An Electrochemical pH-Stat and Its Application to Corrosion Studies [PDF]

An Electrochemical pH-Stat and. Its Application to Corrosion Studies. F. A. Posey, T. Morozumi, and E. J. Kelly. Chemist

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An Electrochemical pH-Stat and Its Application to Corrosion Studies F. A. Posey, T. Morozumi, and E. J. Kelly Chemistry Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee ABSTRACT A n apparatus has been developed which controls automatically the acidity of unbuffered solutions i n the region from pH 4 to 10. A potentiostat is used to control the potential of an i n e r t electrode on which the hydrogen g a s - h y drogen ion reaction occurs in a solution saturated with hydrogen gas. The inert electrode acts as both a sensing element and a r e g u l a t i n g electrode for the control of acidity. C u r r e n t from the potentiostat passes t h r o u g h the i n e r t electrode and an a u x i l i a r y polarizing electrode in an e x t e r n a l compartm e n t separated from the m a i n cell b y a salt bridge or porous plate. Transients which occur d u r i n g the r e g u l a t i n g action are presented and analyzed. The electrochemical p H - s t a t m a y be used to m e a s u r e corrosion rates. Limitations of the device are discussed and a modification is proposed which makes use of a differential amplifier instead of a potentiostat.

P r o b l e m s i n the c o n t r o l of s o l u t i o n a c i d i t y occur f r e q u e n t l y i n s t u d i e s on t h e k i n e t i c s of h o m o g e n e o u s and heterogeneous reactions which involve the cons u m p t i o n or l i b e r a t i o n of h y d r o g e n ions i n solution. T h e d e c r e a s e of a c i d i t y w i t h t i m e d u r i n g the c o r r o sion of i r o n or o t h e r m e t a l s i n u n b u f f e r e d s o l u t i o n s is a n o t a b l e e x a m p l e . A classical s o l u t i o n to the p r o b l e m i n v o l v e s the use of b u f f e r e d s o l u t i o n s in cases w h e r e the p r e s e n c e of b u f f e r i n g r e a g e n t s has no u n d e s i r a b l e effect on r e a c t i o n kinetics. More r e c e n t l y , i n g e n i o u s devices k n o w n as p H - s t a t s h a v e been developed (1-5). These electrochemical ins t r u m e n t s g e n e r a l l y e m p l o y t h e p r i n c i p l e of t h e a u t o m a t i c t i t r a t o r (6) a n d u t i l i z e t h e c o n t r o l l e d a d d i t i o n of r e a g e n t s b y use of e l e c t r i c a l l y d r i v e n b u r e t t e s or s y r i n g e p u m p s . S i m i l a r a p p a r a t u s has b e e n r e p o r t e d for t h e c o n t r o l of a c i d i t y i n processes of i n d u s t r i a l i m p o r t a n c e (7, 8), a n d a r e c e n t r e v i e w on p H a n d its c o n t r o l is a v a i l a b l e (9). A n e e d for a d i f f e r e n t t y p e of p H - s t a t arose i n this L a b o r a t o r y as a c o n s e q u e n c e of a t t e m p t s to m e a s u r e the p o l a r i z a t i o n b e h a v i o r of i r o n a n d o t h e r m e t a l s in u n b u f f e r e d s o l u t i o n s over the p H r a n g e 4 to 10. T h e use of b u f f e r m i x t u r e s in e l e c t r o c h e m i c a l k i n e t i c studies is s o m e t i m e s u n d e s i r a b l e b e c a u s e of the poss i b i l i t y of i n t r o d u c t i o n of e x t r a n e o u s r e a c t i o n s or of specific effects on the k i n e t i c s of i n t e r f a c i a l p r o c esses. I n a d d i t i o n , t h e use of t h e a u t o m a t i c t i t r a t o r t y p e of p H - s t a t possesses some d i s a d v a n t a g e s , p a r t i c u l a r l y i n s t u d i e s r e q u i r i n g t h e a b s e n c e of a t m o s p h e r i c o x y g e n . Besides t h e effort n e e d e d to p r e p a r e s t a n d a r d r e a g e n t s , c o n s i d e r a b l e difficulty m a y be experienced in deoxygenating and pre-electrolyzing the s o l u t i o n s used, a n d c o r r e c t i o n s are n e c e s s a r y for v o l u m e c h a n g e s d u e to t h e a d d i t i o n of r e a g e n t s . I n o r d e r to c i r c u m v e n t these difficulties, a n a p p a r a tus was d e v i s e d w h i c h t a k e s a d v a n t a g e of f a v o r a b l e p r o p e r t i e s of the h y d r o g e n g a s - h y d r o g e n ion r e a c tion on p l a t i n u m or o t h e r i n e r t electrodes. A n elec-

t r o n i c p o t e n t i o s t a t (10, 11) is used to c o n t r o l p r e cisely t h e p o t e n t i a l of a l a r g e p l a t i n u m electrode i n a s o l u t i o n s a t u r a t e d w i t h h y d r o g e n gas. T h e c u r r e n t r e q u i r e d for t h e c o n t r o l of p o t e n t i a l passes t h r o u g h a n a u x i l i a r y p o l a r i z i n g electrode located i n a c h a m b e r e x t e r i o r to the p r i m a r y cell a n d c o n n e c t e d to this cell b y use of a salt b r i d g e or p o r o u s plate. The l a r g e p l a t i n u m electrode acts b o t h as a s e n s i n g elem e n t a n d as a r e g u l a t i n g electrode for t h e a d d i t i o n or r e m o v a l of h y d r o g e n ions. W i t h i n c e r t a i n l i m i t a tions, t h e p r e c i s i o n w i t h w h i c h the p o t e n t i a l of t h e p l a t i n u m electrode is c o n t r o l l e d d e t e r m i n e s t h e d e gree of c o n t r o l of s o l u t i o n acidity. F o r electrode s y s t e m s i n w h i c h the use of a h y d r o g e n a t m o s p h e r e c a n be t o l e r a t e d , this m e t h o d of p H c o n t r o l possesses c e r t a i n a d v a n t a g e s . No c o m p l e x e l e c t r o m e c h a n i c a l devices are n e c e s s a r y w i t h t h e i r a t t e n d a n t difficulties of r e g u l a t i o n , r e a g e n t p r e p a r a t i o n , a n d d e o x y g e n a t i o n . S i n c e n o e x t e r n a l r e a g e n t s are a d d e d b y the c o n t r o l l i n g device, n o s o l u t i o n v o l u m e c o r r e c tions a r e n e c e s s a r y ; this is p a r t i c u l a r l y c o n v e n i e n t i n l o n g - t e r m e x p e r i m e n t s . S o l u t i o n a c i d i t y is c o n t r o l l e d a u t o m a t i c a l l y b y the e l e c t r o n i c p o t e n t i o s t a t , a n d t h e p H m a y be c h a n g e d easily a n d p r e c i s e l y b y m e r e l y c h a n g i n g t h e p o t e n t i a l at w h i c h t h e p l a t i n u m electrode is m a i n t a i n e d . F u r t h e r m o r e , the m e t h o d is m o s t effective i n the p H r e g i o n n e a r n e u t r a l i t y , w h e r e precise p H c o n t r o l is o f t e n difficult to o b t a i n i n u n b u f f e r e d solutions. Some r e s u l t s of e x p e r i m e n t s on the p r o p e r t i e s of t h e e l e c t r o c h e m i c a l p H - s t a t are p r e s e n t e d below, t o g t h e r w i t h a n a n a l ysis of the t r a n s i e n t s e n c o u n t e r e d d u r i n g c h a n g e s of s o l u t i o n acidity. T h e a p p l i c a t i o n of t h e device to the m e a s u r e m e n t of corrosion r a t e s is discussed. I n a d d i tion, a m o d i f i c a t i o n of the m e t h o d is p r o p o s e d w h i c h m a k e s use of a d i f f e r e n t i a l a m p l i f i e r i n s t e a d of a p o t e n t i o s t a t . T h e d i f f e r e n t i a l a m p l i f i e r t y p e of p H stat uses a glass electrode (or o t h e r p H - r e s p o n s i v e e l e c t r o d e ) as t h e p H - s e n s i n g e l e m e n t , is n o t r e -

