The Distribution of Current and Formation of a Salt Film...

The Distribution of Current and Formation of a Salt Film on an Iron Disk below the Passivation Potential

Mark E. Orazem* and Michael G. Miller *'1

Department of Chemical Engineering, University of Virginia, Charlottesville, Virginia 22901

A B S T R A C T

Curren t d is t r ibut ion and surface s t ructure were s tudied for an iron disk in 1M sulfuric acid subjec ted to a un i form axial ve loc i ty at potent ials ca thodic to the pass ivat ion potential . The surface of the e lec t rode was t r ans fo rmed from a granular to a smooth surface at potent ials at which the current was observed to oscillate. The smooth surface was seen initially at the per iphery of the e lect rode and grew inward toward the center of the disk as the potent ia l was increased. In contras t to data ob ta ined for part ial ly pass ivated electrodes, the rate of corros ion was h igher at the outs ide of the disk than in the center. These observat ions are a t t r ibuted to the radial d is t r ibut ion of the potent ia l dr iv ing force for the corros ion react ion and to the format ion of a salt film. Current oscil lat ions are seen on the region of the e lec t rode covered by the salt film. This exp lana t ion is suppor ted by a ma themat i ca l mode l which treats the radial var ia t ion of cur ren t density, potent ia l dr iv ing force for corrosion, and concent ra t ion of ferrous ions adjacent to the e lec t rode surface. Exce l l en t ag reemen t is obta ined wi th the expe r imen ta l results.

A u n i f o r m s o l u t i o n p o t e n t i a l and a u n i f o r m c u r r e n t d i s t r i bu t ion canno t coex i s t on a d isk e l ec t rode (1, 2). This c o n s e q u e n c e of t h e d i sk g e o m e t r y is s ign i f i can t for t h e c o r r o s i o n of i ron d i sks in su l fu r i c ac id b e c a u s e the curren t dens i t i e s are large. L a w (3) and L a w and N e w m a n (4) s h o w e d tha t t he rad ia l d i s t r i b u t i o n of p o t e n t i a l d r i v i n g fo rce c a u s e s t he o u t e r e d g e of t he d i sk e l e c t r o d e to p a s s i v a t e first w h e n t h e p o t e n t i a l of t h e e l e c t r o d e is increased. The i r m a t h e m a t i c a l m o d e l p r o v i d e d good agree- m e n t w i th the e x p e r i m e n t a l resul t s of E p e l b o i n et al. (5) and s u p p o r t e d t h e c o n c l u s i o n tha t t he h y s t e r e s i s ob- s e rved in cu r r en t -po t en t i a l cu rves for this sy s t em can be a t t r i bu t ed to t he po ten t i a l drop b e t w e e n the so lu t ion ad- j a c e n t to t h e e l e c t r o d e and the r e f e r e n c e e l ec t rode . Russe l l and N e w m a n (6) p r o v i d e d e x p e r i m e n t a l verif ica- t ion of th is resu l t t h r o u g h the i r inves t iga t ion of cur ren t - p o t e n t i a l c u r v e s for d i sks of d i f f e r e n t radi i . A n o t h e r resul t of t he m o d e l of L a w and N e w m a n (3, 4) was that i ron d i sks h e l d at p o t e n t i a l s for w h i c h t h e i ron e l e c t r o d e is par t ia l ly pa s s iva t ed shou ld co r rode p re fe ren t i a l ly in t he cen te r . T h e o u t e r r ing of t he disk, in th is case, is pro- t e c t e d by a pa s s ive layer . R u s s e l l and N e w m a n (6) ob- s e r v e d p r e f e r e n t i a l c o r r o s i o n of t h e c e n t e r of i ron d i sks h e l d at p o t e n t i a l s for w h i c h the i ron is pa r t i a l l y p a s s i v a t e d . E p e l b o i n et al. (5), h o w e v e r , o b s e r v e d t h r e e d i s t inc t cases: p re fe ren t i a l co r ros ion at t he cen te r of the disk, p re fe ren t i a l co r ros ion in an ou te r ring, and prefer~ ent ia l co r ros ion in bo th a cen t ra l d isk and an ou te r r ing w i t h an inne r r ing sub jec t to lower rates of corros ion.

A n u m b e r of worke r s have c o n c l u d e d tha t the passiva- t ion of i r o n i n sul fur ic ac id is p r e c e d e d by the fo rma t ion of a f e r rous sal t f i lm (7-14). Th is f i lm m a y be a h y d r a t e d fe r rous salt. The re is e v i d e n c e that t he osc i l la t ions in curren t o b s e r v e d on an i ron disk be fo re the pass iva t ion po- t en t i a l are a s soc ia ted wi th the cycl ic fo rmat ion , g rowth , and d i s s o l u t i o n of t he sal t f i lm (12-14). R u s s e l l (15) and R u s s e l l and N e w m a n (16) p r e s e n t e d r e su l t s o f a m a t h e - m a t i c a l m o d e l ba sed u p o n th is m e c h a n i s m w h i c h s h o w t h e o sc i l l a t i ons o b s e r v e d in t he c u r r e n t - p o t e n t i a l c u r v e n e a r t he p a s s i v a t i o n po ten t i a l . The sal t f i lm p r o v i d e s a ba r r i e r to t he d i f fus ion of h y d r o g e n and fe r rous ions and s u p p r e s s e s t he c o r r o s i o n r e a c t i o n s u c h tha t as t h e sal t f i lm grows , b o t h the c o n c e n t r a t i o n of f e r rous ions adja- cen t to the sur face and the cu r r en t decreases . The pH of t h e s o l u t i o n a d j a c e n t to t he i ron su r f ace was f o u n d to c h a n g e as a r e su l t of t he g r o w t h and d i s s o l u t i o n of t he film. T h e s e o sc i l l a t i ons h a v e also b e e n e x p l a i n e d t h r o u g h app l i ca t ion of b i fu rca t ion ana lyses (17, 18).

T h e i n f l u e n c e o f f luid v e l o c i t y on the f o r m a t i o n of a sa l t f i lm was i n v e s t i g a t e d by A l k i r e and Cange l l a r i (19) for h igh v e l o c i t y f low b e t w e e n pa ra l l e l -p la te e l ec t rodes . T h e y c o n c l u d e d tha t a su f f i c i en t ly h i g h f low ra te c o u l d p r e v e n t r e p a s s i v a t i o n of t h e i ron sur face . T h e i r expe r i -

*Electrochemical Society Active Member. 'Present address: Shell Chemical Company, Oak Brook, Illi-

nois 60521.

m e n t a l resul t s were s u p p o r t e d by a m a t h e m a t i c a l m o d e l (19) w h i c h t r ea ted c o n v e c t i v e d i f fus ion and the po ten t ia l f ield d i s t r i b u t i o n nea r t he d i s s o l v i n g e l ec t rode . T h e i r w o r k i n d i c a t e d tha t r e p a s s i v a t i o n o c c u r r e d at f low con- d i t i ons w h i c h p e r m i t t e d f o r m a t i o n of a f e r rous su l fa t e sa l t f i lm on at l eas t pa r t of t he e l e c t r o d e sur face . At suf f ic ien t ly h igh flow rates, the su r face c o n c e n t r a t i o n is too low to p e r m i t p rec ip i t a t ion of the me ta l salt, and the d i s so lv ing me ta l does no t pass ivate .

