The effect of bubbles on the measured electrochemical parameters during hydrogen evolution on nickel

J 151ectroanal Chem. 184 (!985) 347-356

347

Elsevier Sequow S A , Lausanne - Printed m The Netherlands

THE EFFECt PARAMETERS

OF BUBBLES ON THE DURING HYDROGEN

MEASURED ELECTROCHENIIC~_L EVOLUTION ON NICKEL

J A HARRISON SLnool of Chemtstr), Unwerstty of Nencastle-on-Tyne (Great Britain) A T KUHN Department of Bio-matertals Sctenee, Eastman Dental HospJtal, 256 Grays Inn Roa~ London WC1 8LD (Great Britain) (Recewed 7th June 1984, m revised form 12th September 1984)

ABSTRACT The hydrogen evolution reacuon has been mveslagated at mckel rotating and vertical stalaonary electrodes m 1 M HCI Steady state current-potenual, tmpeda_nce-potentlal and potentml step-current-trine transients results are reported The Lmpedance ,s analysed by eqmvalent ctrcmt to produce double layer capac~ty-potentml, ohrmc res~stanee-ootentlal (and charge transfer reslstance-potmual) curves Some deducuons are made about the bubble layer and ~ts effect on me electron transfer mechamsm for the reacuon

INTRODUC]'ION T h e c o n t i n u i n g f o c u s o n m e a n s o f energ-y s a v i n g s h a s p r o m p t e d m u c h r e s e a r c h o n i n d u s t r i a l e l e c t r o d e s w i t h a vaew t o o v e r p o t e n t x a l r e d u c t i o n s I n t h e l a s t d e c a d e , s u c h studies have mainly been devoted to anodes More recently the emphasLs has partly moved to cathodic studies, and to the hydrogen evolxqng cathode m chlor-alkah processes and water electrolysls. The use of nickel cathodes m such apphcations m p r e f e r e n c e t o i r o n is n o w vc~dely a d v o c a t e d . A n u m b e r o f p u b h c a t a o n s , f o r e x a m p l e M a l e s et al. [1] a n d B r o w n e t al. [2], e x e m p l i f y t h i s a p p r o a c h T h e o v e r a l l h y d r o g e n e v o l u t i o n r e a c u o n is 2H++2e-~H2 H2

(1) ~ (H2)bubb,e s

(2)

Following a study of the correlation of the rates of the hydrogen reaction on various m e t a l s w i t h t h e p r o p e r t i e s o f t h e M - H b o n d , s e e f o r e x a m p l e ref. 3, a l m o s t a l l subsequent investigauons have revolved around the hydrogen atom coverage. In the particular case of nickel, recent investigations [4-6] show such an emphasis. L,ttle * Present addrcms Faculty of Smence & Technology, Harrow College of Higher Educauon, l'4orthv~.ck Park, Harrow HA1 3TP, Great Bntam 0022-0728/85/$03 30

