 Newman J. Electrochemcal Systems, 1973 (Prentce-Hall, Inc., Englewood Clffs, New Jersey) 47 Wang ZH, Wang CY, Chen KS. Two-phase flow and transport n the ar cathode of proton exchange membrane fuel cells. J. Power Sources, 2001, 94, Slattery JC, Brd RB. Calculaton of the Dffuson Coeffcent of Dlute Gases and of the Self-dffuson Coeffcent of Dense Gases. AIChE J., 1958, 4, Cheng X, Zhang J, Tang Y, Song C, Shen J, Song D, Zhang J. Hydrogen Crossover n Hgh- Temperature PEM Fuel Cells. J. Power Sources, 2007, 167, Frere TJP, Gonzalez ER. Effect of membrane characterstcs and humdfcaton condtons on the mpedence response of polymer electrolyte fuel cells. J. Electroanal. Chem., 2001, 503, Sena DR, Tcanell EA, Pagann VA, Gonzalez ER. Effect of water transport n a PEFC at low temperatures operatng wth dry hydrogen. J. Electranal. Chem., 1999, 477, Matsuyama H, Matsu K, Ktamura Y, Mak T, Teramoto M. Effect of membrane thckness and membrane preparaton condton on facltated transport of CO2 through onomer membrane. Sep. Purf. Technol., 1999, 17, US Department of Energy. Hydrogen, Fuel Cells & Infrastructure Technologes Program, 2005

162 7 A Unversal Approach to Mult-Layer Two-Phase Modellng through the General Transport Equaton A mathematcal mult-layer, mult-speces two-phase modellng framework for polymer electrolyte fuel cells (PEFCs) s presented n ths chapter usng the general transport equaton. The general transport equaton was developed n the prevous chapter and appled to brdge the gap that exsts between the benchmark modellng phlosophes n the lterature for transport across the PEFC. In ths chapter, the general transport equaton s appled wth Darcy s law to characterse water transport and water uptake through the porous and quasporous layers of a PEFC under sngle- and two-phase operatng condtons. The characterstc transport equatons and avalable materal propertes from the lterature are then translated nto a sngle-cell fuel cell model whch s mplemented usng the Object Modellng Technque (OMT). The PEFC model s appled to predct and valdate the net water transport rato and water content under a range of operatng condtons. The numercal model exhbts good agreement wth expermental data under both vapour- and lqud-equlbrated condtons. Ths chapter s presented n fve parts. The frst provdes a general revew of the treatment of two-phase flow n the fuel cell modellng lterature and a dscusson of the key concepts. The second part presents the developed system of equatons for mult-component two-phase flow based on the general transport equaton and Darcy s law. The thrd part dscusses the auxlary equatons adopted to smulate two-phase transport whle the fourth descrbes the structure of the model, programmed usng the OMT concept. The ffth part presents the results of the model valdaton, whch s carred out aganst data from three ndependent expermental test cases from the lterature. 7.1 Introducton The dfferent layers of a complete fuel cell assembly can be classed as beng ether porous or quas-porous meda. The gas dffuson layer (GDL), the mcro-porous layer (MPL) and to an extent the catalyst layer (CL) can all be classed as porous meda whle the PEM can

163 7 Two-Phase Modellng through the General Transport Equaton 143 be classed as a quas-porous medum. The GDL, MPL and CL exhbt defnte porous structures under dry or lqud-nfltrated condtons whereas the PEM s generally mpermeable to bulk gas flow yet can behave lke a porous materal when lqud water nfltrates ts polymer structure. Snce two-phase condtons can potentally affect both types of meda under fuel cell operatng condtons, t s possble to consder two-phase transport as a common fundamental process that s theoretcally governed by modes of dffuson, convecton and n the case of the PEM by electro-osmotc drag. The physcal dfferences between porous and quas-porous meda and the mechansms by whch two-phase flow can propagate wthn them are mportant and have to be consdered as well to fully understand water transport n a PEFC. A great deal of effort has already been spent to model transport phenomenon n PEFCs [1,2]. The earler benchmark models developed around the early 1990 s focused manly on establshng a fundamental understandng of the nternal transport mechansms n the GDLs and the PEM [3,4,5]. In essence, these models selectvely modelled dffuson, convecton or electro-osmotc drag as the man modes of water transport usng forms of concentrated soluton theory or dlute soluton theory, as dscussed n the prevous chapter. These were sngle-phase models that dd not rgorously account for the effect that the smultaneous presence of water vapour and lqud water can have on water transport across a layer, water uptake n the PEM and therefore cell performance. Wthn a workng cell, there are actually a multtude of nterdependent phenomenologcal processes that occur whch govern cell performance. Fuel cell models over the years have been developed and adapted accordngly but n dong so have had to apply smplfyng assumptons and/or spatal lmts to the modellng treatment. Wthout some of these assumptons, developers run the rsk of creatng models that are dffcult to solve numercally, computatonally expensve and therefore mpractcal to use for proper fuel cell development. However, the assumptons that are made and the way n whch they are appled are qute often dfferent and as such have resulted n a multtude of numercal models. The followng bref revew focuses on how two-phase transport has been handled n the fuel cell modellng lterature and the underlyng assumptons that have been made. Models for the porous meda are dscussed frst (GDL, MPL, CL), followed by quas-porous meda (PEM).

164 7 Two-Phase Modellng through the General Transport Equaton 144 Fuel cell models explctly dealng wth two-phase transport phenomenon began to appear around the late 1990 s [1,2]. In modellng terms, the problem of two-phase transport was manly prescrbed to the cathode CL and the cathode GDL because of the fact that t s these regons where product water forms frst and has to be removed from to prevent cell floodng. In order to model two-phase water transport n porous fuel cell meda, t s assumed that the nternal porous network can be approxmately treated as a collecton of nonconnected tortuous capllary tubes, where capllary-drven flow s governed by the dfference between gas and lqud phase pressures. The prncpal modes of transport are stll dffuson and convecton but a materal-specfc relatonshp s also requred to defne the level of lqud-phase saturaton wthn a pore as a functon of the capllary pressure. One promnent method that establshed a two-phase treatment based on the capllarytube scheme s now commonly known as the mult-phase mxture model, developed by Wang and co-workers [6,7,8,9,10,11,12,13]. The mult-phase mxture approach s based on conservaton equatons for mass, energy, charge, momentum and speces, the latter two of whch accommodate convecton and sngle-speces dffuson respectvely through Darcy s law and Fck s law. The physcal propertes of the mult-phase flow nfltratng the porous medum such as densty, concentraton, velocty and vscosty are calculated based on the assumpton that the flow can be treated as a chemcal mxture. As such, the mxture propertes and the effectve dffuson coeffcents are calculated based on the local level of saturaton [7]. Ths method has been translated nto a three-dmensonal model and has progressvely elucdated the potental effects of operatng parameters on two-phase transport n porous fuel cell meda such as reactant stochometry and humdfcaton [10,13]. Other subsequent mult-dmensonal models reported by Brgersson et al. [14] and Djlal and coworkers [15,16] have been based on the same fundamental prncpals of mass, energy, charge, momentum and speces conservaton but treat the gas phase and lqud phase separately and descrbe mult-component dffuson for gas-phase transport n Stefan-Maxwell forms. Acosta et al. focused on the functonal form of the capllary pressure-saturaton relatonshp, notng a hysteress n water retenton characterstcs of GDLs durng dranage and mbbton [17]. Ther mult-dmensonal model treats gas and lqud phases separately, accountng for convecton usng an extended form of Darcy s law and Fck s law to descrbe dffuson for each gas component ndvdually.

165 7 Two-Phase Modellng through the General Transport Equaton 145 Treatments based on Darcy s law and Fck s law appear elsewhere too. It s known through expermental studes that two-phase transport can occur as a transent phenomenon wthn a workng cell; the level of saturaton wthn a fuel cell GDL for example can change wth respect to tme under constant current condtons [18]. In order to model two-phase transents, Zegler et al. focused on smulatng cyclo-voltammograms and demonstrated that mass transport lmtatons can ncrease because of the tme-dependant accumulaton of water on the cathode sde of a workng cell [19]. Ther modellng treatment s one-dmensonal and mult-component dffuson and gas-phase pressure drops n the GDLs are neglected. Snglecomponent gas-phase dffuson and lqud-phase convecton n the GDL are descrbed usng Fck s law and Darcy s law respectvely. Natarajan and Van Nguyen [20] and Nam and Kavany [21] appled another approach to model two-phase transport. They assumed that lqud phase flow across the GDL s drven by a gradent n lqud saturaton rather than the phase pressure gradent drectly. Ths treatment s based on a prevous modellng-based study of steam njecton n dry porous meda [22]. Here, Darcy s law s modfed to become a functon of the gradent n lqud saturaton. The capllary pressure-saturaton relatonshp s translated nto a dfferental form and appled through a capllary dffusvty term. Dffuson n vapour-phase s ether modelled n sngle-component form usng Fck s law [21,27] or n mult-component form usng the Stefan-Maxwell equaton [20]. Mazumader and Cole [23,24] and Van Nguyen and coworkers [25,26] have appled the concept of capllary-drven flow n mult-dmensonal modellng frameworks based on the contnuty equatons by usng an addtonal relatonshp for the conservaton of lqud water. The method has also been adopted by McKay et al. to predct the transents of lqud water accumulaton n the GDLs of a fuel cell stack for embedded real tme control [27]. The relatonshp between lqud-phase saturaton and capllary pressure s an mportant one for fuel cell modellng and vares from materal to materal. It depends upon a number of physcal factors ncludng the porosty of the materal, ts absolute permeablty, the hydrophobcty of nternal surfaces, nternal pore rad, materal compresson and also the vscosty of the nfltratng flud. Because ths relatonshp was not defned n the past for porous fuel cell materals the Leverett J-functon was often adopted, whch was orgnally developed n petroleum engneerng as a generc technque to characterse saturaton n sotropc sol beds wth unform wettablty [28]. In fact the Leverett-based approach has

166 7 Two-Phase Modellng through the General Transport Equaton 146 been wdely adopted n many of the two-phase models above and s stll commonly appled because t s smple to use and provdes a superfcal ndcaton of the level of saturaton n the porous layers of a fuel cell. To address the lack of rgour n the Leverett-based approach for fuel cell modellng purposes, other sem-emprcal fts have been developed n recent years for specfc commercally-avalable porous fuel cell meda [17,25,26,29,30]. These studes have focused more on understandng the physcal characterstcs of modern porous fuel cell layers [29], analysng the effect of the true functonal form of the capllary pressuresaturaton relatonshp on two-phase transport [25,26] and the hysteress durng and dranage and mbbton [17,31]. GDLs are treated wth polytetrafluoroethylene (PTFE) or fluornated ethylene propylene (FEP) to ensure that ts nternal pores are hydrophobc, thereby moblsng any lqud water that enters or accumulates wthn t. However, the hysteress demonstrates that the hydrophobsng agent s heterogeneously dspersed wthn the GDL, leavng a porous network whch s partally hydrophobc and partally hydrophlc. As such, once a GDL s nfltrated wth lqud water t may not be easly removed from certan hydrophlc pores. On a smlar note, experment-based studes of commercal GDLs conducted by Van Nguyen and co-workers have concluded that low hydrophlc porosty s ndeed a desrable property for hgh fuel cell performance [26] but that some hydrophlc porosty has to exst to effectvely conduct lqud water away from regons that are already flooded [32]. Overall, these observatons llustrate that nternally the GDL can be a heterogeneous materal wth complex water transport characterstcs. Modern fuel cells employ a b-layer assembly on ether sde of the catalyst-coated membrane (CCM) whch contans both the GDL and the MPL. Fundamentally, the MPL and GDL can have a common carbon-based substrate; the dfference s that the MPL s usually treated wth a hgher level of hydrophobsng agent. In a workng cell the MPL sts between the GDL and CL and can help control the drecton n whch lqud water wthn the cell s transported under certan operatng condtons [11]. The MPL can therefore help mprove cell performance by reducng the lqud water saturaton n the cathode GDL [33]. In terms of modellng, because the MPL s a porous medum two-phase transport can be treated n the same manner as the GDL, but consderaton has to be gven to the fact that capllary flow wll affect ts saturaton characterstcs dfferently because ts physcal propertes wll be dfferent. The treatment of the CL s complex because there are two phenomenologcal processes occurrng smultaneously; potentally two-phase transport and electro-reducton n

167 7 Two-Phase Modellng through the General Transport Equaton 147 the cathode CL or electro-oxdaton n the anode CL. The detaled mathematcal models that have been generated to consder these processes have usually focused on just the cathode sde of the cell [26,34,35,36,37,38]. In mult-layer fuel cell models the CL s often treated as a thn nterface. The PEM plays a central role n water transport and s also affected by two phase phenomenon. Most models assume that the PEM operates under a vapour-equlbrated mode and do not systematcally consder the effect of lqud water comng nto contact wth a boundary. Ths treatment has not changed sgnfcantly n the modellng lterature as evdent n almost all mult-layer fuel cell models referenced above and others [39,40,41,42]. Water transport s predomnantly modelled by adoptng one of three equatons; the Nernst-Planck equaton as establshed by Verbrugge and co-workers, [4,43,44,45,46]; the dffuson equaton n terms of chemcal potental wth an appended term for electro-osmotc drag, as establshed by Sprnger et al. [3]; and the mult-component Stefan-Maxwell equaton as establshed by Fuller and Newman [5]. As dscussed n the prevous chapter, the frst two pertan to dlute soluton theory and are generally applcable for a solute speces when ts concentraton s assumed to be much less than the solvent concentraton, whle the thrd drectly pertans to concentrated soluton theory. The most commonly adopted method s the dlute soluton approach of Sprnger et al, whle the dlute solute approach of Verbrugge and co-workers and the concentrated soluton approach of Fuller and Newman appear much more rarely [47,48,49]. In practce, t s well understood that the charged end groups wthn the polymer electrolyte matrx hold up to a maxmum of around 14 water molecules when equlbrated n water vapour. It s also known that f the PEM s equlbrated wth lqud water the charged end groups can hold up to around 22 water molecules. Ths behavour at unt actvty s commonly attrbuted to Schroeder s paradox [50,51]. In terms of modellng because lqud water n the PEM can affect all modes of transport and therefore the proton conductvty across t, t also needs to be consdered. Generally, ths has not been the case manly because unlke the GDL and MPL, the PEM does not have a defnte rgd porous structure and therefore dffcult to structurally characterse and model usng the conservaton equatons mentoned above or the dlute or concentrated soluton theores n ther standard forms. However, t has been proposed that the presence and nfltraton of lqud water can forcbly create a pore network wthn the PEM, and ths dea has formed the foundaton of one notable modellng approach based on concentrated soluton theory whch departs from the tradtonal treatment of the PEM [52,53,54,55,56].