Th is w o r k p r e s e n t s t he c u r r e n t d i s t r i b u t i o n and changes to the sur face s t ruc tu re of an i ron d isk sub jec t to a u n i f o r m ax ia l v e l o c i t y at p o t e n t i a l s c a t h o d i c to t he pass iva t ion potent ia l . E x p e r i m e n t s were c o n d u c t e d wi th an i m p i n g i n g e lec t ro ly te j e t [see Ref. (20-24)] in 1M sulfu- r ic acid. The v e l o c i t y in t h e ax ia l d i r e c t i o n for th is sys- t e m is u n i f o r m u n d e r geome t r i c cons t ra in t s ou t l i ned by C h i n and T s a n g (20). The r e su l t s of t he e x p e r i m e n t s are e x p l a i n e d w i t h t h e aid of a m a t h e m a t i c a l m o d e l , ba sed on the w o r k of N e w m a n (1), Law (3), and L a w and New- m a n (4), w h i c h t rea ts the radia l va r i a t ion of cu r r en t density, po ten t i a l d r iv ing force for corros ion, and concen t ra - t ion of fe r rous ions ad jacen t to the e l ec t rode surface.

Experimental Study The e x p e r i m e n t a l m e t h o d and resul ts are p r e s e n t e d in

th is sec t ion . A m o r e de t a i l ed d e s c r i p t i o n of t h e expe r i - m e n t a l m e t h o d is g iven by Mil ler (22).

Method. - -The e x p e r i m e n t a l d e s i g n for t he i m p i n g i n g e l e c t r o l y t e j e t s y s t e m is s h o w n in Fig. 1. The e l e c t r o d e has a 99.9985% i ron d i sk e m b e d d e d in an i n s u l a t i n g e p o x y disk . T h e r ad ius of t he e l e c t r o d e was 0.249 cm. T h e r e f e r e n c e e l e c t r o d e was a s a t u r a t e d c a l o m e l e lec- t r ode wh ich was separa ted f rom the ma in cell by a glass frit to avo id c o n t a m i n a t i o n of the e lec t ro ly te by ch lo r ide ions. The so lu t ion was sparged wi th n i t rogen. The coun- t e r e l e c t r o d e was a shee t of p l a t i n u m loca ted in the m a i n c h a m b e r a b o v e the ou t l e t of t h e je t . The r e c i r c u l a t i n g e l e c t r o l y t e f low was d r i v e n by a pe r i s t a l t i c p u m p t h r o u g h a f low d a m p e n e r , m e a s u r e d by a ro tamete r , and r e t u r n e d to t h e m a i n cel l t h r o u g h the g lass nozzle . The nozz le had an ins ide d i a m e t e r of 0.58 cm, was a x i s y m - m e t r i c wi th the i ron disk, and was loca ted 1.74 cm above the e l ec t rode surface.

T h e e l e c t r o d e s w e r e p o l i s h e d to a 10W su r f ace and c l eaned by u l t r a sound in dis t i l led water . The var ia t ion in h e i g h t f r o m the c e n t e r to t he e d g e of t he p r e p a r e d elec- t r o d e s was less t h a n 10W. C u r r e n t - p o t e n t i a l c u r v e s ob- t a ined wi th e l ec t rodes p r epa red in this m a n n e r were re- p roduc ib l e . E l e c t r o c h e m i c a l i n s t r u m e n t a t i o n i n c l u d e d a P r i n c e t o n A p p l i e d R e s e a r c h PAR-173 P o t e n t i o s t a t , a PAR-175 U n i v e r s a l P r o g r a m m e r , and a h igh - speed Hew- l e t t -Packa rd HP-7045A X-Y Recorder .

Resul t s . - -The e l e c t r o c h e m i c a l e x p e r i m e n t s i n c l u d e d m e a s u r e m e n t of c u r r e n t - p o t e n t i a l c u r v e s u n d e r s eve ra l

392

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Vol. 134, No. 2 S A L T F I L M O N A N I R O N D I S K 393

COUNTER- ELECTRODE

i

N 2 I IMPINGING 8OURCE ~ JET

REFERENCE ELECTRODE

|

�9 OUTLET

WORKING ELECTRODE

I i | ~ POXY

IRON

Fig. 1. Schematic representation of the experimental cell incor- porating an impinging-jet electrode.

f lu id ve loc i t i e s , m e a s u r e m e n t of c u r r e n t - t i m e c u r v e s for p o t e n t i a l s s t e p p e d f r o m - 1 . 0 V (SCE) to p o t e n t i a l s n e a r t h e p a s s i v a t i o n p o t e n t i a l , E D X a n a l y s i s of t h e r e s u l t i n g e l e c t r o d e s , a n d o p t i c a l a n d e l e c t r o n m i c r o s c o p y of t h e e l e c t r o d e s .