~3 1985 Elsevier Sequoia S.A

348

a t t e m p t has b e e n m a d e to c h a r a c t e n s e the m e t a l s u r f a c e o n w h i c h the reactaon ~s t a k i n g place, a l t h o u g h it ~s k n o w n that the state o f the s u r f a c e affects the p r o g r e s s o f the b u b b l e f o r m i n g r e a c t i o n O n the o t h e r h a n d s o m e studies have b e e n a i m e d at m e a s u n n g the p r o p e r t i e s o f the bubb.~e layer [ 7 - 1 0 ] withou= c o n s i d e r i n g the e l e c t r o n t r a n s f e r c o m p o n e n t o f the reaction. T h e s e p a p e r s h a v e c o n c e n t r a t e d o n w h e t h e r there will b e an effective d t f f u s m n l a y e r at a s t a t i o n a r y e l e c t r o d e d u e to b u b b l e m o v e m e n t s . T h a t there will be an effective d f f f u s m n l a y e r d u r i n g gas e v o l u t i o n at a stataonary e l e c t r o d e is a s s u m e d b y all the w o r k e r s in the field a n d an a t t e m p t has b e e n m a d e to Fred a q u a n U t a U v e c o n n e c t i o n [7] b e t w e e n ~5, the c u t - o f f d i a m e t e r , the s u r f a c e coverage, a n d the v o l u m e p r o d u c t i o n r a t e o f b u b b l e s . In this w o r k a n a t t e m p t will b e m a d e to c h a r a c t e r i s e the surface, while the h y d r o g e n evolutaon reactaon ~s p r o c e e d i n g , b y the t - t r e s p o n s e t o a p o t e n t i a l step a n d b y the o h m i c resistance a n d the d o u b l e layer c a p a c i t y o b t a i n e d f r o m the t m p e d a n c e . A similar strategy has b e e n u ,ed b y the a u t h o r s f o r i n v e s u g a t i n g the 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 o n p l a t m u m [11]. T h e e l e c t r o n t r a n s f e r p a r t o f the 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, a p p a r e n t l y fast o n p l a t i n u m a n d b u b b l e f o r m a u o n s t r o n g l y mh~blts the overall reaction. E x t e n s i v e m e a s u r e m e n t s have also b e e n m a d e o n a related gas f o r m i n g reaction, c h l o r i n e e v o l u t i o n [ 1 2 - 1 4 ] o n high s u r f a c e area electrodes. EXPERIMENTAL

T h e cell used was a convenlaonal three e l e c t r o d e cell, at a m b i e n t l e u i p e r a t u r e , c o n t a m a n g the vertical m e t a l e l e c t r o d e as a small piece o f sheet (0.3 cm2), e m b e d d e d m plastic, a n d a c o m m e r c i a l s a t u r a t e d calomel r e f e r e n c e e l e c t r o d e (to whach all the p o t e n t m l are referred). In s o m e o f the experaments the e l e c t r o d e was a r o t a t i n g dine e l e c t r o d e m a d e b y e m b e d d i n g a c y l i n d e r o f nickel (0.2 c m 2) m P T F E In tbas w o r k the surface o f all the electrodes were p r e p a r e d b y p o h s h i n g with 6 / 0 c a r b o r u n d u m p a p e r . T h e d o u b l e layer c a p a c i t y - p o t e n t i a l curves for the mdlvadual e l e c t r o d e s a n d then- surface t r e a t m e n t was used as an mdleataon o f the s u r f a c e rou~aness, T h e H C I s o l u t l o n was A n s t a r , a n d the s o l u u o n s were m a d e u p with triply distilled water. T h e e x p e r t m e n t s were carried o u t b y a m i n i c o m p u t e r system, the latest v e r s m n o f which is d e s c r i b e d m a r e c e n t p u b h c a t i o n [15] T h e e q m p m e n t will t m p l e m e n t automatacally xartually all the m e t h o d s o f elect r o d e kmetlcs. In this instance s t e a d y state t - E a n d Z ( ~ ) - E curves h a v e b e e n m e a s u r e d , w~th s o m e p o t e n f i o s t a t i c t - t transients and l i n e a r p o t e n t i a l sweep curves T h e m e a s u r e m e n t o f i m p e d a n c e [16,17] is parlacularly useful. T h e o p e r a l a o n o f the e q m p m e n t is c o m p l e t e l y a u t o m a t i e a n d all the m f o r m a t a o n is p e r m a n e n t l y stored. A q u a n u t a u v e analys~s o f the Z ( w ) - E d a t a was carried o u t b y c a l c u l a t i n g the values o f the usual Cd~-E, R , ~ - E , R ~ - E , o - E sets o f p a r a m e t e r s using the e q u a u o n 1

1

Z ( ,o ) - R ~ = Rot + (1 - J )O,~ - ~/'- + j,oC~l

(3)

