~ti ~\fU~ii'{".ot

..:~

,.; '

·r .<

!'larch1979

A<hes Is, . - " " . '0

~ti ~\fU~ii'{".ot

ofthet~:b:ements^forthede~fee^of ree ee ofPnUo= phy

~

^\

, . Oepartlllentof,Chemis try~

l'ieJllO:ri~l.funiversity

^of

Newf~~~

^.

St.

.J'?hn's

·;

.'.i... :-

~

,

^.

..

'-' : .:;'.-~:

',

~. ,.'~..

"". :: ....

,,'-'," .,, " .' :,'

. ..

'.~fhyd r Oqeniltom$t:i~·B11:..c~,'·~atiiooeS.

' ~i<J . ~ .. , .

cathDd:id'dbln;e<Jrati;Qnof~e&.'l11tho-,;.j~t·to.Ifl.'1O~v~chemi~.

~ .. ~~~~ :~oe~._~I· .~~~~'71Y~ ,-: ~ ~ ~.~1~ ·p~

^{-.::,. ..'}

.. ·:2t;:~:t;E2~:::i'~~;:~:::;~~~: ' \ : . '

' . ~.'

_In

p~t

.2

~f th.

'th_ is,

',tudh~' ~t 'the difft:e.ioil~flelecai-~·:'c~A

•

~~~12 t.;~J~~;; ' . .

.'.'_" wored~uced.frail opon ..e,iccui; Potentiald~.4Y maa.~w:~n'tl•.The

:: i~~e~~'e':c:~.ove·~lta9.r ^an<! ~.·' 9r~th' ~f" ~8.~~4~~_ C~~~~t4~.~~':;~

:;::::·:~t~:~~::::j;;·~!·k'.;;:::;':~ =;:rr,"ce ; .

of the-catbOd'e

bY

"d.orbed·hy~8n^o1ta:1s.-:-n... iI)Cno1~.in'.iirf4e~

."•;. c'.. _'.': .'.:•.:". . . .'i'._.... ....~ •..•'..'.' ..

QOve raq.:f.rolIltblt;byqU>ninriuptoseVet"alday._ of,catllod ieo1Uo h'ranged

' , ' .·~'~S·=E~;:;:~:'2~:~~t'£.=~ '~~·~~~~:,~./.~~~~ir~~, ~i~<:~:~~.~.~- OV.~~l~;t~~~: ~ }L~···~' ^.. ~~~:~. :

log-arlt:hP1

ofthecathodk.ch aiq.-(-ol~rElboth11n earup to Qvalues'.

'~f' ~~ ~o.'~·.~'"~:

^j.

'.n;~~ · l~cu

^...e·

.:~i'~~~Uq.: ~ni ps"~k -.

.

·~~pa:e1~~··D1~qht.'be ·a~~U1u~"to: ~~'~~~~Pti~n 4~' ~:~~;~~~~ ~

:'.~.:

-,--:.':'"

.''-

.-:< .

PART1. CATRlDICDIS \ N'1EGR1ot lOlfOf"l.u.D ,.

pe-n l' =,: ~~~ :~:I :::: ::" , ^,

...- r».

'" ' .

'

...•

r

<.:

' - ' . ' ... . -. ",

.

," ..

^."

" .' '~- P~T'l:: '-~;~~'m ~' ::,~ , J'~IL::' -' ^.

"_ . CA'n!OD~ '~ID'sO~c*"S " -" , ".'

.L:.. t't~. '1.:

:nm ootlCTIotl . :.•

;1." .1:': .

, , -., ' .,'

.

^" ,\, ...,"

~..Dif'f"ualon,ofGo.S P!laSII'HY~l'O'len: ; "'" .-.-

:':,i "

Tlu:o\,lqhS!.1ver ...

;;.>;.•..-.. ... ~, . . ,

'144...,.

"' ~ '~: i'-:'<

· ··· ·· ·· ·- ~ i.D · i[~ ·· l~:

.~~lt.l~ft_tteasur~anUlon~!lVer·~;•. •.15'

.-r

_:~;~_r1a~k:.:_:< ,'; ;_ '::'~ ';_, ~!': . > ·::':·~.-:1· - . : :: ' 15~" "':'

Purl ~ ieationof Solutiol\S"••'. .. :.;.~

~r.ur-tal.· ;'~'-'and 'pEllCed\lre '

'~or'ca~tanC:.M-,u:r-;-nu-;..~,.o

". ;

.,"

.r '

.

<~

:

»

~- ".

.f,

.'

...

C'alibrlltionda~fot." the ,Ufferential'i!alvanOstati e mcthod • •.•~••• •••• • • • • •••~••. •••

,17.:

:~:~~~ ~:t;~f~ ::r. s~l~e~

^-.

~~~~~~. i~

^:

~~ ~-~

^{• ••-. 19 0}

~.

^18.

aYdr6ge~LOve~ltage:f~r

^{silv er}

c~~odes'

^in-1

mo~ _t-.l

^....

•__.H~104at constanti --1. 1 6 lIIAfCln incxp t . AS to AIO•'• • •19 3

i~. :.~~~:~::,~~e"+~O:~~~ :;:".~':l .O:":~l~ ²⁰⁸

20. j::leetrocle capacitance ofa silverelectrode81i.h

~pur~t1ed· <EPl/~.~ HC~?~ :~" , '." '. "-. . _~ 2 10

21. Electrodeca~citanceof a' silverele'ctrodc82in .

\. Z"'" ^{1 ~.i '- ' UCla;, ' ,. .. ;'. . ' 213}

22:;,lec trod ecapac:l~nce

r .:

silver eleetrod e.8,)in , ....:;. \pU;ified~molt IiCI 04••,.'••• . •••". . . ", 214-

23..I'E1a"'E cepacftanceof.a'.sil verelec trod e

a4

in .

..'puri_en.0 ."1.:noti-I,

~i04

^.

"'j '~"'

^{:'.: • ••}

d: e-. . '.: .

2lS

" "1"

~lee ode cap3eitart't::e of a silverelec trod o BS ion '

-0 •

,,).pur~fied

^0,.1'moLC¹'HCI 04•••11''. :. : • • ••••: :(." 216.<

, , ," .. ⁾

•-*' -25. 'Inct'eas~io r-hy~og enccver e q e roreHict:r~e-~.2.in

.',. 1moll~ HC10

4 , . oJ,;• •• • ,,• •-.: ••_••• •• •226. . , 2'6.:'

I~cteas~

^1o(

hym:og~

^coverage

-'~or'

er e cereaeBJ

i~

^{/ ,}

~

^-'

1mol , '" fICl04 •••

" .r •

I• , •• • ••• •," ., '" • •227

~7?^rnceeaee~r~y~en^{co.verage.forelectroli94iTI}

~O.l,:OOl"l- H:l_Q4 :'·" _ ' ' . ~

^{.'•..• :.}

'. ~ ' "

^{.,:•• •,.2 28}

28:'-'I n~t'easeofbydrogencoverag eforele c trod e asin

'. o.l·moi,(-,1~CI04 ^{• •• •_. ,••••_ • • • 229}

LI5.TOFPlGUKES , 1.'.ster?-GrlIhame mod;!!ofthe"r e c tr i cal

~uble

^layer.

2. Pote n tialene rqy diagramfo r veinee reaction .'•

. .

^{' .}

.

3. Eqti.ival "nt'circuit·for'syst em a>thibitingan - adsorpt ionp,;,,:rwloeapac Ltanc e•• ..••.,. •••••.'. • • 4. Simple;s'ischeme:ofal?paratusfor st Udying diff us i on 5. Hye1rogen'perm'ea tiontransien~ .".• ..:•.'••#• • •• • j7' 6. sect,l-o!!" l drawingof ,ell"C,tropolis hing~eUforlea~rod'• •

7: sec~onal d.t:a~ing

^{o(_ i n r}bstt rv oircau,forst Udies' . afle a d -disinteg ration•. :.;•.•• ••.•• •. ~l

a. St':dpping~naly,siscell •• • •• • • ••'•• • • ••• • •.67 .9. AM!ysis of sta"ndardPb2

+Bo~utions^{usin'gDP1I.SV}

(concentrationran'<Je:1.0to,'50.ppm)• •• .70 Calibration

curv;

lorPb2+:malysi,.bYQP ASV

(COtlCentratiOI).·rarig~,,I'to1~0 PPb~ • ••• •. • •• • •• 73 calib rlltion eurveforPb2+~nalYsisbYdiffc ren'tial puls epol=fqra~y(conc'entra t i on'ra ngeI0.1'to60ppm) ••• 12. Quanti tyof'lead disintegr ated~time in'a

prelimiJIary'experim"" t• • ••• •• •

...,."90 Qwl.ntity ofleaddis i ntc<]rat edVBtime in

c. oi eciC^l llCl04

~t' -~~

^{IlIA =-2.}

Quan tity of leaddisi ntegr atedvstime in

O~ 003^molt-1..HC10

4

^at-50IlIA=-2 • • •• •• • • •.••:• 87'

,

17. Qu antityofleaddi s int09r atedVBtiIIIein --.... O.l lllOli.- I.HCIO~at-54lIlA =- 2. •:• • •• • •••.. •;• 15 . Quan ti tyof leaddisintegr atedvs time ,in

a.ai'mo lC¹Hc10

4at-6 0!rIA6n-2 •. • ••• • ••. • • • 13. Quantity oflea d disintegrated'vstiJnein

0.0(13molC1HC104at-30 IlIA=-2

DisintegrationrateQfIu d eathodeva currentdensity in·O. l '\001(-1 HC:04and 0.1 ,,",,1C¹H2sO₄,. .:.•'•. . Pr...el,ecb:olysiscell ..• • • .:.'.• •~'>••

34. Mai!1 cell forGtudiesat BiIvc;rfoi~ s .:•',,~•• •;.••164

Sectiona~ dr_i~

^of

electroPoiish.i~g '~ell\

^{fo r}

silverfoils'•• • •• ••

<.' '. • . , ,' .. '. '-:' . " . . . .