Current-potential curves.--Current-potential c u r v e s , p r e s e n t e d in Fig. 2, w e r e o b t a i n e d at a s w e e p r a t e of 20 m V / s for j e t s p e e d s of 0.10, 0.34, a n d 1.05 m/s. T h e p o t e n - t ia l w a s s w e p t f r o m - 1 . 0 to + 1.0V r e f e r e n c e d to t h e sa tu- r a t e d c a l o m e l e l e c t r o d e l o c a t e d in a s ide c h a m b e r . Oscil- l a t i o n s in t h e c u r r e n t w e r e o b s e r v e d n e a r t he p a s s i v a t i o n p o t e n t i a l . A l so n e a r t h e p a s s i v a t i o n p o t e n t i a l , t h e m e t a l s u r f a c e u n d e r w e n t a c h a n g e in s t r u c t u r e . A t t h e b e g i n - n i n g of t h e sweep , a r o u g h g r a n u l a r s u r f ace was pro- d u c e d . J u s t p r i o r to p a s s i v a t i o n , h o w e v e r , a v e r y u n i f o r m a n d s m o o t h s u r f a c e w as o b s e r v e d . As t h e p o t e n t i a l was i n c r e a s e d , t h e s m o o t h r e g i o n a p p e a r e d in i t i a l ly at t h e pe- r i p h e r y o f t h e e l e c t r o d e a n d p r o p a g a t e d i n w a r d t o w a r d t h e c e n t e r of t h e d i s k u n t i l t h e e n t i r e e l e c t r o d e was s m o o t h . P a s s i v a t i o n t o o k p l ace a t h i g h e r po t en t i a l s . The r a d i a l d e p e n d e n c e of t h e t r a n s i t i o n f r o m a g r a n u l a r to a s m o o t h s u r f a c e c a n b e d i s c e r n e d c l e a r l y at s w e e p r a t e s l ess t h a n 0.5 mV/s , a n d t h e r a n g e of p o t e n t i a l s a s s o c i a t e d w i t h t h i s t r a n s i t i o n c o r r e s p o n d s to t h e p o t e n t i a l r a n g e fo r w h i c h t h e o s c i l l a t i o n s in t h e c u r r e n t w e r e f i rs t ob- se rved . T h e s e o b s e r v a t i o n s a re s i m i l a r to t h o s e r e p o r t e d b y B e c k (14) w h o o b s e r v e d t h e f o r m a t i o n of a sa l t f i lm t h a t i n i t i a l l y p r e c i p i t a t e d at t h e p e r i p h e r y of a s h i e l d e d i ron e l e c t r o d e a n d s p r e a d i n w a r d t o w a r d t he cen te r . T h e t r a n s i t i o n r e g i o n was s t u d i e d t h r o u g h p o t e n t i a l - s t e p ex- p e r i m e n t s p r e s e n t e d in t h e f o l l o w i n g sec t ion .

Potential-step experiments.--The t i m e - d e p e n d e n t cur - r e n t is p r e s e n t e d in Fig. 3 for a d i s k s u b j e c t e d to a 1.05 m/s v e l o c i t y j e t a n d to a n i n s t a n t a n e o u s p o t e n t i a l c h a n g e f r o m - 1 V to a n a n o d i c p o t e n t i a l of 0.62V (SCE). T h e cor- r e s p o n d i n g c u r r e n t - p o t e n t i a l c u r v e o b t a i n e d w i t h a 20 m V / s s w e e p r a t e is g i v e n as c u r v e b in Fig. 2. S i m i l a r resu l t s w e r e o b t a i n e d for p o t e n t i a l s a n o d i c to +0.3V; how- eve r , t h e a m p l i t u d e of t h e o s c i l l a t i o n s i n c r e a s e d a t h i g h e r p o t e n t i a l s as s e e n in Fig. 2. T h e e l e c t r o d e s w e r e h e l d at t h e a n o d i c p o t e n t i a l for t h r e e m i n u t e s ; t h e f i rs t s i x t y s e c o n d s a n d t h e l a s t t e n s e c o n d s w e r e r e c o r d e d .

<

I-- Z 2 0 0

did bllc

- ' l . O f ~ 0.5 V IO 0.5 V !.0 V , r / ~ m - ~S.C,E.

Fig. 2. Measured current as a function of electrode potential referenced to a saturated calomel electrode with jet velocity as a parameter: (a) 1.05 m/s, without deaeration; (b) 1.05 m/s deaerated with nitrogen for 2h; (c) 0.34 m/s, deaerated; (d) 0.10 m/s, deaerated.

T h e c u r r e n t p r e s e n t e d in Fig. 3 a p p r o a c h e s a s t e a d y - s t a t e v a l u e w i t h i n 30s w h i c h i m p l i e s t h a t t h e s y s t e m is in a n u n s t e a d y s t a t e for m o s t o f t h e c u r r e n t - p o t e n t i a l c u r v e o b t a i n e d w i t h a 20 mV/s s w e e p ra te .

A se r i e s of t h e s e p o t e n t i a l - s t e p e x p e r i m e n t s for a con- s t a n t j e t s p e e d p r o v i d e d s t e a d y - s t a t e i n f o r m a t i o n fo r spec i f i c p o i n t s o n t h e c u r r e n t - p o t e n t i a l c u r v e . P h o t o - g r a p h s o f t h e e l e c t r o d e s u r f a c e s a re s h o w n in Fig. 4 for a n o d i c p o t e n t i a l s of +0.30, +0.55, a n d +0.62V at a j e t s p e e d of 1.05 m/s . T h e t r a n s i t i o n f r o m a g r a n u l a r to a s m o o t h su r f ace p r o c e e d e d r ad i a l ly i n w a r d w i t h i nc reas - ing p o t e n t i a l . A t +0.30V t h e d i s k is d o m i n a t e d b y g r a n u - lar c o r r o s i o n w i t h on ly t h e o u t e r e d g e b e i n g s m o o t h . T h e e l e c t r o d e was b o w l s h a p e d a f t e r c o r r o s i o n at +0.62V.

T h e prof i les of t h e e l e c t r o d e s w e r e o b t a i n e d b y a d e p t h of f ield t e c h n i q u e w i t h a Ze i s s i n v e r t e d - s t a g e op t i c a l mi-

, i ~" i i i i I

5 0 0

400

E ~ 300 I.- Z hi ~ 2 0 0

0

1 O 0

0

-I0~

/ t I ~ I I I t 1

175 18o " 5 lo 15 2o 25 TIME (s)

Fig. 3. Measured current as a function of time for an iron electrode subjected to o 1.05 m/s jet of deaerated IM sulfuric acid. The potential was stepped from - 1.0V to +0.62V (SCE) and held for three minutes.


394 J. Electrochem. Soc.: E L E C T R O C H E M I C A L S C I E N C E A N D T E C H N O L O G Y February 1987

sis was p e r f o r m e d . The low m a g n i f i c a t i o n m i c r o g r a p h s h o w n in Fig. 6a s h o w s an o v e r v i e w of t he t r a n s i t i o n f rom the g ranu la r cen t ra l r eg ion to the s m o o t h ou t e r re- g ion . A h i g h e r m a g n i f i c a t i o n m i c r o g r a p h of t h e t rans i - t ion b e t w e e n the g ranu la r and s m o o t h r eg ion is g iven in Fig. 6b. This m i c r o g r a p h shows tha t t he change b e t w e e n t h e g r a n u l a r and s m o o t h r e g i o n s is a b r u p t and o c c u r s r o u g h l y in t he c e n t e r of t he m i c r o g r a p h . T h e su r f ace r o u g h n e s s of the g ranu la r region, s h o w n in Fig. 6c, is due to p re fe ren t i a l co r ros ion at t he gra in boundar ies .

