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Chemical Engineering, Department of
1-1-1991
A Mathematical Model of a Sealed NickelCadmium Battery
Deyuan Fan
Texas A & M University - College Station
Ralph E. White
University of South Carolina - Columbia, white@cec.sc.edu
Follow this and additional works at: http://scholarcommons.sc.edu/eche_facpub
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Publication Info
Journal of the Electrochemical Society, 1991, pages 17-25.
© The Electrochemical Society, Inc. 1991. All rights reserved. Except as provided under U.S. copyright law, this work may not be
reproduced, resold, distributed, or modified without the express permission of The Electrochemical Society (ECS). The archival
version of this work was published in the Journal of the Electrochemical Society.
http://www.electrochem.org/
DOI: 10.1149/1.2085532
http://dx.doi.org/10.1149/1.2085532
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J. Electrochem. Soc., Vol. 138, No. 1, January 1991 9 The Electrochemical Society, Inc.
Table A-II. Volume decrease during discharge for various electrolyte
compositions (no membrane separator present)
pza
pl b
Xka
XZn~
kg" 1-1
XKOR kg- 1-1
0.0818
0.1500
0.2130
0.2190
0.2890
0.2480c
0.2900c
0.2960r
0.0055
0.0183
0.0361
0.0371
0.0634
0.0495c
0.0679~
0.0781r
1.1076
1.2258
1.3616
1.3637
1.5356
1.4720c
1.5890c
1.6530c
0.1201
0.2253
0.3275
0.3369
0.4576
0.3875
0.4622
0.4784
V2/V1
VJV1
1.1060 1.0015 0.0009
1.2065 0.9941 0.0031
1.3099 0.9812 0.0068
1.3198 0.9876 0.0070
1.4532 0.9799 0.0134
1.3743 0.9592 0.0098
1.4586 0.9528 0.0144
1.4773 0.9331 0.0169
a Data from (13), 25~
b Compiled from (12), 20~
c Data from (14), 18~176
For example, in the presence of a weak cationic m e m b r a n e
separator, the transport numbers of K § and OH- can be set
equal (1). Assuming that along with one K § four water molecules are transported from the zinc electrode towards the
nickel electrode compartment, the volurrm of the electrolyte in the zinc electrode c o m p a r t m e n t decreases significantly, as can be seen from Table A-I. If the m e m b r a n e
separator is omitted and only a quarter of the current is
carried by K § a smaller decrease of the v o l u m e is observed
(Table A-II).
In the actual battery system, the electrolyte in the zinc
electrode c o m p a r t m e n t will not be completely depleted in
zincate at the beginning of discharge. However, the electrolyte at the end of discharge will not be saturated but will
be supersaturated with zincate. Furthermore, the properties of chemically and electrochemically formed zincate
solutions are different (18, 19) and during discharge of the
zinc electrode, apart from soluble zinc species, ZnO or related solid zinc c o m p o u n d s are formed. Therefore, the results in Table A-I and A-II must be taken in a qualitative
sense: and it seems that in actual battery systems the volu m e of the electrolyte in the zinc electrode compartment
decreases more than would be expected from the results in
Table A-I and A-II.
17
REFERENCES
1. K.W. Choi, D. N. Bennion, and J. Newman, This Journal, 123, 1616 (1976).
2. J. McBreen, ibid., 119, 1620 (1972).
3. K. W. Choi, D. N. Bennion, and J. Newman, ibid., 123,
1625 (1976).
4. K.W. Choi, P h . D . Thesis, University of California, Los
Angeles (1975).
5. R. G. Gunther and R. M. Bendert, This Journal, 134,
782 (1987).
6. R. E. F. Einerhand, W. Visscher, J. J. M. de Goeij, and
E. Barendrecht, ibid., 138, 1 (1991).
7. R. E. F. Einerhand, W. H. M. Visscher, E. Barendrecht,
and J. J. M. de Goeij, p. 751 of E x t e n d e d Abstracts of
38th ISE Meeting," Vol. 2, Maastricht, 1987.
8. E. H. Hietbrink and R. F. Hill, This Journal, 136, 310
(1989).
9. J. McBreen and E. J. Cairns, in "Advances in Electrochemistry and Electrochemical Engineering,"
Vol. 11, H. Gerischer and C.W. Tobias, Editors,
p. 273, J o h n Wiley & Sons, Inc., New York (1978).
10. K. W. Choi, D. Hamby, D. N. Bennion, and J. Newman,
This Journal, 123, 628 (1976).
11. R. E. F. Einerhand, Ph.D. Thesis, Eindhoven University of Technology, Ei n d h o v en (1989).
12. "H an d b o o k of Chemistry and Physics," 62nd ed., CRC
Press Inc., Boca Raton, FL (1981-1982).