167". 3-6; Theelelltr i cal'c i r cui tfor

ditfuslo~

^{studiesof. .}

silver foils ; ..•.•'.• •••:'. ;...~".'.•.'.". .•"'. • 110

.~....

,..

. ..

. '

Schema t ic oftra ns iStor,switch .'••'."•. •.;'~'" .•'.:•111 DiffereJltia~i~gcircu i t •••'• • •. .~" '~•• •• • •••,17 3 Line:u'

t'e14·~~nt>e.twe7~. ~

of c:ll.llra uon

(~~w-~th

signal)..nddtcalculatedusingdif f eren tia ted

voita~ esignal(logscales) ••• • •~. •. . .•~. .• •.178

.

^.

, .,

^{' .}

OI1ervoltagedecaysigllll.1. and its differentia tedsignal•. .

•.A'

ChronopotentiO'lr am for dissolQtionof. oXide£i1.lll 011 silv~rinKOMsolution.;'•••. • • •'. .•• ••••••".184 PlotsQfrising'tratlsientsfor hydrogen permeation'. "j, through 0.1~thi ck silver .'. .••• •••. • •••'.' •18 7

. .. I

43. Semiloga:r:ithmieplot·of overv o l tage·yS'totaL"charge' passedforeleett'od~sAStoAla .. ;.. .. . . • ..• •195 'I'.imcdeP e ndenc eo'~'o""rvolt:aqeatl..lf.·mA.an-2

.after'dedr~asinqcllt'r en t from

11 .6

lIlAan"2"f or

electrooeA7,.'. ,.•,... • ••;.•••.•.•.•_~•••• 197 '4 5.

Ti.IIle:'~ep90~e~e';f overVolta~e

^at

'~l.li

^lIlAt1II-2.'

afte r

incr"asln'1" c~r"nt

^{lcOlll1.1€...-mA.'cm-2fo r'}

electrodeJll9 •••. .•• •.I'... ..." ••~• .46. 'I'iinedependenoeof OV~ltageat0.116mACIll-2

aft erdccr~inqcurrentfr';'"11. 6Mo'CIl\--2for

ele-ctrOlie,AlO '." ' " •

> .. .'..

'1'• •••.•.•• • ' , '199 5l'It1il09~it:hmicplotof;;';ervoltaqevs tiJne usinq dat:a frOmFi~ell4S^and

46 'J" ' -.' ',' . -

"'~-:'

" ,.- ,:' . .. .

^,200

.48.-Typ i ca lTafe l pl Qtsfor ll,lect:codeAl inunpur i fi ed

,Imoll~~^HCI04 •••• • •.; . ... . •... '• ••'••'. ~~;.~

•••••:10 3 xii

Quantityofle a ddisinteqrat~vs tiJlle in O.lllfOl1-1HC1.04at -115rnA~-2••';

MOl esof Pb2..-insolu tio nVI;ti1lle in

0.l~li-IHCl04at-I M·Clll-2 ••• • • • ••• • •-;'

Moles'·of Pb H in solutJn ystimein' •

llllOll-1

'HCl04 ,a~-~o ·~ '~-·2 ·

^{••••' ;•• •}

~

^{'9 9}

Quantitrof'lead d'iSinte<jra~d,vs.t i' ; in

o.(l1molt.~lHiso4" '~t

-20

!riAcrn-2• •'•• •;'.,;" '"''•:'.i02..

~antity',of.lead·dis'il)t~graa.ed Vstimei~

O.QOlmol"1 -1H2S04,~t^{-94rnA=-2 • •}

. . .

23 : ~antttyofle ad di sintegratedvs timein 0.00'5

~l 1-~

^H2S0

4at'-60mA

e:m-

²••'.

. . .I.. . .

¹⁰⁷

2,4 . Quanti~yofleaddisi ntegr a ted~timein

0.00 5molI- IH2~4^at-ll~^{rnA=-2••. ••• ••••'• ••10 e} QuiUltity of laaddisintegr atedvs' tima ill.

0;'01'molC¹H2S04at-115lIlA=~2 ., . , . : ••• • •••110, 26. Quantity ofle ad, dis i n t e gr a t ed vs time in

0.01inol.,ClH2SO4at :-190 lIlA =-2.:'. ••• •', .'•• • ••.111 21, Quanti ty ofleaddisintegr a t ed vs time in

o.~mol C¹H 2SO

4at":'3S0'mA = -2. ••'.. . .' ',,'.:. ~^{';. .'.112} Quantityof leo:.ddisint~ratedVS.time-in -2

contaminated0.01mo.l'. 1fC104,at-200IlIA an • •. ••.• •114 Quantity of lead disinteq ra ted vetilueill

I~1'1-1^NaOHat·....16'1'II1\=-2.•, ••• ••• , • ••' • • ••l l? ~.

f '

30. Disintegrationrate of1~dcathode vs currentdensity, in0. 00 3'and 0'.01mol,(IHCI 04' • •• • • •: • ••.:: . ,121 31. Disillteg:rationra te oflea d cathode vs currentdensity

in

~.OOI.

^0.005

~d

^0.01mol

C

^1H₂

So 4 . . . . . '."

^{v'•• •·12 2}

59'.

.=.v.,

"

~).

TyPical,;.yafel'plot sfor

ele~trode"A2/n

^{. .'}

.; I.r' l lllQ~ 1

.. .IlC1.04cont..aminated"'ith...g ion 'l.• . ,." ., .203

i~o,'

Ta f e l plots'( or electrode'...5in

pur ifi~

"..." "

llllOlC^I'IiC104 ••••,-",;••••• •,'':•.'.••.'.;, 205 5L 'H,fel

Pl~,for el~~eA6:'-in"

puriUe<i

. l"~ i .t'-:}~elq4

^{•••:.,;'-"'•.•'."•.}

~

^•.'.",,::.

·:'V~liltiin~ ~t ~l~~trodQ t:ap..;~i~~~e ;i.~" OV~rvOl;a~'~",

^.

", i~'~~ii ~~e, ~~~. ~l~~~,: .. ,~::~~, T~~,~:~~~,~ :,:.·, : , ; :'::,~':/ .'

.varill.d.,ono>,eieCUode:ca~Citance^"ith,';';e~1til.ge' and.tota l char<Je for el ec troo llB,2inpiu-if1ed' '.

1",,1

1;',\'HeU;~

_,

". . ., '" :,. . < .: ,~'

_.

":.... : '.',..,

54, Variation.ofeiectrodec"'P"'Cita.nce'withovervoltage

·and" to ta l ' ch...r<j;efoi:electr~ea3in purified. • 1:;x>rt-1 1lC10) •

~

^{•• •• .,••',':.:• ••.•,'.}".".

~

^{.,'••218_}

,55. Vari. ...t~onofej ectsode cllp4citanc,ewith overvoltage .:tot-Illcha:~~f~^{e.lectrode84 in}pur,~fied>:. ^\

"

....~"0.1molt tICl.?4 ~.• • •.,••••.••.'••', , • •,••219

5~:;;;"Yllriation

_{. amf tota1}^of_cIlarge^ele.:ctrode._forele c trodecapllcitanceasin purifiedwith

o~;ta~ell

0.1

~r.,1-l ~164

^",.

:" j ;..-;{' . '.,. . :.,, ';: . ' .-~

²²⁰

.57~ Relationship blltweenQ8c.trode:capadtancasat ~

;.conatnnt; ovetvOl,tageandl~lOl-?)forelec~Od~B3 :.,:.,.

Re.la ,t10na,hipbetweeneleetrOdecapaCitance" at

conlltant·overvoltageil,nd,~1O(-:OJforeleCtrOde 54•'••••,,22a

. "':'". " - "

-

RelationshJ.1ibe~~elec trode capacitancesat

~n8tant.,9"erV~~f~~1l9.e^{,an d}~oglo-:,,~~J::f()l"~.lectrOd~^{..B5•• •"•}~224 L1nellr.rel:atio~hipbetween.ov ervoltageand,loqari thnl

~~ ~~;a~~.~,~ ~~:;n,~1::~S;i~: ~~e~,~~~' ,'. , . _

, I

. . ·1·

r ;-

": .

.LI ST

O~; SYMOO~

.Taf..l cons~"nt.

, 'Total

charqerequired tofoD.II.InOoolayer',of adsorbedhy~en;ll.torn ". . .

"

,

0.5

xv ii i

"Ris.!,. time ooflstant

Half- rise

tiinc

Breakthroughtilflf!"

t:"Tinle"

~ag\

'~ .