E l e c t r o n m i c r o g r a p h s for an e l e c t r o d e h e l d at a m o r e a n o d i c p o t e n t i a l [+0.62V (SCE)] are p r e s e n t e d in Fig. 7. F i g u r e 7a p r o v i d e s an o v e r v i e w of m o s t of t he sur face . T h e e l e c t r o d e was m o s t l y s m o o t h w i t h a sma l l g r a n u l a r r eg ion at t he center . A m i c r o g r a p h of the g ranu la r reg ion is g iven as Fig. 7b. The m i c r o g r a p h of the u n i f o r m reg ion (Fig. 7c) s h o w s a su r f ace p a t t e r n w h i c h m a y be associa- t ed wi th a film. Analys i s of this reg ion by E D X ind ica ted the p r e s e n c e of an i ron o x i d e l ayer w h i c h was no t de- t e c t ed on the g ranu la r surface.

M a t h e m a t i c a l M o d e l A m a t h e m a t i c a l model , p r e s e n t e d in A p p e n d i x A, was

used to exp la in the e x p e r i m e n t a l resu l t s p r e s e n t e d in the p r e c e d i n g sect ion. This m o d e l t rea ts t he coup led effects of t he radia l d e p e n d e n c e of the po ten t ia l of the so lu t ion a d j a c e n t to t h e e l e c t rode , t he c o n c e n t r a t i o n of f e r rous ions ad jacen t to t he e lec t rode , the cu r r en t dens i ty on the e l e c t r o d e , and mass t r a n s f e r to and f r o m the e l ec t rode . T h e n u m e r i c a l m e t h o d is s u m m a r i z e d in A p p e n d i x B. T h e d e v e l o p m e n t p r e s e n t e d in A p p e n d i c e s A and B is based on the w o r k of N e w m a n (1), Law (3), and L a w and N e w m a n (4) for r o t a t i ng d i s k e l ec t rodes . The t r e a t m e n t for t he s t agna t ion reg ion of an i m p i n g i n g j e t is ana lagous to tha t for a ro ta t ing d isk because the ve loc i ty to the d i sk is i n d e p e n d e n t of radia l pos i t ion .

Fig. 4. Optical micrographs of electrodes subjected to a 1.0S m/s jet at potentials of (a) +0.30V (SCE); (b) +0.55V; and (c) +0.62V.

c r o s c o p e at 500 t i m e s magn i f i ca t i on . T h e s e data , refer- e n c e d to t h e e p o x y he igh t , a re p r e s e n t e d in Fig. 5. The e l e c t r o d e prof i les s h o w tha t t h e ra te of c o r r o s i o n is h i g h e r in the s m o o t h reg ion than in the cen t ra l g ranu la r region. E tch tes ts p e r f o r m e d on the i ron sur face wi th 3% n i ta l s o l u t i o n s h o w e d tha t t he g ra in b o u n d a r i e s w e r e u n i f o r m on t h e e n t i r e sur face . T h e o b s e r v e d p h e n o m e - n o n was t h e r e f o r e no t a s s o c i a t e d w i t h a n o n u n i f o r m re- ac t iv i ty of t he e lec t rode . The sh ie ld ing of the i ron d i sk by the e p o x y at the edge p robab ly accoun t s for the r e d u c e d rate of co r ros ion seen at the edge of the e l ec t rode in Fig. 5. U n i f o r m access ib i l i ty of the sur face can be a s s u m e d at t h e b e g i n n i n g of t h e s e e x p e r i m e n t s b e c a u s e the e p o x y and the d i sk are at the same height . As the e l ec t rode corrodes the edges b e c o m e less access ib le and exh ib i t a re- d u c e d ra te of co r ros ion . T h e s e r e su l t s also i n d i c a t e t ha t g o o d b o n d i n g was a c h i e v e d b e t w e e n t h e i ron e l e c t r o d e and the insu la t ing e p o x y disk.

Analysis of the electrode surface.--Electron m i c r o g r a p h s of i ron e l e c t r o d e s s u b j e c t e d to a 1.05 m/s e l e c t r o l y t e j e t are p r e s e n t e d in Fig. 6 and 7. The e l ec t rode in Fig. 6 was h e l d at a p o t e n t i a l of +0.50V. T h e sca le in m i c r o n s is s h o w n in t h e b o t t o m r i g h t - h a n d c o r n e r of e a c h mic ro - graph. The nodu l e s seen on the sur face are due to oxida- t i o n by air w h i c h o c c u r r e d in t r a n s p o r t to t he D o w C h e m i c a l fac i l i t i e s in F r e e p o r t , Texas , w h e r e t he ana ly-

T 0.30

6 7-

o 'G 0 0'. 25 0'. 5 0'. 7'5 .0

r/r o

Fig. 5. Profiles of electrodes with applied potential as a parameter. Curves (a) represents the electrode surface before and (b) represents the electrode after the potential-step experiment.



bution is presented in Fig. 9 and 10 for je t speeds of 0.10 and 1.05 m/s, respect ively . The current d i s t r ibu t ion is un i fo rm at ca thodic potent ia ls (-0.5V) and for currents l imited by mass transfer (1.1V for a jet speed of 1.05 m/s and 0.5V for jet speeds of 0.1 m/s). At intermediate potentials the disk corrodes preferent ia l ly at the outer edge due to a local increase in the potent ia l dr iv ing force for corrosion.

The radial d is t r ibut ion of cur ren t is associa ted with a corresponding distr ibution for the surface concentrat ion of ferrous ions as shown in Fig. 11 and 12. For all potentials, the concen t ra t ion of ferrous ions at the surface of the electrode is either uniform or greatest at the outside edge of the disk. The concentrat ion distr ibution is essen- tially independent of the bulk concentrat ion for bulk ferrous concent ra t ions less than 10-3M, and the m a x i m u m concen t ra t ion is obta ined at the l imi t ing current . The value of the m ax im um surface concentrat ion is independent of je t ve loc i ty because the h igher je t ve loc i ty en- hances mass transfer both to and from the disk. The calculated m ax im um surface concentrat ion obtained in this s tudy was 3.42M. This value is sensi t ive to the value of diffusion coefficient, which was set to 0.1658 • l0 -~ cm/s [fol lowing Russel l and Newman (16)]. The sa tura t ion concentra t ion of ferrous ions in 1M sulfuric acid is 1.52M (25); therefore , the surface concent ra t ions obta ined in

Fig. 6. Electron micrographs of the electrode surface held at a potential of +0 .5V (SCE) and subjected to a ! .05 m/s jet. a) Overview of electrode including central granular region and parts of a smooth region; b) transition from a granular to a smooth surface; and c) central granular region.

