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TRANSPORT PROCESSES IN TEFLONBONDED FUEL CELL ELECTRODES MYUNGCHEEN LEE A DISSERTATION PRESENTED TO THE UNIVERSITY IN PARTIAL FULFILLMENT OF DEGREE OF DOCTOR TH OF THE OF E GRADUATE CO FLORIDA REQUIREMENTS PHILOSOPHY UNCIL FOR Dedicated to my family ACKNOWLEDGMENTS The author wishes to express sincere appreciation to Professor Walker, Jr. , whose invaluable guidance and help made this research project possible and made author's The graduate author i program a s grateful successful to Drs. experience. Shah and Schweyer for serving Supervisory Committee providing helpful suggestions, to Drs. Antal Majthay Luehr serving Supervisory Committee. also indebted to Dr. . Tham helpful discussions suggest tions. With deep mother appreciation author wishes encouragement and his wife, thank Jungboon, Mrs. Roswitha Zamorano typing the manuscript of his dissertation. support of this research by National Aeronautics and Space Administration under Contract NGR 10005022 gratefully acknowledged. TABLE OF CONTENTS Page ACKNOWLEDGMENTS LIST OF TABLES * a a S a a S * a S S S S S S a S S S S S ft S LIST OF FIGURES Viii KEY TO SYMBOLS ABSTRACT . CHAPTER INTRODUCTION . .a . . 1 General Description of Fuel Cell Structure Alkaline HydrogenOxygen Fuel Cell Thermodynamics Kinetics Electrodes Advantages of Porous Diffusion Elec trode s S. . . 11 THE STRUCTURE OF TEFLONBONDED ELECTRODES Characterization Surface of Electrode Material Area Measurements 13 Method of Measurements Experimental Results scuss Estimation of Total Free Sur face Areas of Electrode Components Estimation ness of Catalyst Layer on Teflon Comparison Thick Aggregates he Calculated Meas ured Surface Area of 80:20 50:50 Pure PtblackTeflon Teflon Layer s and Layer 4\ r i 4 C ' f 1 n.r 4 r r A . . 14 TABLE OF CONTENTS (Continued) CHAPTER Page III ELECTRODE REACTIONS , IONIC HYDRATION, AND WATER TRANSPORT Introduction Mass Transfer Electrolyte Matrix Transference The Primary H centrated KOH Numbers ydration in KOH S Numbers solutions in Con Solutions Concentration lyte Matrix Gradients Concentration Electro Gradients ree Water S. 45 Concentration Gradients of KOH Solution Discussion . .*. . . 48 MATHEMATICAL MODEL OF TEFLONCATALYST LAYER AND CALCULATION OF CURRENT DENSITY DISTRIBUTION Introduction Electrode Reaction and Reaction Rate . 56 Ionic Fluxes Potential Oxygen Electrolyte Gradients Transport Phase Electrode Electrolyte Layer Phase Computation of Results SUMMARY the Current Discussion AND CONCLUSION Generation 61 S . 62 0 . . 69 APPENDIX DERIVATION OF FLUX EQUATION EQUATIONS (3 AND (3.36) TABLE OF CONTENTS (Continued) APPENDIX Page CALCULATION OF A GIVEN COMPUTER PROGRAMMING FOR THE COMPUTATION OF CURRENT DENSITY DISTRIBUTION LIST OF REFERENCES S. 94 BIOGRAPHICAL SKETCH LIST OF TABLES Table Page Dependence Surface Area of Platinum Black Pretreatment Temperature Total Free Surface Areas of Teflon and Ptblack Calculated and Measured Surface Are of Pt blackTeflon Mixtures Pure Teflon S. .* 2 Summary of Transference Number KOH Solutions Concentration "Free" Water as a Function Hydration Number . 0 0 . 43 "Free " Water Concentration Concentration Gradients Gradients Electrolyte S. 47 Matrix Fraction of Current Generation Electrode Layer S. 63 Cell Potential Power Density vs. Current Density LIST OF FIGURES Figure Page Schematic Diagram of an Alkaline Hydrogen Oxygen Fuel Cell . 3 A Typical tion for Cell a Cell Potential Current Density Rela . ft . 8 Dependence of Surface Area Platinum Black Pretreatment Temperature S. 18 Scanning Particles. Electron Micrograph Magnification: of Pure 50,000 Teflon Scanning Mixtures Scanning Mixtures Electron Micrograph Magnification: Electron Micrograph Magnification: of PtblackTeflon 36,000 of PtblackTeflon 72,000 Scanning Electron Micrograph of a Fuel Cell Electrode. Magnification: 30,000 Concentration Values "Free " Hydration Water Number Different . . . 44 Scanning the 80:20 Electron Micrograph of the Surface of PtblackTeflon Layer. Magnification: 72,000 Schematic Teflon Diagram of Particles Schematic Model Platinum Black in Electrodes Structure Catalyst the Cata lystTeflon Layer S a a . 54 Schematic Model Structure the Cata lystTeflon Layer with No Windows Current Generation Distribution Electrode Layer a . . . a 64 KEY Activity Onsager TO SYMBOLS KOH electrolyte equation parameter Onsager equation parameter Constant expressing the net adsorption energy Concentration of KOH, mole/l Cfw Concentration of free water, mole/I Concentration of species mole/i Concentration Concentration Concentration of oxidized reduced species substance, substance, i at mole/i mole/i mole/l Total solution concentration, mole/l Diameter of particles, Diameter of 0 adsorbing gas molecule, Diffusivity Diffusivity based on molar based average, on volume average, 2 cm /sec cm /sec Thermal diffusion coefficient of species g/cmsec Diffusion species coefficient and j, cm2/ describing interaction of sec Electronic charge, 1.602 Coulomb Internal energy, J/mole Working c Faraday's ell potential, constant, volt 96,487 Coulomb/equiv. Free energy , J/mole Enthalpy, J/mole Current density, amp/cm Exchange current density, amp/cm lim Limiting current density, amp/cm Catalyst phase current density, amp/cm Electrolyte phase current density, amp/cm Mass flux of species mole/cm /sec Rate constant Conductivity of electrolyte, mho/cm Slope of BET plot Intercept of BET plot Rate Rate constant constant forward reverse reactions reactions Rate constant absence of a potential difference Thickness of electrode layer Molecular weight of Molality species of electrolyte, g/mole mole/kg Number of reactions electrons transferred electrochemical Molar flux of species Partial pressure of adsorbing gas, mmHg Pressure system, atm  n   C I. Im A A __ I Average radius of Teflon aggregates, constant, External 8.314 resistance, joule/mole/ ohm Internal res instance, ohm Primary hydration number Stoichiometric number species Partial entropy species J/moledeg Entropy of transference Temperature Reaction Velocity Velocity Volume of system, number Cal/moledeg species system, velocity species solvent system, Potential the anode, volt Total volume adsorbed gas on surface adsorbent Potential cathode volt Volume of surface adsorbed gas when covered with a mono entire molecule adsorbent layer Reversible Reversible Partial Work Electrical potential potential molar volume of involved the anode, cathode, species the operation work the operation volt volt 1/mole of a cell, J/mole n of a cell, J/mole Electrical work that can be done per an over __ I Greek letters ea Transfer a Transfer coefficient coefficient anode the cathode Symmetry Activity factor coefficient Thickness of electrolytecatalyst phase, Porosity Conductivity Density electrolyte, of electrolyte, mho/cm g/cm Potential Potential electrolyte catalyst phase, phase, volt volt Transfer coefficient Sum of nc Sum of ^r overpotentials overpotentials anode, the cathode, volt volt nohm Ohmic potential loss, volt Equivalent conductance of Equivalent conductance of Electrochemical potential species species species mhocm /equiv. infinite dilution J/mole Total number of ions produced by the dissociation one molecule of electrolyte Number ions species produced by the dissociation of one molecule of electrolyte Conductivity of catalyst phase, mho/cm Subscripts Anode Major Minor Cathode conc Concentration Electrical External Forward Free water Internal Species Species Electrolyte phase Monolayer Oxidized material Open circuit Reverse Reversible Reduced material Catalyst phase Total Working xdirection Hydroxyl Potassium ion Oxygen Water Superscripts Initial Molar Volume value average average Thermal Abstract of University Dissertation of Florida i Degree Presented Partial of Doctor Graduate Council Fulfillment of of Philosophy Requirements TRANSPORT PROCESSES FUEL CELL E By MyungCheen December, 1 IN TEFLONBONDED LECTRODES Lee 976 Chairman: Major Robert Department: . Walker, Chemical Jr. Engineering structure properties of Teflonbonded fuel cell electrodes their componentsplatinum black and Teflon 30 particleshas been investigated in detail compared with previously published works. Recent experiments em playing scanning electron microscopy energy dispersive Xray analysis indicate that Teflon particles are pro late spheroidal aggregates