A Mathematical Model for the Corrosion of Iron in Sulfuric Acidww2.che.ufl.edu/orazem/pdf-files/Gan-MathModel-JES-1987.pdfiron corrosion process, mathematical models of this pro- cess

Vol. 134, No. 6 P A S S I V E F I L M F O R M E D O N I R O N 1357

12. K. Azumi, T. Ohtsuka, and N. Sato, Denki Kagaku, 53, 306 (1985).

13. K. Azumi, T. Ohtsuka, and N. Sato, ibid., 53,700 (1985). 14. U. St imming and J. W. Schultze, Ber. Bunsenges. Phys.

Chem. 80, 1297 (1976), 15. R. A. Fredlein and A. J. Bard, This Journal, 126, 1892

(1979). 16. J. H. Kennedy and K. W. Frese, Jr., ibid., 125, 723

(1978). 17. G. Horowitz, J. Electroanal. Chem. Interfacial

Electrochem., 159, 421 (1983). 18. C. Y. Chao, L. F. Lin, and D. D. Macdonald, This Jour-

nal, 128, 1187 (1981); L. F. Lin, C. Y. Chao, and D, D. Macdonald, ibid., 128, 1194 (1981).

19. R. Nishimura and N. Sato, Bousyoku Gijutu, 26, 305 (1977).

20. K. Tokugawa, Jpn. J. Appl. Phys., 21, 1693 (1982); and ibid., 21, 1700 (1982).

21. R. V. Moshtev, Ber. Bunsenges. Phys. Chem., 72, 452 (1968).

A Mathematical Model for the Corrosion of Iron in Sulfuric Acid

E. C. Gan* and Mark E. Orazem**

Department of Chemical Engineering, University of Virginia, Charlottesville, Virginia 22903

ABSTRACT

A mathematical model is developed for the corrosion of a rotating iron disk in sulfuric acid. The model treats explicitly the coupling of interfacial reactions with the mass transfer of ionic species by migration, diffusion, and convection in both the diffuse part of the double layer and the diffusion layer. The corrosion reactions take place at the metal-electrolyte interface and are characterized by the interactions among heterogeneous reactions. The total current density at an electrode is obtained by summing the partial current densities due to each of these individual heterogeneous reactions. The homogeneous partial dissociation of sulfuric acid is also treated explicitly. This model shows that the mass-transfer- limited currents can be attributed to mass-transfer limitations to the removal of corrosion products from the iron surface coupled with a reduction of the active area of the iron disk. The limiting current obtained from this model is proportional to the square root of the rotation speed and agrees with published experimental results.

The fundamenta l react ion for iron corrosion involves dissolut ion of the metal atoms into their ions. Al though their reaction alone does not reflect the complexi ty of the iron corrosion process, mathemat ical models of this process are general ly based upon this slmpllfiecl vmw. Griffin (1), for example, assumed compet i t ive adsorption be tween an isolated cation and a cation in the oxide layer to mode l the active-t~assive transi t ion. These cat ions were assumed to be the product of the electrode dissolution. With this s imple kinet ic model, he was able to re- produce quali tat ively the "mult ipl ic i ty of steady states" in the region prior to passivat ion. In the model by Law and N e w m a n (2) a modif ied But le r -Volmer re la t ionship was applied to express the simple iron dissolution reaction. Despi te the s impl ic i ty assumed for the corros ion chemis t ry , the mode l p rov ided good account for the kinetic resistance in the double layer and the nonuniform potent ia l d i s t r ibu t ion across the disk surface. The concent ra t ion dependence of a l imi t ing reac tant was in- c luded in their k inet ic express ion in order to t reat the effect of mass-transfer limitation. Epelboin et al. (3) sug- ges ted that the mass- t ransfer - l imi t ing species might be the OH- species. This is unl ikely, however , in an acidic med ium which lacks the hydroxide ion concentrat ion required to just i fy a significant involvement of this species in the pass iva t ion process. Alkire and Cangel lar i (4) re- por ted the impor tance of cer ta in chemica l species by arguing that the impai rment of its concentrat ion buildup due to the inf luence of fluid flow impeded passivat ion. They indica ted a cri t ical ve loc i ty above which pass iva t ion did not occur. Russel l and N e w m a n (5) descr ibed a mode l for the i ron corrosion in sulfuric acid which also inc luded the format ion and growth of a po- rous salt film, By using a simple electrode dissolution react ion and express ing it in the But le r -Volmer form as used by Law and N e w m a n (2), the mode l p rov ided a qua l i ta t ive account of the processes leading to the format ion of the salt film.

The principle advantage of the relatively simple mathemat ica l descr ip t ions g iven above is that u n k n o w n parameters are lumped to provide a minimal number of kinet ic parameters . A more comple te charac ter iza t ion of corrosion mechanisms requires t rea tment of mult iple re-

* Electrochemical Society Student Member. ** Electrochemical Society Active Member.'

actions. A general t r ea tment of mul t ip le e lec t rode reac- t ions by White et al. (6) a l lowed pred ic t ion of the total current density at an electrode under potentiostat ic con- trol. Treatment of mult iple reactions was also expressed in the mathemat ica l mode l ing of LiA1/FeS bat tery by Pollard and Newman (7).

In this work, the complex react ions at the e lec t rode surface are t rea ted by the coupl ing among s imple reac- t ion steps and mass t ransfer to and f rom the e lec t rode surface. This approach incorpora tes both the macroscopic t ransport phenomena in the electrolyt ic solut ion and the microscopic model of the metal-electrolyte interface, allowing explici t t rea tment of the chemical species involved in the system. Passivat ion is considered in this work to be the format ion of a p ro tec t ive oxide layer which reduces the active fraction of the surface. Progres- sive coverage by oxides has been observed by Miller (8) on an iron disk below the passivation potential. Through this approach, the influence of mass transfer on the corrosion current can be characterized without assumption of a mass-transfer-l imited reactant in solution.

Physical Description A one-d imens iona l schemat ic represen ta t ion of the

metal-electrolyte system is presented in Fig. 1. The elec- t rolyt ic solut ion was divided into a di f fus ion layer that adjoins the bulk phase and diffuse part of the double layer, a relatively small region extending from the imagi- nary outer He lmhol tz plane. Unl ike the di f fus ion layer, the diffuse part of the double layer is not electrically neutral. The mathematical depict ion of the metal-electrolyte interface was based on the theory of diffuse-double-layer as developed by Stern, Gouy, and Chapman [see, for example, Parsons (9)]. The microscopic model of the metal- e lec t ro ly te in terface (shown in Fig. 1) inc luded three planes: the inner and outer Helmholtz planes on the elec- t rolyt ic solut ion adjacent to the in terface and the inner surface state on the meta l side. The inner surface state (ISS) was designated to be the plane associated with react ive meta l atoms. The inner He lmhol tz plane (IHP) is the locus of the centers of the first row of ions specifically adsorbed onto the meta l surface. The outer He lmhol tz plane (OHP) is the plane of closest approach for the so lva ted ions associated with the bulk solution. The charge held within the diffuse part of the double layer is balanced by the charge held at the interracial planes IHP

Downloaded 26 Jun 2008 to 128.227.7.250. Redistribution subject to ECS license or copyright; see http://www.ecsdl.org/terms_use.jsp

1358 J. Electrochem. Soc.: E L E C T R O C H E M I C A L S C I E N C E A N D T E C H N O L O G Y June 1987

/ /

/ / ( / / / / /

/

Fig.

/J I 1 l

Diffuse Part of t]~e I I Double Layer ~ ff

1 Di f fus ion Laye r Bulk Solution

I I I J I

. A schematic representation of a metal-electrolyte interface

a n d I S S s u c h t h a t t h e i n t e r f a c i a l r e g i o n is e l e c t r i c a l l y n e u t r a l .

T h e o r e t i c a l D e v e l o p m e n t

W i t h i n t h i s m o d e l , t h e e l e c t r o l y t i c s o l u t i o n is d i v i d e d i n t o a d i f f u s i o n l a y e r a n d a d i f f u s e p a r t of t h e d o u b l e layer . M a c r o s c o p i c t r a n s p o r t e q u a t i o n s are u s e d to cha r - ac t e r i ze b o t h t h e s e r eg ions . Th i s m a c r o s c o p i c c h a r a c t e r i - z a t i o n is c o u p l e d w i t h t h e m i c r o s c o p i c m o d e l of t h e m e t a l - e l e c t r o l y t e i n t e r f a c e w h i c h a l l o w s e x p l i c i t t r ea t - m e n t of i n t e r f ac i a l r eac t ions .

Metal-electrolyte interface.--The i n t e r r a c i a l r e a c t i o n s c o n s i d e r e d in t h i s m o d e l w e r e t h e o x i d a t i o n o f i r o n to f e r rous i ons

Fe <=> Fe ~+ + 2e-

t h e o x i d a t i o n of f e r r o u s ions to f o r m fer r ic ions

Fe 2+ <==> Fe :~+ + e

t h e f o r m a t i o n of a p a s s i v e f i lm

3H20 + 2Fe :~+ <=> Fe20~ + 6H +

a n d t h e h y d r o g e n e v o l u t i o n r e a c t i o n

2H + + 2 e <=>H2

F o r m a t i o n of a f e r r o u s su l f a t e sa l t film, e.g.