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1184

J O U R N A L OF THE E L E C T R O C H E M I C A L SOCIETY

H~ D

TT

Fig. 1. Schematic diagram of potentiostat type of electrochemical pH-stat. A, Electronic potentiostat; B, large platinum electrode; C, auxiliary polarizing electrode; D, inlet and bubbler for hydrogen gas; E, reference electrode; F, stirrer (magnetic); G, salt bridge or porous disk; I, primary cell; II, exterior polarizing chamber.

s t r i c t e d to u s e w i t h s y s t e m s in w h i c h a h y d r o g e n a t m o s p h e r e is m a i n t a i n e d , a n d p o s s e s s e s i m p r o v e d transient response. Experimental

A s c h e m a t i c d i a g r a m of a n e x p e r i m e n t a l cell for t h e e l e c t r o c h e m i c a l p H - s t a t is s h o w n in Fig. 1. T h e potential difference between the large platinum electrode (B) and the reference electrode (E) prov i d e s t h e i n p u t v o l t a g e to t h e p o t e n t i o s t a t . A n y d i f ference between this voltage and the reference volta g e s e t t i n g on t h e p o t e n t i o s t a t a c t u a t e s a flow of current between the platinum electrode and the p o l a r i z i n g e l e c t r o d e in c o m p a r t m e n t II. T h e m a g n i t u d e a n d d i r e c t i o n of c u r r e n t flow a r e s u c h as to minimize the difference between the input voltage and the potentiostat reference voltage. If the rev e r s i b l e p o t e n t i a l of t h e p l a t i n u m e l e c t r o d e in t h e s o l u t i o n in c o m p a r t m e n t I differs f r o m t h e p o t e n t i o s t a t r e f e r e n c e v o l t a g e , t h e flow of c u r r e n t p o l a r i z e s t h e e l e c t r o d e to t h e v a l u e of t h e r e f e r e n c e v o l t a g e . I n a m a n n e r d e p e n d i n g on t h e p o l a r i z a t i o n c h a r a c t e r i s t i c s of t h e h y d r o g e n g a s - h y d r o g e n i o n r e a c t i o n on t h e e l e c t r o d e a n d on t h e r a t i o of e l e c t r o d e a r e a to solution volume, Faradaic current from the hydrog e n g a s - h y d r o g e n ion r e a c t i o n t h e n p a s s e s t h r o u g h t h e e l e c t r o d e i n t e r f a c e a n d t h e c o n c e n t r a t i o n of h y d r o g e n ions in s o l u t i o n i n c r e a s e s o r d e c r e a s e s w i t h t i m e . W h e n t h e p H of t h e s o l u t i o n a p p r o a c h e s t h e v a l u e at w h i c h t h e r e v e r s i b l e p o t e n t i a l e q u a l s t h e p o t e n t i o s t a t r e f e r e n c e v o l t a g e , c u r r e n t flow a p p r o a c h e s z e r o a n d t h e p H is s u b s e q u e n t l y c o n t r o l l e d a u t o m a t i c a l l y w i t h a p r e c i s i o n w h i c h d e p e n d s on t h e c o n t r o l c h a r a c t e r i s t i c s of t h e p o t e n t i o s t a t . T h e p o t e n t i o s t a t u s e d in t h e p r e s e n t s t u d i e s p e r m i t t e d p r e c i s e c o n t r o l of e l e c t r o d e p o t e n t i a l s o v e r a n e x t e n d e d p e r i o d 3 It i n c o r p o r a t e d a c h o p p e r - s t a b i lized o p e r a t i o n a l a m p l i f i e r of h i g h gain. M a x i m u m o u t p u t v o l t a g e w a s --+100v a n d o u t p u t c u r r e n t c o u l d a t t a i n --+25 ma. E l e c t r o d e p o t e n t i a l s w e r e c o n s t a n t to 1 A n i m p r o v e d m o d e l o f t h i s p o t e n t i o s t a t is a v a i l a b l e c o m m e r c i a l l y as t h e M o d e l 610 P o t e n t i o s t a t - G a l v a n o s t a t , m a n u f a c t u r e d b y F a i r port Instruments, Inc., Oak Ridge, Tennessee.

December 1963

w i t h i n -----0.1 m v a t all t i m e s w h e n t h e p o t e n t i o s t a t w a s c o n t r o l l i n g , as c o u l d b e o b s e r v e d o s c i l l o s c o p i cally. R e s p o n s e t i m e of t h i s t y p e of p o t e n t i o s t a t w a s s l o w c o m p a r e d to t h a t of t h e s t r a i g h t - a m p l i f i e r t y p e , but this was a negligible disadvantage for the prese n t p u r p o s e s . T h e e x p e r i m e n t a l cell w a s c o n s t r u c t e d of P y r e x glass w i t h a f r i t t e d glass d i s k to m i n i m i z e d i f f u s i o n b e t w e e n e l e c t r o d e c o m p a r t m e n t s (cf. Fig. 1). A c o m m e r c i a l s a t u r a t e d c a l o m e l e l e c t r o d e w a s e m p l o y e d as r e f e r e n c e e l e c t r o d e . H y d r o g e n gas p u r i fied o v e r c o p p e r t u r n i n g s in a t u b e f u r n a c e w a s effused into t h e s o l u t i o n a n d p r o v i d e d s o m e d e g r e e of s t i r r i n g . A d d i t i o n a l s t i r r i n g w a s p r o v i d e d b y u s e of a T e f l o n - c o a t e d m a g n e t i c s t i r r i n g b a r . T h e p H of t h e s o l u t i o n w a s m o n i t o r e d b y u s e of a c o m m e r c i a l glass e l e c t r o d e ( n o t s h o w n in Fig. 1). B o t h t h e p o t e n t i a l of t h e glass e l e c t r o d e a n d t h e c u r r e n t o u t p u t of t h e p o t e n t i o s t a t w e r e r e c o r d e d w i t h t i m e . S o l u tions w e r e p r e p a r e d w i t h t r i p l y d i s t i l l e d w a t e r , o b tained by redistilling distilled water from the labo r a t o r y s u p p l y in a t w o s t a g e q u a r t z still. A n a l y t i c a l r e a g e n t g r a d e c h e m i c a l s w e r e u s e d in t h e p r e p a r a t i o n of a l l s o l u t i o n s Results

S o m e e x p e r i m e n t a l r e s u l t s a r e s h o w n in Fig. 2 for t h e v a r i a t i o n of t h e glass e l e c t r o d e p o t e n t i a l w i t h t i m e d u r i n g a d j u s t m e n t of s o l u t i o n a c i d i t y b y t h e electrochemical pH-stat. Curves A through D corr e s p o n d to c h a n g e s of 60 m v in t h e p o t e n t i o s t a t r e f e r e n c e v o l t a g e . T h e glass e l e c t r o d e p o t e n t i a l c h a n g e s in a n e x p o n e n t i a l m a n n e r w i t h t i m e a n d f i n a l l y a p proaches and maintains the desired potential. Curves E and F exhibit a somewhat different behavior; c u r v e E s h o w s t h e t r a n s i e n t b e h a v i o r f o u n d for a c h a n g e f r o m p H 4 to p H 9 w h i l e c u r v e F s h o w s t h e

+ .t5

+ .~o

~-

~ * .05

-

o

o

-

.