349

a n d the usual h t t m g p r o c e d u r e . If d i f f u s i o n o f r e a c t a n t o r p r o d u c t m the gas e v o l u u o n r e a c t i o n p l a y s a role m the i m p e d a n c e then eqn. (3) s h o u l d allow the value o f o to be e s t i m a t e d f r o m u n p e d a n c e d a t a Tins was the case for the h y d r o g e n e v o l u u o n reaclaon o n p l a t i n u m , investagated p r e v i o u s l y [11], in wbach a was det e r m i n e d b y the d i f f u s i o n o f m o l e c u l a r H 2 or H 2 bubble., In the p a r t i c u l a r e x p e r i m e n t s o n mekel the reaction is such that m a r e a s o n a b l e ~ e q u e n c y range, 0 1 H z to 1000 Hz, n o effect o f chffuslon ~s seen in the s t a t i o n a r y state i m p e d a n c e curves, a n d the i m p e d a n c e ~s d o m i n a t e d b y d o u b l e l a y e r c h a r g i n g a n d by the f a r a d m c reaction. T h e w o r k m u s t then revolve a r o u n d the d e p e n d e n c e o f the o h m i c resistance a n d the d o u b l e layer c a p a c i t y o n the s u r f a c e state o f the e l e c t r o d e a n d the r o t a t i o n speed o f the e l e c t r o d e f a r a p a r t l c u l a r e l e c t r o l y t e T h e f u n c t i o n o f the r o t a t i n g disc e l e c t r o d e is to vary the b u b b l e p o p u l a t i o n on the e l e c t r o d e and, if possible, to r e m o v e the b u b b l e s c o m p l e t e l y by the m e c h a m s m s h o w n m Fig 3 A c a l c u l a u o n o f the ~mpedance for parallel r e d o x reactions, o n e o f w i n c h c o u l d be h y d r o g e n e v o l u t i o n , has b e e n c a r d e d o u t [18] This t h e o r y w o u l d allow the i n t e r p r e t a t i o n o f the d a t a in t e r m s of a s t a n d a r d rate c o n s t a n t (as a f u n c t i o n o f p o t e n t i a l t,~ highlight the b u b b l e layer intubitaon effects), as has been carried o u t for the c h l o r i n e e v o l u t i o n reactaon [13]. A n a d v a n t a g e o f tins m e t h o d o f d a t a a s s e s s m e n t is that effects for different metal electrodes c a n be q u a n t i t a t i v e l y c o m p a r e d . Tl~s m e t h o d wdl be used at a later d a t e w h e n d a t a o n different m e t a l s is p r e s e n t e d It ~s possible that at frequencies l o w e r than used here the d i f f u s i o n of h y d r o g e n w o u l d be a p p a r e n t as a W a r b u r g ~mpedance, as o b s e r v e d for h y d r o g e n e v o l u t i o n o n p l a t i n u m [11], a n d it m a y be possible m future investigation to detect the r e l a x a u o n o f the b u b b l e layer. O n e f u r t h e r expermaental p o i n t needs to be m a d e . B e c a u s e o f the i n h e r e n t f l u c t u a h o n s m the d a t a d u e to b u b b l e f o r m a t i o n a n d d e t a c h m e n t the c u r r e n t a n d the i m p e d a n c e m e a s u r e m e n t n e e d e d to be a v e r a g e d o v e r sufficient times RESULTS AND DISCUSSION

F i g u r e 1 s h o w s the t - E c u r v e a n d the d o u b l e layer c a p a c i t y curves m e a s u r e d m l M N a C I a n d m 1 M H C I o n the s a m e r o t a t i n g disc m c k e l electrode. In each case the p o t e n t i a l was a d v a n c e d f r o m the negative p o t e n t i a l e n d a n d the p o t e n t i a l held until the s t e a d y state was reached. N a C I s o l u t i o n s d o n o t s h o w a n y a p p r e c i a b l e f a r a d a l c r e a c t i o n m the p o t e n t i a l r a n g e mveslagated w h e r e a s in the H C I solutaon the h y d r o gen e v o l u t i o n r e a c t i o n is the o n l y eleetrochemacal reaction. It is t e m p t i n g to ~dentffy the l o w e n n g o f the d o u b l e layer c a p a c i t y m the p r e s e n c e o f the 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 with the p r e s e n c e o f a b u b b l e layer a n d a r e d u e u o n m the area o f the metal s u r f a c e a v m l a b l e to the electron transfer p a r t o f the h y d r o g e n e v o l u t i o n reaction m e c h a n i s m . T h e p o t e n t i a l o f z e r o c h a r g e (ee, cm) is s t a t e d to be a r o u n d g e c m = - - 540 m V vs S C E [19] so a c a t i o n effect w o u l d be e x p e c t e d m the potenlaal r a n g e u n d e r mvestxsation a l t h o u g h thas w o u l d be e x p e c t e d to be small [20,21]. By c o m p a r i n g the curves o f the d o u b l e layer c a p a c i t y m Fig 1 it m i g h t b e e x p e c t e d that m the r a n g e E = - - 4 5 0 m V to E = - - 5 2 0 m V the metal s u r f a c e is to a large e x t e n t freely a v m l a b l e

