Electrochemical Polarrization - Theoretical Analysis of the Shape of Polarization Curves - Stern &...

7/27/2019 Electrochemical Polarrization - Theoretical Analysis of the Shape of Polarization Curves - Stern & Geary

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56 JOURNAL OF THE ELECT ROCHE MICAL SOCIETY January 1957aqueous reaction to form the hydrated fluorides which aresubsequently dehydrated a t elevated temperatures in anatmosphere of HF gas. Extensive studies were made of theconditions for the preparation of high-purity ZrF4, andpilot plant equipment is described which was used to pre-pare 100 lb batches of the fluorides.The reduction step was investigated thoroughly, par-ticularly for Zr, and those factors which affect metalquality and yield were determined. Reduction yields of96 % were obtai ned with both Zr and Hf. Af ter are-melti ng,the sponge Zr had a hardness of 40-45 Rockwell A andwas readily cold-rolled into sheet. Zr metal thus preparedhad a purity of about 99.8%.

Hf metal , similarly prepared, had a har dness of 69Rockwell A and was hot-rolled but was too brittle to beeasily cold worked. The Hf was low in metall ic impuriti es,but contained considerable amounts of C, N, and oxygen.

ACXNOWLI~DGMENTSThe aut hors are especially grateful to J. W. Starb uek

for his valuable c ontributio n in the experimental redue-

tion studies, to B. A. LaMont and co-workers for thechemical analyses, and to C. Lentz and associates for thespectrographic analyses.

Manuscript received February 23, 1956. ContributionNo. 480. Work was performed in the Ames Laborato ry ofthe A.E.C.Any discussion of this paper will appear in a DiscussionSection to be publi shed in the December 1957 JOURNAL.

REFERENCES1. K. A. WALSrI, U. S. A .E.C. Rep ort No. AECD-3640,(1950).2. D . PETERSON AND H. A. WILI-IEL?r Unpublished work,Am e s Laboratory, Iowa State College, (1950).3 . F . J . LA M B ER T, P . J . H A G ELSTO N, A N D R . O . H U TC lr lI -9SON, Oak Ridge Na tiona l Lab. Repo rt No. Y-595,(1950).4. J. L. WILLIAM S A ND B . W EA V ER , U . S . A.E.C. ReportNo. AECD-3329, (1950).5. M. U. ConEs, Rev. Sei. Instr., 6, 68, (1936).6 . R . M . T R E C O , J. Metals, 5 , 3 4 4 , (1 9 5 3 ) .7 . R . A . F o o s A ND H . A . W IL tI E LM , V . S . A . E . C . ReportISC-693, (1956).

E l e c t r o c h e m i c a l P o l a r iz a t io nI . A T h e o r e t i c a l A n a l y s i s o f t h e S h a p e o f P o l a r i z a t i o n C u r v e s

~ -~ . S T E R N A N D A . L . G E A R YMetals Research Laboratory, Electro Metallurgical Company, A Division of Union Carbide and Carbon Corporation,

Niagara Falls, New YorkABSTRACT

At low overvoltage values, devi ations from Tafel behavi or for a noncorrod ing elec-trode are due prima rily to the reverse reaction of the oxi dation-r eduction system, andat high overvoltages to concentration and/or resistance polarization. It isshown further that the practice of placing straight lines through a few experimentalpoints is extremely hazardous, while the indiscrim inate intr oduc tion of "br eaks " iscontrary to the electrode kinetics described.Further complexities arising from a corroding electrode are described. In this in-stance, the forward and reverse reactions of both of the oxidation-reduction s y s t em sforming the corrosion couple must be considered. This representation of the localpolarization diagram of a corroding metal is more fundamental than that used pre-viously in the l itera ture, and thus provides a clearer picture of the various factorswhich affect the corrosion rate and the shape of polarization curves.A region of linear dependence of potential on applied current is described for acorroding electrode by treatin g it in a manne r analogous to that for a noncorrodingelectrode. An equation is derived relat ing the slope of this linear region to the corrosionrate and Tafel slopes. This relation provides an important new experimental approachto the study of the electrochemistry of corroding metals since, in some instances, in-terfering reactions prevent determination of T~fel slopes at higher current densities.

Polarization measurements are an important researchtool in investi gation s of a variet y of electrochemical phe-nomena. Such measurements pernfit studies of the reac-tion mechanism and the kinetics of corrosion phenomenaand metal deposition. In spite of their wide applicabilityand extensive use, considerable uncertainty in the inter-pretation of polarization measurements still exists. Someof the uncertaint ies include the proper method of plotting

data and the correct interpreta tion of "breaks" in polariza-tion curves. Abrupt changes in slope of overvoltage vs.log curr ent ha ve been give n considerable significance n t hepast few years. Logan (1) examined various methods ofplotting cathodic polarization measurements to evaluatethe correspondence between current required for completecathodic protection of a system and current flow at thepotential break. He reported that the potential break

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V o l . 1 0 4 , N o . 1 E L E C T R O C H E M I C A L P O L A R I Z A T I O N 57method indicated a different current requirement thanthat indicated by other criteria9 In addition, breaks couldbe obtai ned regardless of whether the potential was plot-ted as a linear or logarithmic function of applied current.However, examina tion of the data presented indicates tha tthere is no real experimental evidence pointing towardexistence of breaks. In most cases, the plots would besthave been considered smooth curves rather than a seriesof straight lines. Schwerdtfeger and McDorman (2) pre-sented a theory which perm itte d calcul ation of the corro-sion rate of a metal from its polarization characteristics.The calculation was based on plott ing both anodie andcathodic polarization as linear functions of current andusing currents at the potential "breaks" in a formula de-rived esse ntially from trigonom etric consideratior/si Again,however, experime ntal evidence for the existence of breakswas not clear-cut. Still another discussion of potential"breaks" was presented recently by Johnson and Babb (3)who used irreversible thermodynamics to derive Pearson's(4) equation for the relation between the corrosion cur-rent and potential breaks. Data presented by these in-vestigators for the corrosion of Fe in KC1 solutions indi-eate tha t a great deal of imagination must be used whendrawing the curves in order to obt ain "breaks"9

Changes in slope rather than a sharp break can be ob-tained in H activation overvoltage measurements as aresult of the H being discharged by two different rate-dete rmini ng reactions. Parsons (5) discussed a dual mecha-nism of H discharge and from e nergy considerat ionscalculated the potential ranges where more th an one rate-dete rmin ing step might be expected. However, he did notimply that a "break" should be found. Bockris and Con-way (6) found the cathodic overvoltage vs. log i plots forAg in 0.1-7.0N HC1 solutions showed a marked change inslope at current densities which depended on acid concen-tration. They attribute the change in slope to a change insymmetry of the energy barrier at the electrode interfacerather than to a dual discharge mechanism. Here again asharp break was not found, the two linear portions of theplot being connected by a curve over a short range ofovervoltage values.

