Bockris Jes 1952 Hydrogen Article

8/6/2019 Bockris Jes 1952 Hydrogen Article

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T h e M e c h a n is m o f t h e C a th o d ic H y d r o g e nE v o l u t i o n R e a c t i o n 'J . O ' M . BOCKRIS AND E . C . POTTERImperial College of Science, London, England

A B S T R A C TS o m e o f t h e o u t s t a n d i n g p r o b l e m s o f c o n c e p t a n d m e c h a n i s m i n t h e f ie l d o f c a t h o d i c

h y d r o g e n e v o l u t i o n k i n e t i c s a r e d i s c u s s e d a n d c l ar if ie d . A fu l l d e r i v a t i o n a n d c o r r e la -t i o n o f k i n e t i c e q u a t i o n s w h i c h a s s u m e n o m e c h a n i s m r e v e a l s e x p r e s s i o n s f o r s e v e ra lp a r a n m t e r s w h i c h t a k e w f l u e s sp e c if i c t o o n e o r m o r e m e c h a n i s i n s . T h e u s e o f s t a -t i s t i c a l m e t h o d s o f t r e a t m e n t o f d a t a p r o v e s i n d i s p e n s i b l e in e s t i m a t i n g t h e v a l u e s o ft h e s e p a r a m e t e r s . A f u r t h e r m e t h o d o f a s c e r t a i n i n g t h e m e c h a n i s m o f t h e h y d r o g e n e v -o l u t i o n r e a c t i o n is t o e x a m i n e t h e k i n e t i c s o f t h e i n d i v i d u a l r e a c t i o n p a t h s , s o t h a t t h ee x p e c t e d v a l u e s o f p a r a m e t e r s c o n m m n t o a ll p a t h s m a y b e d e d u c e d . A n u m b e r o f m e c h a -n i s m s i m p o r t a n t i n a c id a n d a l k a l i n e s o l u l i o n s a r e t h u s t r e a t e d , a n d a r e s h o w n t o b e d i s -t i n g u i s h a b l e e x p e r i m e n t a l l y . U s i n g a l r e a d y p u b l i s h e d d a t a , t h e a c t u a l c o n d i t i o n s u n d e rw h i c h v a r i o u s r e a c t i o n p a t h s t a k e p l a c e a t m e r c u r y , s i l v c r, n ic k e l , a n d s m o o t h p l a t i n u mc a t h o d e s a r e c a l c u la t e d . I t i s n o t o n l y p o s s i bl e t o c o m p a r e t h e s e d e d u c e d d a t a w i t h o b -s e r v a t i o n , a n d t h e r e b y v e r i f y t h e o c c u r r e n c e o f a p a r t i c u l a r r e a c t i o n p a t h , b u t a ls o tod e n m n s t r a t e t h e i m p o s s i b i l i t y o f s o m e m e c h a n i s m s i n sp e c if i c c a s e s . T h e r e c e n t a d -v a n c e s w h i c h t h e f o r e g o i n g m e t h o d s h a v e m a d e p o s s i b l e a r e d i s c u s s e d i n r e l a t i o n t od a t a w h i c h h a v e r e c e n t l y b e c o n m a v a i l a b l e .

I. INTRODUCTIONThe electrolytic evolution of hydrogen is gener-

ally chosen as the main subject of experimental andtheoretical research in electrode kinetics because itwas originally thought to be one of the simplestelectrode reactions. This expectation has not beenconfirmed. However, work already done has em-phasized the importance of the reaction, and itspractical significance to studies in corrosion hasstimulated further attempts to solve the problemsdiscovered. In the following, some general equationsof electrode kinetics are formula ted and indicate theexperimental methods best suited to mechanismdeterminations.II . S O M E D I F F I C U L T I E S O F T E C H N I Q U E A N D C O N C E P T

It is notoriously difficult to measure the velocityof an electrode reaction and the correspondingelectrode potential with reproducibility. The bestagreement obtained between workers in differentlaboratories is + 8 my on Hg and =t=20 my on solid(e.g., Ni) cathodes.

Man y different ~ypes of Tafel lines are reportedin the literature. Some of these are collected in Fig.1, from which it is seen that only the first and thelast two represent forms which are free from vitiat-ing influences. The principal vitiating factor in ex-perimental work arises from mimlte traces of im-purities in solution. For example, addition of only

M a n u s c r i p t r e c e i v e d M a r c h 2 6, 19 51 . T h i s p a p e r p r e -p a r e d f o r d e l i v e r y b e f o r e t h e W a s h i n g t o n M e e t i n g , A p r i l 8to 12 , 1951.

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10-1~ gram moles/li ter of As203, CS~, CO, KCN ,etc., detectably affect the electrode potential at agiven current density at nickel cathodes (1). Re-producible results can only be obtained in solutionswhich have been purified by pre-electrolysis on to anauxiliary cathode (2). Use of this method involveslaborious work to determine the amount of pre-electrolysis necessary for a given electrode and solu-tion. The criterion by which the opti mum conditionsfor pre-electrolysis are found is that passage offurther coulombs at higher potentials makes nofurther difference to the experimental results.Even then, the initial state of the solution beforepurification may be difficult to reproduce so thatsometimes less pre-electrolysis is necessary thanat other times.Man y difficulties in preparing the surface of solidmetals in a reproducible, clean state have causedmost studies to t)e made on mercury. In one method(3) the electrode in wire form is heated in a streamof hydrogen to remove oxide films and sealed into athin glass bulb containing pure hydrogen. Afterpre-electrolysis of the solution the bulb is broken by aglass probe thereby immersing the electrode in thepurified and oxygen-free solution. A further possiblemethod would be to heat the wire electrode electri-cally, e.g., inductively inside the cell, containinghydrogen, before placing it in solution.

In addition, a few difficulties connected with thegeneral attitude of much past work to studies of thehydrogen evolution reaction may be mentioned.First, the difficulty of measuring the electrode poten-

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170 JOURNAL OF THE ELECT ROCHEM ICAL SOCIETY A p r i l 1 9 5 2tial, and the comparative ease of measuring the cur-rent, directed attention away from the fact thatthe problems coflnected with overpotential werepurely kinetic, and tha t attentio n should be focusedupon the current. Second, considerable attentionhas been paid to the determination of i0, the current

D I S S O L ~

O LIMITINGCllfiRENT ~ i t~1 R[$I$1A~IC-E RROR i - T Y P E /

I ELECTROCH M CA L~. T Y P ESILVER J

LOG CURRENT DENSITY----~-

DEPOLARIZED2O,~[ OXIOE FILM TYPE~

LOG CUR RENT DENSITYFI~. 1 . Some types o f Tafe l line fo r hydrogen d epos i t ion

16

14

t2

I0,_o

i 6

4

I i i i i i i t

M O F e W ~

2

0 . ,I I I I I I I I3.0 3 .5 4 .0 4 .5 5 ,0 5 .5 6 .0 6 .5 7 .0 7 ,5dp IN sFIG. 2 . Re la t io nsh ips b e twe en exchange cur re n t an dt h e r m i o n i e w o r k f u n c t i o n f o r a n u m b e r o f c a t h o d e s .

passing in either direction at the electrode at thereversible potential, i.e., at zero overpotential.Consider a complete galvanic cell at constanttempera ture consisting of a metal M (the cathodein a cell in which overpotential is measured) and aPt electrode in the same solution as the metal M.There are three potential differences in the cell:VM, that at the b oundary M-solution; Vpt, at theboundary Pt-solution; and X~ the contact potential

difference between the metals. If AV is a potentialdifference measured by means of a potentiometerconnected to wires of composition M, then,

A V = VM - - V p t + X .Now, X ~ ~M -- qh, , where q)M and ~p~ are thework functions of the metals M and Pt respectively(neglecting the Peltier heat in the usual way).Hence,

VM = AV+ Vp t- -~ M+ ~p t.Or, if the experimental conditions are appropriate,so that AV represents a hydrogen overpotential,

VM = ~+ Vr t- -r + r (1)where K is a constant potential difference for allcells in which hydrogen overpotential, 7, is meas-ured at the same pH and temperature. But also,the relation between current density, ic, and poten-tial, for a kinetic electrode process in whieh thereverse reaction can be neglected, is given (seebelow) by an equation of the form,

where a and K1 are constants and the pH is assumedto be constant. Thus,[ - - a ( ~ - r (2 )ic = Kx exp R T "

Therefore, if when ~ = 0, ic = i0, then,[ | (3)= K~exPk R T J '

where K2 is a new constant.A relation of type (3) is indeed observed, and isshown in Fig. 2. It follows, then, that the most ap-propriate potential at which to compare the rate ofthe hydrogen evolution reaction at various electrodematerials is not the reversible hydrogen potentialbut the absolute zero of potential. In the absence ofreliable knowledge of this, the potential of thecharge-free surface appears to be the best referencepotential.Similar conclusions apply to the heat of activa-tion, AH*, which is usually quoted at the reversiblehydrogen potential. However, measurements of i0and AH* retain considerable relevance because theyassist in distinguishing, between various possiblemechanisms of the electrode reactions.Lastly, the rate of the evolution reaction dependsupon the difference of two inner potentials $, i.e.,it depends upon a Galvani po tentia l, where 4~ isdefined by

~b-- ~b+ x, (4)



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V o l . 9 9 , N o . ~ C A T H O D I C H Y D R O G E N E V O L U T I O N R E A C T I O N 171~b b e i n g t h e V o l t a p o t e n t i a l o f a p h a s e a n d x t h es u r f a c e p o t e n t i a l . T h e l a t t e r p o t e n t i a l i s s t r o n g l yd e p e n d e n t u p o n t h e s u r f a c e c o n d i t i o n o f a p h a s e ,a n d h e n c e t h e o v e r p o t e n t i a l a t a g i v e n r a t e o f r ea c -t i o n w o u l d d e p e n d s h a r p l y u p o n t r a c e i m p u r i t i e s .I I I . STATISTICAL METHOD S IN MEASUREMENTS OFHYDROGEN ELECTRODE KINETICS

I n o r d e r t o o b s e r v e w i t h r e a s o n a b l e a n d k n o w na c c u r a c y t h o s e o f t h e t h e o r e t i c a l l y i m p o r t a n t p a r a m -e t e r s i n o v e r p o t e n t i a l s t u d i e s ( e . g . , t e m p e r a t u r ea n d c o n c e n t r a t i o n e f f e c t s ) w h i c h m a y v a r y l i t t l em o r e t h a n t h e r e p r o d u c i b i l i t y o f t h e m e a s u r e m e n t s ,i t i s e s s e n t i a l t o r e p l i c a t e t h e o b s e r v a t i o n s a n d t oa p p l y s t a ti s t i c a l m e t h o d s .

I n a p p l y i n g t h e m e t h o d o f l e a s t s q u a r e s t o e s t i -m a t e t h e p a r a m e t e r s o f a T a f e l li n e , t h o s e fo r m u l a es h o u l d b e e m p l o y e d w h i c h c o r r e s p o n d t o t h e c u r -r e n t a s t h e i n d e p e n d e n t v a r i a b l e a n d t h e p o t e n t i a la s th e d e p e n d e n t v a r i a b le . T h i s m e a n s t h a t t h e s u m so f s q u a r e s o f t h e v e r t i c a l d e v i a t i o n s o f t h e e x p e r i -m e n t a l p o i n t s f r o m t h e c o m p u t e d T a f e l l i n e a r em i n i m i z e d , a n d t h a t , c o n s e q u e n t l y , a p r e d i c t i o n o fp o t e n t i a l a t a s t a t e d c u r r e n t h a s t h e m i n i m u mp o s s i b le e r r o r b a s e d o n t h e o r i g i n a l o b s e r v a t i o n s .T h u s w e h a v e

a n da = ~ - b2 , (5 )

b - n Z x y - Z x 2 y _ N (6 )n ~ x ~ - I F,x ) 2 D 'w h e r e x a n d y t a k e t h e c o r r e s p o n d i n g e x p e r i m e n t a lv a l u e s o f l o g i~ a n d ~ , r e s p e c t i v e l y , n i s t h e n u m b e ro f p a ir s o f o b s e r v a t i o n s , 9 i s ( X y ) / n , a n d ~ i s ( ~ x ) / n .T h e v a r i a n c e s o f t h e T a f e l l i n e p a r a m e t e r s m a y b ec a l c u l a te d f r o m

V ( b ) = [ n ~ Y 2 - (~Y)2]D - N2( n - - 2 ) D ~- ' ( 7 )

V i a ) = V ( b ) [ D / n + ~2], (8)a n d

V(log i0) -- V ( b ) [ D / n + (log i0 - 2) 2] 9b e (9 )

w h e r e V ( b ) , V i a ) , a n d V ( l o g i 0 ) a r e t h e r e s p e c t i v ev a r i a n c e s o f b, a , a n d l o g i 0 , e a c h w i t h n - 2 d e g r e e so f f r e e d o m .