350 t o t h e e l e c t r o n t r a n s f e r r e a c t i o n a n d a t p o t e n t i a l s n e g a t i v e t o E---- - - 5 2 0 m V t h e a v a i l a b l e m e t a l s u r f a c e is p r o g r e s s i v e l y c u t o f f b y t h e b u b b l e l a y e r . T h e r a t i o o f t h e d o u b l e l a y e r c a p a c i t y in N a C l a n d H C I is l i k e l y t o b e a q u a n t i t a t i v e m e a s u r e o f t h e f r e e m e t a l s u r f a c e . A l t h o u g h t h i s is a r e a s o n a b l e h y p o t h e s i s , it will o n l y b e p o s s i b l e to d e s c r i b e this effect c o m p l e t e l y w h e n the d o u b l e layer c a p a c i t y c u r v e s are u n d e r s t o o d . U n f o r t u n a t e l y t h i s is a s u b j e c t w h i c h is n o t y e t u n d e r s t o o d , see, h o w e v e r refs. 2 0 a n d 21. T h e i n f l u e n c e o f a b u b b l e e f f e c t ts a l s o s u g g e s t e d b y t h e e l e c t r o d e

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Fig. 1 (a) Double layer capacity-potential curve for a mekel disc electrode rotating at 34 Hz- The upper curve zs for 1 M NaCI and the lower curve for i .~t HCI (1:))The corresponding steady state current potentml curves In ! M NaCI the current is small

351 rotation speed dependence of the double layer capacity and the current for mckel m 1 M HCI solution. I n F i g 2 t h e c a p a c i t y is s e e n t o b e h i g h e r a t l u g h ~ r r o t a U o n s p e e d s e x c e p t possibly at the most negative potentials. Even under the tughest rotation speeds (100 H z ) at n e g a t i v e p o t e n t m l s t h e d o u b l e l a y e r c a p a c i t y c a n n o t b e m a d e t o rise t o t h a t o f t h e N a C l s o l u t i o n , s h o w i n g t h a t t h e b u b b l e l a y e r c o v e r s t h e e l e c t r o d e s u r f a c e to a s~gnif~cant, e x t e n t . T h e r o t a t i o n d e p e n d e n c e o f t h e i m p e d a n c e p a r a m e t e r s g w e s a method for investigating the mechanism of bubble detachment from the electrode. A

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Fig 3 Possible model for bubble transport at a rotating dxse electrode