approximately spherical Teflon molecules. In a commonly used electrode composition these Teflon aggregate s are coated with one or more layers catalyst crystallites. The dimensions Teflon aggre gates are approximately 1500 3000 diameter Teflon molecules diameter ranges the catalyst from 200 to about crystallites while appears to be Electrode reactions, ionic hydration, water transport, their effects behavior fuel cells have been causes some change concentration of electrolyte gradient the electrolyte matrix and electrode layer. basis structure, the new properties of knowledge electrode components, geo metry a mathematical model been developed to enable one to pr These edict current calculations distribution show,as one electrode might expect, that layer. at high current densities the great majority the current generated very thin layer Teflonbonded catalyst immediately adjacent electrolyte matrix. For oxygen electrode operating at a current density one am pere more than half current is generated the catalystTeflon layer nearest electro lyte matrix current densities current generation is relatively uniform throughout this layer. CHAPTER INTRODUCTION General Description of Fuel Cell Structure the Alkaline HydrogenOxygen Fuel Cell A fuel cell is a direct energy conversion device generating electricity oxidation of a fuel one electrode reduction an oxidant at another elec trode. Thus, chemical energy is converted directly into electrical energy, by which method fundamental limi station of the Carnot cycle is avoided. In principle, therefore, higher efficient cies can attained fuel cells than those attained in heat engines. Hydrogen, hydrocarbons, other compounds can used fuel while oxygen is most frequently used as the oxidant either pure or air. Among various kinds of fuel cells which have been developed, hydrogenoxygen system in alkaline electro lyte ever is probably , its the most technology advanced and widely used. outpaced our How understanding of behavior operative mechanisms. Since gaseous hydrogen oxygen are used fuel depositing a mixture of catalyst binder on a wire screen which serves both as an electron collector mechanical support. If Teflon s used binder, can confer a degree of hydrophobicity electrodes which makes it possible gaseous reactants to diffuse readily to reaction sites. Between anode cathode there an electrolyte matrix which provides electrical insulation between electrodes as well a porous medium through which diffusion and migration can occur under influence concentration poten tial gradients. An electrolyte reservoir also used hold extra electrolyte to assist in evaporation water produced the overall cell reaction; usually sintered metal plate. A schematic diagram of fuel cell shown in Figure 1.1. electrochemical reactions occurring this fuel cell are usually written follows: Anode Cathode 2 + Overall Cell Reaction 2 2 2 However, ions are hydrated and actual reactions should be written follows: Anode 4 [OH *sH20] l+s) H20 + I External Load H2 Excess Water Out Anode Cathode Electrolyte Matrix Electrolyte Reservoir Since water produced at anode consumed cathode, their hy both rdration, the cathode, while he f ater the formation of should d hydrated hydroxyl ion iffuse from the hydroxyl ions s and anode should migrate diffuse from the cathode anode. product water must be removed from the cell to prevent electrolyte dilution. This implies more complicated trans port processes than case when there no hydration hydroxyl ions. Thermodynamics and Kinetics of Electrodes When a chemical reaction is carried electrochemically, work done, given by AE + P  W (1.21) where f\H = enthalpy change of system, Joule/mole; internal energy change system, Joule/mole; = pressure of system, atm; = volume change system, = heat absorbed system, Joule/mole. not only the work of expansion done gases produced, also the electrical work involved transporting elec tric charge around external circuit from anode + P an overall reaction, carried in a cell and which involves transfer of n electrons = n e  V (1.22) r,a) a hypothetical case in which internal resistance of cell ove potential losse are negligible. Conver sion to a molar by multiplying Avogadro' number gives = n F (1.23) r,a) where = Faraday' constant, equal 96,487 coulombs/ equivalent. Since the only forms of work involved the operation electrochemical cell are electrical work work expansion, + P AV (1.24) in addition, process is carried out reversibly, (1.25) where = entropy change of system, Joule/moleK; = temperature of system, Using Equations (1.21), (1.23) , (1.24) , (1.25) , follows that = W = T AH T 27) where free energy change of system, which holds isothermal process, we get n F (1.28) r,c) Writing V  V we get = n F E r (1.29) where electromotive force reversible cell. Thus, ideal fuel cell yields electrical energy equivalent free energy change of reaction. normal energy must be operation supplied at fuel a significant cell, the electrical rate, under these conditions practice, working the cell reversibility cannot potential, an appreciable rate be maintained. an electrochemical (current) device is given  Zn (1.210) where sum of the overpotentials that exist electrodes, electrodeelectrolyte interfaces, ohmic losses in the electrolyte. factors that affect the working voltage of a cell are activation overpoten tial, ohmic losses, and mass transfer (concentration) over = E = E terminal operating cell fuel voltage cell vs. shown current density, in Figure opencircuit voltage often (usually fuel cells) less than the rmo dynamically ference reversible caused potential by possible reactions Ep because inter to impurities. effects impurities generally decrease current den sity increases. always found that there is a sharp initial decrease working potential E with shown section AB of curve in Figure 1.2. This type behavior characteristic of highly irreversible processes attributed to activation linear portion overpotential. in Figure corresponds relatively high current density region in which decrease cell potential with increase of current density is due principally to ohmic losses electrolyte. When porous electrodes are used, only layer of electrolyte the electrolyte matrix but also electrolyte within pores contributes the electrolyte resistance. At sufficient high current densities (i.e. , high local reaction region rates), where most heterogeneous rate reactions is controlled pass rate into a transport of reactants or products from, the electrodes. Region CD in Figure illustrates this effect, which known as concentration (or mass transfer) overpotential. n ih bI rnlhn nnor* i nfl 11I fnil roll +ho r(ivTr n 4 1lim,c 11im,a 0 il i lim Current Density, ohm (1.211) where nohm = ohmic voltage loss , volt; = resistance of external load, ohm; Ve and Va= ele ctrode anode potentials , respective cathode which are and given  c,act c,conc (1.212 a, act Scon(1.213 a,cone where suffixes "act" "conc" denote activation concentration overpotentials, respectively. In many electrochemical reactions, the current at a particular electrode found vary exponentially with potential lationship across between the metalsolution potential interface, rate constant re k of electrochemical reaction can be expressed empirically BVF/RT) (1.214) where rate constant absence a potential difference symmetry factor, = gas constant, 8.314 Joul e/gmoleK  V  V  V  Zqc Sko unit area of electrode surface. relation between re action velocity, current density, depends on number of electrons transferred one act of the overall reaction, = n F v (1.215) rates of electrochemical reactions are a measure of net reaction rates the net current density given (1.216) where forward current reverse current. Therefore, current case density may electrode be expressed reaction since IVF] RT Ff C0  kr r (1B) VF RT (1.217) where reverse are rate reactions constants of absence of forward a metalsolution poten tial difference are the concentrations of oxidized reduced species, respectively. The exchange current density related velocity, in amp/cm forward or backward condition current reaction density at equilibrium, zero in which exchange current density given t \ Using Equation (1.218 the overpotential, which equal potential difference Equation (1.217) can be expressed RT F o exp o r  exp (1B) (1.219) the case of a multielectron