4H20 + F e z+ + SO42- <=> FeSO4:4H.20

is g e n e r a l l y a g r e e d to p l a y a ro le in t h e p a s s i v a t i o n of i r o n in s u l f u r i c ac id . F o r m a t i o n of a s a l t f i lm a t a n o d i c p o t e n t i a l s h a s b e e n a s s o c i a t e d w i t h c u r r e n t o s c i l l a t i o n s u n d e r p o t e n t i o s t a t i c con t ro l . I t is un l ike ly , h o w e v e r , t h a t t h e d i f f u s i o n b a r r i e r a s s o c i a t e d w i t h t h e sa l t f i lm is, in itself, r e s p o n s i b l e for t he s h a r p m a s s - t r a n s f e r - l i m i t e d cur- r e n t o b s e r v e d n e a r t h e p a s s i v a t i o n p o t e n t i a l . I t is a l so u n l i k e l y t h a t t h e l i m i t i n g c u r r e n t is d u e to m a s s - t r a n s f e r l i m i t a t i o n s to t h e t r a n s p o r t of a b u l k - s o l u t i o n spec i e s to t h e s u r f a c e . T h e o b j e c t of t h i s w o r k w as to d e t e r m i n e w h e t h e r t h e e x p e r i m e n t a l l y o b s e r v e d l i m i t i n g c u r r e n t c o u l d b e a t t r i b u t e d to t h e c o u p l i n g a m o n g in t e r r ac i a l re- a c t i o n s . T h e f o r m a t i o n o f a s a l t f i lm, t h e r e f o r e , w a s n o t i n c o r p o r a t e d in t h i s work . A c o m p l e t e m o d e l of t h e cor- r o s i o n of i r o n in s u l f u r i c a c id w o u l d , of c o u r s e , i n c l u d e t h e t i m e - d e p e n d e n t sa l t f i lm f o r m a t i o n as a n i n t e r f a c i a l r e a c t i o n [see, for e x a m p l e , Ref. (5)] in a d d i t i o n to t h e cou- p l i n g a m o n g t h e r e a c t i o n s t r e a t e d in t h i s work .

T h e i n t e r f ac i a l r e a c t i o n s w e r e w r i t t e n in t h e f o r m of a m o d i f i e d B u t l e r - V o l m e r ra te e x p r e s s i o n , i.e.,

r , = k f . l . e x p l n(1;T~I)F A d p ] J - ~ c,m,l

- kh., - e x P k ~ [1]

T h e p o t e n t i a l d r i v i n g force A<P~ for a n a d s o r p t i o n - d e s o r p - t i o n r e a c t i o n is t h e p o t e n t i a l d i f f e r e n c e b e t w e e n t h e I H P a n d O H P p l a n e s w h e r e a s ACPl for a c h a r g e - p r o d u c i n g re- a c t i o n was t a k e n to b e t h e p o t e n t i a l d i f f e r e n c e b e t w e e n

t h e I S S a n d I H P p lanes . T h e s y m m e t r y f ac to r ~ was as- s i g n e d a v a l u e of 0.5. T h e coef f i c ien t s p~.~ a n d q~., a re reac- t i o n o r d e r s for spec i e s i in t h e f o r w a r d a n d b a c k w a r d di- r e c t i o n of r e a c t i o n l, r e s p e c t i v e l y , a n d n is t h e n u m b e r of e l e c t r o n s t r a n s f e r r e d . T h e c o n c e n t r a t i o n v a r i a b l e s in Eq. [2] w e r e e i t h e r s u r f a c e or v o l u m e t r i c v a l u e s , d e p e n d i n g u p o n t h e r eac t ion . T h e f o r m a t i o n of fe r r i c o x i d e was as- s u m e d to b e a su r f ace r e a c t i o n w h i c h r e s u l t e d in a frac- t i o n a l c o v e r a g e of t h e e l ec t rode . B o t h t h e f o r m a t i o n of t h e f e r r i c o x i d e a n d t h e a d s o r p t i o n r e a c t i o n s w e r e as- s u m e d to b e e q u i l i b r a t e d , a n d al l r e a c t i o n s w e r e as- s u m e d to b e r e v e r s i b l e . T h e m e t h o d u s e d to e s t i m a t e v a l u e s for t h e k i n e t i c p a r a m e t e r s is o u t l i n e d in A p p e n d i x A.

T h e i n t e r f a c i a l r e a c t i o n s w e r e i n t e r r e l a t e d b y m a t e r i a l b a l a n c e s for e a c h a d s o r b e d spec i e s i on t h e m e t a l su r f ace a n d t h e i n n e r H e l m h o l t z p lane , i.e.

E sHrl = 0 [2] i

w h e r e si,~ is t h e s t o i c h i o m e t r i c c o e f f i c i e n t for s p e c i e s i a n d r e a c t i o n l. T h e e l e c t r o s t a t i c p o t e n t i a l s a s s o c i a t e d w i t h t h e i n t e r f a c i a l p l a n e s I S S a n d I H P w e r e r e l a t e d to t h e c h a r g e on t h o s e p l a n e s b y G a u s s ' s law, i.e.

-.., - e._., = o- [3] I 2

w h e r e ~ is t h e c h a r g e p e r u n i t a r e a at t h e i n t e r f a c e a n d t h e s u b s c r i p t s 1 a n d 2 d e n o t e t h e two i m m e d i a t e p h a s e s t h a t s a n d w i c h t h e in te r face .

Electrolyte.--The a q u e o u s e l ec t ro ly t i c s o l u t i o n was as- s u m e d to c o n t a i n f e r r o u s a n d f e r r i c i o n i c s in s u l f u r i c ac id . T h e i n c o m p l e t e d i s s o c i a t i o n of s u l f u r i c ac id g ives r i se to five ion ic spec ies ; H +, Fe 2+, Fe :~+, SO42-, a n d HSO4 . T h e c o n c e n t r a t i o n s of t h e s e i o n i c s p e c i e s a n d t h e e lec- t r o s t a t i c p o t e n t i a l c o n s t i t u t e t h e s ix m a c r o s c o p i c va r i a - b l e s of t h e m o d e l . T h e p r i n c i p a l a s s u m p t i o n s of t h e m o d e l w e r e t h a t p h y s i c a l p r o p e r t i e s of t h e f lu id w e r e c o n s t a n t a n d t h a t r a d i a l d e r i v a t i v e s of c o n c e n t r a t i o n c o u l d be n e g l e c t e d . The l a t t e r a s s u m p t i o n is va l id u n d e r m a s s - t r a n s f e r l i m i t a t i o n s w h e r e t h e c u r r e n t d i s t r i b u t i o n is u n i f o r m (10). M a r a t h e a n d N e w m a n (11) a n d N e w m a n (12) h a v e s h o w n , h o w e v e r , t h a t t h e c u r r e n t d i s t r i b u t i o n on a r o t a t i n g d i sk e l e c t r o d e is n o n u n i f o r m b e l o w t h e l im- i t i n g c u r r e n t . U n d e r c o n d i t i o n s w h e r e t h e c u r r e n t d e n - s i ty is n o t u n i f o r m on t h e d isk , t h e m o d e l d e v e l o p e d h e r e is r e s t r i c t e d to t he c e n t e r of t he disk . A d d i t i o n a l a s s u m p - t i o n s a re i n h e r e n t in t h e m i c r o s c o p i c m o d e l d e s c r i b e d a b o v e . U n d e r t h e s t e a d y - s t a t e a s s u m p t i o n , t h e e x p r e s - s i on of t h e m a t e r i a l b a l a n c e for e a c h i o n i c s p e c i e s is g i v e n by

V - Ni = Rj [4]

w h e r e R~ is t he r a t e of h o m o g e n e o u s g e n e r a t i o n a n d _N, is t h e f lux of spec i e s i. T h r o u g h a s s u m p t i o n of a d i l u t e elec- t ro ly t i c so lu t i on , t he f lux e q u a t i o n s c a n be g i v e n b y

N~ = -z,u,FcjVd) - DLVc~ + c~v_ [5]

w h e r e u~ is t h e m o b i l i t y for spec i e s i, (P is t h e e l e c t r o s t a t i c p o t e n t i a l , D~ is t h e d i f f u s i o n coe f f i c i en t of spec i e s i. a n d v is t h e v e l o c i t y . T h e f lux i n c l u d e s m i g r a t i o n a l , d i f fu- s iona l , a n d c o n v e c t i v e c o n t r i b u t i o n s . T h e ax ia l v e l o c i t y n e a r a r o t a t i n g d i sk e l e c t r o d e can be a p p r o x i m a t e d by a p o w e r se r ies (13).

v z = ~ - ~ ' ( - a r 2 + ~ - + ~ - r + . . . ) [6]

w h e r e ~ is t h e d i m e n s i o n l e s s d i s t a n c e g i v e n b y ~ = z ~ , a = 0.51023, a n d b = -0 .616.

I n t h e a b s e n c e o f h o m o g e n e o u s r e a c t i o n s i n v o l v i n g f e r r o u s a n d fer r ic ions , Eq. [4] b e c o m e s

V. N_Fr = V - NFe3+ = 0 [7]

T h e h o m o g e n e o u s d i s s o c i a t i o n o f s u l f u r i c a c id w a s as- s u m e d to be e q u i l i b r a t e d , t h e r e f o r e

V �9 NI,+ = V �9 N_so~2- [8]


Vol. t34, No. 6 MATHEMATICAL MODEL 1359

and

[ H + ] [ S O ~ - ] . , - K,,,, [9]

[HSO4-]

where K,,,, is the dissociation constant for sulfuric acid. The solut ion close to the surface (i.e., within the dif-

fuse part of the double layer) is not e lect r ica l ly neutral . Poisson 's equation

V~p_ F ~ ZlC ~ [10] E i

relates potent ia l to the charge densi ty in solution. For the solution sufficiently far from the surface, electroneu- trality

Z zici = 0 [11] i

can replace Eq. [10] in the diffusion layer. Equa t ions [7]-[11], coupled with conservat ion of charge

V. i = O [12]

p rov ide the re la t ionships needed to obtain the electrostatic potent ia l and concent ra t ions in the electrolyte . The va lue of the e lec t rode potent ia l and the equat ions governing the interface provide boundary condi t ions at the meta l -e lec t ro ly te interface. At the outer edge of the di f fus ion layer, concent ra t ions were set to bulk values, and the potential was set equal to zero.

Numerical Method The coupled nonlinear differential equations pre-

sented earlier were solved under the pseudo-steady-state condition. These equations were linearized, posed in finite difference form, and solved numerically using Newman's (14) BAND method coupled with Newton- Raphson iteration. This work involves the coupling of equations that govern regions with greatly different scal- ing lengths (i.e., the diffuse double layer and diffusion layer). Another feature is the local inversion (15, 16) of the large number of interfacial equations to a smaller number involving only bulk variables. The iterative method demonstrated quadratic convergence which was usually achieved in less than 6 iterations. The program

g

c.o

g Lt3"

g

g

g s

g ~ - ~ . 3 2

/

- b . 0 4 o'.24

V - r , V ( N H E )

1 0 0 0 s "]

f --

5OO

f -

1 0 0

0'- 52 ,. 80

Fig. 2. Calculated total current density as o function of potential referenced to the outer limit of the diffuse part of tee double layer with rotation speed as a parameter.