13. T. P. Dirkse, This Journal, 106, 154 (1959).
14. V. G. Sochevanov, J. Gen. Chem. U.S.S.R., 22, 1119
(1952).
15. D. C. Hamby, N. J. Hoover, J. Wirkkala, and D. Zahnle,
This Journal, 126, 2110 (1979).
16. M. J. Isaacson, F. R. McLarnon, and E. J. Cairns, Abstract 147, p. 214, The Electrochemical Society Extended Abstracts, Vol. 87-2, Honolulu, HI, Oct. 18-23,
1987.
17. R. E. F. Einerhand, Ph.D. Thesis, Chap. 5, pp. 83-98,
Ei n d h o v en University of Technology, Eindhoven
(1989).
18. C. Cachet, B. Saidani, and R. Wiart, Electrochim. Acta.,
33, 405 (1988).
19. V. E. Dmitrenko, M. S. Zukov, V. I. Baulov, and A. V.
Kotov, Sov. Electrochem., 19, 1414 (1983).
A Mathematical Model of a Sealed Nickel-Cadmium Battery
Deyuan Fan* and Ralph E. White**
Department of Chemic'al Engineering, Texas A&M University, College Station, Texas 77843-3122
ABSTRACT
A mathematical model for the charge and discharge of a sealed nickel-cadmium (Ni-Cd) battery is presented. The
model is used to study the effect of transport properties of the electrolyte and kinetic parameters of the electrode reactions
on the cell performance during the charge and discharge period. The model can also be used to demonstrate the changes
of cell performance during cycling. Some comparisons between model predictions and experimental results indicate that
the m o d el predictions appear to fit the experimental data well. Sensitivity analyses illustrate that the sealed nickel-cadm i u m battery operates under activation control. It is also shown theoretically that oxygen generated on the positive electrode during charge is reduced electrochemically on the negative electrode.
It is well k n o w n that the performance of a nickel-cadm i u m battery is based on the c o m p le x chemical and electrochemical p h e n o m e n a (1-4) involved in the battery.
These c o m p l e x p h e n o m e n a can be understood better
through mathematical modeling of the battery. Similar
work has been done for other battery systems such as the
model for the nickel-zinc battery by Choi and Yao (5) and
the model for the lead-acid battery by Gu et al. (6), both for
flooded/vent conditions. In October 1989, Bouet and Richard (7) presented their discharge performance model for
the nickel hydroxide electrode at the 176th Meeting of The
Electrochemical Society. However, their model includes
* Electrochemical Society Student Member.
** Electrochemical Society Active Member.
only the nickel positive electrode and does not include
sealed cell conditions and the oxygen reaction. Recently,
Nguyen et al. (8) proposed a mathematical model for the
lead-acid battery under sealed conditions during discharge, but a model for predicting the cell performance
under sealed conditions during charge has not been presented. To assist researchers and designers in the investigation and d ev el o p m en t of sealed nickel-cadmium batteries, a detailed mathematical model of a sealed, starved
separator nickel-cadmium cell is presented here that can
be used to predict the performance of a cell not only during discharge, but also during charge, rest, and cycling. A
description of the model equations, qualitative comparisons between the model predictions and experimental re-
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d. Electrochem. Soc., Vol. 138, No. 1, January 1991 9 The Electrochemical Society, Inc.
18
Region 1
P~eifiv~
~l~of~d~
Region 2
Region a
Separator
Negative electrode
061
at
1 (MNi(OH)2 MN~OOH)
F \ ~
PNiOOH/JNi
[2]
i2 = 0
0+2
-
[3]
o
[4]
O=
+1 = 0
0Co 2
[5]
- 0
[6]
ax
where, o n discharge a n d at rest
[
I
9 =0
x=o
I
z=g,
x%/t
z=~ + l2
x=(s + z,)/z
I
x=l
x:l
9
/ C ~1(
IEI--EO1 ) ~l
JNi = amaxtZot,ref ( - - $
\Cref/
\6max1 -- 6ol /
Fig. 1. A schematic of a hermetically sealed, starved separator, sinter plate nickel-cadmium cell (cross-sectional view).
sults, a n d sensitivity analyses of the m o d e l s i m u l a t i o n s to
the m o d e l p a r a m e t e r s are p r e s e n t e d below.