transfer reaction, the general form of current densityoverpotential orexp o ' a F] RT  exp relation RT (1.220) where are transfer coefficients of reactions anode the mechanism of cathode, the overall respectively, reaction. depend study mathematical formulation and solution of electrode models, this equation most important. Advantages of Porous Diffusion Electrodes an electrochemical useful for practical energy applications conversion it should b system e able to be pro vide good power density. Because need to minimize activation overpotential at desired currents, facil itate mass fuel transfer the oxidant reaction sites, in hydrogenoxygen because fuel cells both are gaseous, porous diffusion electrodes are used. e much rates of real to apparent area (i.e., much larger concentra tions of reaction sites are available), also fact that they permit much higher limiting currents. Another vantage of porous electrodes that catalyst, form of pores, very thereby fine particles, reducing can be dispersed considerably within the quantity of catalyst used. The difficulty understanding behavior and mecha nisms of electrode reactions in porous electrodes arises mainly from their extremely complex physical structure the consequent difficulty of describing them geometrically that mathematical analysis can be carried out. One of principal purposes this study to examine detailed structure of Teflonbonded fuel cell electrodes relate this structure their performance transport processes, etc. , that we can use information under standing and evaluating the behavior and mechanisms per forming electrodes in designing electrodes capable of improved performance. CHAPTER STRUCTURE OF TEFLONBONDED ELECTRODES Characterization of Electrode Material Teflonbonded fuel cell electrodes are made of three different materials; catalyst, Teflon, finemeshed metal screen. In many cases platinum black used catalyst because of its excellent catalytic properties, i.e. , high exchange current density in alkaline elec trolyte. very fine black powder; crystallite size been so small clearly that resolved individual scanning crystallites have not electron microscopy, i.e., the crystallite diameter less than (=100 How ever, surface area measurements using BET gas adsorp tion method [l] , average crystallite diameter widely used calculated platinum black to be about (Englehard + 10 fuel its cell grade) asreceived state, catalyst exists agglomerates micron in diameter. Teflon an aqueous emulsion (DuPont), is usually used Teflon component of electrodes. a nega tively charged hydrophobic colloid containing polytetra is relatively stable temperatures about 3500C. Electron microscopic examination of welldispersed pure Teflon particles reveals that although size varies from 5000 A in diameter, the majority of particles are prolate spheroid shape , the minor and major diameters being about 1000 1500 A and 2000 3000 respectively. also noted that a single Teflon particle appears an aggregate diameter) reported small which may spherical particles be Teflon molecules. the manufacturer to have Teflon a mean molecular weight calculation suggests that a molecule this molecular weight should have a diameter about Several scanning electron micrographs of welldispersed Teflon particles are shown later on pages 29. finemeshed metal screen used provide mechan ical support the catalyst layer serve as an elec tron collector the electrons generated. Goldplated nickel screen about 100 mesh used for most alkaline fuel cells. Surface Area Measurements 2.2.1 Method Measurements surface areas of platinum catalyst, pure Teflon, and electrodes were measured BET method. This method . L __ pretreated about 15 hours 200220C while stream of moisture pure and helium flows adsorbed through species. After cell remove the measurement sample reweighed to determine dry weight. continuous and Eggertsen flow method nitrogen used developed by Nelsen adsorbate helium is used as carrier gas. A mixture of nitrogen and helium of known composition is passed through sample effluent composition is monitored by thermal conductivity measurements. When sample is cooled liquid nitrogen, adsorption nitrogen indicated by a peak on a recorder chart. After adsorption equilibrium is established, recorder pen returns original baseline. sample tube allowed to warm by removing liquid nitrogen producing a peak coolant, causing chart whi desorption nitrogen reverse direction adsorption peak. area under the desorption peak a measure of the nitrogen adsorbed. This peak area was calibrated injecting a known amount of nitrogen into nitrogenhelium stream to give a peak of similar magnitude area desorption peak. amount nitrogen adsorbed is cal culated by comparing these two peak areas. Adsorption, sorption, calibration are done at several relative nitrogen or ESure rati ns in thFhe ranaer from n nE 11 1Di lfA n  %I P V C P VC (2.21) where = partial pressure adsorption , mmHg; saturation solid pressure sample at adsorption temperature over of coolant, mmHg; total face volume (STP) adsorbed gas on sur adsorbent, = constant = volume expressing the (STP) adsorbent surface net adsorbed ga is covered adsorption when energy; entire with a monomolecular layer, When left hand side of the equation plotted ordinate versus relative pressure , P/P , a straight line with slope intercept is obtained. If we note that Slope Intercept 22) 1 V C m then we can determine from (2.23) where slope intercept straight line. This value, multiplied proper factor area covered per unit amount of nitrogen, gives surface n rc~n t .7 c\7 In r rx rtrr a 7i1 acrli + k2 crmnl l rl.h Q I f 1\/ ! 2.2.2 Experimental Results and Discussion Weighed samples of platinum catalyst (Englehard fuel cell grade platinum black) were heated in a stream of flowing from 100 helium to 400 for oC. about Then hours temperatures surface area was ranging measured described in Section 2.2.1. Since is standard procedure to sinter fuel cell electrodes fabricated with Teflon platinum catalyst mixtures temperature between surface area temperature range 300350 was studied carefully. data are shown Table in Figure Table Dependence of Pretreatment Surface Area of Platinum Black Temperature. Temp. of Pretreatment, OC Surface Area, m2/g 100 45.3 150 46.0 200 48.9 250 49.6 300 48.1 310 44.2 320 37.8 330 12.1 Temperature Pretreatment, is clear occurred when that temperature surface was area between There is a gradual increase surface area retreating temperature increased slight changes in surface area between are probably significant. However , the reduction surface area seems to have already begun advantages sintering Teflon at 310 oC must be weighed surface area loss lost in surface area. sintering may the other lost fairly hand early during the icant 2.2.3 life of entire Estimation an electrode, life of of Total fuel cell. Surface Areas of Electrode Components surface areas of platinum black catalysts Teflon particles can be estimated by calculation from informa tion obtained their sizes. Assuming that both catalyst crystallites and Teflon molecules are spherical their surfaces smooth, we can calculate surface areas from (Surface Area Particles in 1 f a Single gram) Particle) (Number Sd2 IT d = 6/pd (2.24) 2, * tt. a a 4 4.. Ut  .1. "I C    n a large decrease pretreating against it may not signif and Free i d3 .,1,,,, ,,, r .,: I~U~M e. u rr e. In comparing the calculated surface areas with those measured BET method exclusion surface area presence of neighboring particles should considered fraction excluded surface area can estimated from the following [3: + d) (2.25) where fraction of excluded surface area; = coordination number, i.e. , number contacts particle; = diameter adsorbate used BET method, = diameter of particle, cm. Therefore, by using Equations (2.24) 2.25) noting that specific gravity of Teflon that platinum s 21.45 while letting the molecular diameter Teflon Ptblack range from 200 to 300 A and to 60 respectively, A for nitrogen, and n we get results shown Table 2.2. Comparing results with surface area of platinum black experimentally measured, 45 m2/g, we can estimate that, assuming packing condition of platinum black to be random to randomclose, average size single catalyst crys tallite ranges from in diameter. Considering r, rmnrnr,4 4 nfl i^r*^ 4 ,l 1 I4 4 Y 1nf 3p rmn <" mv ^j v C? \ V Q Q F Fr^ <"mnn /4" C1t .