%:

7 O

? O

'C)

' O

' c ) :

' O :

w -

' O :

m - 'C:):

5 0 0

,u0~

1 0 0 0 s "1

-0.60 -b.32 -b.04 o'.24 o'.s2 o.so

V - ep o , V ( N H E )

Fig. 3. Calculated active area as a function of potential referenced to the outer limit of the diffuse part of the double layer with rotation speed as a parameter.

l is t ings and the parameters used in this ma themat i ca l mode] are provided in Ref. (17). Discuss ion of the local inversion technique is presented in Appendix B. The no- tation used in Appendix B follows that of Refi (14).

Results and Discussion The results obtained with this model are presented to

il lustrate the important features that have been observed exper imenta l ly for iron corrosion in similar systems. The inf luence of key parameters on model resul ts is also discussed.

Current-potential behavior.--The current -potent ia l curves obtained through this model are presented in Fig. 2 with rotation speed as parameter. These results are given within a potential range of -0.57-0.57V (NHE) and are referenced to the potential of the outer limit of the diffuse part of the double layer. This presentation is consistent with the common treatment of the diffuse part of the double layer as being part of the interface in models of electrode kinetics. At each of these rotation speeds, the current density reaches a limiting value within a cer- tain range of potentials. This limiting-current plateau is associated with a concurrent reduction of the fraction of active area of the iron disk, as shown in Fig. 3. The limiting current plateau is observed because the exponential increase of current with potential expected for a Tafel re- gime is compensated by an exponential decrease of the active electrode area with potential. In effect, the mass- transfer-limited reactant is the active part of the iron electrode itself. This result was obtained by simultane- ous solution of the governing kinetic and transport equations in which the active fraction AF,. was a variable, not by subsequent adjustment of the calculated results.

The values of limiting current calculated from this model agree with the value determined by the relation

i..i = 0.17496 ~/~ [13]

as defined by Law (18) for the experimental results of Epelboin et al. (19). This dependence of limiting current on the square root of rotation speed is also consistent with the experimental results of Russell and Newman (5). The dependence of the calculated limiting current on the square root of rotation speed is presented in Fig. 4. This result is consistent with mass-transfer limitations to


1360 J. Electrochem. Soc.: E L E C T R O C H E M I C A L SCIENCE AND T E C H N O L O G Y June 1987

l l~ I I I 1

<

g

g

~ O0 8.00 16.00 2 4 . 0 0 32.00 40.00

,/~ ,~1/2

Fig. 4. The calculated limiting current as a function of the square root of rotation speed.

a r o t a t i n g d i sk [see, for e x a m p l e , L e v i c h (20)]. I t m u s t be e m p h a s i z e d t h a t t h e m o d e l d o e s n o t a c c o u n t for t h e n o n u n i f o r m c u r r e n t or p o t e n t i a l d i s t r i b u t i o n a c r o s s t h e d i s k sur face . Hence , t h e c a l c u l a t e d c u r r e n t d e n s i t y is ap- p r o p r i a t e for t h e c e n t e r of t h e d i s k u n d e r c o n d i t i o n s w h e r e t h e c u r r e n t d i s t r i b u t i o n , is n o t u n i f o r m o n t h e d i sk . T h e c u r r e n t d i s t r i b u t i o n , h o w e v e r , is u n i f o r m un - d e r m a s s - t r a n s f e r l i m i t a t i o n s .

I t c a n also b e n o t e d t h a t for h i g h e r r o t a t i o n speed , t h e c u r r e n t - p o t e n t i a l b e h a v i o r is s h i f t e d anod ica l ly . Th i s be- h a v i o r is s h o w n m o r e c lea r ly in Fig. 3. A n e x p l a n a t i o n for t h i s p h e n o m e n o n c a n be r e l a t e d in t e r m s of t h e s u r f a c e c o n c e n t r a t i o n of f e r rous ions . A m o r e a n o d i c p o t e n t i a l is

r e q u i r e d at h i g h e r r o t a t i o n s p e e d s to c r e a t e a s u f f i c i e n t s u r f a c e c o n c e n t r a t i o n of f e r rous ions to f avor f u r t h e r oxi- d a t i o n to fe r r ic ions , w h i c h is u l t i m a t e l y r e s p o n s i b l e for p a s s i v a t i o n : H e n c e , a p o t e n t i o s t a t i c d e l a y in p a s s i v a t i o n is o b s e r v e d . A l k i r e a n d C a n g e l l a r i (4) h a v e i n d i c a t e d in t h e i r r e s u l t s t h a t f lu id v e l o c i t y p l a y s a ro le in s w e e p i n g a w a y c o r r o s i o n p r o d u c t s s u c h as f e r r o u s i o n s f r o m t h e i r o n s u r f a c e . T h i s r e s u l t is o n l y s e e n for p o t e n t i a l s t h a t a re m o r e c a t h o d i c t h a n t h e p o t e n t i a l s a t w h i c h t h e l imi t - i n g c u r r e n t p l a t e a u is o b s e r v e d . A t t h e l i m i t i n g - c u r r e n t p l a t e a u , t h e c a l c u l a t e d c o n c e n t r a t i o n o f f e r r o u s i ons c lose to t h e s u r f a c e r e a c h e s a v a l u e of 1.3M. Th i s v a l u e is b a s e d u p o n t h e a s s u m p t i o n t h a t t h e d i f f u s i o n coe f f i c i en t of f e r rous ions is 0.5 x 10 '~ cm-Us. T h e su r f ace c o n c e n t r a - t i o n o b t a i n e d for a d i f f u s i o n c o e f f i c i e n t of 0.1658 x 10 -~ cm2/s [as u s e d by R u s s e l l a n d N e w m a n (5)] was 3.0M. T h e f e r r o u s ion c o n c e n t r a t i o n r e m a i n s u n c h a n g e d w i t h i n t h e l i m i t i n g - c u r r e n t r e g i o n a n d is i n d e p e n d e n t of b o t h po- t e n t i a l a n d r o t a t i o n s p e e d . T h e r e s u l t s s h o w t h a t t h e m a s s - t r a n s f e r - l i m i t e d c u r r e n t s c an be a t t r i b u t e d to m a s s - t r a n s f e r l i m i t a t i o n s to t h e r e m o v a l of c o r r o s i o n p r o d u c t s f r o m t h e i r on su r f ace c o u p l e d w i t h f o r m a t i o n of a n o x i d e layer .

Concentration dis tr ibut ion.--The c o n c e n t r a t i o n profi- les of HSO4 , H +, Fe 2+, a n d SO42- in t h e d i f f u s i o n l a y e r a n d t h e d i f fu se p a r t of t h e d o u b l e l aye r for p o t e n t i a l s of - 0 . 5 6 a n d 0.51V (NHE) are s h o w n in Fig. 5 a n d 6. T h e c h a n g e of s ca l e b e t w e e n t h e d i f f u s e p a r t o f t h e d o u b l e l a y e r a n d t h e d i f f u s i o n l a y e r is e v i d e n t in t h a t t h e con- c e n t r a t i o n d e r i v a t i v e s a re e q u a l at t h e b o u n d a r y b e t w e e n t h e two reg ions . In t h e d i f f u s i o n layer , t h e f lux t h a t char - a c t e r i ze s t h e t r a n s p o r t of ion ic spec i e s is p r e d o m i n a n t l y c o n v e c t i v e . At a c a t h o d i c p o t e n t i a l of - 0 . 5 6 V (NHE), t h e d i s s o l u t i o n of i r on is i n h i b i t e d . At e q u i l i b r i u m , t h e con- c e n t r a t i o n p rof i l e of f e r r o u s i o n s as we l l as o t h e r i o n i c s p e c i e s in t h i s r e g i o n a t t a i n a c o n s t a n t v a l u e w h i c h ap- p r o x i m a t e s t h e c o n c e n t r a t i o n a t t h e b u l k p h a s e , as s h o w n in Fig. 5. T h e i n c r e a s e in f e r r o u s i on c o n c e n t r a - t i o n n e a r t h e s u r f a c e b e c o m e s m o r e p r o n o u n c e d at a m o r e a n o d i c p o t e n t i a l (see Fig. 6). T h e f e r r o u s i on con- c e n t r a t i o n r e a c h e s a m a x i m u m v a l u e w h i c h r e m a i n s con-

I

Diffuse Par t

O

g

C o to

5

I I I

of the Double Layer

HSO~

H +

.~ SO~"

0 ~ _. Q

~ 4'.oo 8'.oo 1~.oo 1~.oo P o s i t i o n , ~ / A

so~-

0.00 0'.30

[ I I

Diffusion Layer

HSO~

H +

Fe2+

2 0 0 ~, 6 0 0 ~, 9 0 1 ~. 2 0 1 �9 5 0

Posi t ion , z/~

Fig. 5. Concentration distribution of HSO4-, H § SO42-, and Fe 2+ ions in the diffuse part of the double layer and the diffusion layer at a potential of - 0 . 5 6 V (NHE) with u rotation speed of 100 s-L Position in the diffuse part of the double layer and the diffusion layer are scaled to the Debye length k and the characteristic mass-transfer length 8, respectively.


Vol. 134, No. 6 M A T H E M A T I C A L M O D E L 1361

Fe2+

r

Diffuse I I

P a r t of t he Double Layer

HSO~

o ~

C)-

o o

00'.00

s o , = -

0.00 0.30 0,60

H § i 8t 4.00 .00 12.00 16.00 20

Position , z/A

t I I

Diffusion Layer

HSO~

H §

Fe2+

0'. 90 1 '. 20

Position , z/6

.50

Fig. 6. Concentration distribution of HSO4-, H § SO42-, and Fe 2+ ions in the diffuse part of the double layer and the diffusion layer at a potential of 0.51V (NHE) with a rotation speed of 100 s -1. Position in the diffuse part of the double layer and the diffusion layer are scaled to the Debye length h and the characteristic mass-transfer length 5, respectively.

s t a n t t h r o u g h o u t t h e l i m i t i n g - c u r r e n t reg ion . T h e r e s u l t s i n d i c a t e t h a t m a s s - t r a n s f e r l i m i t a t i o n s to t h e r e m o v a l of c o r r o s i o n p r o d u c t s f rom t h e i r on s u r f ace a n d t h e subse - q u e n t b u i l d u p of f e r r o u s i o n s l ed to p a s s i v a t i o n . I n t h e l i m i t i n g - c u r r e n t r e g i o n , a c o r r e s p o n d i n g d r a s t i c r e d u c - t i o n in t h e ac t ive f r a c t i o n of t h e d i sk s u r f ace is o b s e r v e d , as s h o w n in Fig. 3.