Model Development
A l t h o u g h the detailed m e c h a n i s m s of the electrode reactions in the n i c k e l - c a d m i u m cell are n o t t h o r o u g h l y u n d e r stood, it is generally agreed that t h e m a i n electrode reactions i n t h e cell c a n be w r i t t e n as (1-4, 9-13)
Positive Electrode
2NiOOH + 2H20 + 2e-
discharge
~
2Ni(OH)2 + 2 OHcharge
[A]
1
discharge
2 OH-
- O 2 + H 2 0 + 2e-
2
[B]
charge
Negative Electrode
discharge
Cd(OH)2 + 2e
Cd + 2 OH
[C]
charge
2 OH-
discharge 1
--->
- 02 + H20 + 2e
charge
2
[D]
A s c h e m a t i c of a sealed n i c k e l - c a d m i u m cell is s h o w n in
Fig. 1. The cell consists of the following regions a n d
b o u n d a r i e s : (i) the c u r r e n t collector of the positive electrode (x = 0); (ii) the positive or nickel electrode (region 1,
0 < x < ll); (iii) t h e interface b e t w e e n the positive electrode a n d the separator (x = 10; (iv) the separator m a t r i x
(region 2, 11 < x < l, + 12); (v) the interface b e t w e e n the separator a n d t h e negative electrode (x = L~+/2); (vi) the negative or c a d m i u m electrode (region 3, It + l2 < x < /); a n d
(vii) the c u r r e n t collector the negative electrode (x = l).
There are six explicit u n k n o w n s ( d e p e n d e n t variables)
in the model; (i) base c o n c e n t r a t i o n s , c; (ii) solid material
porosity, e; (iii) potential in the solid phase, +,; (iv) potential in the l i q u i d phase, +2; (v) superficial c u r r e n t d e n s i t y in
the electrolyte, i2; a n d (vi) o x y g e n concentration, Co2. The
i n d e p e n d e n t variables are the spatial coordinate x a n d
t i m e t.
The g o v e r n i n g e q u a t i o n s a n d the b o u n d a r y c o n d i t i o n s
for these six variables for the n i c k e l - c a d m i u m cell are pres e n t e d next. T h e c o n c e n t r a t e d solution theory has b e e n
used to derive these equations.
C e n t e r o f the positive electrode.-Oc
Ox
- 0
exp[~aJ
]
[7a]
L--R~aj]
[7b]
a n d o n charge
JNi = amaxlZol.ref / - - /
\Cref/
\Emaxl
-
6ol /
-
[aa,F
]
exp[-R---~j -
[-ar
exp
]/
where
Tla = +l,Ni -- +2 -- UNi/Cd
[7c]
UNi/Cd = UNiOOH/Ni(Ott)2 -- UCd(OH)2/Cd = 1 . 2 9 9 V
[7d]
and
Based o n the cell c o n s t r u c t i o n in w h i c h the c u r r e n t collector is e m b e d d e d in the center of a porous electrode (see
Fig. 1), Eq. [1] a n d [6] are u s e d to r e p r e s e n t the c o n d i t i o n
that the flux of the electrolyte (KOH) and the flux of oxygen are both zero. E q u a t i o n [2] is the g o v e r n i n g e q u a t i o n
for porosity c h a n g e s of the n i c k e l electrode, where the
transfer c u r r e n t jNi, defined as OiJOx, is the local c u r r e n t
per u n i t v o l u m e d u e to the electrode reaction. E q u a t i o n [3]
shows that at the c e n t e r of the electrode all of the c u r r e n t
leaves the liquid p h a s e (electrolyte) a n d enters the solid
phase (current collector). C o n s e q u e n t l y , the potential gradient in the l i q u i d phase is equal to zero, Eq. [4]. The solid
phase potential is arbitrarily set to zero at x = 0, Eq. [5].
E q u a t i o n s [7a] a n d [7b] are the kinetic expressions for the
electrode reactions in the positive electrode. E q u a t i o n s [7c]
a n d [Td] give the overpotential e x p r e s s i o n a n d the corresp o n d i n g open-circuit (equilibrium) potential for the
n i c k e l - c a d m i u m cell.
R e g i o n 1: positive e l e c t r o d e . - - O h m ' s law in the solution
i2
ex~ K%
0+2
OX
+
RT
F
(1 - t~
a In c
~X
[8]
C o n s e r v a t i o n of charge
extol a + 1,NiOOH
i2 - ErNzOOH 61
-
OX
- icen
[9]
Transfer c u r r e n t
ai2
ox
- JN, + Jo2
[10]
P o r o s i t y variation
[1]
ael _ 1
Ot
(MNi(OH,2
F \ pNi(OH)2
MN~OOHtjN~
[11]
PNiOOH/
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d. Electrochem. Soc., Vol. 138, No. 1, January 1991 @ The Electrochemical Society, Inc.
Electrolyte material balance
Ot
Ot
Ox \
[12]
Ox/
Oxygen material balance
OCo~+
__06'
6,
0 (Do26~x I 0Co2~
/
_
1 Jo~
+ ~-F
[13]
19
Equations [15], [19] and [20] are in accordance with the continuity of the flux conditions of the electrolyte, superficial
current density and oxygen at this interface. Equation [16]
is the material balance in the solid phase. Equation [17]
shows that all of the current through the cell is in the solution at this interface. Since the current in the solid phase is
equal to zero, the potential gradient in the solid phase at
this interface is also equal to zero, as given in Eq. [18].