The purpose of this discussion is to analyze the shapeof polarizatio n curves in terms of modern concepts of elec-trochemistry. It is shown that man y of the reported breaksin polarization curves are not real, and result either fromattempts tc~.apply activation overvoltage theory to dataobtained unde r conditions where other t ypes of overvolt-age are included in the measurements, or from a combina-tion of insufficient data and an erroneous assumption thata break must exist. In such a presentation, it is convenientto consider first the shapes of polarization curves for anoncorr oding electrode, then to extertd the anal ysis to in-clude further complexities which arise from local actioncurrents.

i ~ O N C O R R O D I N G E L E C T R O D E S Y S T E MConsider a substance Z in a solution containing its ions

Z+2 In such a system at equilibrium, the rat e of oxidationThis might be Cu in equi libriu m with Cu+. The same

analysis also applies to an inert electrode in an oxidation-reduction system such as Pt in a ferrous-ferric solution orin a reducing acid solution saturated with H gas.

* o . Z ~ o B t . ' E . . . . . i . . . . . . . . J . . . . . . . . , ' , ' ~ ; , ,N /

; q x r 1 7 6~ O i ( : ] E O U l U B R I U M P O T E N T I A L

Z0 . 2 , . . . . . . . I , ,. 0 1 .I I I 0 I 0 0

C U R R E N T (M I C R O A M P E R E S )FIG. 1. Relationship between overvoltage and currentfor the anodic and cathodic reactions of a single electrodesystem.

of Z is equal to the rate of reduction of Z+(Z+ + e ~ Z).The reacti on rate and current flow are directly related ae-cording to F ar ad ay s Law. If {, is defined as the current inthe forward (reduction) direction (Z+ + e -~ Z) andg~ as the curre nt in the reverse (oxidation) dire ction(Z --* Z+ + e), the electrode equil ibrium may be expressedin the form

~ z = ~ = i o , z ( I )where i o , , is comm only called the exchange current9 Whenthe reaction rate is controlled by a slow step requiring anactivation energy, the dependence of current on over-voltage m ay be expressed as 2

~ ) (III )= / o ,~e x p + ~ , ,where the overvoltage, 7, is the difference between thepotential of the working electrode and the equilibrium po-tential of the reaction being studied, and/3'~ and fl~ areconstants. For a system with a symmetrica l energy barrier

9 tat the electrode inte rface, fl~ is equal to fl~P. Therefo re, Eq.(II) and (III) may be written as

~7 = -fl ~ log 7 - 9 (IV)~ o , z~ ( v )/ = q - f l ~ log -=-

Zo,z

where r = 2.3 fl~ = 2.3 fl~'.To aid in visualizing the relations given by Eqs. (IV)and (V), they have been plotted on Fig. 1 by arbitrarilygiving fl~ a va lue of 0.100 v an d i o . ~ a value of 1.0 #a. These

Other investigators have expressed these equations inmore fundamental terms. They are simplified here in ordern o t to detract from the main purpose of the discussion.Excellent literature reviews and discussions on the subjectare presented by Bockris (7, 8) and Vetter (9).



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58 J O U R N A L OF 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 J a n u a r y 1 9 5 7are of the same order of magnitude commonly found byexperiment; exchange current values generally vary fromI0 ~ to 100/aa and ~ values from 0.03 to 0.30 v.

Fig. 1 illustrates the relationship between the oxidationand reduction rates and the exchange current at the equi-libr ium pote ntia l and the effect of overvoltage on these rates.When the electrode equilibrium is disturbed by externalpolarization, the reaction rates change in accord with thecurves in Fig. 1. Experimentally, however, the individualoxidation or reduction rates cann ot be measured. The ex-ternal c urrent used for polarization actually is a measureof the difference between the two rates. For example, ifthe electrode under discussion (Fig. 1) is cathodically po-larized from its equil ibrium potentia l to a n overvoltageof -0 .1 v, the rate of reduction is equivalent to 10 /~awhile the rate of oxidation is 0.1 #a. The external currentrequired to polarize to this potential is the difference be-tween ~ an d ~ , or 9.9 ga. If the absolut e difference be-tween the forward and the reverse reaction currents isdefined as g, so that

- ~, = g~ (VI)then ~ is the external cathodic curren t when the electrodeis polarized to some overvoltage val ue, ~7. It is evide nt t hat$~ approaches $~ at overvoltage values sufficiently removedfrom the reversible potential. It is importa nt to emphasizeagain t hat experimentally the only factors measured direc-tly are y and ~ or ~. The individual rate of oxidation orreduction cannot be measured. Although theory showsthat there is a linear (Tafel) relationship between y andlog ~ or log ~, only ~ vs. log ~ is measured and plotted.Therefore, subst itu tin g Eq. (VI) in Eq. (IV), the theo-retical relationship between overvoltage and the logarithmof the external cathodic current is obtained.

n = - ~ , m g : (VII)$o,zUsing the same arbitra ry values for the constants ~

an d io, . . as indicated previously, and knowing the relationbetween ~ and L (Eq. V), a plo t of the variat ion of y withlog ~ may be co nstructed. This is shown i n Fig. 2. 3 Notethat deviation from a Tafel slope exists at the low valuesof applied current. Only when the reverse (oxidation) cur-rent, L, becomes insignificant in comparison to the for-ward or reduction current can a tru e Tafel relation be ex-pected. Further, Tafel slopes cannot be obtained untilapplied currents reach magnitudes of several times i o , ~ .If it is assumed that experimental verification of a linearrelationsh ip between ~ and log ~ requires linea rity over arange of about two logarithmic cycles of current, reliableestimates of the Tafel const ants ~ and io.~ require meas-ureme nts in the region of 1000 times i ... .

s Points shown on this figure and all subsequent figuresare not experimental. They are calculated from the de-rived equations and are included to illustrate the need forconsiderable data to define accurately the shape of a po-larization curve. It is quite evident, on inspection ofseveral of the figures, that insufficient data might lead toa series of straight lines.4 These consta nts are derived exper imentall y from dataobtained in the Tafel region, f~= is obta ined by measure -

(

~ - O I8>t l . I~ - ' O 2. JO>(Eh i>o _ 0 . 5

- O . ~ 8 4

NOBLE7 % " ~ . X o , ,X ' ~ r z

~ o\

Bz= moo %oI o , = I . O . l aA M P \ o \\

~ C T I V E~ , . . . . . . . . i , , , ,H , , I . . . . . . . . I

i i t 4 T l ~

\ \o, , , ,,,, ,I , N+ . . . . .

Ol I.O IO IOO I,OOO IQOOOA P P L I E D C A T H O D I C C U R R E N T , ~ x ( M IC R O A M P E R E S )

FIG. 2. Relationship between overvoltage and appliedcathodic current for a single electrode system.O l 1 - - " - , ~ . , k . . ~ ~ , , i ~ + . % i i i f i L l ' I I I I ' I * I I I , I I I I I I I [ I ' I . . . . .I h O B L E ~ o Q ~ + ~ - I zI / 0%

I / < r z %,- m | \ ~- 0 . 2 oN

=(. 9

> ' O . 3 7 ~ = ' ( 3 z L O G ~ + ; " ~ - - I o , " n F~z = o . l oo " ,,o ,, ,

o I o , z = 1 .O ~ A M PIL = 5 O O O . ~ A M P " " \ x- 0 .4 2 . 3 n ~ = O . 0 5 9

- a f t ]~ , C T I V E

, , , , J , , , i , , , . . . . . i . . . . , , , , i , i L I ' , , , I , i f , , ,0 . I 1 .0 I 0 I 0 0 1 , 0 0 0 I 0 , 0 0 0A P P L I E D C A T H O D IC C U R R E N T , ~ x ( M I C R O A M P E R E S }

FIG. 3. Effect of concentration polarization on the re-lationship between overvoltage and applied cathodiccurrent for a single electrode system.The measurement of activation overvoltage may be

complicated by two interfering phenomena--concentra-tion polarization and resistance drop effects--when thevalue of the exchange current is large. Concentration po-larization occurs when the reaction rate or the appliedexternal current is so large that the species being oxidizedor reduced canno t reach the surface at a sufficiently rapidrate. Th e solutio n adj acen t to the electrode surface be-comes depleted of the reacting ions, and the rate then iscontrolled by the rate at which the reacting species candiffuse to the surface. The electrode potential changessharply in this region until a potential is reached where anew reaction proceeds. The change in potential caused byment of the slope of ,1 vs. log i~ in the Tafel region, whileio,= is found by ext rapolati on of the Tafel region to thereversible potential.