T h e c o n c e n t r a t i o n d i s t r i b u t i o n s a t a n o d i c p o t e n t i a l s re f lec t n o t o n l y c o n v e c t i v e d i f f u s i o n b u t t h e a d d e d con- s t r a i n t s i m p o s e d b y t h e r e q u i r e m e n t s of e l e c t r o n e u t r a l - i ty a n d t h e pa r t i a l d i s s o c i a t i o n of su l fu r i c acid. As s h o w n in Fig. 6, m a x i m a are o b s e r v e d in t h e c o n c e n t r a t i o n dis- t r i b u t i o n s of HSO4-, SO4 ~ , a n d Fe 2+. At h i g h r a t e s of corros ion , e l e c t r o n e u t r a l i t y r e q u i r e s t h a t t h e c o n c e n t r a t i o n of c a t i o n s d e c r e a s e n e a r t h e e l e c t r o d e s u r f a c e a n d t h a t t h e a n i o n s i n c r e a s e n e a r t h e s u r f ace to a c c o m m o d a t e t h e i n c r e a s e d c o n c e n t r a t i o n of t h e p o s i t i v e l y c h a r g e d fer- r o u s ions . T h e s e a d j u s t m e n t s are a lso r e f l ec t ed in t he dis- s o c i a t i o n of su l fu r i c ac id s ince H + d e c r e a s e s n e a r t h e sur- f ace a n d HSO4- i n c r e a s e s to c o m p e n s a t e p a r t i a l l y t h e p o s i t i v e l y c h a r g e d e n v i r o n m e n t c r e a t e d b y a r i se in t h e f e r r o u s i o n c o n c e n t r a t i o n . S i n c e H +, SO42-, a n d HSO4- i ons a re a lso i n v o l v e d in t h e e q u i l i b r a t i o n of a d i s soc ia - b le acid , t h e c o n c e n t r a t i o n d i s t r i b u t i o n s o b s e r v e d for t h e H +, H S O ( , a n d SO~ ~- i o n s in Fig. 6 a re r e s p o n s e s to ac- c o m m o d a t e b o t h t h e h o m o g e n e o u s p a r t i a l d i s s o c i a t i o n of s u l f u r i c a c id a n d t h e e l e c t r o s t a t i c i m b a l a n c e c r e a t e d in t h e d i f f u s i o n layer . As a resu l t , t h e p H in t h e v i c i n i t y of t h e e l e c t r o d e s u r f a c e is a l t e r e d . F o r c l a r i ty , t h e c o n c e n - t r a t i o n p ro f i l e s of f e r r i c i ons a re s h o w n s e p a r a t e l y a n d are d i s c u s s e d l a t e r in t h i s sec t ion .

W i t h i n t h e d i f fu se p a r t of t h e d o u b l e layer , e l e c t r o n e u - t r a l i t y is n o l o n g e r va l id . D u e to t h e c lo se r p r o x i m i t y to t h e m e t a l su r face , t h e c o n v e c t i v e m a s s - t r a n s f e r c o n t r i b u - t i o n is u n i m p o r t a n t . T h e m a g n i t u d e of t h e ax ia l v e l o c i t y in t h i s r e g i o n is of t h e o r d e r 10 - '~ cm/s or sma l l e r . U n l i k e t h e d i f f u s i o n layer , t h e b e h a v i o r of c o n c e n t r a t i o n d is t r i - b u t i o n w i t h i n t h i s r e g i o n is s t r o n g l y d e p e n d e n t u p o n e l e c t r o s t a t i c i n t e r a c t i o n s a t t h e m e t a l s u r f a c e . D e p e n d - i ng on t h e n a t u r e of t h e c h a r g e d su r face , t he c h a r g e d spe- c ies c lose to t h e su r f ace wil l r e s o o n d in a c c o r d a n c e to t h e

c o u l o m b i c f o r c e s of a t t r a c t i o n or r e p u l s i o n . F o r a n e g a - t i v e l y c h a r g e d s u r f a c e (see Fig. 5), p o s i t i v e l y c h a r g e d spec i e s s u c h as H + a n d Fe 2+ are a t t r a c t e d t o w a r d t h e surface a n d t h e n e g a t i v e l y c h a r g e d spec i e s are r epe l l ed . T h e t r e n d is r e v e r s e d for a p o s i t i v e l y c h a r g e d su r f ace in Fig. 6. A k e y p a r a m e t e r in t h i s s t u d y is t h e p o t e n t i a l of ze ro c h a r g e w h i c h was c h o s e n to b e 0 V (NHE). E x p e r i m e n t a l s t u d y of t h e c a p a c i t y of t h e m e t a l e l e c t r o d e c o u l d b e u s e d to d e t e r m i n e t h i s p a r a m e t e r . W h i l e t h e c o n c e n t r a - t i o n d i s t r i b u t i o n n e a r t h e s u r f a c e is d i c t a t e d b y t h e na- t u r e of t h e c h a r g e d s u r f a c e , d i f f u s i o n a l a n d m i g r a t i o n a l m a s s t r a n s f e r a re a lso i n s t r u m e n t a l in t h i s r eg ion . A spe- c ies n o t i n v o l v e d w i t h i n t e r f a c i a l r e a c t i o n s wi l l e x p e r i - e n c e a c o n c e n t r a t i o n g r a d i e n t s u c h t h a t d i f f u s i o n bal - a n c e s e x a c t l y m i g r a t i o n d r i v e n b y t h e p o t e n t i a l g r a d i e n t . T h e f lux of a spec i e s i n v o l v e d w i t h a n i n t e r f ac i a l r e a c t i o n a t a f in i t e r a t e wi l l b e d r i v e n p r i m a r i l y b y p o t e n t i a l a n d c o n c e n t r a t i o n g r a d i e n t s .

F i g u r e s 7 a n d 8 are p r o v i d e d to s u m m a r i z e t h e b e h a v - ior of c o n c e n t r a t i o n d i s t r i b u t i o n of H + a n d F & + ions for t h e d i f f u s i o n l a y e r w i t h p o t e n t i a l as p a r a m e t e r . F r o m Fig. 7, t h e p H in t h e s y s t e m is s h o w n to i n c r e a s e w i t h po- t e n t i a l . P a r t i c u l a r l y a t a n o d i c p o t e n t i a l s , t h e r e g i o n in t h e v i c i n i t y of t h e c o r r o d i n g s u r f a c e t e n d s to b e l e s s ac id ic . Th i s r e s u l t is c o n s i s t e n t w i t h B e c k ' s (21) o b s e r v a - t i o n w h i c h was a t t r i b u t e d to sa l t f i lm f o r m a t i o n . H e s t a t e d t h a t t h e i n c r e a s e in t h e p H at t he m e t a l su r f ace is d u e to t h e i n c r e a s e in F e 2+ i o n s r e s u l t i n g f r o m t h e h in - d r a n c e of t h e s a l t f i lm to o u t w a r d t r a n s p o r t o f t h i s spe- c ies . D e s p i t e n e g l e c t of t h e sa l t - f i lm f o r m a t i o n , t h i s m o d e l i n d i c a t e d loca l c h e m i c a l c o n d i t i o n s t h a t a g r e e q u a l i t a t i v e l y w i t h B e c k ' s o b s e r v a t i o n p r i o r to p a s s i v a - t ion . T h e r e s u l t s a s s o c i a t e a n i n c r e a s e in b o t h t h e p H a n d F e ~+ ion c o n c e n t r a t i o n to a s i gn i f i can t d e c r e a s e in t h e ac- t ive p o r t i o n of t h e e l e c t r o d e sur face . I n c l u s i o n of t h e sa l t f i lm s h o u l d e n h a n c e t h i s effect .

As s h o w n in Fig. 8, t h e r e is a p r o n o u n c e d d e p l e t i o n of fe r r i c ions n e a r t h e su r f ace at a n o d i c p o t e n t i a l s . Th i s c an b e e x p l a i n e d in p a r t b y t h e i n v o l v e m e n t of t h i s spec i e s in t h e f o r m a t i o n of a p a s s i v e o x i d e f i lm w h i c h is f a v o r e d at s u c h a n o d i c po t en t i a l s . In a d d i t i o n , t h i s p a s s i v a t i o n reac-



+

r

o I I I

- .