"\

M'

ixx

Change in overvol tage with¢

*

or withthe time of cathodic polarisation

surface hydrogen atom coverage Increase in surface hydrogen atom coverage Chemical potential of the electrolyte Total nUlllber of ions in the solution Dimensionless parameter in equation (43) Inner potential of the electrode metal Inner potential of the bulk solution Potential in the inner Helmholtzplane Potentialin the outer Helmholtz plane Potential at the pre-electrodestate constant in equation (IO) Change in 41*

Angular frequency

, i I

\

THEORETICALINTRODUCT I ONoroPARTS~AND .2

This·th"s is is ' div i d e din t otwo parts . In the ;tirstpart,ca.tltodic

'"

^'

disint e gratio nofl.ea din aci d so l u t ions is"xiUlIine d a\ld in the.ee c cne'

'..' -/ . r

part, theadsorptionand absorption Of-,hYdrOge nbysil ve r inacid

. . . . 'f .

~olutions a~e descri~~d.• 'since thes e

tt""

^top-ic,sa~~gUfHcie?~~-"

sl.ml.1a r toh~y_e"a):~~theo ret ica lInt rod uct i on,-theol'e't!i~al^..'

:on~~~7ia~.~~.s':

^{'a re'}

_~~~e·n.:·b.~f:or~ .pr~ ^{"1 :} f~ :.~e/n.d:~~;.tand.~~~ ^: ~_f. ~~ ^.'

phy s i c a l,b as is of,theph e no:nena encountered;in;this"'thesis•.

" n;".,

·-·.Th~r~.~1~al Intr~u~~l~n~'co;;~ai~S thr"lte d~~f~{e:~:t Se9ti~n~',

:..;" Hydrogen.~en:ol;aqe.

B. Adsorptionps eudocap&c:itance. ".

pc meationof

~Ydr09j!~'~~~'~rough' M~talS ."

^.

.,

. "

iChan" " in overvoltage witht*,o r with theUIIl<!

,ofcathodicpol a ri s atio n . surfa.eehydrogen...toolcoverage•

\Iner".. se in'8~fac.1!Ih~_drO<Jenatom'c~verage' .\.Ch.'

elIIi. aar pOte~ti~l'

^of

~ele:Q~:~~o~~t,e

'.

\~tal_ ".~er.

^{of,ions,i nthe}

soiuti~~

. .Y1Jii~~S~~le5~,~~~~til~+·~ua~,io~.~:43)

Jnnm:

~_~n~,~~,

":

~e '~,~~~,r ~.e~l

inn er pl)tentialof the bulk!ioll1tiori

! , -;'.>:' , '' ,

Po t e n ti alin !;he inner He1Jnholtzplane

l " , , ".

Potentialin the -outer Helmholtz pl a n e

p~tential

^atthe,

~re-el~.;;trode

,",tat e Con s ta n t .in equation (10) Cha ng e.int*

.J~il~arfrequency

\ ,

,

.

/

. '/ I '

t;

"

"' <c-':~

"

,"<".

.

. '.

. ... .~,~,

~-~ .~ .>~~

. r

";'i;....

~~ ~~ ,'~

\

~.,

meta~s ~uchas Pt,Au,cau"i~gocc u:r;re nc eof aTafel.slopeof

Z.;

~'l. However, thisview has-beencr iticis edby.tves (6), Knorr(6 !! ) ·andLewis(7). IvesfOWld ithar d tobelie v e that at toeca~:yticaliyac tJ-VCp~electrod~s~tomrecOlllbin a tion(2) is very. fast ,b utisrate limitin9' whileat the'in a Ctive Rgitisvery slowbut.is

not~ ~.i:te l~itinq.

^{,I ntac t,}

th~

^{Ta f e lsl opeot}

2'~:r , ;'

~snot'Wli~ue,£<:>1"slowhy drog en atomrecOlllbin a tio n~ec aus :it is..Lso • ,•f,?undwhenHZ ttiUlspo r tis l"ate limi ting (Ga):

(C': ) MaS~-TranSf?rtorDif.fusion'Ove.rvolta9~

Mas s-transportovervc a eeee ;'\n'uises when a51,owcrenepcrt, .proces~res ponsiblefo rde pleti :noraC~~l~tionofreacta~t5.

. or-products.'.respec tively,cnceaqainresulti ngin indirec t

retar d ation of c!Ut.rqeir..ns f e r, e.g .

H~O:q. (bul~'.Sol~ti~n) s~' H30~

(i nterfa c e) , '.

H~aq

;; n terhcel:S!Ow'

H:

a q(bulklSOlution) .

,M.!Issitransport·

-,

p'rocessespl ayan iJnpo rtant ro l ein 1:heh.e. r..

atca ta lY t ica lly activemetal ssupl'f asPt,II>, Rh and Pd (7)where the rat..

of-h~roqen

ion discharge,

i;~. reac~ion I,

^{or::fhydJ;'0gen}

gencra~ion,

^i:e.reaction s 2

an~

^3,

~a:n''3e

s1,gnificantly

qreater tti'~

^_\...

-".the rate'atWhich H

2ist>rall s!X>r tedtoor.froll' theint e r fa ce•

."nle tr:sport oi'H30:q. ionsfram.thebulkSOlution to

the~501ution

•

'e~ec&~interce

^maybera tedetel:llliningat

~ ~

^3atquite

fwill

c.;t.thodic curr e nts - and'litlOwer pH at;suf fi c i e ntly hiqh.ca.thoMc -1. R'owever,ca lcu1atedva.1-uesof~(8,9)in0.1 and1~1t .

TheSt r uctun.ofthe Elec trica lOoub ~e-LaYe r The interphasebetweenametallic elec trod e and anaqueous solutionofan eiectrolytebehaveslike anele c tri c alcapa ci to r and is ge ne r a lly~knowriasthe electrical.doub~e"layer.,This .fact was

, . '

, :

.

"

re alizedbyH.elJl'lholtz(10)alJilost a.cent\.lry ago. .Toaccountforthi s phe nome non . HelJnhol tzpropOsedII.modelof"theinterphase.in whic h .allthe excesschar?eonthe

~tal

islocated at its surface and the r eexistsinthe solution arigi~lyheld·la ye r'o foppo s ite l y cMrged ions in<Iplaneparallel'tothe surfaceof thee1ectrode,a~^{'very .}

clo s o

tOi~.~le~din9

^{to the}

developme~tof a'po~nti~l '~~~~

across thein t e rp hase. Thispotenti a lcha ng es sha>:plyfrOOli~

valueintheele ctr o de to thatatthe centa- e of theionic layer, Thi s is the He lmol tz 'pa r a llel-plate-capa citbrmodel,o f tileion ic doublehyer . Accuratemeasuremen tso~the numericalvalueofthe do\lble layercapa c i tance showedthat thein terph a s e can never be represen~byaparalle l-p late -cap acitoras proposedby Helr.lholtll..

AnilIlte:mdtivetoHelmholtz' s modelpropos e d independentlyby Gouy(11 ) andChapman(1 2)predicts adependence ofthe measlU'ed capacitanceboth on potentialand onelectrolyte concentrations . This ID-ode l caee

to

'be kno...n as thedif f us e-doublelaye r lIIOdeL '!'he'GOuy-.

. . ,

^.

.Chapnllln theory"];eads toaone,dimens ionalDebyeHuck eliCillic atmosphere typeof distribution withthe.potentialfal.l"i.~'loff more gradua lly thr OU!ilh the diffuselaye r .

The Gouy.:.chapnanm.odelisnotverysuitab~efor the ca se,o!real ionsandStern (13) sl,Ig'lestedthatasatisfactory theory of thedo ubl e layermUs~takeinto accountboth thefinites~~of thead so r be d.

(

~

- "

addsolutionsbubbl ed rapidlybygasareles sthan4_mVupto I..-50 IlIAem-2(the maxJ,lllumcurr entde nsityof the'

pre:;-nt'-~rk:_-

^....../'

Onsilverci'lthode sl. Even thoughitdoes notseem possib18toeliJlintlte '\. o;nt1rel Y b.Yextr eme ly vigorOU sstir ringof thecatho l yte,itseems ._.~t~econ tributio no~'\.tothetotalll,ppa nmtevervcrteaecan be

.~evertsma,ll,in stirred80 1U; 100. sc\iJnini s h~tstil~further

DJlCwo u l dhav e to usea rotatingdi s c electrode orsimila r mechanical'- device!"

(dl iRDrop OVervoltage.tlO:

,. '

.

Anothercontributiontothe experimentally obserVedove,?,oltage istMtdue to a potentialdropbetweenworking~ndref e re nce elec trod es. This isn'oecausedbyany sl ow proces sinthe o"verall, reactionbut

is

af~tion^of~e.^effectiveelectrical J:Ce >:i stance between thereferen c eelectrod~and'theca thode .and.of the current f.llow if19between theca th~eand theanodeduringelectrolys,is.

'lttempts /l.f e madetominimi zethe effect of,this Potentialdropin pract ice'bypla cingthereferenoeelec trod e lorgener ally thetipof aco nn e c t i ontoit;designatedII.LU99i ncap i lla ry)closetothe cathodeorusingoscilloscopictechniques toIrI.i;la surethe- open-circuit electrqde-'potentialinne4iatelYsubsequenttothe interru!?t1on ofthe currentf~. 111emeaS~edovervoltageV~lbeexc l us i ve Of, IlO•

ThUS. the totalIrleasurooovervol,~ge.~e.tS'isthesum 0:

indiVid~} overvo~tage5,i.e.

>,1

.'

'I,

:

rji_ -_,_ _

. . ' -

141

- r

( C -~--- ~~

. \ (

~-_.~) f ' I

IHPOHP

\- \

I I

I' I

....