W h e n r e p l i c a t i o n o f o b s e r v a t i o n s i s c a r r i e d o u t ,i t i s o f t e n d e s i r e d t o r e p l a c e t h e p o p u l a t i o n o f T a f e ll in e s s o o b t a i n e d b y o n e m e a n l in e . T h e p a r a m e t e r so f t h i s l i n e m a y b e c a l c u l a t e d b y b u l k i n g t h e o b -s e r v a t i o n s a n d a p p l y i n g ( 5 ) a n d ( 6 ) , b u t t h e v a r i -a n c e s o f t h e s e p a r a m e t e r s c a n n o t b e f o u n d b ya p p l y i n g e q u a t i o n s ( 7 ) t o ( 9 ) to s u c h b u l k e d d a t a .

I n t h e s e c i r c u m s t a n c e s t h e r e q u i r e d v a r i a n c e s a r ec a l c u l a t e d f r o m e q u a t i o n s o f t h e t y p e ,

_ E ( p i - p ) 2 ( 1 0 )V ( /5 ) n r ( n r - 1 )'w h e r e V ( p ) = v a r i a n c e o f p ,

p i = t h e v a l u e o f t h e p a r a m e t e r p o f th e-thj T a f e l l i ne ,p = ( Z p ~ ) / n ,

a n d n r = n u m b e r o f T a f e l l in e s i n t h e p o p u l a -t i o n .

I t c a n b e s h o w n t h a t t h e r e l a t io n b e t w e e n l o g i0a n d a b s o l u t e t e m p e r a t u r e , T , i s

log i0 = log B AH * (11)2 . 3 0 3 R T 'w h e r e l o g B c o n t a i n s a t e m p e r a t u r e t e r m , b u t i su s u a l l y c o n s i d e r e d t o b e t e m p e r a t u r e i n d e p e n d e n to v e r t h e r a n g e s o f t e m p e r a t u r e o f t e n u s e d e x p e r i -m e n t a l l y . I t i s e v i d e n t f r o m ( 11 ) t h a t s in c e l og Bi s f o r m a l l y t h e v a l u e o f lo g i0 a t i n f i n i t e t e m p e r a t u r e ,t h e v a l u e o f l o g B i s o b t a i n e d b y a l o n g e x t r a p o l a -t ion o f the obs e rved re l a t ion . A l s o , s ince log i0i s i t s e l f o b t a i n e d b y l e n g t h y e x t r a p o l a t i o n o f aT a f e l l i n e , i t i s n o t s u r p r i s i n g t h a t p u b l i s h e d v a l u e so f l o g B s h o w l a c k o f a g r e e m e n t ( 4 ) . I n o r d e r t oo b t a i n t h e m o s t p r o b a b l e v a l u e s o f AH 0* a n d l o gB f r o m t h e d a t a , i t i s c l e a r t h a t b y t r e a t i n g 1 / T ast h e i n d e p e n d e n t v a r i a b l e a n d l o g i0 a s t h e d e p e n d e n tv a r i a b l e , e q u a t i o n s a n a l o g o u s t o ( 5 ) t o ( 8 ) c a n b ea p p l i e d .

T h e e x p e r i m e n t a l a c c u r a c y w h i c h m u s t b ea c . h i e v e d t o a t t a i n a n y d e s i r e d l i m i t s o f e r r o r i n a ne s t i m a t e o f l o g B m a y b e c a l c u l a t e d in t h e f o l lo w i n gway . T he va r i ance o f log i0 , V( log i0 ) , i s g iven w i ths u f f i c i e n t a c c u r a c y b y

w h e r e V ( m ) i sm is

D ' is

V ( m ) D ' (12)V(log i0) - n ' 't h e v a r i a n c e o f m ,H*/2 . 303R ,t h e a p p r o p r i a t e d e n o m i n a t o r c o r r e -

s p o n d i n g t o D , i n ( 6 ) ,a n d n ' i s t h e n u m b e r o f p a i rs o f o b s e r v a t i o n s

o f log i0 and 1 / T .A l s o , t h e v a r i a n c e o f l o g B , V ( l o g B ) , i s o b t a i n e df r o m a n e q u a t i o n a n a l o g o u s t o ( 8 ) a s ,

V ( l o g B ) = V ( m ) [ D ' / n ' + ~2], (13)w h e r e ~ = Y r / n ' = ( F . 1 / T ) / n ' . F r o m ( 1 2 ) a n d ( 1 3 )a n d n o t i n g b y a n a l o g y t o ( 6) t h a t D ' / n ' = Z ( r - e )~ ,

V ( l o g B ) Z ( r - - ~.)2 (14)V ( l o g i 0 ) = + _I n o r d e r t o u s e ( 14 ) n t l m e r i c a l l y su p p o s e t h a t t h e

v a l u e s o f r a r e d e r i v e d f r o m t h e e x p e r i m e n t a l



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172 J O U R N A L O F T H E E L E C T R O C H E M I C A L S O C I E T Y A p r i l 1 9 5 2t e m p e r a t u r e s 0 ~ 1 0 ~ 2 0 ~ 3 0 ~ a n d 4 0 ~ a n d f u r -t h e r m o r e , l e t it b e a r b i t r a r i l y d e c i d e d t h a t t h e m a x i -m u m i n a c c u r a c y t o l e r a b l e i n l o g B c o r r e s p o n d s t o9 5 p e r c e n t c o n f i d e n c e l i m i t s o f 4 - 0 . 5 . H e n c e , a s -s u m i n g t h a t t h e e r r o r s i n l o g B a r e n o r m a l l y d i s -t r ib u te d , we ha ve 3 .18 x /V- ( log B) = 0 . 5 , wh e re 3 .18i s t h e v a l u e o f S t u d e n t ' s t f o r 3 d e g r e e s o f f r e e d o ma n d t h e 0 . 0 5 p r o b a b i l i t y l e v e l . H e n c e f r o m ( 1 4 )V( log i0 ) i s 0 . 000286 . Now, f rom (6 ) and (9 ) i t i ss een ,V(log io)

V ( b ) [ ( l o g i o - log ~)2 + Z (log i~ - logic) 2] (15)5 2

w h e r e l o g i~ = 2 . T h i s e q u a t i o n m a y b e a p p l i e d tot y p i c a l e x p e r i m e n t a l d a t a f o r t h e m e r c u r y c a t h o d e ,w h i c h ( r e f e r e n c e s h o w s ) g i v e s t h e m o s t r e p r o d u c i b l eo v e r p o t e n t i a l m e a s u r e m e n t s . L e t l o g i ~ t a k e t h en i n e v a lu e s, - 7 , - 6 . 5 , - 6 , . - . - 3 , s o t h a t t h ev a l u e o f l o g i~ i s - 5 . 0 . T a k i n g b a n d l o g i0 f o r t h em e r c u r y c a t h o d e i n a q u e o u s a c i d s o l u t i o n a s 0 . 1 1 5v o l t a n d - 1 2 . 0 , r e s p e c t i v e l y , a n d u s i n g t h e v a l u ef o r V ( l o g i 0 ) c a l c u l a t e d a b o v e , i t i s f o u n d t h a t V ( b )i s 0 .0592 9 1 0 6 ( c o r r e s p o n d i n g t o 9 5 % c o n f i d e n c el i m i t s i n b o f 4 - 0 . 0 0 0 6 v o l t ) . S u c h a n a c c u r a c y i ne s t i m a t i n g t h e s l o p e o f t h e T a f e l l i n e i s u n a t t a i n -a b l e e v e n w i t h m o d e r n t e c h n i q u e s . T h i s i s e v i d e n ts i n ce a n e r r o r o f o n l y 1 m v i n e s t i m a t i n g t h e o v e r -p o t e n t i a l a t 1 0 7 a m p / e r a 2 a n d a s i m i l a r e r r o r i n t h eo p p o s i t e d i r e c t i o n a t 1 0 3 a m p / e r a 2 i s s u f f i c i en t t oc a u s e a n i n a c c u r a c y o f 4 - 0 . 0 0 0 5 v o l t i n b .

I n a r e c e n t i n v e s t i g a t i o n u s i n g n i c k e l c a t h o d e s( 1 0 ) o n e t w e n t i e t h o f t h e e x p e r i m e n t a l T a f e l l i n e sa t t a i n e d l e s s t h a n t h e a b o v e i n a c c u r a c y i n s l o p e ,b u t t h e s l o p e o f t h e m e a n l i n e o f a p o p u l a t i o n o fT a f e l l i n e s c o u l d n o t b e d e t e r m i n e d w i t h a n a c c u r -a c y ( 9 5 % c o n f i d e n c e l i m i t s ) g r e a t e r t h a n 4 - 0 .0 0 4v o l t . T h e 9 5 p e r c e n t c o n f i d e n c e l i m i t s f o r l o g Bw e r e o n t h e a v e r a g e 4 - 2 . 2 , e a c h l i m i t b e i n g b a s e do n a n a v e r a g e o f 2 5 p a i r s o f o b s e r v a t i o n s . I t , t h e r e -f o r e , a p p e a r s t h a t t h e q u a n t i t y B i s n o t a u s e f u ld i s t i n g u i s h i n g c r i t e r i o n o f r e a c t i o n m e c h a n i s m .

W h i l e v a r i a n c e s ( w h i c h s h o u l d b e q u o t e d w i t ht h e i r n u m b e r o f d e g r e e s o f f r e e d o m ) a r e i n d e p e n -d e n t o f d i s tr i b u t i o n o f e r ro r s t h e y a r e n o t r e a d i l ya s s i m i l a b l e a s m e a s u r e s o f e r r o r , a n d i t i s c u s t o m a r yt o a s s u m e ( i n t h e a b s e n c e o f e v i d e n c e o t h e r w i s e )t h a t t h e d i s t r i b u t i o n o f e r r o r s i s n o r m a l s o t h a tc o n f i d e n c e l i m i t s m a y b e q u o t e d . S o m e c a u t i o n i sn e c e s s a ry h e r e ; f o r if i t is a s s u m e d t h a t t h e p a r a m -e t e r s b a n d l o g i 0 o f t h e T a f e l l i n e h a v e n o r m a l d i s -t r i b u t i o n o f e r r o r s , t h e n t h e e r r o r s i n i 0 i t s e l f a r e n o tn o r m a l l y d i s t r i b u t e d . C o n s e q u e n t l y , t h e d i s t r i b u -t ion o f e r ro r s o f X wh ich i s c a l cu lab le f ro m i0 ( seel a t e r ) i s n o t n o r m a l , a l t h o u g h i t i s u n l i k e l y t h a t s e r i -o u s e r r o r w o u l d a r i s e b y a s s u m i n g n o r m a l i t y .

IV . GENERAL EQUATIONSA . C u r r e n t a n d P o t e n ti a l

S u p p o s e t h a t k i i s t h e s p e c i f i c r a t e c o n s t a n t o fa n u n s p e c i f ie d r a t e - d e t e r m i n i n g s t e p i n t h e f o r w a r dd i r e c t i o n o f a r e a c t i o n ( i o n s d e p o s i ti n g ) . T h e n ,

k T ( (AG*)I~k~ = K h - exp ~ / , (16 )w h e r e ( A G* )~ i s th e s t a n d a r d f r e e e n e r g y o f t h ea c t i v a t e d c o m p l e x o f t h e r a t e - d e t e r m i n i n g s t e pw i t h r e s p e c t t o t h e i n i t i a l s t a t e ( h e r e a s s u m e d t o b eX g r a m i o n s o f h y d r o g e n i o n s c o n s t i t u t i n g p a r t o ft h e m o n o l a y e r a d j a c e n t t o t h e e l e c t ro d e s u r fa c e ,o f t e n t e r m e d t h e H e l m h o l t z d o u b l e l a y e r ) o f t h er e a c t i o n , w h e r e ~ i s t h e t r a n s m i s s i o n c o e f f ic i e n t,a n d w h e r e ]c a n d h h a v e t h e i r u s u a l m e a n i n g s . L e ta , b e t h e a c t i v i t y o f H 3 0 + i o n s i n t h e i n i t i a l s t a t e .T h e n t h e f o r w a r d v e l o c i t y ~ i s

: al]r (17)A l s o , t h e f o r w a r d c u r r e n t i s

; = ~XF, (18)w h e r e X i s t h e n u m b e r o f e le c t r o n s n e c e s s a r y s ot h a t o n e a c t o f th e r a t e - d e t e r m i n i n g s t e p c a n o c c u r .