- 0 . 5 6 and 0 V -_

o -

g -

n o -

%'. O0 0'. 30 0', 60 0', 90

Pos i t ion , z/~

I', 20 1 ~0

Fig. 7. Concentration distribution of H + ions in the diffusion layer at rotation speed of 100 s ~ with potential as a parameter. Position is scaled to the characteristic mass-transfer length.

tion is also coupled to the various activities occurring within the diffusion layer as discussed earlier in this section�9

Influence of kinetic parameters.--The m i c r o s c o p i c ap- p r o a c h u s e d in m o n i t o r i n g t h e e l e c t r o d e r e a c t i o n s in- v o l v e p a r a m e t e r s s u c h as t h e r e s p e c t i v e r a t e a n d equ i l i b - r i u m c o n s t a n t s � 9 Whi le t h e s e p a r a m e t e r s a re wel l de f ined , t h e i r v a l u e s a re n o t wel l e s t a b l i s h e d a n d are u n a v a i l a b l e in t h e l i t e r a t u r e . H e n c e , t h e i n i t i a l k i n e t i c p a r a m e t e r s w e r e d e r i v e d b y e x p r e s s i n g t h e e l e c t r o c h e m i c a l r eac -

tz

+

o

o -

o ~

o

- 0 . 5 6 and 0 V

...--

0.51

0'. O0 0', 30 0'. 60 0'. 90 1 '�9 20 .50

Posi t ion , z/b,

Fig. 8. Concentration distribution of Fe a+ ions in the diffusion layer at rotation speed of 100 s -~ with potential as a parameter. Position is scaled to the characteristic mass-transfer length.

t i o n s in f o r m s of B u t l e r - V o l m e r r a t e e x p r e s s i o n s a n d b y u s i n g t h e a s s u m p t i o n t h a t a d s o r p t i o n - d e s o r p t i o n r eac - t i o n s are e q u i l i b r a t e d . T h e p a s s i v a t i o n r e a c t i o n was also a s s u m e d to b e e q u i l i b r a t e d in t h i s w o r k . T h i s m e t h o d p r o v i d e d a n a p p r o x i m a t i o n of t h e s e u n k n o w n p a r a m e - ters . To t h e e x t e n t poss ib l e , l i t e r a t u r e v a l u e s of e x c h a n g e c u r r e n t d e n s i t i e s a n d s t a n d a r d cel l p o t e n t i a l s w e r e u s e d to o b t a i n v a l u e s of k i n e t i c p a r a m e t e r s (see A p p e n d i x A). A d d i t i o n a l v a l u e s w e r e o b t a i n e d b y m a t c h i n g t h e ca lcu- l a t e d c u r r e n t - p o t e n t i a l c u r v e s to e x p e r i m e n t a l va lue s � 9 T h e i n f l u e n c e of t h e s e k i n e t i c p a r a m e t e r s was s t u d i e d to p r o v i d e a s y s t e m a t i c a p p r o a c h to t he c u r v e - f i t t i n g of cal- c u l a t e d r e s u l t s to m a t c h t h o s e o b t a i n e d e x p e r i m e n t a l l y � 9 T h e key k i n e t i c p a r a m e t e r s t h a t w e r e a d j u s t e d to m a t c h t h e e x p e r i m e n t a l d a t a we re ks, k4, a n d ET.

As seen in Fig. 9, the current-potential curve is shifted anodically with a decrease in the rate constant for the iron dissolution reaction k2. The implication of this anodic shift reflects the requirement that an increase in the potential driving force for this reaction compensate for a decrease in the rate constant. A decrease of the rate constant for the ferrous-oxidation reaction k, causes the limiting-current plateau to become broader as shown in Fig. I0. This observation can be explained in that ferric ion formation is required to create a chemical envi- ronment conducive to passivation. Conversely, an increase in the rate constant greatly decreased the potential range in which the current was constant. Hence, the extent of the limiting-current plateau can be related to the extent of passivation on the electrode surface. The model presented here does not provide for the sudden drop in current associated with complete passivation. A second mechanism for the conversion of a partially protected surface to a completely protected surface may be needed. The equilibrium constant for the passivation reaction E7 has a primary influence on the value of the limiting current, as shown in Fig. ii. A decrease in the equilibrium constant for the passivation reaction causes the reaction equilibrium to be shifted away from oxide formation. Each of the parameters discussed here has a unique influence on the current-potential curve. A

o

o ~

,5

o "

8

0 - 0 , 6 0

I I I I

-0.32 -0.04 0'.24 0'.52 0.80

V - @o ' V ( N H E )

Fig�9 9�9 Calculated total current density as a function of potential referenced to the outer limit of the diffuse part of the double layer with the rate constant for the oxidation of iron as a parameter. The rotation speed was 100 s -t. Curve o, k2 = 1.512 • 105 cmVmoP-s; curve b, ks = 1 �9 • 106 cmVmoP-s; curve c, k2 = 1 .$12 • 107 cmVmoP-s.


Vol. 134, No. 6 M A T H E M A T I C A L M O D E L 1363

g i I I I

- - d

~2

g , 2 - a

$ Q -

Q -

~ -b.32 -b.o4 o'.24 o'.s2 o.~o

V - r ' V ( N H E )

Fig. 10. Calculated total current density as a function of potential referenced to the outer limit of the diffuse part of the double layer with the rate constant for the oxidation of ferrous ions as a parameter. The rotation speed was 100 s -1. Curve a, k4 = 5 .020 x 10 -2 cm2/mol-s; curve b, k4 = 5 .020 x 10 .3 cm2/mol-s; curve c, k4 = 5 .020 • 10 4 cm2/ mol-s; curve d, k4 = 5 .020 x 10 -6 cm2/mol-s.

c u r r e n t - p o t e n t i a l c u r v e w h i c h c lo se ly c o r r e l a t e s to ex- p e r i m e n t a l r e su l t s can t h e r e f o r e be o b t a i n e d t h r o u g h c o m b i n a t i o n of t he se u n i q u e inf luences .

Conclusions At the l im i t i ng -cu r r en t pla teau, t he ca lcu la ted concen-

t r a t ion of fe r rous ion c lose to t he e l e c t r o d e su r face is in- d e p e n d e n t of bo th the ro ta t ion speed and potent ia l . This resu l t shows tha t the mass - t r ans fe r - l imi t ed cu r ren t s can be a t t r i bu t ed to mass - t r ans fe r l imi ta t ions for the r e m o v a l of co r ros ion p roduc t s f rom the i ron sur face c o u p l e d wi th t h e pa r t i a l p r o t e c t i o n o f t he su r f ace by an o x i d e layer . T h e c u r r e n t l i m i t e d in th i s w a y is p r o p o r t i o n a l to t he squa re root of ro ta t ion speed.

This w o r k does no t a c c o u n t for e i t he r t he n o n u n i f o r m po ten t i a l and cu r r en t d i s t r i bu t ion across the d i sk sur face or t h e p o t e n t i a l d r o p in t he e l e c t r o l y t i c so lu t ion . U n d e r m a s s - t r a n s f e r l im i t a t i ons , h o w e v e r , t h e c u r r e n t d e n s i t y is un i fo rm, and the va lues of l imi t ing cu r r en t ca lcu la ted f rom this m o d e l agree wi th the e x p e r i m e n t a l resu l t s ob- t a i n e d by E p e l b o i n et al. (19) and R u s s e l l and N e w m a n (5). The l im i t i ng -cu r r en t p l a t eau o b s e r v e d for i ron in sul- fur ic ac id m a y be a s soc ia t ed wi th a r e d u c t i o n of the frac- t ion of ac t ive area o f t he i ron disk. This p r o g r e s s i v e surface c o v e r a g e o f o x i d e s is c o n s i s t e n t w i t h t h e E D X analys is p e r f o r m e d by Mil ler (11, 22) on an i ron d isk be- l o w t h e p a s s i v a t i o n po t en t i a l . His r e su l t s i n d i c a t e d t h e p r e s e n c e of an ox ide layer in the l im i t i ng -cu r r en t r eg ion w h i c h was no t d e t e c t e d at m o r e c a t h o d i c po t en t i a l s . More (pre fe rab ly in situ) obse rva t ions are n e e d e d to ver- ify Mi l l e r ' s r e su l t s . T h e s e r e su l t s , h o w e v e r , a re cons i s t - e n t w i t h t h e p o s t u l a t e t h a t c u r r e n t o sc i l l a t i ons a r e c a u s e d by pa r t i a l p a s s i v a t i o n and d e p a s s i v a t i o n of t h e m e t a l u n d e r t h e sal t film. The ac t i ve f r a c t i o n c a l c u l a t e d h e r e w o u l d in th i s case be c o n s i d e r e d to be a t ime - a v e r a g e d value.

T h e c o n c e n t r a t i o n d i s t r i b u t i o n of ion ic spec i e s in- v o l v e d in the sys t em i l lus t ra te the coup l ing of e l ec t rode p r o c e s s e s and mass t rans fe r in e l e c t r o c h e m i c a l sys tems . A t p o t e n t i a l s w h e r e t h e g e n e r a t i o n o f f e r rous ions be- c o m e s s ign i f ican t , t h e c o n c e n t r a t i o n of o t h e r c h a r g e d

r

Q -

C:)-

I K I I

/ / f~

%0.so -b.3z -b.04 0'.24 o'.s2

V - q~o �9 V ( N H E )

t ~

.go

Fig. 11. Calculated total current density as a function of potential referenced to the outer limit of the diffuse part of the double layer with the equilibrium constant for the passivation reaction as a parameter. The rotation speed was 100 s -1. Curve a, E7 - 0.2 x 10 "~; curve b, E7 = 0.4 x 10-13; curve c, E7 = 0.8 x 10 -13.

spec ies near the sur face was found to di f fer cons ide r ab ly f r o m the b u l k c o n c e n t r a t i o n s . The c o n c e n t r a t i o n dis t r i - bu t ion c lear ly shows the in f luence of h o m o g e n e o u s par- t ia l d i s s o c i a t i o n of su l fu r i c ac id on the pH c lose to t h e surface. It is also shown tha t the pH in the v i c in i ty of the e l e c t r o d e su r f ace i n c r e a s e s s ign f i can t ly at p o t e n t i a l s c lose to pas s iva t i on . Th is c o n d i t i o n is c o n d u c i v e to p a s s i v a t i o n and has b e e n e x p e r i m e n t a l l y o b s e r v e d by a n u m b e r of w o r k e r s (21-23). A s ign i f i can t i n c r e a s e in ferric ions b e c o m e s e v i d e n t at only ve ry anod ic potent ia ls , and th i s r e s u l t is c o n s i s t e n t w i t h t he e x t r e m e l y a n o d i c e q u i l i b r i u m p o t e n t i a l of 0.77V (NHE) for t h e fe r rous - o x i d a t i o n react ion .

The a p p r o a c h p r e s e n t e d here p rov ides an e x p l a n a t i o n for t he e x p e r i m e n t a l l y o b s e r v e d l im i t i ng -cu r r en t p l a t eau a s s o c i a t e d w i t h an i ron d i sk in su l fu r i c ac id in t e r m s of t h e i n t e r a c t i o n a m o n g su r f ace r eac t ions . T h e t r e a t m e n t of m u l t i p l e e l ec t rode reac t ions and the obse rved in terac- t i ons a m o n g t h e s e r e a c t i o n s is u se fu l in d e v e l o p i n g an u n d e r s t a n d i n g of e l e c t r o c h e m i c a l s y s t e m s i n v o l v i n g c o m p l e x reac t ions and can be app l i ed to o the r hydrody- n a m i c sys t ems as wel l as to o the r me ta l sys tems .