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V o l . 1 0 ~ , N o . 1 E L E C T R O C H E M I C A L P O L A R I Z A T I O N 5 9c o n c e n t r a t i o n p o l a r i z a t i o n m a y b e r e p r e s e n t e d i n i t s si m~p l e s t f o r m ~ a s

R T iL - ~~? . . . . = 2 .3 ~ - l o g i L ( V I I I )w h e r e i L i s t h e l i m i t i n g d i f f u s i o n c u r r e n t f o r t h e f o r w a r dr e a c t i o n , R t h e g a s c o n s t a n t , T t h e a b s o l u t e t e m p e r a t u r e ,a n d F F a r a d a y ' s c o n s t a n t . W h e n ~ a p p r o a c h e s 0 . i i L ,c o n c e n t r a t i o n p o l a r i z a t i o n s t a r t s t o b e c o m e s i g n i f i c a n t e x -p e r i m e n t a l l y . T h e s h a p e o f a c u r v e , i n c l u d i n g b o t h a c t i v a -t i o n a n d c o n c e n t r a t i o n p o l a r i z a t i o n , i s i l l u s t r a t e d i n F i g . 3 .F o r t h e p u r p o s e o f t h i s i l l u s t ra t i on , i L h a s a r b i t r a r i l y b e e ns e l e c t e d a s 5 0 0 0 / z a. T h e l i m i t i n g d i f f u s i o n c u r r e n t i s af u n c t i o n o f t h e c o n c e n t r a t i o n o f t h e r e a c t i n g s p e c i e s , t h es t i r r i ng r a t e o f t h e s o l u t i o n , a n d a l l t h e o t h e r f a c t o r s w h i c hi n f l u e n c e t h e m a x i m u m r a t e a t w h i c h a n i o n c a n a p p r o a c ha s u r f a c e . ~

E x a m i n a t i o n o f F i g . 3 s h o w s t h a t d e v i a t i o n f r o m T a f e lb e h a v i o r c a u s e d b y c o n c e n t r a t i o n p o l a r i z a t i o n i s q u i t em a r k e d a n d i l l u s t ra t e s t h e d i f fi c u l ti e s i n o v e r v o l t a g e m e a s ~u r e m e n t s w h e n w o r k i n g n e a r t h e l i m i t i n g d i f f u s i o n c u r r e n t .N o t e t h a t i t w o u l d b e q u i t e c o n v e n i e n t t o s e p a r a t e a ne x p e r i m e n t a l c u r v e o f t h i s t y p e i n t o a t l e a s t t h r e e d i s t i n c ts t r a i g h t l i n e r e g i o n s a n d t h e n t o a t t e m p t t o i n t e r p r e t t h eb r e a k s t h e o r e t i c a l l y . S u c h c o m p l i c a t i n g i n t e r p r e t a t i o n s a r eo b v i o u s l y u n n e c e s s a r y . S t e r n ( 1 3 ) i l l u s t r a t e d t h e i n t e r -f e r e n c e w h i c h o c c u r s w h e n H o v e r v o l t a g e m e a s u r e m e n t sa r e c o n d u c t e d i n t h e r e g i o n w h e r e c o n c e n t r a t i o n p o l a r i z a -t i o n b e c o m e s s i g n i f ic a n t . B o t h S t e r n ( 1 4 ) a n d K i n g ( 1 5 )c r i t i c iz e d t h e r e c e n t w o r k o f S c h u l d i n e r ( 1 6) , p o i n t i n g o u tt h a t t h e b r e a k s i n t h e r e p o r t e d H o v e r v o l t a g e c u r v e s o n P tw e r e c a u s e d b y c o n c e n t r a t i o n p o l a r i z a t i o n e ff e ct s . I n a d -d i t i o n , K i n g p o i n t e d o u t t h a t c o r r e c t i o n s f o r c o n c e n t r a -t i o n p o l a r i z a t i o n c a n n o t b e m a d e q u a n t i t a t i v e l y w i t h o u ta c c u r a t e d a t a f o r i o n d i f f u s i o n r a te s . U n f o r t u n a t e l y , h o w -e v e r , c o n c e n t r a t i o n p o l a r i z a t i o n a p p e a r s t o h a v e b e e no v e r l o o k e d a g a i n i n m o r e r e c e n t w o r k w i t h P d ( 1 7 ) . I t i si n t e r e s t i n g t o n o t e t h a t m o r e t h a n 2 5 y e a r s a g o B o w d e n( 1 8 , 1 9 ) r e c o g n i z e d t h e p o s s i b i l i t y t h a t c o n c e n t r a t i o n p o -l a r i z a t i o n w a s t h e c a u s e o f b r e a k s w h i c h h e o b t a i n e d d u r -i n g H o v e r v o l t a g e m e a s u r e m e n t s o n 1 4 g .

R e s i s t a n c e b e t w e e n t h e r e f e r e n c e e l e c t r o d e a n d t h e p o -l a r i z e d e l e c t r o d e c o n t r i b u t e s s t il l a t h i r d t e r m t o t h e t o t a lo v e r v o l t a g c m e a s u r e d . T h i s i s a l i n e a r f u n c t i o n o f c u r r e n ta n d c a n b e e x p r e s s e d a s ~/ ~o s = $ x K ~ . I f t h e r e s i s t a n c et e r m K ~ ~ i s a r b i t r a r i l y g i v e n a v a l u e o f l 0 o h m s , t h e r e -s u l t i n g d e v i a t i o n f r o m T a f e l b e h a v i o r a p p e a r s a s i l l u s -t r a t e d i n F i g . 4 . N o t e h e r e a g a i n t h a t i t i s n o t o n l y a s i r e -

5 T o b i a s , E i s e n b e r g , a n d W i l k e ( 1 O , 1 1 ) a n d P e t r o c e l l i( 1 2 ) h a v e p r e s e n t e d e x t e n s i v e d i s c u s s i o n s o n c o n c e n t r a t i o np o l a r i z a t i o n .

6 T h e l i m i t i n g d i f f u s i o n c u r r e n t f o r H i o n r e d u c t i o n i nH C I c o n t a i n i n g a n i n d i f f e r e n t e l e c t r o l y t e a n d s t i r r e d b yn a t u r a l c o n v e c t i o n i s a p p r o x i m a t e l y 1 0 0 g a / c m ~ a t p H 3 . 1 ,1 0 0 0 # a / c m ~ a t p H 2 . 1 , a n d 1 0 , 0 0 0 t t a / c m z a t p H 1 . 1 ( 1 3 ) .

