Vol. 134, No. 6
PASSIVE FILM FORMED ON IRON
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. Stimming and J. W. Schultze, Ber. Bunsenges. Phys.
Chem. 80, 1297 (1976),
15. R. A. F r e d l e i n and A. J. Bard, This Journal, 126, 1892
(1979).
16. J. H. K e n n e d y and K. W. Frese, Jr., ibid., 125, 723
(1978).
17. G. Horowitz, J. Electroanal. Chem. Interfacial
1357
Electrochem., 159, 421 (1983).
18. C. Y. Chao, L. F. Lin, and D. D. Macdonald, This Journal, 128, 1187 (1981); L. F. Lin, C. Y. Chao, and D, D.
Macdonald, ibid., 128, 1194 (1981).
19. R. N i sh i m u r a 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
h o m o g e n e o u s partial dissociation of sulfuric acid is also treated explicitly. This m o d e l shows that the mass-transferlimited 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.
T he f u n d a m e n t a l r e a c t i o n for iron c o r r o s i o n i n v o l v e s
dissolution of the metal atoms into their ions. A l t h o u g h
their reaction alone does not reflect the c o m p l e x i t y of the
iron corrosion process, m a t h e m a t i c a l models of this process are g e n e r a l l y based u p o n this slmpllfiecl vmw.
Griffin (1), for example, a s s u m e d c o m p e t i t i v e adsorption
b e t w e e n an isolated cation and a cation in the oxide layer
to m o d e l the active-t~assive transition. T h e s e cations
were a s s u m e d to be the p r o d u c t of the electrode dissolution. With this s i m p l e k in e t ic model, he was able to rep r o d u c e qualitatively the " m u l t i p l i c i t y of steady states"
in t he r e g i o n prior to passivation. In the m o d e l by Law
and N e w m a n (2) a m o d i f i e d B u t l e r - V o l m e r r e l a t i o n s h i p
was applied to express the simple iron dissolution reaction. D e s p i t e t h e s i m p l i c i t y a s s u m e d for the c o r r o s i o n
c h e m i s t r y , the m o d e l p r o v i d e d good a c c o u n t for the kinetic resistance in the double layer and the n o n u n i f o r m
p o t e n t i a l d i s t r i b u t i o n across the disk surface. The conc e n t r a t i o n d e p e n d e n c e of a l i m i t i n g r e a c t a n t was inc l u d e d in t h ei r k i n e t i c e x p r e s s i o n in o r d e r to treat t h e
effect of mass-transfer limitation. E p e l b o i n et al. (3) sugg e s t e d t h a t t h e m a s s - t r a n s f e r - l i m i t i n g species m i g h t be
t he O H- species. This is unlikely, h o w e v e r , in an acidic
m e d i u m wh i ch lacks the h y d r o x i d e ion c o n c e n tr a ti on required to justify a significant i n v o l v e m e n t of this species
in t he p a s s i v a t i o n process. A l k i r e and Cangellari (4) rep o r t e d the i m p o r t a n c e of c e r t a i n c h e m i c a l species by
arguing that the i m p a i r m e n t of its c o n c e n tr a ti o n buildup
due to t h e i n f l u en ce of fluid flow i m p e d e d passivation.
T h e y i n d i c a t e d a critical v e l o c i t y a b o v e w h i c h
p a s s i v a t i o n did n o t occur. R u s s e l l and N e w m a n (5) des c r i b e d a m o d e l for the iron c o r r o s i o n in sulfuric acid
w h i c h also i n c l u d e d the f o r m a t i o n and g r o w t h of a porous salt film, By using a simple electrode dissolution rea c t i o n and e x p r e s s i n g it in the B u t l e r - V o l m e r form as
u s e d by Law and N e w m a n (2), the m o d e l p r o v i d e d a
q u a l i t a t i v e a c c o u n t of the p r o c e s s e s l e a d i n g to t h e form a t i o n of the salt film.
The principle advantage of the relatively simple mathe m a t i c a l d e s c r i p t i o n s g i v e n a b o v e is t h a t u n k n o w n parameters are l u m p e d to provide a m in im a l n u m b e r of kine ti c p a r a m e t e r s . A m o r e c o m p l e t e c h a r a c t e r i z a t i o n of
corrosion m e c h a n i s m s requires t r e a t m e n t of m u l t i p l e re* Electrochemical Society Student Member.
** Electrochemical Society Active Member.'
actions. A g en er al t r e a t m e n t of m u l t i p l e e l e c t r o d e reactions by White et al. (6) al l o w ed p r e d i c t i o n of the total
cu r r en t density at an electrode u n d er potentiostatic control. T r e a t m e n t of multiple reactions was also e x p r e s s e d
in t h e m a t h e m a t i c a l m o d e l i n g of LiA1/FeS b a t t e r y by
Pollard and N e w m a n (7).
In this work, the c o m p l e x r e a c t i o n s at the e l e c t r o d e
su r f ace are t r e a t e d by the c o u p l i n g a m o n g s i m p l e reaction steps and mass t r a n s f e r to and f r o m the e l e c t r o d e
surface. This a p p r o a c h i n c o r p o r a t e s both t h e macroscopic t r a n s p o r t p h e n o m e n a in the electrolytic solution
and the microscopic m o d el of the metal-electrolyte interface, allowing explicit t r e a t m e n t of the chemical species
i n v o l v e d in the system. Passivation is considered in this
w o r k to be the f o r m a t i o n of a p r o t e c t i v e o x i d e layer
w h i ch reduces the active fraction of the surface. Progressive coverage by oxides has been observed by Miller (8)
on an iron disk below the passivation potential. Th r o ugh
this approach, the influence of mass transfer on the corrosion current can be characterized w i t h o u t a s s u m p t i o n
of a mass-transfer-limited reactant in solution.