352

suggested m e c h a m s m for tins is s h o w n d i a g r a m m a t i c a l l y m Fig. 3. T h e s t r e a m h n e velocity d i s t n b u u o n , gtven b y the well k n o w n e q u a t i o n s [22], o u t s i d e the dlffusaon layer ]s responstble for movang the b u b b l e s o u t w a r d s . H o w e v e r a c o m p l e t e investigation o f flus effect wall require m o r e extensive sets o f d a t a then p r e s e n t e d he~-e a n d wall be the subject o f future work. It m a y also be possible to investigate b u b b l e f o r r m n g r e a c t m n s t h e o r e t i c a l l y m a w a y s~rmlar to electrocrystallisation r e a c t i o n [23], using the m e t h o d s o f c o m p u t e r s i m u l a t i o n T h e t - E curves, Fig. 4a, s h o w a rise m the s t a t i o n a r y value o f the c u r r e n t with r o t a t m n speed T h e c o r r e s p o n d i n g log t - E c u r v e s ( c o r r e c t e d for the m e a s u r e d o h r m c resistance) are s h o w n m Fig. 4b). T h e log t - E curves have, overall, a Tafel slope o f s o m e 170 mV, but the potential region f r o m E = - - 4 0 0 m V to E = - - 5 2 0 m V seems to have slope n e a r e r to 120 inV. T h e exact value o f the Tafel slope d e p e n d s on the extent of the b u b b l e layer a n d ]s a f u n c t m n o f s u r f a c e rouaJmess a n d the a m o n present in the solution. As e x p e c t e d from the c o n n e c t i o n b e t w e e n the

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F~g 4 (a) s - E c u r v e for a m c k e l r o t a t m g d l s c e l e c t r o d e m 1 M H C I a t t w o r o t a t m n s p e e d s T h e l o ~ e r c u r r e n t c a r v e Js for 34 H z a n d the t u g h e r c u r r e n t c u r v e m for 89 I-Iz (b) l og i - - E ( c o r r e c t e d for t he m e a s u r e d R,., v a l u e ) c u r v e s for the ~ - E d a t a m (a)

353

c h a r g e t r a n s f e r resLstance the c u r r e n t a n d the T a f e l s l o p e the c h a r g e t r a n s f e r r e s m t a n c e d e c r e a s e s w~th r o t a t i o n s p e e d i n c r e a s e T h e m e a s u r e d o h r m c r e s i s t a n c e rises with r o t a u o n r a t e d e c r e a s e . A f u r t h e r effect Is s h o w n m F~g. 5. T h e s t e a d y s t a t e c u r r e n t at a fLxed p o t e n t a a l ts n o t c o n s t a n t b u t o s c d l a t e s m the m a n n e r s h o w n m the figure. T h e figure s h o w s the d e c r e a s e in c u r r e n t o n an irutaally b u b b l e free e l e c t r o d e u n t d the a v e r a g e v a l u e o f the c u r r e n t is c o n s t a n t (the s t e a d y state). I t c a n b e seen t h a t the a p p r o a c h to the a v e r a g e s t e a d y s t a t e ~s a s l o w p r o c e s s t a l o n g l o n g e r t h a n 100 s T t u s t i m e s e e m s to b e l o n g e r at s t a t a o n a r y e l e c t r o d e s , see also ref. 11. A s d i f f u s i o n r e a c h e s a s t e a d y s t a t e m m s at a r o t a t i n g dtsc ~t s e e m s h k e l y t h a t the m e c h a m s m o f b u b b l e f o r m a t i o n , g r o w t h , p a c k i n g a n d e v e n t u a l l y d e t a c h m e n t are r e s p o n m b l e for this effect. Strndar m e a s u r e m e n t s h a v e b e e n m a d e o n a vertical s t a t a o n a r y m c k e l e l e c t r o d e . T h e m e a s u r e m e n t s w e r e t a k e n on the s a m e e l e c t r o d e e a c h u m e a d v a n c i n g the p o t e n t i a l f r o m the negatave end. Single p o t e n t m l p u l s e m e a s u r e m e n t s o n a n t m t m U y b u b b l e free e l e c t r o d e s h o w an t - t r e s p o n s e o f the t y p e s h o w n m F~g 6. T h e l o n g t i m e r e v o l v e d in the ~-t t r a n s i e n t s o c c u r s b e c a u s e the m e c h a n i s m o f b u b b l e d e t a c h m e n t has s l o w e d d o w n m the a b s e n c e o f a m o v i n g s o l u u o n n e a r to the e l e c t r o d e T h i s effect s e e m s to c a u s e a m e m o r y effect m the Z ( t o ) - E and ~ - E d a t a . T h u s ff the e l e c t r o d e w a s held at a n e g a u v e potentaal f o r a l o n g t i m e tt w a s p o s s i b l e to m a k e a n t m p e d a n e e , Z ( t ~ ) - E a n d I - E run, wath the e l e c t r o d e s t a t e c b a r a c t e n s e d b y the holding potentml. T w o mckel electrodes, one hghtly roughened and one smooth, w e r e i n v e s t i g a t e d m 1 M H C I F i g u r e 7 s h o w s a n d e x a m p l e o f a log t - E c u r v e t c o r r e c t e d for the m e a s u r e d v a l u e o f the o h m a c r e s i s t a n c e ) m 1 M H C I s o l u t i o n I t is i n t e r e s t i n g t h a t e v e n t h o u g h the b u b b l e l a y e r Is p r e s e n t t h e T a f e l s l o p e is s o m e 106 m V . T h e low v a l u e o f the s l o p e s e e m s to c o r r e l a t e w i t h the c h a n g e m d o u b l e l a y e r c a p a c i t y with p o t e n t m l , F~g. 8. It s e e m s to b e c o n n e c t e d w~th the p a r t i c u l a r m e c h a r u s m f o r b u b b l e r e m o v a l at a s t a t i o n a r y e l e c t r o d e T t u s p r o b a b l y r e v o l v e s s t r e a m l i n e s g e n e r a t e d b y n s m g b u b b l e s T h e d a t a f o r the s t a t i o n a r y verUcal elec-