<t>..

t o)

FiQ:I. The

cha;Q~,

^and

:poie~tiO~. diSl ri~Ji~ '

^{in the'}

ere en t ccr

double ,loyer, (0 1

'~ccordin9 t ~ Slern

^and (b)

~ccoidin9 t~.(,Gra'h~me

^with .negative"

Polari~~tjon.

^{of.the meta}

^i.,

^r/>m'

^<PI ' <P~ on~:iI'$

^{are Inner'}

~ '

^.':

p'ote~'ia'

of

etectrode , potent~oJ i(l'.the·inn.er, '.Hein;'~oI'iz'plane," , potent io'linthe outer.

_He\m,h~t'z , p1~ne

,and.i.nner pa tentlo !·ofthe"

. ,c

b~'k'

^{of setutle n,}

r~tPe c!iveIY. A s'

^shOWfl

~ m ; 4>; . ·~~.d· :4>~ .

,nego fl...e_with respect 10

If\

=0.

.

^.

.

I I

( \

.

ions and any spedfi"chemisorPt~nin"teractionthey maysUff erwi th .the electrodesurface. He consider..dthat in the case of, e.g. a

negatively charged surface ,a layerof p:>s1ti v.eion!! h he l d at the in t er f a o e by chemisorptiveor'e~eotrostat icattractions.' The double layer region

fro..

thesu;faC(!' -~^the'centreor-the first layer of

. ". ." .

positiveio""is tefeJ:re<.lt:oas thecan pa c t or Hel.Jlholtz layer,

.

' .

. ' .

,

there isa"har~^pOtenti;'l~.~p^{in thllHefltz}p~t^o.t

the

?Ouhl e"' :aY.'ilr .'Outsid ",lli~' ~el.Jllholblaye~ ,^{tllere .rsit}dif~use^or~uy­

Chapnan laytll\ overwhich the potential dropsgradua~lytothatin the.

bulk of thesol\ltiOn.(~,*,Fig_14). ,.'Stern'",'modelof the double ,layer is aotuaily a oomtinationof the twoprllviO~5lIlOdelsandthetotal capacitallce of thisPIOdsl canbederived in thefol low i ngway_ The potential differencebetweentheelect:od~,¢>1lI'andthebulkQfthe solution ,'5'...ybewrit t en a5

(5)

". ' . " .~

The~tential'at,the outerHe1Jllhoit.z.plane otl OHPJ,isde notedby4l l,

,

" -

^\.

and si nceitis~ssUilled,~at.<l'g is equaltoacre(by~c~ventionlthen

electrode.'\., qives -.,.-""....-'7..

"m

^}) ¢>Ill - '2'

.:?

\

^.(7)

~

. . _~

"" .

1 L.+ !...

. _~n+'

¹

ra

Cd• l• Cft CG '~

.·.,.,.,-....,c....;...,~ .

-.ll-

-:

latenl repulsionbet'~een,ndghbouring.ions ofthe samesign.

., ." " . '. ' . -. . '. . "

st:ren9thde.creas ..d~from'F-tcr","hlle'tlleadllQ;babi lity'inc~'eased

'. .'_', .:... '.- . . If~" . .. . -, ,

from ',F'toI . I t WIlSfur tl\e r,propos!!dby Bockri set althat'image'

".'.

"

'. ""'.." ~^'".' . ':.; ' . :.. ' " ,'.

energyshf)u~dnot becons idered asthe orig inof '~specific'

.

" ., . , ' '. .,"

-

". ' ,"

::'::::t~::·::;.~:: :::.:::":::. ·::<;o::::.::~:~::~--<

rO~9hlY acco~di.~ " to,:the ,cube, ,~t ~e '~~~~~~~7~,s, ,,~~ile,:~9:

^{ener g y}

^.'1

Ifquldcl)angebyaneq ligible~Ullt;'A~$Q ,$pecHic,a9-s~Uon',iIl .,,'

'not a<~;'~nomenon '~es trict~' tt: ~~'i~n!, " SUffi~i'~~'1;lY lar<j!Cati~ni 'i S~i~ '~~~'i~:-;~'~nclIlena: .- ~ever', ~dk~i

^••

t ,~i. ·ad~a"t~~':"~~ ·

tli1J":'$;'~~~~ic adsoip~~~~ '~s :'~' func~on Of,,'th~,"~ag~e~'-

^and

ti~ 'o~',' .. ..

, h;~~at~~~,:,::,:·t ·;~i ~~.t ,,~.~le'layef~ro~sed, b~: ~~.~~:~~' ~

lias sbnila r tothat,proposedby-Gr ahouoeb ut it', takasintQaccoun t

:~~~'~t ~?~?:'"t

.ass~ ia.te~.durill'l'bra~port.with;:adllfini.te,n~'7r..Ofwa terInOl,ecule ",.,:-', WO"k~OfLevineee"1,i~geenergyresu~ting'fromthe iMgl!f~I'(:es­

~nt~ractionhetweenthetest'(the~dserbedien ) IllId ind\i<:edch" rg es wassuggested"s

~~

orig',ill ofspec H J.c

adsCll;p~OIl

ⁱⁿ

COlltrll,~t

^{wi th}

.:

Gr~aJ&e'~ vi~~~hi~h ^.' ~ug,9,es.ted.~: ^{, i-n..,} ~~;;';iHC'~'6:p'ti~n

^.,is'd.lia

toi:b..f~~-tian"'~fa''~v":h~t

,b.:;nd

'!luperJmpesedu~n'ei;Wtro~tatic

" in~~r~~~on: " "Gra~~"~~~' Le~ine. ~~;a~~~c~~~a~" ~~s "c;i'uc'i'sed' b~'~

^.

.' "'B;;kr~s ,: ~:-"anathan'~~d'" Mu~i,,~'"(~;:) ~' .,, Bo~~~S:,::~~:.~l :~,9mpar~:'~~~' ~~~ ^__,.

,s,~eng~~ ~o~,',perC~~-~h~ide

^boqcis

~itl(th"_.!.d;Orb~il~t{:-

^,:n:e'

b6~~

... ,.

^'(

\

_{where;d.1. .h the}

.lCp9r~nUllY

deteI1ained capacit a n c e :'C'«-p'!" ./I CiJ,.is the

c-"'~c1tl1nC'e

^otHe laho l u'or,

~~

^..rlayer

~ _CG~ c~ ~··th. ~: .

.::

.

.., .

' .. ^:.:.-

^.

',.

'

....

,

~.,. .

.

/

/

. J

. '

, . '. ' .',

.'..

:

.correspond,ing'tothil,cenu-...of the;,L.Y~:l'

o f

tlydril.ted' ·1.ons.(O!fp },~•

.'

- .

^{" . " " , .~,}

.

^'

.

~~nll.ll.Y.ther eh,a gradualp:lten*~dropfrOlll.~:'tOHPi ntothebuik.

oftheso1 uUoh.t~pot~ntl:i'-l'ojI.-

?'. '.' .

. .

5ubsecluen tto Stern's-»elthen have been"~r~t_'furtb<:tr .,ProPos&1Jl..

rn.:m :reti~

^thll:-..dei"'1:

v~'ti~~ detll.il~: · ~~~,l'IPe<:.lfiC -

'. '.

~:~~:~~?··(:~f~~e.· ~,~~~:ap~7~:i: ~<V~ l ;:.i~l"~.~:._~1~tl~~·~

troalan elecb:'ostati c od 9'i n .-dep"'n~en t on,thenAtureof the,!,etd

. :~ -~~ ion-B.'invo1.vedi, '~~. in part~c~lar

^•.

h~;ide '10ns-~n lIl~rc~;'

'. ,'-."'" ', "," ....;,:', ,-:',-,',' .'.,.', '- ,- '":':. .::.: .:< "

ledcorahame (141to dev elopa...ad..lof thelnbu:phull wh i ch COllilia ts'

·~· :':::~:; ::::,:l'~~::,::;,,~:,,::=y.:::::~ . ::'

::~'fe e~

^{...ctroc1•.}

^to._ .Pl~ne. pass.~~ ,thr_~~~

" "

cen~es~;

^the"._.;."

:.. spec if i cal;y"!,4sorJ:>ed iona. 'l1\isisthe1.JUler He 1Jlhol tz.,plane_(IRP)

., "

'. ~ .

p1.ane;t.oHP'.wh i ch pa....throuIJh'th ecen,tres

v

^{,tMhydratoJ.l.ons.•}:..-. ~.·~:·:

. .u.ta~~e·~~ ';·lO.~t,~~,~~, tO ·~ el~tr::-,,"' ':':~'

^{" •.'}

the

diff~e

^'double

l&Y~':" ;'i~e lb' .u lusu~te. ' ~,;Il8CJa:tiYe" pO~' ,. '/ :..,:... . ';'''0. of·"'. nul ~~ .V"~h";',"·i"~

. " "

0_ '

in

"","oUol,;··

f~:th.... ~ec~or1~· o~. ~tenilil

,iJll•'.t?'the'

Pl.~". cc:r~e

^..