+ '_v^ Table Total Free Surface Areas of Teflon Ptblack. Diameter, A Calculated Geometric Surface Area, m2/g Free Surface Areas, m2/g Teflon Platinum Black 37.1 (25)43.7 44.5 (35)43.5 41.7 33.9 2.2. Estimation Aggregates of Catalyst Layer Thickness on Teflon In order to be able to estimate thickness of black surface layer area on Teflon of Teflon aggregates aggregates is necessary the packing to know the condition of Ptblack crystallites on surface of Teflon aggregates. From information size shape of Teflon ag gregates we can calculate surface area of Teflon aggregates __ e*_ 'I _ Surface Area Aggregate) of Teflon (Number (Surface Area of Aggregates of a Teflon Teflon) dAd AB e 6 AB (2.26) where = major diameter of a Teflon aggregate, = minor diameter of a Teflon aggregate, cm; = eccentricity, e =/d A 2  dB / dA = roughness factor; = porosity. Therefore , substituting 2500 1250 1.5, 0.36 (for randomclose packing), 2.22 we get external surface area of Teflon aggregates m2/ in >3. thickness of Ptblack catalyst layer the mix tures of Thickness Ptblack (Bulk Teflon Volume can of Ptblack be calculated as in 1 follows: of Mixture)/ (Teflon Aggregate p(1c) Surface Area (Surface Area in 1 of Mixture) g of Teflon Aggregates x x) (2.27) where fraction of Teflon in a mixture; = density = porosity Ptblack of Ptblack crystallites, catalyst g/cm layer. Therefore, with an assumption that packing of Ptblack  ) 70 A and a 50:50 mixture Considering fact a catalyst that layer crystallite thickness size of Ptblack has been estimated to be to 40 A in diameter, we can see that 50:50 mixture fairly significant fraction of with Ptblack catalyst surface catalyst, connection of Teflon although aggregates there can s tendency is not till of catalyst coated continuous particles collecting in the crevices first. 2.2.5 Comparison of 80:20 a Calculated 50:50 PtblackTeflon Measured Layers Surface Areas Pure Teflon Layer we assume PtblackTeflon of electrodes, that surface layers we can areas change estimate components during surface areas of formation Ptblack Teflon mixture layers of different ratios from calculations by using pure calculated su component rface surface areas with areas. the measured Comparison ones these shown Table 2.3. Table Calculated Teflon Mixtures and Measured Surface Areas of Pure Ptblack Teflon Ptblack:Teflon ratio Calculated Surface Area, Measured Surfa Area, 2/ m /g 80:20 m /g As we can see results shown above, there is a significant difference between calculated mea sured surface areas pure Teflon. Since pure Teflon sample was prepared filtration, pressing, sintering measurement of surface area, there must have occurred a considerable reduction surface area during these processing, particularly sintering 310C which would If we cause use softening measured and binding surface of Teflon area aggregates. Teflon + 0.3 m2/g xn/g in calculating surface area mix tures, we obtain results shown parenthesis Table 2.3. Comparing these results with measured surface areas PtblackTeflon layers of different ratios, can still notice considerable differences between cal culated and measured surface areas. This can also attri buted softening bonding Teflon aggregate during sintering, which can cause some portion Ptblack to be buried them. This can shown by fact that calculated surface area of Ptblack from the measured surface areas of 80:20 50:50 mixtures pure Teflon about 27 m2/g, which would mean that there was loss about surface area of Ptblack. Formation of Electrodes Platinum black is weighted out and dispersed several minutes in water containing a wetting agent, Triton X100, in an amount equal 6% of weight of catalyst amount of using Teflon an ultrasonic 30 emulsion agitator. added requisite to Ptblack disper sion ultrasonic agitation repeated an addi tional several minutes. The mixture filtered very fine pore filter. After catalyst mixture is partially dried room temperature, finemeshed metal screen placed paper the the pressed at catalyst screen about layer, followed by absorb water 5000 psi. laying filter "sandwich" filter papers are then peeled off, electrode sintered about 20 minutes. Structure of Electrodes In understanding various phenomena occurring in an operating fuel cell, is essential to know the structure catalyst performance of layer cell. this a great Since catalyst influence on layer of electrode consists a mixture of very small hydrophylic Ptblack particles hydrophobic Teflon particles, their arrangement wettability layer will of electrodes have , thereby a great influence influencing transport Most published work structure of Teflon bonded fuel basic cell electrodes structure of [4,5] catalys is based t layer is one of ,lew that fairly large catalyst aggregates more or less surrounded by Teflon particles, two materials existing interpenetrating lattices which provide continuous transport paths both liquid gas. This view illustrated schematic diagram below. TEFLON PARTICLES LIQUID BRIDGES PHASE CATALYST AGGREGATE GAS SPACE recent experiments employing scanning electron microscopy energy dispersive Xray analysis have raised serious questions the accuracy of the view described above. Indeed, they suggest very strongly that struc fiir nf 1 t 7=> Ic r\T^nre i h ! I I I  "hP Itrll+a wfTlF rn ratios have been made, these reveal several significant details of structure of the catalystTeflon layer summarized below; The Size, Particles Shape, Substructure of Teflon Scanning electron micrographs (SEM) pure Teflon settled dispersion on a glass revealed that coverslide Teflon from a particles dilute are roughly prolate spheroidal in shape, there some evidence that these particles are aggre gates of closely packed spheres as can seen in Figure particle 2.2. substructure of substantially more the Teflon obvious SEM of catalystTeflon mixtures seen in Figures 2.4, which are scanning electron micro graphs of PtblackTeflon suspensions settled filter paper in Figure which scanning electron micrograph of fuel cell electrode. increased visibility substructure may the contrast provided catalyst crystal lites packing the crevices between Teflon spheres. one assumes that individual molecules are spherical, calculations by using mean molecular weight MM and density 2.22 show that size of a Teflon molecule ranges from Figure 2.2: Scanning Electron Micrograph of Pure Teflon Particles. R i rriir Magnification: Pl 41 on rn MA Cnrn nFn Dh n vrdl. 9 'I Cr^atr rir r \ O '4hl =rl1 Figure 2.4: Scanning Teflon Mi Electron Micrograph of xtures. Magnification: SPtblack 72,000.  S a C S  e  r ' r f Distribution Ptblack the CatalystTeflon Layer It has been noted earlier that scanning elec tron microscopy resolved individual catalyst crystallites, electron micrographs of catalyst Teflon mixtures suggest very strongly that catalyst particles coat surface of the Teflon aggregates. large catalystTeflon ratios > 80 wt. multiple layers of catalyst particles appear coat surface of the Teflon aggregates fill interstices between them. This phenomenon appears Teflon to be particles further are substantiated by negatively charged fact that Ptblack particles are positively charged. They would, therefore, attracted to each other. This view catalystTeflon layer illustrated diagrams below. TEFLON CATALYST TENDENCY OF CATALYST AGGREGATE TEFLON MIXTURE TO FIRST COLLECT CREVICES BETWEEN TEFLON MOLECULES Particle Packing Pore Structure packing arrangement seems to be very close among Teflon molecules in an aggregate, there were obviously macropores existing a more less random manner. In order f to be effective or porous there must diffusion be an electrodes appropriate amount of catalyst which, after being wetted electro lyte, provides reaction sites heterogeneous electrochemical reactions. Moreover, catalyst layer must also provide electron conduction paths, liquid ph products, iase mass transfer gaseous paths flow paths. reactants When propor tion of catalyst great, the catalystTeflon catalyst will form a more layer less continuou exist as matrix isolated that "islands Teflon ," in particles will which condition there would be no continuous gaseous channels with catalyst Teflon layer. This would cause very limited utilization electrodes owing large gas diffusion resistance, 1.e., almost reaction would occur near the electrodegas interface, resulting in a