Transport processes in teflon-bonded fuel cell electrodes

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Title:
Transport processes in teflon-bonded fuel cell electrodes
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xvi, 96 leaves : ill. ; 28 cm.
Language:
English
Creator:
Lee, Myung-Cheen, 1942-
Publication Date:

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Subjects / Keywords:
Fuel cells   ( lcsh )
Genre:
bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

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Thesis:
Thesis--University of Florida.
Bibliography:
Includes bibliographical references (leaves 94-95).
Statement of Responsibility:
by Myung-Cheen Lee.
General Note:
Typescript.
General Note:
Vita.

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Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 000207984
notis - AAX4788
oclc - 04083149
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TRANSPORT PROCESSES IN TEFLON-BONDED
FUEL CELL ELECTRODES


MYUNG-CHEEN 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 10-005-022


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


Hydrogen-Oxygen


Fuel


Cell


Thermodynamics


Kinetics


Electrodes


Advantages of


Porous


Diffusion


Elec-


trode s


S. . . 11


THE


STRUCTURE


OF TEFLON-BONDED


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


Pt-black-Teflon


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 TEFLON-CATALYST


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


(3.3-6)








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


Pt-black


Calculated


and Measured


Surface Are


of Pt-


black-Teflon 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 Pt-black-Teflon


36,000


of Pt-black-Teflon


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
Pt-black-Teflon Layer. Magnification: 72,000


Schematic


Teflon


Diagram of
Particles


Schematic Model


Platinum Black
in Electrodes


Structure


Catalyst


the Cata-


lyst-Teflon


Layer


S a a . 54


Schematic


Model


Structure


the Cata-


lyst-Teflon


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/cm-sec


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/mole-deg


Entropy of


transference

Temperature


Reaction

Velocity

Velocity


Volume of


system,


number


Cal/mole-deg


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


electrolyte-catalyst


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


mho-cm /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

x-direction


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


Myung-Cheen

December, 1


IN TEFLON-BONDED


LECTRODES


Lee


976


Chairman:


Major


Robert


Department:


. Walker,
Chemical


Jr.
Engineering


structure


properties


of Teflon-bonded


fuel


cell


electrodes


their


components--platinum black and


Teflon


30 particles--has


been


investigated


in detail


compared


with


previously published


works.


Recent experiments em-


playing


scanning


electron


microscopy


energy


dispersive


X-ray


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


Teflon-bonded


catalyst


immediately


adjacent


electrolyte


matrix.


For


oxygen


electrode operating


at a current density


one


am-


pere


more


than


half


current


is generated


the catalyst-Teflon


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


Hydrogen-Oxygen


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,


hydrogen-oxygen


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


(1.2-1)


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


(1.2-2)


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


(1.2-3)


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


(1.2-4)


in addition,


process


is carried out


reversibly,


(1.2-5)


where


= entropy


change of


system,


Joule/mole-K;


= temperature of


system,


Using


Equations


(1.2-1),


(1.2-3) ,


(1.2-4) ,


(1.2-5) ,


follows


that


= W


= T








AH T


2-7)


where


free


energy


change of


system,


which holds


isothermal


process,


we get


-n F


(1.2-8)


r,c)


Writing V


- V


we get


= -n F E


r (1.2-9)


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


(1.2-10)


where


sum of


the overpotentials


that


exist


electrodes,


electrode-electrolyte


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


open-circuit


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 i-h bI rnlhn


nnor-* i nfl


11I


fnil


roll


+-ho r(ivT-r n 4-


































1lim,c


11im,a


0 il i
lim


Current


Density,









ohm


(1.2-11)


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


(1.2-12


a, act


Scon(1.2-13
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 metal-solution


potential


interface,


rate constant


re-


k of


electrochemical


reaction


can be


expressed empirically


-BVF/RT)


(1.2-14)


where


rate constant


absence


a potential difference


symmetry


factor,


= gas


constant,


8.314


Joul


e/gmole-K


- 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


(1.2-15)


rates


of electrochemical


reactions


are


a measure of


net


reaction


rates


the net


current density


given


(1.2-16)


where


forward


current


reverse


current.