Region 2: s e p a r a t o r . - - O h m ' s law in the solution
ot - 7x
where the kinetic expression for oxygen reaction is
Jo2_~ amaxlZ ~
(
r~'aF, ~1
~l _--_%1 )~1 [
\6m , -- %,,
0*2
OX
0 In c
- t o) - OX
RT
k--(1
F
[21]
Current in solution
/exp[-fiTn
( Co~ ] e x p [ ~ - . ~ j j
i2
ex2
K%
i2 = /cell
[22]
,~ = 0
[23]
6 = f~ate~p
[24]
Solid phase potential
[14a]
\CO2,ref/
Porosity
where
n'a = *l,Ni -- *2 -- UO2/Cd
[14b]
Electrolyte material balance
and
UO2/Cd = Uo2/o H -- UCd(OH)2/Cd = 1.21V
0C
[14c]
Equation [8] is a modified form of Ohm's law for the electrolyte which indicates that the curent in the electrolyte is
driven by the electric potential gradient and the electrolyte
concentration gradient. Equation [9] is Ohm's law for the
solid phase. Equation [10] defines the transfer current that
exists because of the electrode reactions which cause a
gradient of the superficial current density in solution,
OiJox. Equation [11] is the material balance in the solid
phase which describes the porosity changes with time due
to the conversion of the active solid materials with different densities by the electrode reaction. Equations [12] and
[13] are the mass balance of the electrolyte (KOII) and oxygen (02), which indicate that the electrolyte and the "effective" oxygen concentration at any position changes with
time because of the electrode reaction and mass transfer.
Mass transfer of OH is considered to be only diffusion and
migration. Convection transport of OH- is neglected. The
exponents, e x l and extol, in these equations are tortuosity
factors for the porous electrode. The concept of an effective oxygen concentration is used to provide a means of accounting for both gas and liquid phase transport of oxygen
without including separately the gas phase and dissolved
oxygen transport in the electrodes and the separator. The
same concept applies to the apparent diffusion coefficient
of oxygen, Do2. This is very important during overcharge
process.
02C
6 - - = D6~ Ot
Ox2
[25]
Oxygen material balance
6 0Co2
Ot
ex2 ~2CO2
D
=
~
[26]
Ox2
Equation [21] again is a modified form of Ohm's law for the
electrolyte, which is similar to Eq. [8] in the positive electrode region. Since the solid phase of the separator is not
conductive, the current is carried totally by the liquid
phase as shown in Eq. [22] and the potential of the matrix
is arbitrarily set to zero, Eq. [23]. Equation [24] shows that
the void space available to the electrolyte is equal to the
porosity of the separator, %~p,times the level of liquid saturation in the separtor, fiat. Finally, Eq. [25] and [26] are the
material balance of the electrolyte and oxygen concentration.
Interface between region 2 a n d 3.-0esat6sep)eX2 OC
ex3 04
0X [ region2 = {[3 ox region3
[27]
Mcd)
063
1 (Mcd(OH)2
Ot - 2F \ ~
P~a/Jcd
[28]
Interface between region 1 and 2.-t51
exl ~
a6i
= (fsat6sep)ex2 aC__
reglonl
_1
at
i2 =
[15]
icen
[29]
dX I region2
(MNi(oIt)2MNiOOH.)jN1
F \ PNi(OH)2
r)X
c3X
[16]
= 0
[30]
region3
PNiOOH/
i2 = ic~,,
0*,,N,
O*l'Cd
[17]
= 0
[18]
(L~t6sep)
~2 0.21
--
6~x3 0*2
=
~X region2
(fsat6sep)eX2 ~
reglonl
-
[31]
-
~X Iregion3
= 6ex3 0Co2 [
[32]
3 0~-Irog,on3
region2
where, on discharge and at rest
exI ~ ' 2
El
(~X regionl
ee• 0Co2
= 0esat6sep)
ex2 0*2
-I~X region2
= 0esatesep) ex2 0Co2
[19]
Jcd = ~max3~o3,ref
[20]
\Cref/
\{!max3 -- 603 /
exp[~lcJ
1-
exp
IL---K~ncjj
1}
[33a]
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20
J. E l e c t r o c h e m .
Soc.,
Vol. 138, No. 1, January 1991 9 The Electrochemical Society, Inc.
1.5 .... ,
and on c h a r g e
(c)~3(~-~o~1~3
L6
1.7 I
\Cref/
1.5
JCd = amax31o3xef - 9
\Emax3
-
Eo3 /
-
. . . .
,
. . . .
,
. . . .
,
. . . .
,
. . . .
,
. . . .
,
. . . .
,
. . . .
,
. . . .
,
. . . .
,.