- .05

- .10 0

t

2

3

4

5

6

7

8

9

t0

tt

t2

t3

14

t5

TIME (mmutes)

Fig. 2. Variation of glass electrode potential with time during adjustment of solution acidity by electrochemical pH-stat. Solution, 0.5M NaCI; temperature, 25~ atmosphere, H2. Curve

Potential change, mv

pH, approx. Initial Final

A

--60

5

6

B C D E F

--60 --60 --60 --300 -I- 3 O0

6 7 8 4 9

7 8 9 9 4

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VoL 110, No. 12

ELECTROCHEMICAL pH-STAT

1185

p H - s t a t is capable of controlling pH to approximately +__0.01 pH unit over an indefinite period.

tO-2

A

Discussion

Theory o~ operation.--The forms of the transients in Fig. 2 and 3 m a y be calculated by use of wellk n o w n concepts of electrochemical kinetics (12). The net flux (vs ( t ) ) of h y d r o g e n ions at the interface of the platinum electrode due to the h y d r o g e n g a s - h y d r o g e n ion reaction m a y be expressed by Eq. [1]. a In Eq. [1], ka a n d k c are the

t0 3

t0-4

t

2

3

4 5 6 7 8 TiME (minutes)

9

i!

~0

Fig. 3. Variation of current from potentiostat with time during adjustment of solution acidity by electrochemical pH-stat. Solution, 0.SM NaCI; temperature 25~ atmosphere, Ha. Curve A B C D

Potential change, mv --60 +60 --60 -I-60

pH, approx. Initial Final 4 5 5 4 5 6 6 5

k--.C~ - EtCh+ (t)

v~(t) =

[1]

l+--fiTa f" +--fiT ko electrochemical specific rate constants for the anodic and cathodic partial processes, respectively, of the reaction, 2 H + ( a q ) - F 2 e - = H a ( g ) . Equation [1] takes formal account of the existence of limiting currents due to mass transfer of the reactants, dissolved molecular hydrogen (CHa) and h y d r o g e n ions (CH+ ( t ) ) . The diffusion coefficients of Ha and of H + are symbolized by Da and Dc, respectively, and 8a and $c are the corresponding hypothetical thicknesses of the Nernst diffusion layer. The current as a function of time is given simply by Eq. [2], where i(t) FSVN(t) [2] =

behavior observed on readjusting the acidity from pH 9 to pH 4. These curves resemble and are closely related to the usual acid-base titration curves. I n flection points m a y be noted in curves E and F in the vicinity of pH 7 (glass electrode potential +0.05v) ; these sigmoid curves are obtained when the equivalence point of water is crossed during changes of pH. Typical variations of current with time during adjustment of pH are shown in Fig. 3. Faradaic current varies exponentially with time and approaches zero as the solution acidity approaches the value determined b y the setting of the potentiostat reference voltage. The slopes of the curves in Fig. 3 depend on the value of the platinum electrode potential, on the kinetic parameters of the h y d r o g e n g a s - h y d r o g e n ion reaction, and on the ratio of electrode area to solution volume. For example, the slopes of curves A a n d D are essentially the same, and these transients were obtained at the same electrode potential. Although the data in Fig. 3 correspond to pH transients like those in curves A - D of Fig. 2 (curve C of Fig. 3 corresponds to curve A of Fig. 2), v e r y similar behavior is observed for current transients corresponding to curves E and F. Other experiments were performed in which solution acidity was changed suddenly b y additions of acid or base to the solution. The transients observed during the readjustment action of the potentiostat are similar in every respect to those shown in Fig. 2 and 3. Several experiments were also performed to test the degree of control over an extended period. No significant l o n g - t e r m changes in the value of the glass electrode potential greater than 1 mv were detected, and m o m e n t a r y fluctuations were also no greater than 1 my. Therefore, the electrochemical

S is the electrode area. It is assumed that the h y d r o gen g a s - h y d r o g e n ion reaction is the only source of Faradaic current at the interface. Equation [2] neglects n o n - F a r a d a i c currents like those due to charging of the electrical double layer and to adsorption or phase formation or decomposition reactions on the electrode surface. H y d r o g e n ion concentration in the bulk of the solution m a y be assumed to change with time according to Eq. [3], where V is the volume of the solution and t + is the riCH+ (t)

S

dt

V

(1 -- t + ) V s ( t )

[3]

transference n u m b e r of hydrogen ions (assumed constant) t h r o u g h the diaphragm which separates electrode compartments (cf. G of Fig. 1). Equation [3] m a y be integrated to give Eq. [4] for the variation of CH+ (t) = CH+ (o)e -~t +

/Ca CHa( 1 __ e_~t ) [4] kc

with S V

(1 -- t+)kc

6a

_

~c

_

1 + - 5 - j ka + --b-;-- kc h y d r o g e n ion concentration with time; note that in the new steady state C H + ( ~ ) ___ __ka CHa.Th e curkc rent as a function of time is given b y Eq. [5] E g u a t i o n [1] does n o t r e p r e s e n t a n y p a r t i c u l a r m e c h a n i s m of t h e h y d r o g e n g a s - h y d r o g e n ion reaction. I t is u s e d h e r e b e c a u s e it p r o v i d e s an a d e q u a t e s i m p l e a p p r o x i m a t i o n to t h e f o r m of 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 s in n e u t r a l a n d m o d e r a t e l y acid solutions. The t h e o r y m a y be d e v e l o p e d also f o r specific m e c h a n i s m s of t h e h y d r o g e n e v o l u t i o n reaction, a n d in g e n e r a l the resulting equations a r e c o n s i d e r a b l y m o r e c o m p l i c a t e d t h a n those presented here.