Physical Description
A o n e - d i m e n s i o n a l s c h e m a t i c r e p r e s e n t a t i o n of t he
metal-electrolyte system is p r esen t ed in Fig. 1. The elect r o l y t i c s o l u t i o n was d i v i d e d into a d i f f u s i o n layer that
ad j o i n s t h e b u l k phase and diffuse part of the d o u b l e
layer, a relatively small region e x t e n d i n g from the imaginary o u t er H e l m h o l t z plane. U n l i k e the d i f f u s i o n layer,
the diffuse part of the double layer is not electrically neutral. The m a t h e m a t i c a l depiction of the metal-electrolyte
interface was based on the theory of diffuse-double-layer
as d e v e l o p e d by Stern, Gouy, and C h a p m a n [see, for example, Parsons (9)]. The microscopic m o d e l of the metale l e c t r o l y t e i n t e r f a c e (shown in Fig. 1) i n c l u d e d t h r e e
planes: the inner and outer Helmholtz planes on the elect r o l y t i c s o l u t i o n a d j a c e n t to t h e i n t e r f a c e and the i n n e r
surface state on t h e m e t a l side. The i n n er surface state
(ISS) was designated to be the plane associated with rea c t i v e m e t a l atoms. The i n n e r H e l m h o l t z plane (IHP) is
the locus of the centers of the first row of ions specifically
a d s o r b e d onto the m e t a l surface. Th e o u t er H e l m h o l t z
p l an e (OHP) is the plane of closest a p p r o a c h for t he
s o l v a t e d ions associated with the bulk solution. T he
charge held within the diffuse part of the double layer is
balanced by the charge held at the interracial planes I H P
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
/J
I
1
/
/
Diffuse Part of
l
t]~e I
Double Layer
~
I
ff
1
Diffusion Layer
Bulk
//(
/
/
/
/
/
Solution
I
I
I
J
I
/
Fig.
. A schematic representation of a metal-electrolyte interface
SCIENCE
t h e I S S a n d I H P p l a n e s . T h e s y m m e t r y f a c t o r ~ w a s ass i g n e d a v a l u e of 0.5. T h e c o e f f i c i e n t s p~.~a n d q~., a r e react i o n o r d e r s for s p e c 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 dir e c t i o n o f 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 o f
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 e a c t i o n . T h e f o r m a t i o n o f f e r r i c o x i d e w a s ass u m e d to b e a s u r f a c e r e a c t i o n w h i c h r e s u l t e d in a fract i o n a l c o v e r a g e of t h e e l e c t r o d e . 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 ass u m e d to b e e q u i l i b r a t e d , a n d all r e a c t i o n s w e r e ass 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.
The interfacial reactions were interrelated by material
b a l a n c e s for e a c h a d s o r b e d s p e c i e s i o n t h e m e t a l s u r f a c e
a n d t h e i n n e r H e l m h o l t z p l a n e , i.e.
E
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
neutral.
Theoretical
Development
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
into a diffusion layer and a diffuse part of the double
l a y e r . 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 c h a r acterize both these regions. This macroscopic characteriz 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 o f t h e
metal-electrolyte interface which allows explicit treatment of interfacial reactions.
Metal-electrolyte interface.--The i n t e r r a c i a l r e a c t i o n s
considered in this model were the oxidation of iron to
ferrous ions
F e <=>F e ~+ + 2et h e o x i d a t i o n of f e r r o u s i o n s to f o r m f e r r i c i o n s
F e 2+ <==>F e :~+ + e
t h e f o r m a t i o n of a p a s s i v e film
3H20 + 2Fe :~+ <=>Fe20~ + 6H +
and the hydrogen evolution reaction
2H + + 2 e
<=>H2
F o r m a t i o n o f a f e r r o u s s u l f a t e s a 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 r o l e i n t h e p a s s i v a t i o n o f
i r o n i n s u l f u r i c a c i d . F o r m a t i o n o f a s a l t film a t a n o d i c
potentials has been associated with current oscillations
u n d e r p o t e n t i o s t a t i c c o n t r o l . It is u n l i k e l y , 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 salt film is, in itself, r e s p o n s i b l e for t h e s h a r p m a s s - t r a n s f e r - l i m i t e d curr 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 . It is a l s o
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 s p e c i e s to
t h e s u r f a c e . T h e o b j e c t o f t h i s w o r k w a s to d e t e r m i n e
whether the experimentally observed limiting current
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 i n t e r r a c i a l rea 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 film, 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 w o r k . A c o m p l e t e m o d e l of t h e corrosion of iron in sulfuric acid would, of course, include
t h e t i m e - d e p e n d e n t s a l t film 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)] i n a d d i t i o n to t h e coup 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 w o r k .
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 w r i t t e n i n 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 r a t e 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 - ~
- kh., - e x P k ~
June 1987
AND TECHNOLOGY
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 f o r 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 o n t h o s e p l a n e s b y G a u s s ' s law, i.e.
-..,
- e._.,
I
[3]
= o2
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
the subscripts 1 and 2 denote the two immediate phases
that sandwich the interface.
Electrolyte.--The a q u e o u s e l e c t r o l y t i c s o l u t i o n w a s ass 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 i n s u l f u r i c
acid. The incomplete dissociation of sulfuric acid gives
r i s e to five i o n i c s p e c i e s ; H +, F e 2+, F e :~+, SO42-, a n d HSO4 .
T h e c o n c e n t r a t i o n s o f t h e s e i o n i c s p e c i e s a n d t h e electrostatic potential constitute the six macroscopic variables of the model. The principal assumptions of the
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 l u i d w e r e
constant and that radial derivatives of concentration
c o u l d b e n e g l e c t e d . T h e l a t t e r a s s u m p t i o n is v a l i d u n d e r
mass-transfer limitations where the current distribution
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
o n a r o t a t i n g d i s k 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 limiting current. Under conditions where the current density is n o t u n i f o r m o n t h e d i s k , 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 h e c e n t e r of t h e disk. A d d i t i o n a l a s s u m p tions are inherent in the microscopic model described
above. Under the steady-state assumption, the express i o n o f t h e m a t e r i a l b a l a n c e f o r e a c h i o n i c s p e c i e s is
given by
V - Ni = Rj
[4]
w h e r e R~ is t h e 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 flux of s p e c i e s i. T h r o u g h a s s u m p t i o n o f a d i l u t e elect r o l y t i c s o l u t i o n , t h e flux e q u a t i o n s c a n b e 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 s p e c 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 c o e f f i c i e n t of s p e c i e s i. a n d v
is t h e v e l o c i t y . T h e flux i n c l u d e s m i g r a t i o n a l , d i f f u sional, and convective contributions. The axial velocity
near a rotating disk electrode can be approximated by a
p o w e r s e r i e s (13).
vz= ~-~'(-ar
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.