168 7 Two-Phase Modellng through the General Transport Equaton 148 Although the above revew s not completely exhaustve, t provdes a reasonable understandng of the manstream modellng efforts n two-phase fuel cell smulaton and the physcal phenomenon that occur under two-phase condtons. What becomes clear, though, s that whle each pece of work s fundamentally focused on descrbng two phase flow, the manner n whch fundamental transport theory and expermentally-obtaned relatons are appled s not unversally consstent. The purpose of the current work s to apply the general transport equaton (GTE) from fundamental transport theory to model two-phase flow n the porous and quas-porous layers of the PEFC. In the prevous chapter, the theoretcal valdty of the GTE was proven by dervng all the benchmark transport equatons used n the modellng lterature. The GTE was then translated nto a smple sngle-phase model and smulated results were valdated aganst publshed data. In the current study, the establshed understandng s extended by demonstratng a smple yet theoretcally consstent method by whch two-phase transport can be modelled n the porous and quas-porous layers of the cell usng the GTE. Ths common root has not been demonstrated n the lterature to date. The theoretcal framework s then translated nto a workng one-dmensonal mult-layer, two-phase fuel cell model whch ncorporates recent sem-emprcal data fts to characterse the physcal propertes of modern fuel cell materals. The model s appled n two parts. Frst, t s appled to smulate a set of expermental test cases; the modellng results are valdated aganst expermental data to verfy the predcted water transport and water uptake characterstcs nsde a workng cell. Second, the model s appled to study the effects of PEM thckness, anode humdfcaton and cell compresson on lqud water nfltraton, water transport and water uptake characterstcs across the PEM when two-phase operatng condtons are establshed nsde the PEFC. The second part s presented n chapter Theoretcal Equatons for Two-Phase Transport n Porous and Electrolytc Quas-Porous Meda All the transport layers of a fuel cell can be treated as fundamentally beng porous or quas-porous. For both types of meda, nternal transport under two-phase condtons s n general a common phenomenologcal process and can therefore be treated as a common

169 7 Two-Phase Modellng through the General Transport Equaton 149 process n modellng terms. As such, transport under two-phase condtons can be descrbed for both types of fuel cell meda usng the GTE. Ths secton focuses on dervng the functonal form of the theoretcal equatons for two-phase-drven transport n porous and quas-porous fuel cell meda The General Transport Equaton The GTE s taken from the prevous study of PEFC transport mechansms and derved from the molecular theory of gases and lquds as presented n chapter 6. It descrbes the movement of a speces as part of a mult-speces concentrated soluton system due to the followng modes of transport; dffuson due to concentraton gradents convecton due to pressure gradents thermal dffuson due to temperature gradents electro-osmotc drag due to an electrc feld In ts generalsed form, the GTE appears as follows; M c µ + s T p RTn& ρ H + = RT c c j m T c ξ D, c c T j D j m v ρ ρ j v D j, mem j, mem v D j + ρ j Th ξ j Th D ρ ln T (7-1) In the current modellng framework, the effects of temperature gradents are neglected ( T = 0), leadng to the followng reduced form of the GTE; c M ρ µ p RTn& H + c c m T ξ D, m ρ ρ v D ξ j, mem j, mem j = RT j c c c T j D j [ v v ] j (7-2) The second term of the left hand sde of equaton 7-2 accounts for electro-osmotc drag and does not occur n electro-neutral materals such as the GDL or MPL. Two ndetermnate gradents appear n equaton 7-2; frst, the electrochemcal potental gradent and second the phase pressure gradent. In order to solve the phase

170 7 Two-Phase Modellng through the General Transport Equaton 150 pressure gradents, therefore, an addtonal relatonshp based on the flud dynamcs of the system s requred,.e., Darcy s law: k Jκ vj = p J ; J = lq, gas µ J (7-3) where κ k J = absolute permeablty of the materal, = relatve permeablty pre-factor, µ J = vscosty of the flud P J = pressure gradent n the phase J. The followng sub-sectons descrbe how the GTE and Darcy s law are appled to solve the two characterstc gradents for two-phase flow n porous and quas-porous fuel cell meda Theoretcal Equatons for Two-Phase Transport n Porous Meda Concentraton gradents The electrochemcal potental of a speces can be defned as [57]; c µ = RT + zf φ c (7-4) Substtutng ths nto 7-2 for porous meda where electro-osmotc drag does not occur ( ξ = 0 ) and assumng that the water vapour behaves as an deal gas yelds; c p = RT gas ρ 1 ρ RT + ( n& c n& c ) j p gas D j j j (7-5) where the molar flux of speces s defned as can be related to the proton flux by; n & = c v. The total water flux across the cell

171 7 Two-Phase Modellng through the General Transport Equaton 151 I J n& w = n& = H 2F α = + (7-6) It s assumed that water vapour travels along that proporton of the porous network of a gven layer whch s not saturated by lqud water. The local saturaton, s, s calculated usng the local capllary pressure: P cap = P P (7-7) gas lq As such, t s assumed that the proporton of the total amount of water that travels through the porous network n vapour form can be determned by the fracton ( 1 s), whereas that whch occurs n lqud form through the saturated pores can be determned by s. The flux of water vapour can now be defned as n w, vap ( s) Iα E = 1 (7-8) where α A = α for anodc porous layers ( ) α C = 2 1+α for cathodc porous layers The densty of the gas-phase mxture s calculated as; ρ gas = c M (7-9) Pressure Gradents Pressure gradents are accounted for usng Darcys law, as gven by equaton 7-3. The relatve permeablty pre-factor k J for lqud and gas phases respectvely s calculated as; k = s lq m (7-10) k gas ( s) m = 1

172 7 Two-Phase Modellng through the General Transport Equaton 152 The velocty of phase J s converted to flux rates usng n & = v c J J J whch yelds; p J n& J µ J = c k κ J J (7-11) The flux of water vapour s calculated usng equaton 7-8 whle that of lqud water s calculated as; n, lq = siα E (7-12) It s assumed that mult-component transport occurs n the vapour phase whle water alone consttutes the lqud phase Theoretcal equatons for two-phase flow n quas-porous meda Concentraton gradents The general transport equaton gven by equaton 7-2 can be appled for a threespeces polymer electrolyte system where water s the prmary speces, and hydrogen ons and the sold polymer electrolyte respectvely become the secondary speces j. For such system, the GTE becomes: c w M µ w p = ρ RT 1 ct D c + RTn& H + c w, H + m T ( c n& c n& ) + ( c n& c n& ) w D ξ H + w w, mem H + w 1 D w, mem w mem mem w (7-13) Gven that water wthn the PEM has no net charge,.e., z = 0, the electrochemcal potental of water can be defned as follows usng equaton 7-4; w

173 7 Two-Phase Modellng through the General Transport Equaton 153 w w w c = RT c µ (7-14) By groupng terms and notng that the flux of the membrane phase s zero,.e., 0 = mem n& yelds w mem w T m H w mem w mem H w w H H w H w T w w D c c RTn D n c D n c D n c c RT p c RT,,,, ξ ρ ρ = & & & & (7-15) Rearrangng equaton 7-15 to descrbe the net water flux across the PEM yelds; = p RT c c c D c D c n D c D c n w T w T mem w w m H w w H w mem mem H w H w ρ ρ ξ,, 1,, & & (7-16) Equaton 7-16 descrbes the total molar flux of water across the PEM. In the present state, 7-16 does not explcate the dfference between water transport n vapour-equlbrated and lqud-equlbrated states. However, t s possble to postulate a physcal model for the PEM system based on a prevous treatment [52] n order to do ths. The PEM s charactersed by hydrophlc sulfonc acd stes whch are tethered to a hydrophobc fluorocarbon backbone. The PEM essentally contans a myrad of these polymer chans and the resultng structure s often referred to as a polymer matrx. It s assumed that on the surface of the PEM, the polymer chans are orentated n a way that exposes the fluorocarbon backbone, resultng n a hghly-hydrophobc surface. In the physcal model, t s prmarly assumed that the polymer matrx s quas-porous n nature and contans nternal hydrophobc pathways that can be forcbly expanded by capllary acton. Durng ntal hydraton, t s assumed that water molecules become strongly assocated to the charged end groups. As hydraton contnues, the charged end groups begn to form nverted mcelles whch contan water. As hydraton contnues further, these water clusters grow larger and synonymously create weak water networks between them n the collapsed hydrophobc pathways. When the boundares of the PEM are n contact wth

174 7 Two-Phase Modellng through the General Transport Equaton 154 saturated water vapour, the ndvdual channels between water clusters are well-establshed and defnte. When lqud water comes nto contact wth one of the boundares, t s assumed that the hydrophobc skn whch ntally covers the outer surface s forced to re-orentate, exposng the hydrophlc charged end groups nstead. Ths can subsequently allow lqud water to nfltrate the PEM along the channels n the water network and dependng upon the lqud pressure at the boundary can forcbly expand them va capllary acton. As the lqud water nfltrates the PEM, the water clusters enlarge further. When all the boundares of the PEM are n contact wth lqud water, the water clusters enlarge to ther maxmum permssble thermodynamc states and all the ntally-collapsed hydrophobc channels are forcbly expanded and completely flled wth lqud water. Accordng to the descrpton above, there are as such two polar states that the PEM can operate under; frstly, a collapsed state where the PEM s equlbrated wth water vapour and secondly a fully expanded state where the PEM s equlbrated wth lqud water. It s possble for the PEM to equlbrate wth water vapour and lqud water smultaneously, creatng a transtonal regme where a fracton of expandable pores are actually expanded. Ths may occur when the cathodc bondary s n contact wth lqud water whle the anodc boundary s not. Under ths regme, t s possble for two transport modes to co-exst; a vapour-equlbrated transport mode n the collapsed regon of the PEM, and a lqudequlbrated transport mode n the lqud-flled network of expanded pores wthn the PEM. In terms of water content, denoted λ, ths transtonal regme descrbes the ncrease of water content from ts maxmum value for a fully vapour-equlbrated state (around 14) to ts fully lqud-equlbrated state (around 22). It s assumed that the magntude of the capllary pressure n the expanded lqud-flled pore network s drectly related to and therefore defnes the fracton of pores that are actually expanded. The expanded pore fracton s denoted s epf. Conceptually, the pore expanson fracton s smlar to saturaton n the capllary pressure-saturaton relatonshp for GDLs but wth the notable dfference that the pore expanson fracton represents the fracton of pores between water clusters whch are ntally collapsed that are forcbly expanded by nfltratng

175 7 Two-Phase Modellng through the General Transport Equaton 155 lqud water whereas saturaton represents the fracton of pre-exstng open pores whch become completely flled wth the nfltratng lqud water. By assumng the physcal model above, equaton 7-16 can be recast to consst of two parts; one part relatng to the vapour-equlbrated mode and the other to the lqudequlbrated mode. Assumng that the expanded pore fracton determnes the proporton of flow occurrng n lqud- and vapour-equlbrated networks n an dentcal manner to pore saturaton n equatons 7-8 and 7-12, and groupng coeffcent terms for vapour-equlbrated and lqud-equlbrated phases yelds; c w 1 = c T ( s ( IΦ + Φ ) + ( s )( IΦ + Φ ) IΦ ) epf 2, lq 3, lq 1 epf 2, vap 3, vap 1α (7-17) where c H + cmem Φ1 = + ; Dw, H + Dw, mem Φ 2, J c = D w w, H + c ξ + D m w, J w, mem ; (7-18) Φ 3, J ct ρ w = p RTρ J The gradent n water content, where water content s defned as the number of water molecules per charge ste s calculated as; c λ = c w mem (7-19) where c mem ρ = M dry mem (7-20)

176 7 Two-Phase Modellng through the General Transport Equaton 156 Pressure Gradents Pressure gradents across the quas-porous PEM regon can be calculated usng Darcy s law, as gven n equaton 7-9. The permeablty pre-factor k J s calculated here dfferently as a functon of the volume fracton of water that occupes the PEM, f. The general defnton of the volume fracton of water n the PEM s; f = V mem λv w + λv w (7-21) where the partal molar volume of speces s calculated as; M V = ρ (7-22) In the case of the PEM, the densty s taken as the dry value. Based on statstcal arguments, the effectve hydraulc permeablty of the PEM s defned as [53] k lq = f f lq 2 (7-23) where f lq corresponds to the maxmum lqud-phase water content; f lq = V λ mem lq,max λ V w lq,max V w (7-24) It s assumed that λ 22 based on lterature values [58,59]. lq, max =

177 7 Two-Phase Modellng through the General Transport Equaton Sub-Models for the Physcal Propertes of PEFC Meda and Infltratng Fluds The valdty of the theoretcal equatons for two-phase transport descrbed n the precedng secton can be tested by applyng them through a one-dmensonal modellng framework for the PEFC. In the current work, ths s done through an sothermal model whch treats the fuel cell has havng seven regons of potental nterest. The anode and cathode sdes of the cell can each contan a supply channel, a GDL and an MPL. The central layer s the PEM. The purpose of ths secton s to dscuss the sub-models that are requred to supplement the two-phase transport equatons descrbed n the precedng secton. These submodels are manly adopted from the lterature and account for the operatng condtons, the physcal propertes of the fuel cell layers and the physcal propertes of the workng fluds that nfltrate the cell. The man assumptons of the current model are as follow; 1. the fuel cell operates under steady-state condtons 2. two-phase flow n the channel can be treated as mst flow 3. thermal dffuson due to temperature gradents can be neglected 4. gravtatonal effects on two-phase transport can be neglected 5. the catalyst layers can be treated as a thn nterface 6. convectve flow across the PEM only occurs n the ntrudng lqud water network Fgure 7-1 llustrates the potental modellng doman; snce the MPL s used selectvely n practce, the modellng structure wll treat the MPL as an optonal layer. If the MPL s dsregarded, nterface A-2b or C-2b would dsappear and nterface A-2 or C-2 would represent the nterface between the GDL and the PEM. The CL s shown n Fgure 7-1 for llustraton purposes. The composton of the reactant supples to the anode and cathode channel regons of the cell are determned usng the mult-speces nput model developed n chapter 5. The composton wthn each channel s determned as a functon of reactant humdfcaton temperature, dry gas composton, stochometry, the net water transport rato and current

178 7 Two-Phase Modellng through the General Transport Equaton 158 densty. The model nherently accommodates condtons where one or nether of the nlet gases are partally/fully humdfed. Fgure 7-1 PEFC cell structure for the one-dmensonal two-phase model Sub-models for the Inlet and Channel Regons The exstng mult-speces nput model s mproved n two regards. Frst, a smple thermodynamc sub-model s devsed whch calculates anode and cathode supply stochometres drectly from the flow rates of the supply gases. Ths s useful for model valdaton/applcaton purposes when flow rates are provded from experment rather than stochometry. Second, another smple sub-model s devsed to calculate the boundary pressures and concentratons of the gas-phase consttuents for the sde of the GDL that nterfaces wth the channel. The key equatons are dscussed n more detal n the appendx Sub-models for the Porous Layers The equatons gven n Table 7-1 descrbe the local pressure-dffusvty product, vscosty, lqud phase saturaton and compresson effects n GDL and the MPL. Local values are calculated by takng nto account the effectve porosty of the layer and local level of saturaton. It s assumed that the effectve porosty depends upon the level of cell compresson.