Therefore,


current


case


density may


electrode


be expressed


reaction


since


IVF]
RT


Ff C0


- kr
r


(1-B)


VF
RT


(1.2-17)


where


reverse


are


rate


reactions


constants of


absence of


forward


a metal-solution


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


(1.2-18


the overpotential,


which


equal


potential


difference


Equation


(1.2-17)


can


be expressed


RT F


o exp
o r


- exp


(1-B)


(1.2-19)


the case of


a multielectron


transfer


reaction,


the general


form of


current density-overpotential


orexp
o '


a F]
RT


- exp


relation


RT


(1.2-20)


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 hydrogen-oxygen


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


Teflon-bonded


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 TEFLON-BONDED


ELECTRODES


Characterization


of Electrode


Material


Teflon-bonded


fuel


cell


electrodes


are


made of


three


different materials;


catalyst,


Teflon,


fine-meshed


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)


as-received


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 well-dispersed


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 well-dispersed


Teflon


particles


are


shown


later


on pages


-29.


fine-meshed metal


screen


used


provide


mechan-


ical


support


the catalyst


layer


serve


as an elec-


tron


collector


the electrons


generated.


Gold-plated


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


200-220C 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


nitrogen-helium


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 E-Sure


rati ns


in thFhe


ranaer


from


n nE-


11 1Di lfA


n -


%I









P V C
P VC


(2.2-1)


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


2-2)


1
V C
m


then


we can


determine


from


(2.2-3)


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


300-350


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


(2.2-4)


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)


(2.2-5)


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


(2.2-4)


2.2-5)


noting


that


specific


gravity


of Teflon


that


platinum


s 21.45


while


letting


the molecular


diameter


Teflon


Pt-black


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 random-close,


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


3-p rmn <" mv --^j v


C? \ V Q Q


F F-r^


<"-mnn /4"


C1-t .+


'_v^








Table


Total


Free


Surface Areas of


Teflon


Pt-black.


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 Pt-black


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


(2.2-6)


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


random-close


packing),


2.22


we get


external


surface


area


of Teflon


aggregates


m2/
in >3.


thickness of


Pt-black


catalyst


layer


the mix-


tures of


Thickness


Pt-black


(Bulk


Teflon


Volume


can


of Pt-black


be calculated as


in 1


follows:


of Mixture)/


(Teflon Aggregate


p(1-c)


Surface Area


(Surface Area


in 1


of Mixture)


g of Teflon Aggregates


x x)


(2.2-7)


where


fraction


of Teflon


in a mixture;


= density

= porosity


Pt-black


of Pt-black


crystallites,


catalyst


g/cm


layer.


Therefore,


with an


assumption


that


packing


of Pt-black


- )








70 A and a


50:50 mixture


Considering


fact


a catalyst


that


layer


crystallite


thickness


size


of Pt-black has


been


estimated


to be


to 40 A in diameter,


we can


see


that


50:50 mixture


fairly


significant


fraction of


with


Pt-black


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


Pt-black-Teflon


Measured


Layers


Surface Areas


Pure


Teflon


Layer


we assume


Pt-black-Teflon


of electrodes,


that


surface


layers


we can


areas


change


estimate


components


during


surface


areas of


formation

Pt-black-


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


Pt-black-


Teflon


Pt-black: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


Pt-black-Teflon


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


Pt-black


to be buried


them.


This


can


shown by


fact


that


calculated


surface


area


of Pt-black


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 Pt-black.


Formation


of Electrodes








Platinum black


is weighted


out and


dispersed


several minutes


in water


containing


a wetting


agent,


Triton


X-100,


in an amount


equal


6% of


weight of


catalyst


amount of


using


Teflon


an ultrasonic


30 emulsion


agitator.


added


requisite


to Pt-black 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,


fine-meshed 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


Pt-black


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


X-ray


analysis


have


raised


serious questions


the accuracy


of the


view described


above.


Indeed,


they


suggest


very


strongly


that


struc-


f-iir nf


1 t 7=>


-Ic r\T^nre i -h


! I I I -


"hP Itrll+-a wf-TlF rn








ratios


have


been made,


these


reveal


several


significant


details of


structure of


the catalyst-Teflon


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 catalyst-Teflon mixtures


seen


in Figures


2.4,


which


are


scanning


electron micro-


graphs of


Pt-black-Teflon


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 D-h n vrdl.