1.4
expl_-R-~< j - exp L - ~ % j
j
[33b]
1.3
,.~ -+~_
and
~ _ : ~
~ ~O~o...
1.!
n~ = r
- r
[33c]
1.0
O.9
Region 3: negative electrode.--The e q u a t i o n s g i v e n
b e l o w for t h e n e g a t i v e e l e c t r o d e are a l m o s t t h e s a m e as
t h o s e u s e d in t h e p o s i t i v e e l e c t r o d e region.
O h m ' s law in t h e solution
O.B
3
2
1
O.7
0.6
i2
Ke~x3
0r
-
0x
RT
~ In c
0,5
(1 - t ~ - -
+ -F
[34]
ax
0.4.
0.3
C o n s e r v a t i o n of c h a r g e
D i s c h a r g e Rate:
1:= 10 m&/cm 2
15 mA/am 2
3: = 30 mA/cm 2
0.2
i2 -
Er Eexm3 0~)l'Cd
Cd 3
0.1
[35]
-- icen
0X
2: =
o.o oi;" '&'
" ",;.;" ' ",;.;" ' '&'
0i2
OX
[35]
- Jcd + J02
0Co2
ox
0e3
1 (Mcd(OH)2 Mca]
0t - 2F ~ ~
P~-d/Jcd
[36]
Electrolyte material balance
ac
oe3 O
( -1_ ~ )t ~
to
~Oe
x)
e3--Ot + c--Ot = --Ox De~3
Jcd + ~ Jo2 [37]
Oxygen material balance
0Co2
~t
+
~e3
~ /,~
- = -Co~-~t
~x
~'-'m ~
~ ~Co21
ax /
+
1
"
~ #o2
[38]
9
I ~-~o~ ~r
The e q u a t i o n s u s e d at this b o u n d a r y are v e r y similar to
t h o s e at t h e c e n t e r of t h e positive e l e c t r o d e e x c e p t that the
solid p h a s e p o t e n t i a l is already established so the transfer
c u r r e n t c o n d i t i o n is u s e d instead of setting a v a l u e for r
The a p p r o p r i a t e e q u a t i o n s g i v e n a b o v e on d i s c h a r g e and
rest or on c h a r g e w e r e p u t into finite difference f o r m and
solved n u m e r i c a l l y u s i n g a p e n t a d i a g o n a l B A N D ( J ) subr o u t i n e (14) and an i m p l i c i t s t e p p i n g t e c h n i q u e for t h e
t i m e derivatives. T h e fixed p a r a m e t e r s u s e d in the calculations are g i v e n in Tables I-III. The p a r a m e t e r values g i v e n
w i t h o u t r e f e r e n c e s are a s s u m e d values. The s i m u l a t e d results are p r e s e n t e d and d i s c u s s e d next.
~
r-~'oF
t Tjexpv
,oj/1 ]
/
[45]
Discharge characteristic.--The m o d e l s i m u l a t e d cell
v o l t a g e vs. t i m e c u r v e s for three d i s c h a r g e rates (solid
r~'~F,]
eo3/'J t e x p [ ~
. . . .-
- 0
Results and Discussion
w h e r e t h e kinetic e x p r e s s i o n for o x y g e n r e a c t i o n is
Jo2 = amax3i'~
' '~'.;
Fig. 2. Discharge characteristic of a nickel-cadmium cell
Porosity variation
~
' ','.;' ' ','.;,' ' ','.;" ' ','.;' ' ",'.;" ' ;.;'
Time (hrs)
Transfer current
Co2 ~
i.O
[39a]
2.0 h r
II1.t~
and
1.6 h r
I1.0
~'c = r
-- r
-- UO#Cd
1.0 hr
[39b]
0.6 hr
?.11
Center of the negative electrode.--
--
0.0 hr
oc
0x
- 0
[40]
~
7.0
=
4.6
o
0%_1
Ot
Mcd]jca
(Mcd(OH)2
2F
\ PCd(OH)2
[41]
PCd /
~--"
8.0
.~
6.6
e,l
i2 = 0
[42]
II1.0
Pos.
0i2
Ox
- Jcd
Neg.
[43]
4.0
,
0.0
0r
-
0x
Sep.
4.5
0
[44]
0,2
Dimensionless
0.4
Spatial
0.8
Coordinanee
0.8
(X)
t,O
Fig. 3. Electrolyte concentration profiles at different discharge times
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J. Electrochern. Soc., Vol. 138, No. 1, January 1991 9 The Electrochemical Society, Inc.
lines) and t h e c o r r e s p o n d i n g e x p e r i m e n t a l data [data
points, refer to Ref. (15)] are s h o w n in Fig. 2. It can be seen
that t h e m o d e l has a v e r y g o o d fit to t h e e x p e r i m e n t a l results. B o t h t h e m o d e l p r e d i c t i o n s and the e x p e r i m e n t a l results i n d i c a t e that t h e cell voltage drops q u i c k l y f r o m the
open-circuit potential (1.30V) to certain v a l u e s at t h e beg i n n i n g of discharge, t h e n decays v e r y slowly d u r i n g the
m a i n c o u r s e of discharge, and finally falls off u p o n complete discharge.