179 7 Two-Phase Modellng through the General Transport Equaton 159 The pressure-dffusvty product s defned by the Slattery-Brd equaton, as dscussed n the prevous chapter, but modfed to account for the tortuosty of the porous network, ts effectve porosty and lqud saturaton. The phase vscosty s requred n equaton 7-9 to calculate the phase pressure drop. The vscosty of water vapour and lqud water are calculated as functons of temperature, whle that of ar and hydrogen are taken as fxed values. The vscosty of the vapour-phase mxture s calculated usng the mole fractons of the consttuent speces. Two-phase fuel cell models typcally adopt the Leverett approach to macroscopcally characterse the level of saturaton n a porous dffuson layer as a functon of the local capllary pressure usng equaton 7-7. For a gven capllary pressure, t s possble to calculate the level of saturaton usng the standard Leverett J-functon as gven by equatons 7-29 and Whle ths method s readly adoptable, there are two man drawbacks to ts use: (1) because of the stochastc nature and heterogeneous hydrophobcty of a GDL or MPL, t s dffcult to obtan a meanngful contact angle for equaton 7-29, and; (2) the local porosty and permeablty are lkely to change accordng to the compresson pressure exerted onto the workng cell. The current model ncludes a unfed sem-emprcal approach whch s specfcally developed for the PTFE-treated porous carbon paper fuel cell layers manufactured by SGL [60]. Ths method s based on the Leverett functon, but modfed to take nto account key physcal characterstcs assocated to fuel cell meda, whch are not experenced n sol bed systems such as the level of hydrophobc fll, the cell compresson pressure and the compressed porosty of the materal. In the current framework, the standard Leverett method s appled when the specfc form of the capllary pressure-saturaton relatonshp s unknown or undefned for the porous materal n queston, and the valdated Leverett method s appled specfcally when SGL-manufactured porous materals are used. The recent lterature dentfes a hysteress n the capllary pressure-saturaton relatonshp of GDLs durng water dranage and mbbton [17,31,61], a phenomenon that has been encountered n petroleum engneerng [62]. The expermental data suggests that the heterogeneous dstrbuton of the hydrophobsng agent through the porous layer creates hydrophlc and hydrophobc domans whch result n dfferent capllary pressure-saturaton profles accordng to whether water s beng removed from or nfltratng n to the porous

180 7 Two-Phase Modellng through the General Transport Equaton 160 Pressure-Dffusvty p gas D eff j = p Vscosty ln µ T crt w,vap gas D j ε 3 / 2 ( 1 s) (7-25) τ 1 = = K 1 T T crt 1 6 µ 0.21 / 0.79 = Pa-s O2 N2 6 µ H = Pa-s 2 = vap x µ 4 / 3 1 T T crt / 3 1 T T crt 1 7 / 3 (7-26) µ (7-27) lnµ w,lq 1 Tcrt = T T T crt 1 4 / 3 1 1/ T T crt 1 Saturaton vs. Capllary Pressure: Standard Leverett J-Functon p cap J = ( s) 7 / 3 (7-28) 1 / 2 ε (7-29) γ cosθ J ( s) K 2 ( s) 2.120( 1 s) ( 1 s) = s 2.120s s 3 3 f θ < 90 o f θ > 90 Saturaton vs. Capllary Pressure: Valdated Leverett J-Functon p J cap ( s ) = γ T nwp ε K 1 / 2 0.4C comp ( T ) 2 J ( s ) nwp 2 3 ( wt% snwp snwp ) 2 3 ( wt% 12.68snwp snwp ) ( wt% 14.1s s ) ln wt% = wt% wt% 1.7 Surface tenson of water nwp nwp o ln s 3.416ln s s nwp nwp nwp 0.00 < s 0.50 s 0.65 < s nwp nwp nwp < 1.00 (7-30) (7-31) (7-32) γ = 1.78T N/m (7-33) Compresson Effects = (7-34) Y comp Y u / c ε 2 ε = b1 C + b2c where b 1 = ; b2 = SGL 24 -Seres (7-35) b1 = ; b3 = SGL10BB Table 7-1 Key equatons for the porous regons of the PEFC

181 7 Two-Phase Modellng through the General Transport Equaton 161 layer. Whle the current work does not make a dstncton between water dranage or mbbton, t s antcpated that these newer profles wll be adopted nto the current modellng framework n due course as more becomes clear about the phenomenon n fuel cell materals. As dscussed prevously, t s assumed that cell compresson affects the porosty and the thckness of the porous layers. It s assumed that the change n thckness and porosty can be calculated usng a common sem-emprcal relatonshp as gven by equaton 7-34 where Y denotes ether porosty ε or layer thckness t layer and the substrpts comp and u / c denote compressed and uncompressed states respectvely. The compressve stran depends upon the specfc structural propertes of the porous layer n queston and wll therefore vary from materal to materal. In the current study, the relatonshp gven by equaton 7-35 s employed where C s the compressve pressure wth unts of MPa Sub-models for the Quas-Porous Layers In the current treatment, the quas-porous PEM s treated as a ternary system consstng of water, protons and polymer electrolyte where water transport can occur n lqud- or vapour-equlbrated networks. The equatons gven n Table 7-2 descrbe the physcal propertes of the quas-porous ternary system ncludng dffusvty, electro-osmotc drag, hydraulc permeablty, vscosty, pore expanson, molar volumes, Ohmc resstance and proton conductvty. Compresson effects on water uptake and dmensonal changes are taken nto account through the mechancal propertes of the polymer electrolyte. In order to solve equaton 7-17, the dffuson coeffcent of water n the PEM must be known. The dffuson coeffcent of water depends upon the water content of the PEM. For an unconstraned Nafon-based PEM system, the well-known expermentally-derved expresson gven by equaton 7-36 s used [3]. For Nafon-based composte membranes there s a penalty to pay n the water dffuson coeffcent because of the nternal structural renforcement. In essence, structurally renforced membranes contan an nert matrx whch s mpregnated wth Nafon. As such, the general form of the above equaton apples but has to be modfed by a pre-factor k dff to account for the loss of dffusvty, where 0.00 k < Ths results n equaton The lterature demonstrates a wde scatter n < dff

182 7 Two-Phase Modellng through the General Transport Equaton 162 the value of k dff at all values of λ [63] and an understandng of the dependence of k dff on λ has not been demonstrated yet. The magntude of the electro-osmotc drag coeffcent s assumed to change accordng to whether the transport occurs n the lqud- or vapour- equlbrated network. For the vapour-equlbrated mode, the electro-osmotc drag coeffcent s taken as unty. For the lqud-equlbrated mode, the temperature-dependency of 7-38 s adopted [53]. Hydraulc permeablty and the vscosty of lqud water are requred to calculate the hydraulc pressure gradent across the PEM. There s a scatter n the range of values for Nafon n the lterature wth respect to hydraulc permeablty. Meer et al. calculate to cm 2 dependng upon the local water content usng expermental measurements [64,65]. Verburgge and Hll ntally adopt a value of cm 2 [43] whle Bernard and Verbrugge later report a value of cm 2 based on a water-balance measurements [4]. The latter s adopted n the current model, whch sts wthn the range of these values. The vscosty of lqud water s calculated smply usng equaton In order to determne the contrbuton of vapour- and lqud-equlbrated transport modes on the net water transport across the PEM as gven n equaton 7-17, t s necessary to calculate the fracton of pores n the PEM that are forcbly expanded by the ntrudng lqud water. In the adopted physcal model for the quas-porous PEM regon, t s assumed that pore expanson s drven by capllary acton when a boundary of the PEM comes nto contact wth lqud water [53]. For a gven capllary pressure, t s possble to calculate the correspondng pore radus of the local capllary tube usng the Young-Laplace equaton, as gven by equaton Ths radus represents a crtcal dmensonal threshold; all pores wth a radus larger than the crtcal radus wll be collapsed whereas those wth a smaller radus wll be expanded and completely flled wth lqud water. Usng pore-sze dstrbuton data for Nafon measured usng standard contact porosmetry [66,67] and assumng that the measured mcropores correspond to the channels n the PEM, t s possble to calculate the fracton of channels that are expanded by lqud water usng equaton 7-40 [53].

183 7 Two-Phase Modellng through the General Transport Equaton 163 Dffusvty of water n polymer electrolyte; non-renforced Nafon-based PEMs D ( λ λ ) exp 2416 w, mem( Nafon ) = 10 λ 303 T (7-36) Dffusvty of water n polymer electrolyte; structurally-renforced, Nafon-mpregnated PEMs D = k D (7-37) w, mem( GORE) dff w, mem( Nafon) Dffusvty of protons n water 5 2 D H + w = cm / s, Electro-osmotc drag coeffcent ξ vap = ξ lq = 2.55exp R Pore expanson r s crt epf 2γ cosθ = p lq ln r = 1 erf 2 1 crt T ( ) ln Molar volume free-swellng PEM V + (7-38) (7-39) (7-40) tot = Vwλ Vmem (7-41) c c w mem λ = V tot 1 = V mem Proton conductvty across the PEM σ = σ o ( f f ) o 1.5 E a 1 exp R T Local water content and actvty ref 1 T 2 3 λ = a 39.85a + 36a ; 1 a = c 2 2 1/ ( c1 + c2λ + 216( c3 c4λ + c5λ ) ) 2 2 c c + c λ + 216( c c λ + c λ ) 1/ / ( ) 1/ c8 (7-42) (7-43) (7-44) 0 < a (7-45) where c1 = ; c2 = ; c3 = ; c4 = ; c5 = ; c6 = 1/2160; c7 = /2160; c8 = 797/2160 Local actvty as a functon of water pressure a = p w, vap p sat w Table 7-2 Key equatons for the quas-porous regon of the PEFC (7-46) (7-47)

184 7 Two-Phase Modellng through the General Transport Equaton 164 In the case of a compressed PEFC, the effect of PEM constrant on the water uptake across the PEM s calculated based on the mechancal propertes of the PEM. A full explanaton of the assumptons adopted and equatons appled for ths mechancal sub-model s provded n the appendx. In the complete PEFC model, the manner n whch the effect of compresson on PEM thckness s accounted for requres some explanaton. In the frst nstance, the model s allowed to calculate the water content at the anodc and cathodc boundares assumng a free-swellng state. These boundary condtons are then modfed accordng to the level of compresson, whch n return automatcally modfes the ntermedate water content profle wthn the PEM and also allows the actual thckness of the membrane to be calculated as a functon of ts free-swellng equvalent state. Because the calculaton of PEM thckness requres the average water content across the membrane to be known, a small number of teratons have to be carred out wthn the quas-porous layer submodel. The teratons allow the average water content to converge to a stable value, whch corresponds to the actual thckness of the PEM. The proton conductvty for Nafon-based PEMs s calculated usng percolaton theory [68], as gven by equaton 7-44, where σ o s the crtcal conductvty of Nafon and f o s the threshold volume fracton at whch the nsulator-to-conductor transton occurs [53]. It s assumed that the crtcal conductvty can be set to 0.5 S/cm [53] based on the measured conductvty of Nafon under vapour-equlbrated [69] and lqud-equlbrated condtons [70]. It s assumed that the nsulator-to-conductor transton occurs n Nafon when λ = 2 whch translates to f = [53]. The actvaton energy E a reflects the Arrhenus dependence of conductvty on temperature and assumed to equal 11 kj/mol [53]. Equaton 7-44 s appled wth these parameters to calculate the local conductvty based on the local volume fracton of water and temperature. It s assumed that conductvty ncreases as a functon of f untl a second threshold for the volume fracton of water s reached. If more water s added beyond ths pont, the effect on mprovng the contnuty of pathways for proton conducton across the PEM becomes neglgble. The lterature suggests that ths second threshold occurs when f = [53]. Therefore, for calculaton purposes t s assumed that f = when f > In the case of structurally-renforced PEMs that are mpregnated wth Nafon, t s assumed that equaton 7-44 can be appled equally.

185 7 Two-Phase Modellng through the General Transport Equaton 165 In order to translate the nterfacal vapour pressures between the approprate anode porous layer and the PEM for the quas-porous layer model, a relatonshp s needed to calculate water content as a functon of actvty. An nverse relatonshp s also requred to covert water content nto actvty to defne the boundary pressures for the porous layers of the cathode sde of the cell. Tradtonally, these relatonshps have been derved from a sememprcal ft for data at 30 C [58] frst used by Sprnger et al. [3]. Snce then other chemcal models have been proposed n the modellng lterature [53,70]. The chemcal model of Weber and Newman s drectly dependant on temperature [53] whle the Brunauer-Emmett- Teller (BET) approach of Thampan et al. s a functon of the relatve humdty at the CL- PEM nterface [70]. In the current model, the sem-emprcal ft of Zawodznsk et al. [58] gven by equaton 7-45 and ts rearranged form of 7-46 are appled because they capture the functonal form and magntude of the relatonshp relatvely well and are smple to apply. 7.4 Modellng Structure for a One-Dmensonal Two-Phase PEFC Model The modellng framework for the sngle-cell, one-dmensonal mult-phase fuel cell model s mplemented usng the object modellng technque (OMT) [71,72]. The modellng framework comprses of three repeatng object-orentated models, namely; (a) the channel model: ths ncludes the mult-speces nput model gven n the appendx; (b) the porous layer model: ths ncludes the transport equatons 7-4 to 7-10 and the auxlary equatons n Table 7-1, and (c) the quas-porous layer model: ths ncludes the transport equatons 7-17 to 7-24 and the auxlary equatons n Table 7-2. The object-orentated approach s adopted because t enables the modellng framework to be adaptable and much less senstve to massve restructurng durng further development. The approach also elmnates repeatng lnes of codes whch descrbe fundamentally dentcal phenomenologcal processes that can reoccur n dfferent parts of the physcal system. The applcaton of the general transport equaton therefore nherently lends tself well to the OMT approach. From the users perspectve, the OMT approach results n a much more ntutve modellng framework as well, where modellng elements correspond to physcal components of the fuel cell and boundares between elements reflect nterfacal boundary condtons between physcal components.