7 T h e r e s i s t a n c e i s a f u n c t i o n o f s o l u t i o n c o n d u c t i v i t y ,d i s t a n c e b e t w e e n t h e r e f e r e n c e e l e c t r o d e a n d t h e s a m p l e ,a n d t h e g e o m e t r y o f t h e s y s t e m . B a r n a r t t ( 2 0) h a s p r e -s e n t e d a n a n a l y s i s o f t h e m a g n i t u d e o f t h e I R d r o p e x -p e c t e d a s a f u n c t i o n o f b o t h t h e c u r r e n t d e n s i t y a n d t h es o l u t i o n c o n d u c t i v i t y . K , m a y a c t u a l l y b e a f u n c t i o n o fa p p l i e d c u r r e n t i f t h e c o n d u c t a n c e o f t h e s o l u t i o n a d j a c e n tt o t h e e l e c t r o d e i n t e r f a c e c h a n g e s ( 2 1 ) .

c r - - - - ~ : ~ , , , , : . . . . . , . . . . . . . . , . . . . . . . . , . . . . . . .NOBLE// ~162 z/ / I z % . .

- O . I " x \ o \~ 1 7 6

~-0.~ r~+izo ~ =-,oz LOG o-'T~,z IxKr " \ x. ~ z = m o o ~o I o , z = 1 . 0 . ~ A M P ~o,9 t - 0 3 ~ > = \K r = I 0 O H M S ~ ,\ \

-O.4 \\A C T I V E ' ~

- 0 . 5 . . . . . . . . . l . . . . . . . . I . . . . . . . . I . . . . . . . . * . . . . . . .0 .1 1 .0 I 0 I 0 0 1 , 0 0 0 I O p O 0APPLIED CATHODIC CURRENT, x(MICROAMPERES)

F I G . 4 . E f f e c t o f r e s i s t a n c e p o l a r i z a t i o n o n t h e r e l a t i o n -s h i p b e t w e e n o v e r v o l t a g e a n d a p p l i e d c a t h o d i c c u r r e n tf o r a s i n g l e e l e c t r o d e s y s t e m .p l e m a t t e r t o d r a w a b r e a k i n t h i s cu r v e , b u t t h a t t h e r ei s c o n s i d e r a b le l a t i t u d e i n c h o i ce o f t h e b r e a k p o s i t i o n .

CORRODING ELECTRODE SYSTEMO n e a d d i t i o n a l f a c t o r i s r e s p o n s i b le f o r d e v i a t i o n s f r o m

T a f e l l i n e a r i t y i n t h e l o w - c u r r e n t r e g i o n : c o r r o s i o n o r lo c a la c t i o n c u r r e n t . W h e n s h i f t i n g f r o m a n o n c o r r o d i n g t o ac o r r o d i n g s y s t e m , n l a n y c o m p l i c a t i n g f a c t o r s ar i s e . T w oc o - e x i s ti n g e l e c t r o c h e m i c a l r e a c t i o n s n o w a p p e a r : t h e p r e -v i o u s l y d i s c u s s e d o x i d a t i o n r e d u c t i o n s y s t e m , Z + + e ~ - Z ,a n d t h e o x i d a t i o n r e d u c t i o n s y s t e m o f t h e m e t a l , M + + eM . E a c h o f t h e s e s y s t e m s h a s i t s o w n e x c h a n g e c u r r e n ta n d T a f e l s l o p e s o t h a t t h e s t e a d y - s t a t e p o t e n t i a l o f t h ec o r r o d i n g m e t a l o c c u r s w h e r e t h e t o t a l r a t e o f o x i d a t i o ne q u a l s th e t o t a l r a t e o f r e d u c t i o n . T h u s a t t h e s t e a d y -s t a t e c o r r o s io n p o t e n t i a l ,

~ z + ~ , , , = ~ + T ~ ( I X )w h e r e Sm i s t h e r a t e o f r e d u c t i o n o f M + a n d Fm i s t h e r a t eo f o x i d a t i o n o f m e t a l M , a n d ~z a n d L a r e t h e r a t e s o f r e -d u c t i o n a n d o x i d a t i o n o f s p e c i es Z , r e s p e c t i v e l y . S i n c e t h ec o r r o s i o n r a t e b y d e f i n i t i o n i s ~ ,,, - { m , i t is e v i d e n t t h a tt h e r a t e m a y a l s o b e d e f i n e d a s ~ , - T~ a t t h e c o r r o s i o np o t e n t i a l . W h e n t h e c o r r o s io n p o t e n t i a l i s s u ff i c ie n t l y r e -m o v e d f r o m t h e e q u i l i b r i u m p o t e n t i a l s o f t h e r e a c t i o n s ,F ,, a n d T~ b e c o m e i n s i g n i f i c a n t i n c o m p a r i s o n t o {~ a n d T ,~ .T h u s t h e c o r r o s i o n r a t e b e c o m e s e q u a l t o 5 o r ~ . T h i sh a s b e e n u s e d d i r e c t l y b y S t e r n ( 13 ) t o c a l c u l a t e c o r r o si o nr a t e s o f Y e f r o m H o v e r v o l t a g e m e a s u r e m e n t s , a n d i n d i -r e c t l y b y E l z e a n d F i s h e r (22) t o d e t e r m i n e c o r r o s i o n r a t e si n i n h i b i t e d a c i d e n v i r o n m e n t s . F i g . 5 i l l u s t r a t e s t h e p o -t e n t i a l - c u r r e n t r e l a t i o n s h i p s f o r s u c h a m i x e d e l e c t r o d es y s t e m . T h e m e t a l o x i d a t i o n r e d u c t i o n s y s t e m h a s b e e nd r a w n a s s u m i n g a n io,m o f 0 .1 # a , a ~ m v a l u e o f 0 .0 6 0 v ,a n d a r e v e r s i b l e p o t e n t i a l o f - 0 . 1 6 0 v . T h e T a f e l c o n -s t a n t s f o r t h e Z o x i d a t i o n r e d u c t i o n s y s t e m a r e a s p r e -v i o u s l y d e s c r ib e d . T h u s , e q u a t i o n s f o r t h e v a r i o u s r e a c t i o n



5/8

60 JOURNAL OF T HE E L E CT ROCHE MICAL SOCIE T Y January 1957+0.1

~ m O , I I A -o~ \ , \a C T I V E % ,- 0 4 ' , , , , , , , , I . . . . . , , , I , ~ . . . . . . I , , , , , , , , I , , , , , ,o . I I . O I o I o o L O O 0 IO000

A P P L I E D C A T H O DI C C U R R E N T , ~ (M I C R O A M P E R E S )Fzo. 6. Relationship between overvoltage and appliedcathodic current for a corroding electrode system.

0 t . . . . . . j / T % . .. . .. . . I ' '. ~ . . .. . l . . .. . .. . I . . . . . "N O 6 L E / / " , , ( . - - I z , , , ' "o , . .< . j - - - % ,

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~.=-#=LOG'J--~t-~m*23-KT,-LOG~-'rto,z - . r k " "%Bz = o ,1 oo ~ ' .