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trode were obtmned by holding the potential at a starting potential, usually at the most negative potenual, and then after each Z(a~) measurement m o v i n g the potential and waiting Ulal,I the current was apparently m the steady state as deduced from the variation m the current (carried out automaucaUy). A typical result for the analys~s of the Impedance into parameter curves is s h o w n in Fig. 8 where the Ce]-E curve is displayed. The shape of the curve has some s i m d a n t y to that the rotating disc, and a small hump is visible at around E = - - 4 5 0

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m V . H o w e v e r the c u r v e is clearly m u c h a f f e c t e d b y the b u b b l e layer. T h e d o u b l e l a y e r c a p a c i t y values, at low potentials, f o r the r o u g h e l e c t r o d e are are a b o u t a f a c t o r 2 d i f f e r e n t f r o m the that o f a s m o o t h electrode. This c o m p a r e s with the r o u g h n e s s for the s a m e electrodes measu, ed b y T a l y s u r f o f 0.2 g m ( p e a k to t r o u g h ) f o r the p o l i s h e d a n d 5.0 ittm f o r the r o u g h nickel electrode. It is p r e b a b l e , therefore, t h a t the r o u g h e l e c t r o d e h a s p r o p o r t i o n a t e l y less e l e c t r o c h e m i c a l l y acttve area. T h e effect o f r o u g h e n i n g m a y n o t a l w a y s b e beneficial u n d e r a c t u a l o p e r a t i n g c o n c h t i o n s . Similar m e a s u r e m e n t s h a v e b e e n m a d e in N a O H solutaon a n d these will b e r e p o r t e d in a separate paper. CONCLUSIONS It Is n e c e s s a r y for the m v e s U g a t l o n o f gas e v o l v i n g r e a c t i o n s a t the r o t a t i n g chsc a n d the s t a l a o n a r y electrode, to m e a s u r e the m a p e d a n c e c h a r a e t e r i s t t c s o f the electrode. Thus is n e e d e d in o r d e r to d e t e r m i n e the b u b b l e - f r e e area o f the e l e c t r o d e f r o m the do,.'ble l a y e r c a p a c i t y curves, a n d to r e m o v e t h e o h m i c e x m t n b u t i o n f r o m the p o t e n .al correctly. It is t h e n possible to i n t e r p r e t the s t e a d y t - E c h a r a c t e r i s t i c in t e r m s ~,t" the e l e c t r o n t r a n s f e r p a r t o f the m e c h a n i s m T h e a b s o l u t e m a E n i t u d e o f the d o u b l e l a y e r c a p a c i t y c o u l d also b e u s e d as a m e a s u r e o f real a r e a in c o m p a r i n g n e w c a t a l y t i c electrodes. H o w e v e r it w o u l d b e n e c e s s a r y to c a r r y o u t a c o m p a r i s o n o f the b e h a v i o u r o f the n e w e l e c t r o d e m a t e r i a l m c o m p a r i s o n with k n o w n m e t a l - e l e c t r o l y t e d o u b l e l a y e r c a p a m t y curves. I n the p a r t i c u l a r case o f m c k e l it a p p e a r s t h a t the d a t a c a n b e e x p l a i n e d b y a n e l e c t r o n e x c h a n g e r e a c t i o n wbach is kinetica_lly h i n d e r e d a n d w h i c h takes p l a c e at the free m e t a l s u r f a c e in t h e p r e s e n c e o f an extensive b u b b l e layer. T h e d e t a i l e d c h a r a c t e r i s t i c s o f the b u b b l e l a y e r h a v e y e t to b e i n v e s t i g a t e d LIST OF SYMBOLS