Supp os e a po ten t i a l d i f fe rence AO~ i s app l i ed be -t w e e n t h e e l e c t r o d e a n d t h e i n i t i a l s t a t e o f t h e r e a c -t i o n . I f t h i s p o t e n t i a l d i f f e r e n c e i s p o s i t iv e i t r e t a r d st h e f l o w o f r e a c t a n t s o v e r t h e e n e r g y b a r r i e r o f t h er a t e - d e t e r m i n i n g s t e p , i . e . , i t m a k e s ( A G * ) I m o r ep o s i t i v e . T h e p o t e n t i a l d i f f e r e n c e i n c r e a s es ( A G* )Iby /~XFA~b~ wh ere /~2~q~c is th e po te nt ia l dif fer en cet h r o u g h w h i c h t h e e l e c t r o n s p a s s b e f o r e t h e y r e a c ht h e t r a n s i t i o n s t a t e . ( W o r k d o n e o n t h e s y s t e ma f t e r i t h a s p a s s e d t h e t r a n s i t i o n s t a t e d o e s n o ta f f e c t t h e v e l o c i t y of t h e r e a c t i o n . ) H e n c e 0 < f~ < 1 .

v a r i e s w i t h t h e r e a c t i o n m e c h a n i s m , a n d i s ac o m p l e x q u a n t i t y , e x c e p t i n c e r t a i n s i m p l e m e c h a -n i s m s . T h u s , i n t h e d i s c h a r g e r e a c t i o n H ~ O + ~ - e - +M H - t- H 2 0 , ~ = 1 i f t h e e n e r g y b a r r i e r is s y m -m e t r i c a l . G e n e r a l a n d l i m i t i n g v a l u e s o f ~ a r e e v a l u -a t e d b e l o w fo r c o m m o n m e c h a n i s m s . F r o m ( 16 ),(17 ) , and (18 ) ,

= KXF -f f a~ exp R T . (19)B y a s i m i l a r a r g u m e n t ,i -~ K},F aF ex p

(20). ( ( z x a * h - ( 1 - ~ ) x~ + ~ F )~ 7~

w h e r e ( A G* )2 i s t h e s t a n d a r d f r e e e n e r g y o f a c t i v a -t i o n o f t h e r e v e r s e r e a c t i o n r e f e r r e d t o t h e i n i t i a l



5/18

V o L 9 9 , N o . 4 C A T H O D I C H Y D R O G E N E V O L U T I O N R E A C T I O N 173s t a t e o f t h i s r e a c t i o n , a n d a F i s th e a c t i v i t y o f t h ee n t i t i e s i n t h i s i n i t i a l s t a t e .

I f 5 ~ = A ~ b,, t h e r e v e r s ib l e p o t e n t i a l ,- - i '= 0 , wh e re ~ = i0 = ~ . (21 )

Fr om (19 ) , (20 ), and (21 ) and s ince v = A~b~ - - &b~,z = io e x p \ - ~ ) , ( 22 )

= io ex p (-~ (1 -RT~)XvF~], (23)

= - i o L e x p k , - R T )(24)

- - e x p ( ( 1 - ~ X v F ) I "

E q u a t i o n ( 2 4 ) i s t h e m o s t g e n e r a l e x p r e s s i o n f o r t h ec a t h o d i c c u r r e n t , a n d r e p r e s e n t s a m o r e f r u i t f u l f o r mo f t h e r e l a t io n s h i p t h a n h a s b e e n s t a t e d h i t h e r t o .

S p e c i a l C a s e 1 . R e l a t i o n b e t w e e n i ~ a n d y a ta p p r e c i a b l e o v e r p o t e n t i a l s ( e . g. , v m o r e n e g a t i v et h a n a b o u t - 7 5 m y , se e s p ec i al c as e 3 ) .

E q u a t i o n ( 2 4 ) b e c o m e si ~ = i 0 [ e x p ( ~ X T/F ~/j, ( 25 )

o rR T R Tv = ~ In i0 -- ~,~ , in i~. (26)p ^ ~

E q u a t i o n ( 2 6 ) i s T a f e l ' s e q u a t i o n ,

o r= a - b l o g i o ( 2 7 )

R T= a - - a F I n i ~ ( 2 8 )s o t h a t , c o m p a r i n g ( 2 6 ) a n d ( 27 ) a n d ( 2 8) , i t f o ll o w st h a t :

R Ta = ~ I n i o , ( 2~ )2 . 3 0 3 R T

b - - - , (30)~ h Fa = fiX. (31)

E q u a t i o n (3 1) s h o w s t h a t a i s a c o m p o s i te q u a n t i t y ,a n d n e e d n o t b e b e t w e e n 0 a n d 1 s i n c e f l a n d Xc a n h a v e m a x i m u m v a l u e s o f 1 a n d 2 , r e s p e c t i v e l y .T h u s , t h e e x p e r i m e n t a l l y o b s e r v e d v a l u e s o f a o f2 , w h i c h h a v e b e e n d i f f i c u l t t o e x p l a i n h i t h e r t o ,a re a s pec ia l c a s e o f eq ua t ion (31 ) .

S p e c i a l C a s e 2 . - - R e l a t i o n b e t w e e n ir a n d v a tl o w o v e r p o t e n t i a l s ( e . g ., n l e ss n e g a t i v e t h a n - 2 0m v ) .

B y e x p a n d i n g e x p o n e n t i a l s , e q u a t i o n ( 2 4 ) b e -c o m e s ,

i~ = Xi0 ~F (32)R TT h u s , i ~ a n d ~ a r e l i n e a r l y r e l a t e d a t s u f f i c i e n t l y

l o w o v e r p o t e n t i a l s . A l s o , f r o m ( 3 2 ) a n d f o r m a l l ya l l o w i n g f o r t h e p o s s i b i l i t y o f Oi~//O~?d e p e n d i n g o n 7 ,

X = - - F i0 \ ~ / , - . 0 " ( 33 )X ( se e R e f . 2 1 ) c a n b e t e r m e d t h e e l e c t r o n n u m b e r

o f t h e r e a c t i o n a n d i s e s t i m a t e d e x p e r i m e n t a l l y b ya p p l y i n g e q u a t i o n ( 3 3) . A s s h o w n b e l o w , X i s a v a l u -a b l e d i a g n o s t i c c r i t e r i o n o f r e a c t i o n m e c h a n i s m s .

S p e c i a l C a s e 3 . - - R e l a t i o n s c o n n e c t e d w i t h n o n -l i n e a r i t y b e t w e e n ~ a n d l o g i c .

F r o m ( 2 4 ) ,~XnF~ [1 - f ] , (34)i~ = i0exp R T ]

w h e r ef = exp \ R T ] " (35)

W h e n t h e d e p a r t u r e o f t h e T a f e l l i n e [ s e e e q u a t i o n( 2 7 ) ] f r o m l i n e a r i t y d u e t o t h e r e v e r s e c u r r e n t i n( 20 ) i s j u s t d e t e c t a b l e e x p e r i m e n t a l l y , t h e n f i sj u s t d i s t i n g u i s h a b l e f r o m z e ro , a n d v = ~ . T h es m a l l e s t d e t e c t a b l e a n d s i g n i f i c a n t v a l u e o f f , i .e . ,f.~ , d e p e n d s o n t h e e x p e r i m e n t a l d e s i g n , b u t , p r o -v i d e d a m i n i m u m n u m b e r o f a b o u t f i ve pa i l' s of ob -s e r v a t i o n s f a l l w i t h i n a r e g i o n a b o u t 0 . 0 2 5 v o l t o ne i th e r s ide o f ~ .~ , i t m ay be a s s um ed th a t f~ i s 0 .05 .T h e r e f o r e , f r o m ( 3 5 ) ,

f ~ = 0 .0 5 = e x p \ R T ] , ( 36 )o r a t 2 0 ~ w i t h ~ e x p r e s s e d n u m e r i c a l l y i n v o l t s ,

0 . 075X = - - ( 37 )E q u a t i o n (3 7) g i v e s a n a l t e r n a t i v e m e t h o d o f e s-t i m a t i n g X e x p e r i m e n t a l l y a n d h a s n o t b e e n p r e -v i o u s l y d e s c r i b e d .

B . P o t e n t ia l a n d T i m e1 . D u r i n g B u i l d - u p o f O v e r p o t e n l ia l

F o r a c o m p l e t e l y p o l a r i s a b l e e l e c t r o d e , t h e n e tc o n s t a n t c a t h o d i c c u r r e n t i s t h e s u m o f t h e c o n -d e n s e r ( i' ) a n d f a r a d a i c ( i ' ) c u r r e n t s :

i~ = i ' + i ' . (38)L e t C b e t h e d i f f e r e n t i a l c a p a c i t y o f t h e e l e c t r o d e -

s o l u t i o n i n t e r f a c e . T h e n ,- C d ~ t = i ' d t (39)



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174 J O U R N A L O F T H E E L E C T R O C H E M I C A L S O C I E T Y A p r i l 1 9 52where dyt a n d d t a r e i n f i n i t e s i m a l c h a n g e s i n ma n d t i m e , t , r e s p e c t i v e l y . L e t ~ t a n d % b e v a l u e s o f

a t t imes t = t an d t = o r r e s pe c t ive ly . S ince i "i s g i v e n b y ( 2 4 ), t h e n f r o m ( 2 4 ), ( 3 8 ) , a n d ( 3 9 ),

[ (d~ = i~ - io e x pat ~ ] ( 4 0 )- - e x p ( ( i - R ~ X n t F ) ] .Spec ia l Case 1 . dC /d~ = 0 ; ~ t m o r e n e g a t i v e

t h an - 7 5 m y .E q u a t i o n ( 4 0 ) b e c o m e s

- C d ' - ~ t = i ~ - i ~ fl~_~F ) ] . (41)L e t

i " _ f , (42)io

a n d s u p p o s e . f ' < 0 . 05 s o t h a t i " i s n e g l i g ib l e i n ( 3 8 ),t h e n f r o m ( 38 ) a n d ( 3 9 ),

io = Cdm (43)d t "H e n c e , f r o m ( 4 2 ) a n d i f f ~ < 0 . 05 , d ~ t / d t i s a con -s t a n t . T o f i n d t h e r e g i o n o f o v e r p o t e n t i a l i n w h i c ht h i s r e s u l t i s v a l i d , w e a p p l y ( 3 8 ) w h i c h b e c o m e si~ = i " a t t = ~ , s o t h a t f r o m ( 2 5) ,

i~ = i 0 [ e x p ( / ~ F ) ] . (44)A l s o f r o m ( 2 5 ),

i " = io [ e x p ( f l ~ F ) ] . (45)T h u s , f r o m ( 4 2 ) , ( 4 4 ) , a n d ( 4 5 ) ,

f ' = e xp ( f l X ( ~ % r e ) F ) . (46)F o r e x a m p l e , l et f ' = 0 . 0 3 , t h e n f r o m ( 4 6 ) , t a k i n g at y p i c a l v a l u e o f 2 . 3 0 3 R T / ~ X F f r o m e x p e r i m e n t a s0 . 12 , % - w = - 0 . 1 5 , i .e . , t h e r e l a t i o n o f p o t e n -t i a l t o t ime i s l i nea r [ (43 ) i s va l id ] to w i th in 0 . 15v o l t o f t h e c o n s t a n t v a l u e n ~ .

S p e c i a l C a s e 2 . d C / d y = 0 ; ~ m o r e n e g a t i v et h a n - 7 5 m v ; ( v~ - v t) l es s n e g a t i v e t h a n - 2 0mg .

L e t ~ - ~ t = An ; a t t = h , A7 = A~I a n d a t t =t~, A~? = AV :. He nc e , f ro m (40) an d (44) ,d , , _ d t c . i ~ ( / ~ F ) ]

(47)9 [ 1 - e x p \ - - R - T / J "

O r , i n t e g r a t i n g b e t w e e n h a n d t2 a n d t h e c o r r e s p o n d -i n g v a l u e s o f A ~ ,

C R T [ x , . F 7h - t ~ - i o ~ X F e R T - / I n ( A n ~ - A ~ 2 ) . ( 4 8 )E q u a t i o n ( 4 8 ) i n d i c a t e s t h a t d u r i n g t h e i n i t i a lb u i l d - u p o f o v e r p o t e n t i a l , ~ t r e l a t i v e l y r a p i d l y

r e a c h e s p r a c t i c a l l y c o n s t a n t v a l u e s . F o r e x a m p l e ,w i t h 2 . 3 0 3 R T / B ~ F = 0 .1 , t h e t i m e r e q u i r e d f o ro v e r p o t e n t i a l t o r i s e f r o m w i t h i n 1 0 m v t o w i t h i n1 m v o f ~ i s t h e s a m e a s t h a t r e q u i r e d f o r t h e i n -t e r v a l 1 m y t o 0 .1 m v f r o m % .2 . Dur ing Decay(i ) R e la t ions in wh ich i t i s a ss umed tha t dC /d~ = O .