186 7 Two-Phase Modellng through the General Transport Equaton 166 The channel model s appled to determne the thermodynamc condtons n the gas supply channels and to determne the boundary condtons at nterfaces A1 and C1. The model s therefore appled twce to smulate two objects; the anode and cathode gas channels. The porous layer model s appled to determne the concentraton and phase pressure profles through the thcknesses of the GDLs and MPLs. The model can be appled twce ntally to smulate two objects; the anode and cathode GDLs. Ths provdes the boundary condtons at nterfaces A2 and C2. The model can then be appled once or twce more to smulate two more objects f they appear n the structure of the smulated cell; the anode and/or cathode MPL. Accordngly, ths provdes the boundary condtons at nterfaces A2b and/or C2b. The dfferental equatons n the porous layer model are solved by treatng them as ntal value problems usng the Runge-Kutta scheme. The quas-porous layer model s appled to determne the water content profle and the pressure profle of the ntrudng lqud phase through the PEM. Because the PEM s a non-repeatng object n a sngle-cell, the quas-porous layer model s appled once. The quas-porous layer model s also solved as an ntal value problem usng the Runge-Kutta scheme from the anodc boundary to the cathodc boundary. Each fuel cell layer s dscrtsed nto ffty data ponts. The overall smulaton terates the net water flux across the cell untl the end result at nterface C2 or C2b from the quasporous layer model for the PEM s the same as the end result at nterface C2 or C2b from the porous layer model for the cathode GDL or MPL, agan dependng on whether or not the MPL s present. If two-phase condtons exst n the PEM, then convergence s judged by comparng lqud phase pressures at nterface C2 or C2b. If sngle-phase condtons exst, then convergence s judged by comparng the PEM water content at nterface C2 or C2b as obtaned from the quas-porous layer model to that calculated from the local actvty from the porous layer model for the cathode. The general scheme s smlar to that appled n the prevous chapters and shown n Fgure 7-2.

187 7 Two-Phase Modellng through the General Transport Equaton 167 Fgure 7-2 Smulaton flowchart for the object-orentated sngle-cell, two-phase mult-layer one-dmensonal PEFC model

188 7 Two-Phase Modellng through the General Transport Equaton Expermental Valdaton Net water transport per proton In order to valdate the net water transport calculatons of the model, eghteen test cases are taken from prevously publshed expermental data for a Nafon-based sngle cell tested wth E-TEK GDEs [49,54]. The actve cell area s 50 cm 2 and the porosty, tortuosty and uncompressed thckness of the gas dffusers are taken as 0.4, 7 and 250 µm respectvely [49]. Four operatng parameters and two parameters assocated wth the PEM are altered n the study; operatng current densty, cell temperature, relatve humdty (RH) (anode supply and cathode supply), stochometry (anode supply and cathode supply), PEM thckness and PEM equvalent weght. The frst sxteen results correspond to a cell operated wth Nafon 105 (equvalent weght of 1000 C/equv. and dry thckness of µm) and the remanng two to Nafon 112 (equvalent weght of 1100 C/equv. and dry thckness of 50.8 µm). The model s valdated by comparng the smulated net water flux per proton to that calculated from expermental measurements for each test case. Snce the net water flux rato α s defned relatve to the rate at whch hydrogen s oxdsed, the net water flux per proton s β = 0. 5α. Fgure 7-3 compares the smulated and expermental values of the net water flux per proton. A postve value of β corresponds to net water flux n the drecton of the cathode channel, whereas a negatve value corresponds to net water flux n the drecton of the anode channel. The results show that the model correctly predcts the drecton of net water transport n all eghteen test cases. The results also show that n all test cases, the predcted net water transport from the model s n the same order of magntude and wthn reasonable agreement of the expermental value. Cases 1, 2 and 9-16 demonstrate that wth both supples fully humdfed, the net water transport occurs n the drecton of the cathode. Ths holds true for both non-sobarc condtons as evdent n cases 1 and 2 and sobarc condtons as evdent n cases By removng anode humdfcaton, the net water flux swtches drecton and occurs n the drecton of the anode, as evdent n cases 3 and 4. If the cathode humdfcaton s removed

189 7 Two-Phase Modellng through the General Transport Equaton 169 Table 7-3 Test cases for model valdaton Fgure 7-3 Comparson of smulated and expermental values of net water flux per proton for the 18 test cases nstead, the net water flux contnues to occur n the drecton of the cathode, as evdent n cases 5 and 6. Cases 7 and 8 show that when nether supply s humdfed, the natural tendency s for the net water flux to occur n the drecton of the anode. For these test condtons therefore the drecton of net water flux across the Nafon 105 PEM s more senstve to anode humdfcaton than cathode humdfcaton, appled pressure dfferentals, current densty and hydrogen stochometry. Under the sobarc condtons of cases 17 and 18 where the Nafon 112 PEM s used, the net water flux occurs n the drecton of the anode even wth both supples fully humdfed. Ths ndcates that for the test condtons

190 7 Two-Phase Modellng through the General Transport Equaton 170 consdered, the net effect of water back-transport can be retarded when a thcker PEM wth a longer transport path s used Ohmc Resstance across the PEM In addton to valdatng the net water transport per proton across the cell, t s also necessary to predct the water uptake across the PEM and the effect that ths has on membrane performance. Ths s performed n two steps n the current study. The frst step s presented here whch focuses on valdatng the specfc resstance across the PEM aganst expermental data under vapour-equlbrated condtons. The second step s presented n secton and focuses on the drect valdaton of water content per charge ste across the PEM aganst expermental data obtaned from magnetc resonance magng (MRI) under vapour- and lqud-equlbrated condtons. For a gven set of operatng condtons, the model can determne the dstrbuton of water across the membrane n terms of water content per charge ste. By usng equaton 7-44, t s possble to translate ths dstrbuton nto a profle of proton conductvty across the PEM. Conductvty can be nversed to gve specfc resstance ρ, whch has unts Ohm-cm. In the current study, we use the specfc resstance profles presented by Takach et al. [73] obtaned for a 5cm 2 actve area PEFC wth a 200 µm PEM, SGL-25BC based GDL and MPL assembles and operated at 353K wth 20% RH. Hydrogen and oxygen are fed to the anode and cathode sdes of the cell respectvely under ambent condtons both at a flow rate 0.2 slpm. The 200 µm PEM s fabrcated wth seven embedded Pt potental probes between eght 25.4 µm Nafon NRE211 PEMs, whch s then hot-pressed to gve a total thckness of 200 µm. The potental probes enable the specfc resstance profle to be determned n-stu. The valdaton s carred out at four current denstes under steady-state condtons; 0.2 ma/cm 2, 0.1 A/cm 2, 0.2 A/cm 2 and 0.3 A/cm 2. The results are presented n Fgure 7-4. Fgure 7-4 (a) shows that the model s able to reproduce the expermental results under these sngle-phase condtons. The results suggest that the specfc resstance at the anode ncreases wth current densty, whle that at the cathode decreases. Fgure 7-4 (b)

191 7 Two-Phase Modellng through the General Transport Equaton 171 shows the smulated water content profle across the PEM for the smulated profles of specfc resstance gven n Fgure 7-4 (a). These results show that the gradent n water content ncreases wth ncreasng current densty; at low current, the dstrbuton n water content s generally unform and lnear. However, as current densty ncreases, the anode sde of the PEM dehydrates whle the hydraton at the cathode sde ncreases. The water content s generally wthn the band of 3 to 5 water molecules per charge ste, demonstratng that under these operatng condtons the PEM operates well wthn the vapour-equlbrated lmt of 14/ (a) (b) Fgure 7-4 (a) Specfc resstance profle across the PEM for smulated (lne) and measured (ponts) results at 0.2 ma/cm 2 ( ), 0.1 A/cm 2 ( ), 0.2 A/cm 2 ( ) and 0.3 A/cm 2 ( ); (b) smulated water content

192 7 Two-Phase Modellng through the General Transport Equaton Water Content across the PEM The purpose of ths sub-secton s to valdate the smulated water content per charge ste across the PEM when lqud water nfltrates the PEM. Ths s done by usng the water content profles presented by Ikeda et al. [74] deduced from magnetc resonance magng (MRI) scans of a 6cm 2 actve cell area PEFC operated at 70 C and 0.2 A/cm 2 wth a 254 µm thck Nafon-1110 PEM and Toray GDLs. The flow rates of the hydrogen and oxygen supply gases are both set to 0.1 slpm at 1 bar. The relatvely large thckness of the PEM s necesstated n part by the spatal resoluton of the MRI system. The results are however relevant for the valdaton of the current modellng framework. Three levels of relatve humdty (RH) for the supply gases are consdered; 40%, 80% and 92%. These partcular MRI-generated results were chosen because the operatng condtons explctly nvoke vapour- and lqud-equlbrated water uptake across the PEM. The results are presented n Fgure 7-5. Fgure 7-5 Smulated and measured water content profles as a functon of non-dmensonal PEM thckness for three levels of supply gas relatve humdty; 92%, 80% and 40% [74]. Fgure 7-5 demonstrates that for the test cases consdered, the 40% and 80% RH states nvoke vapour-equlbrated transport across the PEM, whereas the 92% RH state nvokes vapour- and lqud-equlbrated transport. Wth 92% RH, the water content per charge ste exceeds the vapour-equlbrated lmt of 14 and approaches the lqud-equlbrated lmt of 22. Wth 80% RH, the water content stays below the vapour-equlbrated lmt

193 7 Two-Phase Modellng through the General Transport Equaton 173 throughout the thckness of the PEM and confned to the range of 5-11 water molecules per charge ste. Wth 40% RH, the water content profle s the flattest throughout the thckness of the PEM and lmted to the range of 2-4 water molecules per charge ste. The smulated results show that the water content generally ncreases from the anodc boundary to the cathodc boundary. In the case of 92% RH, the smulated results suggest that the water content exceeds the vapour-equlbrated lmt n the vcnty of the anodc boundary and reaches the lqud-equlbrated lmt half-way through the PEM. From ths pont, the smulatons suggest that all the pores of the PEM are forcbly expanded by the ntrudng lqud water rght the way up to the cathodc boundary. In the case of 40% and 80% RH, the smulated results suggest a gradual ncrease n water content from the anodc boundary to the cathodc boundary. For all three test cases, the model correctly predcts the magntude of the water content per charge ste, and the predcted profles n all three cases also follow the general trend captured by the MRI-based measurements. There s a notceable dscrepancy between the smulated and measured results n the fnal data pont for the 92% and 80% RH cases. It s possble that these fnal ponts could occur as an artefact of the expermental setup and measurement system. The expermental and smulated results from the prevous sub-secton and Fgure 6-2 also suggest that the water content should ncrease contnuously through the PEM from the anodc boundary. It s noted that the measurement of water content profles through n-stu technques s generally an under-developed area of fuel cell scence and engneerng, as dscussed by St- Perre [75]. In order to effectvely valdate fuel cell models, t s benefcal to augment costeffectve n-stu measurement technques by whch reproducble water content profles can be determned for expermental fuel cells that employ representatve fuel cell materals. 7.6 Conclusons The lterature dentfes that the movement of water n the porous layers of a PEFC s descrbed by forms of Fck s law and Darcy s law to descrbe dffuson and convecton respectvely. Dffuson s used to descrbe the effect of concentraton gradents manly on vapour phase transport whle convecton s manly used to descrbe the effect of phase

194 7 Two-Phase Modellng through the General Transport Equaton 174 pressure gradents on lqud and vapour phase transport. The local dfference n phase pressures s used to defne the local level of saturaton n the porous medum usng expermental capllary pressure-saturaton curves. The lterature also shows that water movement across the PEM s modelled prmarly usng dlute soluton theory and occasonally usng concentrated soluton theory. The common underlyng assumpton s that transport across the PEM s manly governed by a vapour-equlbrated state, but ths does not consder the nternal change n structure when the boundares of the PEM come nto contact wth lqud water. In the current work, a common fundamental modellng approach s presented based on the prevously-developed general transport equaton whch s used wth Darcy s law to descrbe two-phase transport across both porous and quas-porous layers of a PEFC. The purpose of the two-phase GTE treatment developed n the current work s to demonstrate a smple yet theoretcally consstent and effectve method to predct water uptake and transport through the dfferent layers of the PEFC. The GDL and MPL are treated as porous but deformable structures wth predetermned levels of hydrophobc fll materal. The PEM s treated as a quas-porous layer whch contans nternal channels that can be forcbly expanded by capllary acton when a boundary comes nto contact wth lqud water. Ths quas-porous treatment s based on a prevously presented physcal model and drectly accounts for Schroeder s paradox [52]. Cell compacton and membrane constrant are also explctly modelled n the current framework; the compacton pressure s used to characterse the capllary pressure-saturaton relatonshp for the porous layers and translated nto a degree of constrant for the quas-porous layer to characterse water uptake and transport across t relatve to ts free-swellng equvalent state. In the context of a smple object-orentated 1D two-phase fuel cell model, the calculated results usng the GTE treatment are shown to be consstent wth the expermentally-obtaned net water flux data for 18 test cases publshed n the lterature for an E-TEK/Nafon confgured cell [49,54]. Calculated profles of water content across the PEM under a range of current denstes and RH condtons that nduce vapour- and lqudequlbrated water uptake are also consstent wth data measured for SGL/Nafon confgured cells usng embedded potental probes [73] and MRI scannng [74]. The agreement n

195 7 Two-Phase Modellng through the General Transport Equaton 175 magntude - and drecton of flow n the valdaton of net water flux - between calculaton and measurement confrms the valdty of the two-phase GTE treatment. The current modellng framework successfully demonstrates that mult-component two-phase transport n the porous and quas-porous layers of a PEFC can be effectvely smulated usng the GTE, whch s derved drectly from fundamental transport theory. The object-orentated modellng framework enables a ready assessment of the overall water transport and water uptake that occurs through the cell, and also allows a detaled look at the consttuent transport modes. The theoretcal technque therefore demonstrates the common nature of electrochemcal transport n fuel cell materals and provdes a fundamentally common mechanstc approach that can be readly appled n order to smulate t. 7.7 References 1 Wang CY. Fundamental Models for Fuel Cell Engneerng. Chem. Rev., 2004, 104(10), Weber AZ, Newman J. Modelng Transport n Polymer-Electrolyte Fuel Cells. Chem. Rev., 2004, 104(10), Sprnger T, Zawodznks T, Gottesfeld S. Polymer Electrolyte Fuel Cell Model. J. Electrochem. Soc., 1991, 138, Bernard D, Verbrugge M. A Mathematcal Model of the Sold-Polymer-Electrolyte Fuel Cell. J. Electrochem. Soc., 1992, 139, Fuller T, Newman J. Water and Thermal Management n Sold-Polymer Electrolyte Fuel Cells. J. Electrochem. Soc., 1993, 140, Wang CY, Cheng P. Multphase Flow and Heat Transfer n Porous Meda. Adv. Heat Transfer, 1997, 30, Wang ZH, Wang CY, Chen KS. Two-Phase Flow and Transport n the Ar Cathode of Proton Exchange Membrane Fuel Cells. J. Power Sources, 2001, 94, Pasaogullar U, Wang CY. Two-Phase Transport and the Role of Mcro-Porous Layer n Polymer Electrolyte Fuel Cells. Electrochm. Acta, 2004, 49, Pasaogullar U, Wang CY. Lqud Water Transport n Gas Dffuson Layer of Polymer Electrolyte Fuel Cells. J. Electrochem. Soc., 2004, 151(3), A399-A Pasaogullar U, Wang CY. Two-Phase Modelng and Floodng Predcton of Polymer Electrolyte Fuel Cells. J. Electrochem. Soc., 2005, 152(2), A380-A Pasaogullar U, Wang CY, Chen KS. Two-Phase Transport n Polymer Electrolyte Fuel Cells wth Blayer Cathode Gas Dffuson Meda. J. Electrochem. Soc., 2005, 152(8), A1574-A1582