9 'I


Cr^-atr- rir


r \ O '4---hl =rl1---



















































Figure


2.4:


Scanning
Teflon Mi


Electron Micrograph of
xtures. Magnification:


SPt-black-


72,000.


- S a C -S -


e


-


r '


-r f









Distribution


Pt-black


the Catalyst-Teflon


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


catalyst-Teflon


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


Pt-black


particles


are


positively


charged.


They would,


therefore,


attracted


to each


other.


This


view


catalyst-Teflon


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 catalyst-Teflon


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 electrode-gas


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.


Pt-black 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]


vj-v.
3 i1


T
D -I
Pu- VnT
PiJ


(3.1-1)


where


= electrochemical


potential


species


, Joule/mole;


= partial


entropy


species


Joule/mole-deg;


= 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


(3.3-1)


then


takes


form


C1 1i


C.c.
l 3
T .
Tij3


-V.


(3.3-2)


are


the diffusion


coefficients describing the


interactions


between


species


potassium hydro-


xide


solutions


we have


two


independent


equations


C+C
+ o


C_C+
c-c+
+ C
1-_+


C T o+


(3.3-3)


ccC
- o


CC,
- +


CT
T


(3.3-4)


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








(3.3-4).


can


For


be written as


steady-state conditions,


follows


these


(see Appendix


flux equations


details):


= Cv
+-+ J


vRTCo
0


it
+ +
+ + Cv


(3.3-5)


PC C


\RTCo
0


it
z F


+ C_v
-o


(3.3-6)


where


diffusion


coefficient


electrolyte and


given


(z+
O- +


zV9
+ 0+


3.3-7)


- 0-


diffusion


numbers


(with


respect


velocity

the sol


of water.


vent


velocity)


transference

are defined


follows:


zV
+ 0+


Z+ o+
+ o+


(3.3-8)


- oz
0-


The measured diffusion


coefficient,


related


V by


DCT
C


3.3-9)


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


(3.3-10)


Substitution


of Equation


(3.3-10)


into


Equations


(3.3-5)


(3.3-6)


gives


= -v D 1


Rn C
Zn C


VC + t+ C+
z+F +-o


(3.3-11)


= -VD 1
L


n C -o
0 VC
in C


it_
z F


(3.3-12)


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
0-0O


(3.3-13)


where Cfw


concentration


free water.


It was


already


assumed


that


transport


is essentially


one-dimensional,


flux


equations


become


-vD


d nC
d n C


(3.3-14)


+ 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


(3.3-16)


where


ionic
tion,


conductance
cm2/ohm;


of species


infinite dilu-


A,B


= constants.


Thus,


transference


number


potassium


is given


0
+ BA

+ BAO


(3.3-17)


+ 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)


(3.3-18)


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


(3.3-15)


From the electrode


reactions


at both anode


cathode


can


seen


that


flux of


"free"


water


from the


anode


cathode


is one-half


hydroxyl


flux


in opposite


direction.


Therefore,


following


can be written.


H20,x
2


dC
fw
= -D +
dx


= -N


/2
-,x


(3.5-1)


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


(3.5-2)


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 -rr4-a 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


(3.5-3)


N
-2x
2


fw o,x,


Equation


(3.5-3)


yields


1
z F


C
2Cf]
fw


d n Cf
dnCfw
d in C
j


(3.5-4)


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 = (3.5-5)
o dp


-,X








Therefore,


Equation


(3.5-4)


becomes


Cfw M t
fw o +


v z DF


C
+2C fw1

dpc
c dC


(3.5-6)


density-concentration relation


of KOH


solution,


an equation


that relates


the density with


concentration


been


developed


from


density-concentration


data[15] by


using the Lagrange


interpolation


formula.


p(C)


1.00086


0.04930


- C(0.0143


- C(0.000059


- 0.0000014c)


(3.5-7)


Differentiation


of Equation


(3.5-7)


gives


0.04930


- C(0.00286


- C


.000177


0.0000056C)


(3.5-8)


concentration


gradients of


solution


calculated


from


Equation


5-6)