Acknowledgment This w o r k was s u p p o r t e d by t h e O r g a n i c C h e m i c a l s

D e p a r t m e n t , D o w C h e m i c a l USA, and by the Cen te r for I n n o v a t i v e T e c h n o l o g y gran t no. CIT-MAT-85-027.

M a n u s c r i p t s u b m i t t e d J u n e 2, 1986; r e v i s e d m a n u - sc r ip t r e c e i v e d Oct. 6, 1986. This was P a p e r 10 p r e s e n t e d at t he Bos ton , MA Mee t ing of the Socie ty , May 4-9, 1986.

A P P E N D I X A

Calculation of Kinetic Parameters The in i t ia l k ine t i c p a r a m e t e r s s u c h as t he ra te and

e q u i l i b r i u m cons tan t s used in this w o r k were ca lcu la ted us ing l i t e ra tu re va lues of e x c h a n g e cu r r en t dens i t i e s and s t a n d a r d cel l p o t e n t i a l s for t h e e l e c t r o d e r eac t i ons . An e x a m p l e o f t he m e t h o d for o b t a i n i n g t h e s e k i n e t i c pa- r a m e t e r s is p r e s e n t e d h e r e for t he o x i d a t i o n of m e t a l a t oms to fo rm fer rous ions. This c h a r g e - p r o d u c i n g reac- t ion was wr i t t en as


1364 J. Electrochem. Soc.: ELECTROCHEMICAL SCIENCE AND TECHNOLOGY

Table A-I. Input parameters for the metal-electrolyte interface

June1987

i Reaction (i) ki E, 1 Fe2+]ads r Fe z+ ~ 0�9 x 10 a mol /cm a 2 Fe r Fe~+],d~ + 2e 0.151 • 10 '~ cm4/mol~-s 0.818 • 10 -~ mol~/cm 4 3 Fe a+ ads ~ Fe ~+ ~ 0.158 x i 0 '~ mol/cm ~ ~ 4 Fe~+l~a~ r Fen+lads + e 0�9 X 10 TM cm~/mol-s 0.183 x 10 ~o mol /cm ~ 5 SO~=-t~r ' SO4 ~ co 0.198 x 10 4 mol /cm a 6 H+]ads <::> H + ~ 0.511 x 10 ~ mol /cm a ~ 7 Pass ivat ion reaction ~ co 0.400 x 10 ~a 8 Film format ion ~ - - - - 9 2H+[ad~ + 2e- r H~ 0.190 x 1022 cm2/mol-s 0.665 x 10 'a cm/mol

10 HSO4 lad~ r HSO4- ~ 0.828 x 10 z moYcm a

Distance be tween OSS and ISS 5, 0.1 • 10 -7 em Distance between 1SS and 1HP 82 0.2 x 10 -~ em Distance between IHP and OHP 8a 0.2 x 10 ~ cm

Permit t ivi ty of solution e~,,m 0�9 • 10 " C/V-cm Permit t ivi ty of metal e~,.t 0.885 x i 0 - ' a C/V-cm

Densi ty of sites at ISS F,ss 0.166 x 10 ~ mol/cm ~ Densi ty of sites at IHP Fray 0.120 • 10 -~ mol /cm ~

These parameters are not independen t and were de te rmined from combinat ion of the other equi l ibr ium constants . b 2Fe3+l~ + 3H20 r Fe2Oa]ad~ + 6H+l~,s r Inf luence of this reaction was not incorporated in this work.

F e <=> F e ~+ + 2e - [A- l ]

w h i c h c a n b e c o n c e p t u a l l y b r o k e n u p i n t o t h e f o l l o w i n g s e q u e n c e

F e <:v F e 2 + l ~ + 2e - [A-2]

Fe2+l~d,~ r F e z+ [A-3]

T h e f e r r o u s i o n s w e r e p e r c e i v e d to b e a d s o r b e d to t h e in- n e r H e l m h o l t z p l a n e a n d t h e a d s o r p t i o n - d e s o r p t i o n r e a c - t i o n o f E q . [3] w a s a s s u m e d to b e e q u i l i b r a t e d i n t h i s w o r k .

B y e x p r e s s i n g E q . [2] i n t h e f o r m o f E q . [14], o n e o b - t a i n s t h e f o l l o w i n g r a t e e x p r e s s i o n

r = F = k z ' e x p V % - F ~ ,

w h e r e k2 a n d k_~ a r e t h e f o r w a r d a n d b a c k w a r d r a t e c o n - s t a n t s fo r r e a c t i o n [2], r e s p e c t i v e l y . T h e p o t e n t i a l V is t h e p o t e n t i a l d i f f e r e n c e b e t w e e n t h e m e t a l a n d t h e s o l u t i o n a d j a c e n t to it. T h i s p o t e n t i a l d i f f e r e n c e c a n b e w r i t t e n in t e r m s o f t h e s u r f a c e o v e r p o t e n t i a l ~ a n d e q u i l i b r i u m po - t e n t i a l g,, a s V = n~ + V,,. U n d e r t h e a s s u m p t i o n t h a t r e a c - t i o n [3] i s e q u i l i b r a t e d , o n e c a n e q u a t e t h e f o r w a r d a n d b a c k w a r d r a t e to g i v e

k~ " % " F I H p = k_, " y , " FmpC~=+,~ [A-5]

k_~ = Y2 = ~ % C F ~ 2 + , ~ [A-6]

w h e r e Cr~2+.~ is t h e b u l k c o n c e n t r a t i o n o f f e r r o u s i o n s a n d k, a n d k_, a r e t h e f o r w a r d a n d b a c k w a r d r a t e c o n - s t a n t s f o r r e a c t i o n [3]. T h e n u m b e r i n g s y s t e m u s e d h e r e f o l l o w s t h a t u s e d i n T a b l e A - I a n d A-I I .

A t t h e e q u i l i b r i u m p o t e n t i a l V,,, i is e q u a l to 0 a n d Eq . [4] c a n b e r e a r r a n g e d to g i v e

[ k 2"'Y2"-?e 2 ] R T 1og~ FZ,ss [A-7] V ~ 2F ~ k ( %

B y s u b s t i t u t i n g Eq . [6] i n t o E q . [7], o n e o b t a i n s

R T [ k _ ~ ' k , . y~ 2 ]

T h e e q u i l i b r i u m c o n s t a n t E is d e f i n e d to b e t h e r a t i o o f t h e f o r w a r d to t h e b a c k w a r d r a t e c o n s t a n t , t h u s E q . [8] c a n b e r e p r e s e n t e d b y

R T [ %2 F~,ss] [A-9] Vo = - ~ - - l o g ~ k

w h e r e t h e s u b s c r i p t s 1 a n d 2 d e n o t e r e a c t i o n s [3] a n d [2], r e s p e c t i v e l y .

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 i,, i s t h e v a l u e o f t h e c a t h o d i c t e r m or t h e a n o d i c t e r m o f r e a c t i o n [2] a t e q u i - l i b r i u m . B y u s i n g t h e c a t h o d i c t e r m , o n e o b t a i n s

'~ 2 F - k-2 " e x p - Vo ' y2 �9 Ye 2 " PmeFaIss [A-10]

a n d t h i s e q u a t i o n c a n b e f u r t h e r s i m p l i f i e d b y s u b s t i t u t i n g V,, f r o m Eq . [9] to g i v e

o r

i,, - k_o " 7,," % " FIsp " F,ss C~2+.~ [ A - I l l 2F

i . ]-2 E, = E2 CFe2+.~ 2Fk_2%%Flm.F~ss [A-12

T h e f r a c t i o n a l c o v e r a g e o f e a c h s p e c i e s a d s o r b e d o n t o in- t e r r a c i a l p l a n e I H P w a s a s s u m e d to b e e q u a l to 0.1, a n d t h i s g a v e a v a l u e o f 0.5 f o r t h e f r a c t i o n a l c o n c e n t r a t i o n o f v a c a n t s i t e s y,.. U n d e r t h e a s s u m p t i o n t h a t 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 is e q u a l to 0.1 • 10 '~ A / c m 2 a n d t h r o u g h s u b s t i t u t i o n o f t h e v a l u e s o f Fmp a n d F.ss g i v e n i n T a b l e A-I , E, c a n b e r e - e x p r e s s e d a s

E1 = 3.70 x 10-22(k_2'O(E2)(Crr 2+~) [A-13]

E q u a t i o n [13] p r o v i d e s a r e l a t i o n s h i p a m o n g k_2, E,, a n d E2. T h e e x p l i c i t e x p r e s s i o n o f t h e c o n c e n t r a t i o n a l l o w s t h e f l e x i b i l i t y o f v a r y i n g t h e s y s t e m c o n c e n t r a t i o n w i t h - o u t h a v i n g to r e c a l c u l a t e t h i s k i n e t i c p a r a m e t e r � 9 O t h e r k i n e t i c p a r a m e t e r s t h a t a r e f u n c t i o n s o f b u l k c o n c e n t r a - t i o n w e r e s i m i l a r l y t r e a t e d in t h i s w o r k .

A t e q u i l i b r i u m , b o t h r a n d ~ a r e e q u a l to z e r o , t h e r e - fo re , Eq . [4] c a n b e u s e d to e v a l u a t e E~, i.e.

k2 _ Y2 Y e 2 F 2 m s . e x p - R T "J [A-14] E 2 - k_2 %

T h e v a l u e o f E2 w a s d e t e r m i n e d to b e 8�9 • 10 -3 m o l 2 / c m 4 b y u s i n g a c a l c u l a t e d e q u i l i b r i u m p o t e n t i a l (Vo) o f - 0 . 4 8 1 V .