Fr om (41) w i th i~ = 0 , an d * t~ mo re nega t ivet h an - 7 5 m y ,

dt - C exp , (49)w h e r e n 't i s t h e o v e r p o t e n t i a l l s e c o n d s a f t e r t h e c o r n-m e n c e m e n t o f d e c a y . I n t e g r a t i n g ,

t - - io~XF exp \ R T ] - F eons t . (50)At t = 0, 7t~ = ~ . H e n c e ,

C o n s t . = - i 0 / 3 X ~ e x p . ( 51 )F r o m ( 5 0 ) a n d ( 5 1 ) ,

t - i 0~ X F e x p \ R T ] exp . (52)Spec ia l Cas e 1. ~ 't = % - A {, wh ere Av' is less

n e g a t iv e t h a n - 2 0 m y .U s i n g t h i s c o n d i t i o n in ( 52 ) y i e l d s

e x p R T ] ( 5 3 )flXFi~ tC R T

H a v i n g r e g a r d t o t h e c o n d i t i o n f o r A ~ ', ( 53 ) b e c o m e s, iot exp . (54)

E q u a t i o n ( 5 4 ) s h o w s t h a t t h e i n i t i a l d e c a y o f o v e r -p o t e n t i a l i s l i n e a r w i t h t i m e . H e n c e , l i n e a r e x t r a -p o l a t i o n s t o z e r o t i m e i n t h e c o m m u t a t o r m e t h o d o fm e a s u r i n g o v e r p o t e n t i a l a r e v a l i d u n d e r t h e a b o v ed e f i n e d c o n d i t i o n s .

Spec ial Case 2 . A~' m o r e n e g a t i v e t h a n a p p r o x i -m a t e l y - 5 9 m v ( n o rm a l d e c a y ); n t m o r e n e g a ti v et h a n - 20 m v .



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Vol . 99 , No . ~ C A T H O D I C H Y D R O G E N E V O L U T IO N R E A C T I O N 175Apply ing t h i s cond i t i on t o (52) , and t hus neg l ec t -

in g e x p ( ~ X 7 ~ F ) / R T gives,e x p ( x T ; Ft - f lXFio \ R T ]" (55)

, R T R T C R T9 . 7t = ~ In t -- ~--~ In BXFi0--" (56)Hen ce f rom (56) and (30),

dTi 2 .303RT- - b . ( 5 7 )d( log t) /~XF

E q u a t i o n ( 57 ) s h ow s th a t o v e r p o t e n t i a l d e c a y sloga r i t hmica l l y wi th t ime unde r t he above cond i -t i ons and t h a t t he s l ope o f t he l oga r i t hmic d ecaycurve i s t he same a s t ha t o f t he co r re spond ing Ta fe ll ine [cf . Bu t ler (24)] .Special Case 3. 7 't l es s n e g a t i v e t h a n - 2 0 m y .

From th i s cond i t i on , t he f a rada i c cu r ren t i" ,i s g iven by (32) , a l so f rom (38) , i n wh ich dur ingdecay i~ = 0 , and us ing (39) i t fo l l ows t ha t

dT' t ~ io 7t Fd t - C R T " (58)In t eg ra t i ng (58) ,

CRT ,t - k/~0ff m [ 7, [ + con st. (59)E q u a t i o n ( 59 ) s h o w s t h a t t h e d e c a y c u r v e o f o v e r -p o t e n t i a l a g a i n s t t im e b e c o m e s a s y m p t o t i c t o t h et ime ax i s , t he r e l a t i on be ing exponen t i a l . The equa -t i on may be used t o f i nd t he d i f f e ren t i a l c apac i t y(25) .(it) Rela t ions in which dC/d7 = f (7 ) .

D u r i n g d e c a y , i" = C dT'Jdt. Using t h i s i n (38 )and (39) g ives

d7t d,/t- c - c ( 6 0 )o r

i r JC = ( d ' ) _d T t ~ _ d [ , hd t ] (61)

w h e r e t h e v a l u e s o f C, dT't/dt, a n d dTt /d t r e fe r t o t hes a m e o v e r p o t e n t i a l 7 .

Fur the r , i f (54 ) i s app l i ed t o i n f in i t e s ima l changesd u r i n g d e c a y ,

s o t h a t= - - ~ e xp \\ d - i / , , R T / (62)

In C = In io R T \ d t / ,h " (63)

Eq ua t io n (61) enab l e s e s t ima te s o f d i f f e ren t ia l c a -p a c i t y o b t a i n e d f r o m t h e b u i l d - u p o f o v e r p o t e n t i a lt o b e c o r r e c t e d f o r f a r a d a i c c u r r e n t f r o m o b s e r v a -t i ons o f t he co r re spond ing decay cu rve (22) . Thed i f f e r e n t i a l c a p a c i t y m a y b e o b t a i n e d f r o m t h e d e -cay cu rve by app l i ca t i on o f (63 ) , i t be ing a l so neces -sa ry t o know the va lues o f b and l og i 0 o f t he co r -re spond ing Ta fe l l i ne .

C. Current and T emperature 2From (19) and (21) ,

t~T ( (AG *)~io = ~XF ~ - a l exp -

(o = KXF ~ - ar ex p ~-7~ / , (64)] , ( 6 5 )whe re tAG*)1 i s t he s t anda rd f r ee ene rgy o f ac t i va -t i on fo r t he fo rward d i r ec t i on o f t he r a t e -de t e rmin-ing s t ep a t t he r eve r s ib l e po t en t i a l . Hence ,

w h e r e( A H : ( 6 6 )0 = B e x p R T / '

B = KF ~ - a, exp , (67)a n d A H * a n d A S * a r e re s p e c t i v e ly t h e h e a t a n den t ropy o f ac t i va t i on co r re spond ing t o (AG*) I .A s s u m i n g A H * a n d A S * a r e n o t t e m p e r a t u r e d e -p e n d e n t , a n d t h a t o v e r sm a l l r a n g e s o f t e m p e r a t u r eB is constant , the plot of In i0 against ; 1 /7 ' has as lo p e o f - A H * / R .

F u r t h e r , w h e n n is m o r e n eg a t iv e t h a n - 7 5 m y ,(25) and (66) give

ic = B e A H * ; T ~ T F ) . (68)Hen ce , t ak ing B an d ~3~ a s t emp era tu re i nde -

p e n d e n t ,

( 0(ln ic )~ _ AH * + f l~TF (69)- o T ~ ] , R T 2From (26) , and wi th cond i t i ons a ssumed a s fo r (69 ) ,(0 , ) = - ( 7 0 )Fro m (69) and (70) i t fo ll ows t ha t

( 0 7 ) A H0* + ~ T F ( 71 )~o = flX FT2 O t h e r r e l a t i o n s b e t w e e n c u r r e n t a n d t e m p e r a t u r e h a v e

b e e n g i v e n b y A g a r ( 2 3 ) .



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176 ,JOURNAL OF THE ELECTROCHEMICAL SOCIETY A p r i l 1 9 5 2V . P O S S I B L E R E A C T I O N P A T H S O F T H E H Y D R O G E N

E V O L U T I O N R E A C T I O N 3A . S o u r c e o f P r o t o n i s H~O +

The possible paths are (M being a metal atom):s l o wH30 + + e _____~ MH + H20fastMH + MH ____, 2M + H2fastH~0 + + e ___~ MH + H~OslowMH + MH ___, 2M + H2slowH~0 + + e ___~. MH -~" H 2 0fastH a O + + M H + e _ _ _ , I .i~ + H 2 0fastH~O+ + e -- -~slowH~0+ + MH + e )

(A )

(B )

(C)

MH + H20 (D)H 2 -~ - H 2 0

B . S o u r c e o f P r o t o n i s H 2 0slowH20 + e , MH + OH - (E)fastMH + MH ____ . t {2 -~- 2MfastHoO + e _____~ MH + OH- (F)slowMH + MI~ __---~ H2 + 2MslowH20 + e ~ MH + OH - (a)fastH20 + MH + e ____> H2 + OH- + MfastH~.O + e ____~ MH + 0 H - (H)slow HHo -4- OH- + MH20 -4- MH + e _

In alkaline solution it is also possible that themeta l M ~+ ion discharge is an inte rmediate step inthe evolution reaction.

slowM~+ + ze ~ M 1M~ + zH20 fa st M~+ + zH + z O H - (I)MH + MH fast+- H~ + 2M

fastM]+ + ze M ~M~ + zH20 slow M~+ + zH +z OH - (J)MH + MH fa st H.~ + 2M

fas tM~+ + ze M 1M1 + zH20 _____~fastM]+ + zH + zO H- (K)

slowMH + MH ____~ H2 + 2Ma T h e r e a c t i o n p a t h s s u g g e s t ed a r e b y n o m e a n s e x h a u s -

t i v e , e . g . , i t is p o s si b l e t h a t t h e d i s c h a r g e o f h y d r o x o n i u mi o n s m a y o c c u r w i t h a n e l e c tr o c h e m i c a l d e s o r p t io n i n v o l v -i n g w a t e r , i . e ., H ~ O + M H + e ~ H 2 + O H - + M .

M~ + + ze slow Ml- - - - - - +M1 + zH,O fas t M~+ + zH + zOH- (L)- - - - - )H20 + M~H + e fast H2 +O H- +M 1M~ + + ze fast M~

- - - - - )Ml + zH20 slow M~+ + zH + zO H- (M)- - - - . +H20 + M1H + e fast H2 + OH - +M 1--_~M~+ + ze fast Mx- - - - - - - >~ 1 "31-Z H 2 0 fast M~+ -4- zH -4- zOH- (N)

)Ho.O + Mt H + e slow H 2 + OH- + M1- - - - - - +The kinetics may be complicated by the presence

of: (a) simultaneous reactions in which, say, twodesorptive reactions proceed at the same velocityin the steady state; (b) dual reactions in which twostages ill the evolution have virtually the sameenergy barrier (to within, say, 3 kcal); (c) linkedreactions, where the energy barriers of various stepsare of appreciably different heights, but the kineticsof the overall process depend upon the heightsof two or more energy barriers.

It has been shown recently that discharge fromwater molecules in acid solutions is improbable(5). Hence, reactions E to N are likely only in al-kaline solutions. The reactions A to D are the bestknown and the most reliable material exists by whichtheir kinetics, developed below, may be comparedwith experiment. A, B, and D are commonl y termed:The Slow Discharge, Atomic Hydrogen, and Elec-trochemical Mechanisms of the electrolytic evolu-tion of hydrogen, respectively.V I . T H E K I N E T I C S O F S P E C IF I C R E A C T IO N P A T H S

The most important reaction paths will be con-sidered here in some detail. It will be assumed thatthe adsorption of hydrogen upon the electrode isgoverned by a Langmuir isotherm and that thevelocity of the reverse desorption reaction may beneglected at potentials not near the reversible hy-drogen potential.A . T h e S o u rc e o f t h e P ro to n s i s H~O + a n d t h e A t o m i c

H y d r o g e n R e a c t i o n is D e s o r p ti v e ( P a t h s A a n d B )1 . G e n er a l K i n e t i c E q u a t i o n s

The reactions and velocities Vl, v2, va to be consid-ered a r e :

v~ MH, (72)3 0 + + e _ _ _ .~)2MH -- 4 H~O+ + e, (73)



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V o l . 9 9 , N o . 4 C A T H O D I C H Y D R O G E N E V O L U T I O N R E A C T I O N 177a n d

V3M H + M H _ ~ H 2 + 2 M ( 74 )L e t a l~ + b e t h e a c t i v i t y o f h y d r o g e n i o ns i n t h e

e l e c t r i c a l d o u b l e l a y e r i n g r a m e q u i v a l e n t s p e r l i t e r 4 ;a , b e t h e a c t i v i t y o f h y d r o g e n a t o m s o n t h e e le c -t r o d e s u r f a c e i n g r a m a t o m s p e r c m 2 ; a n d x b e t h ef r a c t i o n o f t h e s u r f a c e c o v e r e d w i t h a d s o r b e d h y d r o -g e n ( x i s m o r e r i g o r o u s l y d e f i n e d a s t h e f r a c t i o n o ft h e a v a i l a b l e s u r f a c e c o v e r e d ) . T h e n a n = l 0 - 9 xi f t h e r e a r e 10 1~ f r e e s p a c e s f o r a d s o r p t i o n p e r c m e ,o f t h e e l e c t r o d e s u rf a c e , a n d a s s u m i n g t h e a c t i v i t yc o e f fi c ie n t o f t h e a d s o r b e d h y d r o g e n i s u n i t y i tf o l l o ws , (~ = k~ all+(1 -- X) e xp - - 2 R T / ' (75)

v~ = /~ 1 0 -~ x ex p \ 2 ~ ] ' ( 7 6 )a n d

va = ka 10-1Sx , (77 )wh ere k ~ , k ~ , k 3 a r e sp ec i f i c r eac t i o n v e lo c i t i e s , an dt h e e n e r g y b a r r i e r o f t h e d i s c h a rg e r e a c t i o n i s a s -s u m e d t o b e s y m m e t r i c a l . 3 r = ( A r - - ~-) w h e r eA r i s t h e i n n e r p o t e n t i a l d i f f e r e n c e o f c a t h o d e a n ds o l u t i o n a n d ~- i s t h e p o t e n t i a l d i f f e r e n c e b e t w e e nt h e b u l k o f th e s o l u t i o n a n d t h e p l a n e p a s s i n gt h r o u g h t h e c e n t e r o f t h e i o n s a d j a c e n t t o t h ec a t h o d e s u r f a c e .