~i.nq

:tt):

t;h~.:~

centresofIIlayerot,.pec i fi ca lly adsorbed ion •.{I1Il'1. at vhic:hthe Potontb,l'iS

~l.-.:~en: ~e~e

^hI

a '-~harp .pot:'"ni:i'"ai.;dr·op

^to

'V;~: ,~l&~,'_

But ler'stheory oriqinated1nide"sofGurney,but Butlera110llel1for thea.dsorpt ionofatomi chydt09'en onthe elect rode, in keeping

,,~th

^thesl>gg" s t ion of

"oriu~i

^{etaI, and}\PPli ed thiS' additional

f,~eto;r

^as

~ cortec~~e

^{G'Jr n eytheo ry •. ' '}

E1~ctrontunnell~ng

i;

ofgnat",i9~ific';'nce to;~lec.~ontransf~

r~aCF6ata,~ta~.iKlIUtion'·inte~fac.~~ Ind';od,'i~,istheeciltr.~l llct'ln

the,:~'leory Of·.~" ,'electroeh~l~~~:'rea.cti.ol1li

^...,

~ttheW~

⁽²²⁾

-Pointed o~'t^,that.~~~.d.s·.'a~d ~Mctk>~pith'

±-...

intheGame,'butthe

lfIOd~ ·~f:aCh!~~~~g. 01~ctr~n twlllclll~g'may v~ry~'wi~

^the'

~~e~~Il1, ' ~::g.

-bond ~~n'g, t..,i{e s~e't~~inq , S~"lt6hi~' ofd~ff~~~nt bo~S' ~ s~iv~nt

libration etc. According

tof M atth';";;:,

Iltanypo~ti"'l,

,tho

',favourE'd

.' " .- " ,',.-.

mode lIillbe that ....hichtends toqivE' the va l ueofsynBletryfactoryof 0.5 tos..ti~f!theele!tron tunn<!l1 ing·eondi

7

^:i.6na:e .l'li nim\llllactivation

en,e~y

vhi "oh.;b

~.(!!l~t;d

to

the syPll\fl~y fac~r.) .,

Lateraoc:k rh

'a~

,.M~tth/!\lS_(2.~)11l9g7,S~',thllttunnel.li ngis,~SSillh2:!!r~f ~H"';;'"20...:

bondstretc hesuntiltheeh ctroncan beac(:ep ,t e,l.. intoanempt y leve l ';f,

$~itAblee(ler9Y :' ~ellinq

^{is '"}

radiationl.es~

tra nsi.tion. In

'. .' :" - ' .

otherwords,.i fel.a<;tron s tlllllleltI1rOughthe.;barrier.atth~Gurfac'e of.",

~.. tal,they.oCne outwithtt.e sameene r'.JllldS_th_eyhadinthe meta l.

The-inter f a c i a l pote ntialdUf eriiuJ-c e,a t theel ectrode~eleetrol.yte

i~t~rf~C':'i~fl~encell·thQ-h. e . r.·'^{rate du eto}.('~·l.it1i-"effect^onthe

c~ncentration.Qf H~O~

.ions at"the,.Pre;-e' *trodesta:t e ,.theplane fran vhich,rea ctallu.einbar kupontheaaU\P<lt i on'i1t~p,and (b)itl infl,lle n ce

o~

^theactiva tion'

el)e~

^'Of

the.' .r~e-transfe~

step. 'l'IIl!

p're-~lectrode

^.,

state,ofpc;te ilti:a·l. ,.·._i~'though,t.tobe located atthe OllP~.e.41·..~2j

· ^.

Suchadsorp tionma.y becalled

~Uivale ~

^(..qu.dcha r'lC9 on the

e~~~e

and in.tho!!.Bolution ' partof thedoubl e laye r ) . If ions pos sessnO p:dmaryhyiltation..,~te:r. the~^can

-IS:"

. . _~~r~;;:~~

HCl, maintains

~.

essentially constant,a nd

=-=---- ~ependent

^ofCfJ 30,(24),so that the,double layer

etfec~\n

^the'h.e.r.

ma ybeneg l ected.

. '" I

as "hoI;ninFigure 2.ilf.'he solid cur veat therightshoWsthepotentia l enerqyof theinitial

stat~(H30:'

in solution....e- in t.he /Weal)and .the

S~Hd':Cu:r ;~

at the

le~t·.showS ~eIlOtentfal

energy

~f

the

f.\~~\.,J.-'.l.1~

eta. te lM-Hads'+H20 1I01ecUle).re.spectively.Plo.tte<!against:the { 'distancefr~the" el ,,!,,tr6de surface inthe,ab~enc".

'?--

^{theelectriCal}

pote ntialdilfeu nce,.i.e.~ -41·...O. By ,increasing- the.'met a l .,

:::::::.:O:1:'::=::~-~;~1;,:~~·~·~~1" ~ ~'

(H30:~ ~

^e-l

~s

shifte,ci"by an i1JllC>unt·(q.m-q.oJ' !

to"" .~;h~

han¢!line.withoutchang~of^itssha~.^witha~C01Is~u~nt~~.ase^of

.

. ^/

^.

.-

the act,ivationfreeelUlrqy,of1i

7

^{!-Sehargeby.SOllIe}fJ::ac U';>nt'tof the·

tot"lpote n t ial energycha~esul.tingfI'Olllthe potent:l.al.differenoe , - --'----,--,-,,-:-;;:--'-,' -

.

I.e_.lSo(Cl(q.m~$"j'F.Simultaneously,~eaeti Vat:l.on.free,e~ergyfor hydrg,genio nisati o ntneeeee..s byan lllIIOutlt(1-0.)l~", ~-4>·)F;

1I0rei"portan~isthekine tic effeet(b). WeusUl'lllthatthe potentia l

~t

is

app~ied

,l n ..xces s,<;>f

th~ r~v

.. rsibl.. poten ti:i .; .e.

the Dvervoltage,'operate s,a,croj<sthere g i on bet ween'.the electrode (\andthe,

pre-ele~~o<le ~iat,e·

•..

:~t~in~1~1~9.

the

~iffU8e'; ,.~1~~~.

and aidsor opPosesChaI.ge-tJ:llnBfere,crOS!<~nte~eJd·~th.~

~~,:::::2:e:e:::::':'~:: ::::dO:'~:'!::~-"

aS 1.Jopl e two d imens i~e1--e~IHi!eOF~

diagramofthe typeusedbyButler(17)orIloriu ti'andPo1any i (21)

I

I

-~

---~

or, If the rNctant.h .. aolve nt. , lecul..or i tthe-hydro ni\lllIo ns an·..

S~i}:lcal~!iIIdso-rbtd. atth ..IIIP.U.. ... ."- ~ll.

CO~i~r

^{H.re t ..U:ec tIll.). I fth"a is '"}

~tentif.l d;ft"rence-

^.

betveentiMbollk.chUa n&nd.tot.eOHP.the1'130~ions_ba~"todo";;-rt. . to·U U1b thbpotential"hillto reacht.'",p~e-electrod....tate. Ass".,inq

that

the!'.11anequli u,rt,..dist d bu U QIlbeeweee thll collc"'nttllt.io n!If H30+ionsatu.:·pu-e18CtrodeBUt:e .C

H

a ~~·th

^..bulk"

C(>~~::::::­

~f ~O;q _ion., ~H]O:' ·~~~.: ~an

^{use ,Ure}

Bpl;t~nn ~l

^..

t~:~uti~n··la"

^".

relat e thetwoc:onee'ntrationa

,',

(9)

"'hereF~·11the ,.lec tr leal workrequir~

to

'ca rryII\II'Iitcharge

~

.

ttU:0"9hthepot..n~l.diff erencefromt.>wbulkaoll,ltionto the..r..-

-. .+

el ec trode8t.a~anda..nd,. vetheir _ 1II\~••·ItH30"'l'lons

~^..'the?nly oaUOnllpr...tinthe801u~; tilePO,t.~tJ..I1..~the pr e-elec trode .. tate..111beconceatra tlOlidepend~t.

llnd~_ l!"u.pleUaitlnqcondH:.IOllS,,.~(24)

.howell.

fr~

-

--

.

^{- ,}

'"'

the theoryof the elec tr ioal doubl"la.yer.th a t

nOl

••• .•c'~ ~:

when~~h 1eon.Unt•.~Kti. tutin9 (lO)into(i)Of\!!;";-u~dobtain . :an

e~n

...ion in wh i ch

C~30 .:·cons~nt .

^':t1ll

l.~~p;.nd ^{.. .} nc~

^O!

~.p!!.. ten~ii.l

^{' .}

^{1 ',.-,.:}

(a tcons t a nt,c.d.)

on~~

concen trati o n in'dilu t 4l

"Cid'SOlu'tiOns~,

".t

the absenceof....

uppo~ti~-;iGetr~~e.

^>In <;:onHClIlCdwith ...hig-h '

1 , ^: '.':0:"

. :~::::.~:~::i:: :::)~Cl::":::~,":: :~~::o::.:~::~:. _, ' ~ ' If

~~p ~

I'

. _~ d~P~~.""

" _,---'

=~,=t?-~'~

"

l"eroo,u~g=,~

.. ',- , 'U TI6

'-'---"

ene.rgycurves9iv~~by the geOIlIet r io;al,~q\Ultion^{l). •} ~n6 1 1+,U n6

, , l '

2

",here6 1^and-6

2,are&n<Jles ofin<;:l.in.lotSOn ofthli'aner<jy..urtacesfor

, a:n~ 1137:Q' ~·~.~SI?eCd~e~y

^(8.ee.Fi9'2)

~ U~in,! t:hi.~ g~pl~

:.g ea.".tdc cOnc~p~'.,'.it i~,~,"~' _t~,see ,_'tha t??<~:a.~.t.hatl.~_thG,-S,1.~?,e6!r.e6q~L then-a

~

^{c. s.}(i.valu';'which1s

oft.e~"fo~d-

ⁱⁿ

p~acti.~e). '

^,',

, foo',~:~~ni·:::t::,: :~·:!:::t;F:i;~:~'t:~:~ . ',. '

iONil...