In the absence of homogeneous reactions involving
f e r r o u s a n d f e r r i c ions, Eq. [4] b e c o m e s
c,m,l
[1]
T h e p o t e n t i a l d r i v i n g f o r c e 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 rea c t i o n w a s 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
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 i d w a s ass u m e d to b e 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]
Downloaded 26 Jun 2008 to 128.227.7.250. Redistribution subject to ECS license or copyright; see http://www.ecsdl.org/terms_use.jsp
Vol. t34, No. 6
MATHEMATICAL
1359
MODEL
and
[H+][SO~-].
,
[HSO4-]
- K,,,,
[9]
w he r e K,,,, is the dissociation constant for sulfuric acid.
The s o l u t i o n close to the surface (i.e., w i t h i n the diffuse part of the d o u b l e layer) is not e l e c t r i c a l l y neutral.
Pois s o n ' s equation
V~p_
F
~
E
ZlC~
[10]
i
relates p o t e n t i a l to the charge d e n s i t y in solution. F o r
the solution sufficiently far from the surface, electroneutrality
Z
zici = 0
%:
7
O
?
1000
O
500
'C)
'O
[11]
,u0~
i
can r e p l a c e Eq. [10] in the d i f f u s i o n layer. E q u a t i o n s
[7]-[11], co u p l ed with conservation of charge
V. i = O
[12]
p r o v i d e the r e l a t i o n s h i p s n e e d e d to obtain th e electrostatic p o t e n t i a l and c o n c e n t r a t i o n s in the electrolyte.
T he v a l u e of t h e e l e c t r o d e p o t e n t i a l and the e q u a t i o n s
g o v e r n i n g the interface p r o v i d e b o u n d a r y c o n d i t i o n s at
the m e t a l - e l e c t r o l y t e interface. At the o u te r e d g e of t h e
d i f f u s i o n layer, c o n c e n t r a t i o n s w e r e set to bulk values,
and the potential was set equal to zero.
Numerical Method
The coupled
nonlinear differential equations
presented 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 NewtonRaphson
iteration. This work involves the coupling of
equations that govern regions with greatly different scaling 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
c.o
1000
f
Lt3"
s "]
--
g
5OO
f
'c):
'O:
w
-
'O:
m 'C:):
-0.60
-b.32
-b.04
V
- ep o , V
o'.24
-
g
100
/
g
s
-b.04
-~.32
V
- r
o'.24
, V
0'- 52
o.so
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.
listings and the p a r a m e t e r s used in this m a t h e m a t i c a l
m o d e] are p r o v i d e d in Ref. (17). D i s c u s s i o n of the local
inversion t e c h n i q u e is p r esen t ed in A p p e n d i x B. The notation used in A p p e n d i x B follows that of Refi (14).
Results and Discussion
The results obtained with this m o d el are p r esen t ed to
illustrate the i m p o r t an t features that have been observed
e x p e r i m e n t a l l y for iron corrosion in similar systems. The
i n f l u e n c e of key p a r a m e t e r s on m o d e l results is also
discussed.
i..i = 0.17496 ~/~
g
~
o'.s2
(NHE)
Current-potential behavior.--The c u r r e n t - p o t e n t i a 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 certain 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 regime is compensated
by an exponential decrease of the
active electrode area with potential. In effect, the masstransfer-limited reactant is the active part of the iron
electrode itself. This result was obtained by simultaneous 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
g
g
s "1
,. 80
(NHE)
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.
[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
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1360
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
ll~
I
I
I
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 o f f e r r o u s i o n s to f a v o r f u r t h e r oxid a t i o n to f e r r i c 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
passivation: Hence, a potentiostatic delay in passivation
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 i n
their results that fluid velocity plays a role in sweeping
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 f o r p o t e n t i a l s t h a t
a r e 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 at w h i c h 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 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
plateau, the calculated concentration of ferrous ions
c l o s e to t h e s u r f a c e r e a c h e s a v a l u e o f 1.3M. T h i s v a l u e is
based upon the assumption that the diffusion coefficient
o f f e r r o u s i o n s is 0.5 x 10 '~ cm-Us. T h e s u r f a c e 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 o f 0.1658 x 10 -~
cm2/s [as u s e d b y R u s s e l l a n d N e w m a n (5)] w a s 3.0M. T h e
ferrous ion concentration remains unchanged within the
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 o f b o t h potential and rotation speed. The results show that the
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 a n b e 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
from the iron surface coupled with formation of an oxide
layer.
1
<
g
g
~
O0
8.00
16.00
,/~
32.00
24.00
J u n e 1987
40.00
,~1/2
Concentration distribution.--The c o n c e n t r a t i o n profiles o f HSO4 , H +, F e 2+, a n d SO42- i n 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 f u s e p a r t of t h e d o u b l e l a y e r for p o t e n t i a l s of
- 0 . 5 6 a n d 0.51V ( N H E ) a r e s h o w n i n Fig. 5 a n d 6. T h e
change of scale between the diffuse part of the double
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 i n t h a t t h e c o n c e n t r a t i o n d e r i v a t i v e s a r e 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 t w o r e g i o n s . I n t h e d i f f u s i o n layer, t h e flux t h a t c h a r a c t e r i z e s t h e t r a n s p o r t of i o n i c s p e c 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 . A t 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 o f i r o n is i n h i b i t e d . A t e q u i l i b r i u m , t h e c o n c e n t r a t i o n p r o f i l e o f f e r r o u s i o n s as w e l l as o t h e r i o n i c
s p e c i e s i n 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 app 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 i n Fig. 5. T h e i n c r e a s e i n f e r r o u s i o n 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 o n c o n centration reaches a maximum value which remains con-
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 s k [see, for e x a m p l e , L e v i c h (20)]. I t m u s t b e
emphasized that the model does not account for the
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 s u r f a c e . H e n c e , 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 app r o p r i a t e for t h e c e n t e r o f 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 s k . 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 u n der mass-transfer limitations.