F i g u r e 3 p r e s e n t s the profiles of the electrolyte concentration for a typical d i s c h a r g e process at a rate of
10 m A / c m 2, w h i c h is a p p r o x i m a t e l y a 2h rate. It indicates
that the e l e c t r o l y t e c o n c e n t r a t i o n increases in all t h r e e regions. This i n c r e a s e is not d u e to the g e n e r a t i o n of O H - in
the e l e c t r o d e reaction, b e c a u s e O H - does n o t appear in the
overall cell reaction. A l t h o u g h OH is g e n e r a t e d on the
positive e l e c t r o d e a c c o r d i n g to r e a c t i o n [A], it diffuses
t h r o u g h t h e s e p a r a t o r and is r e d u c e d on the n e g a t i v e elect r o d e a c c o r d i n g to r e a c t i o n [C]; therefore, the overall accum u l a t i o n of O H - d u e to the e l e c t r o d e reactions is s i m p l y
zero. This i n c r e a s e in the electrolyte c o n c e n t r a t i o n is due
to t h e overall w a t e r c o n s u m p t i o n . D u r i n g discharge, w a t e r
is c o n s u m e d w i t h i n t h e positive e l e c t r o d e region w h i c h directly causes t h e overall electrolyte c o n c e n t r a t i o n to increase. I n addition, b e c a u s e of the g e n e r a t i o n of O H - in the
positive e l e c t r o d e a c c o r d i n g to reaction [A] and t h e cons u m p t i o n of O H - in the n e g a t i v e e l e c t r o d e a c c o r d i n g to reaction [C], t h e i n c r e a s e of electrolyte c o n c e n t r a t i o n in the
positive e l e c t r o d e is greater t h a n that in the n e g a t i v e electrode.
F i g u r e 4 p r e s e n t s t h e p r e d i c t e d porosity profiles of the
solid materials as a f u n c t i o n of t i m e at a d i s c h a r g e rate of
10 m A / c m 2. As can be seen, t h e porosity of b o t h electrodes
d e c r e a s e s d u r i n g discharge, b e c a u s e d u r i n g discharge t h e
e l e c t r o d e active materials are c o n v e r t e d f r o m their d e n s e
state, e.g., N i O O H and Cd, to a loose state, e.g., Ni(OHh and
Cd(OH)2. T h e d e c r e a s e in t h e solid material density will result in a d e c r e a s e in the overall v o i d v o l u m e . The porosity
s h o w s an a l m o s t u n i f o r m d e c r e a s e across the e l e c t r o d e
section; therefore, t h e e l e c t r o d e reaction rate is not a
strong f u n c t i o n of spatial position. This feature is quite different f r o m t h a t of t h o s e s y s t e m s u n d e r diffusion control
(8). This implies that t h e d i s c h a r g e process p r o b a b l y is
u n d e r a c t i v a t i o n control b u t n o t u n d e r diffusion control.
Charge characteristic.--Figure 5 s h o w s the s i m u l a t e d
and e x p e r i m e n t a l (15) v a l u e s of the cell potential u n d e r
three c h a r g e rates. Qualitative a g r e e m e n t again exists bet w e e n the e x p e r i m e n t a l and s i m u l a t e d values. F i g u r e 6
s h o w s that t h e electrolyte c o n c e n t r a t i o n c o n t i n u o u s l y de. . . .
1.0
0,9
0,7
E
O.6
0.0 h r
0,5 h r
1,0 h r
1.5 h r
-~
E.O h r
0.4
o
0.3
Pos.
0.0
.
0.0
.
.
.
/
Sep.
.
,
,
0,2
Dimensionless
,
0.4
.
.
.
.
Neg.
.