Discussion Compar i son be tween the mode l ca lcula t ions and the

expe r imen t a l resul ts shows that the ring format ion, observed at potent ia ls where cur ren t osci l la t ions are also observed, can be at t r ibuted to formation of a ferrous sul- fate salt film. The expe r imen ta l cur ren t d is t r ibut ion, as de t e rmined by the e lec t rode profiles, suppor t the hy- pothesis that local current oscillations take place on the region of the electrode covered by the salt film.

Formation of a salt f i lm . - -The calculated average current density on the disk electrode is presented in Fig. 8 as a funct ion of the disk potential referenced to a saturated calomel reference electrode with the hydrodynamic constant (see Eq. [A-lb]) as a parameter. The hydrodynamic constant was obtained from comparison of exper imenta l va lues of the mass- t ransfer l imi ted cur ren t dens i ty to a modificat ion of the Levich equat ion [see Ref. (20)]. Inde- pendent measurement of mass-transfer l imited currents on r ing e lec t rodes has also been used to obtain the hydrodynamic constant (24). The results presented in Fig. 8 are equ iva len t to those obta ined by Law and N e w m a n (3, 4) for the ro ta t ing disk e lec t rode with the excep t ion that the passivation of the electrode is not included. This ex tens ion would follow Law and N e w m a n (3, 4) but is not needed for this work because the precipi tat ion of the salt film precedes passivat ion. The radial cur ren t distri-

Fig. 7. Electron micrographs of the electrode surface held at a potential of +0.62V (SCE) and subjected to a 1.05 m/s jet. a) Overview of electrode including central granular region and parts of a smooth region; b) transition from a granular to a smooth surface; and c) smooth outer region.


396 J. Electrochem. Soc.: ELECTROCHEMICAL SCIENCE AND TECHNOLOGY February 1987

U

..4

('~ I .t I

147 s -I

/

~/f//// / . . . . . . /

O

- / / , / '

O"

o/ ~ 0~.0 0 ' .5 1' ,0 1 . S

V - # s c e " V Fig. 8. Calculated average current density as a function of electrode

potential referenced to e saturated calomel electrode with hydrodynamic constant as e parameter. Dashed lines ere for the reference electrode located at infinity and solid lines are corrected for the location of the reference electrode used in the experimental study,

these calcula t ions are well wi th in the range for which precipi tat ion of a ferrous salt film is to be expected.

The radial distr ibution of surface concentrat ion of ferrous ions suggests that a ferrous salt film forms on the electrode at anodic potentials, extending radially inward with increas ing e lec t rode potential . A radius of transi-

o o

r/r o

Fig. 10. Calculated current distribution on the disk at a jet speed of 1.05 m/s (a = 147 s 1) with cell potential as a parameter.

t ion was defined to be the radius of granular corros ion such that rt = ro if the ent ire disk exper iences granular corrosion and rt = 0 if the entire disk corrodes smoothly. The radius of t rans i t ion was obta ined by measur ing the average radius for the granular region in pho tographs such as those presented in Fig. 4. The radius of transit ion between granular and uniform corrosion is presented in Fig. 13 as a function of potential for je t velocit ies of 0.1, 0.34, and 1.05 m/s. The t ransi t ion f rom granular to smooth corrosion takes place at a more anodic potential at high je t speeds.

0

O0 O"

C~"

O"

O"

. . . . I I 1 I

0.2 V(SCE)

0 , 1

0 . 0

- 0 . 1

- 0 . 2

- 0 . 3

Q .

% o o'.2 o'.4 'o'.6 o'.8

-0.4

-0.5

. 0

r / r o Fig. 9. Calculated current distribution on the disk at a jet speed of

0.1 m/s (a = 16 s -1) with cell potential as o parameter.

E

c.i

,4

o

4-

,T

IN-

~

,i-

6"

o

,I -, L J

0.2 V(SCE)

0.1 /

0.0

-0.2 ~

-0.3

- 0 . 4

- 0 . 5

:) 0 ' . 2 07 .4 0 ' . 6 0 ' . 8 1 . 0

r/r ~

Fig. 11. Calculated surface concentration of ferrous ions on the disk at o jet speed of O. 1 m/s (a = 16 s -1) with cell potential as a parameter.


- , 4

, 4

V o L 1 3 4 , No. 2

eo

~I u ~

I

.4

O.O O.Z 0 .4 0 .6 0 .8 ! .0

r/r o

Fig. 12. Calculated surface concentration of ferrous ions on the disk at a jet speed of 1.05 m/s (a = 147 s -1) with cell potential as a parameter.

C o m p a r i s o n b e t w e e n t h e m a t h e m a t i c a l m o d e l a n d t h e e x p e r i m e n t a l r e s u l t s r e q u i r e s d e t e r m i n a t i o n of t h e cri t i- ca l c o n c e n t r a t i o n for p r e c i p i t a t i o n of a f e r r o u s sa l t f i lm a n d a d j u s t m e n t for t h e e f fec t of t h e l o c a t i o n of t h e refer - e n c e e l e c t r o d e r e l a t i ve to t h e d i sk e l ec t rode . T h e c o n c e n -

0 ~

I t )

6"

Aal.05 m/S

I I I

~ a - ,i / ~ 0.0 0~.5 1'.0

S A L T F I L M O N A N I R O N D I S K 397

1 . 5

V - esc e , V

Fig. 13. Radius of transition from granular to uniform corrosion as a function of electrode potential referenced to a saturated calomel electrode with jet speed as a parameter: A) 1.05 m/s; �9 0.34 m/s; and ~) 0.1 m/s. Solid lines are calculated values adjusted for the location of the reference electrode used in these experiments.