= I O ~ A M P- 0 . 3 I L ' z= 5 0 0 0 ~ A M P x x\ "K = I 0 O H M S ~ " x x2 ~ R T9 n F = 0 . 0 5 9

A C T I V E ~ ~ ' x. . . . . . . d I I I l l l l l l I i , , i , , , l , , i 1 , i i i i ' i i l l , 'o l I .O I 0 I O O 1 , 0 0 0 I ~ 0 O 0A P P L JE D C AT H O D IC C U R R E N T . T , ( M I C R O A M P E R E S )

FIG. 7. Effect of co ncentra tion polari zation a nd re-sistance polarization on the relationship between over-voltage and applied cathodic current for a corroding elec-trode system.



6/8

V o l . 1 0 ~ , N o . 1 E L E C T R O C H E M I C A L P O L A R I Z A T I O N 61S i n c e t h e v a r i a t i o n s o f ~ a n d i ~ w i t h 7 a r e k n o w n [ E q .

( X I ) , ( X I I ) , a n d ( X I I I ) ] , E q . ( X V I t ) p e r m i t s a c a l cu l a -t i o n o f t h e p o t e n t i a l c h a n g e a s a f u n c t i o n o f a p p l i e d c a -t h o d i c c u r r e n t . A s i m i l a r e q u a t i o n m a y b e d e r i v e d f o ra n o d i c p o l a r i z a t i o n a n d w o u l d b e o f t h e f o r m :

7 = - - 0 . 1 6 0 + f l ,, l o g ~ + i ~ + $ ,, ( X V I I I )io.mF i g . 6 s h ow s t h e e x p e c t e d c u r v e f o r t h e o v e r v o l t a g e a s

a f u n c t i o n o f t h e a p p l i e d c a t h o d i c c u r r e n t , ( ~ ) , f o r t h es y s t e m d e s c r i b e d a b o v e . T h i s s h o u l d b e c o m p a r e d w i t hF i g . 2 w h i c h s h o w s t h e c o r r e s p o n d i n g c a t h o d i c p o l a r i z a -t i o n c u r v e f o r a n o n c o r r o d i n g e l e c t r o d e w i t h t h e s a m eT a f e l c o n s ta n t s . N o t e t h a t d e v i a t i o n fr o m T a f e l b e h a v i o ro c c u r s a t m u c h h i g h e c p o l a r i z i n g c u r r e n t s f o r t h e c o r r o d i n ge l e c t r o d e . T r u e T a f e l b e h a v i o r i s n o t e v i d e n t u n t i l p o -l a r i z i n g c u r r e n t s o f t h e o r d e r o f s e v e r a l t i m e s t h e c o r r o s io nc u r r e n t a r e a p p l i e d .

I f c o n c e n t r a t i o n p o l a r i z a t i o n a n d r e s i s t a n c e d r o p e f f ec t sa r e in c l u d e d i n t h e m e a s u r e m e n t s , E q . ( X V I I ) b e c o m e s7 = - f l ~ l o g i o , z

R T+ 2 . 3 ~ F - l o g iz - "ix - iz~ ~ K ~(xix)

F o r t h e s a m e v a l u e s o f iL a n d K , u s e d p r e v i o u s l y , F i g . 7s h o w s t h e e f f e c t o f e x t e r n a l a p p l i e d c a t h o d i c c u r r e n t , ~ , ,o n t h e m e a s u r e d p o t e n t i a l , 7 . F i g . 7 c o n t a i n s o n l y a v e r ys h o r t r e g i o n w h i c h e x h i b i t s t h e T a f e l s l o p e , ~ , . T h i s i s ,o f co u r s e , d u e t o t h e c h o i c e o f n u m b e r s u s e d i n t h i s e x a m -p l e . A n i n c r e a s e i n t h e c o r r o s i o n c u r r e n t o r i n K , a n d ad e c r e a s e i n i z w o u l d c o m p l e t e l y e l i m i n a t e a n y o b s e r v a b l eT a f e l b e h a v i o r . I t i s w o r t h e m p h a s i z i n g h e r e a g a i n t h a tw i t h a c u r v e s u c h a s F i g . 7 a v a r i e t y o f s t r a i g h t l i n e s e c -t i o n s m a y b e d r a w n w i t h b r e a k s p l a c e d a t c o n v e n i e n tp o s i t io n s . O b v i o u s l y , su c h a t r e a t m e n t w o u l d b e q u i t e i n -c o r r e c t a n d c o n t r a r y t o t h e e l e c t r o d e k i n e t i c s d e s c r i b e d .

LINEAR VS. T AFEL POLARIZATION BEHAVIORI n a d d i t i o n t o t h e p r o b l e m o f p o l a r i z a t i o n b r e a k s , t h e

q u e s t i o n a r i s es c o n t i n u a l l y a s t o w h e t h e r p o l a r i z a t i o ns h o u l d b e a l i n e a r o r l o g a r i t h m i c f u n c t i o n o f a p p l i e d c u r -r e n t . F o r e x a m p l e , S t r a u m a n i s , S h i h , a n d S c h I e e h t e n ( 2 5 ,2 6 ) h a v e f o u n d T a f e l b e h a v i o r f o r H o v e r v o l t a g e o n T i i nH C 1 , H B r , a n d H ~ SO ~ , b u t r e p o r t a l i n e a r d e p e n d e n c e o fo v e r v o l ta g e o n a p p l i e d c u r re n t i n H F . I n a d d i t i o n , th e s ea u t h o r s s h o w t h a t t h e l i n e a r r e la t i o n is m a i n t a i n e d i f t h eT i d i s so l v e s, w h i le th e T a f e l r e l a t i o n h o l d s i f t h e T i c e a s e st o d i s s o l v e b e c a u s e o f f l u o r id e a d d i t i o n s . T h a t t h e s e r e -s u l t s a r e i n a c c o r d w i t h t h e e l e c t r o d e k i n e t i c s d e s c r i b e da b o v e i s i l l u s t r a t e d h e r e .

A N o n c o r r o d i n g E l e c t ro d eB u t l e r a n d A r m s t r o n g ( 2 7 ) h a v e s h o w n t h a t t h e o v e r -

v o l t a g e o f a r e v e r s i b l e e l e c t r o d e i s a l i n e a r f u n c t i o n o f a p ~p l i e d c u r r e n t f o r v a l u e s o f o v e r v o l t a g e o n l y s l i g h t l y r e -m o v e d f r o m t h e r e v e r s i b l e p o t e n t i a l . P r o o f o f t h i s c a n b ef o u n d i n t h e f o l lo w i n g d e r i v a t i o n . R e a r r a n g e m e n t o f E q s .

~ . O t ' ~ d )~ B z .i I t

o\~ . o ~ o ~ - o ~

A ~ U E D e A r M o e l e C U R RZ N T , 7~ (M I C R O ~ PE R E S )F I ~ . 8 . L i n e a r r e l a t i o n s h i p b e t w e e n o v e r v o l t a g e a n da p p l i e d c u r r e n t f o r a s i n g l e e l e c t r o d e s y s t e m a t o v e r -v o l t a g e v a l u e s o n l y s l i g h t l y r e m o v e d f r o m t h e r e v e r s i b l ep o t e n t i a l .