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 s p e e d , 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 a n o d i c a l l y . T h i s beh a v i o r is s h o w n m o r e c l e a r l y i n Fig. 3. A n e x p l a n a t i o n for
this phenomenon can be related in terms of the surface
c o n c e n t r a t i o n of f e r r o u s ions. A m o r e a n o d i c p o t e n t i a l is
O
I
I
I
[
I
I
HSO~
g
I
Diffusion L a y e r
Diffuse P a r t of the D o u b l e Layer
HSO~
H+
H+
C
o
to
5
so~-
SO~"
.~
Fe2+
0
Q
~
~
_.
4'.oo
8'.oo
Position
1~.oo
, ~/A
1~.oo
20
0.00
0'.30
0 ~, 6 0
0 ~, 9 0
Position ,
z/~
1 ~. 2 0
1 950
Fig. 5. Concentration distribution of HSO4-, H § SO42-, and Fe2+ 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.
Downloaded 26 Jun 2008 to 128.227.7.250. Redistribution subject to ECS license or copyright; see http://www.ecsdl.org/terms_use.jsp
Vol. 134, No. 6
MATHEMATICAL
r
I
Diffuse P a r t
I
MODEL
t
of t h e D o u b l e Layer
1361
I
I
Diffusion Layer
HSO~
o~
Fe2+
HSO~
H§
C)so,=-
Fe2+
o
00'.00
H§
i
4.00
8t .00
12.00
16.00
Position , z/A
20
0.00
0.30
0,60
0'. 90
1'. 20
.50
Position , z/6
Fig. 6. Concentration distribution of HSO4-, H § SO42-, and Fe2+ 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.
stant throughout the limiting-current region. The results
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
corrosion products from the iron surface and the subseq u e n t b u i l d u p o f f e r r o u s i o n s l e d to p a s s i v a t i o n . I n t h e
limiting-current region, a corresponding drastic reduct i o n in t h e a c t i v e f r a c t i o n o f t h e d i s k s u r f a c e is o b s e r v e d ,
as s h o w n in Fig. 3.
The concentration distributions at anodic potentials
reflect not only convective diffusion but the added constraints imposed by the requirements of electroneutrality a n d t h e p a r t i a l d i s s o c i a t i o n o f s u l f u r i c acid. A s 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 dist r i b u t i o n s o f HSO4-, SO4 ~ , a n d F e 2+. A t h i g h r a t e s of corrosion, electroneutrality requires that the concentration
of cations decrease near the electrode surface and that
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 a c e 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 o f t h e p o s i t i v e l y c h a r g e d ferr o u s ions. T h e s e a d j u s t m e n t s are also r e f l e c t e d in t h e diss o c i a t i o n o f s u l f u r i c acid s i n c e H + d e c r e a s e s n e a r t h e surf a c e a n d H S O 4 - 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
positively charged environment created by a rise in the
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 H S O 4 i o n s a r e also 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 o f a d i s s o c i a b l e 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 i n Fig. 6 a r e r e s p o n s e s to accommodate both the homogeneous partial dissociation
of sulfuric acid and the electrostatic imbalance created
i n t h e d i f f u s i o n layer. As a r e s u l t , t h e p H in t h e v i c i n i t y o f
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 t y , t h e c o n c e n tration profiles of ferric ions are shown separately and
are d i s c u s s e d l a t e r in t h i s s e c t i o n .
W i t h i n t h e d i f f u s e 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 v a l i d . D u e to t h e c l o s e r p r o x i m i t y to
the metal surface, the convective mass-transfer contribut 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 a x i a 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 -'~ c m / s or s m a 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 distrib 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
electrostatic interactions at the metal surface. Dependi n g o n t h e n a t u r e o f t h e c h a r g e d s u r f a c e , t h e c h a r g e d species c l o s e to t h e s u r f a c e will 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 o f 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
s p e c i e s s u c h as H + a n d F e 2+ a r e a t t r a c t e d t o w a r d t h e surf a c e a n d t h e n e g a t i v e l y c h a r g e d s p e c i e s are r e p e l l e d . 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 s u r f a c e in Fig.
6. A k e y p a r a m e t e r i n t h i s s t u d y is t h e p o t e n t i a l o f z e r o
c h a r g e w h i c h w a s c h o s e n to b e 0 V (NHE). E x p e r i m e n t a l
study of the capacity of the metal electrode could be
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 nature of the charged surface, diffusional and migrational
m a s s t r a n s f e r a r e also i n s t r u m e n t a l i n t h i s r e g i o n . A species not involved with interfacial reactions will experie 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 balances exactly migration driven by the potential gradient.
T h e flux of a s p e c i e s i n v o l v e d w i t h a n i n t e r f a c i a l r e a c t i o n
at a finite rate will be driven primarily by potential and
concentration gradients.
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 o f 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 o f H + a n d F & + i o n s 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 potential. Particularly at anodic potentials, the region in
t h e v i c i n i t y o f 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
acidic. T h 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 w a s a t t r i b u t e d to s a l t film 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 h e m e t a l s u r f a c e is
d u e to t h e i n c r e a s e i n F e 2+ i o n s r e s u l t i n g f r o m t h e h i n d r a n c e o f t h e s a l t film to o u t w a r d t r a n s p o r t o f t h i s species. D e s p i t e n e g l e c t o f t h e s a l t - f i l m f o r m a t i o n , t h i s
model indicated local chemical conditions that agree
qualitatively with Beck's observation prior to passivat i o n . 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 ~+ i o n c o n c e n t r a t i o n to a s i g n i f i c a n t d e c r e a s e in t h e act i v e p o r t i o n o f t h e e l e c t r o d e s u r f a c e . I n c l u s i o n of t h e salt
film s h o u l d e n h a n c e t h i s effect.