sharp decrease in elec trode efficiency. the other hand, when there exists high a proportion of Teflon, the dis reactions would occur mostly the electrolyte matrix side electrode, which also an other inefficient use of electrodes. Considering previous two extreme cases, there ought to be a certain intermediate elec trode composition in which there enough cata lyst to allow a continuous enough paths Teflon continuous for that electrolyte electron there wi phase conduction, be adequate con tinuous paths transfer gaseous reac tants. Industrially, electrodes with 80 wt. Ptblack have been considered near optimal are most widely used, modeling achieved. transport these no entirely electrodes There exists a need processes occurring adequate been to identify operating all elec trodes to devise a mathematical mode electrode which will make it possible to correlate known electrode the model, behavior with to design improved predictions of electrodes. CHAPTER ELECTRODE REACTIONS, IONIC HYDRATION, AND WATER TRANSPORT Introduction Alkaline fuel cells, as pointed Kordesch [6] , are technologically the most advanced fuel cell type today. Despite their high power output and increasingly lower cost, many problems remain to be solved before they can have ex tensive commercial applications. concentration gradients of electrolyte matrix of an operating fuel cell have been measured by Miller Fornasar [7], Lundquist and Vogel [8]. However , the transport free water within electrolyte matrix has been discussed litera ture. this chapter we will look into problem of water transport the electrolyte matrix in relation electrode reactions ionic hydration to develop ways estimating the concentration gradients of free water electrolyte the matrix. The overall reaction product alkaline hydrogen oxygen fuel cell is water. Water generated reaction must removed from cell to avoid dilution of the elec the cathode solvator hydroxyl ions formed there. reactions electrodes can be written as follows: Anode reaction: *s H20] 2 4 (l+s) H20 + Cathode reaction: l+2s) H20 + 4[OH *s H20] Overall reaction: + 02 2H20 where s is primary hydration number hydroxyl ion. can seen that water must transferred cathode both to maintain the cathode reaction sol vate hydroxyl ions produced there. Water transport from the anode cathode involves transport sol vent water whereas water transport from the cathode anode involves transport hydrated hydroxyl ions. ions electrolyte are hydrated our principal concern is with hydroxyl ions these carry most intracell current and they participate electrode reactions , whereas potassium ions do not. As pointed out by Bockris [9], water may be regarded being bound ions two ways: strongly bound (ii) weakly bound. Strongly bound water  called pri mary hydration sheath is held so strongly that moves with ion. Weakly bound water  called medium. Only primary hydration sheath will be con sidered mary here. hydration The number sheath of of water molecules is called pri primary hydration number ion. Mass Transfer Electrolyte Matrix The electrolyte matrix usually consists thin sheet of specially processed asbestos with the voids tween the asbestos fibers being filled with electrolyte, which, this case, is concentrated potassium hydroxide. transport takes place the electrolyte solution which has three constituents: water, potassium, hydro ions. However, these ions do not exist as bare ions: rather, they exist solvated o0ns the water primary hydration sheath around fairly tightly bound that it moves with ion. the hydrated hydroxyl ion moves from a region of high KOH concentration to one of concentration, hydration number increases and a relationship of following form can be written: *SlH20 + sl) = OH *s2H20 Since concentration in a fuel cell usually large since according to Bockris Saluja [10] hydration ____ _._ I _ _ small that an average value s can be used over entire electrolyte matrix. In a multicomponent system the momentum flux depends only upon velocity gradients energy flux depends upon temperature gradient. electrolyte matrix considered, although there may some local varia tions temperature, temperature differences across the matrix are small compared absolute temperature. Therefore constant temperature will be assumed electrolyte matrix. Also, because the electrolyte con tainted small void spaces electrolyte matrix, convection will be assumed to be absent, i.e., the bulk velocity of not necessary fluid the matrix to consider mass or molar equations flux of a species zero. Hence, of motion depends energy. both mechanical driving force s (ordinary, pressure, forced diffusion) thermal diffusion effects. The multicom ponent diffusion equation [11]: + s.VT _ 1 p p ctc i ] CTij T l] vjv. 3 i1 T D I Pu VnT PiJ (3.11) where = electrochemical potential species , Joule/mole; = partial entropy species Joule/moledeg; = diffusion coefficient 2/ cm /sec;  ~~ ~ ~ C  C. V . 1 1 ^ k f II I It was already assumed that temperature electrolyte matrix constant and gradient pres sure usually very small. Thus, thermal diffusion pressure diffusion terms are usually of only secondary importance and may be neglected. Equation (3.31) then takes form C1 1i C.c. l 3 T . Tij3 V. (3.32) are the diffusion coefficients describing the interactions between species potassium hydro xide solutions we have two independent equations C+C + o C_C+ cc+ + C 1_+ C T o+ (3.33) ccC  o CC,  + CT T (3.34) where = concentration total free water, moles/I; = concentration of potassium ion, moles/i; = concentration of hydroxyl ion, moles/I; = total solution concentration, moles/i; = electrochemical potential potassium ion, Joule/mole; = electrochemical potential hydroxyl ion, Joule/mole. = RT (3.34). can For be written as steadystate conditions, follows these (see Appendix flux equations details): = Cv ++ J vRTCo 0 it + + + + Cv (3.35) PC C \RTCo 0 it z F + C_v o (3.36) where diffusion coefficient electrolyte and given (z+ O + zV9 + 0+ 3.37)  0 diffusion numbers (with respect velocity the sol of water. vent velocity) transference are defined follows: zV + 0+ Z+ o+ + o+ (3.38)  oz 0 The measured diffusion coefficient, related V by DCT C 3.39) In m where the mean molal activity coefficient and m is molalit It can be shown that relation between gradient = Cv PC C T vRTC = D[1 in C  So in C (3.310) Substitution of Equation (3.310) into Equations (3.35) (3.36) gives = v D 1 Rn C Zn C VC + t+ C+ z+F +o (3.311) = VD 1 L n C o 0 VC in C it_ z F (3.312) For water, water, total that flux to water consists of hydration, flux due that free to con section. Since potassium ions do not enter into elec trode reactions, net flux of potassium ions zero and flux of hydration water with potassium ions zero. Thus, we have NH 2 = DVCf fw + sN_ +Cvo 00O (3.313) where Cfw concentration free water. It was already assumed that transport is essentially onedimensional, flux equations become vD d nC d n C (3.314) + C~v VC + + C v z F o In order solve these equations, necessary to know transference number hydration number o0ns. Transference Numbers Solutions transference number fraction total current carried by that ion. Several methods measuring transference numbers are known several em pirical equations concentration have transference been developed. number However, function most aforementioned studies have been done intensively on dilute solutions studies in concentrated electrolytic solutions have been less frequent. Among empirical equations the Onsager equation, according to which the equivalent con ductance ion, given (3.316) where ionic tion, conductance cm2/ohm; of species infinite dilu A,B = constants. Thus, transference number potassium is given 0 + BA + BAO (3.317) + B\ / i 1  1A SA 2 While Onsager theory predicts concentration depend ence of transference number, applicable only low concentrations. Recently, Merenkov [12] measured transference num of potassium in solutions of high concentrations. was found that transference number of potassium was independent temperature from to 65 OC but that decreased with increase in KOH concentration transfer ence number of potassium ion was correlated the empirical equation 0.260 0. 