( I V ) a n d ( V ) a n d s u b s t i t u t i o n o f t h e s e i n t o E q . ( V I ) y i e l d sg~ = i o , . [ 1 0 - ~ / e = - 1 0 + ~ / ~ . ] ( X X )F o r s m a l l v a l u e s o f 7 // 3~ w h e r e 1 0 ' / ~ m a y b e a p p r o x i -

m a t e d b y 1 - 7 /B~ (2 .3 ) and 10+ ~/~ ~ m a y b e a p p r o x i -m a t e d b y 1 + 7 // 3~ ( 2 .3 ) , E q . ( X X ) r e d u c e s t o

~ = - (2) (2.3) ( io ,~)7/fl , a n d ( X X I )- i o , . ( 2 ) ( 2 . 3 ) ( X X I I )

T h u s , m e a s u r e m e n t s o f o v e r v o l t a g e c l o s e t o t h e r e v e r s i b l ep o t e n t i a l w i ll y i e l d r e s u l t s i n a c c o r d w i t h E q . ( X X I I ) .F o r t h e s y s t e m Z + + e ~ Z wh ere B~ = 0 .100 and io.~ =d . )1 .0 ~a (F ig . 1 ) , Eq . (X X II ) ind ica te s th a t d -~,--, 7+0 =- 0 . 0 2 1 7 v / # a . F i g . 8 is a p l o t o f 7 a s a f u n c t io n o f 7~c a l c u l a t e d f ro m E q . ( V I I ) f o r s m a l l v a l u e s o f 7 . N o t e t h a tt h e l i n e a r r e l a ti o n p r e d i c te d b y E q . ( X X I I ) a p p l i es f or ~v a l u e s u p t o a b o u t 2 0 m y .

C o r r o d i n g E l e c t ro d eT h e s a m e a n a l y s i s m a y b e a p p l i e d t o a c o r r o d i n g e l e c-

t r o d e w h e r e t h e c o r r o s i o n p o t e n t i a l i s d e t e r m i n e d b y t h ei n t e r s e c t i o n o f t w o l o g a r i t h m i c p o l a r i z a t i o n c u r v e s . T h ec o r r o s i o n c u r r e n t i n t h i s e a s e i s a n a l o g o u s t o t h e e x c h a n g ec u r r e n t o f a n o n c o r r o d i n g e l e c t ro d e .T h u s 8

~ = - 2 . 3 i . . . . e ( ~ % . + - - -R ~ ) a n d ( X X I I I )de ) /3, t3m,+0 = - (2 .3) ( i r ( /~, + f l~) (X X IV )

F o r t h e m i x e d e l e c t r o d e s y s t e m d e s c r i b e d e a r l ie r a n d i l l us -t r a t e d i n F i g . 5 ,

d _ e~ = - 0 . 0 0 4 0 v / t ~ aa z ~ / e~ OF i g . 9 i s a p l o t o f e a s a h m c t i o n o f ~ c a l c u l a t e d f r o m E q .( X V I I ) f o r s m a l l v a lu e s o f e. H e r e a g a i n a l i n e a r r e l a t i o nb e t w e e n e l e c t r o d e p o t e n t i a l a n d a p p l i e d c u r r e n t i s fo u n d .I t i s i m p o r t a n t t o n o t e t h a t t h e l i n e a r b e h a v i o r e x t e n d s t o

s e i s t h e d i f f e r e n c e b e t we e n t h e p o l a r i z e d p o t e n t i a l a n dt h e c o r r o si o n p o t e n t i a l .



7/8

6 2 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 J a n u a r y 1 9 5 7

" x.0 I - - D I C~ g ~ z B m "z > _ - o ' - 2 . 3 i r z + , ~ m ) " , 0 0 0 4 (:S wj j " - . 0 2z z 9

o oa . a .

,

-.0 50 Z "~ 4 5 6 7 8 9 I0 II 12 13 14 15A P P LIE D C A T ,OOl C C U R R E N T .T ( M IC R OA M P E R E S )

F I G . 9 . L i n e a r r e l a t i o n s h i p b e t w e e n p o t e n t i a l a n d a p -p l i e d c u r r e n t a t p o t e n t i a l s o n l y s l i g h t l y r e m o v e d f r o m t h ec o r r o s i o n p o t e n t i a l . ~ i s t h e d i f f e re n c e b e t we e n t h e p o -l a r i z e d p o t e n t i a l a n d t h e c o r r o s i o n p o t e n t i a l .a p p l i e d c u r r e n t v a l u e s h i g h e r t h a n t h e c o r r o s i o n c u r r e n t .A s s t a t e d p r e v i o u s l y , T a f e l b e h a v i o r w o u l d n o t b e i n d i -c a t e d u n t i l a p p l i e d c u r r e n t v a l u e s a p p r o x i m a t e l y t e nt i m e s i . . . . a r e r e a c h e d .

I n t h e d a t a r e p o r t e d b y S t r a u m a n i s ( 25 , 2 6 ) f o r t h el i n e a r d e p e n d e n c e o f H o v e r v o l t a g e o n a p p l i e d c u r r e n t f o rT i i n H F , t h e r e g i o n w h e re T a f e l b e h a v i o r w o u l d b e e x-p e c t e d t o a p p e a r h a d n o t b e e n r e a c h e d e x p e r i m e n t a l l y b e -c a u s e o f t h e h i g h c o r r o s i o n c u r r e n t u n d e r t h e c o n d i t i o n so f t e s t . F o r e x a m p l e , t h e c o r r o s i o n r a t e o f T i i n 1 N H Fh a s b e e n r e p o r t e d a s e q u i v a l e n t t o 8 5 m a / c m 2 ( 2 8) , w h i l et h e o v e r v o l t a g e m e a s u r e m e n t s w e r e n o t c a r r i e d f a r t h e rt h a n 5 0 m a / c m 2.

E q . ( X X I V ) i s v a l u a b l e f r o m b o t h a t h e o r e t i c a l a n d a ne x p e r i m e n t a l p o i n t o f v i e w , s i n c e i t r e l a t e s t h e c o r r o s i o nr a t e a n d t h e T a f c l s l o p e s t o p o l a r i z a t i o n m e a s u r e m e n t sc l o se to t h c c o r r o s i o n p o t e n t i a l . T h u s , l o w c u r r e n t p o -l a r i z a t i o n m e a s u r e m e n t s c o m b i n e d w i t h c o r r o s i o n r a t ed a t a p e r m i t a c a l c u l a t i o n o f o n e o f t h e T a f e l s l o p e s i f t h eo t h e r i s k n o w n . T h i s i s o f g r e a t v a l u e w h e n c o n c e n t r a t i o np o l a r i z a t i o n o r I R d r o p e f f e c t s i n t e r f e r e w i t h m e a s u r e -m e n t s a t t h e h i g h e r c u r r e n t s . I n a d d i t i o n , m e a s u r e m e n t sa r e m a d e c l o s e t o t h e c o r r o s io n p o t e n t i a l , t h u s e l i m i n a t i n ga n y s u r f a c e c h a n g e s w h i c h m a y r e s u l t f r o m h i g h c u r r e n tp o l a r i z a t i o n .