A s s h o w n i n 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
f e r r i c i o n s n e a r t h e s u r f a c e at a n o d i c p o t e n t i a l s . T h i s c a n
be explained in part by the involvement of this species 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 film w h i c h is f a v o r e d at
s u c h a n o d i c p o t e n t i a l s . I n a d d i t i o n , t h i s p a s s i v a t i o n reac-
Downloaded 26 Jun 2008 to 128.227.7.250. Redistribution subject to ECS license or copyright; see http://www.ecsdl.org/terms_use.jsp
1362
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
o
I
I
I
-.
-_
-0.56
and 0 V
o+
r
g-
n
o-
%'. O0
0'. 30
0', 60
Position
0', 90
I', 20
1 ~0
, z/~
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 app r o a c h u s e d i n 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 inv 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 e q u i l i b rium constants 9 While these parameters are well defined,
t h e i r v a l u e s a r e n o t w e l 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 the literature. Hence, the initial kinetic parameters
were derived by expressing the electrochemical reac-
June 1987
tions in forms of Butler-Volmer rate expressions and by
using the assumption that adsorption-desorption react 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 w a s also
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 . T h i s m e t h o d
provided an approximation of these unknown parameters. To t h e e x t e n t p o s s i b l e , l i t e r a t u r e v a l u e s o f 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 cell 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 o f 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).
Additional values were obtained by matching the calcul 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
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 w a s 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 h e c u r v e - f i t t i n g of calc 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 k e y 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 w e r e 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 environment
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
I
I
I
I
o
o
oo ~
o~
tz
o
0.51
,5
- 0 . 5 6 and 0 V
+
...-o"
8
0-0,60
0'. O0
0', 30
0'. 60
Position
0'. 90
, z/b,
1 '920
-0.32
-0.04
V - @o '
0'.24
0'.52
0.80
V (NHE)
.50
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.
Fig9 99 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
= 19
•
106 cmVmoP-s; curve c, k2 = 1 . $ 1 2 •
107 cmVmoP-s.
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Vol. 134, No. 6
MATHEMATICAL
MODEL
1363
g
I
i
I
I
I
--
K
I
I
d
/
~2
r
g
,2-
/
a
t~
f~
$
Q-
Q-
Q-
C:)-
~
-b.32
o'.24
-b.o4
V
- r
' V
o'.s2
o.~o
(NHE)
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 . 0 2 0 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 l o s e l y c o r r e l a t e s to experimental results can therefore be obtained through
c o m b i n a t i o n of t h e s e u n i q u e influences.
Conclusions
A t t h e l i m i t i n g - c u r r e n t plateau, 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 of f e r r o u s ion c l o s e to t h e e l e c t r o d e s u r f a c e is ind e p e n d e n t of b o t h t h e r o t a t i o n s p e e d and potential. This
r e s u l t s h o w s 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 can
b e 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 for 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 iron s u r f a c e c o u p l e d w i t h
t h e p a r t i a l p r o t e c t i o n o f t h e s u r f a c e b y 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 t h i s w a y is p r o p o r t i o n a l to t h e
s q u a r e r o o t of r o t a t i o n speed.
T h i s w o r k d o e s n o t a c c o u n t for e i t h e r t h e n o n u n i f o r m
p o t e n t i a l and c u r r e n t d i s t r i b u t i o n across t h e d i s k s u r f a c e
or t h e p o t e n t i a l d r o p in t h e e l e c t r o l y t i c s o l u t i o n . U n d e r
mass-transfer limitations, however, the current density
is u n i f o r m , and t h e v a l u e s of l i m i t i n g c u r r e n t c a l c u l a t e d
f r o m this m o d e l a g r e e w i t h t h e e x p e r i m e n t a l r e s u l t s obt a i n e d b y E p e l b o i n et al. (19) a n d R u s s e l l a n d N e w m a n
(5). 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 o b s e r v e d for iron in sulf u r i c a c i d m a y be a s s o c i a t e d w i t h a r e d u c t i o n of t h e fract i o n of a c t i v e area o f t h e i r o n disk. T h i s p r o g r e s s i v e surf a c e 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
a n a l y s i s p e r f o r m e d b y Miller (11, 22) on an iron d i s k bel o w t h e p a s s i v a t i o n p o t e n t i a l . His r e s u 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 o x i d e layer in t h e l i m i t i n g - c u r r e n t r e g i o n
w h i c h w a s n o t d e t e c t e d at m o r e c a t h o d i c p o t e n t i a l s .
M o r e ( p r e f e r a b l y in situ) o b s e r v a t i o n s are n e e d e d to verify M i l l e r ' s r e s u l t s . T h e s e r e s u l t s , h o w e v e r , a r e c o n s i s t ent with the postulate that current oscillations are
c a u s e d b y p a r t i a l p a s s i v a t i o n a n d 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 salt film. T h e a c t i v e 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 t h i s c a s e be c o n s i d e r e d to b e a t i m e 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 i o n i c s p e c i e s inv o l v e d in t h e s y s t e m illustrate t h e c o u p l i n g of e l e c t r o d e
p r o c e s s e s and m a s s t r a n s f e r in e l e c t r o c h e m i c a l s y s t e m s .
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 r o u s i o n s bec o m e s s i g n i f i c a n 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
%0.so
-b.3z
-b.04
V-
q~o 9 V
0'.24
o'.s2
.go
(NHE)
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.
s p e c i e s n e a r t h e s u r f a c e was f o u n d to differ c o n s i d e r a b l y
f r o m t h e b u l k c o n c e n t r a t i o n s . T h e c o n c e n t r a t i o n distrib u t i o n clearly s h o w s t h e i n f l u e n c e of h o m o g e n e o u s partial d i s s o c i a t i o n of s u l f u r i c a c i d on t h e p H c l o s e to t h e
surface. It is also s h o w n t h a 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 i n c r e a s e s s i g n f i c a n t l y at p o t e n t i a l s
c l o s e to p a s s i v a t i o n . T h i s 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 a n d 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 i g n i f i c a n 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 o n l y v e r y a n o d i c potentials,
a n d t h i s r e s u l t is c o n s i s t e n t w i t h t h e 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 ( N H E ) for t h e f e r r o u s o x i d a t i o n reaction.