t r a t i o n at w h i c h a sa l t f i lm was p r e s u m e d to f o r m was ob- t a i n e d b y m a t c h i n g t h e f r a c t i o n of l i m i t i n g c u r r e n t i / iHm at w h i c h t h e r i ng e f fec t a n d t h e c u r r e n t o sc i l l a t i ons w e r e f i rs t o b s e r v e d to t h e c a l c u l a t e d c u r r e n t - p o t e n t i a l c u r v e s g i v e n in Fig. 9 to ge t t h e d i s k p o t e n t i a l r e f e r e n c e d to i n f i n i t y . T h e c o n c e n t r a t i o n a t r / r o = 1 for t h i s p o t e n t i a l w a s o b t a i n e d for a j e t v e l o c i t y of 1.05 m/s to b e 3.11M. T h i s v a l u e w a s i n d e p e n d e n t of j e t v e l o c i t y a n d is 2.05 t i m e s l a r g e r t h a n t h e s a t u r a t i o n c o n c e n t r a t i o n r e p o r t e d for f e r r o u s ions in 1M su l fu r i c ac id (25). T h e f ac to r of 2.05 is c o n s i s t e n t w i t h t h e w o r k of B e c k (14) w h o o b s e r v e d s u p e r s a t u r a t e d c o n c e n t r a t i o n s of t h e o r d e r of 1.8-2.6 t i m e s t h e s a t u r a t e d v a l u e b e f o r e t h e o n s e t of sa l t f i lm for- m a t i o n . T h e t r a n s i t i o n r a d i u s b a s e d u p o n t h i s c o n c e n t r a - t i o n is p r e s e n t e d b y so l id l i ne s in Fig. 13 as a f u n c t i o n of t h e e l e c t r o d e p o t e n t i a l r e f e r e n c e d to t h e c a l o m e l e lec- t rode . T h e a c t u a l l o c a t i o n of t h e r e f e r e n c e e l e c t r o d e was b e l o w t h e p l a n e of t h e disk , a p o s i t i o n t h a t is u n d e f i n e d in t h e m a t h e m a t i c a l s o l u t i o n . A n e f f e c t i v e l o c a t i o n w a s o b t a i n e d b y m a t c h i n g t h e s o l u t i o n to t h e e x p e r i m e n t a l r e s u l t s fo r t h e h i g h - s p e e d je t . No a d d i t i o n a l a d j u s t m e n t was m a d e for t h e l o w e r ve loc i t i e s .

C u r r e n t o s c i l l a t i o n s . - - T h e c o m b i n e d r e s u l t s of Fig. 2 ( cu rve a or b), 4(a), a n d 5 ( cu rve for V = 0.3V) i n d i c a t e t h a t o sc i l l a t i ons a re n o t o b s e r v e d w h e n t h e c o r r o s i o n o c c u r s w i t h a g r a n u l a r m o r p h o l o g y . T h e o sc i l l a t i ons m u s t t h e r e - fore b e a s s o c i a t e d w i t h t h e o u t e r p o r t i o n of t h e e l e c t r o d e w h i c h c o r r o d e s w h i l e c o v e r e d b y a su l f a t e sa l t f i lm. T h e s u r f a c e prof i le s h o w n in Fig. 5 for V = 0.30V ind i - c a t e s t h a t s h i e l d i n g b y t h e e p o x y r e s u l t s in r e d u c e d cor- r o s i o n ra t e s on ly o n a l i m i t e d r e g i o n of t h e e l e c t r o d e be- t w e e n r / ro = 0.87 a n d r / ro = 1. T h i s a p p e a r s to b e c o n f i r m e d b y s h a r p b r e a k s in t h e s u r f a c e prof i les for V = 0.55 a n d V = 0.62V t h a t a lso o c c u r n e a r r /ro = 0.87. I t m a y a l so b e h e l p f u l to t h i n k in t e r m s of t h e a s p e c t r a t i o f o r m e d b y d i v i d i n g t h e d i s t a n c e a w a y f r o m t h e m e t a l - e p o x y b o u n d a r y in t h e r - d i r e c t i o n b y t h e d e p t h b e l o w t h e e p o x y p l a n e in t h e z -d i rec t ion . Th i s r a t io is 2.6 at r /ro = 0.87 a n d 10 at r / ro = 0.5.

T h e c u r v e for V = 0.55V (Fig. 5) s h o w s r e d u c e d corro- s i o n r a t e s f r o m r / ro = 0.6-1.0. A s s u m i n g t h a t s h i e l d i n g c a n on ly a c c o u n t for r e d u c e d r a t e s in t h e r e g i o n of r/r , , = 0.87-1.0, w h a t l e a d s to t h e r e d u c e d c o r r o s i o n r a t e s be- t w e e n r/r , , = 0.6-0.87? O n e p o s s i b l e a n s w e r to t h e q u e s - t i o n is t h e o c c u r r e n c e of p e r i o d i c p a s s i v a t i o n a n d ac t iva - t i o n of t h e r e g i o n u n d e r t h e sa l t film. T h e e x p e r i m e n t s in t h i s w o r k h a v e s h o w n tha t , a t V = 0.55V, a sa l t f i lm c o v e r s t h e s u r f a c e f r o m r / r , = 0.45-1.0. T h e c o r r o s i o n r a t e de- c r e a s e d in t h e r e g i o n of r/r , , = 0.6-0.87 w i t h o u t t h e i n f l u e n c e o f s h i e l d i n g . I f t h e i n f l u e n c e of a sa l t f i lm w e r e n o t c o n s i d e r e d , t h e h i g h e r p o t e n t i a l d r i v i n g force for cor- r o s i o n in t h i s r e g i o n w o u l d lead , n o t to r e d u c e d , b u t to i n c r e a s e d c o r r o s i o n ra tes . P e r i o d i c p a s s i v a t i o n a n d act i - v a t i o n in t h e r e g i o n b e t w e e n r/r , , = 0.6-0.87 (or to 1.0) w o u l d c r ea t e t h e o b s e r v e d c u r r e n t osc i l l a t ions . T h e t i m e s p e n t in t h e p a s s i v a t e d s t a t e w o u l d c a u s e t h e t i m e - a v e r a g e d c o r r o s i o n r a t e o n t h e r e g i o n b e t w e e n r /r , , = 0.6-0.87 to b e less t h a n t h e n e a r l y u n i f o r m c o r r o s i o n ra t e o b s e r v e d in t h e r e g i o n b e t w e e n r/r , , = 0.45-0.60. T h i s m e c h a n i s m for c u r r e n t o sc i l l a t i ons is c o n s i s t e n t w i t h t h e r e s u l t s of t h e o n e - d i m e n s i o n a l t i m e - d e p e n d e n t m a t h e - m a t i c a l m o d e l d e v e l o p e d b y R u s s e l l a n d N e w m a n (15, 16). T h i s h y p o t h e s i s is a lso s u p p o r t e d b y t h e o b s e r v a t i o n b y E D X of a n o x i d e f i lm in t h e r e g i o n c o v e r e d b y a s a l t f i lm a t 0.62V (SCE) w h i c h w a s n o t s e e n o n t h e g r a n u l a r su r face . I t is n o t n e c e s s a r y , h o w e v e r , to a s s u m e p e r i o d i c a c t i v e / p a s s i v e cyc l i ng . P e r i o d i c c h a n g e s in t h e sa l t f i lm p o r o s i t y or in t h e e x p o s e d a rea u n d e r t h e sa l t f i lm c o u l d a l so e x p l a i n t h e c u r r e n t o s c i l l a t i o n s a n d r e d u c e d cor ro - s i o n r a t e s . E i t h e r h y p o t h e s i s w o u l d b e c o n s i s t e n t w i t h t h e o b s e r v a t i o n t h a t t h e a m p l i t u d e of t h e c u r r e n t osci l la- t i o n s b e c o m e s l a r g e r as a l a r g e r p o r t i o n o f t h e d i s k be- c o m e s c o v e r e d b y t h e sa l t film.