i~-.DDITIONAL CA USE S FOR TA FEL DE VIAT IONT h e T a f e l c o n s t a n t s f o r F i g . 5 h a v e b e e n p i c k e d c o n -

v e n i e n t l y t o y i e l d a s in g l e T a f e l r e l a t i o n a t t h e c u r r e n t si l l u s t r a t e d i n F i g . 6 . I n s p e c t i o n o f F i g . 5 , h o w e v e r , r e v e a l st h a t ~,~ Le c o m e s s i g n i f i c a n t i n r e s p e c t t o $~ a t v e r y h i g hc u r r e n t v a l u e s . I n t h i s c u r r e n t r e g i o n , t h e T a f e l s l o p e o fF i g . 6 w i l l g r a d u a l l y c h a n g e f r o m ~ t o f ~ . W h e n ~ >> $ ~,a n e w T a f e l s l o p e e x is t s w i t h a v a l u e o f f l ~ . A p l 0 t o f t h eo v e r v o l t a g e c u r v e f o r t h i s s i t u a t i o n i s p r e s e n t e d i n F i g . 1 0.O b v i o u s l y , a d i f f e r e n t ch o i c e o f / ~ , f l , ~ , i . . . . a n d i . . . . c o u l dc r e a t e t h i s s h i f t i n T a f e l s l o p e a t l o w e r c u r r e n t s a n d s m a l l e rv a l u e s o f o v e r v o l t a g e . I t i s i m p o r t a n t t o n o t e t h a t t h ec h a n g e i n s l o p e t a k e s p l a c e g r a d u a l l y a n d r e s u l t s i n a c u r v ew h i c h i s o n l y " T a f e l - l i k e " i n n a t u r e o v e r a c o n s i d e r a b l er a n g e o f c u r r e n t . I t w o u l d b e a s i m p l e m a t t e r , a l t h o u g hi n c o r r e c t , t o d r a w s e v e r a l T a f e l l in e s t h r o u g h t h i s c u r v e .T h u s , i t i s e v i d e n t t h a t r e a l T a f e l b e h a v i o r w i ll n o t b e o b -

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APPLIs CATHODIC CURRENT.~x(MICROAMPERES)FIG. 10

s e r v e d i n a p o t e n t i a l r a n g e w h e r e t w o o r m o r e r e d u c t i o nr e a c t i o n s o c c u r a t s i m i l a r r a te s .A f u r t h e r e x t e n s i o n o f t h e c o n c e p t s p r e s e n t e d h e r e s h o w s

t h a t a n i m p r o v e m e n t i n t h e e f fi c ie n c y o f r e d u c i n g M + a ta n y g i v e n p o t e n t i a l m a y b e a c h i e v e d b y i n c r e a s i n g f l z ,d e c r e a s i n g / ~, ~, i n c r e a s i n g i . . . . d e c r e a s i n g i . . . . o r b yr e d u c i n g t h e d i f fe r e n c e b e t w e e n t h e r e v e r s i b l e p o t e n t i a l so f t h e t w o o x i d a t i o n r e d u c t i o n s y s t e m s . T h u s , t h e a n a l y s i sp r e s e n te d h e r e i s im p o r t a n t i n t h e s t u d y o f m e t a l p l a t in ge f fi c ie n c y a s w e l l a s c o r r o s io n p h e n o m e n a .

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

b e m a d e m o r e e x t e n s i v e b y i n c l u d i n g e v e n a t h i r d o x i d a -t i o n r e d u c t i o n s y s t e m 2 I t i s d o u b t f u l w h e t h e r a d e t a i l e dd i s c u s s io n o f s u c h a s y s t e m w o u l d b e o f b e n e f it a t t h ep r e s e n t , b u t i t w i l l b e i n c l u d e d i n a f u t u r e p u b l i c a t i o n .I t i s w o r t h n o t i n g i n p a s s i n g , h o w e v e r , t h a t t h e p o l a r i z a -t i o n c u r v e s w o u l d b e e v e n m o r e c o m p l e x t h a n t h o s e d i s -c u s s e d h e r e .

T h i s a n a l y s i s h a s i ll u s t r a t e d s e v e r a l i m p o r t a n t c o n c e p t sw h i c h a r c w o r t h l i s t i n g fo r e m p h a s i s .

1 . T h e r e p r e s e n t a t i o n o f a c o r r o d i n g m e t a l b y p o l a r i z a -t i o n d i a g r a m s s h o u l d b e e x t e n d e d t o i n c l u d e t h e r e v e r s er e a c t i o n s o f t h e v a r i o u s o x i d a t i o n r e d u c t i o n s y s t e m s w h i c ha r e o p e r a t i v e .

2 . D e v i a t i o n s f ro m T a f e l b e h a v i o r m a y b e c a u s ed b yl o c a l a c t i o n c u r r e n t s , c o n c e n t r a t i o n p o l a r i z a t i o n , a n d I Rd r o p e f f ec t s, a n d b y a c h a n g e i n t h e p r e d o m i n a n t e l e c t r o d er e a c t i o n .3 . A n e x p e r i m e n t a l p o l a r i z a t i o n c u r v e m a y s h o w a l i n e a rd e p e n d e n c e o f p o t e n t i a l o n a p p l i e d c u r r e n t f o r s m a l la m o u n t s o f p o l a r i z a t i o n .

4 . A n e q u a t i o n h a s b e e n d e r i v e d w h i c h r e l a t e s t h e s l o p eo f t h e l i n e a r r e g i o n o f a p o l a r i z a t i o n m e a s u r e m e n t t o t h ec o r r o s io n r a t e a n d t h e T a f e l s lo p e s . T h i s e q u a t i o n w i l lp r o v e v a l u a b l e w h e n i n t e r f e r i n g r e a c t i o n s p r e v c n t t h e d e -t e r m i n a t i o n o f t h e T a f e l c o n s t a n t s a t h i g h e r c u r r e n ts .

5 . T h e s h a p e o f a n e x p e r i m e n t a l e l e c t ro c h e m i c a l p o -l a r i z a t i o n c u r v e , e i t h e r c a t h o d i c o r a n o d i c , c a n b e a n a l y z e d

9 A n e x a m p l e o f t h i s w o u l d b e F e c o r r o d i n g i n a c i d w i t ha d e p o l a r i z e r s u c h a s o x y g e n o r f e r r i c i o n .



8/8

V o l . 1 0 ~ , N o . 1 E L E C T R O C H E M I C A L P O L A R I Z A T I O N 6 3i f s u f fi c ie n t d a t a a r e o b t a i n e d t o p e r m i t a n a c c u r a t e d e -s c r i p t i o n o f t h e c u r v e . P l a c i n g s t r a i g h t l i n e s t h r o u g h f o u ro r f i v e e x p e r i m e n t a l p o i n t s i s h a z ar d o u s , w h i l e t h e i n d i s -c r i m i n a t e i n t r o d u c t i o n o f " b r e a k s " i s c o n t r a r y t o m o d e r ne l e c t r o c h e m i c a l c o n c e p t s . S u f f i c i e n t i n f o r m a t i o n c o n c e r n -i n g t h e s y s t e m s h o u l d b e a v a i l a b l e t o e s t i m a t e w h e t h e rc o n c e n t r a t i o n p o l a r i z a t i o n o r r e s i st a n c e d r o p e f fe c ts h a v eb e e n i n c l u d e d i n t h e m e a s u r e m e n t s .

A l t h o u g h t h i s an a l y s i s c o n t a i n s o n l y c a l c u l a t e d p o l a r -i z a t i o n c u r v e s , a s u b s e q u e n t d i s c u s s i o n w i l l i l l u s t r a t e h o we x p e r i m e n t a l m e a s u r e m e n t s c o m p l y w i t h t h e e l e c t r o d ek i n e t i c s d e s c r i b e d .