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200 8 Water Transport Studes In ths chapter, the electrochemcal PEFC model developed n chapter 7 s appled to nvestgate a number of practcal factors that affect water transport across the PEM n a PEFC. The effects of PEM thckness, anode humdfcaton and PEM constrant on twophase water transport for a cell wth a non-renforced PEM are nvestgated. The effect of structural renforcement wthn the PEM on water transport s also nvestgated. 8.1 Introducton To test the mechanstc equatons developed n chapters fve and sx, the models generated therewth were appled to smulate transport characterstcs across the PEFC under vapour-phase condtons. However, water transport characterstcs across the cell are lkely to change when the operatng condtons and cell confguraton nvoke two-phase condtons at the cathodc PEM boundary and sngle-phase condtons at the anodc PEM boundary. Ths s a commonly-observed phenomenon n operatonal fuel cells. The am of ths chapter s to generate a basc understandng of how water dstrbutes wthn the non-renforced PEM under these condtons and how the dstrbuton relates to the underlyng transport processes usng the two-phase model developed n chapter seven. Three rudmentary parameters are consdered ndvdually n the two-phase study ntally; PEM thckness, anode humdfcaton and cell compresson. The study then holstcally consders the effect of all three parameters on the Ohmc resstance of the PEM. The fnal part of ths chapter focuses on structurally-renforced membranes and ams to elucdate the effect that structural renforcement has on water transport. The model s appled to smulate measured data ponts for resstance across the polymer electrolyte, whch are obtaned usng electrochemcal mpedance spectroscopy (EIS). For each smulated data pont, the model reveals the magntude of the underlyng transport mechansms and the water content, whch s collected and dscussed.

201 8 Water Transport Studes Non-Renforced Membranes To carry out water transport studes for a PEFC wth a non-renforced PEM, a number of smulatons were run to determne a general set of representatve fuel cell operatng condtons where two-phase transport wthn the layers of the cell can be acheved wthout completely floodng the cathodc porous layers. These parameters are summarsed n Table 8-1. These parameters were used for all smulatons n ths chapter unless stated otherwse. Parameter Value Anode supply condtons Anode nlet pressure 1 bar H 2 supply flow rate 0.5 slpm Anode RH 0% Cathode supply condtons Cathode nlet pressure 1.5 bar Ar supply flow rate 0.5 slpm Ar humdfcaton temperature K Cathode RH 100% Cell Parameters Actve cell area 25cm 2 Cell temperature K Cell compresson 0 MPa GDL Propertes Anode and Cathode [1] GDL porosty 0.9 GDL thckness 300 µm GDL tortuosty 1.5 GDL PTFE content 5% GDL permeablty cm 2 MPL Propertes Anode and Cathode [1,2] MPL porosty 0.4 MPL thckness 25 µm MPL tortuosty 1.5 MPL PTFE content 23% MPL permeablty cm 2 Table 8-1 Base operatng condtons & materal propertes used n the PEFC model for the water transport studes, unless otherwse stated.

202 8 Water Transport Studes PEM Thckness The PEM s charactersed by two fundamental propertes that can be set through materal selecton, namely the equvalent weght and the thckness of the PEM. Early PEFCs commonly employed Nafon 117 whch has an equvalent weght of 1100 g/mol and thckness of 7 mls (178 µm). However modern PEMs are typcally much thnner and can be structurally renforced. Examples nclude Gore-18 and Gore-25 whch have 18 and 25 µm thcknesses respectvely. Non-renforced membranes nclude DuPont-manufactured Nafon 1135, NRE-211 and NRE-212 whch have 89, 25 and 51 µm thcknesses respectvely. The equvalent weght of the renforced membranes s typcally 950 g/mol whereas the nonrenforced membranes have the same equvalent weght as Nafon 117. The structural renforcement can lmt the dffusvty of water across the polymer electrolyte, whch affects net water transport. Ths wll be nvestgated separately n secton 8.3. Ths sub-secton wll focus on the effects of PEM thckness at an equvalent weght of 1100 g/mol. The transton towards thnner PEMs has occurred because the thnness of the PEM can enhance ts hydraton and therefore ts proton conductvty under workng fuel cell condtons, as shown by sngle-phase smulatons [3]. The precse effect that the thckness of the PEM has on two-phase transport across t s relatvely less well-defned. The effect of fve PEM thcknesses are consdered n the current study; 25.4, 36.8, 50.8, 63.5 and 76.2 µm. Fgure 8-1 shows the expanded thckness of the unconstraned PEM accordng to the smulated water uptake. Fgure 8-1 also shows that n all fve cases, the thckness of the freeswellng PEM ncreases by over 10% of ts orgnal value. The percentage expanson falls as a functon of PEM thckness suggestng that the thnner membranes are most susceptble to dmensonal change as a consequence of water uptake for the smulated condtons. For the condtons gven n Table 8-1, the anodc porous layers do not experence lqud phase transport; however, the cathodc porous layers do whch results n a lqud phase boundary pressure at the cathodc PEM nterface. The sngle phase boundary condtons at the anode nterface and two phase boundary condton at the cathode nterface result n a transtonal regme across the PEM where both vapour- and lqud- equlbrated networks co-exst. Fgure 8-2 shows the water content profle across the PEM whle Fgure 8-3 shows the lqud pressure and correspondng pore expanson profles.

203 8 Water Transport Studes 183 Fgure 8-1 Expanded membrane thckness and percentage change n thckness as a functon of the orgnal thckness for fve smulated PEM thcknesses Fgure 8-2 shows that for all fve cases the water content through the PEM ncreases above 14 water molecules per charge ste. Because of the sngle-phase boundary condtons at the anode, the local water content at ths nterface s well below 14 for all cases. In the case of the 25.4 µm PEM, the nterfacal water content approaches 10. From Fgure 8-2, t can be seen that the λ=14 lmt s reached wthn a short dstance from the anodc boundary n the thnner PEMs. The lqud phase therefore penetrates a greater proporton of ts thckness from the cathode nterface than n the thcker PEMs, as evdent n Fgure 8-3 (a). Fgure 8-3 (b) shows the pore expanson that results from the ntruson of the lqud phase. For the boundary condtons consdered here, the pore expanson occurs gradually, ncreasng steadly from zero where the vapour-only regme ends towards unty at the cathodc PEM boundary. The actual depth of lqud penetraton s between 14 µm and 17 µm for all fve cases as shown n Fgure 8-4 whch ndcates that the thckness of the PEM does not sgnfcantly control the absolute depth of lqud water ntruson.

204 8 Water Transport Studes 184 Fgure 8-2 Water content profle as a functon of non-dmensonal poston along the expanded PEM thckness for the fve dfferent PEM thcknesses (a) (b) Fgure 8-3 Lqud ntruson profles for fve dfferent PEM thcknesses as a functon of nondmensonal poston along the expanded PEM thckness. (a) Lqud pressure; (b) pore expanson profle. Note that the x-axs starts at 0.4.

205 8 Water Transport Studes 185 Fgure 8-4 Depth of lqud water penetraton from cathodc PEM boundary for fve PEM thcknesses. Fgure 8-5 shows the drecton and magntude of the net water transport per proton, β, across the PEM and Fgure 8-6 resolves the vapour and gas phase components of net water transport wthn the PEM as a functon of thckness for the fve thcknesses consdered. The components of net water transport per proton n the vapour- and lqud- equlbrated networks can be calculated as; β β vap lq = ( 1 sepf ) β = ( 1 sepf ) 2 = s β = s epf epf α 2 α (8-1) (8-2) The calculated results gven n Fgure 8-5 show that for the smulated condtons, the net water flux occurs n the drecton of the anode and s manly domnated by vapour phase transport. It should be noted that the magntude of the average vapour and lqud phase components of net water flux do not reflect the contnuous flow of water n ther respectve phases from one boundary of the PEM to the other, but the thckness-averaged fluxes that occurs n the collapsed and expanded regons of the PEM. Fgure 8-5 ndcates that the contrbuton of lqud phase flow generally remans unchanged as the thckness of the PEM s ncreased and that ts average flux always occurs n the drecton of the cathode.

206 8 Water Transport Studes 186 Fgure 8-5 Net water transport per proton and average vapour and lqud phase components for fve PEM thcknesses Fgure 8-6 shows that n all fve cases, there s a steady vapour-phase flux across the PEM n the regons where there s no lqud water ntruson and no correspondng lqud phase flux. However, n the regons where lqud water does ntrude the PEM, both vapour and lqud phase fluxes change non-lnearly n the shape of two opposng arcs. The lqud phase flux ncreases from zero headng n the drecton of the cathode, peaks, and then decreases. The vapour phase flux ncreases n magntude from the steady-state value for the vapour-only regme headng n the drecton of the anode, peaks and then decreases. In the case of the thnner PEMs, because the relatve depth of lqud nfltraton s greater, the bmodal non-lnear transport develops at a much closer dstance to the anode than n the case of the thcker PEMs where t s retarded towards the cathode. In order to understand the nature of the non-lnearty, attenton has to be turned to the underlyng phenomenologcal transport processes.

207 8 Water Transport Studes 187 Fgure 8-6 Water flux per proton as a functon of non-dmensonal poston along PEM thckness. Grey - lqud phase; black vapour. ( ) 25.4 µm; (+) 38.1 µm; ( ) 50.8 µm; ( ) 63.5 µm; ( ) 76.2 µm. Theoretcally, the general transport equaton gven n equaton (7-15) can be resolved nto sx components of net water transport, namely that due to proton movement, convecton and dffuson each n lqud phase and vapour phases. The magntude of each component can be derved as: ( 1 s ) Φ 2, vap β H +, vap = epf ; 2Φ1 1 β Φ 3, vap β conv, vap = ( 1 sepf ) ; β 2IΦ ctot ( 1 sepf ) cw H +, lq conv, lq = s epf = s epf Φ 2, lq 2Φ Φ 1 3, lq 2IΦ tot β dff, vap = ; β dff, lq = sepf cw 2IΦ1 2IΦ1 1 c (8-3) (8-4) (8-5) and by defnton β = (8-6) J βh, J βconv, J βdff, J

208 8 Water Transport Studes 188 where J denotes phase. The water flux due to proton movement occurs as a combnaton of proton dffuson and electro-osmotc proton flux due to the electrc feld. The net water transport per proton flux s defned as;, + = β mode vap βmode, lq β (8-7) Based on these parameters, t s possble to resolve the lqud and vapour curves for the 25.4 µm PEM gven n Fgure 8-6 nto consttuent parts. Fgure 8-7 shows the correspondng water transport curves as a functon of PEM thckness fracton. Convecton n the vapourequlbrated network s assumed to be neglgble accordng to the assumptons of the model, and so β 0. conv, vap = From the results n Fgure 8-7 t becomes mmedately evdent that water transport across the PEM s manly domnated by ts dffuson through the PEM and ts nteracton wth proton movement. Along the frst 50% of the thckness of the PEM, water transport s domnated by dffuson and proton-nduced flux n the vapour-equlbrated network n the absence of lqud water nfltraton. The dffusve flux occurs n the drecton of the anodc boundary where there s less water than the cathode boundary, as evdent n Fgure 8-2. The proton flux occurs n the opposte drecton, whch causes the proton-nduced water flux n the vapour-equlbrated network to occur n the drecton of the cathode as well. From these two transport modes, t s the dffusve flux whch s greater n magntude and therefore results n a net water flux n the drecton of the anode. Along the latter 50% of the thckness of the PEM, both vapour- and lqud-equlbrated transport modes occur, whch results n addtonal dffusve and a proton-nduced water flux n the lqud-equlbrated network. As the nfltraton of lqud water and the pore expanson ncreases towards the cathodc boundary, the magntude of the fluxes n the vapour-equlbrated networks tal-off, whle the lqud phase fluxes n the lqud-equlbrated networks become more domnant and ncrease n magntude. These characterstcs explan the non-lnear nature of the lqud and vapour components of the net water flux descrbed n Fgure 8-6. In an dentcal manner to the vapour phase fluxes, the lqud phase dffusve flux occurs n the drecton of the anode, whereas the proton-nduced flux occurs n the drecton of the cathode. The nterestng observaton here for lqud phase transport s that t s the proton-nduced flux whch margnally domnates over the dffusve flux and results n an average lqud phase flux that

209 8 Water Transport Studes 189 occurs n the drecton of the cathodc boundary, as ndcated by Fgure 8-5. Ths can be attrbuted to equaton 7-45 whch reflects the fact that the electro-osmotc drag coeffcent n a lqud-nfltrated regon wll be hgher than n the collapsed regons. These basc characterstcs are generally true for the remanng four membrane thcknesses as well, and so do not need to be dscussed ndvdually. Fgure 8-7 Vapour and lqud phase components of net water transport as a functon of poston along PEM thckness for the 25.4 µm PEM case. Fgure 8-8 confrms that the gradent n water content throughout the thckness of the PEM s greatest n the thnner membranes, whch nvokes a large dffusve component of net water transport towards the anode, partcularly n the domnant vapour-equlbrated network as observed n Fgure 8-5 Fgure 8-7. As the thckness ncreases, the gradent n water content reduces, whch wll reduce the dffusve component of net water transport for both phases. Interestngly, for the fve thcknesses consdered the gradent n water content n general ncreases qute suddenly n the lqud-nfltrated regon. The large consequent dffusve flux created towards the anode n the lqud phase as shown n Fgure 8-7 s however not suffcent to overcome the proton nduced flux n the opposte drecton.