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1186

JOURNAL i(t) =

FZ[ka~eH 2 - -

OF THE

kTCH+(o) ]

e -st

ELECTROCHEMICAL [5]

~a - ~c 1 -]- --~--a ka -t- --~--c kc w h i c h is o b t a i n e d b y c o m b i n a t i o n of Eq. [1], [2], a n d [4]. E q u a t i o n [5] is of t h e f o r m

a n d t h e r e s u l t s s h o w n in Fig. 3 f o l l o w this e q u a t i o n closely. F o r a c o n s t a n t r a t i o of e l e c t r o d e a r e a to s o l u t i o n v o l u m e , t h e t i m e c o n s t a n t p a r a m e t e r fl v a r i e s o n l y w i t h e l e c t r o d e p o t e n t i a l ; for e x a m p l e , t h e s l o p e s of c u r v e s A a n d D in Fig. 3 a r e e s s e n t i a l l y t h e s a m e , e v e n t h o u g h CH+ (o) differs in t h e t w o cases. T h e t i m e r e s p o n s e of t h e glass e l e c t r o d e p o t e n t i a l , V g ( t ) , is g i v e n b y Eq. [6]. This e q u a t i o n a c c o u n t s for r e s u l t s l i k e t h o s e of c u r v e s A,

RT

V g ( t ) - - Vg(O) =

_

R T In F

F

CH+ ( t )

in

e -m+

CH+ ( o ) _

(i--e

-~t)

[6]

kcC~+ (o)

B, C, a n d D i n Fig. 2, b u t n o t for t h e r e s u l t s of c u r v e s E a n d F, w h e r e t h e n e u t r a l i t y p o i n t of w a t e r ( p H 7) is c r o s s e d d u r i n g t h e a d j u s t m e n t a c t i o n of t h e p H stat. M o d i f i c a t i o n of t h e t r e a t m e n t to i n c l u d e t h e effect of t h e i o n i z a t i o n of t h e a q u e o u s s o l v e n t into h y d r o g e n ions a n d h y d r o x i d e ions a c c o u n t s for t h e f o r m of c u r v e s E a n d F in Fig. 2. I n t h i s case Eq. [3] is m o d i f i e d to i n c l u d e t h e s t o i c h i o m e t r y of t h e w a t e r i o n i z a t i o n e q u i l i b r i u m , w h i c h m a y b e e x p r e s s e d as u s u a l b y Kw = C H + - C o n - . I n t e g r a t i o n of t h e m o d i fied f o r m of Eq. [3], w i t h use of t h e p a r a m e t e r fl d e fined in Eq. [4], l e a d s to Eq. [ 7 ] for t h e v a r i a t i o n of h y d r o g e n ion c o n c e n t r a t i o n , CH+ ( t ) , w i t h t i m e .

[1 + [

CH+(~)

--CH+(t)

[C~+

(oo)1~

]

]

CH+ (~) - - C-S~+(o) Kw [Cu+(~)]2 CH+ ( t )



]

CH+ (o)

D e c e m b e r 1963

SOCIETY

c u r v e s is f a i r l y g o o d in v i e w of t h e a p p r o x i m a t i o n s m a d e in t h e d e r i v a t i o n . E q u a t i o n [7] d o e s n o t d e s c r i b e r e s u l t s l i k e c u r v e E of Fig. 2 b e c a u s e t h e m e c h a n i s m of t h e h y d r o g e n r e a c t i o n differs in a c i d a n d b a s i c r e g i o n s . T h e e x a c t f o r m of t h e t r a n s i e n t d e p e n d s on t h e p a r t i c u l a r r e a c t i o n m e c h a n i s m a n d its v a r i a t i o n w i t h pH. I n t h e b a s i c r e g i o n , t h e o v e r all s t o i c h i o m e t r y of t h e e l e c t r o d e r e a c t i o n m a y b e e x p r e s s e d b y 2H20 + 2 e - = H 2 ( g ) + 2 O H - ( a q ) . It is f o u n d in this case t h a t t h e flux e q u a t i o n h a s a f o r m d i f f e r e n t f r o m t h a t of Eq. [1], s u c h t h a t t h e h y d r o g e n ion c o n c e n t r a t i o n c h a n g e s w i t h t i m e a c c o r d i n g to a n e x p r e s s i o n w h i c h is s i m i l a r in f o r m to Eq. [7], but which has different parameters. E q u a t i o n s [4], [5], [6], a n d [7] a r e g o o d a p p r o x i m a t i o n s to t h e e x p e r i m e n t a l b e h a v i o r p r o v i d e d t h e p o t e n t i o s t a t c o n t r o l s t h e p o t e n t i a l of t h e p l a t i n u m e l e c t r o d e a t t h e c h o s e n v a l u e . I n case t h e c u r r e n t r e q u i r e m e n t s a r e such t h a t m o r e c u r r e n t t h a n t h e m a x i m u m o u t p u t of t h e p o t e n t i o s t a t is n e e d e d for t h e c o n t r o l of p o t e n t i a l d u r i n g a t r a n s i e n t , t h e e l e c t r o d e p o t e n t i a l is n o t c o n t r o l l e d , a n d t h e c u r r e n t o u t p u t r e m a i n s e s s e n t i a l l y c o n s t a n t at a l i m i t i n g v a l u e (iL) u n t i l c o n t r o l is r e - e s t a b l i s h e d . D u r i n g t h i s p e r i o d , t h e r a t e of c h a n g e of h y d r o g e n ion c o n c e n t r a t i o n is g i v e n b y Eq. [8]. W h e n c o n t r o l is r e established, subsequent variations

riCH+ ( t ) dt

(1 - - t+ )iL

FV

[8]

of CH+ ( t ) a r e g i v e n , as b e f o r e , b y Eq. [3] a n d [4] or b y Eq. [7]. O p t i m u m c o n d i t i o n s f o r u s e of t h e e l e c t r o c h e m i c a l p H - s t a t r e q u i r e a l a r g e r a t i o of e l e c t r o d e a r e a to s o l u t i o n v o l u m e . T h e u s e of p l a t i n i z e d p l a t i n u m e l e c t r o d e s is a d v a n t a g e o u s in t h i s r e s p e c t . I n g e n eral, a n e x c e s s of i n e r t e l e c t r o l y t e is a d v a n t a g e o u s , a n d t h e t h e o r e t i c a l a n a l y s i s of t r a n s i e n t b e h a v i o r is m u c h s i m p l e r in t h i s case b e c a u s e t h e effect of v a r i a t i o n s in t h e t r a n s p o r t n u m b e r s of h y d r o g e n a n d h y d r o x i d e ions is m i n i m i z e d . G o o d m e c h a n i c a l s t i r r i n g i m p r o v e s t h e p e r f o r m a n c e b y d e c r e a s i n g Sa a n d 8c of Eq. [1] a n d e n s u r e s t h a t Eq. [3] is a g o o d a p p r o x i m a t i o n . A n i n c r e a s e of t e m p e r a t u r e i n c r e a s e s t h e e x c h a n g e c u r r e n t d e n s i t y of t h e h y d r o g e n r e a c t i o n on t h e p l a t i n u m e l e c t r o d e a n d d e c r e a s e s r e sponse time. T h e p H of t h e s o l u t i o n is v a r i e d e a s i l y

by changing the setting of the potentiostat reference C H + (00) C H + (t) C H + (O)



e

=

e -~t

[7]