,
,
0.6
Spatial C o o r d i n a n c e
,
i
0.8
,
l.O
(X)
Fig. 4. Porosity profiles of solid material at different discharge times
21
Table I. Properties of the electrolyte
Properties
Values
Cell temperature (T)
Ref. basic
concentration (Cr~f)
Ref. oxygen
concentration (co2.ref)
Diffusion coefficient
of KOH (D~oH)
Diffusion coefficient
of oxygen (Do2)
Transference
number (t~
Electrolyte
conductivity (z)
References
298.15 K
7.1 real;liter
(2), p. 580
1.0 mol/liter
2.13 • 10 5 cm2/s
(2), p. 591
1.00 • 10-3 cm2/s
0.78
(2), p. 598
0.67 S/cm
(2), p. 593
Table II. Electrode and separator properties
Positive Separator Negative
(Region 1) (Region 2) (Region 3) Reference
Properties
Half thickness
(era)
Porosity
(funy charged) (e)
Maximum charge
(Qma~,C/cm3)
Surface area
( ~ , cm2/cm3)
Tortuosity factors
(ex/exm)
Saturation level
0.036
0.0125
0.040
(15)
0.41
0.75
0.64
(2), p. 45
2082
--
3032
(12)
5600
--
5600
--
2.5/0.5
--
2.5/0.5
2.5
--
0.9
--
--
Table III. Thermodynamic and kinetic parameters
Properties
Open-circuit
potential (V)
iol.ref(A/cm2)
io3re~(A/cm2)
Number of
electrons (n)
c~
C~a3
~:
c~c~
~1
~3
~1
~3
Main
reactions
Oxygen
reaction
Reference
1.299
1.21
(2), p. 533
6.1 • 10-s
6.1 • 10-s
2
1.0 x 10-9
1.0 • 10-~
2
(5), p. 15
(5), p. 15
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.O
creases d u r i n g c h a r g e and o v e r c h a r g e d u e to p r o d u c t i o n of
w a t e r in t h e p o s i t i v e electrode. F o r a 1.5 r e c h a r g e ratio (3h
charge time/2h d i s c h a r g e time), the electrolyte concentration drops f r o m a b o u t 8.5 mol/liter to a b o u t 6.4 mol/liter.
F i g u r e 7 indicates that porosity of b o t h t h e positive and
t h e n e g a t i v e e l e c t r o d e increases as e x p e c t e d . The porosity
of the p o s i t i v e e l e c t r o d e returns to its original v a l u e gradually u p o n overcharge, b u t t h e porosity of t h e n e g a t i v e elect r o d e c o n t i n u e s to increase u p o n 1.0 r e c h a r g e ratio and
slightly passes t h r o u g h its original v a l u e (0.55). W h e n t h e
o v e r c h a r g e continues, the porosity q u i c k l y drops b a c k to
its original v a l u e (0.55), w h i c h is p r o b a b l y due to t h e t i m e
delay of o x y g e n diffusion.
T h e effect of o x y g e n is v e r y i m p o r t a n t in a nickel-cadm i u m battery. T h e cell p e r f o r m a n c e is greatly affected by
t h e o x y g e n g e n e r a t i o n and r e d u c t i o n process. H e r e we ass u m e that all o x y g e n exists only in the solution phase; and
an a p p a r e n t o x y g e n diffusion coefficient (Do2) and an effective o x y g e n c o n c e n t r a t i o n (Co2) are u s e d to a c c o u n t for
t h e t w o - p h a s e t r a n s p o r t of oxygen. As can be seen f r o m
Fig. 8, o x y g e n is g e n e r a t e d on t h e positive e l e c t r o d e acc o r d i n g to r e a c t i o n [B], diffuses t h r o u g h the separator, and
is r e d u c e d e l e c t r o c h e m i c a l l y on t h e n e g a t i v e e l e c t r o d e acc o r d i n g to r e a c t i o n [D]. N o t e that the o x y g e n builds up significantly in t h e p o s i t i v e e l e c t r o d e and r e d u c e s in the negative e l e c t r o d e r e g i o n n e a r t h e separator.
This process of o x y g e n r e d u c t i o n in the cell can be exp l a i n e d by c o n s t r u c t i n g a simplified E v a n s plot for the
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J. Electrochem. Soc., Vol. 138, No. 1, January 1991 9 The Electrochemical Society, Inc.
22
1.0
1.T
OAt
t.6
1.5
3
S
1
O.O
.4
,_.__-~-~--~.
1,3
-~
o--~o~ ~
_,,,- - , x - 6 ~
+ +-. + - + - -
u
0.7
1.2 C
3.0 hr
1.1
1.0
1.5 h r
O.S
O.S
1,0 h r
0.8
=
-~
r
0.5 hr
2.0 hr
0.0 hr
O.4
0.7
0.0 hr
S.5
0.3
0.5
0.4
0.3
Charge
0.2
Pos.
Rate:
1: = 10 mA/cm
:~
Sep.
Neg.
2: = 15 m A / c m 2
3: = 30
e.!
ma/cm 2
O.O
o.o
,,,i
0.0
....
i ....
0.2
, ....
0.4
0.8
i ....
0.8
, ....
i ....
1.0
Time
i ....
1.2
i ....
1.4
(hrs)
1.6
i ....
1.8
I ....
2.0
. . . .
0.0
,.
,
.
0.2
,
Dimensionless
2.2
,
I
0.4
.
.
Spatial
.
.
.
. .
O.O
.
Coordinenee
i
. . . .