210 8 Water Transport Studes 190 Fgure 8-8 PEM water content profle as a functon of the non-dmensonal membrane poston for fve PEM thcknesses. The gradent n water content change n water molecules per charge ste dvded by the length ncrement n µm. λ ' s defned as the local Anode Humdfcaton One way of mprovng the hydraton of the PEM from the anodc boundary s to humdfy the fuel supply, although there s a system-level penalty to be pad for the ncreased complexty. Although the mplcatons of anode humdfcaton on water uptake has been well defned for sngle-phase vapour-equlbrated condtons, t s less well defned for when lqud water ntrudes the PEM. Fgure 8-9(a) shows the calculated water content as a functon of PEM thckness fracton for the fve thcknesses consdered n the prevous subsecton; all operatng condtons are the same as those gven n Table 8-1 apart from the anode RH whch s now set to 100%. Compared to Fgure 8-2, t s evdent that fuel humdfcaton drectly mproves the hydraton of the PEM from the anodc boundary. In the case of the 25.4 µm PEM, the water content at the anodc boundary has ncreased from around 10 water molecules per charge ste to 13. In the case of the 76.2 µm PEM, the water content at the same nterface has ncreased from above 2 molecules per charge ste to around 6. Fgure 8-9(b) shows that the addtonal humdty affects the lqud water network n the PEM. Compared to Fgure 8-3, t can be seen that the lqud network ntrudes a much larger

211 8 Water Transport Studes 191 proporton of the membrane thckness. For the 25.4 µm PEM, the lqud water network now ntrudes around 85% of ts thckness and over 35% n the case of the 76.2 µm PEM. (a) (b) Fgure 8-9 Lqud ntruson profles for fve dfferent PEM thcknesses as a functon of nondmensonal poston along the expanded PEM thckness. (a) Water content; (b) lqud ntruson pressure profle. Fgure 8-10 shows the net water flux per proton across the PEM for each of the fve cases, and the consttuent average parts n vapour- and lqud- equlbrated networks. The results here are dfferent to those n Fgure 8-5. The average water transport per proton n the lqud network occurs n the drecton of the anodc boundary, as observed prevously. However, wth the addton of anode humdfcaton, the average vapour phase transport occurs n the drecton of the cathodc boundary. Ths can be explaned by Fgure 8-11,

212 8 Water Transport Studes 192 whch shows the dffuson and proton-nduced components of the vapour-equlbrated flux for the 38.1 µm PEM. The results suggest that wth anode humdfcaton, because the PEM s nherently better hydrated, the magntude of the drag component nduced by proton flux towards the cathodc boundary s greater relatve to the magntude of the dffusve component n the opposte drecton. The net vapour phase component s therefore postve. The excepton to ths observaton s the 25.4 µm PEM, whch suggests a dependence on membrane thckness. For the 25.4 µm PEM, Fgure 8-11 (a) shows that the proton-nduced flux s greater than the dffusve flux n the vapour-only regon closest to the anode. However, the protonnduced vapour phase flux decreases n magntude more abruptly than the dffusve vapour phase flux as lqud nfltraton ncreases towards the cathode. Overall, therefore, the dffusve flux domnates n the vapour-equlbrated network and results n a net vapour phase flux occurrng n the drecton of the anode, as shown n Fgure The proton-nduced flux s contnuously greater n magntude than the dffusve flux n the lqud-equlbrated network, whch explans the observaton of Fgure 8-10 and results n a large net lqud-phase flux occurrng n the drecton of the cathode. Fgure 8-10 Net water transport per proton and average vapour and lqud phase components for fve PEM thcknesses. Anode and cathode supples are saturated

213 8 Water Transport Studes 193 (a) (b) Fgure 8-11 Vapour and lqud phase components of net water transport as a functon of poston along PEM thckness wth both fuel supples fully humdfed. (a) 25.4 µm case; (b) 38.1 µm case PEM Constrant Operatonal fuel cells are typcally compressed to mnmse reactant leaks from the perpheres and to ensure good contact between the electron-conductng layers of the cell. In an unconstraned state, the PEM has a natural tendency to swell wth water uptake. If the compressve force appled to the cell s suffcently hgh, the PEM may also become physcally compressed under certan operatng condtons. If on the other hand the

214 8 Water Transport Studes 194 compressve force s relatvely low, t may allow the PEM to swell and may subsequently mpart a compressve force onto the adjacent layers of the cell. By lmtng the natural tendency of the PEM to swell, there s a reducton n the amount of water that the polymer end groups can hold. Ths may affect water management strateges and could affect cell performance. The purpose of ths part of the study therefore s to examne what role membrane constrant has on net water transport and water uptake when the PEM s subjected to two-phase condtons at the cathodc boundary. Fgure 8-12 (a) shows the effects of compresson on the thckness of the 25.4 µm PEM. In the unconstraned state, the thckness of the PEM ncreases by over 15% of ts drystate value. However, as constrant s ncreased, the expanson s curtaled. The pont of zero dmensonal change occurs n ths case when the degree of constrant s just above 0.4. In the fully constraned state, the thckness of the PEM s reduced by around 25% of ts dry-state value. The effect on the average water content s shown n Fgure 8-12 (b). Fgure 8-12b shows the average water content wthn the PEM and also the average water content wthn the PEM normalsed to the thckness of the free-swellng PEM. The average water content wthn the PEM ncreases wth constrant, suggestng that compresson causes water molecules to become packed much closer together. However, when normalsed to the thckness of the free-swellng PEM, the results confrm that the PEM holds much less water when t s compressed than when t swells freely, as would be reasonably expected. Relatve to the free-swellng PEM whch holds 14.6 molecules per charge ste, a fully constraned PEM holds 10.6 molecules per charge ste. The effect on net water transport s shown n Fgure 8-12c. The average water content s calculated relatve to the thckness of the freeswellng PEM. The results show that the average water content drops wth ncreasng constrant from a free-swellng value of 14.6 to a fully constraned value of The net water transport occurs n the drecton of the anodc boundary regardless of constrant, but ts magntude margnally ncreases wth respect to ncreasng constrant. Consderng the average vapour- and lqud-equlbrated transport components of net water transport shows that both dverge wth constrant. The lqud-equlbrated component ncreases n magntude n the drecton of the cathodc boundary wth ncreasng constrant and the vapourequlbrated component also ncreases n magntude but n the drecton of the anodc boundary. These changes n water transport are attrbuted to the effect of constrant on the thckness of the PEM. A reducton n overall thckness causes the gradent n water content

215 8 Water Transport Studes 195 and extent of lqud nfltraton wthn the PEM to ncrease causng the dffusve and electroosmotc drag components to ncrease respectvely. (a) (b) (c) Fgure 8-12 Compresson effects on PEM thckness, water content and water transport; (a) change n PEM thckness as a functon of degree of constrant; (b) change n average water content; (c) water flux profles.

216 8 Water Transport Studes 196 Fgure 8-13 (a) shows the superfcal gradent n water content as a functon of constrant, calculated as; λ λ = λ A 2b C 2b t mem, c (8-8) (a) (b) Fgure 8-13 Effect of PEM constrant on PEM water content and lqud nfltraton. (a) Superfcal gradent n water content as a functon of degree of constrant; (b) lqud network ntruson pressure as a functon of non-dmensonal PEM thckness for dfferent degrees of constrant.

217 8 Water Transport Studes 197 The gradent ncreases wth constrant, whch allows the magntude of the dffusve component of net water transport to ncrease. Because the dffusve flux s more domnant n the vapour phase, t causes the vapour component of net water transport to ncrease n magntude wth constrant, as shown n Fgure 8-12(c). Fgure 8-13 (b) shows the ntruson pressure of the lqud water network for dfferent levels of constrant. The results suggest that greater constrant allows the lqud water network to penetrate a greater proporton of the thckness of the PEM. As a result, the ncrease n local water content allows more water to be electro-osmotcally dragged back to the cathode. Ths causes the lqud component of net water transport to ncrease wth constrant as shown n Fgure 8-12(b) because the water flux due electro-osmotc drag s most domnant n the lqud phase Parameter Effects on PEM Resstance It s possble to generate a holstc understandng of the combned effects of PEM thckness, compresson and anode humdfcaton by consderng the resstance across the PEM. The proton conductvty at each mesh pont across the PEM can be calculated usng equaton 7-44 as a functon of the local volume fracton of water, whch tself s calculated as a functon of the local water content usng equaton The resstance across the constraned PEM s then calculated as [3]; r proton = t mem, cons 1 dz σ 0 (8-9) In ths part of the study, all fve thcknesses are consdered wth ncreasng degrees of constrant and three states of nlet humdfcaton. All other condtons are kept the same as those gven n Table 8-1. The followng three states are consdered n Fgure 8-14 (a) (c): Fgure 8-14 (a): anode saturated to 60 C, cathode saturated to 90 C Fgure 8-14 (b): anode dry, cathode saturated to 90 C Fgure 8-14 (c): anode dry, cathode saturated to 60 C The frst two states ensure a partal pressure of lqud water at the cathodc nterface. The thrd state ensures that water only exsts n vapour phase at the cathodc nterface.

218 8 Water Transport Studes 198 Fgure 8-14 (a) shows that by humdfyng both supples and by ensurng that the cathodc boundary of the PEM s n contact wth lqud water, the Ohmc resstance of the PEM can be kept generally lower than 0.1 Ohm-cm 2. Fgure 8-14 (b) shows that by removng the anode humdfcaton, the Ohmc resstance ncreases. For the thcker membranes, the effect s more drastc but generally speakng the Ohmc resstance s well below 1 Ohm-cm 2. Fgure 8-14 (c) shows that by removng the anode humdfcaton and by reducng the saturaton temperature of the cathode supply from 90 C by 30 C - thereby nvokng a vapour-equlbrated only transport mode - the Ohmc resstance ncreases furthermore and can be well above 1 Ohm-cm 2 n the thcker membranes. Fgure 8-14 (a) (c) also show that for all the cases consdered, t s the thnnest membranes have the least Ohmc resstance. Overall, the results suggest that the lqud water at the cathodc boundary can help to reduce the resstance across the PEM. The smulated phenomenon can be attrbuted to the ncrease n local water content that occurs throughout the thckness of the PEM when lqud water ntrudes the PEM from the cathode boundary, and results n a correspondng ncrease n local conductvty. Another observaton from all three graphs n Fgure 8-14 s that the resstance of the PEM decreases wth ncreasng membrane constrant. Referrng back to the prevous dscusson on membrane constrant, t has been establshed that by constranng the membrane, the PEM wll hold less water than ts free-swellng equvalent state and also that by ncreasng constrant the PEM s less lkely to expand beyond ts dry state and more lkely to shrnk n thckness. The results of Fgure 8-14 suggest that the decrease n water content wth respect to constrant s less severe than the smultaneous decrease n thckness. Ths means that the net effect of membrane constrant s to tghten the dstrbuton of water clusters wthn t because even though the water content drops slghtly, the overall volume of the PEM decreases more substantally and causes the volume fracton of water to ncrease. Ths s shown n Fgure 8-12b. Consequently under these condtons, t s feasble for the pathways for proton conducton to mprove because the charged end groups are packed closer together. These results are consstent wth dscussons n the lterature [4]. From a molecular vewpont, t s well known that proton movement can be orentated by two mechansms, namely vehcular transport and Grottus hoppng [5,6]. In the frst of these, t s assumed that protons bnd wth water to form hydronum complexes (H 3 O + ) whch dffuse as molecular ons down a concentraton gradent [7]. In the second, t s assumed that

219 8 Water Transport Studes 199 the protons essentally hop from one water molecule to the other ndependently wthout relyng upon water as a vehcle. In both of these mechansm, there s a clear dependence on the local water content and the closeness of water clusters throughout the PEM. Based on the dependence of conductvty on the volume fracton of water the modellng results suggest that the net proton transport mechansm s mproved partcularly when lqud water nfltrates the PEM. The results have already shown that dependng upon the thckness of the PEM, the nfltraton of lqud water can ndeed ncrease the water content markedly. The results also suggest that by constranng the membrane, there s an effect on the arrangement of the hydrophlc domans wthn the PEM whereby water clusters are forced closer together even though the total amount of water that the PEM holds can be forcbly reduced. Membrane constrant therefore also appears to mprove the net proton transport mechansm. In concluson, therefore, the best scenaro for proton conductvty appears to be n a regme where lqud water s allowed to nfltrate the PEM n order to prolferate local water content, and whch s also constraned n order to tghten the dstrbuton of water clusters wthn t. The modellng results suggest that ths can be acheved wth a thn PEM whch s constraned and operated wth a cathodc boundary that s n contact wth lqud water. There are a number of clear lmtatons to ths concluson. Frst, t has to be acknowledged that the repeated nfltraton and expulson of lqud water n and out of the PEM could hasten the onset of performance degradaton and cell falure as dscussed n Chapter 3. Fgure 8-1 would suggest that ths s especally true for thn PEMs whch are most prone to aggressve dmensonal change. Second, t also has to be acknowledged that the thckness of the PEM lmts the rate of fuel and contamnant crossover as shown n Chapters 5 and 6 respectvely, although both are also nversely proportonal to current densty. Thrd, the lqud water at the cathodc boundary has to be establshed wthout floodng the porous layers. Although the floodng of porous layers has not been explored explctly n the current study, t can be controlled by the physcal parameters of the GDL and MPL.

220 8 Water Transport Studes 200 (a) (b) (c) Fgure 8-14 Resstance maps for dfferent levels of constrant and PEM thcknesses. (a) anode saturated to K and cathode saturated to K (P(lq) > 0 at the cathode); (b) dry anode and cathode saturated to K (P(lq) > 0 at the cathode); (c) dry anode, cathode saturated to K (P(lq) = 0 at the cathode) 8.3 Structurally-Renforced Membranes Structurally-renforced PEMs are beng ncreasngly used n modern PEFCs. As dscussed n the precedng chapter, these membranes contan an nert matrx whch s mpregnated wth polymer electrolyte n order to acheve electrochemcal and mechancal propertes that the polymer electrolyte cannot provde on ts own. The two predomnant characterstcs that are sought are:. low shrnkage upon hydraton

221 8 Water Transport Studes 201. hgh mechancal strength These propertes ensure dmensonal stablty and therefore durablty under PEFC operaton condtons. It s the nert matrx - whch s typcally based on PTFE - that provdes the structural renforcement. The PTFE can take the form of a porous sheet (20-30% wt.% renforcement), an embedded yarn (10 wt. % renforcement) or as a fbrl dsperson (2-5 wt. %). The renforcement can allow the thckness of structurally-renforced membranes to be as low as 5 20 µm [8]. Whle the lterature demonstrates that structurally renforced membranes can exhbt a lfe-tme that s one order of magntude longer than non-renforced membrane of comparable thckness [9], what s not so clear s the effect that renforcement has on water transport characterstcs. Ye and Wang [10] determned the transport propertes of water through structurally-renforced membranes and noted the followng based on hghfrequency response measurements: 1. electro-osmotc drag coeffcent: the drag coeffcent held a value of around 1.07 over a large relatve humdty range between 40% and 95% 2. dffuson coeffcent: the dffuson coeffcent of water was lkely to be anywhere between a factor of 0.1 and 0.9 of that for a non-renforced Nafon membrane over a large range of water contents (t was nferred that measurements were carred between 4 and 15 water molecules per charge ste). The electro-osmotc drag coeffcent s consstent wth that measured for Nafon (precedng secton) for vapour equlbrated condtons. Ths therefore suggests that the renforcement does not affect the mechansm by whch water s dragged due to proton mgraton. The dffusvty of water, however, s clearly affected. One possble mechansm could be the hydrophobc nature of the PTFE, whch may be lmtng the moblty of water molecules wthn the PEM and therefore restrctng ts dffusvty. The purpose of ths nvestgaton s to smulate and understand the measured proton conductvty of a PEFC employng a structurally-renforced PEM over a range of operatng condtons.