:. the ..

8~::,~d':d~CtroC~~cal.. ,fr(l~e.l;et:~l'of.a c tive:t.l;0n tbr.the

,' toJ;W~~ re.i~t·i·On·(l) ~~~ome,j .; ,

' . -

whereCI isthe cathod i c'tra n sfer.coe f fi ci e nt.

S~ndar~:elec troch~ical-frea."ner 9Y~factivation^{,'f O;},i o nis ation oflIad s

ir~~~r~s~ r~:.ctiOO

^{of '}

\iJJ ,~..

^.

. . 'tii+ ...

'(1.' -'alFE

, ,

i~'

t.M _:...

~ic·tiar.sf~rcOeft.i"'e'i~nt:.

~" "tJ;+'

^{are'stand a:rll.'}

i)h~Cll~"'"f~-e~--energi~~ of'·a"tivati.~'n

^atzero

I /

~.----...-/

.~-16-

~~~;~ ^{SUR FACE}

L

..,

.,1

! '~'\- ' . ^{. ,}

^,

~~

")\ Fig . '.~. " ^Potenlidl 'energ y

diagram

Jor ,elec trod~ " ' reoction ~:.-- . "

'" ' .

~~:.:.

. ' . ,.. , ." , " '. .', :, -. ,>

/~.

'.:.-

", ..

fl30cq:F"e +M~H2:0+M-Hads

. .The soli d.

curve~.ot.

1 .h .e < feft

.C1n~;

::> ': '.: ' , ' ,; ." . <" :;~. ".":..'.'

< ,, ': '

· -": :7"'·'-:/ ':,;-;,·:""·.,,,··~' ··

'. ,·t~ ~,.right -rep ...es~nt 'the.p

ctentio! '

en~r~'pr oftle s,':.of fino!".ond.":.

, ,', '" >. ;" , "'"

'-~~-:.--.,.-<'>.'

.. , " :.:".. ... ; .'.,'

~:..i~jtj ?I_:-~f.D.'fS.-r e-spe'Cf~,~ Y, .i.n.'Ihe·:.ab~~nc.,~.·:Of.~n_:,,'.~le~ld~Q I.:

-dl

fft:rence ~ ~ ^{T he'} ~osh7d~,: i::~;',"e_ ^.

+

~',:.

(

.

-'19-

Substitu ting th,e lafthandsLd eof equa tio n (17) into equation (lS) . }his wi llbeco nv erte dto

r r -.- [-P (~) (l

h ^-&H^Ie·llJO^{'exp <-}

~lJ

RT ⁾⁽

(l-

I'VC~30

^0.

o.(oe+~- ~)

^ClFIl

~J ~: I-. -'-T-.J,x[expl~JJ •

{-f'.(~)

((1 -9HlCHi.l +ax

(~Hl·-:a

.(1 -

aj-t.G-+++;\l:,t#J)

".·~I·~'

^{11' J}

e~ [-:

o J;! . .-.. ,

RT"~. "

··The\termf~ithin.

^{r)is-

allO~e>;. _exp.t";ssion· t~r ,tlIe

^{,excha nge}

c urre'f'

dcnkty"aM

theJ:efO~~

^the

catho~iC C1Urr;~~.~~nsity

^isexpress ible

. ,... _. "' _.I

(20 )

",'.

.e_...

• " < •

-]l'he eQuil:1entexpres!I.l,.on forthe a.nodic'cu:ren~dens i,ty,is

•

~

^"r

~~{ io'eXP[~ ^{'!. i. '} ~~)F,nl

^{,- "( 0I... IU)}

. . . : ..J .

•~uation~:(20 )and- (21jan",basicreiationsih'e!ec trodek~netics

.,

". .

.and much of'the.wor~in;!It~dy~n/Jel e c trode processes'ii>d~reC~d toward:-.~'{alUll.tionof 10anda •.

Thto..~etelec trode ClU'r e nt

i is

~edt fferenc ebetwee:n-thetwo

i~iVid~l c~ren~, 1. ~,.

^1:;

r. "" t. ;

Thus,'the

n~t "curren~

^denSity

1;'givenby

(22)

· .

" thoug hnot ac c ura te,1IIiI)'"be l1Secl forthe determination

Of~

for II>dny hiqhcvcrvorceccmetals . for whichexperimen tallIIea surem J nt: are ..,.

IV. Doub l~-LaYerEffectli onCharqe-TransCer

.ar ec e changesin overvoltagewill';liverisetochan<Jes.1n~*.

th..refore,therateof tileel ec tro ch emi calreactio~willbeafflict ed onlyby partof the applied overvol tage

(25)

Ther e f o r..,the effectivepotentialdifferencewhich entersiii'"to the activationene>:gy would be~tbetweenthee~ect.r~·s{lxfaceand the pre-electrodestat e. Dependingonthe lIa<Jnitude ofilI*,the current-overvoltagerelationship,i. ...(22).maybe.."rio\,l,Slydi&tor ted by the effe ctof¢*:-~eeffectof4>*was previouslyignor ed inthe considerationof 'kineticef fect of t1ie inter fac i alpot;entlll1difference.

Equa tio n

J(22 )can be revritten wi ththe¢*term takeninto aCGountas.

i • i~^{{exp,(o.-R;)t*FJ[exp}(-~)

(2 6 )

----wherethe true ex changecurrent de ns i t yi~is~l'tothe eqUaland opposi~ecurrentdensitiesat the equilibriUPl potantlalEo for1'.-0, that is, in the abse nc eofthe doublelaye r effect. ColIlparinqeq~tions

At~11overvo1ta'les ,Le. I~ I

2.

10 mV, the el<ponentiait~r."ln^of .equation(22)canbe expandedtoa' sin'lle~rmand therefore

Under thes e~nditions'.thecur-rent,density.is,'dire~tlYproportio~

to l>othtM"exc;"'nqecurrentderisityandtheovervol~9",e.·.·.This'i "

• ," .., " . "'1,,

;~::::9it:~::~"~::ro:i:~~::::: ::n: ,::~~::::in~ ~'

,A tlarge ,".'1.

cathodic

Qvervoltage,Le.

Inl

~100lIN"

o neof

theoomponentcurrents(anod ic,cl,lrr<mt)beoorn~neg l i gibly small.

'I'hen then~t"c,h,rentj::an be equated to thecath~ic^currentden s i tY.

There fore, athig h ' ca thodi cpolarisation,

.

.

Equation,(2~1can\:Iewritten' in ,the form oftheTaf el equation ,

\i. e _'-1).;,;' a - b10/110 ,(- il.

Pl:O~ ~f ,~Tl

^....

g~i~~~.logI0,

^{I-i>under'th es e},a s sumed.

=nditio~s '.-soou'id

bel,i~~.u:.··^{The!ac,t:or b=116':"'vat 298 K}

(ii:'h ..

'0.5)

!My

be

~~ed wi~,ihe exPer:i:me~tal1y ~erv.ed ~aibe"~~ .l Ext.J:aP'?l~tion·

/ ofTaf,,:i

J).;J..~ts 'to

rr"'J'Il1So

pe:-:~,.':l.et

..

~,n.;~on

0,f ,:1₀."'Ttull ",,,,\:hod,..

','

-<>

1 _ ' 0 0 :-

a'ldi~fo llOws that

1n(-i ) ~ ~~6+I~j

, ..

' .

(20)

(24 )

\

"'n" (1 -~)Ll.<jl.

-23'-

(~)

,

\

Inthe eaSein whichthere,is no sp ecific...dsorptio n,lI¢-can be calc ulated from~i;ff\1Seaoub le-layertheory byeerU4ti;ng1/>*..rli

2 ILe. thepre-elec~estateat~l. Then 4'2" can becaicUla,ted, '.us ln\JGouy-Cllapman

th&Ot:Y

fal"aZ-Zd<>etr.Ol yteas

(2 9' )

(30)

where

'lm

19 thechargeon

th,:

m7t!l^{1per~iteeee,f;,is,the}di,.electtic co nstantinthediffus e laye r and~onistheconce ntrationof.ca tidns Orani ons (f oraso lutioncqnb ining Z-Zelectrolyte,Ccati o n';'C..nion1 inthe:"olutio n. Th~s caicuiated.values^{of ....}~^{•.can beusedtotest:}

equ ation12SJand the r eby(26 )witheXper1mentalres,:,-lts; In practice,

(~,..b •

i fcorrect eoi\(-,il ver~us,C-n}\'Plo'b are:ndepe~den't';C:thesup~rting.

elec t ro lyte,it.isaS~~edtnat double layer effectsar~suita,bly account edfor. andac~ur..tek~neticpar ameters lM.y beob~in"e"us i ng:_. equa tion·(26 ) .

Theequa tion(26) canbewri ttenfor thecathodich.e.r. Ln-the

<0=

i~

^exp I (.+.2 :T

") ~]

(31) Here,i twas~9<'linas sumed that,'"'"~2' A plot otthe.loqarithm oftilele ft-band Side ?;equatio n (31)"'9~in$t^{(+2·'::'n)is-linear}

j

l 1

- - )

(22)and (26l.the apparent,measured.excbangecurrentl'density 10 mayhI!defi ned by

1 0

_ i~exp (( el-R;)F¢") (27) •

Since

~.

varies wi ththe

elec~e

^{potentialand the}

~ncentrati~

ofions1.n'theso lu ti on , i tisobviou.s frOln'(26)that

the

k.in~tic pal2metersObtai ned'frompOl aris ':ltio ncurves usinq (22),alone

w ill

be",= OnIl0 1l5'tovaryll1q' exten ts. 'nulre.'o!:Il,-i ncalc:ulatinga,cc:ura te electrode

~tiC ~a~

^one

mus~ ^take

^intoacco un t "'.

eff;"'~"

^.

In electrodekineticstudiesthe ionics~engthis often held constantby the lise of

~

excessof

'i~ert el~ctrolyte.

One of,the i.IIlpo r t..'ln tfunctionsofthis support:jng"l~ctroiyte"isbjsuppr es !II th e ..*Potentialandtored \lc ei~svariationwiththe electrod"e potentialasfa r as possib le.

In exp<:'lrimen ts'inwb.ich thebehavi our ofu:etab in,pure acid

"olutionsis studied, it:is not possibletoadd supportinqelectroly tes. tn otherCaSeS inwhichsuchane,lectro l yteis adde d;the,re s ults

?ft..mdepend stronq lyonthe foni'cOOIZlponen t5ofthe5uppo rtinq .electrolytes ~ In ordertorationalizeth,e s e effects and' to obtain

accur ate kine ticinf or m":U o n from,r awdata,the termscontai ning

4>*mustbeunders tood .

In th.eabsenceof,~pecifica<;!sot'ptionofsuppopg <!J.ectrol yte,

... ,..,

' .

the.changeof overvoltage~nres ul t ,ing frCllll avariation~.at

~

=nstant current is

t.

, ,

Adso rption ofIlydroqen.byMetals

It isgenerallyacceptedthat theads orb edhy d r 0genproduc ed duringthedischa.rq eofH30~ions or the ionisa tionofH2mol ecUles

,,_bymetalswitll,"EO,(K-H)~.213 ~lII01-

1

(21)'~~~inqtheh. ~.or .is

, chernlsci r b ed On

.

tht-lIIstalele<:trOde s.. ':.

'I1Ie

- ,^{1Jtlldy of}hydrog,en.ads6!-ption- . . ia'he lP f u l:inth<l'eluc:l.dat~n·^of~emec h im i W"0ofthe'h :e.r•..':tlUibl9 Wah.o-.r . ',

ad~.orbedH atCllU'

^are

·~~\IC~-'·~~(f con;J,UICd:. ·. The ·,i~rf~"e

".'