T h e a p p r o a c h p r e s e n t e d h e r e p r o v i d e s an e x p l a n a t i o n
for 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 p l a t e a u
a s s o c i a t e d w i t h an i r o n d i s k in s u l f u r i c a c i d in t e r m s of
the interaction among surface reactions. The treatment
of m u l t i p l e e l e c t r o d e r e a c t i o n s and t h e o b s e r v e d interact i o n s a m o n g t h e s e r e a c t i o n s is u s e f u 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 r e a c t i o n s a n d can be a p p l i e d to o t h e r h y d r o d y n a m i c s y s t e m s as w e l l as to o t h e r m e t a l s y s t e m s .
Acknowledgment
This work was supported by the Organic Chemicals
D e p a r t m e n t , D o w C h e m i c a l U S A , a n d by t h e C e n t e r for
I n n o v a t i v e T e c h n o l o g y g r a n 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 s c r i p t r e c e i v e d Oct. 6, 1986. This w a s P a p e r 10 p r e s e n t e d
at t h e B o s t o n , MA M e e t i n g of t h e S o c i e t y , May 4-9, 1986.
APPENDIX A
Calculation of Kinetic Parameters
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 s u c h as t h e r a t e a n d
e q u i l i b r i u m c o n s t a n t s u s e d in this w o r k w e r e c a l c u l a t e d
u s i n g 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 and
s t a n d a r d cell p o t e n t i a l s for t h e e l e c t r o d e r e a c t i o n s . A n
e x a m p l e o f t h e 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 par a m e t e r s is p r e s e n t e d h e r e for t h e o x i d a t i o n of m e t a l
a t o m s to f o r m ferrous ions. This c h a r g e - p r o d u c i n g react i o n was w r i t t e n as
Downloaded 26 Jun 2008 to 128.227.7.250. Redistribution subject to ECS license or copyright; see http://www.ecsdl.org/terms_use.jsp
June1987
J. Electrochem. Soc.: ELECTROCHEMICAL SCIENCE AND TECHNOLOGY
1364
Table A-I. Input parameters for the metal-electrolyte interface
i Reaction (i)
1 Fe2+]adsr Fe z+
2 Fe r Fe~+],d~ + 2e
3 Fe a+ ads ~ Fe ~+
4 Fe~+l~a~r Fen+lads + e
5 SO~=-t~r ' SO4~
6 H+]ads<::>H +
7 Passivation reaction ~
8 Film formation ~
9 2H+[ad~+ 2e- r H~
10 HSO4 lad~r HSO4Distance b e t w e e n OSS a n d ISS
Distance between 1SS and 1HP
Distance between I H P and O H P
Permittivity of solution
Permittivity of metal
Density of sites at ISS
Density of sites at I H P
ki
~
0.151 • 10'~cm4/mol~-s
~
09
X 10 TM cm~/mol-s
co
~
co
-0.190 x 1022cm2/mol-s
~
5,
82
8a
e~,,m
e~,.t
F,ss
Fray
E,
09
0.818
0.158
0.183
0.198
0.511
0.400
-0.665
0.828
0.1 •
0.2 x
0.2 x
09
0.885
0.166
0.120
x
•
x
x
x
x
x
10 a mol/cm a
10-~ mol~/cm 4
i 0 '~ mol/cm ~ ~
10 ~o mol/cm ~
10 4 mol/cm a
10~ mol/cm a ~
10 ~a
x 10 'a cm/mol
x 10 z moYcm a
10 -7 e m
10 -~ em
10 ~ cm
• 10 " C/V-cm
x i 0 - ' a C/V-cm
x 10 ~ mol/cm ~
• 10-~ mol/cm ~
T h e s e parameters are not i n d e p e n d e n t and were d e t e r m i n e d from c o m b i n a t i o n of the other equilibrium constants.
b 2Fe3+l~ + 3H20 r Fe2Oa]ad~ + 6H+l~,s
r Influence of this reaction was not incorporated in this work.
F e <=> F e ~+ + 2 e which can be conceptually
sequence
[A-l]
broken up into the following
F e <:v F e 2 + l ~ + 2 e Fe2+l~d,~ r
F
=kz'exp
V
i,, - k_o " 7,," % " FIsp
2F
[A-2]
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 i n ner Helmholtz plane and the adsorption-desorption
react i o n o f E q . [3] w a s a s s u m e d t o b e e q u i l i b r a t e d i n t h i s
work.
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 tains the following rate expression
r=
and this equation
can be further
s u b s t i t u t i n g V,, f r o m E q . [9] to g i v e
%-F~,
k~ " %
" FIHp
=
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
of ferrous ions
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
follows that used in Table A-I and A-II.
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 E q .
[4] c a n b e r e a r r a n g e d to g i v e
V~
By substituting
RT
2F
1og~
[ k 2"'Y2"-?e 2
]
FZ,ss
~k(%
[A-7]
[ k _ ~ ' k ,.y~ 2
E, = E2 CFe2+.~
i.
]-2
2Fk_2%%Flm.F~ss
[A-12
The fractional coverage of each species adsorbed onto int 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 t o 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 t o 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
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
the flexibility of varying the system concentration without having to recalculate this kinetic parameter 9 Other
kinetic parameters that are functions of bulk concentration were similarly treated in this work.
At equilibrium, both r and ~ are equal to zero, theref o r e , E q . [4] c a n b e u s e d t o e v a l u a t e E~, i.e.
E2-
k2
k_2
_
Y2 %Ye2 F 2 m s . e x p - R T
"J [A-14]
T h e v a l u e o f E2 w a s d e t e r m i n e d
t o b e 8 9 • 10 -3 m o l 2 / c m 4
by using a calculated equilibrium
p o t e n t i a l (Vo) o f
-0.481V.