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 TEFLON-CATALYST


LAYER AND


CALCULATION OF CURRENT DENSITY DISTRIBUTION


Introduction


Investigation


the electrode


structure


scanning


electron


microscopy


(SEM)


energy


dispersive


X-ray


analysis


(EDXA)


yielded much


information


on how


platinum black


catalyst


Teflon


particles


are mixed


to form


catalyst-Teflon


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


Pt-blac


k-Teflon 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


black-Teflon mixture


From


these


observations


it appears


that


following


processes


occur


during


formation


an electrode:


When


a well-dispersed


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 black-coated 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 4-nrf^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 catalyst-Teflon


electrolyte.


layer


Thus,


by means


intra-aggregate


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


catalyst-Teflon


layer.








tions


between


Teflon


aggregates


which may


limit


transport


gaseous


reactants.


TEFLON WITH


INTRA-AGGREGATE VOIDS


PHASE CONNECTING WINDOWS


ELECTROLYTE-WETTED CATALYST


ELECTROLYTE
MATRIX


9,


- 1000-3000A


-'--30-50A


Figure


4.3:


Schematic


Model


Structure of


Catalyst-Teflon


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,-~ ~~~~~ ~ ~ ~~ ----1-t2-- --- ~n.. U-


T.'/// /////I / /111/ll///il /t f l f l/// / I IfD


1 I __1l


"1 I. 1 ~. '_ 1 -


r)














TEFLON


WITH


INTRA-AGGREGATE VOIDS

ELECTROLYTE-WETTED CATALYST
/


S- -////////


1000-3000A

- 30-5 0A


-V-


Figure


4.4:


Schematic


Model


Structure


Catalyst-Teflon


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


x-direction


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


(4.2-1)


= 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


.2-1


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


x-direction


be written


D*v C


dpx
dx


i t*
Z 1
z F
1


+ Clv*
1 1


.3-1)


x(


V*v2c


dx
e
dx


i t*
a 2
z7F
2


+ C v*
2 2


4.3-2)


(
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


.3-2


can


be rearranged


to give


C due
dx


1
F


C
CT]


.3-3


Since


= vRT9ina,


C+C4)V4


*" d9na
dinC


(see


Appendix


Equation


V2CDV

(C+C4)v


(4.3-


dinC
dx


becomes


CT


.3-4


C+C t2
4 2


Substitution


into


Equation


.3-4)


gives


+ C4)


.3-5


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


C-s
2 +
n 2


t2
2V2


nC4
4-


(4.4-2)


dx
dx


where


K iS


conductivity


the electrolyte


stoichiometric


coefficient


species


equation


z1
S1M1


z
2
+sM2
2 2


Substituting


= vRTina


into


Equation


(4.4-2)


elec-


trode


reaction


equation


gives


dz
dx


v RT
nF


2.5C]
+ i
4


dRna dC
dinC dx


(4.4-3)


Equations


(4.4-1


(4.4-3)


can


solved with


B.C.


i.e.,


= 0,


and at


Oxygen


Transport


Electrolyte


Phase


concentration


oxygen


the electrolyte phase


will


vary


both


r- and x-directions.


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


(4.5-1)


where


After


di
dx


is given


several


Equation


mathematical


(4.2-1).


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 )


4.5-2)


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


(4.2-1)


gives


Il'K1


+ K


3(x)


-})-


F( s
"s


- )







To solve


for C(x) ,


C3(x)


(x) ,


's(x),


(x)


, Equations


(4. 3-5),


(4.4-1) ,


(4.4-3)


4.5-2) ,


(4.5-3)


can be


com-


bined


with


accompanying


boundary


conditions.


Computation


the Current


Generation


Equations


(4.3-5) ,


(4.4-1) ,


(4. 4-3) ,


5-2)


(4. 5-3)


were


integrated


numerically


using


the quadratic


Runge-Kutta


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))


4.6-1)


calculation of


current


generation


specific


surface


area


of Pt-black


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 catalyst-Teflon


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


liquid-phase


gas-phase


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


hydrogen-oxygen


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


X-ray


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


catalyst-Teflon


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


X-ray


analysis


techniques were


used


investigating


detailed


structure of


pure


Teflon


catalyst


layer


of different


platinum black-Teflon


ratios.