~~~cen~lltion :6f adsorbed ~ydroqe~

^',1s

"~~(\9h~" ~-be '~t.e':'·tl:~~ ;d~~~ni:lent;

^'

•

~nt~~~~~n"~~ncernin~ '~e: 4ds~rp~{~n'-~f ~;d~~;;n.ll~ -~~- ~>_~~f~C~

of-

~~-: elR·~u.od~

_. . , be .obtai ned_{- . '.'}

,tr~-_ suitah:le

_{. . "}

~in.;.t~c .studi~s in~lV'i~~

- - .

me,uurements of the,~lectrodecap:,clt~nceor'surfa~e'7'verage"d!:·th~.

elec tI'ode by.adsorbedhYd ~en.

I. TheAdsorpti onPseud ooa pa dtanc e

Ear l y inv e s ti 'l'ilti o nS"Ofthe h.e .t:.

n;vel1l~

\28,2<11·the

PFes~nce

ofH

ad satoms,'bUt:.t:he existence:ofan ad!'orp tionps eu d'2c ap a c1t.anc 9 , Cps' :d iJeto<ids";.rhedllydrogena\:Orlls...as firstpre dic't ed anddemons trated by Eucken".ndWebluspOl.·~~tenn pseudoca paci tancewa .. introoU:ced byGrahame \(31) tt..di sti"9 uiB.h thecapdc i tanceariBi~.ina~eaction

. $Uch11$:

(1)or(3) whichis assoc i a:t ed ....ithcharg eu;':nsfer across theinterface frOll1the striCtlyno~-faradai.ccapaci~assooia~

wi ththe..dependenoeof ionioande.lect:J:;onicCharge'inthedoubie layeronpoten~"l. 'Thepr e fi x~pseudo~'1sused becausec refers

/ ., ' . " .: . "- . p~ ^•

to'II.leaky' -;;apacitor,that eIl.nnctexistWlles ~the interphas e le a ks ,

.Binding energ lesofadsoibedhy.dr og-enatoms'onlIIe~~~s,

. . t (

;

and ha stheslope

*.

^Thetrue tra nsfer'coefficient'"isthus ob ttlined..

The,theoryof do\1blelayer,e ffe c ts can be extendedtosystems inwhichsp~cificad s orptio nof support.j.nge.lectroiyt~occura.

Tr~atlnentfo r specificadsorptio~ismo.reu~cer~inttla."in the

_. :'"~.J,~ ~ence^6fsI;'I!Clf i c,a ds or ption bljc';use'de~ilS,of thedoubll!>layer .' s,tr >ij: t u;e';~s'De~h~Y(26)' lK>t~''-are npthUy,under~tOod.'.'At

leas tom"eff~ts"lnay.be'co nlii der ed ;,(Il lpllrt.'1dco~~age·ai .

.. ,.-. '-r-""" :: ". ' :". ' -:

electrod~'~y,s pec ifi c a llyaa~~rbed.iO~ "'hic~. ,caWies ',~ :re<luctio~.in: .~ecurrent,'at C:on!ltant-Ove:rvoltaqe.because~~the.decr,;;asedarea

...dlabl oforcur.re nt flow nmnely.the uncovered part of the electrod eand (~) ~aria tion.0:~ePo: ential~*or~2,(i t.isa!"Jumed thatthe pre-electrodestateJnaYst i U'oo i denti fi edwiththeoHPl

.

,

caus e dbyspecificadsorption. Anionsp.ecificads or p tionCauSes

~2

^{to,be les,S}

POSit~~e

^and

incr~ses ~e

^{rat e of.}'r..'d UCtiOnof

~30:q

ions at.. given,ca thodi cover voltage. Ontheotherhandjcati on speei,fic,ads~.J;:Ption.hal>,th e oPPositi>".fCecton~2and

;O!"

the,.ra t e ofuduc tion

~f

^H₃

0 :

Q

i~ns.

on:e,Frumki n,correc~ i",?~the effec t.of~.or.-.;,~o~the kinetic

p<U"<Ulleters)i,~oftenneglectedin,ldn e tic' .s t udi e sot,the behaviou r. ,....' of metal..

i~' ~ur (!

^acid'so l u tions. This !MY be'j ustified'

~hen

^hiqh':

electroly teooncentrations~re ,used50 thatth~vari'atio/l.of

+ *

. '

I

II / /

R .'

, F, '

Cps

(0)

Fig.3. Equivalent cir cuit

tor.

syst em exhibitin g

on .

adsorpti on

pseudccopc cltonce. ...

to)"Volmer discharge

with

1Tof,el

' de~or~tio~,._. ^step,

(bl Volmer.discbc rqe with 'Heyi oYsky.

- oksorption-

step. 'R-~Reaction resistance:RF1for chargfflg

step

and

R F2 " for desorption

st~P.

respe ctively.

'\

\

\ -2& -

t~tis. unlesscharge istran~ferted

\

..."ros si t(32)...

Sine.._however,,,~ectrontf.u<6ferislineuen.t.i~lrsquir elll'lnl fo ,,",theformationof adsorbed hJdrogenat<'>trts.the pz;es e nce

of

these adsorbed intermediatesonthe'

sU~f¥:e

^{isequivalentto.the"tp r age}

.of el~·tr icitY

^"

~"~ in~ertac~ \s'

^":

~,.c~~deriSe~>·:~

^the

correspo~din9

^.

cap.,.'.

'~ .

^{ce,'c.b<.haves..'.'.'.'.}

~ \< Oi.

nary...capa".itan,,"

"?". . , ."", . ..

^{t"i t}

.. .._ •. , p s ....' : . ..

,< ', ,: ,

may var;;y to a,"uch great",r fx t e nt(re~~.tive'·toe.e"dOublelayer ' ca~acitllncelwithpotentiai·aridf.,equcncy. .'.

::.'

Tlie"~l~~~~Ch~ical behaviour\Of:~.h~ e1e.c:trode-eiec~olYtoi

^r

int~rfa,:e

^{"a n}

~ r~presented

^by

thte'l.ectri~a1

^{!?eh...'o.urO.f}equiv a l e'nt circuit elCltlcnts(J2;'J2a.32b ).

so ~ong

^as.an

id~r-t'ri.SeQ

^el,,<;trOd., * te c<:lnside.redand no f/lradaicChar~e-t\~psfett.e.1nvo lv,ed.theC~~CitllnCe representationof thedo ublelayer s adeq uate. Whanacharqll-

.

^\

transferprocesscan occur at&r4~ependentontheereeeecee pot ent.ial;represent4tio~'as⁴f,.;re '~ac1 tan~e^isin/ldeq ':'/lte. In

"" CaSethe ads or p t ion

pse~ocapa.~

^{'tanceplaysan}

illIportan~

^role

in thetotal aee e uee e electrode.~ap;l,i tanee .,The ,a<;lgo r ption

pseudooapaci~nC"

^must

h~Charqed _th.r~~., .

^h,thenon-Ohllli.C

re&i"tanc .~,

"',' ~«MP''"':"' ,,~ , Lven""'."'ftd' '"

^Ch.