It is a s s u m e d in t h e d e r i v a t i o n of Eq. [7] t h a t t h e t r a n s f e r e n c e n u m b e r of h y d r o g e n ions ( a n d / o r h y d r o x i d e i o n s ) is n e g l i g i b l y s m a l l , so t h a t ( 1 - t + ) 1. E q u a t i o n [7] r e d u c e s to Eq. [ 4 ] w h e n t h e q u a n t i t y Kw/CH+ (~) is sufficiently s m a l l . A l t h o u g h Eq. [7] c a n n o t b e s o l v e d e x p l i c i t l y f o r CH+ ( t ) e x c e p t for c e r t a i n l i m i t i n g cases, t h e v a r i a t i o n of t h e c u r r e n t a n d t h e glass e l e c t r o d e p o t e n t i a l w i t h t i m e m a y b e c a l c u l a t e d b y u s e of Eq. [7] w i t h Eq. [2] a n d [6]. T h e d a s h e d l i n e in Fig. 2 (cf. c u r v e F ) w a s c a l c u l a t e d b y u s e of Eq. [7], w h e r e t h e c o n s t a n t B w a s c h o s e n to fit t h e e x p e r i m e n t a l c u r v e a t p H 7. T h e agreement between theoretical and experimental

voltage by the appropriate amount; for example, a 59 m y c h a n g e of t h e r e f e r e n c e v o l t a g e at 25~ c h a n g e s t h e p H b y one unit. M e a s u r e m e n t of corrosion r a t e s . - - T h e k i n e t i c s of r e a c t i o n s w h i c h p r o d u c e or c o n s u m e h y d r o g e n ions m a y b e m e a s u r e d at c o n s t a n t a c i d i t y b y u s e of t h e e l e c t r o c h e m i c a l p H - s t a t . T h i s c a p a b i l i t y is p a r t i c u l a r l y v a l u a b l e in t h e case of c o r r o s i o n r e a c t i o n s since t h e t e c h n i q u e p r o v i d e s a c o n t i n u o u s m e a s u r e m e n t of c o r r o s i o n r a t e as a f u n c t i o n of t i m e w i t h o u t t h e n e c e s s i t y for w e i g h t loss o r p o l a r i z a t i o n m e a s u r e ments. In the absence of external polarizing current, t h e r a t e of c o r r o s i o n of a n i s o l a t e d m e t a l l i c e l e c t r o d e equals the rate of the hydrogen evolution reaction on its surface, p r o v i d e d t h e r e d u c t i o n of h y d r o g e n ions is t h e sole c a t h o d i c process. F o r t h i s case, Eq.

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Vol. 110, No. 12

ELECTROCHEMICAL

[3] m a y b e m o d i f i e d to g i v e Eq. [9], w h e r e Rx is t h e r a t e of i n c r e a s e of h y d r o g e n ion c o n c e n t r a t i o n

dCH+ ( t ) dt

S

--

V

(1 - - t + ) v N ( t ) + R x

[9]

i n s o l u t i o n d u e to t h e c o r r o s i o n o r o t h e r r e a c t i o n (R~ is n e g a t i v e in t h e case of a c o r r o d i n g m e t a l ) . T h e s o l u t i o n of Eq. [ 9 ] is g i v e n b y Eq. [10] CH+ ( t ) = CH+ (O) + ~

Rx

( 1 - - e -~t)

[10]

w h e r e t h e c o n d i t i o n t h a t CH+ ( t ) = CH+ (O) a t t = 0 h a s b e e n used. T h e c u r r e n t t r a n s i e n t i n d u c e d on i m m e r s i o n of t h e c o r r o d i n g m e t a l e l e c t r o d e is t h e n g i v e n b y Eq. [11]. I n t h e n e w s t e a d y state, t h e c u r rent passing

FVRx

i(t)

=

(l--t+)

( 1 - - e -~t)

[11]

through the interface of the platinum electrode just compensates the current due to reduction of hydrogen ions on the corroding electrode, so that the m e a s u r a b l e c u r r e n t is g i v e n b y Eq. [12]. I n Eq. [12], icorr is i(oo)

=

--

FVR~

icorr

(I - - t + )

(l--t+)

[12]

the corrosion current of the metallic electrode in the absence of external polarizing current. Figure 4 shows typical examples of current transients obtained from the pH-stat on immersion of an iron electrode into solution. Data points were taken from recordings of the current transients and the solid lines are fits of Eq. [ 1I] to the data. The degree of control of solution acidity by the electrochemical pH-stat during the time of immersion of the corroding electrode depends on the rate of the corrosion reaction. The hydrogen ion concentration in the new steady state, CH+ (oo), is given b y Eq. [13], w h i c h f o l l o w s f r o m 500

,

250

h

o

, 200 E ~50 uJ

ioo ? 50

c

o o

~

TIME (minutes}

Fig. 4. Variation of potentiostat current with time following immersion of iron electrode into solution. Solution, 0.5M NaCI, Electrode, zone-refined iron; atmosphere, H2. Curve A B C D

pH 2.9 3.5 4.0 4.5

Temp. ~ 70 70 50 50

pH-STAT

1187

C~+(c~) = Crr+(o) +

Rx

fl

,= CH+(o)

Eq. [10] a n d [12]. E q u a t i o n r a n g e d to g i v e Eq. [14] for t h e CH + ( up ) - - - - 1 CH+ (O)

ico~ FVflCH + (o)

icorr

--[13]