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 9roximate values for the kinetic parameters; however
some of the calculated values were modified in order 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 mental values 9 A study of the influence of some of these
kinetic parameters
was discussed in the section on
Influence of kinetic parameters to provide a systematic
approach to the curve-fitting of calculated results to
match those obtained experimentally.
Table A-II. Input parameters for the electrolytic solution
]
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 t o b e t h e r a t i o o f
t h e f o r w a r d t o 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]
can be represented by
Vo = - ~R-T- l o g ~
[k
%2
F~,ss]
[A-9]
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],
respectively.
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,, is 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 o r 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 librium. By using the cathodic term, one obtains
'~
-
[A-Ill
E q . [6] i n t o E q . [7], o n e o b t a i n s
RT
2F
C~2+.~
by
or
E1 = 3.70 x
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 f o 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
potential difference between the metal and the solution
a d j a c e n t t o 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 i n
terms of the surface overpotential ~ and equilibrium pot 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] is 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
" F,ss
simplified
k-2 " e x p
-
Vo ' y2 9 Ye2 " PmeFaIss [A-10]
Electrolyte: 1.0M H2SO~, 0.04M FeSO4, 0.002M Fe.,(SO0a
1
2
3
4
Species index, i
H+
Fe ~+
SO,2Fe'a+
Species
+1
+2
-2
+3
Charge n u m b e r , z,
D,
9.312 • 10-~ cm2/s
Diffusivity, D~:
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
Dissociation constant for
sulfuric acid
v
0.01
cm2/s
K i n e m a t i c viscosity
100 S 1
Rotation speed
R
8.3143 d/mol-K
Gas c o n s t a n t
T
300 K
Temperature
F
96,487 C/equivalent
Faraday's constant
5
HSO4
-i
Downloaded 26 Jun 2008 to 128.227.7.250. Redistribution subject to ECS license or copyright; see http://www.ecsdl.org/terms_use.jsp
MATHEMATICAL
Vol. 134, No. 6
APPENDIX B
MethodologyforLocalInversion
GI* = G~ -
A~.k(j) Ck(j - 1) + B~,k(j) Ck(j) + D~,k(j) Ck(j + 1)
[B-l]
w h e r e N-(n + 1) variables appear at only one m e s h point
N J, In light of the b o u n d a r y conditions at m e s h point N J,
Eq. [B-l] can be simplified at that point to
2
2
A~.k(NJ)Ck(NJ - 1) +
k=l
Bi.k(NJ) Ck(NJ)
k~l
Are
~b
Ci
w he r e D~.k(NJ) = O. Alternatively, Eq. [B-2] can be broken
up into
Di
k=l
k=l
E~
F
i
inm
geq
kf,!
+
Bi,k(Nd) Ck(NJ) [B-3]
k=n+l
for 1 -< i -< n, and
k=l
B,.k(NJ) Ck(NJ)
k=l
+
Pi,|
qi,l
B.k(NJ) Ck(NJ)
[B-4]
k=n+l
R
Ri
for n + 1 -< i ~ N. This permits Eq. [B-4] to be written in
m a t r i x form
B'C=F
[B-5]
w h e r e B denotes the tensor with individual e l e m e n t s B~,k,
and F denotes the v e c t o r with individual e l e m e n t s
F, = GI(NJ)
-
kb,l
Ni
n
A,.k(NJ) Ck(NJ - 1) + 2
r
rl
Si,i
T
t
ul
AL,.(NJ) Cm(NJ - 1) + B~.m(NJ) Cm(NJ)
[B-6]
m=l
v~
VZ
The matrix form in Eq. [B-5] can be m a n i p u l a t e d to give
Ck(NJ) =
2
Bk,,-1 FI
[B-7]
l=n+l
w h e r e n + 1 -< k -< N. In e x p a n d e d form
Ck(NJ) = 2
Bk.C' Gi(NJ)
l=n+~
2
l=n+l
-"
nl~I
-- 2
2
1=11+1
SkA-ISl.m(NJ)Cm(gJ) [B-g]
m=l
S u b r o u t i n e L O C I N V does not p r o v i d e e x p l i c i t l y v a l u e s
for Bk.,-~; t h e r e f o r e it is c o n v e n i e n t to d e n o t e t h e produets s u c h a s Bk,1-1 G~(NJ) by primes. This r e d u c e s Eq.
[B-8] to
Ck(NJ) = ~
G',(NJ) -
~
l=n+l
2
l--n+l
-- ~d
l=n+l
A'I,m(NJ) Cm(NJ - 1 )
m--1
2
S'l,m(NJ)Cm(NJ) [8-9]
m-1
Finally, s u b s t i t u t i o n 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 -
~
k=n+l
Bi,m* = Bi.m -
~
B~,kA'~,m(NJ)
l=n+l
~
~
k=n+l
l=n+l
Bi.kB',.m(NJ)
B,.k G'I(NJ)
L I S T OF S Y M B O L S
D
G~(NJ) = ~_~ A~.k(NJ) Ck(NJ - 1) + ~.j S~.k(NJ) Ck(NJ)
2
l=n+l
By the above procedure, Eq. [4] can be solved i n d ep e ndently of Eq. [3]; thus Eq. [2] can be collapsed into Eq. [10]
that involves only the n m acr o sco p i c variables.