^< "'pro,,' 0 '

^Ch'

rat~_o ftheH]OaqiO,ndi.barges~pr.Odu cing Hads' Thesee r e e

.c"'!"'ina ti onof CpIIand~l mu.s ~bei'npar a llel withCd•I.,\lirn:e i t

p ro."'"

".;",,,,' Ch

'~

. .Ch'.do lolAy« ' " . :' , .,,"" """

*Th echaracteristicof anidealPOla.ri~edelectrodeis that '

ther e is no

~XChange o~ electric·~~~te b,,~een

^{the two-phases.}

I

uns a thh ctor ymanual proced ures and the rise-ti_ dePe ndenceof the capaci tanc e RIiIkesi trath erdJ tf iGulttoin te rpre tthere su l ts forCp~values ob ta i nedby thes eeeeecae. nixe ce.diffe r entia t ion ofthe open- ci rc u1 t df>CoIlY cur veis.f r ee from someof thesedis-

C"

Thedi r ectdif f e r entia l galvanostatic m.ethodvesdevelopedby Anger ste in,,;'Kozl0w:skaan? Conway (38 )andla.terConway,Gileadiand Anger!l'te~n-Ko:Z:lOWSka(39 ) pointe\}cue'~atanymethodbas edOn the

-~.at'e^{of decay}of"):,t~ntia;lOn op;,n-circuitfO~l~i.e~^steady-state'

POlaris~tionwi.llrcpreoenta true-equllibd,l.Il'\'pseudoc apac1 tance ,

i.e.th<!;valuecorr~sP;;,ndingto,a ninfi ni te l ylow freq,,;'.,ncy~

a.c.-b r i dg e method, and istheref o retob~preferr~. The'-direct di ffer.m t ia lgalvano~~ic^method(ra pi d-ope ncirc uitd~cay )^{isr:w;'s t} sui tab lefa rst udies Ofthe potential dependence~fads orption pseu do capa ci t an c e s . Thismethodisba.sed~theassumptionthat

. -i

theF;u~aicpr o c e s s takingplace durifi'J'stead y·statepolarisa tion , continuesonopen-circuitbyase lf -disc har ge·proces swhich lI\OIllentarily ,at the beginn1;'"ofthe open -c'ircuit.tra nsient ,ha~the.

Sal!le rah astha t cor re spo ndi ng to'th einitia l st eady-s b te polar- is ationcur r e ntde.nsi t y Olt thein stant of current.in t e rrupti on.

OForinsta nc e,intheh.e.r.involvinq steps(1 ) and (3),the open- Jr-eUitdis cha rgeof the

a~orpt1on

psaudo capacitance «curs

by

continuing-desa:~t1onoflI_{a dll}byste p(3)withreverseof stepIl) pr ovid i ng theelec tro nsfor ..tep (3) .

.'

if hydroq",n

.:

r"",ombinationto;the d""orptionstep.1n the h.e.r••Cps is also snort-cl I"cuitedby'"second non-ohmic re s i s t i ve component.

~2'whi c h i$the"ec i p r oe al ofth~rat e ofre Combi na t i on . The re: re s e nta t i o n ,!,s,

»r:

^as shown in Figure:la. Thewhol e of-the OOmhinationpf~l'^Cpsand~2^is,i~p.\n.ll~la~ro"s^{Cd:l.in the} caseofa no n':'id" llUypoled sab l edeetJ:ode.

~en des,i~Ptio~

^isbyen

e1ec_~chemiCll.l"s·t1'lP"i. e.,

(ltC>rll+ion _deS?r pt\i.on'( 3 ), 1' 11;

sP"cill.l J;'eti:esentat~on ~8:

^{t'e;iuiredas. shownin}

"Fig ure

J~, Wh~~ tth~ hon-o~o ,resista~~e\ ~2'

corresponding to ..;; thereo;!proc,H rateof thelIe yr ov sk y"tcg'+iondesorptionstep16

'drawnwithtwQparallel input chan;u,ls.·one for electronsandK 30:Q ions and the otherfo.r th" "ads

a t\' s

remov edi!l.SequtVa1:n t'charge

iTomCps ' '

IL

De ~~'cmination

^{of Adso}r ption

p~eudoeapacita noo

InvOlv i ng Open-circ:u i t De ca y

Me thods fordetenTlin~,tiOn"Ofthe oapacitllnc"-potential rel a tio ns h i pha v e be e nbasedon(al\jl!Oa'l!tr1caldif f ere n tia tio n of a. c,galva no,.taticch~gingcurves,e.g.the double-charg inq methOd of'De va natha n, Bockri"andMehl(331, or of open-ci rc ui tclecaycurvesby ConwayandGi l ea di (,34,35,36 1 ,(b)direc~.~br~;lecapac itance stud ies, (30,37t-or {~ldirect differlmt i ationofchargin g

9 t

dec ay curve s(38) . Theinterpretationof"" s uIts for,Cps values frOll\thea.c : ca.,a<;ita nc.

stud i!:s

is

colnp licatedby the1111;'ge freq ue ncyde p e nd enceofthe capacitancewhi chwa s still ol;>$l!t ve ddo\.m.to-ver ylow·frequencies.

Theme thods'1 nv 01 v1 n9 qeomeericdiffere ntiation rely on ra ther

whereby the oxid;,.Uonof theadsorbedhydrogen "tornsh completed befol'",'r e adso rp tio n beCOCll!s appreciab le. Breit!!r,Knorr and . volkl (42) usedthismethodto rthe noble ltIl!tAls Pt.Pd ,re,Rh

and Auupde,rcathodi c{>Qlal'is~tion. ^-Themethod.can only belIUCCeS"~

.- ,' ,

. . : '

^\ ,

(33)

. . .

.

^.

cha r q i ngmethod toOVerC O/Ile

t., i"

difU<;:ulty. ApplicationofcycHc:.

VoltaImletry'(43-)isanoenexdir'ectmethod used widelyfor ev aluati on

of

⁹₁₁^on'the

I~Oble m<lt&~~

^ant'

~eir '

^alloys.

Each va.Lueof'"hyd r 'ogen,ver"qecorre spond stoIIchar g eqH

r<iquir~d- to._r~a~h

^that

~~erage

^{froml"er o}

';'vera~e.

^i.e.

fullyapp li e difthere' h a.c on s i dl!1:ab l e potenti::"ldif~erencebetween the potential correSpOOe!in9'to'th~·c;>;IlIIpi~tion~f'adsorbedhYdroqe~

Wherek' is the ch a rgeneededtoform a,completeIOOnolayerof adsorbedhydrogen'atonls. Its,nurne~ic alval ue'18 oftheorder of 200'-\Ie =-2fora

lJydr~en _lltom O~cuPY.in'J

^"-:81"'1'1,;,site on.the

$u'r.fa'~e

ofa met/Jl.:,~evariati~!1ofeM'andhence ofqit, withoveJ:VOltag8 givesrise,toaps e udocap,, <::i tail.c e

." ." . - .'. .,"

withads~~b^..e:hydr~om^{oxida'Uonat the}sUve r e l ec trOde" in alkaline .,soluti o n . Th er efor e,~vanathan"tal(33 )deve lopeda double

)

Theelectrod. capacitance,Cexpt' can be-ca l c u lated from the ini tialrateof decay(~l.t^..o~inqthe followingequat~on

'I .,

• "(* ) t-:O

\,. (32)

, I

^{I, ,}

-

"

wh e r e .,1 Is the ste,ady-stat.ecathodiccurrent.dens i t y atthe

::,.«"::o::':":::::'.::~·,::":t:t,:'::<P::';~·~'

"WI~c1.l.'~ell n\J~e~l^{..,.I f}~~_s_^«.c~.l:'^at..,:~:ry~^..8IIlan"al~.es<:. , ^.

o~.

cathodic chuge

~ssed

^•.-Q.';hen

~t' c.i!l~ ~'~ss~e~ ~~~-Cex~t'.-

Cd.,t,..

atthis va l ue,o f:'Qandthelnc re a $",of Cexp tw:ith-Qcanbeuso<Lto

, ,

evaluateCp s ' Le.Cp s'. (Ce~~t'-Cd.~~!;. o t hllrwise

w e

must~ co n t e n t ·...i.th

M . _ps "

that istitl':increllSll of pseudocaplI.cH:an cewi th -Q" Bypolarisingthe elect,I:<;>de a:.var,J,ous

eurren5

dens,ides-1 and record ing-n at the instant,of interruptionotcurren t ,followedby

",

··· f

open-circui tdecay. Cps or r':"ther llCps' can "':ob!Ai~edas a, ftinctiol).

of·overvoltage .

III. Ev.alUationof·Hyd mq en Coverase

. " '.-'"

Ttlehydroqen·.cove rageellcanbedirectlyobt~ne,ib;yllIea sur i ng preci s e l y the chargerequiredtorde pos itionor removal ofhydrogen atoms "on

. '

the 6urf ace,o f'thellIet..I, 'Qver:certain' .

pot~nti.a~

^rlnge.

Therapidgalvanostaticcharginqmethod'WasOriginat~dbyBawden alld Ridu l(40)

.ind ·~ad

^bypears6n

and·~~tler ( 4'~) -'and othl!r~'

^{UI.

Di~fi"ultiellassociatedW~thther~sorptiono~ hy~"rif1'Olll;

l~ve<l h.ydrogelll'lOleO::Ul~S

ⁱⁿ

so~

^{ution .orfrOlll}

b~.bleson .~e

I

ele"trode,,~re.lllinilliJ.:r:~,^byuei~high al)Odi:cw:ren~·den6i.tie6^r,

I