F V fl

[13] m a y b e r e a r -

=1

icorr

(1 - - t+ )to [14] d e g r e e of c o n t r o l o f a c i d i t y as a f u n c t i o n of t h e c o r r o s i o n r a t e of t h e m e t a l l i c e l e c t r o d e . I n Eq. [14], io is t h e e x c h a n g e c u r r e n t of t h e h y d r o g e n g a s - h y d r o gen ion r e a c t i o n on t h e p l a t i n u m e l e c t r o d e p r i o r to i m m e r s i o n of t h e c o r r o d i n g e l e c t r o d e . T h i s e q u a t i o n s h o w s t h a t t h e p H c h a n g e i n c u r r e d as a c o n s e q u e n c e of t h e c o r r o s i o n r e a c t i o n m a y b e m i n i m i z e d b y i n c r e a s i n g t h e e x c h a n g e c u r r e n t of t h e p H - c o n t r o l l i n g e l e c t r o d e of t h e p H - s t a t . F o r sufficiently s m a l l c o r r o s i o n r a t e s , t h i s effect c a n b e r e l a t i v e l y u n i m p o r t a n t , p a r t i c u l a r l y if a p l a t i n i z e d p l a t i n u m e l e c t r o d e is u s e d w i t h t h e p H - s t a t . ~ T h e p r e s e n t m e t h o d f o r t h e m e a s u r e m e n t of c o r r o s i o n r a t e s is m o s t u s e f u l w h e n t h e c o r r o s i o n r a t e r e m a i n s e s s e n t i a l l y c o n s t a n t w i t h t i m e . I n t h e case of c o r r o s i o n r a t e s w h i c h v a r y w i t h t i m e , t h e m e t h o d r e m a i n s u s e f u l p r o v i d e d t h e t i m e r e q u i r e d for a s i g n i f i c a n t v a r i a t i o n of icorr is l a r g e c o m p a r e d to l/ft. I f t h e c o r r o s i o n r e a c t i o n p r o d u c e s m e t a l l i c ions in s o l u t i o n w h i c h u n d e r g o a p p r e c i a b l e h y d r o l y s i s at t h e p H in q u e s t i o n , i ( o o ) no l o n g e r e q u a l s i . . . . / ( 1 - - t + ) , a n d t h e t r e a t m e n t m u s t b e c o r r e c t e d for t h i s effect. A l t e r n a t i v e l y , if c o r r o s i o n r a t e s w e r e known independently, the method might be useful for i n v e s t i g a t i n g t h e h y d r o l y s i s of c o r r o s i o n p r o d ucts. I n f a v o r a b l e cases, t h i s m e t h o d o f c o r r o s i o n r a t e m e a s u r e m e n t is c a p a b l e of p r o v i d i n g a n i n d e p e n d e n t c h e c k on v a l u e s of c o r r o s i o n r a t e e s t i m a t e d b y e x t r a p o l a t i o n of T a f e l l i n e s to t h e c o r r o s i o n p o t e n t i a l or b y m e a s u r e m e n t of t h e p o l a r i z a t i o n r e s i s t ance. Disadvantages and modifications.--Certain d i s a d v a n t a g e s a r e i n h e r e n t in t h e u s e of t h e p r e s e n t d e v i c e for t h e c o n t r o l of a c i d i t y , p a r t i c u l a r l y in t h e p r e s e n c e of a c o r r o d i n g e l e c t r o d e on w h i c h p o l a r i z a tion measurements are desirable. (a) The necessity f o r use of a h y d r o g e n a t m o s p h e r e l i m i t s t h e u t i l i t y of t h e d e v i c e to s y s t e m s in w h i c h h y d r o g e n c a n b e t o l e r a t e d . ( b ) T h e t r a n s i e n t r e s p o n s e is r e l a t i v e l y s l o w a n d d e p e n d s g r e a t l y on t h e c h a r a c t e r i s t i c s of t h e h y d r o g e n r e a c t i o n on t h e p l a t i n u m e l e c t r o d e a n d on t h e a r e a to v o l u m e r a t i o . (c) T h e d e g r e e of c o n t r o l of p H in t h e p r e s e n c e of a h o m o g e n e o u s o r h e t e r o g e n e o u s r e a c t i o n w h i c h p r o d u c e s or c o n s u m e s h y d r o g e n ions d e p e n d s on t h e r a t e of t h a t r e a c t i o n (cf. Eq. [ 1 4 ] ) . ( d ) T h e l a r g e p l a t i n u m e l e c t r o d e is g r o u n d e d in t h e u s u a l p o t e n t i o s t a t i c c o n f i g u r a t i o n , so t h a t u s e of a s e c o n d e l e c t r o n i c p o t e n t i o s t a t or o t h e r g r o u n d e d c u r r e n t s o u r c e on a c o r r o d i n g (or o t h e r ) e l e c t r o d e in t h e s a m e cell is a w k w a r d . A d i f f e r e n t t y p e of e l e c t r o c h e m i c a l p H - s t a t w a s designed and constructed which largely eliminates, T h e u s e o f p l a t i n u m e l e c t r o d e s m a y present difficulties i n c e r t a i n m e d i a , e s p e c i a l l y c h l o r i d e S o l u t i o n s . T h e f i n i t e d i s s o l u t i o n r a t e of platinum in chloride solutions produces platinum ions which may b e r e d u c e d o n o t h e r e l e c t r o d e s u r f a c e s i n t h e cell, c a u s i n g significant c h a n g e s i n t h e k i n e t i c s of r e a c t i o n s o c c u r r i n g a t t h e s e surfaces. I f t h i s effect is t r o u b l e s o m e i n specific cases, i t m a y b e n e c e s s a r y t o r e p l a c e t h e p l a t i n u m w i t h a less r e a c t i v e m a t e r i a l ( p y r o l y t i c g r a p h ite, p o r o u s c a r b o n , b o r o n c a r b i d e , e t c . ) .

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1188

J O U R N A L OF THE ELECTROCHEMICAL SOCIETY

s

Fig. 5. Schematic diagram of differential amplifier type of electrochemical pH-stat. A, Differential amplifier; B, platinum electrode; C, auxiliary polarizing electrode; D, glass electrode; E, reference electrode; F, stirrer (magnetic); G, salt bridge or porous disk; I, primary cell; II, exterior polarizing chamber.

at least in principle, the difficulties mentioned above. Although the same type of cell as that in Fig. 1 is employed, so that the method of production or consumption of h y d r o g e n ions by an electrochemical reaction at an inert electrode is unchanged, the control of acidity is accomplished b y use of a differential amplifier instead of a potentiostat. Figure 5 shows schematically the experimental arrangement. The difference in the potential of a glass electrode (D) (or other pH-responsive electrode) and a reference electrode (E) is the input potential to the differential amplifier (A). This potential is opposed by a reference voltage at the input of the amplifier, in a m a n n e r similar to that used in potentiostats. A n y difference between the input potential and the reference voltage is amplified by the differential a m plifier and drives a current through the circuit consisting of electrodes B and C. The polarity of the current is such that the pH change caused by the equivalent electrochemical reaction at electrode B shifts the potential of the glass electrode in the proper direction to reduce the difference between the input potential and the reference voltage. Current output is zero when the input potential equals the reference voltage setting and any change in acidity as detected b y the glass electrode causes immediate corrective action. A Philbrick Model P2 solid state differential operational amplifier is used in the modified electrochemical pH-stat. P o w e r is supplied from m e r c u r y cells (Type TR-136), so that the entire apparatus can be floated with respect to ground potential. By this means, the modified pH-stat m a y be operated simultaneously with other line-operated instruments without the introduction of ground loops or other related difficulties. The open loop gain of this amplifier is approximately 3 x 104, and the input impedance is approximately 10l~ ohms. The m a x i m u m output voltage is --+10v and the m a x i m u m output current is --1 ma; although the output capability is somewhat less than that of conventional differential

D e c e m b e r 1963

amplifiers, it is still sufficient to provide good regulating action over the pH range from 4 to 1O when used with cells of moderate size. Feedback resistors of appropriate values m a y be used to lower the gain of the amplifier in cases where m a x i m u m gain is undesirable. The apparatus is constructed so that it m a y be used also as a conventional potentiostat (cf. Fig. 1) by a slight change in the wiring arrangement. The differential amplifier type of p H - s t a t is not limited to use with cells in which a h y d r o g e n atmosphere is maintained. It is capable of controlling pH providing any suitable electrochemical reaction occurs on the platinum electrode which liberates or consumes hydrogen ions in a m a n n e r which depends on the direction of current flow. The transient response is not exponential, as in the case of the potentiostatic type of pH-stat. At m a x i m u m gain, the full output of the amplifier is obtained when the difference between the input potential and the reference voltage exceeds ca. --+ 0.3 my. Under these conditions, the modified p H - s t a t operates essentially as a "go-no go" device. Current flow stops when the glass electrode potential attains the value determined by the reference voltage setting (see below, however). When the amplifier is operated at m a x i m u m gain, full output is obtained w h e n E(t) - - - - V g ( t ) - VR -V g ( t ) - - V g ( o o ) exceeds ca. --+0.3 mv; here, e(t) is the difference betwen Vg(t), the glass electrode potential vs. the reference electrode, and Vm the reference voltage. If the input signal required for full output is designated by el, the (constant) current output (i0 is given approximately b y Eq. [15], where i (t) is the current through A i(t)

electrode B of and Z is the Hydrogen ion cording to Eq. gration.