[B-2]
G~(NJ) = 2
~
k=n+l
k=l
GI(NJ) =
1365
and
Consider the general equation
Gi(j) = 2
MODEL
VO
z~
active fraction of iron surface
0.51023
-0.616
co n cen t r at i o n of species i, mol/cm ~
diameter, cm
diffusion coefficient of species i, cm~/s
e q u i l i b r i u m constant for reaction l
Faraday's constant, 96,487C/equiv
current density, A/cm 2
limiting 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 l e c t r o n s t r a n s f e r r e d in e l e c t r o d e
reaction
reaction order for species i in the forward direction of reaction l
r e a c t i o n o r d er for species i in t h e b a c k w a r d direction of reaction 1
excess-charge density, C/cm 2
universal gas constant, 8.3143 J/ m o l - d eg K
rate of h o m o g e n e o u s p r o d u c t i o n of sp ecie s 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
G r eek Characters
Aq~l
potential driving force for reaction l
~,
s y m m e t r y factor for reaction 1
characteristic length of the diffusion layer
e
permittivity, farad/cm
dimensionless axial distance from disk
D eb y e length, cm
v
kinematic viscosity, cm2/s
charge density, C/cm ~
cp
electrostatic potential, V
12
rotation speed, radian/s
Subscripts
I SS
associated with the inner surface states
IHP
associated with the inner H e l m h o l t z plane
OHP
associated with the outer H el m h o l t z plane
REFERENCES
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2. C. G. Law, Jr. and J. Newman, ibid., 126, 2150 (1979).
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63, Prentice-Hall, Inc., Englewood Cliffs, N J (1962).
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AND TECHNOLOGY
June 1987
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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
T h e p u r p o s e of t h i s r e s e a r c h was to d e t e r m i n e w h e t h e r o x y g e n m o l e c u l e s , h y d r o g e n ions, or a l u m i n u m ions i n i t i a t e
t h e 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 alloy 6061 in a q u e o u s c h l o r i d e solutions. C o r r o s i o n - p o t e n t i a l a n d a c - i m p e d a n c e meas u r e m e n t s s h o w t h a t p H is t h e d o m i n a n t factor in a c c o r d a n c e w i t h t h e c r e v i c e - c o r r o s i o n m e c h a n i s m 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 . It is f u r t h e r p r o p o s e d t h a t c r e v i c e c o r r o s i o n o c c u r s 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 p r e v a i l o v e r film rep a i r m e c h a n i s m s in t h e c r e v i c e w h e n t h e p H d r o p s to v a l u e s n e a r 4. I n t h i s p H r e g i m e a l u m i n u m i o n 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 f a v o r e d o v e r i n s o l u b l e a l u m i n u m o x i d e f o r m a t i o n at t h e s o l u t i o n - s o l i d interface. It is o b s e r v e d t h a t
t h e critical 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 A l k i r e a s s e r t is t h e i n i t i a t o r of c r e v i c e c o r r o s i o n
also p r o d u c e s a p H n e a r 4 via h y d r o l y s 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 b e n o r e a s o n to d i s c a r d t h e u s e of F o n t a n a
a n d G r e e n e ' s c r e v i c e c o r r o s i o n m e c h a n i s m o n t h e b a s i s of t h e s e e x p e r i m e n t s .
T h e u s e o f a l u m i n u m alloys i n 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 o f i n c r e a s e d f u e l e c o n o m y . P u r e a l u m i n u m is m e c h a n i c a l l y w e a k r e l a t i v e to steel, so it m u s t b e 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 o f a l u m i n u m , it c a n d e g r a d e a surface's corrosion resistance, or passivity. The passivity of
an aluminum alloy used in automotive applications can
be very important, because automobiles are frequently
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 o n e of t h e m o r e i n s i d i o u s f o r m s o f
corrosion which frequently affects automotive products.
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 i d e a s as f o l l o w s (3).
1.Initially, anodic and cathodic reactions can take
p l a c e in t h e c r e v i c e , as w e l l as o u t s i d e t h e c r e v i c e .
2. E v e n t u a l l y , o n l y 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
crevice because depletion of oxygen in the crevice prevents the cathodic reaction from occurring there.
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 i n t h e c r e v i c e b y m i gration of chloride ions from the bulk solution into the
crevice where the metal ions are produced.
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 i n t h e c r e v i c e l o w e r s t h e
pH in the crevice by hydrolysis.
5. C h l o r i d e i o n s a n d h y d r o g e n i o n s i n t h e c r e v i c e catalyze t h e a n o d i c r e a c t i o n in t h e c r e v i c e w h i c h a c c e l e r a t e s
crevice corrosion.
H e b e r t a n d A l k i r e c o n d u c t e d e x p e r i m e n t s o n t h e initia t i o n o f c r e v i c e 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 i n dilute, 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, and hydrogen ions are not the major factors associated with the initiation of crevice corrosion of aluminum. They attribute the initiation of crevice corrosion of
a l u m i n u m to t h e a t t a i n m e n t o f 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 i o n s i n t h e c r e v i c e .
The results of this study indicate that hydrogen ions
a n d o x y g e n a r e i m p o r t a n t i n t h e i n i t i a t i o n of c r e v i c e corr o s i o n o f a l u m i n u m alloy 6061 i n c h l o r i d e s o l u t i o n s in accordance with steps 1 through 4 of the model proposed
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 also 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 i o n 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 i n t h e p H r a n g e of a b o u t 8.4-4.4 bec a u s e t h e f o r m a t i o n o f 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 e v i c e
c o r r o s i o n p r e v a 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 o f
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 film b r e a k d o w n m e c h a n i s m s c a n p r e v a i l .
Experimental Description
Specimen alloys and working eLectrodes.--Aluminum
a l l o y 6061 w a s 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 v e r s a 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 alloys (1). It
possesses good formability and corrosion resistance
with medium strength. Typical automotive applications
a r e 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 o f AA6061 in w e i g h t p e r c e n t is l i s t e d as follows: m a g n e s i u m (1.0), s i l i c o n (0.60), c o p p e r (0.28), c h r o 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 l o y w a s
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 i o r to t h e r o l l i n g o p e r a t i o n ,
a n d t h e n a g e d f o r 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 s u r f a c e s w e r e a b r a d e d
w i t h 600-grit s i l i c o n c a r b i d e p a p e r . 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 i n c l e a n p a p e r e n v e l opes in the ambient laboratory atmosphere before use.
The oxide films formed on these abraded surfaces were
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 i n 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 w a s n o t c o n sidered necessary. Working electrodes were constructed
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 des 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 requires a fluorocarbon washer between the circumference
o f 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 p r e v e n t the electrolyte from leaking into the electrode as-
*Electrochemical Society Active Member.
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