I n t h e s t e a d y s t a t e ,v~ - v2 - 2v3 = 0. (7 8)

S o lv in g (7 5 ) , ( 7 6 ) , ( 7 7 ) , an d (7 8 ) fo r x g iv es t h er e a l s o l u t i o n :

- - ( a , + a 2 ) - 4- g / ( a l + a2) ~-+ 8a, a3 ( 7 9 )4a 3~-w h e r e

a n d

ACF '~a l = / q a n + e x p 2 ~ ] ' ( 80 )

a 2 = 1 0 -9 k ~ e x p \ 2 ~ / ' ( 8 1)

a3 = 10-1Sk3. (82 )T h e c u r r e n t i s , t h e r e f o r e ,

i~ = 2Fv3 = 2F10-~Sk~x ~ = 2Fa 3x ~ ( 8 3 )= F [ - - ( a l "-~ a2) -4- % /( a l -4- a2)2 -4- 8ala.~]2. (84)8a 3

4 For ease o f represen ta t ion the suff ix H30 + is replacedby H +.

2 . K i n e t i c s w h e n D i s c h a rg e i s R a t e - D e t e r m i n i n g( P a t h A )

(i ) G e n e r a l c o n d i t i o n f o r s l o w d i s c h a r g e m e c h a n i s m .- - T h e c o n d it io n is

10 (al -]- a2) < a3, ( 8 5 )w h e r e t h e f a c t o r 1 0 i s a n a r b i t r a r y l i m i t o f s i gn i fi -c a n c e . T h e u s e o f t h e t e r m s " a " i n t h e c o n d i t i o nr a t h e r t h a n t h e " k " t e r m s p r o v i d e s f o r t h e p o s s i b i l -i t y o f c h a n ge s o f m e c h a n i s m o c c u r r i n g o n v a r y i n gp o t e n t i a l o r h y d r o g e n i o n c o n c e n t r a t i o n . T h el i n k i n g o f a~ a M a 2 b y a p o s i t i v e s i g n i n t h e c o n d i t i o ni s c le a r , s i n c e , b y t h e n a t u r e o f t h e r e a c t i o n s c o n -c e r n e d , a d e c r e a s e i n a 2 i n c r e a s e s x , t h e r e b y d e -c r e a s i n g a ~ a n d i n c r e a s i n g a 3 : t h a t i s , a d e c r e a s e i n a2i n c r e a s e s t h e p r o b a b i l i t y o f t h e s l o w d i s c h a r g em e c h a n i s m , a s s h o w n b y t h e c o n d i t i o n ( 8 5 ) a b o v e .

(ii) C o v er ag e o f s u r f a e e . - - F r o m ( 8 5 ) a n d p r o v i d e d( a ~ + a 2 ) 2 > 1 0 a 2 ( a ~ + a ~ ) , i . e . ,

a l > 9 a2 , ( 8 6 )i t i s e a s y t o s h o w t h a t 8a~a3 > (a~ + a2) 2 . H en ceu s i n g t h i s c o n d i t i o n i n ( 7 9 ) i t f o l l o w s

x = 9 (87)(iii) T a f e l l i n e . - - F r o m (8 0 ) , ( 8 3 ) , an d (8 7 ) i t

f o l l o w s (c = F k l a H + e x p - - 2 R T / " (88)H e n c e f r o m ( 2 7 ) , ( 2 9 ) , a n d ( 3 0 ) f o r t h e s l o w d i s -c h a r g e m e c h a n i s m ,

a = 0 .5 ; (89)an d , s in ce X = 1 ,

= 0 .5 . (90)( iv ) E f fe c t o f p H i n p u r e d i l u te a c i d s o l u t i o n . -

A s s u m i n g t h a t t h e S t e r n m o d e l o f t h e e le c t r ic a ld o u b l e l a y e r p r e v a i l s a t t h e m e t a l - s o l u t i o n i n t e r -f a c e , t h a t t h e s o l u t i o n i s d il u t e , t h a t s p e c i fi c a d -s o r p t i o n o f i o n s i s a b s e n t , a n d t h a t t h e i n t e r r a c i a lp o t e n t i a l c o n d i t i o n s a r e m o r e t h a n a b o u t 0 . 3 v o l t sf r o m t h o s e o f t h e e l c c t r o c a p i l la r y m a x i m u m , t h e f o l -l o w i n g e q u a t i o n s m a y b e v a l i d l y u s e d ,

a n+ = ( an +) B e x p ( - ~ T F ) ,

a n d

A C e = A C t + n ,A r = R T In ( a l l+ ) . ,

t" = Co nst . - t - ~ ' In (aH+)B,

(91)(92)(93)

(94)



10/18

1 7 8 J O U R N A L O F T H E E L E C T R O C H E M I C A L S O C I E T Y A pr i l 1952where (an+)B is the activ ity of hyd rogen ions in theb u l k o f t h e s o l u t i o n . U s i n g t h e s e e q u a t i o n s i n ( 8 8 )

2 R Ti t i s f o u n d t h a t n = C o n s t . I n i~ . T h e r e -Ff o r e , o v e r p o t e n t i a l i s i n d e p e n d e n t o f t h e p H o f t h es o l u t io n w i t h t h e a b o v e m e c h a n i s m u n d e r t h e c o n -d i t i o n s ( 8 5 ) a n d ( 8 6 ) .

( v ) Effect of p H in the presence of excess neutrals a l t . - - I n t h e p r e s e n c e o f e x c e s s n e u t r a l s a l t ( e . g .,L aC 1 3) ~ d e c r e a s e s t o a c o n s t a n t v a l u e n e a r z e r o.U n d e r t h e s e c o n d i t i o n s ( 9 1 ) , ( 9 2 ) , ( 9 3 ) , a n d ( 9 4 )m a y b e c o m b i n e d t o

77 = C on st . - 2R_F l n i ~ - t - % T I n ( a , , + ) B . ( 9 5 )E q u a t i o n ( 95 ) s h o w s t h a t u n d e r t h e a b o v e c o n d i t i o n s( 8 5 ) a n d ( 8 6 ), o v e r p o t e n t i a l s h o u l d d e c r e a s e n u -m e r i c a ll y b y 58 m v a t 2 0~ u p o n d e c r e a s in g t h ep H o f t h e s o l u t i o n b y o n e t ~ n i t .( v i ) Effect of neutral salt at constant p H . - - F r o m( 8 8 ) , ( 9 2 ) , ( 9 3 ) , a n d ( 9 4 ) , a n d c o n s i d e r i n g ( a l l + ) ,a s c o n s t a n t ,

,7 = Co n s t . 2 R T In ic -- ~-. (96 )YS i n c e o n a d d i t i o n o f n e u t r a l s a l t t o t h e e l e c t r o l y t e~" b e c o m e s m o r e p o s i t i v e a n d a p p r o a c h e s z e ro ,o v e r p o t e n t i a l i n c r e a s e s n u m e r i c a l l y .3. Kinet ics when Atomic Combinat ion is Rate-Deter-

m i n i ng ( P a t h B )( i) Gen eral condi tion fo r atomic hydrogen m echa-

n i s m . - - C o m p a r i n g w i t h ( 8 5 ) , t h e c o n d i t i o n i s10ca < a l ~ a~. (97)

(ii) Coverage of sur face.--Using c o n d i t i o n ( 9 7 )a n d a l s o t h e c o n d i t i o n

9a2 < a l , (98)a n d a l s o s i n c e % / 1 ~ - n = 1 + 8 9 w h e r e n i s s m a l l ,i t f o l l o w s

a ,x - . (99)a l + 6 2(i i i) T a f e l l i ne . - - F r om ( 8 0 ) , ( 8 1 ) , ( 8 2 ) , ( 8 3 ) , a n d

( 9 9 ) ,i ~ - - 2 F 10 -1 8 ks a la l - ~ - 6 2

---- 2F k s l 0 -1~ k~lO i A4~F 91 - I- ~a ~H + e x p ~d ( A ~ ) y i e l d sE v a l u a t i o n o f d ( l n ic )

d(A ~b) _ b _ 1 + klk2 H--------~0-9 exp \~][A~bF~d ( l n i ~) 2 . 3 0 3 2 F k ~ 1 0 9 ( A4 ~F ~ "R T k l a a e x p \ R T ]

( 101)

H e n c e v a l u e s o f a a n d , t h e r e f o r e , o f f l a r e c o m p l e xf u n c t i o n s o f p o t e n t i a l , a n d c a n b e c a l c u l a t e d f r o m( 1 0 1 ) b y t h e u s e o f ( 2 9 ) a n d ( 3 0 ) , t a k i n g ~ a s 2 .T w o i m p o r t a n t l i m i t in g c o n d i t i o n s a r i se f r o m ( 1 0 1 ) .Lim it ing condit ion 1 :

I f k 2 1 0 - 9 e x p > 1 0 , ( 1 0 2 )

b - 2 . 3 0 3 R T _ 0 . 0 2 9 a t 2 0 ~ ( 1 0 3 )2 FT h e r e f o r e ,

a = 2 a n d ~ = 1 , a s } , = 2 ( 1 0 4 )Limit ing condi t ion 2 :

I f A 0 t e n d s t o - ~ ,b ~ ~ , ( 1 0 5 )

s o t h a t a ~ 0 , a n d ~ ~ 0 . ( 1 0 6 )T h e f o r m s o f ( 1 0 0 ) c o r r e s p o n d i n g t o ( 1 0 3 ) a n d ( 1 0 5 )a r e , r e s p e c t i v e l y ,

[k laI t+12 ( 2 A ~ b F ~ic = 2 F k s [ _ ~ - 2 J e xp R T ] 'a n d

i c = 2 F k a l 0 - 18 .

( 1 0 7 )

( 1 0 8 )E q u a t i o n ( 1 0 8) c le a r l y i n d i c a t e s t h e l i m i t in g c u r -r e n t c a u s e d b y t h e a t o m i c c o m b i n a t i o n r e a c t io n .

( i v ) Ef fec t o f pH in pure d i lute ac id so lu t io n . -U s i n g ( 9 1 ) , ( 9 2 ) , a n d ( 9 3 ) i n ( 1 0 7 ) i t f o l l o w s

R T= C o n s t . - 2 F - I n i c . ( 1 0 9 )E q u a t i o n ( 10 9 ) i n d i c a te s t h a t w i t h t h e a b o v e m e c h -a n i s m o v e r p o t e n t i a l i s i n d e p e n d e n t o f t h e p H o ft h e s o l u t i o n . I t is e v i d e n t f r o m ( 1 0 8 ) t h a t t h e m a g -n i t u d e o f t h e l im i t in g c u r r e n t i s i n d e p e n d e n t o f p H .

( v ) Effect of pH in the presence of excess neutrals a l t . - - E qua t i on ( 1 09 ) s h o w s t h a t ~ i s i n d e p e n d e n to f ~" a n d , t h e r e f o r e , i s i n d e p e n d e n t o f p H i n t h ep r e s e n c e o f e x c e s s n e u t r a l s a l t. E q u a t i o n ( 1 0 8)s h o w s t h a t t h e l im i t in g c u r r e n t i s i n d e p e n d e n t o f t h ep r e s e n c e o f n e u t r a l s a l t.