047(/C + 1) (3.318) the other hand, Knobel [13] determined transfer ence number potassium in KOH solutions EMF method; found that transference number of potassium was 0.2633 that it was independent of concentration over concentration range the Onsager from theory 0.03 experimental predictions results of Knobel and Merenkov fuel are cell summarized operations in Table 3.1. concentrated solutions of KOH are used. Therefore, the Merenkov's data, which are only ones available high concentrations, will used later calculations. 3.4 The Primary Hydration Numbers Table Summary Transference Number Data Solutions. Transference Number from Concentration KOH Solutions Onsager Knobel Merenkov 0.03 0.261 0.2633 .205 0.251 .2633 0.198 0.232 .187 .166 .176 .2633 .108 .088 0.072 10.0 0.064 hydration number "free" example, water present 30 wt. important bearing the electrolytic solution, amount solutions. hydration number of both potassium and hydroxyl ions is equal to one, then concentration hydration number "free " the i water ons 36.4 is equal moles/l, to four, while there will not be "free" water available. The concentration "free" water different values hydration number various   concentrations tabulated Table ___ ro ___ __ Table Concentration of "Free" Water a Function Hydration Number. Concentration Concentration Free Water, Solution Moles/I Cf , fw moles/l 49.76 42.11 38.29 34.46 18.52 10.20 ".4   9.86 45.87 26.14 6.41 13.44 41.52 14.65 concept ionic hydration been investigated by many workers used several determining experimental hydration methods number have ions. been However, the different experimental methods give contradictory results because of a lack of a really precise definition of hydration number. Recently, Bockris [10] used the compressibility method to determine sum of hydration numbers of ions in solutions of halides. combining compressibility measurements of ionic vibration potential, individual hydration numbers certain cations anions were estimated. According these results, hydration number of potassium in dilute solutions is 3 while that hydroxyl I I Concentration of KOH, 10 gmole/1 30 wt. solution. obvious, therefore, that hydration solution, number must there vary with concentration little experimental information concerning concentration dependence hydration numbers of potassium and hydroxyl ions at high con centrations. From some of limited information available in Bockris' paper [10], hydration number potassium and hydroxyl ions may be estimated extrapolating the data available. This procedure results, 30 wt. KOH solu tion, in an estimated hydration number of potassium ion hydroxyl ion. These values are, however, very tentative owing the extrapolation required. Since they are best estimates available, they are used next section to estimate concentration gradient electrolyte matrix Concentration different Gradients current densities. Electrolyte Matrix Having estimated hydration numbers trans ference numbers of ions flux equations potassium ion, hydroxyl ion, and water can be solved. concentration gradients of "free" water that of electrolyte electrolyte matrix can be estimated follows: NH, H2O,x dCf fw  D + dx (3.315) From the electrode reactions at both anode cathode can seen that flux of "free" water from the anode cathode is onehalf hydroxyl flux in opposite direction. Therefore, following can be written. H20,x 2 dC fw = D + dx = N /2 ,x (3.51) Since, according Faraday' s law, "free" 1 z F water concentration gradient can be expressed terms of the hydration number ions, the diffusivity, the current density, that dC fw dx 1 +  2 i 1 z DF (3.52) Values diffusion coefficient of the electrolyte various concentrations, taken from Bhatia' s results [14] , are converted into the molar average frame (see Appendix With available data on diffusivity various values hydration number, concentration gradients "free" water at different KOH concentrations can be calculated function of current density. results of "free" water concentration gradients are summarized Table 3.3. r r'nrnn rr4a n fn4l Qlrl /inn ,X r^"r ^ ^ Q I+ c 1 t r ^ s K Table "Free" Water Concentration KOH Gradients. Concentration, moles/i Hydration Hydroxyl ion, 1.91 4.16 6.80 9.86 13.44 078i .236i .199i 075i 171i 0.074i .143i .071i .110i .365i 0. 274i 0.221i 0.108i 0.470i 0.303i 0.202i 0.552i 0.610i 0.285 0.220i vD 1 Since X n C icn C . 1 z F dC it dx+it +C dx z F and N H20,x V  o,x (3.53) N 2x 2 fw o,x, Equation (3.53) yields 1 z F C 2Cf] fw d n Cf dnCfw d in C j (3.54) term where d Zn C , fw d n C  is the partial can molal shown to volume of be equal Cfw solvent water given by V = (3.55) o dp ,X Therefore, Equation (3.54) becomes Cfw M t fw o + v z DF C +2C fw1 dpc c dC (3.56) densityconcentration relation of KOH solution, an equation that relates the density with concentration been developed from densityconcentration data[15] by using the Lagrange interpolation formula. p(C) 1.00086 0.04930  C(0.0143  C(0.000059  0.0000014c) (3.57) Differentiation of Equation (3.57) gives 0.04930  C(0.00286  C .000177 0.0000056C) (3.58) concentration gradients of solution calculated from Equation 56) are summarized in Table 3.4. Discussion From Table can seen that, the estimated values of density transference one ampere hydration numbers, a mean KOH a current concentration 30 wt. 6.80 KOH concentration gradient  C, .* nfl 4 1^ a t I* i ,,, ~ /1 _ ^ __ 1 __7 _ 1 A L n __ .. F% r^ r~ I i  _ ] I Table KOH Concentration Gradients in Electrolyte Matrix. Concentration, moles/i Hydration No. Hydroxyl Ion, 1.91 4.16 6.80 9.86 .0243i .0210i 0172i 0123i .0133i 0090i .0109i *0040i 0. 0179i 0. 0082i 0.0048i 0. 0151i 0125i 0.0049i 0.0024i ference between anode the cathode even high current density one ampere appears to be almost negligible. CHAPTER MATHEMATICAL MODEL OF TEFLONCATALYST LAYER AND CALCULATION OF CURRENT DENSITY DISTRIBUTION Introduction Investigation the electrode structure scanning electron microscopy (SEM) energy dispersive Xray analysis (EDXA) yielded much information on how platinum black catalyst Teflon particles are mixed to form catalystTeflon layer the electrode. basis s information we can understand how the electrode ported, is wetted, what gaseous the means reactants ionic, can electronic, trans and water transport are. Mathematical modeling these catalyst Teflon layers been done to relate these findings predicted performance the electrodes. A scanning electron micrograph surface layer of Pt:Teflon Figure (Magnification the weight ratio 72,000) . 80:20 is shown From studies this similar following conclusions can be drawn: Teflon aniqregates are prolate spheroids of sizes 2000 3000 A in the major axis 1000 _ _ Y T consist of aggregates of spherical Teflon mole cules with diameters of Figure 4.1: anning Electron Micrograph Surface 80:20 Ptblac kTeflon Layer Magnification: 72,000 Owing to thin extremely small size catalyst crytallites cannot be is clear that less face than area they resolved SEM, have an equivalent diameter From measurement BET gas sur adsorption method and the estimation packing condition as shown in Chapter seems very likely that the dia meter of a single catalyst crystallite range of to 40 to be relatively uniform. ratio of platinum black to Teflon increases, chances of observing majority bare of Teflon Teflon decrease, aggregates are great coated platinum black in the electrode 80:20 platinum blackTeflon mixture From these observations it appears that following processes occur during formation an electrode: When a welldispersed suspension of platinum black is mixed with Teflon dispersion (which nega tively charged hydrophobic colloid) the Teflon aggregates are coated with platinum black. During filtration this mixture the catalyst coated aggregates settle filter medium and form a layer of platinum blackcoated Teflon par tides. When filter cake is pressed, these particles are compacted together very tightly. During expand, bonded sintering process, soften, contact one layer with more less Teflon another continuous aggregates to form a structure. basis of these observations conjectures electrode can be pictured as consisting of gas channels of n a, r. r. 9^ r% n 4nrf^v/ 4y . n 4 *rrn; ;I r^ c? /" A t l/1^^1 /l * *C I nvh rr n f 9^ H n layer gas p is wetted enetrates and penetrated the catalystTeflon electrolyte. layer Thus, by means intraaggregate voids and electrolyte penetrates extra aggregate voids where catalyst crystallites lie. Gas, electrolyte, catalyst meet at surface Teflon aggregates shown schematically in cross section Figure CATALYST 4.2. TEFLON r AGGREGATE TEFLON 4MOLECULE INTRA AGGREGATE VOIDS CRYSTALLITES ELECTROLYTE MATRIX EXTRA AGGREGATE VOIDS CURRENT COLLECTOR Figure 4.2: Schematic Teflon Diagram of Particles Platinum Black in Electrodes. Catalyst A cylindrical multicompartment model as shown Figure is a much simplified but fairly reasonable approx imation structure catalystTeflon layer. tions between Teflon aggregates which may limit transport gaseous reactants. TEFLON WITH INTRAAGGREGATE VOIDS PHASE CONNECTING WINDOWS ELECTROLYTEWETTED CATALYST ELECTROLYTE MATRIX 9,  10003000A '3050A Figure 4.3: Schematic Model Structure of CatalystTeflon Layer. Although model described above represents struc ture of electrode layer very well, there arises a problem in mathematical modeling existence of windows which limit transport gaseous reactants. sake of simplicity in mathematical modeling limitation time, model shown in Figure 4.4, which same the multicompartment model except having windows, adopted this work. 2,~ ~~~~~ ~ ~ ~~ 1t2  ~n.. U T.'