=

h

~1

- -

Z

[15]

Fig. 5, A is the gain of the amplifier, cell impedance (assumed constant). concentration changes with time ac[16], which gives Eq. [17] on inte-

dCH+ (t)

(l--t+)

dt

FV

i(t)

(1-- t+)A ----

FVZ

el------T

[16] Cn+ (t) ----CH+ (O) -- ~t

[17]

The concentration of hydrogen ions changes linearly with time because of the constant output current, and the corresponding variation of glass electrode potential is given b y Eq. [18]. The time (~) required for a RT CH+ (t) V~(t) = V~(o) + In

F

CH+ (O)

RT

=V~(o)+~

In (\ 1

CH+(o) t )

[18]

change in the glass electrode potential of Vg(oo) -Vg(o) follows from Eq. [18] as Eq. [19]. For Vg(oo)--Vg(o)0, and 9 , > 0 ; and for Vg( ~ ) -- Vg(o)

> 0

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Vol. 110, No. 12 I

o

1189

ELECTROCHEMICAL pH-STAT I

I

I

I

dC~+ ( t )

L

0

=

(1-- t+)

=

dt

-10 b-

[Vg(t) -- Vg(~) ]

FVZ

a_ - 2 0

o ,F.o

i(t)

FV (l--t+)A

-

[21]

I n t e g r a t i o n of Eq.

[21] w i t h use of t h e r e l a t i o n , RT [ CH+(t) ] V g ( t ) ----Vg(o) + ~ l n l e a d s to Eq.

50

F

CH+ (o)

'

[22] for the variation of CH+ (t) with time. In Eq. [22],

-40

g z -50

o

IVy(o} =

+ - -

z - 60

I

I 2

I 5

I 4 TIME ~ m ~ n u f e s )

I 5

I 6

li

I 7

Fig. 6. Variation of glass electrode potential with time during adjustment of solution acidity by differential amplifier type of pHstar. Solution, 0.5M NaCI; temperature, 25~ atmosphere, H2; pH change, 4 to 5.

=li F +

I

+ - RT

[ V g ( o ) -- Vg(oo) ]

e

(i -- t + ) A R T

-- e

I

CH+(0) l - - e Y

RT

[V~(oo) -- V g ( o ) ]

1

[19]

Ez < O, a n d y < 0. E q u a t i o n s [17], [18], a n d [19] a r e a p p r o x i m a t e l y c o r r e c t f o r t h e o p e r a t i o n of t h e m o d i f i e d p H - s t a t at m a x i m u m gain, a l t h o u g h n o a c c o u n t is t a k e n of t h e effect of t h e i o n i z a t i o n c o n s t a n t of w a t e r on t h e t r a n s i e n t b e h a v i o r in t h e p H region near neutrality. Figure 6 shows a typical e x p e r i m e n t a l r e s u l t o n t h e v a r i a t i o n of t h e glass electrode potential with time during the adjustment a c t i o n at m a x i m u m gain. T h e d a s h e d l i n e in F i g . 6 is a t h e o r e t i c a l c u r v e c a l c u l a t e d b y u s e of Eq. [18]. S i n c e t h e a m p l i f i e r o u t p u t is i n d e p e n d e n t of p H f o r E(t) > El, s o m e d i f f i c u l t y m a y b e e x p e r i e n c e d in t h e c o n t r o l of a c i d i t y n e a r n e u t r a l i t y . O s c i l l a t i o n s of p H a n d of c u r r e n t m a y o c c u r b e c a u s e of a t i m e l a g in t h e r e s p o n s e of t h e glass e l e c t r o d e to h y d r o g e n ions l i b e r a t e d o r c o n s u m e d at t h e p l a t i n u m e l e c t r o d e . A finite t i m e of m i x i n g is u n a v o i d a b l e , a n d t h e current "overshoot" produced by this means depends on t h e r a t e a n d m o d e of s t i r r i n g a n d on t h e o u t p u t c u r r e n t of t h e a m p l i f i e r . O s c i l l a t i o n s m a y b e r e d u c e d or e l i m i n a t e d b y p r o v i d i n g m o r e efficient s t i r r i n g , b y i n c r e a s i n g t h e i m p e d a n c e of t h e cell ( w i t h e x t e r n a l r e s i s t a n c e , if d e s i r e d ) so t h a t less c u r r e n t is p r o d u c e d at f u l l o u t p u t , o r b y r e d u c i n g t h e g a i n of the amplifier. I n case t h e d i f f e r e n t i a l a m p l i f i e r is o p e r a t e d at r e d u c e d gain, so t h a t , f o r e x a m p l e , E1 --~ -----10 m v m i g h t be r e q u i r e d to p r o d u c e t h e f u l l o u t p u t , t h e t r a n s i e n t b e h a v i o r differs f r o m t h a t of Eq. [17] a n d [18] w h e n ~(t) = Vg(t) -- V R : Vg(t) -- Vg(oo) < ~i. T h e current through the platinum electrode is given b y Eq. [20] instead of by Eq. [15], and the rate of

A A i ( t ) = - - - ~ [ V g ( t ) - - VR] = - - ~ - [ V g ( t ) - - V g ( ~ ) ] [20] c h a n g e of h y d r o g e n ion c o n c e n t r a t i o n f o l l o w s Eq. [21] i n s t e a d o f Eq. [16].

1

[ V g ( o ) -- V ~ ( o o ) ]

RT + - -

J

V~(r

CH+ ( t ) e RT CH+ (o)

F2VZCH+ (o)

t

[22]

l i ( x ) ----~ ' x - d ~ is t h e l o g a r i t h m i c i n t e g r a l (12). F o r o ln$ e ( t ) ~-- el, t h e t r a n s i e n t b e h a v i o r is g i v e n b y Eq. [17], w h i l e f o r e ( t ) < el, Eq. [22] a p p l i e s . T h e d e g r e e of c o n t r o l of t h e m o d i f i e d p H - s t a t in t h e p r e s e n c e of a c o r r o d i n g e l e c t r o d e o r o t h e r r e a c t i o n w h i c h p r o d u c e s or c o n s u m e s h y d r o g e n ions m a y be c a l c u l a t e d f r o m Eq. [23], w h e r e Rx (cf. Eq. [ 9 ] ) is t h e r a t e

riCH+ ( t ) dt

--

(1 - - t + )

FV

i(t)

+ Rx

[23]

of i n c r e a s e of s o l u t i o n a c i d i t y d u e to t h e c o r r o s i o n (or o t h e r ) r e a c t i o n (Rx is n e g a t i v e f o r a c o r r o d i n g A A m e t a l ) . W i t h i ( t ) -[ V g ( t ) - - VR] Z Z ART CH+ ( t ) IVy(t) -- Vg(o)] - in , the deZF CH+ (O) g r e e of c o n t r o l in t h e s t e a d y s t a t e a t t a i n e d a f t e r i m m e r s i o n of t h e c o r r o d i n g e l e c t r o d e i n t o s o l u t i o n is g i v e n b y Eq. [24].