T h e p i c t u r e o f a c o r ro d i n g m e t a l p r e s e n t e d h e r e is co n -s i s t e n t w i t h t h e c o n c e p t o r t h e o r y o f m i x e d p o t e n t i a l so r i g i n a l l y t r e a t e d b y W a g n e r a n d T r a u d ( 29 ) a n d s u b se -q u e n t l y d i s c u s s ed b y P e t r o c e l l i (3 0 ). T h e c o n c e p t o f d i s-c r e t e a n o d i e a n d c a t h o d i c a r e a s i n e l e c t r o c h e m i c a l c o rr o -s i o n m a y b e c o n s i d e r e d a s p e c i a l ca s e o f t h i s t h e o r y .

M a n u s c r i p t r e c e i v e d F e b . 2 4, 19 56 .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 i o 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 57 JO U RN A L.L I S T O F S Y M B O L S U S E D

~ = C a t h o d i c o r r e d u c t i o n c u r r e n t o f Z o x i d a t i o nr e d u c t i o n s y s t e m .~,~ = C a t h o d i c o r r e d u c t i o n c u r r e n t o f M o x i d a t i o n

r e d u c t i o n s y s t e m .~ = A n o d i c o r o x i d a t i o n c u r r e n t o f Z o x i d a t i o nr e d u c t i o n s y s t e m .~,,~ = A n o d i c o r o x i d a t i o n c u r r e n t o f M o x i d a t i o nr e d u c t i o n s y s t e m .io .~ = T h e e x c h a n g e c u r r e n t o f t h e Z r e a c t i o n . T h i si s e q u a l t o t h e o x i d a t i o n o r r e d u c t i o n c u r -

r e n t a t e q u i l i b r i u mio.m = T h e e x c h a n g e c u r r e n t o f t h e M r e a c t i o n . T h i si s e q u a l t o t h e o x i d a t i o n o r r e d u c t i o n c u r -r e n t a t e q u i l i b r i u m

d n~ = T h e T a f e l s l o p e o r ~ f o r t h e Z o x i d a t i o nr e d u c t i o n s y s t e m . dnt~,~ = T h e T a f e l s l o p e o r d ~ o g i f o r t h e M o x i d a t i o nr e d u c t i o n s y s t e m .

~ = T h e e x t e r n a l a p p l i e d c a t h o d i c c u r r e n t .~ = T h e e x t e r n a l a p p l i e d a n o d i c c u r r e n t .n = O v e r v o l t a g e o r d i f f e re n c e i n p o t e n t i a l b e t w e e n

a p o l a r i z e d e l e c t r o d e a n d a n e l e c t r o d e a te q u i l i b r i u m f o r t h e s a m e r e a c t i o n .~/ . . . = C o n c e n t r a t i o n o v e r v o l t a g e .~ s = R e s i s t a n c e o v e r v o t t a g e .

i L = L i m i t i n g d i f f u s io n c u r r e n t .i ~ = L o c a l a c t i o n c u r r e n t .Q o ~ = C o r r o s i o n c u r r e n t o r t h e l o c a l a c t i o n c u r r e n ta t t h e c o r r o s i o n p o t e n t i a l .

K , = R e s i s t a n c e f a c t o r f o r c a l c u l a t i n g t h e I R d r o pi n c l u d e d i n p o l a r i z a t i o n m e a s u r e m e n t s .T h i s f a c t o r i n c l u d e s t h e s o l u t i o n c o n d u c -t i v i t y a n d t h e s y s t e m g e o m e t r y .= T h e d i f f e r e n c e b e t w e e n t h e p o t e n t i a l p o l a r i z e db y a p p l i e d c u r r e n t a n d t h e c o r r o s io n p o t e n -t i a l .

d ~ ) = T h e s l o p e o f t h e o v e r v o l t a g e v s . c u r r e n t c u r v ek

f o rs m a l l o v e r v o l t a g e v a l u e s .

= T h e s l o p e o f t h e ~ v s . c u r r e n t c u r v e f o r s m a l ld~ ~-~o v a h l e s o f e .R E F E R E N C E S

1. K. H. LOGAN, Corrosion, 10, 206 (1954) .2. W. J. SCttWERDTFEGER AND 0 . N. M c D o R M A N , ThisJ our na l , 99, 407 (1952) .3. P. A. JOHNSON AND A. L. BABB, Ind. Eng . Che m. , 4 6 ,518 (1954).4 . J . M. PEARSON, Trans. Electrochem. Soc. , 81,483 (1942) .5 . R . PARSONS,J . Ch i m . Phy s . , 49, C 82 (1952) .6. J . O' M. BOCKRIS AND B. E. CONWAY, Tr ans . Far adaySoc. , 48, 724 (1952) .7 . J . O ' M . B o c K R I S A ND E . C . POTTER, Th i s J our na l , 99 ,169 (1952).8 . J . O ' M . B o c ~ m s , " M o d e r n A s p e c t s of E l e c t r o c h e m i s -t r y , " A c a d e m i c P r e s s I n c . , N e w Y o r k (1 95 4) .9 . K . J . VETTER, Z . E l e k tr oc he m. , 50, 435 (1955) .10 . C . W. TOBIAS, M. EISENBERG, AND C . R . W I L X E , Th i sJ our na l , 99, 395C (1952) .1 1 . C . R . W l L K E , M . EISENBERG, ANDC . W . TOBIAS, bid . ,100, 513 (1953).12 . J . V . PETROCELLI, bid . , 98, 187 (1951) .13 . M. STERN, ib id . , 102, 609, 663 (1955).14 . M. STERN, ib id . , 102, 356 (1955) .15 . C . V . KING, ib id . , 102, 193 (1955).

16. S. SCHULDIN~R, ib id . , 101, 426 (1954).17. J . P . HOAR E AND S. SCHULDINER, ib id . , 109., 485 (1955).18 . F . P . BOWDEN, Tr ans . Far aday Soc . , 24, 473 (1928) .19 . F . P . BOWDEN,Proc. Roy . Soc . , 126A, 107 (1930) .20. S. BARNARTT, Th i s J our na l , 99, 549 (1952) .2 1 . J . N . A G A R A ND F . P . BOWDEN,Proc. Roy . Soc . , 1 6 9 A ,206 (1938).22 . J . ELZE AND H. FISHER, Th i s J our na l , 99, 259 (1952)2 3 . U . R . EVANS, " M e t a l l i c C o r r o s i o n , P a s s i v i t y , a n dP r o t e c t i o n , " p . 3 5 0 , L o n g m a n s G r e e n a n d C o . , N e wY o r k ( 1 9 4 8 ) .2 4 . H . H . U n L I G , ed . , " C o r r o s i o n H a n d b o o k , " p . 4 36 , J .W i l e y & S o n s , I n c . , N e w Y o r k ( 19 48 ).25. M. E. STRAUMANIS, S. T . SHIH, AND A. W. SCHLECH-TEN, J . Phy s . Che m. , 59, 317 (1955) .2 6 . M . E . STBAUMANIS, S. T. SHIH, AND A. W. SCHLECH-TEN, Th i s J our na l , 102, 573 (1955).27. f t . A. V. BUTLER AND G. ARMSTRONG, J . Chem. Soc . ,1934, 743.28. M. E. STRAUMANIS AND P. C. CHEN, T h i s J o u r n a l , 9 8 ,234 (1951).2 9 . C . W A G N E R AN D W . TRAUD, Z. Elek trochem. , 44, 391(1938).3 0 . J . V . PETROCELLI, Th i s J our na l , 97, 10 (1950).

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