Cdl 8

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356

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REFERENCES 1 M H Miles, G KJssel, P W T Lu and S Srtmvasan, J Electrochem S o c , 123 (1976) 332 2 D E Brown, M,N Mahmood, A K. Turner. S M Hall and P O Fogarty, InL J Hydrogen Energy. 7 (1982) 405 3 A T Kulm, C J Morumer, G C Bond and J Lmley, J Electroanal C h e m , 34 (1972) 1 4 L Angely, G Bronoel and G Peslerbe, J EleetroanaL C h e m , 96 (1979) 203 5 B E. Conway, L Bal and D F Te:,sler. J Electroanal Chem., 161 (1984) 39 6 A P Brown, M Krumpelt, R O Louffy and N P Yao, Electrocbam Acta, 27 (1982) 557 7 K Stephan and H Vog4 Electrochtm Acta 24 (1979) 11 8 L J J Janssen and E B a r e n d r ~ h t , Eleetroehtm Aeta, 28 (1983) 341 9 A T Kuhn and IV Stevenson, ElectrochJm Act,a, 27 (1982) 29 10 L A J Janssen ana J G Hoogland, FAectroeh.tm Acta, 15 (1970) 1013 11 J A H a m s o n and A T Kuhn, Surf Technol 19 (1983) 249 12 J A. H a m s o n m C Jackson ( E d ) , Modern Chlor-Alkah Technology, Vol 2, Elhs-/-lorv,ood, Ctuchester, 1983, p 246 13 J A Harrison D L Caldwell and R_E. White Eleetrochtm. Acta, 28 (1983) 1561 14 J.A l-tarnson, D L Caldgell and R E Wtute, Electrocbam. Acta, 29 (1984) 203 15 J A H a m s o n , Electrochlm Aeta, 27 (1982) 1113 16 D D Macdonald and MCI'-I M c K u b r e m J O ' M Boekns , B E Conway and ILE. W l m e ( E d s ) , Modern Aspects of Electrochemastry Vol 14. Plenum Press, New York, 1982 p 61 17 M Sluyters-Rehbaeh. J H Sluyters m A J Bard ( E d ) , Electroanalyucal Chemasuy, Vol 4, Marcel Dekker, New York, 1970. p 1 18 J A Harnson, Electrocbam Acta, 29 (1984) 703 19 S Trasatla m H Gertscher and C W. Tobms ( E d s ) , Advances m Electrochermstry and Electrochermcal Enganeermg, Vol 10, Wdey-mte.,-scaence, New York, 1977, p 213 20 I L Cooper and J.A Harrison, Electrochtm Aeta, 29 (1984) 1147. 2! I L Cooper and J.A. H~.~,.rnson, Electrocb~m Acta, 29 (1984) 1165 22 V G Levach, Physlcochetmcal Hydrodynan~cs, Prentaee-Hall, N e w York, 1962 -23 J A H a m s o n and S K Rangarajan, Faraday Symposaum R e p o t , 12, 1977