222 8 Water Transport Studes Expermental Materals For the purposes of the current study, an 18 µm structurally-renforced PEM whch s coated wth anode and cathode catalyst (SR-CCM) s employed wth an equvalent weght of 950 g/mol, dry densty of 2 g/cm 3 and footprnt of cm 2. Two sets of results are consdered n the present study to reveal the characterstc behavour of the SR-CCM. In the frst case (case 1), two standard GDL-MPL assembles were employed on both sdes of the SR-CCM; characterstc propertes are estmated from the lterature [1,11]. The standard materal contans a carbon-paper GDL wth a bulk porosty of 0.9, nomnal thckness of 300 µm and PTFE content of 5 wt%. The bulk porosty of the MPL s 0.4 and has a nomnal thckness of 25 µm and PTFE content of 40 wt %. In the second case (case 2), the standard GDL-MPL assembly employed for the cathode s replaced wth a smlar GDL-MPL assembly that contans no PTFE n the GDL. Expermental Setup A sngle-cell fxture wth a serpentne flow channel was used as the test cell. A bespoke system wth dgtal mass flow controllers, data acquston and an RBL programmable load bank was used for gas supply, humdty control and electronc load control. An Autolab 302N frequency response analyser and potentostat were used for n-stu proton conductvty measurements based on electrochemcal mpedance spectroscopy (EIS). Zvew software (Scrbner Assocates, Inc.) was used to analyse the collected AC mpedance data. Expermental Procedure The compacton pressure appled to the cell s 1.5 MPa. Fgure 20 provdes the flow rates and equvalent calculated stochometres of the anode and cathode as a functon of current densty when operated wth humdfed hydrogen and dry ar respectvely. The

223 8 Water Transport Studes 203 cathode s operated open-ended whle the anode s dead-ended and purged perodcally to remove any condensate n the anode flow felds. The anode nlet pressure s set to 1.5 bar whle the cathode nlet pressure s ncreased from around 1.0 bar to around 1.1 bar wth current densty. The EIS measurements are taken from the cell over a range of operatng current denstes ( A/cm 2 ). It s assumed that the x-ntercept on the Nyqust plot of the PEFC frequency response reflects the total resstance of the cell,.e., the sum of resstance to the flow of protons and electrons. The resstance to the flow of electrons n the electron-conductng parts of the cell such as the end plates and carbon substrate porous layers were measured ex-stu (at nomnal thcknesses where approprate) and determned to be 42 mω-cm 2 for the standard case and 40 mω-cm 2 for the second case. It s assumed that these values are not lkely to change n-stu and therefore assumed to be constant. Subtractng these fgures from the measured x-ntercept gves the value of Ohmc resstance to proton flow, whch s charactersed prmarly by the proton conductvty of the PEM. Ths s lkely to change n-stu due to the operatng condtons of the cell and the water uptake that occurs as a result. In ths nvestgaton, the resultng resstance of the PEM s smulated usng the model developed n the prevous chapter. Fgure 8-15 Appled anode ( ) and cathode ( ) flow rates n standard ltres per mnute (black) and calculated stochometres (grey) Results and Dscusson In order to nvestgate the effect of SR-CCMs on water transport, the dffusvty scalng factor n the PEFC model s tuned untl the smulated resstance to proton flow

224 8 Water Transport Studes 204 predcted by the model agrees wth that obtaned from measurement. In dong so, each current densty s smulated turn-by-turn usng the measured boundary condtons of the channel gases (flow rates, pressures, nlet gas temperatures), and the average cell temperature whch s estmated from the measured nlet and outlet temperatures of both anode and cathode supples. Fgure 8-16 shows the membrane resstance from measurement, the smulated membrane resstance and the tuned dffusvty scalng factor for both test cases. Interestngly, the tuned values for the scalng factor result n an almost straght-lne relatonshp wth current densty ntersectng the orgn for both test cases yet generate very close correlatons between the smulated and measured membrane resstance, whch have a non-lnear dependence on current densty. The smulatons suggest that for test condtons consdered, the dffusvty scalng factor les n the range of Fgure 8-16 Membrane resstance and tuned dffusvty scalng factor as a functon of current densty. ( ) measured case 1 (agdl/cgdl: 5/5 wt. % PTFE); ( ) measured case 2 (agdl/cgdl: 5/0 wt.% PTFE); ( ) smulated values. Fgure 8-17 shows the smulated thckness-averaged water content curves whch correspond to the results of Fgure The results show that the water content s ntally low for both cases but rses sharply and peaks n the A/cm 2 band. Ths results n the ntal fall n membrane resstance observed n Fgure Thereafter, the water content gradually falls, whch results n the hgh membrane resstance observed n Fgure 8-16 for both cases up to 0.9 A/cm 2. The low ntal water content can be explaned by the dryng effect that s caused by the hgh ntal stochometres of the cathode supples, notng that the cathode gas s suppled dry. Ths causes the cell to loose the small amounts of mosture

225 8 Water Transport Studes 205 generated n the form of product water n the cathode catalyst layer. As the stochometry settles to around 2 for both supples after 0.2 A/cm 2, the subsequent changes n water content are less abrupt. Fgure 8-17 Smulated thckness-averaged water content as a functon of current densty for case 1 and case 2 as a functon of current densty. Fgure 8-18 shows the electro-osmotc drag and dffusve components of net water flux across the PEM. Fgure 8-18(a) shows that the electro-osmotc drag component ncreases n almost drect proporton to current densty. Fgure 8-18(b) however shows that the dffusve component has a non-lnear dependence on current densty. The ntal dffusve flux s hgh n magntude, whch demonstrates that the concentraton gradent s suffcently hgh to drve transport across the PEM from the cathodc boundary to the drer anodc boundary even though the scalng factor s lmtng the dffuson coeffcent. Because the stochometry of the cathode supply s hgh up to 0.25 A/cm 2, the dryng effect begns to lmts the concentraton of water at the cathodc PEM boundary and therefore reduces the dffusve flux. As current densty ncreases to 0.9 A/cm 2, the producton of water ncreases whle the cathode stochometry decreases, whch has the net effect of ncreasng the concentraton of water at the cathodc PEM boundary. Ths has the effect of ncreasng the water content gradent across the PEM and therefore ncreases the magntude of the dffusve flux. Overall, therefore, the non-lneartes observed n Fgure 8-16 Fgure 8-18 occur as a result of the operatonal setup n terms of reactant supply and the subsequent effect on membrane hydraton.

226 8 Water Transport Studes 206 (a) (b) Fgure 8-18 (a) Electro-osmotc drag (b) and dffusve components of (c) net water flux across the PEM as a functon of current densty. Test case 1 ( ); test case 2 ( ). (c)

227 8 Water Transport Studes 207 What remans to be explaned s the dfference n the tuned dffusvty scalng factor between cases 1 and 2 whch appears to enhance both electro-osmotc and dffusve fluxes across the PEM, as shown n Fgure In order to explan ths, attenton s turned to Fgure 8-19 whch shows the calculated membrane thckness for each case. The results show that the hghly-constraned PEMs do not undergo aggressve dmensonal change. For both cases the smulatons suggest that the change n thckness between the two cases s around 0.1% of the nomnal thckness of 18 mcrons. However, the results reveal that from the two cases, t s the second whch allows the greatest amount of expanson; case 1 allows a 1.7% expanson whereas case 2 allows a 1.8% expanson. Ths margnal dfference can be attrbuted to the dfference n PTFE contents n the cathode GDLs. For case 2, there s no PTFE n the cathode GDL whch appears to allow slghtly more expanson than for case 1 where the cathode GDL s arguably more rgd due to the 5 %wt. PTFE content. The results therefore suggest that the dffusvty scalng factor may have a dependence upon the compressed state of the SR-CCM. Even though the dfference n expanson s only 0.1% of the nomnal thckness, the effect on the scalng factor s more profound; at 0.9 A/cm 2 the dffusvty scalng factor s lmted to 0.3 for case 1 whereas t ncreases to 0.4 for case 2. Therefore, because the water s more moble n case 2, the magntude of ts dffusve flux rato s greater n magntude than case 1 (n the drecton of the anode from the cathode). Ths mproves the hydraton of the PEM but also allows a slght ncrease n the electro-osmotc drag (n the opposte drecton from anode sde to cathode sde). Interestngly, Fgure 8-18(b) suggests that t s the dffusve flux that s greater n magntude than the electro-osmotc drag flux under the test cases consdered, bearng n mnd that the cathode supply s at a lower pressure than the dead-ended anode supply. The results suggest that the structural renforcement that naturally curtals the dffusve flux and lmts the water content of the PEM also therefore retards the amount of water that can be electroosmotcally dragged back. Therefore water s allowed to travel n the drecton of the anode, whch may assst n delayng the onset of mass transport lmtatons due to cathode floodng. Ths phenomenon could be nherent to most low-pressure applcatons of SR-CCMs n PEFCs.

228 8 Water Transport Studes 208 Fgure 8-19 Change n PEM thckness as functons of current densty. ( ) Case 1; ( ) case Conclusons The mult-layer 1D two-phase fuel cell model developed n Chapter 8 has been appled to examne water transport and water uptake characterstcs through the PEM when the cathodc PEM boundary s n contact wth lqud water. The conclusons are: 1. The effect of PEM thckness - The smulated results show that for a gven set of operatng condtons, the depth of lqud water penetraton from the cathodc boundary s largely unaffected by the thckness of the PEM when unconstraned. The results show that the net water flux per proton n the lqud network of the PEM also remans largely unaffected by the thckness of the PEM, but that the same does not hold true for transport n the vapourequlbrated mode. The magntude of the net water flux n the vapour-equlbrated mode decreases wth ncreasng PEM thckness, suggestng that a longer transport path can retard the vapour-phase transport across the PEM. Overall, therefore, net water transport decreases n magntude wth PEM thckness. The results from ths frst set of smulatons where the anode gas s suppled dry also show for all smulated thcknesses that the dffusve water flux domnates over the proton-nduced flux n the vapour phase, but that the proton-nduced flux domnates over the dffusve flux n the lqud phase. 2. The effects of anode nlet gas humdfcaton - The results suggest that by humdfyng the anode supply, the hydraton of the anode sde of the PEM mproves and can also allow a

229 8 Water Transport Studes 209 more extensve lqud water network to form whch reaches deeper towards the anodc sde of the PEM from the cathodc boundary. The results also suggest that the proton-nduced water flux n vapour- and lqud-equlbrated networks are greater n magntude than the dffusve components because of the ncreased water content throughout the thckness of the PEM, whch causes the net water transport to occur n the drecton of the cathode for the thcker membranes. However, the results also suggest that the effect of electro-osmotc drag flux n the vapour regon can be senstve to the thnness of the PEM and the depth of lqud water penetraton. 3. The effects of cell compresson on membrane constrant - The results demonstrate that PEM constrant can easly restrct ts water content relatve to ts free-swellng state and can also be accompaned by a decrease n the thckness of the PEM. If the change n thckness wth constrant s more severe than the change n water content, the gradent n water content can ndeed ncrease, whch can hasten both lqud and vapour phase transport. However, for the test condtons consdered, a substantal change n net water transport was not observed. The results also suggest that PEM constrant can cause water molecules to become packed closer together. The results also demonstrate that cell compresson may allow the lqud water network to nfltrate deeper nto the polymer matrx from the cathodc boundary towards the anodc boundary. 4. Combned effects of PEM thckness, humdfcaton and compresson - For the smulated condtons, the results suggest that low Ohmc resstance can be acheved for thn membranes whch are operated n a constraned state and wth a cathodc boundary that s n contact wth lqud water. The lmtaton of ths concluson s that reducng the thckness of the PEM wll cause a greater crossover of hydrogen, as shown n chapter Effects of structurally-renforced membranes - The expermental results obtaned from n-stu mpedance data and smulaton suggest that for a hghly-compressed PEFC, the dffusvty scalng factor for structurally renforced membranes can be as low as (.e., the dffusvty of water n a structurally-renforced PEM could be less than 40% of that typcally measured n an non-renforced PEM such as Nafon). The results suggest that the dffusvty scalng factor depends upon the compressed state of the PEFC and the structural rgdty of surroundng layers. For the two test cases consdered n the current study where the PEFC s operated n a hghly-compressed state, the results from smulaton show that the

230 8 Water Transport Studes 210 SR-CCM wll stll tend to swell but that ts change n thckness s lmted to less than 2%. The smulated results however suggest that the constraned state of the PEM has an effect on the dffusvty scalng factor; a 0.1% dfference n the change n thckness allows the maxmum dffusvty scalng factor at 0.9 A/cm 2 to ncrease from 0.3 to References 1 Krewer U, Yoon HK, Km HT. Basc model for membrane electrode assembly desgn for drect methanol fuel cells. J. Power Sources, 2008, 175, Yang WW, Zhao TS. Numercal nvestgaton of effect of membrane electrode assembly structure on water crossover n a lqud-feed drect methanol fuel cell. J. Power Sources, 2009, 188, Sprnger T, Zawodznks T, Gottesfeld S. Polymer Electrolyte Fuel Cell Model. J. Electrochem. Soc., 1991, 138, Weber AZ, Newman J. A Theoretcal Study of Membrane Constrant n Polymer-Electrolyte Fuel Cells. AIChE Journal, 2004, 50(12), Molanen DE, Ptelc IR, Fayer MD. Water Dynamcs n Nafon Fuel Cell Membranes, the Effects of Confnement and Structural Changes on the Hydrogen Bond Network. J. Phys. Chem. C, 2007, 111(25), Zawodznsk TA, Deroun C, Radznsk S, Sherman RJ, Smth VT, Sprnger TE, Gottesfeld S. Water Uptake by and Transport Through Nafon 117 Membranes. J. Electrochem. Soc., 1993, 140(4), Pe H, Hong L, Lee JY. Polymer Electrolyte Membrane Based on 2-Acrylamdo-2-Methyl Propanesulfonc Acd Fabrcated by Embedded Polymerzaton. J. Power Sources, 2006, 160, Savadogo O. Emergng Membrane for Electrochemcal Systems, Part I Hgh Temperature Composte Membarnes for Polymer Electrolyte Fuel Cell (PEFC) Applcatons. J. Power Sources, 2004, 127, Lu W, Ruth K, Rusch G. Membrane Durablty n PEM Fuel Cells. J. New. Mat. Electrochem. Systems, 2001, 4, Ye X, Wang CY. Measurements of Water Transport Propertes Through Membrane-Electrode Assembles, I. Membranes. J. Electrochem. Soc., 2007, 154(7), B676-B Ihonen J, Mkkola M, Lndbergh G. Floodng of Gas Dffuson Backng n PEFCs. J. Electrochem. Soc., 2004, 151(8), A1152-A1161

231 9 Conclusons and Future Work The am of ths thess was to develop a unversal electrochemcal theory to descrbe the mechansms of electrochemcal transport n PEFCs, whch reconcles the benchmark modellng phlosophes n the lterature and demonstrably predcts sngle-phase and twophase flow phenomenon. It s known that electrochemcal transport s nfluenced by cell confguraton, materal composton and operatng condtons n a fuel cell and therefore governs fuel cell performance, cost and longevty. As such, the development and applcaton of the general transport equaton n ths thess has establshed a means of understandng the mechansms of electrochemcal transport n porous and quas-porous layers n the PEFC. Ths study s the frst to provde a structured understandng of how transport across all porous and quas-porous layers of the PEFC can be mechanstcally modelled and demonstrates a common fundamental approach for both porous and quas-porous electrochemcal systems. The verfcaton of smulated predctons wth expermental data establshes confdence n the descrbed nformaton provded by the general transport equaton. It s therefore beleved that the verfed modellng framework can be used drectly to support the desgn process of PEFCs. 9.1 Conclusons The followng prncpal conclusons can been drawn from the thess. Fundamental Concepts: The fundamental concepts of fuel cell performance and the factors that affect thermodynamc effcency have been descrbed n the early part of ths thess. A thorough revew of the practcal factors that affect the performance of the PEFC has also been presented, whch provdes a comprehensve understandng of the techncal challenges and state-of-the-art concepts for PEFC technology and the sgnfcance of electrochemcal transport.