T h e m e t h o d p r e s e n t e d h e r e w a s u s e d to d e t e r m i n e a p - 9 r o x i m a t e v a l u e s f o r t h e k i n e t i c p a r a m e t e r s ; h o w e v e r s o m e o f t h e c a l c u l a t e d v a l u e s w e r e m o d i f i e d i n o r d e r to m a t c h t h e c a l c u l a t e d c u r r e n t - p o t e n t i a l c u r v e s to e x p e r i - m e n t a l v a l u e s � 9 A s t u d y o f t h e i n f l u e n c e o f s o m e o f t h e s e k i n e t i c p a r a m e t e r s w a s d i s c u s s e d i n t h e s e c t i o n o n I n f l u e n c e o f k i n e t i c p a r a m e t e r s t o p r o v i d e a s y s t e m a t i c a p p r o a c h to t h e c u r v e - f i t t i n g o f c a l c u l a t e d r e s u l t s t o m a t c h t h o s e o b t a i n e d e x p e r i m e n t a l l y .

Table A-II. Input parameters for the electrolytic solution

Electrolyte: 1.0M H2SO~, 0.04M FeSO4, 0.002M Fe.,(SO0a

Species index, i Species Charge number , z,

Diffusivity, D~:

Dissociat ion cons tant for sulfuric acid

Kinemat ic viscosity Rotat ion speed Gas cons tan t Temperature Faraday ' s cons tan t

1 2 3 4 H + Fe ~+ SO,2- Fe'a+ +1 +2 - 2 +3

D, 9.312 • 10 -~ cm2/s D~ 0.500 • 10-:' cm2/s D~ 1.065 • 10 -a cm2/s Dr 1.000 x 10 -~ cm2/s D~ 1.330 • 10 -a cm2/s

K 0.012 mole/liter

v 0.01 cm2/s 100 S 1

R 8.3143 d/mol-K T 300 K F 96,487 C/equivalent

5 HSO4 -i


Vol. 134, No. 6

A P P E N D I X B

M A T H E M A T I C A L M O D E L

Methodology for Local Inversion Consider the general equat ion

Gi(j) = 2 A~.k(j) Ck(j - 1) + B~,k(j) Ck(j) + D~,k(j) Ck(j + 1) k = l

[B-l]

where N-(n + 1) variables appear at only one mesh point N J, In light of the boundary condit ions at mesh point N J, Eq. [B-l] can be simplified at that point to Are

2 2 ~ GI(NJ) = A~.k(NJ) Ck(NJ - 1) + Bi.k(NJ) Ck(NJ) b k= l k ~ l C i

[B-2] D D i

where D~.k(NJ) = O. Alternatively, Eq. [B-2] can be broken E~ up into F

i G~(NJ) = ~_~ A~.k(NJ) Ck(NJ - 1) + ~.j S~.k(NJ) Ck(NJ) inm

k = l k = l g e q

kf , !

+ Bi,k(Nd) Ck(NJ) [B-3] kb,l k=n+l Ni

for 1 -< i -< n, and n

G~(NJ) = 2 A,.k(NJ) Ck(NJ - 1) + 2 B,.k(NJ) Ck(NJ) Pi,|

k= l k = l q i , l

+ B.k(NJ) Ck(NJ) [B-4] R k = n + l R i

for n + 1 -< i ~ N. This permits Eq. [B-4] to be wri t ten in matr ix form r

B ' C = F [B-5 ] rl Si , i

where B denotes the tensor with individual e lements B~,k, and F denotes the vector with individual e lements T

t F, = GI(NJ) ul

- AL,.(NJ) Cm(NJ - 1) + B~.m(NJ) Cm(NJ) [B-6] v~ m = l VZ

VO The matr ix form in Eq. [B-5] can be manipulated to give z~

Ck(NJ) = 2 Bk,, -1 FI [B-7] l = n + l

where n + 1 -< k -< N. In expanded form

Ck(NJ) = 2 Bk.C' Gi(NJ) l=n+~

2 -" l = n + l nl~I

-- 2 2 SkA-ISl.m(NJ) Cm(gJ) [B-g] 1=11+1 m=l

Subrou t i ne LOCINV does not p rov ide expl ic i t ly values for Bk.,-~; therefore it is conven ien t to denote the prod- uets such a s Bk,1-1 G~(NJ) by primes. This reduces Eq. [B-8] to

Ck(NJ) = ~ G',(NJ) - ~ 2 A'I,m(NJ) Cm(NJ - 1 ) l = n + l l - -n+l m--1

-- ~d 2 S'l,m(NJ) Cm(NJ) [8-9] l = n + l m-1

Finally, subs t i tu t ion of Eq. [B-9] into Eq. [3] yields the form

G~*(NJ) = 2 A~.m*(NJ) Cm(NJ - 1) + B,m*(NJ) Cm(NJ) m - 1

[B-10] where

Ai,m*=Ai,m - ~ ~ B~,kA'~,m(NJ) k = n + l l = n + l

Bi,m* = Bi.m - ~ ~ Bi.kB',.m(NJ) k = n + l l = n + l

1365

and

GI* = G~ - ~ 2 B,.k G'I(NJ) k = n + l l = n + l

By the above procedure, Eq. [4] can be solved independ- ently of Eq. [3]; thus Eq. [2] can be collapsed into Eq. [10] that involves only the n macroscopic variables.

LIST OF SYMBOLS

active fraction of iron surface 0.51023 -0.616 concentrat ion of species i, mol/cm ~ diameter, cm diffusion coefficient of species i, cm~/s equi l ibr ium constant for reaction l Faraday's constant, 96,487C/equiv current density, A/cm 2 l imiting current, A/cm ~ dissociation constant for sulfuric acid, mol/cm 3 anodic rate constant for reaction l cathodic rate constant for reaction l flux of species i, mol/cm2-s n u m b e r of e lect rons t ransfer red in e lec t rode reaction reaction order for species i in the forward direction of reaction l react ion order for species i in the backward direction of reaction 1 excess-charge density, C/cm 2 universal gas constant, 8.3143 J /mol-deg K rate of homogeneous p roduc t ion of species i, mol/cm~-s radial position coordinate, cm reaction rate for reaction l, mol/cm~-s stoichiometric coefficient for species i and reaction l absolute temperature, deg K time, s mobility of species i, cm2-mol/J-s fluid velocity, cm/s velocity in the r-direction, cm/s velocity in the z-direction, cm/s velocity in the O-direction, cm/s charge number of species i

Greek Characters Aq~l potential driving force for reaction l ~, symmetry factor for reaction 1

characterist ic length of the diffusion layer e permitt ivity, farad/cm

dimensionless axial distance from disk Debye length, cm

v kinematic viscosity, cm2/s charge density, C/cm ~

cp electrostatic potential, V 12 rotation speed, radian/s

Subscripts ISS associated with the inner surface states IHP associated with the inner Helmhol tz plane OHP associated with the outer Helmholtz plane

REFERENCES 1. G. L. Griffin, This Journal, 131, 18 (1984). 2. C. G. Law, Jr. and J. Newman, ibid., 126, 2150 (1979). 3. I. Epelboin, C. Gabrielli, M. Keddam, and H. Taken-

outi, Electrochim. Acta, 20, 913 (1975). 4. R. Alkire and A. Cangellari, This Journal, 130, 1252

(1983). 5. P. P. Russell and J. Newman, ibid., 133, 59 (1986). 6. R. E. White, S. E. Lorimer, and R. Darby, ibid., 130,

1123 (t983). 7. R. Pollard and J. Newman, ibid., 128, 491 (1981). 8. M. Miller, M.S. Thesis, Univers i ty of Virginia, May

1985. 9. R. Parsons, "Modern Aspects of Electrochemistry," 1,

103 (1954). 10. J. Newman, "Elect rochemical Systems," pp. 307-310,

Prentice Hall, Englewood Cliffs, NJ (1973). 11. V. Marathe and J. Newman, This Journal, 116, 1704

(1969). 12. J. Newman, ibid., 113, 1235 (1966). 13. V. G. Levich, "Phys icochemica l Hydrodynamics ," p.

63, Prentice-Hall, Inc., Englewood Cliffs, NJ (1962).



14. J. N e w m a n , Ind. Eng. Chem. Fundam., 7,514 (1968). 15. M. E. Orazem, Ph .D. D i s s e r t a t i o n , U n i v e r s i t y of Cali-

fornia, Berke ley , J u n e 1983 (LBL-16131). 16. R. E. White , Ph .D. D i s se r t a t i on , U n i v e r s i t y o f Califor-

nia, Berke ley , M a r c h 1977 (LBL-6094). 17. E. C. Gan , M.S. Thes i s , U n i v e r s i t y of Vi rg in ia , May

1986. 18. C. G. Law, Jr. , Ph .D. D i s s e r t a t i o n , U n i v e r s i t y of Cali-

fornia, Berke ley , 1980.

19. I. Epelboin, C. Gabrielli, M. Keddam, J. C. Lestrade, and H. Takenouti, This Journal, 119, 1632 (1972).

20. V. G. Levich, "Physicochemical Hydrodynamics," pp. 60-78, Prentice-Hall, Inc., Englewood Cliffs, NJ (1962).

21. T. R. Beck, This Journal, 129, 2412 (1982). 22. M. Miller and M. E. Orazem, This JournaL, 134, 392

(1987). 23. H. H. Uhlig , This Journal, 108, 327 (1961).