( v i ) Effect of neutral salt at constant pH. ~ i su n a f f e c t e d b y t h e p r e s e n c e o f n e u t r a l s a l t ( s ee 1 0 9 ).4. Min im um Coverage o f Ca thode by Hydrogen for

Ato mi c Combination to be DesorptiveF r o m ( 1 6 ), ( 7 7 ), a n d ( 8 3 ),

2 F ~T 1 0 -1 8 x2 , ( 1 1 0 )ci f (AG*)I i s t a k e n a s z e r o t o g i v e a m a x i m u m v e l o c -i t y o f c o m b i n a t i o n , ~ = 1 , a n d k l i n ( 1 6 ) i s i d e n t i f i e d



11/18

Vol . 99, No. 4 C A T H O D I C H Y D R O G E N E V O L U T I O N R E A C T I O N 1 7 9w i t h k a i n ( 8 3 ) . H e n c e , t h e l e a s t p o s s i b l e c o v e r a g ef o r t h e a t o m i c h y d r o g e n r e a c t io n t o m a i n t a i n ac u r r e n t d e n s i t y o f i~' a m p / c m ~ i s g i v e n b y

x = 1 0 ~ . ( 1 1 1 )B. The Source of Protons is H ~ O + and the Electro-

chemical Reaction is Desorptive (Paths C and D)1 . General K ine t i c Equat ions

T h e r e a c t i o n s a n d v e l o c i t i e s t o b e c o n s i d e r e d a r eVlH a O + q - e - - - ~ M H , ( 72 )

M H _ _v ~_ . Ha O + + e , ( 7 3 )a n d

V4H a O + + M H - b e - - - - * H ~ . ( 1 1 2 )v , a n d v 2 a r e g i v e n b y ( 7 5 ) a n d ( 7 6 ) . v~ i s g i v e n b y

v~ = tc~lo-ga~+x e x p - - 2 R T ] " ( 1 1 3 )T h e s t e a d y s t a t e v a l u e o f x y ie l d e d b y r e a so n i n g

a n a l o g o u s t o t h a t l e a d i n g t o ( 7 9 ) i s

w h e r ex - a l ( 1 1 4 )al -~- a2 -~- a4'

a 4 = k 4 1 0 - g a ~ * e x p - - 2 R T ] "T h e c u r r e n t i s , t h e r e f o r e ,

2Fk~k4 1 0- 9( al l+ ) 2 e x p ( z~4~F'~2RT](k ~ - b k 4 1 0 - ~ ) a . + q - k 2 1 0 9 e x p \ ~ ]

F r o m ( 1 1 6 ) ,d ( a ~ )

d ( l n i c )1 + k 21 o ~ ( ~ F ~(/ c~ ~ k 4 1 0 - 9 ) a ~+ e x p \ R T ]

( 1 1 5 )

9 ( 1 1 6 )

( 1 1 7 )2 R T 1 + (k ~ ~ - k 4 1 0 - 9 ) a n + e x p \ ~ - ] _ ]

- (k~ + k, IO-9)aH+R T e x p \-~/32. Kinet ics when D ischarge is Rate-D etermining

(Path C)(i ) General condition for slow discharge mechanism.

- - T h e c o n d i ti o n i s10(a~ + a2) < a t . ( 1 1 8 )

(it) Coverage of sur face.--Uti l iz ing ( 1 1 8 ) i n ( 1 1 4 ) ,a n d a l s o f r o m ( 8 0 ) a n d ( 1 1 5 ),

x = a~/a4 = k~ /lO-gk4. ( 1 1 9 )(ii i) T a f e l l i ne . - - C ond i t i on ( 1 1 8 ) u t i l i z e d i n ( 1 1 6 )

g i v e s ,A C F ~ ( 1 2 0 )i c = 2 F k l a H + e x p 2 R T ] '

w h i c h r e l a t i o n i s v e r y s i m i l a r t o t h a t f o u n d f o r ar a t e - d e t e r m i n i n g d i s c h a r g e r e a c t i o n f o ll o w e d b y a na t o m i c h y d r o g e n d e s o r p t i o n s t e p . H e n c e , a = 0 . 5a n d f l = } a s h = 2.

( i v ) Effect of pH in pu re dilute acid solution, ( v )ef fect of p H in presence of exce ss neutral sal t, a n d( v i ) effe ct of neutral salt at constant p H . - - T h e s et h r e e e f f e c t s a r e a s a l r e a d y g i v e n i n S e c t i o n A , 2 .3. Kinetics when Electrochemical Step is Rate-Deter-

m i n i ng ( P a t h D )(i ) Ge ner al condition fo r electrochemical mecha-

n i s m . - - T h e c o n d i t i o n i s10a4 < a l -b a2 . (121 )

(it) Coverage o f sur face . - -Spec ia l c a s e ( a )10al < a2 . (122 )

F r o m ( 1 1 4 ) , ( 1 2 1 ) , a n d ( 1 2 2 ) ,X = a t ~ a 2 . ( 1 2 3 )

S p e c i a l c a s e ( b )10a2 < a t . ( 1 2 4 )

F r o m ( 1 1 4 ), ( 1 2 1 ), a n d ( 1 2 4 ),x -~ 1. (125)(i i i) Tafe l l ine . - -Spec ia l c a s e ( a ) . C o n d i t i o n s

( 1 2 1 ) a n d ( 1 2 2 ) . F r o m ( 1 1 6 ) , (c = 2 F k ~ k~(a~+)2 e x p . ( 1 2 6 )F r o m ( 2 7 ) , ( 2 9 ), a n d ( 3 0 ) i t f o l l o w s t h a t

a = 3 / 2 ( 1 2 7 )as } , = 2 , f l - - 3 / 4 . (128 )

( i v a ) Ef fec t o f pH in pure d i lu te ac id so lu t ion . -U s i n g ( 9 1 ) , ( 9 2 ) , ( 9 3 ) , a n d ( 9 4 ) i n ( 1 2 6 ) i t f o l l o w s

2 R T= C o n s t . - - - I n G . ( 1 2 9 )3 FH e n c e w i t h t h e a b o v e m e c h a n is m u n d e r t h e a b o v ec o n d i ti o n s o v e r p o t e n t i a l i s i n d e p e n d e n t o f t h e p Ho f t h e s o l u t i o n .

( v a ) Effect of pH in the presence of excess neutrals a l t . - - F r om ( 9 1 ) , ( 9 2 ) , ( 9 3 ) , a n d ( 1 2 6 ) a n d a s ~" - ~ 0i t f o l l o w s t h a t :

= C o n s t . 2 R T I n i c q- RT- 3 - F - ~ - I n ( a H + ) s . ( 1 3 0 )



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180 J O U R N A L O F T H E E L E C T R O C H E M I C A L S O C I E T Y A p r i l 1 9 5 2E q u a t i o n ( 13 0) s h o w s t h a t u n d e r t h e a b o v e c o n d i -t i o n o v e r p o t e n t i a l d e c r e a se s n u m e r i c a l l y b y 1 9 m va t 2 0 ~ u p o n d e c r e a s in g th e p H o f t h e s o l u ti o n b yo n e u n i t .

(v i a ) Effec t o f neutral sal t a t cons tant p H . - - F r o m(91) , (92 ) , (93 ), and (126) a nd cons ide r ing (a . + )Ba s c o n s t a n t ,

2 R T- - Co ns t . - 3 F - In i , - ~ ' /3 . (131)H e n c e , a s ~" b e c o m e s m o r e p o s i t i v e a n d a p p r o a c h e sz e ro o n a d d i t i o n o f n e u t r a l s a l t , o v e r p o t e n t i a li n c r e a s e s n u m e r i c a l l y .

(iiib) T a f e l l i n e . - - S p e c i a l cas e (b ) . C ond i t ions(121) and (124) . F rom (116) ,

io = 2FkaaH +10 -9 exp 2 R T ] "

F r o m ( 2 7 ), ( 2 9 ) , a n d ( 3 0) i t f o ll o w s t h a ta = 0 .5 (133)as h = 2 , /3 = 1/4 . (134)

( ivb) Ef fe c t o f pH in pur e d i lu t e ac id s o lu t ion ,(vb) e f fec t o f pH in the presence of excess neutralsalt, (vib) e ff ec t o f ne u t r a l s a l t a t c ons tan t p H . - -Cons ide ra t ion o f (91 ) , (92 ) , (93 ) , and (132) s howst h a t t h e a b o v e t h r e e e f f e c ts a r e a s a l r e a d y g i v e n i nS e c t i o n A , 2 .C . The Sour c e o f t he Pr o tons i s Wate r and a Me ta l

C a t ion Tak e s Pa r t i n the Re ac t ion : A Spe c ia lCase

R e f e r e n c e t o t h e r e a c t i o n p a t h s E t o N i n d i c a t e st h a t m a n y m o r e p o s s i b i l i t i e s e x i s t f o r t h e m e c h a -n i s m o f t h e e v o l u t i o n o f h y d r o g e n w h e n t h e s o u r c eo f t h e p r o t o n s i s w a t e r t h a n w h e n i t i s t h e h y d r o x o -n i u m i o n. S in c e l it t le d a t a a s y e t e x i s t w i t h w h i c h c o m -p a r i s o n m a y b e m a d e , t h e k i n e t ic s o f th e s e s c h em e sw i l l b e f o r m u l a t e d h e r e o n l y i n o n e s p e c i a l c a s e .I t h a s b e e n r e c e n t l y s h o w n b y B o c k r i s a n d W a t s o n( 6) t h a t t h e e v o l u t i o n o f h y d r o g e n a t m e r c u r y c a t h -o d e s f r o m a q u e o u s a l k a l i n e s o l u t i o n s i n v o l v e s t h ea l k a l i o r a l k a l i n e e a r t h m e t a l c a t i o n . H e n c e , t h epos s ib i l i t i e s in th i s c a s e a re :

s lowM ~+ + ze ~ M / H g ( a)M / H g + z H 2 0 f_~ ast M , + + z H g H + z 0 H - (b )

o r,f a s tM ~+ + ze - - - + M / H g ( c )

M / H g f a s t M ~+ + z e ( d )M / H g + z H2 0 sl~ + z H g H + z O H - (e)

I n b o t h r e a c t io n s c h em e s d e s o r p t i o n o f h y d r o g e nm a y o c c u r b y m e a n s o f t h e r e a c t i o n s ,

H g H + H g H ~ H 2 + 2 H g ( f)H 2 0 + H g H + e ~ H : + O H - . ( g)

I t i s i m p r o b a b l e t h a t r e a c t i o n ( a ) o c c u rs b e c a u s ee v i d e n c e i s a v a i l a b l e ( 7 ) t h a t a l k a l i m e t a l d e p o s i t i o no c c u rs o n H g w i t h o u t b e i n g a c c o m p a n i e d b y a n a p -p r e c i a b l e o v e r p o t e n t i a l . R e a c t i o n s c h e m e c de f wi l l ,t h e r e f o r e , b e f o r m u l a t e d . I t c a n b e s h o w n t h a t v e r ys i m i l a r r e s u l t s a r e o b t a i n e d f o r t h e s c h e m e c de g (6) .

L e t v5 b e t h e v e l o c i t y o f r e a c t i o n c , v~ t h a t o f d ,v7 th a t o f e, and Vs th a t o f f . L e t X l be the f rac t iono f th e s u r f a c e o f m e r c u r y c o v e r e d w i t h a l k a l i m e t a la t o m s i n t h e s t e a d y s t a t e a n d x2 b e t h e s i m i l a r f r a c -t i o n f o r h y d r o g e n a t o m s . T h e n ,(5 = k s a n + ( 1 - - X l - x2 ) e x p 2 ~ ] ' ( 13 5)

v6 = k 6 10 - 9 x l e x p \ 2 R T - ] ' ( 1 36 )v r = k 7 ( 1 0 - 9 X l ) t a H 2 0 , (137)

w h e r e x i i s r a i s e d t o t h e p o w e r 8 9 n a c c o r d a n c e w i t ht h e e x p e ri m e n t a l d a t a o f J o fa a n d P e c h k o v s k a y a( 8 ) o n t h e v e l o c i t y o f r e a c t i o n b e t w e e n p o t a s s i u ma m a l g a m a n d w a t e r , a H ~ o i s t h e a c t i v i t y o f w a t e r ,a n d k s -k r a r e v e l o c i t y c o n s t a n t s .