C o n c l u s i o n s

T h e m a t h e m a t i c a l a n d e x p e r i m e n t a l s t u d y p r e s e n t e d h e r e p r o v i d e s e v i d e n c e t h a t c u r r e n t o sc i l l a t i ons r e p o r t e d for i r o n d i s k s in s u l f u r i c a c id a re o b s e r v e d w h e n a s a l t


398 J. Electrochem. Soc.: E L E C T R O C H E M I C A L S C I E N C E A N D T E C H N O L O G Y F e b r u a r y 1987

film covers the surface. The coupl ing of the effects of convect ive diffusion with the variation of potential in the electrolyte causes the precipitat ion of the salt film on a disk electrode to occur first at the periphery of the disk, ex tending inward as the potential is increased. This sup- ports the previous work of Beck (14) who also observed the format ion of a salt film that ini t ial ly prec ip i ta ted at the per iphery of an iron electrode and spread inward toward the center. This result has been observed both on a disk sub jec ted to a submerged imping ing je t ( reported here) and on a rotating iron disk (26). The precipitat ion of the salt film is accompanied by a change in the electrode morphology from a granular surface to a smooth surface. The salt film acts as a diffusion barrier, making the higher regions more accessible to corrosion and provid- ing a leveling effect. The increased rate of corrosion un- der the salt film as compared to the center of the disk is caused by the h igher potent ia l dr iv ing force present at the per iphery. Par t of the e lec t rode covered by the salt film exhibi ted reduced corrosion rates, and this observa- t ion may be due to per iodic ac t ive/pass ive cycl ing or other periodic changes associated with the salt film.

Acknowledgments This material is based upon work supported by the Or-

ganic Chemicals Depar tment , Dow Chemical USA, and by the Center for Innovat ive Technology grant No. CIT- MAT-85-027. Elec t ron mic roscopy and EDX analyses of the e lec t rodes were per fo rmed by Dow in Freeport , Texas. The use of the laboratory facilities of the Applied Elect rochemis t ry group in the Materials Science Depart- men t at the Univers i ty of Virginia and the ass is tance of Gregory S. Hickey are gratefully acknowledged.

Manuscr ip t submi t ted Jan. 22, 1986; revised manu- script received Ju ly 30, 1986. This was Paper 9 presented at the Boston, MA, Meeting of The Society, May 4-9, 1986.

A P P E N D I X A Theoretical Development

The disk electrode was of finite size and was assumed to be embedded in an infinite insulating plane. The walls of the cell and the counte re tec t rode were assumed to have no effect on the disk. Di lu te-solut ion theory with cons tan t diffusion coefficients, mobil i t ies , and act ivi ty coefficients was assumed to apply.

The Schmidt number Sc~ = v/D~ is large in electrolytic solut ions, and the concent ra t ions differ from their bulk values in only a thin region near the surface. In this region the fluid velocity can be approximated by

Vr = A r z ~ N / ~ 7 ~ v and v~ = -Az212~/-~7~v [A-la]

for a rotating disk where A = 0.51023. The fluid veloci ty near the electrode surface subjected to an impinging jet is given by (19, 22)

v~ = BrzAX/-~v and v~ = -Bz2ax/aT~v [A-lb]

where B = 1.312 and a is a hydrodynamic constant which is propor t iona l to the average je t velocity. Correlat ions reported for its dependence on the distance between the je t nozzle and the electrode are summarized by Chin and Tsang (20). For either system the equat ion of convect ive diffusion can be writ ten in the form

Oci Ocil_ 1 O~ci r o ~ - r - ~ o/] J 3 o~ ~ [A-2]

where

[ Av \,t3 _ _

for the rotating disk and

/ By \1/3 +=zt m, )

for the impinging jet system. A solution can be obtained for this system by a separation of variables, i.e.

Ci~Cl,~[l-I - ~ Am( r /2m ~}m(i~) } [A-3] ,~=o k To /

where the funct ions Ore(0 satisfy the different ial equat ion

O"m + 3~20'm - 6m~Om = 0 [A-4]

subject to the boundary condit ions Om = 1 at ~ = 0 and Om = 0 as ~ --+ oo. The concentrat ion at the surface of the disk is therefore given by

c~ ~ Am( r / 2m ] [A-5] m=o \ ro /

The coefficients Am are determined by matching the current densi ty obtained from the flux evaluated at the elec- t rode surface

sii - Di Oci ~-o nF ~ - z _ [A-6]

to the current density obtained from kinetic expressions or to the current density obtained from Ohm's law, also evaluated at the electrode surface, i.e.

0(P ~-o [A-7] i = -K 0z _

The validity of this approach rests upon the assumptions that the diffusion layer is thin, that the current near the e lec t rode is carr ied only by diffusion of ionic species (valid for an excess of suppor t ing electrolyte) , and that the concentrat ion in the outer region is uniform.

The potent ia l in the bulk is obta ined by solut ion of Laplace's equation, V20 = 0, subject to a specified current distr ibution at the electrode surface, a zero deriva- t ive condit ion on the insulating plane, and a value of zero for the potent ia l infini tely far from the disk. A solut ion for the e lect ros ta t ic potent ia l was given by Newman (1) for this system in terms of rotational elliptic coordinates

rp RT s BkP~k(~)M2k(O [A-8] nF k=0

where

z = ro~ r = ro[(1 + ~2)(1 - ~12)] 1/2

and P2k(~) is the Legendre polynomial of order 2k. M2k(~) is a Legendre funct ion of imaginary a rgumen t which satisfies

d~ (1 + ~) ~ - j 2k(2k + 1)M2k [A-9]

with the boundary condit ions

M2k= l a t ~ = 0 a n d M 2 k = 0 a s { ~ o o

The potential at the surface of the electrode is therefore given by

RT ~ BkP2k(n) [A-10] r176 - nF k=o

The potent ia l of the solut ion adjacent to the e lec t rode also enters into kinetic expressions for the corrosion reaction. A kinetic expression can be chosen for the corrosion of iron which exhib i t s the mass- t ransfer l imi ted m a x i m u m current, e.g. (3, 4)

0+)~ } i - k~ - e x p ( V - @o) nF ~ t RT

- kcc~ - R T ( V - r 1 7 6 [A-11]

The anodic react ion given by this express ion is presumed to be l imi ted by an unspeci f ied species. Such an express ion is cons is ten t with the observed dependence of the l imi t ing current on the square root of hydrodynamic constant. The reaction order p was assumed to be equal to one. Through Eq. [A-11], the effect of mass- transfer l imitations to the anodic reaction can be treated wi thou t expl ic i t solut ion of the equa t ion of convec t ive diffusion. Thus, the coefficients Bk can be de te rmined from (4)