This


provided


information


size,


shape,


and microstructure


catalyst-Teflon


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


catalyst-Teflon


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


catalyst-Teflon


layer.


This


point


should be


investigated


future


work,


should


influence of


impurities


oxygen


system.














APPENDIX


DERIVATION
(EQUATIONS


OF FLUX EQUATIONS


3-5)


AND


(3.3-6)


From Faraday'


s Law,


we have


z.N.
1 1


Z C.v.


(A. 1-1)


Since


solution,


as a whole,


is electrically neutral,


we have


z.C.
i i


(A. 1-2)


Thus


Equation


(A. 1-1)


can


be written


ziC.v
12-


C.i)v
1


z.C.
211


- v


A.1-3)


Therefore,


electrolyte


such


as KOH,


we have


Fz+C+


+ Fz C


- v


(A.1-4)


From Equations


(3.3-3)


(3.3-4) ,


we have


= F


= F


= F








- o


Vy


CC+
CTD+_


- v


(3.3-4)


Adding


last


two equations,


we get


RTC-


C o
To+


- v+)


- v


(A. 1-5)


electrochemical


potential


the electrolyte,


given


e = ++


(A. 1-6)


stoichiometric


concentration


the electrolyte can be


written


(A. 1-7)


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. 1-8)


Eliminating v+


from Equations


(A. 1-4)


(A.1-8) ,


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. 1-9)


- V


Therefore


- 0-


z F(


- z V
0-


C CVy
T


RTC


+ 0o+ 0-
- z V
0-


(A. 1-10)


Substituting


Equations


(3.3-7)


(3.3-8)


into


Equations


(A. 1-10)


we get


- v


CTCVpe
T e


A. 1-11)


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.1-12)


Substituting


Equation


(A. 1-12)


into


Equation


(A.1-11),


- v


CTCVu
T e


z F


(A. 1-13)


VRTC


Hence


-_cT


URTC


z F


- O


(3.3-6)


Similarly,


can be


shown


that


Cv
+ +


vDCT


VRTC


CVve


it
z F


(3.3-5)


+ C














APPENDIX


DERIVATION OF EQUATION


(3.3-10)


electrochemical


potential


the electrolyte


given by


0
= vRT9n (Cf a )
e +


(A. 2-1


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.2-2)


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.2-4)


C.M.
3J3


C
C M
o o


A. 2-5)


Therefore


C
oCM
00


d9nym
dinm


dny+
dnm


CT
C
O


diny+
d Qnm


(A.2-6)


Hence


we get


dinf+


vRTCo


dk nC


CViy
e e


A. 2-7)


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. 2-4)


(A.2-8)


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.2-9)


= 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.2-10)


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. 2-11)


Substituting


Equation


(A. 2-11)


into


Equation


(A.2-7),


thus get


VRTC


dinC
dinC


(3.3-10)


= 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. 3-1)


- v


(A. 3-2)


Substitution


Equation


(A. 3-1)


into


Equation


(A.3-2)


gives


AP


PBVB


V --
MB-1-


(CAVAVA


+ CVBVB)


- C,


S '


7- pCvVn


(A. 3-3)


VA
MA
A


PA VA


* n


n








= CAVA
AA


- CA
-A


- CACBVBVB
ABBB


(A. 3-4)


Since


CAVA

= CBV
BB


= J*
A

BJ*
B


+ C v*
A

+ C v*
B


AVA


Equation


(A. 3-4 )


+ 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. 3-5)


Since


+ JB


, Equation


3-5)


becomes


+ CB)
B


(A. 3-6)


-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. 4-1)


Substitution


of Equation


2
dC3
d3r
2
dr


D dC3
r dr


.1-1)


- C3


into


cai
nFC3


Equation


*C (x)
rO
. ^ .


(A. 4-1)


gives


exp -


eai
nF


[C1i(x)

. o .


F(es
exps
exp R
*R


(A. 4-2)


C4 (x)


F(*s


O
nFCD
3 3


exp


(A. 4-3)


= C3


- C3
"3


(2F
exp-


-q)
j


A.4-4)


Then


Equation


(A. 4-2)


becomes


F(s