A t l o w a n d m e d i u m c u r r e n t d e n s i t i e s, l > > x l , x 2.A l s o , i n t h e s t e a d y s t a t e ,

v5 - - v 6 - - v r = 0 , (138)v7 -- Vs = 0. (13 9)

A c c o r d i n g t o t h e m e c h a n i s m s u g g e s t e d ,k~ all+ ex p 2 R T ] >> k710 - 9/2 aH2o

(140)< ~ kG 1 0 9 e x p \ 2 R T - ] "

F r o m ( 1 4 0 ) b y a n a r g u m e n t s i m i l a r t o t h a t u s e d i nt h e d e r i v a t i o n o f ( 8 8 ) , o n e o b t a i n s

( k 4 8 9 ~ ( z ~ F ~ ( 14 1 )i o = Fk 7 \ k 6 ] aH20(aM*+)~ x p 2 R T - ] "B u t ,k 5ke exp _ ( a G * ) ~ - ( a G * ) ~ )R-T (142)(e x p - - R T ] 'w h e r e A G5 i s th e s t a n d a r d f r e e e n e r g y c h a n g e i nr e a c t i o n ( c) . B e c a u s e t h e d e p a r t u r e f r o m i r re v e r s -ib i l i t y in (135) an d (136) i s s m a l l i t fo l lows th a ta p p r o x i m a t e l y ,

AG5 = -- ze~oF (143)



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Vol . 99, No. 4 CATHODIC HYDROG EN EVOLUTION REACT ION 181w h e r e e '0 i s t h e r e v e r s i b l e e l e c t r o d e p o t e n t i a l f o r t h ea l k a l i m e t a l c o n c e r n e d a t u n i t a c t i v i t y i n m e r c u r y .H e n c e , f r o m ( 1 4 1 ) a n d ( 1 4 2 ) a n d ( 1 4 3 ) ,i r = zFau~o ( a M ~ + )' k 7 e x p 2 ~ [ e0 - - A 4 ] . ( 1 4 4 )A r e a s o n a b l y g o o d v a l u e o f e ~ c a n b e o b t a i n e d f r o mt h e e m f o f a r e v e r s ib l e a m a l g a m e l e c t r o d e o f t h et y p e M a m a l g a m / M ~+ i o n s a t u n i t a c t i v i t y . I fi t is a s su m e d t h a t t h e i n t e r a c ti o n e n e r g y b e t w e e n Ma n d H g i s i n c l u d e d i n e~ , a n d t h a t i t i s c o n s t a n t

T A B L E I . Characteristics of various

B. Numerical Calculat ions1. General Remarks and Prel iminary Calculat ionsThe results of calculations presented here are to

be regarded as of order accuracy only. This is dueto (i) the approximation involved both in theequations themselves and in the method of numer-ical application. (e.g., calculation of reversible elee-trode potential, see below), and (i i) the inaccuracyof some of the experimental and theoretical data.The following results are intended to be exemplify-

mechanisms of cathodic hydrogen evolution

C h a r a c t e r i s t ic o f m e c h a n i s m

A c i d s o l u ti o n m e c h -a n i s m s

A l k a l i n e s o l u t i o nm e e h a I l i s m s

S l o w d i s c h a r g e

C o n d i t i o n s f o r a p p l i c a t i o n

1 0 (aL + a2 ) < a t9a2 < ata s t a t m n i e H ( A )

S l o w a t o m i c H 1 0 as < a l + a~F a s t d i s c h a r g e ( B ) 9 a~ < a lS l o w d i s c h a r g e 1 0( a~ + a ~ ) < a ~F a s t e l e c t r o c h e m i c a l ( C )S l o w e l e c t r o c h e m i c a l

F a s t d i s c h a r g e ( D )

S l o w d i s c h a r g e f r o m H t l 3w i t h e i t h e r f a s t a t o m i c n( E b o r f a s t e l e c t r o c h e m i c a lf r o m H ~ O * ( G )

S l ow M / H g ) r e a c t i o nF a s t M z + d i s c h a r g eF a s t a t o m i c H ( J )

a , + a2 > 1 0 a4[ a~ > 1 0 m

'al > 10a2

A n a l o g o u s t o m e c h a n i s m sw i t h d i s c h a r g e f r o m | h O +

a s > 1 0 a T < a e

W i$y lm e t renelX b a n

o l

I2 2 . 1

- - i2 I I

I2 t I

- - i

z 2

cat[ LO(~nngY I a H + ) B A r , im r I

- - i

m1 ;

11

N e u t r a l s a l te f f e c t a tc o n s t a n t p HP u r e s o l o. + E x c e s sn e u t r a l s a l t

N i l ~ m o r e n e g .- - v R T

N i l N i l N i l

N i l ~ m o r e n e g .- - ~ R TF

N i l 1 - T R T ~ m o r e n e g .l + v F

N i l 1 - ' y R T ~ m o r e n c g .F

- - 2 R T - - R T ~ m o r e p o s .Y Y

- - R T R T 0 [ n( a~ u z +) B - - R T~ - 4 7 ~ - 9 0 l n ( a , + ) B - Y - N i l

I f ~ = 0 . 5~ , = B t t r r ie r d i s y m m e t r y f a c t o r = F r a c t i o n o f p o t e n ti a l a s s i s t i n g f o r w a r d d i r e c t io n o f r a t e - d e t e r m i n i n g s t e p .* A s s u m i n g u n i v a l e n t a l k a l i m e t a l i o n.~: A s s u m i n g t h a t r e l a t i o n ~- = c o n s t 4 - ~ I n ( a n + ) B is v a l i d .

over a small change of activity, then the electrodepotential e, is given by

, 1e a = e 0 + - - I n ~ , ( 1 4 5 )where C M ---- concentration of alkali metal M inHg. From (145), knowing e, experimentally, e'0 isfound.V I I . D I s c u s s i o N O F M E C H A N IS M A T H g , A g , N i ,

A N D P t C A T H O D E SA. Table of Dist ing uishing Cri teria

These are given in Table I which is based uponthe general results to be found in Sections IV and VI.

ing rather than exhaustive (e.g., throughout, theconcentration of hydroxonium ions in the electricaldouble layer has been taken to be 10-1 gram equiv-alents per liter and no quantitative examinationhas been made of the effect of variation of concen-tration).Evaluation of terms such as exp (AeorF) /RT hasbeen made by expressing A4: as the potential of thereversible hydrogen electrode with respect to theeleetroeapillary maximum of the metal concerned.The approximations involved in this procedure,involving the neglect of the potential difference atthe interface due to adsorbed solvent dipoles,should be recognized; in comparison of rates onvarious metals, this error is less serious because it is



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182 JOURNAL OF THE ELE CTROC HEMI CAL SOCIETY Apr i l 1952reasonable to assume that the dipole contributionsare approximately the same at different metals.

The terms AG~*, AG2*, AG*, and AG* (where AG*is a standard free energy of activation; 1 and 2refer respectively to the forward and reverse direc-tions of the discharge of hydroxonium ions; ~nd 3and 4 refer respectively to the forward atomic hy-drogen and electrochemical desorption steps) havebeen obtained as follows. AG* and AG* have beentaken from calculations by Parsons (26) of the ener-getics of the discharge reaction 5. AG* (for the atomic

T A B L E I I. C e r t a i n n u m e r i c a lRe v e r s i b l e IH poten- ILog i0 ]tiai referred AG~*Ca- (aa+ = to electro- kcalthode 0.1) capillar ymaximumvolts

H gA gN i

-12 +0.20-7 --0.046- 6 - - 0 . 3 0 t

3 83131

Log k~

- 1 5 . 5- 1 0 . 3- 1 0 . 3

u a n t i t i e s a t 2 0 ~

AG~* Log k~ k~/k2kcal

2 3 .2 - 4 . 5 - - 1 1 .02 3 . 9 - - 5 . 0 - 5 . 32 3 . 6 - 4 . 7 - 5 . 6

V a l u e o b t a i n e d f r o m i n t e r p o l a t i o n o f a n o b s e r v e d r e la -t i o n b e t w e e n 9 a n d t h e p o t e n t i a l o f t h e e l e c t r o c a p i l l a r ym a x i m u m f o r a n u m b e r o f m e t a l s .T A B L E I I I . P o t e n t i a l c o n d i t i o n s f o r s l o w d i s c h a rg e m e c h -

a n i s m ( P a t h A ) a t 2 0 ~Cathode Condi tion (85) : Condi tion (86) :Overpotential in volts Overpotent ial in volts

H gA gN i

M o r e p o s i t i v e t h a n - 1 .4M o r e p o s i ti v e t h a n - 0 . 5 4M o r e p o s i t iv e t h a n - 0 . 2 9

M o r e n e g a t i v e t h a n- 0 . 4 3

A l l v a l u e s ~ s a t i s f yc o n d i t i o nA l l v a l u e s s a t i s f yc o n d i t i o n

T A B L E I V. S u r f a c e c o v e r a g e w i t h h y d r o g e n a t v a r i o u s o v e r -p o t e n t i a ls ( P a t h A )

Overpotentia]Cathode (volts) --0A

Hg Coverage x l0 -6"2Ag Cover age x 10 2"6Ni Coverage x 10 1'5

--0.3 -0.5 --0.7 --1.0 --1s

10 a'4 10 4.5 10 3.4 10 2"4 Sat, d.10 L~ 10 ~ Sat d. surface.10 ~ Satur ated surface

hydrogen desorption) will be shown below to have avalue of approximately zero. AG* (for the electro-chemical desorption) cannot yet be calculated evenwith sufficient accuracy for the present purposes;k~, where n = 1, 2, or 3 depending on the reactionconcerned, has been calculated from AG* by meansof the equation,

k, = ~ - exp - R T ] " (146)A l l n u m e r i c a l v a l u e s q u o t e d i n f o l l o w i n g s e c t i o n s h e n c e

d e p e n d u p o n t h e a c c u r a c y o f th e s e v e r y a p p r o x i m a t e c a l -c u l a t i o n s , e x c e p t f o r v a l u e s c a l c u l a t e d h e r e c o n c e r n i n gp l a t i n u m .

Table II gives numerical values of some of thequantities used in the following calculations.2. Potential C ond ilions for Applicability of SlowDischarge Mech anism (Path A)

The two conditions to be satisfied for (88) toapply are (85) and (86). Numerical application ofthese conditions gives the results of Table III.3. Coverage of Surface (x) for Slow Discharge Mecha -nism (Path A)

Table IV gives the surface coverages at variousoverpotentials obtained by applying equation (87)at 20~4. The Value of AG* for Atomic Hydro gen Desorp-lion

For smooth Pt cathodes the observed experimen-tal slope of the Tafel line at current densities ofabout 10 2 _ l0 ~ amp/cm 2 indicates t hat theatomic hydrogen mechanism is rate-determining.The limiting current density for this mechanism isfound to be 30 amp/era 2 in 1N aqueous acid solu-tion (13). Substituting in (146) it follows that,

AG* = --2.5 kcal approx.k3 = 1014'2

The correct value of AG* can therefore be taken asabout 0 kcal, the corresponding value of k3 being10 2's at ordinary temperature. With the approachof saturation appreciable departures from idealityamong the hydrogen atoms on the surface arelikely to occur. Hence, the react'ion may be some-what slower than indicated by the value of AG*.A low value of AG* would be expected because thereaction concerned is a surface radical reaction. Toa first approximation it is assumed that AG* (andalso k3) are the same for all cathodes.5. The Value of lcl/k2 for Pt Cathodes

Utilizing the ahove determined value of AG*(or k3) in (100), (80), and (81) referred to the ape-cial case of the exchange current i0 so th at '1 = 0,it follows that

k l / k 2 = 1 0 - 1 4 " 4 .6. Calculation of the Course of the Tafel L ine for the

Pt CathodeSubst ituting the above obtained values 8 for k3

and kl/k2 in (100) gives the complete Tafel equa-6 I n t h i s c a l c u l a t i o n t h e e x p e r i m e n t a l v a l u e o f k s i .e .

1 0 L4-2, h a s b e e n u s e d i n o r d e r t h a t t h e l i m i t i n g c u r r e n t s h a l la p p e a r a t 3 0 a m p / c m 2. I f t h e v a l u e o f k 3 = k T / h = 10 ~ *i s u s e d t h e l i m i t i n g c u r r e n t a p p e a r s a t 1 a m p / e r a 2. I ne i t h e r c a s e t h e f o r m o f t h e c a l c u l a t e d T a f e l l i n e r e m a i n st h e s a m e . T h e v a l u e s o f l o g i0 a n d t h e r e v e r s i b l e h y d r o g e np o t e n t i a l r e f e r r e d t o t h e e l e c t r o c a p i l l a r y m a x i m u m h a v eb e e n t a k e n a s - 3 , a n d + 0 . 2 8 v o l t s , r e s p e c t i v e l y .



15/18

VoL 99, No. 4 C A T H O D I C H Y D R O G E N E V O L U T I O N R E A C T I O N 183t i o n f o r h y d r o g e n e v o l u t i o n f r o m a q u e o u s 0 . 1 NH C 1 . T h e t w o l i m i t i n g s l o p e s d e d u c e d i n ( 1 0 3 )a n d ( 1 0 5) a r e s h o w n ( s e e F i g . 3 ) .7. Mini mu m Coverage of Cathode by Hydrogen for the

Atomic Hydrogen Mechanism to be DesorptiveT h e r e q u i re d m i n i m u m c o v e r a g e i s o b t a i n e d f r o m( l l 1 ) a s a f u n c t i o n o f c u r r e n t a n d i s g i v e n in T a b l e V .