232 9 Conclusons and Future Work 212 The revew dentfed that the PEFC s susceptble to twenty-two common faults whch can be nduced by forty-eght general causes. These twenty-two common faults can pertan to the PEM, CL, GDL, BPP and sealng materal. The revew has been used to construct a system of fault trees for the PEFC whch provdes a valuable nsght nto the mechansms by whch modes of performance degradaton can propagate and result n sgnfcant performance loss (through ncreases n actvaton, mass transport, Ohmc or effcency losses) or cell falure [1]. The revew dentfes that electrochemcal transport and water management n partcular s crucal to understandng how PEFC technology can be desgned for performance, longevty and cost. Benchmark Modellng Technques: The benchmark modellng approaches for electrochemcal transport n the fuel cell modellng lterature have been descrbed, ncludng how they have been appled to smulate transport across the varous layers of the cell. The dscusson dentfes dlute soluton theory and concentrated soluton theory as the man modellng branches for transport n porous and quas-porous layers. The theory of electrode knetcs has also been dscussed and a sem-emprcal approach based on the thn nterface assumpton has been developed to descrbe the processes that occur n the anode and cathode catalyst layers. Mult-Layer Modellng wth Mult-Speces Input: The modellng work carred out n ths thess began wth the development of a multspeces nput model whch s demonstrably coupled to a one-dmensonal modellng framework based on dlute soluton theory. The mult-speces nput model establshes the capablty to handle mult-component nput gases and drectly couples the boundary condtons n the supply channels wth the cross-flow that occurs through the PEFC. The composton of the reactant supply gases n the channels of the PEFC s calculated based on the ntal dry gas composton, stochometry, pressure and relatve humdty of the supply gases, the cell operatng current densty and flud cross-flow through the cell. The model has been mplemented and valdated aganst expermental data for the Ballard Mark IV PEFC n the open lterature.

233 9 Conclusons and Future Work 213 The model has been appled to smulate the effect of CO posonng n the cathode catalyst layer due to contamnaton n the anode supply. The smulaton results confrm that when a PEFC s operated on a 30% carbon doxde / 70% hydrogen fuel supply wth up to 50 ppm carbon monoxde, the crossover of CO across the PEM can reduce the cathode potental at 1 A/cm 2 by up to 15%. The results also show that by ncreasng the CO content of the fuel supply from 10 ppm to 100 ppm, there s a correspondng ncrease n the rate of CO crossover by one order of magntude for all current denstes tested (0 to 1 A/cm 2 ). Fundamental Theory of Electrochemcal Transport n PEFCs: Ths thess has consdered how the fundamental theory of molecular transport can be appled to smulate mult-component flow through PEFC meda; the underlyng phlosophy has focused on establshng a unfyng mechanstc treatment for multcomponent electrochemcal transport across the mult-layer PEFC, ntally payng attenton to sngle-phase systems and then two-phase systems. In Chapter 6 a general transport equaton has been developed from the molecular theory of gases and lquds [2] and can account for thermal dffuson, molecular dffuson, convecton and electro-osmotc drag n mult-speces form n porous and potentally quas-porous meda. The theoretcal valdty of the general transport equaton has been proven by dervng the key transport equatons n the lterature developed by Bernard et al., Sprnger et al., and Newman et al. The general transport equaton can be merged wth the mult-component nput model as descrbed n Chapter 5 to study the factors affectng sngle-phase mult-component electrochemcal transport though the PEM. The numercal valdty of the general transport equaton has thus been proven by smulatng a PEFC n 1D wth a three-speces PEM system (water, electrolyte, protons) under sngle-phase condtons. The numercal valdty has been demonstrated by comparng the generated results aganst benchmark water content curves publshed n the open lterature. The results show that for smulatons based on dlute soluton theory, a c c factor s nherently assumed to be equal to unty, whch consequently j T leads to an over-predcton n the spatal concentraton dstrbuton of a speces. Ths

234 9 Conclusons and Future Work 214 s most notceable at current denstes exceedng 0.5 A/cm 2 for the test cases consdered. The applcaton of the general transport equaton through a mult-layer 1D model n Chapter 6 has elucdated the dependence of hydrogen crossover on the thckness of the PEM, cell operatng temperature and current densty. The results reveal that at 80 C, 1 atm reactant supply pressure and 1 A/cm 2, the nomnal membrane thckness for less than 5 ma/cm 2 equvalent crossover current densty s 30 µm. The relatonshp between hydrogen crossover wth current densty dentfed n ths thess has been used recently to explan fluorde release rates measured n chemcally degraded operatonal PEFCs by other researchers [3,4,5]. The Mechansms of Two-Phase Transport n PEM Fuel Cells The fnal part of the thess has extended the applcaton of the GTE to model twophase mult-component flow through a mult-layer PEFC. It has been demonstrated that the general transport equaton developed n Chapter 6 can been appled wth Darcy s law to smulate two-phase flow through the porous (GDL, MPL) and quasporous layers (PEM) of a PEFC. Mult-component nput gases can be handled usng a modfed form of the mult-component nput model developed n Chapter 5. It has been demonstrated that lqud nfltraton n porous layers can be accounted for by employng the standard and valdated Leverett J-functons. To account for lqud nfltraton n the quas-porous layer and therefore Schroeder s paradox, a physcal model descrbed elsewhere has been adopted [6]. The model assumes that lqud water can forcbly create a lqud network through the partally hydrophobc and partally hydrophlc PEM when t comes nto contact wth a boundary. The modellng treatment has consdered the porous layers of the PEFC such as the GDL and MPL to be compressble under fuel cell compacton forces. It s shown that compresson effects on the PEM can be handled usng a mechancal sub-model whch calculates the water uptake profle across the membrane based on ts compressed thckness and thermodynamc boundary condtons. The model can be mplemented usng the object-orented modellng technque, whch enhances the usablty and adaptablty of the code for future work. Smulaton results have been valdated aganst expermental water transport and water uptake data for both sngle- and two-phase operatng condtons from the open

235 9 Conclusons and Future Work 215 lterature [7,8,9,10]. The model confrms the measurements taken from water balance tests, specfc resstance profles across the PEM from embedded probe tests and water content profles obtaned through MRI scannng. The results show that the thckness of the PEM, anode gas humdfcaton and cell constrant can all contrbute towards reducng the resstance to proton transport by allowng lqud water to penetrate a greater proporton of ts thckness, thereby mprovng proton conductvty. 9.2 Future Work The modellng work presented here represents a sgnfcant step towards representatve smulatons of the complete PEFC under a range of desgn and operatng condtons. The results presented n ths thess demonstrates the capablty of the present modellng framework to provde nsghts to physcal processes occurrng wthn a fuel cell. It s antcpated that the macroscopc treatment developed n the thess s one modellng tool that can nterface wth a range of capabltes n order to establsh a comprehensve PEFC development system for the purposes of PEFC desgn, n-stu charactersaton and dagnostcs. The followng provdes a dscusson of future work n order to explot the work of ths thess. The current macroscopc modellng framework s mplemented through a onedmensonal treatment. Ths allows the bulk processes across all relevant layers of the PEFC to be consdered n a sngle smulaton, accountng for cross-flow through the PEM by treatng t as an electrochemcal system. Fundamentally, because the porous and quas-porous layers of the PEFC exhbt complex collapsble structural characterstcs, t s dffcult to capture the behavour that occurs wthn them comprehensvely usng mult-dmensonal approaches based on computatonal flud dynamcs (CFD) or the lattce Boltzmann (LB) technque, for example, n solaton. Therefore, the modellng work descrbed n ths thess serves a purpose that s not rgorously satsfed by such approaches. However, n dong so, the current modellng framework s reduced to a one-dmensonal treatment whch neglects to consder the macroscopc channel effects n the reactant supply channels and the nlet and ext manfolds of the PEFC. In addton, t does not elucdate how mult-component and potentally mult-phase flow propagates through the actual heterogeneous three-dmensonal

236 9 Conclusons and Future Work 216 porous structures of the PEFC. The overall soluton therefore les n harnessng the relatve merts of all three approaches n order to comprehensvely smulate both macroscopc and mcroscopc processes occurrng wthn the PEFC Mcroscopc Modellng The lattce-boltzmann (LB) modellng technque s a statstcal method that can smulate mult-speces, mult-phase and reactve flows through a pre-defned model of a three-dmensonal porous structure wth prescrbed surface propertes. It has the potental to smulate the precse movement of gas components and lqud water through representatve geometrc models of heterogeneous porous structures n the PEFC such as the GDL, MPL and CL. However, n order for the LB model to work correctly the physcal boundary condtons at opposng faces of the three-dmensonal structural model of a gven PEFC layer have to be specfed, whch are mpossble to measure expermentally. These boundary condtons (phase pressures and partal pressures of gas consttuents at layer nterfaces, flow rates through ndvdual layers) can be generated by the theoretcal treatment developed n ths thess. To date, a mult-dmensonal LB model has been specfcally developed and appled wth representatve three-dmensonal dgtal models of a carbon-paper GDL obtaned from X-ray computed mcro-tomography n order to valdate the smulated gas-phase permeablty through ts porous structure [11]. The next step s to apply representatve fuel cell boundary condtons between fuel cell layers from the model descrbed n chapter 7 to smulate multspeces transport through the porous structure of the GDL. Fgure 9-1 s an ntal snglephase LB smulaton of oxygen nfltraton through a carbon paper cathode GDL as part of a mult-component mxture comprsed addtonally of ntrogen and water vapour. The smulaton s carred out usng boundary condtons generated drectly by the model presented n chapter 7.

237 9 Conclusons and Future Work 217 (a) (b) Fgure 9-1 Sngle-phase mult-component Lattce Boltzmann smulaton of oxygen permeaton through a carbon paper GDL; (a) X-ray tomography model of a carbon paper GDL; (b) smulated nfltraton of oxygen usng boundary condtons from the model presented n chapter 7

238 9 Conclusons and Future Work Macroscopc Modellng Computatonal Flud Dynamcs CFD modellng s a powerful tool that can predct the behavour of lamnar and nonlamnar flows through complex three-dmensonal geometres such as bpolar plate channels, fuel cell nlet manfolds and ext manfolds. Exstng CFD codes readly deal wth multphase flows and heat transfer, whch as dscussed can both be domnant factors n the performance of operatonal PEFC systems. As dscussed n Chapter 3, as the partal pressure of water exceeds the saturaton vapour pressure for a gven temperature n the channels of the cells, water vapour wll start to condense. Subsequent floodng wll have an mpact on the planar current densty dstrbuton across the cell hence cell performance. In addton, planar temperature dfferences can also develop across the footprnt area of a cell, dependng on the heat generated due to electrcal loses, the thermal conductvty of the hardware components of the PEFC and the thermal conductvty of the coolant and reactant supples. All of these factors can affect heat loss to coolng envronments. If as a result the local cell temperature s excessvely hgh, water n the cell wll evaporate leadng to membrane dehydraton. Ths results n a drop n local current densty and therefore cell performance. In order to locally resolve the cross-flow through the compressble porous and quasporous layers of the PEFC as a functon of the local thermo-fludc condtons n the channels, t s possble to nterface the model descrbed n Chapter 7 wth a mult-phase three-dmensonal CFD treatment that accounts for heat transfer. CFD models cannot readly predct the cross-flow through the PEFC and have to fx the net water flux rato a-pror [12,13]. They do not consder two-phase effects on the performance of the PEM or compresson effects ether [14]. By combnng models, however, a comprehensve assessment of cell confguraton and desgn can be carred out to determne how performance n operatonal fuel cells can be sustaned n spte of the development of planar non-unform two-phase transport and thermal gradents.

239 9 Conclusons and Future Work 219 Fgure 9-2 demonstrates the prncpal of mult-scale modellng based on the GTE, LB and CFD technques dscussed above. The LB model s used to determne bulk propertes of the vsualsed PEFC materal sample, whch n the frst nstance are suppled to the GTE and CFD models. Exstng CFD models can determne the dstrbuton of reactants n the flow felds of the anode and cathode b-polar plates. The GTE model determnes the phase pressures and boundary condtons between layers wthn the PEFC, whch can be suppled back to the LB model to vsualse how the flow actually behaves wthn the porous structure of the materal (.e., the GDL, MPL or CL) under representatve fuel cell operatng condtons. Ths therefore provdes vtal nformaton about the porous structure whch can assst the next teraton of materal desgn. Fgure 9-2 Mult-Scale PEFC Modellng The Hardy-Cross Method Implementaton of numercal technques based on CFD often result n computatonally-ntensve models that requre days or weeks to generate results. It can be more advantageous to strategcally employ less computatonally-ntensve models at dfference stages of cell/stack development whch may not be as hghly-accurate as CFD models, but able to generate a qualtatve and quanttatve assessment of macroscopc fuel cell performance n terms of flow feld confguraton n a relatvely short space of tme.