Table B-I. Model parameters

Anodic transfer coefficient Cathodic transfer coefficient Reaction order of limiting reactant Number of electrons transferred Anodic rate constant Cathodic rate constant Bulk solution conductivity

~ = 1.0 ur = 1.0 p= 1.0 n= 2.0 nFk, = 1.000 • 107 A/crn 2 nFk~ = 2.078 • 10 -~G A/cm 2 K = 0.4 (g~" cm) -1

f0' Bk - (4k + 1) n~F2ro i(~)~P2k(~)d~ [A-12]

M'2k(0) RTK~

The rate of the corrosion reaction (see Eq. [A-11]) is inde- pe nden t of the surface concent ra t ion of ferrous ions at the anodic potentials where the salt film is presumed to form. This al lows a part ial decoupl ing of the equa t ions such that the Am coefficients can be obtained from the Bk coefficients through solution of

where

and

Ni "IT Bk- ~ Qk,mAm [A-13]

4 & ,,=o

(a /1/2~_ B]) t '/3 n2F2Dici,~

(4) I/ (4k + 1) O'm(0) ~(1 - ~2)mp2k(~l)d~ Qk.m - M'2k(0)

Ana logous express ions have been obta ined for the ro ta t ing disk sys tem (1, 3, 4) with the excep t ions that within the expression for Ni the constant B is replaced by A and the hydrodynamic constant a is replaced by the rotation speed ~.

A P P E N D I X B Salution Technique

Model pa ramete rs are p resen ted in Table B-I. The coefficients Bk were obtained from Eq. [A-12] [see Law (3) and Law and Newman (4)]. This step requires an iterative solution. The coeff icients A~ were subsequen t ly obta ined from Eq. [A-13]. This solution requires values for O'm(0) which were taken from N e w m a n (1). The use of va lues ob ta ined for a rota t ing disk is val id because the solution of Eq. [A-4] for Om is not affected by the choice of the rotating disk or impinging je t system. The concen- t ra t ion of the mass- t ransfer l imi ted species obta ined in this manne r th rough Eq. [A-5] were cons is ten t with the express ion (1 - i/iHm). This is expec ted because the Am coefficients were obtained from the Bk coefficients which were obta ined from a kinet ic express ion (Eq. [A-11]) in which the surface concentrat ion of the rate l imiting species was given by (1 - i/i,~m).

LIST OF SYMBOLS

a hydrodynamic constant for impinging jet, s- ' A 0.51023 Am coefficient in the expansion for concentrat ion B 1.312 Bk coefficient in the expansion for potential c~ concentra t ion of species i, tool/1 D, diffusivity of species i, cmVs F Faraday's constant, 96,487 C/eq i local current density, A/cm 2 i ~ mass-transfer l imited current density, A/cm 2

ka anodic rate constant, mol/s �9 cm 2 kr cathodic rate constant, cm/s n number of electrons transferred N~ defined following Eq. [A-13] p reaction order of l imit ing reactant P2k Legendre polynomial of order 2k Qk.m defined following Eq. [A-13] r radial position, cm ro electrode radius, cm rt radius of t rans i t ion f rom granular to smooth sur-

face, cm R universal gas constant, 8.2143 J /mol �9 K si s to ichiometr ic coefficient of species i in e lect rode

reaction Sc~ Schmidt number, ~/D~ T temperature, K vr radial velocity, cm/s v~ axial velocity, cm/s V applied electrode potential, V a, anodic transfer coefficient ~ cathodic transfer coefficient

rotational elliptic coordinate K bulk solution conductivi ty, (~ �9 cm) ' Om defined by Eq. [A-4] v kinematic viscosity, cm2/s p density, kg/cm ~

rotational elliptic coordinate 4) electrical potential, V �9 o solution potential adjacent to electrode, V

rotation speed of disk, s- '

REFERENCES 1. J. Newman, This Journal, 113, 1235 (1966). 2. L. Nanis and W. Kesselman, ibid., 118, 454 (1971). 3. C. Law, Jr., Ph.D. Thesis, Univers i ty of California,

Berkeley, CA (1980). 4. C. Law, Jr., and J. Newman, This Journal, 126, 2150

(1979). 5. I. Epelboin, C. Gabrielli, M. Keddam, J. C. Lestrade,

and H. Takenouti, ibid., 119, 1632 (1972). 6. P. P. Russell and J. Newman, ibid., 130, 547 (1983). 7. W. J. Muller, Trans. Faraday Soc., 27, 737 (1931). 8. K. Schwabe, Z. Physik. Chem., 214, 343 (1960). 9. Yu. P. Abakumova and N. N. Milyutin, J. Appl. Electro-

chem., USSR, 45, 809 (1972). 10. R. A. Alkire, D. Ernsberger, and T. R. Beck, This Jour-

nal, 125, 458 (1978). 11. R. A. Alkire and S. Perusich, Corros. Sci., 23, 1121

(1983). 12. J. H. Bartlett, Trans. Electrochem. Soc., 87, 521 (1945). 13. J. H. Bartlett and L. Stevenson, This Journal, 99, 504

(1952). 14. T. R. Beck, ibid., 129, 2412 (1982). 15. P. P. Russell, Ph.D. Thesis, Universi ty of California,

Berkeley, CA (1984). 16. P. Russell and J. Newman, This Journal, 133, 59 (1986). 17. J. B. Talbot and R. A. Oriani, Electrochim. Acta, 30,

1277 (1985). 18. J. B. Talbot, R. A. Oriani, and M. J. DiCarlo, This Jour-

nal, 132, 1545 (1985). 19. R. Alkire and A. Cangellari, ibid., 130, 1252 (1983). 20. D. T. Chin and C-H Tsang, ibid., 125, 1461 (1978). 21. P.T. Gilbert and F. L. Laque, ibid., 101, 448 (1954). 22. M. G. Miller, M.S. Thesis, Universi ty of Virginia,

Charlottesville, VA (1985). 23. H. Schlichting, "Boundary Layer Theory," 4th ed.,

p. 181, McGraw-Hill Book Company, New York (1960).

24. G. S. Hickey, M.S. Thesis, Univers i ty of Virginia, Charlottesville, VA (1986).

25. C. Linke, in "Solubil i t ies ," 4th ed., p. 1049, A.C.S., Washington, DC (1958).

26. C. Diem, M.S. Thesis, Universi ty of Virginia, Charlottesville, VA (1986).


The Distribution of Current and Formation of a Salt Film...

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