- 0 2 0 ] J l r

-- 01 1 ~

- 0 ,1 (

+005

~ " ~ , , ,-3.0 -2 0 - IO 0 1.0 2.0l o g Ic

FIG. 3 . Ca lcu la ted course o f Tafe l l ine fo r the smoothp la t inum ca thode in 0 .1N HC1 a t 20~ (as suming pa thB is ra te de te rmin ing) .

9. Conditions for Applicability of Slow DischargeMechanism (Path C)

T h e c o n d i t i o n t o s a t i s f y f o r (1 2 0 ) t o a p p l y i s (1 1 8 ) .H o w e v e r , i n t h i s c a s e i t i s n o t p o s s i b l e t o c a l c u l a t es u f f i c i e n t l y a c c u r a t e v a l u e s o f k , o r A G * f o r p o t e n t i a lc o n d i t i o n s t o b e f o u n d . L i m i t i n g v a l u e s f o r k , a n dA G * w h e n P a t h C is r a t e - d e t e r m i n i n g h a v e t h e r e -f o r e b e e n c a l c u l a t e d a n d a r e g i v e n i n T a b l e V I I .

C a l c u l a t i o n s o f A G * b y s t a t i s t i c a l m e c h a n i c a lm e a n s a r e c o m p l e x a n d h a v e o n l y b e e n a t t e m p t e db y C o n w a y ( 9) i n t h e c a se o f A g . H e f i n d s ( h G * ) ^ ~9 k c a l , i n w h i c h c a s e , t h e r e f o r e , d i s c h a r g e w o u l d b er a t e - d e t e r m i n i n g i f t h e d e s o r p t i o n w e r e e le c t r o -c h e m i c a l .T A B L E V I I . Limiting values of k4 and AG*~ for Path C to berate-determinin at 20~

C a t h o d e k 4 l i m i t f o r P a t h C , A G * l i m i t f o r P a t h C ,R a t e - d e t e r m i n i n g R a t e - d e t e r m i n i n g

H g

A g

When ,1 more negativet h a n - 0 . 4 3 v o l t k ,m u s t b e > 1 0 5 . ~k4 m ust be > 1O ~ ata l l overpo ten t ia ls

When ,1 more nega t ivetha n --0.43 vol t aG~mu s t be < 24 kca l~G~ mus t be < 17 kcala t a l l overpo ten t ia ls

Ni As fo r Ag As fo r Ag

T A B L E V I I I . Maximum values of surface coverage or PathC to be rate-determiningC a t h o d e M a x i m u m v a l u e o f x

H g

T A B L E V . Minimum coverage or atomic hydrogen desorptioni c a m p / c m ~ x

1 0 - t ~lO-g10-610-3

110

10-810-4.510-3lO-i .61 (sa td . su rface )S a tu ra t e d s u r fa c e A gN i

10 ~ a t ov erpo ten t ia ls more nega t ive than -0 .43v o l t10- ' a t a l l overpo ten t ia lsAs fo r Ag

T A B L E V I . Potential conditions for atomic hydrogen mech-anism (Path B) at 20~C a t h o d e

H gAgN i

Co n d i t i o n ( 9 7) [ Co n d i t i o n ( 9 8). . . . .v e r p o t e n t i a l i n v o l t s O v e r p o t e n t i a l i n v o l t s

More nega t ive th an ' More pos i t ive than- 1 . 6 5 [ - 0 . 4 3Mo re nega t iv e than I All va lues sa t is fy con--0 . 7 8 th a n d i t io nMore nega t ive All va lues sa t is fy con--0 . 6 4 d i t i o n

8. Potential Conditions for Applicability of AtomicHydrogen Mechanism (Path B)

T h e t w o c o n d i t i o n s t o b e s a t i s f i e d f o r ( 1 0 0 ) t oa p p l y a r e ( 9 7 ) a n d ( 9 8) . N u m e r i c a l a p p l i c a t i o n o ft h e s e c o n d i t i o n s g i v e s t h e r e s u l t s o f T a b l e V I .F o r s m o o t h p l a t i n u m c a t h o d e s , t h e u s e o f t h e e x -p e r i m e n t a l v a l u e s o f k,/k2 i n c o n d i t i o n ( 9 7 ) s h o w st h a t f o r t h e a t o m i c h y d r o g e n m e c h a n i s m t o a p p l ya t ~ = 0 , k l m u s t b e > 1 0 - 6 " s .

10 . Coverage of Surface for Slow Discharge Mecha-nism (Path C)

T h e c o v e r a g e x i s g i v e n b y ( 1 19 ) , a n d b y u s i n gt h e l i m i t i n g v a l u e s o f k4 g i v e n i n T a b l e V I I a m a x i -m u m v a l u e o f x c a n b e c a l c u l a t e d ( s e e T a b l e V I I I ) .11 . Conditions for Applicability of ElectrochemicalMechanism (Path D)

T h e c o n d i t i o n t o s a t is f y fo r P a t h D t o b e r a t e -d e t e r m i n i n g i s ( 1 21 ) , b u t s i n ce k 4 a n d A G * a r e n o tk n o w n a c c u r a t el y , T a b l e I X g i v es l im i t i n g v a lu e so f t h e s e q u a n t i t i e s ( c f. S u b s e c t i o n 9 ) .12 . Potential Conditions for Applicabi lity of a =

and a = 89when Path D is Rate-DeterminingT h e c o n d i t i o n t o b e s a t i s f i e d f o r a t o h a v e v a l u e s

o f ~ a n d 8 9 a r e , r e s p e c t i v e l y , ( 1 2 2) a n d ( 1 2 4 ). T h ep o t e n t i a l c o n d i t i o n s a p p r o p r i a t e t o b o t h v a l u e s o f

a r e g i v e n i n T a b l e X .



16/18


17/18

Vol. 99, No. ~ CATHODIC HYDRO GEN EVOLUTION REACT ION 185(VII, B, 2) show that mechanism A cannot takeplace at overpotentials more negative than -0.3volt, and it is interesting to note that the Tafelline begins to attain a limiting current at aboutthis potential when measurements are made using afresh cathode surface (10).

(iN) In alkaline solution.--The coefficient a is89and )` is observed to be 1 (10), which indicatesthat mechanism E or G is operative. This is con-firmed by the interpretation of the observed pHeffects.4. Smooth Platinum in Acid Solution

The value of a at intermediate current densitiesindicates that the mechanism is B (16). The mecha-nism at current densities above the limiting cur-rent density may be C or D, but is probably Dowing to the saturation of the surface with ad-sorbed hydrogen at the limiting current density.

V I I I . S U M M AR Y O F S O M E R E C E N T A D V A N C E SThe controversy concerning the value of b in

the Tafel equation now seems resolved experi-mentally as follows. If the solutions are pure, bis not (except transiently at a limiting current)great er than about 0.13, i.e.,/~ > 0.45/),. This fac tconfirms that the energy barrier for the dischargereaction is usually nearly symmetrical and is inaccordance with the equations formulated in Section(VI). Higher values of b are probably connectedwith a distortion of the energy barrier (the positionof the transition state complex being displacedtoward the electrode) due to the specific adsorptionof poisons on the electrode.

The realization of the use of )` as a distinguishingcriterion of mechanism, and its intensive statisticalapplication, has made available a criterion of greaterpower than previously existed.

Knowledge of AH0* and the potential of the elec-trocapiUary maximum aid application of the quan-titative conditions established above.

In recent years, it has been suggested (17) thatprototropic transfer of hydrogen from water in thesolution to water adsorbed on the electrode, andalso (18) that the atomic hydrogen desorption re-placed at higher current densities by electrochemicaldesorption are the main rate-determining reactionsto be considered for the hydrogen evolution reaction.Evidence in favor of the first was based mainlyupon the constancy of the factor B for various elec-trolyte concentrations and for a few metals. Con-sideration of (67) shows that the first requirementwould be expected for any mechanism, however,and it has in any case been shown in an earlier sec-tion of this paper t ha t a sufficiently accura te ex-

perimental determination of B is prohibitively diffi-cult [see also Butler (19)]. In order tha t the proto-tropic transfer theory can yield a satisfactorytheory of pH effects and of reversible electrode po-tentials an unusual structure of the double layer hasto be assumed (20). Forecasts made upon this basisof similarities between hydrogen and oxygen over-potentials have also not been confirmed (27). Thesecond theory (18) suffers the fundamental disad-vantage that it involves the formulation of thekinetic processes at working hydrogen electrodesin terms of equations applicable only under equi-librium conditions; it is impotent in indicating ex-pected pH and salt effects; and the explanationsuggested for different values of b is based on ex-perimental results which are not in accord withthose obtained using very pure solutions.

Lastly, a quantitative, statistical mechanicalformulation of the discharge reaction from bothhydroxonium ions and water has recently beenmade (5). This work indicates rates of the dischargereaction in good accord with those experimentallyobserved on the two electrode materials considered(Hg and Ni). There also appears to be only a verysmall probability that discharge can proceed fromwater molecules in acid solution.

ACKNOWLEDGMENTThanks are due to Dr. R. Parsons for critical dis-

cussion and to Dr. R. G. H. Watson for verificationof the numerical calculations.

A n y d i s c u s s i o n o f t h i s p a p e r w i l l a p p e a r i n a D i s c u s s io nS e c t i o n , t o b e p u b l i s h e d i n t h e D e c e m b e r 1 9 52 i s s ue o f t h eJOURNAL.

REFERENCES1 . J . O 'M . BO CK RIS A ND B . E . CONWAY,Trans. FaradaySoc., 45,989 (1949).2 . A . M . A Z Z AM , J . O ' M . B O C K R I S , B . E . CONWAY, AND

H . RO SEN BERG , Trans. Faraday Soc., 46, 918 (1950).3. J. O'M . BOCKRIS AND n. E. CONWAY, J . S c i . I n s I r u -ments, 25,283 (1948).4 . J . O ' M . B O C K m S , Chem. Revs., 3, 561 (1948).5. R. PARSONS AND 3. O'M . BOCKmS, Trans . Faraday Soc . ,

47,914 (1951).6 . J . O 'M . BO CK mS A N D R . G . H . WATSON,J . chim. phys.,49, 1 (1952).7 . J . H EY RO V SK Y , Disc. Faraday Soc., l , 212 (1947).8 . J . JOFA AND Z. B. PECHKOVSKAYA,Doklady Akad. Nauk.S.S.S.R., 59,265 (1948).9 . B . E . CONWAY,T h e s i s , U n i v e r s i t y o f L o n d o n ( 19 49 ).

1 0 . J . O 'M . BO CK RIS A ND E. C . PO TTER, J. Chem Phys.,March (1 9 5 2 ) .

11 . A. N. FRVMKIN, Acta Physicochim. U.R.S.S., 18, 23(1943).1 2. F . P . B O W D E N A N n K . E . W . G a E W , Disc. Faraday ~oc.,1, 86 (1947).

1 3 . A . M. A ZZA M A N D J . O 'M . BO CK RIS, Nature, 165, 403(t95o).



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186 JOURNAL OF THE ELECTROCH EMICAL SOCIETY Apri l 19521 4 . E . C . POTTER,U n p u b l i s h e d r e s u l t s .15 . P. LUKOVTSEV,S. LEWINA, AND A. N. FRUMKIN,ActaPhysicochim. U.R.S.S., 11, 21 (1939).1 6. A . M . A Z Z AM , T h e s i s , U n i v e r s i t y o f L o n d o n ( 19 49 ).17 . H. EYRING, S . GLASSTONE, AND K . J . LAIDLER, J .Chem. Phys., 7, 10 53 (1939).18 . A. HICKLING AND F. W. SALT, Trans. Faraday Soc.,

38, 474 (1942).1 9 . J . A . V . BUTLER,J. Chem. Phys., 9 ,2 7 9 (1 9 4 1 ) .2 0 . G . E . KIMBALL,S. GLASSTONE, AND A . GLASSNER, .Chem. Phys., 9, 91 (1941).

21 . J . H ORIUTI AND M. IKUSIMA,Proc. Imp. Acad. Tokyo,15, 39 (1939).

22 . B. KABANOV AND J. JOFA, Acta Physicochim. U.R.S.S.,10, 616 (1939).

2 3 . J . N . A 6 A R , Disc. Faraday Soc., 1, 81 (1947).24 . J . A. V. BUTLER, Trans. Faraday Soc., 28, 379 (1932).25 . P . LUKOVTSEVAND S. LEWINA, J. Phys. Chem. U.S.S.R.,

21,599 (1947).26 . R. PARSONS, Z. Elektrochem., 55, l l l (1951).27 . A. HICKLING AND S. HILL,Disc. Faraday Soc., 1, 236

(1947).

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Bockris Jes 1952 Hydrogen Article