AC Impedance Studies of Aluminum Alloy 6061 in Chloride Solutions

The Role of Oxygen, Hydrogen Ions, and Aluminum Ions in Initiating Crevice Corrosion

Richard F. Reising* General Motors Research Laboratories, Physical Chemistry Department, Warren, Michigan 48090

ABSTRACT

The p u r p o s e of th i s r e sea rch was to d e t e r m i n e w h e t h e r o x y g e n molecu les , h y d r o g e n ions, or a l u m i n u m ions in i t ia te t he c rev ice co r ros ion of a l u m i n u m alloy 6061 in a q u e o u s ch lo r ide so lu t ions . Co r ro s ion -po t en t i a l a n d a c - i m p e d a n c e mea- s u r e m e n t s s h o w t h a t pH is t he d o m i n a n t fac tor in a c c o r d a n c e w i th t he c rev ice -co r ros ion m e c h a n i s m p r o p o s e d by F o n t a n a a n d Greene . It is f u r t h e r p r o p o s e d t h a t c rev ice co r ros ion occurs b e c a u s e film b r e a k d o w n m e c h a n i s m s preva i l over f i lm re- pa i r m e c h a n i s m s in t h e c r ev i ce w h e n t h e pH d r o p s to v a l u e s n e a r 4. In t h i s pH r e g i m e a l u m i n u m ion d i s s o l u t i o n is t h e r m o d y n a m i c a l l y favored over i n so lub l e a l u m i n u m oxide f o r m a t i o n at t he so lu t ion-so l id interface. I t is o b s e r v e d t h a t t he cr i t ical a l u m i n u m ion c o n c e n t r a t i o n (0.005-0.025N) w h i c h H e b e r t a n d Alk i re a s se r t is t he in i t i a to r of c rev ice co r ros ion also p r o d u c e s a p H nea r 4 via hydro lys i s . I t is c o n c l u d e d t h a t t h e r e a p p e a r s to be no r e a s o n to d i sca rd t he u se of F o n t a n a a n d G r e e n e ' s c rev ice co r ros ion m e c h a n i s m on t he bas is of t h e s e e x p e r i m e n t s .

T h e u se of a l u m i n u m al loys in t h e a u t o m o t i v e i n d u s t r y is i n c r e a s i n g as a r e s u l t of t h e e m p h a s i s o n w e i g h t r e d u c - t i o n of i n c r e a s e d fue l e c o n o m y . P u r e a l u m i n u m is me- c h a n i c a l l y w e a k r e l a t i ve to steel , so i t m u s t be s t r e n g t h - e n e d b y a l l o y i n g (1, 2). W h i l e a l l o y i n g i m p r o v e s t h e m e c h a n i c a l s t r e n g t h of a l u m i n u m , i t c a n d e g r a d e a sur- f ace ' s c o r r o s i o n r e s i s t a n c e , or pass iv i ty . T h e p a s s i v i t y of a n a l u m i n u m a l loy u s e d in a u t o m o t i v e a p p l i c a t i o n s c a n b e v e r y i m p o r t a n t , b e c a u s e a u t o m o b i l e s a re f r e q u e n t l y e x p o s e d to c o r r o s i v e e n v i r o n m e n t s .

C r e v i c e c o r r o s i o n is one of t h e m o r e i n s i d i o u s f o r m s of c o r r o s i o n w h i c h f r e q u e n t l y a f fec t s a u t o m o t i v e p r o d u c t s . T h e r a t e - c o n t r o l l i n g m e c h a n i s m s for c r e v i c e c o r r o s i o n a r e g e n e r a l l y t h o u g h t to b e u n d e r s t o o d . F o n t a n a a n d G r e e n e h a v e s u m m a r i z e d t h e s e ideas as fo l lows (3).

1 . In i t i a l ly , a n o d i c a n d c a t h o d i c r e a c t i o n s c a n t a k e p l ace in t h e c rev ice , as wel l as o u t s i d e t he c rev ice .

2. E v e n t u a l l y , on ly t h e a n o d i c r e a c t i o n c a n o c c u r in t h e c r e v i c e b e c a u s e d e p l e t i o n of o x y g e n in t h e c r e v i c e pre - v e n t s t h e c a t h o d i c r e a c t i o n f r o m o c c u r r i n g the re .

3. C h a r g e n e u t r a l i t y is m a i n t a i n e d in t he c r ev i ce b y mi- g r a t i o n of c h l o r i d e i o n s f r o m t h e b u l k s o l u t i o n i n t o t h e c r ev i ce w h e r e t h e m e t a l ions a re p r o d u c e d .

4. T h e m e t a l c h l o r i d e s o l u t i o n in t h e c r ev i ce l o w e r s t h e p H in t h e c r ev i ce by hyd r o l y s i s .

5. C h l o r i d e ions a n d h y d r o g e n ions in t h e c r ev i ce cata- lyze t h e a n o d i c r e a c t i o n in t h e c r ev i ce w h i c h a c c e l e r a t e s c r ev i ce co r ros ion .

H e b e r t a n d Alk i re c o n d u c t e d e x p e r i m e n t s on t h e ini t i - a t i o n of c r ev i ce c o r r o s i o n for a l u m i n u m s p e c i m e n s in di- lu te , a q u e o u s , 0.05N c h l o r i d e s o l u t i o n s at a m b i e n t r o o m t e m p e r a t u r e s (4). T h e y c o n c l u d e d t h a t o x y g e n , c h l o r i d e ions , a n d h y d r o g e n ions a re n o t t h e m a j o r f ac to r s assoc i - a t e d w i t h t h e i n i t i a t i o n of c r e v i c e c o r r o s i o n of a l u m i - n u m . T h e y a t t r i b u t e t h e i n i t i a t i o n of c r ev i ce c o r r o s i o n of a l u m i n u m to t h e a t t a i n m e n t of a c r i t i c a l c o n c e n t r a t i o n (0.005-0.025N) of a l u m i n u m ions in t h e c rev ice .

T h e r e s u l t s of t h i s s t u d y i n d i c a t e t h a t h y d r o g e n i ons a n d o x y g e n are i m p o r t a n t in t h e i n i t i a t i o n of c r ev i ce cor- r o s i o n of a l u m i n u m al loy 6061 in c h l o r i d e s o l u t i o n s in ac- c o r d a n c e w i t h s t e p s 1 t h r o u g h 4 of t h e m o d e l p r o p o s e d b y F o n t a n a a n d G r e e n e . T h e s e r e s u l t s a lso s u g g e s t t h a t t h e " c r i t i c a l " a l u m i n u m ion c o n c e n t r a t i o n is r e a l l y a manifestation of the hydrolysis step in the mechanism

b e c a u s e 0.005N a l u m i n u m c h l o r i d e s o l u t i o n s p r o d u c e p H v a l u e s n e a r 4. I t is p o s t u l a t e d t h a t p a s s i v a t i o n m e c h a - n i s m s c a n p r e v a i l in t h e p H r a n g e of a b o u t 8.4-4.4 be- c a u s e t h e f o r m a t i o n of i n s o l u b l e a l u m i n u m o x i d e s is t h e r m o d y n a m i c a l l y f a v o r e d at t h e l i q u i d - s o l i d i n t e r f a c e in t h i s r e g i o n (5). T h e m e c h a n i s m s w h i c h i n i t i a t e c r ev i ce c o r r o s i o n p r eva i l b e l o w p H 4.4 b e c a u s e t h e f o r m a t i o n of s o l u b l e a l u m i n u m i o n s is t h e r m o d y n a m i c a l l y f a v o r e d a n d f i lm b r e a k d o w n m e c h a n i s m s can preva i l .

Experimental Description Specimen alloys and working eLectrodes.--Aluminum

al loy 6061 was c h o s e n for t h i s s t u d y b e c a u s e it is o n e of t h e m o r e ve r sa t i l e h e a t - t r e a t a b l e a l u m i n u m al loys (1). I t p o s s e s s e s good f o r m a b i l i t y a n d c o r r o s i o n r e s i s t a n c e w i t h m e d i u m s t r e n g t h . Typ ica l a u t o m o t i v e a p p l i c a t i o n s a re in h e a v y d u t y s t r u c t u r e s s u c h as f o r g e d w h e e l s w h e r e c o r r o s i o n r e s i s t a n c e is n e e d e d . T h e n o m i n a l c h e m i c a l c o m p o s i t i o n of AA6061 in w e i g h t p e r c e n t is l i s t ed as follows: m a g n e s i u m (1.0), s i l i con (0.60), c o p p e r (0.28), chro- m i u m (0.20), a n d a l u m i n u m ( b a l a n c e ) (1). T h e a l loy was in a T-6 t e m p e r : i.e., h e a t e d to a p p r o x i m a t e l y 538~ (1000~ r a p i d l y q u e n c h e d p r io r to t h e ro l l ing o p e r a t i o n , a n d t h e n a g e d for s e v e r a l h o u r s a t a p p r o x i m a t e l y 204~ (400~ to a t t a i n m a x i m u m s t r e n g t h (2). T h e s p e c i m e n s w e r e p u n c h e d (1.6 c m {5/8 in.} d i a m ) f r o m 0.16 c m (1/16 in.) AA6061 s h e e t m e t a l a n d t h e i r su r f ace s w e r e a b r a d e d w i t h 600-gri t s i l i con c a r b i d e paper . T h e s p e c i m e n s w e r e t y p i c a l l y s t o r e d for a b o u t 2 w e e k s in c l e a n p a p e r e n v e l - o p e s in t h e a m b i e n t l a b o r a t o r y a t m o s p h e r e b e f o r e use . T h e o x i d e f i lms f o r m e d o n t h e s e a b r a d e d s u r f a c e s w e r e e s t i m a t e d to b e 2-5 n m t h i c k a t t h e t i m e t h e e x p e r i m e n t s w e r e b e g u n (2, 6-8).

T h e s e e x p e r i m e n t s w e r e d e s i g n e d to e x p o s e a l u m i - n u m to e l e c t r o l y t e s f o u n d in c r e v i c e s , so t h e c o n s t r u c - t i o n of e l e c t r o d e s w i t h a c r e v i c e g e o m e t r y was n o t con - s i d e r e d n e c e s s a r y . W o r k i n g e l e c t r o d e s w e r e c o n s t r u c t e d f r o m s p e c i m e n s a n d f l u o r o c a r b o n s p e c i m e n h o l d e r s de- s i g n e d t o . a c c e p t flat s p e c i m e n s a n d e x p o s e 1 c m 2 of t h e s p e c i m e n to t h e t e s t s o l u t i o n . T h i s e l e c t r o d e d e s i g n re- q u i r e s a f l u o r o c a r b o n w a s h e r b e t w e e n t h e c i r c u m f e r e n c e of t h e s p e c i m e n a n d t h e s p e c i m e n h o l d e r w i n d o w to pre - v e n t the electrolyte from leaking into the electrode as-

*Electrochemical Society Active Member.


Documents

A Mathematical Model for the Corrosion of Iron in Sulfuric Acidww2.che.ufl.edu/orazem/pdf-files/Gan-MathModel-JES-1987.pdfiron corrosion process, mathematical models of this pro- cess