/// /////I / /111/ll///il /t f l f l/// / I IfD 1 I __1l "1 I. 1 ~. '_ 1  r) TEFLON WITH INTRAAGGREGATE VOIDS ELECTROLYTEWETTED CATALYST / S //////// 10003000A  305 0A V Figure 4.4: Schematic Model Structure CatalystTeflon Layer with No Windows. owing slowness reduction oxygen catalyst surface. following assumptions were made development of the mathematical model to simplify computations: Steady state, i.e. , constant current density. Isothermal. Diffusion coefficients other physical pro perties are independent of electrolyte concentra tion. concentration assumed vary xdirection only. The diffusion oxygen through gaseous space restricted. Both cations and anions have same primary hydration number. Electrode this work Reaction taken Reaction to be 2. Rate The electrochemical reaction the oxygen electrode be written H20 +  4[OH *2H20] convenience we denote *2H20, *2H20, and H20 species respectively, equations which follow. Although several mechanism of workers reduction [16,17] oxygen have studied in alkaline solutions on platinum catalysts, still inadequately understood. However, the work of Gnanamuthu Petrocelli [18] suggested that a suitable rate equation dix dx (x) C4 (x) [ Oexp(F(s o ]exp(F(rs I o s G )/RT) t))/RT) R (4.21) = ai where = current density catalyst phase, amp/cm = surface area unit volume of electrode, cm2/cm3 = exchange current density, amp/cm = concentration species , gmole/ = concentration = potential = potential of species catalys i at t phase, electrolyte phas , gmole/1 volt; e, volt. Equation .21 must solved with following boundary conditions = 0,  L, where = apparent current density being drawn from electrode, /cm Ionic Fluxes Electrolyte Phase At steady a binary state electrolyte mass system fluxes can xdirection be written D*v C dpx dx i t* Z 1 z F 1 + Clv* 1 1 .31) x( V*v2c dx e dx i t* a 2 z7F 2 + C v* 2 2 4.32) ( x Since = C1 + C2 + C4 + C4 C v* T x = Clv, 1 1,x + C2v + C4v 4 4 = Clv, 1 1,x + CV4,x 4 4,x ClVl,x C44,  i/F,  N4 Equation .32 can be rearranged to give C due dx 1 F C CT] .33 Since = vRT9ina, C+C4)V4 *" d9na dinC (see Appendix Equation V2CDV (C+C4)v (4.3 dinC dx becomes CT .34 C+C t2 4 2 Substitution into Equation .34) gives + C4) .35 FD'CT which will solved using one boundary conditions, namely, Potential Gradients Electrode Layer potential drop in catalyst phase is governed by = N1 = NI,x/2 l, x where o conductivity catalyst. current carried by the ions related poten tial following equation [20] d dx dx K F Cs 2 + n 2 t2 2V2 nC4 4 (4.42) dx dx where K iS conductivity the electrolyte stoichiometric coefficient species equation z1 S1M1 z 2 +sM2 2 2 Substituting = vRTina into Equation (4.42) elec trode reaction equation gives dz dx v RT nF 2.5C] + i 4 dRna dC dinC dx (4.43) Equations (4.41 (4.43) can solved with B.C. i.e., = 0, and at Oxygen Transport Electrolyte Phase concentration oxygen the electrolyte phase will vary both r and xdirections. In work by Tham [21], were assumed to vary direction only, these to predicted current densities which agreed reasonably well with experimental values, i.e., ' 's  L, + sM4 ne 4~ 4 flux equation oxygen 2 dC D3 dC3 2 + 2 r dr dr 1 dis nF dx nF dx (4.51) where After di dx is given several Equation mathematical (4.21). operations (see Appendix following equation was obtained C1 (x)C4 c c 1 4 r2F(4 exp RT RT q(DEN) C1(x)C4 e 2F exp O 1 4 (I (q (ro K1 (qro)  K1 (q(r I (qr 2 6+6 ) 4.52) C (x) where 0 nFCD 3 3 exp Bessel functions of zero order; = Bessel functions first order; = K1 (q(r .(qr o(qro )I (q(r +6)). Substitution average value of C, (x) for C3 (x into Equation (4.21) gives Il'K1 + K 3(x) }) F( s "s  ) To solve for C(x) , C3(x) (x) , 's(x), (x) , Equations (4. 35), (4.41) , (4.43) 4.52) , (4.53) can be com bined with accompanying boundary conditions. Computation the Current Generation Equations (4.35) , (4.41) , (4. 43) , 52) (4. 53) were integrated numerically using the quadratic RungeKutta method; computer program computation cur rent density distribution is given in Appendix 5. Numerical values of properties electrolyte such as electro lytic conductivity, partial molal volume, activity electrolyte, other necessary terms were expressed form of polynomial equations functions concentration. specific conductance of KOH was taken from the data by Klochko and Godneva [22] was expressed polynomial form by using Lagrange interpolation formula follows: = 0.59876 + C (0.608757  C(0.0684246 0.00229369C)) 4.61) calculation of current generation specific surface area of Ptblack catalyst was taken to be 45 m /g (from Chap an exchange current density oxygen 5.0x10 amp/cm was used [23] Results Discussion calculated fractional current generation given in Table current generation profiles in the elec trode layer are shown in Figures functions catalyst agree re layer thickness asonably well with current density. those obtained These from actual results operating fuel cells [24,25]. From Figures one can see that low current densities the distribution current generation is quite uniform , while at high current densitie s the majority current is generated that portion the catalystTeflon layer near electrolyte matrix. Cell potential and power density are tabulated in Table , and these are plotted as function of current density in Figure 4.7. From Figure we can see that limiting current density approximately amp/cm . and maximum power density 0.70 watts/cm is obtained at a current density about 1.00 amp/cm It should be noted, however, that this work was assumed that there were no gas transport limitations; moreover, it was also ass umed that the oxygen contained no impurities which could build the gas spaces introduce gaseous concentration gradients. Thus, model for which calcula tions are presented probably overestimates to some degree 44N% CM 0 in CM O In CN CM amp/cm app / amp/cm amp/cm2 amp/cm2 0.005 Distance Electrode Layer, Distance Electrode Layer , cm Figure Cumulati Fraction Current Generation Electrode Layer 66 Table 4.2 Cell Potential and Power Density Current Density, amp/cm2 0.010 vs. Cell Potential, volt Current Density. Power, watt/cm2 1.085 0.011 0.050 1.058 0.053 0.100 1.039 0.104 0.200 1.009 0.202 0.300 0.979 0.294 0.400 0.948 0.379 0.500 0.914 0.457 0.600 0.878 0.527 0.700 0.841 0.589 0.800 0.802 0.641 0.900 0.762 0.686 1.000 0.704 0.704 1.100 0.631 0.694 0.5 1.0 Current Density, amp/cm generated near the electrolyte matrix because enormous difference between liquidphase gasphase transport coefficients, and because low solubility oxygen in concentrated KOH. CHAPTER V SUMMARY AND CONCLUSION After a brief description fuel cells their per formance these are related thermodynamics kinetics of the electrode reactions, transport processes occurring in an alkaline hydrogenoxygen fuel cell are dis cussed along with problems associated with the design electrodes cipal having studies improved completed by performance. author However, reported prin this dissertation are concerned with: determination surface areas of electrode components evaluation effect processing temperatures surface areas, estima tion of particle sizes geometry the components electrodes, investigation details of micro structure of fuel cell electrodes by means scanning elec tron microscopy energy dispersive Xray analysis resulting the development structure, on concentrate a new