CH+( o o )

+

F2VZRx (i - t+)A~T

-- e

[24]

CH+ ( o )

E q u a t i o n [24] s h o w s t h a t b e t t e r c o n t r o l of a c i d i t y is o b t a i n e d a t h i g h gain, b u t t h i s a d v a n t a g e is c o u n terbalanced by an increased tendency toward oscill a t i o n , as d i s c u s s e d a b o v e . T h e c u r r e n t in t h e s t e a d y s t a t e is g i v e n b y Eq. [25], w h i c h is i d e n t i c a l to Eq. [12] ; b o t h t h e p o t e n t i o s t a t a n d t h e i(~)

=

FVRx (l--t+)

=

ico~r (l--t+)

[25]

differential amplifier types of electrochemical pHstar are useful for measuring corrosion rates of metals. The potentiostat type is inherently more stable than the modified or differential amplifier type, although the transient behavior of the latter is superior in certain cases. Both devices should prove to

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1190

JOURNAL

OF

THE

ELECTROCHEMICAL

be u s e f u l i n s i t u a t i o n s w h e t h e r a u t o m a t i c c o n t r o l of p H is i m p o r t a n t in studies on r e a c t i o n kinetics. Manuscript received April 22, 1963; revised m a n u script received J u l y 5, 1963. This paper was presented at the New York Meeting, Sept. 29-Oct. 3, 1963. The paper is based on work performed for the Office of Saline Water, U. S. D e p a r t m e n t of the Interior, at the Oak Ridge National Laboratory, Oak Ridge, Tennessee, operated by U n i o n Carbide Corporation for the U. S. Atomic E n e r g y Commission. A n y discussion of this paper will appear in a Discussion Section to be published in the J u n e 1964 JOURNAL. REFERENCES 1. J. B. Neilands and M. D. Cannon, Anal. Chem., 27, 29 (1955). 2. K. I. Wood, ibid., 32, 537 (1960). 3. M. Murayama, J. M. Conlon, and G. C. Riggle, ibid., 33, 1454 (1961). 4. L. Josefsson, C. E. Ryberg, and R. Svensson, ibid., 34, 173 (1962). 5. S. W. Thorne, J. Sci. Inst., 39, 593 (1962). 6. J. J. Lingane, "Electroanalytical Chemistry," p. 158, Interscience Publishers, Inc., New York (1958). 7. J. E. Breeze, Labs. Natl. Res. Council Can., Radio and Elec. Eng. Div. Rept. No. ERA-166 (1949), N.R.C. No. 1889. 8. W. B. Murray, J. A m . W a t e r W o r k s Assoc., 51, 1318 (1959). 9. R. G. Bates, Chimia, 14, 111 (1960). 10. H. Gerischer and K. E. Staubach, Z. ~ l e k t r o c h e m . , 61, 789 (1957). l l . P. Delahay, in "Advances i n Electrochemistry and Electrochemical Engineering," Vol. 1, p. 304, P. Delahay, Editor, Interscience Publishers, Inc., New York (1961). 12. K. J. Vetter, "Elektrochemische Kinetik," S p r i n g e r Verlag, Berlin (1961). 13. E. J a h n k e and F. Emde, "Tables of Functions," p. 1, Dover, New York (1945).

A CH+ (t) CH2 Dc ha, 6c

Da,

E(t) el F

7 i(t) icorr io iL il Kw ka, k~ R Rx S T t t+ T V V~(t) VR VN(t) Z

SOCIETY

December

1963

SYMBOLS gain of differential amplifier c o n v e n i e n t combination of kinetic p a r a m eters (cf. Eq. [4]), sec -1 hydrogen ion concentration, moles/era 3 concentration of dissolved molecular h y d r o gen, m o l e s / c m 3 diffusion coefficients of H2 and H +, cm2/sec hypothetical thicknesses of Nernst diffusion layer, cm difference b e t w e e n glass electrode potential and reference voltage of differential amplitier, v i n p u t voltage required for full output of differential amplifier, v F a r a d a y ' s constant, c o u l o m b s / e q u i v a l e n t convenient combination of p a r a m e t e r s (cf. Eq. [16] ), moles/cm3-sec net c u r r e n t through electrode interface, amp corrosion c u r r e n t of metallic electrode, amp exchange c u r r e n t of the h y d r o g e n g a s - h y drogen ion reaction, amp m a x i m u m output c u r r e n t of potentiostat, amp m a x i m u m output c u r r e n t of differential a m plifier, amp ionization constant of water, molesf/cm 6 electrochemical specific rate constants of anodic and cathodic partial processes, cm/sec gas constant, j o u l e s / ~ rate of increase of hydrogen ion concentration due to corrosion (or other reaction), moles/cm3-sec electrode area, cm 2 absolute temperature, ~ time, see transference n u m b e r of hydrogen ions time required to change glass electrode potential by Vg( ~ ) - - Vg (o), see volume of solution, cm 3 glass electrode potential vs. reference electrode, v reference voltage of differential amplifier, v net flux of h y d r o g e n gas-hydrogen ion r e action, moles/cm2-sec cell impedance, ohms

On the Formation of Electrochemical Etch Pits on the (111) Face of Copper Ugo Bertocci, L. D. Hulett, and L. H. Jenkins Solid State Division, Oak Ridge National Laboratory, 1 Oak Ridge, Tennessee ABSTRACT I n an effort to elucidate the role of defects on the anodic behavior of copper single crystals, i n f o r m a t i o n has been gathered about the etch pits formed at dislocations on the (111) face. Anodic etching has been carried out i n chloride, chloride/bromide, bromide, and chloride/iodide solutions, with and without copper salt added, as well as in CH3COOH, H 2 8 0 4 , and HC104. I n halide solutions dislocation pits have been found to be formed over a large range of curr e n t densities and solution compositions, whereas no preferential nucleation at dislocation intersections has been detected in other solutions. The role of small misorientations of the surface from (111), as well as the etching of (100) and (110) surfaces has also been investigated. The influence of such parameters as c u r r e n t density, solutic-n compositions, and orientation of the copper surface on the formation and characteristics of such pits is discussed. S e v e r a l e t c h a n t s w h i c h cause pits to be d e v e l o p e d at p o i n t s w h e r e dislocations i n t e r s e c t t h e s u r f a c e of copper c r y s t a l s h a v e b e e n d e v e l o p e d ( 1 - 3 ) . A l t h o u g h the r e a c t i o n ( s ) o c c u r r i n g on t h e m e t a l s u r face is e l e c t r o c h e m i c a l i n c h a r a c t e r - - f o r w h i l e t h e m e t a l is oxidized to copper ions, a n o x i d i z i n g a g e n t such as C u ++, F e +++, Brf, S2Os--, etc., is r e d u c e d 1 O a k R i d g e N a t i o n a l L a b o r a t o r y is o p e r a t e d b y U n i o n C a r b i d e C o r p o r a t i o n f o r t h e U n i t e d States A t o m i c E n e r g y Commission.

at the s u r f a c e - - s u c c e s s f u l a n d r e p r o d u c i b l e m e t h o d s for f o r m i n g etch pits at d i s l o c a t i o n s b y t h e a p p l i c a t i o n of a n e x t e r n a l e m f h a v e o n l y r e c e n t l y b e e n r e p o r t e d (4). S u c h a m e t h o d is a d v a n t a g e o u s for n o t o n l y c a n the anodic a n d cathodic r e a c t i o n s b e s e p a r a t e d i n space, b u t also t h e m a g n i t u d e of t h e c u r r e n t flowing a n d p o t e n t i a l at t h e electrode c a n be c o n trolled a n d / o r measured.

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