physical evaluation of on gradients picture of influence of and mass transport, electrode ion hydration development of a physical and mathematical model analysis, develop ment of a computer program for use in predicting electrode Surface areas of platinum catalyst, Teflon 30 particles, their mixtures in different ratios were measured BET adsorption method; these have been compared with geomrretrical calculations to provide information their sizes microstructure catalystTeflon layer, particularly in relation results obtained by scanning electron microscopy. dependence of surface area platinum black temperature of pretreatment was also measured and related to electrode processing procedures. was also found that surface area platinum catalyst depends strongly pretreatment temperature range 350 C. sintering This temperature finding was during very electrode important as fabrication nominal is about 310 "C. sintering example, temperatures it was are shown very that close present electrode temperature which catalyst itself sintered , producing large re duction in surface area. need for very good temperature control during electrode sintering was demonstrated. Scanning electron microscopy energy dispersive Xray analysis techniques were used investigating detailed structure of pure Teflon catalyst layer of different platinum blackTeflon ratios. This provided information size, shape, and microstructure catalystTeflon layer arrangement distribution of catalyst and Teflon aggregate These studies showed, for example, that on the mean molecular weight Teflon and its density, conform conclusions drawn from electron microscopy. aggregates have a prolate spheroidal shape with minor major diameters of 1000 1500 (100 and 2000 3000 appe (200 ar to nm) , spheres respectively, with diameters while ranging the molecules from 200 30 nm). 80:20 In a platinum black commonly used electrode Teflon, composition Teflon aggregates are seen to be coated with one or more layers of catalyst crystallites. This the exact opposite previously held view of structure catalystTeflon layer, namely, that this layer consists of roughly spherical glomerates of catalyst (diameter about one micrometer) surrounded by prolate spheroidal Teflon particles. sub structure Teflon particles been previously reported. size be determined individual clearly catalyst scanning crystallites could not electron microscopy owing resolution limitations of technique, these studies did enable to d determine that crystallite size was less than However, this information, combined with that derived from surface area studies made it possible to demonstrate that the catalyst crystallite size is almost certainly range of nm). the oxygen electrode a product at the hydrogen elec trode since concentration influences concentration of electrolyte components, is reasonable to expect that ion hydration will affect electrode behavior. Indeed, hydration was found to have a significant influence on concentration "free" water. this work a primary hydra tion number both potassium and hydroxyl ions seems reasonable KOH concentration used fuel cells, this value was used calculation mathematical modeling equations. it impossible Unfortunately, to examine in detail limitations of influence of time made ionic hydration mathematical modeling; that will be a prin cipal objective further research this area. Based information obtained earlier from studies size distribution of electrode components structure analysis of electrodes, was devised utilize a schematic this model information for mathematical n in calculating concentration current generation profiles. A set modeling equations was developed computations done. results were generation analyzed to provide distribution information electrode on current layer different current densities. The distribution of current generation magnitude limiting current density given by mathematical modeling oxygen electrode show that at higher current densities determine more adequately the effective mass transport properties electrode layer to develop analyze more realistic models. aggregate voids of Teflon Considering particles fact have that very narrow, intra tortuous, interconnected gaseous paths that the electrolyte wets the catalyst layer coated surface of Teflon aggregates, seems very likely that there could be some hindrance to mass transport oxygen catalystTeflon layer. This point should be investigated future work, should influence of impurities oxygen system. APPENDIX DERIVATION (EQUATIONS OF FLUX EQUATIONS 35) AND (3.36) From Faraday' s Law, we have z.N. 1 1 Z C.v. (A. 11) Since solution, as a whole, is electrically neutral, we have z.C. i i (A. 12) Thus Equation (A. 11) can be written ziC.v 12 C.i)v 1 z.C. 211  v A.13) Therefore, electrolyte such as KOH, we have Fz+C+ + Fz C  v (A.14) From Equations (3.33) (3.34) , we have = F = F = F  o Vy CC+ CTD+_  v (3.34) Adding last two equations, we get RTC C o To+  v+)  v (A. 15) electrochemical potential the electrolyte, given e = ++ (A. 16) stoichiometric concentration the electrolyte can be written (A. 17) C V+ Hence = C(v+u+ = Cw Therefore, we get CV~i e e RTC C C TD T o+  v ) +7 RTC C o (A. 18) Eliminating v+ from Equations (A. 14) (A.18) , we get RTC C + o CDo T o + Fz C CVv + + + C C+V+, 0o+  V 0 RTC C C o + Z+Po+ + 0+0 z V  0 o+ 0 (A. 19)  V Therefore  0 z F(  z V 0 C CVy T RTC + 0o+ 0  z V 0 (A. 110) Substituting Equations (3.37) (3.38) into Equations (A. 110) we get  v CTCVpe T e A. 111) z F Since solution is electrically neutral z+C+ z C z C C+ Hence z C C+  z Z+o+ + o+ C C+ o(Z+ o+ (A.112) Substituting Equation (A. 112) into Equation (A.111),  v CTCVu T e z F (A. 113) VRTC Hence _cT URTC z F  O (3.36) Similarly, can be shown that Cv + + vDCT VRTC CVve it z F (3.35) + C APPENDIX DERIVATION OF EQUATION (3.310) electrochemical potential the electrolyte given by 0 = vRT9n (Cf a ) e + (A. 21 where the mean molar electrolyte activity is a proportional coefficient of ity constant. gradient electrochemical potential electrolyte then give = vRT Cf a, + n (Cf. a 0a + Ca + vRT Cf (A.22) Therefore vRT Caf f 9C atnfC 3nC ml, * ac f+ ax The measured diffusion coefficient of the electrolyte, related D by vM m) (1 dZny+ d dnm (A.24) C.M. 3J3 C C M o o A. 25) Therefore C oCM 00 d9nym dinm dny+ dnm CT C O diny+ d Qnm (A.26) Hence we get dinf+ vRTCo dk nC CViy e e A. 27) diny+ d dZnm The measured diffusion coefficient of the electrolyte, is also related to D by following relation vM m 0 + Mm dinfi dinC =  + fI + C+ S* o r\ I From Equations (A. 24) (A.28) we get d~nfi dnC dZny+ dinm dQnp dZnC SMC C M O O MC CoMo OO MC C M O O dZnp dnC MC dinp dknC pdQcnp o dnC pdRnp o dinC MC  P (A.29) = C M O O + MC C M O O + MC (C M 0 0 + MC) DC aC Multiplying each side the above equation by C, we get dnp dnC C C p C 0 MC +P P MC +  (A.210) ptnC dCnp dC 1 p M p 0 aC MC P dZnf d nC diny di nm dRnC dZnC SMC p MC Po dinC dZnC MC PO MC  P d nC dZnC o (A. 211) Substituting Equation (A. 211) into Equation (A.27), thus get VRTC dinC dinC (3.310) = D APPENDIX CONVERSION (VOLUME AVERAGE F MOLAR AVERAGE F OF D 'RAME RAME TO D* DIFFUSIVITY TO DIFFUSIVITY) Since the diffusion data that we have on from Bhatia are volume average frame only, they have transformed into the molar average frame to be used our equations. The diffusion flux volume average frame can related that the molar average frame following manner. a binary system, from the defini tion volume average frame, V PBB MB (A. 31)  v (A. 32) Substitution Equation (A. 31) into Equation (A.32) gives AP PBVB V  MB1 (CAVAVA + CVBVB)  C, S ' 7 pCvVn (A. 33) VA MA A PA VA * n n = CAVA AA  CA A  CACBVBVB ABBB (A. 34) Since CAVA = CBV BB = J* A BJ* B + C v* A + C v* B AVA Equation (A. 34 ) + BVB becomes + C v*) CBVB  (J* B + C v*) B AVB (C J* BA + CC Bv* AB  C J* AB  CC A (CBJ* BA  C J*) AB (A. 35) Since + JB , Equation 35) becomes + CB) B (A. 36) DvVCA Since DVC (CA+CB) A B D VCA JA = VBVCA becomes Therefore, (CA+CB) V A BB J*A A = D* APPENDIX CALCULATION OF C3(r,x) FOR A GIVEN flux equation for C3 [26] 2 d C d~c3 dr2 dr D dC3 r dr 1R RF di s dx (A. 41) Substitution of Equation 2 dC3 d3r 2 dr D dC3 r dr .11)  C3 into cai nFC3 Equation *C (x) rO . ^ . (A. 41) gives exp  eai nF [C1i(x) . o . F(es exps exp R *R (A. 42) C4 (x) F(*s O nFCD 3 3 exp (A. 43) = C3  C3 "3 (2F exp q) j A.44) Then Equation (A. 42) becomes F(s 