0.6
l.O
(X)
Fig. 7. Porosity profiles of solid material at different charge times
Fig. 5. Charge characteristics of a nickel-cadmium cell
electrode reactions in the cell. Figure 9 is an Evans plot for
the electrode reactions [A-D]. The parameters used in preparing this plot are listed in Table IV. It is important to
note that Fig. 9 is only a qualitative representation of the
actual electrochemical process in the model and in the cell,
but it is consistent with the model predictions. During the
charging period, oxygen generation on the positive electrode is along the positive branch (AB) and the electrochemical reduction of oxygen on the negative electrode is
along the negative branch (ACD). This hypothesis is consistent with the results presented by Turner (16) in which
he stated that oxygen recombination may be due to the
electrochemical reduction of oxygen on the cadmium of
the negative electrode and that the recombination rate depends u p o n the a m o u n t of metallic c a d m i u m on the negative electrode. Further consideration of Fig. 9 reveals that
it is highly unlikely that Cd is oxidized to Cd(OH)2 during
the charging process because cadmium is cathodically
protected. This is true because on charge the potential of
the negative electrode is lower than the equilibrium potential of the electrode reaction [C], which is obviously on the
Cd(OH)2 reduction branch of the Evans plot of the cadm i u m electrode part (EF).
Voltage control charge characteristic.--In order to avoid
pressure buildilp due to oxygen generation during charge
and overcharge, a voltage control charging technique is
frequently used. In this charge mode, a constant charge
current is applied at the beginning of charge when the cell
voltage reaches a set value (1.35V) and is then changed to
constant voltage charge, which allows the charge current
to drop. This technique was developed based on the electrochemical p h e n o m e n a shown in Fig. 9. According to
Fig. 9, the entire process of oxygen generation, diffusion,
and o x y g e n reduction is more likely to be controlled by
diffusion of oxygen through the separator. If the charging
rate is fast and the charging efficiency is low (e.g., during
overcharge), then the cell pressure will increase quickly
due to o x y g e n generation. If a constant voltage is applied,
the oxygen generation, diffusion, and reduction will reach
g.5
D.O
~g.
O.O h r
8,5
0.5 h r
tLO
__
J
l.O h r
1,5 h r
7.5
/
2.0 hr
/
7.0
2.5 h r
J
8
3.0
6.5
hr
~J
S.O
5.5
o
S.O
4.5
Pos.
4,0
Sep.
Neg.
3.5
,
S.O
0.0
,
t
,
,
,
0.2
Dimensionless
r
.
.
0.4
Spatial
.
.
.
.
O.O
.
.
,
0.8
. . . .
1.0
Coordinenee (X)
Fig. 6. Electrolyte concentration profiles at different charge times
0.0
o.z
0.4
0.8
0.8
t.o
Dimensionless Spatial Coordinanee (X)
Fig. 8. Oxygen concentration profi[esat differentcharge times
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J. Electrochem. Soc., Vol. 138, No. 1, January 1991 9 The Electrochemical Society, Inc.
23
Table IV. Parameters used in preparing the Evans plot
t.5
t
Electrode
Active materials
1.0
+o&"
o.s5, A "'~
r~
Negative
Cd(OH)JCd
6.1 • 10-~
6.1 • 10 5
1.0 • 10-~
1.0 • 10 9
0.44
-0.86
0.35
0.35
io for main
reaction (A/cm2)
io for oxygen
reaction (A/cm2)
Equ. potential in
7.1M KOH (V)
02 potential in
in 7.1M KOH ~ (V)
0.44 I*"
0.~
Positive
NiOOH/Ni(OH)2
0.0
a Refers to oxygen partial pressure as 1 atm.
-0.5
-0.88 F
~0
-1.0
-0.88
Y
r
~
F
-2.5_11.0,
,
,
,
I
-B.O
Current
,
,
,
Density
(Log
,
s
I
-1.0
,
T
,
'
4
.0
i n A/ern z
i
Fig. 9. Evans plot for the electrode reactions in a nickel-cadmium
cell.
Sensitivity analysis.--It is i m p o r t a n t to d e t e r m i n e the
sensitivity of t h e m o d e l p r e d i c t i o n s to changes in the elect r o d e kinetic p a r a m e t e r s and t r a n s p o r t properties. If the
m o d e l p r e d i c t i o n s are relatively i n s e n s i t i v e to one or m o r e
parameters, t h e n a fairly w i d e r a n g e of values for t h e s e par a m e t e r s could be u s e d w i t h o u t significantly affecting the
p r e d i c t i o n s of t h e model. T h e sensitivity of the m o d e l predictions to c h a n g e s in p a r a m e t e r s is d e t e r m i n e d by monitoring t h e c h a n g e in cell voltage. While h o l d i n g all other
p a r a m e t e r s constant, the p a r a m e t e r of interest is pert u r b e d slightly a n d the resulting c h a n g e in cell voltage is
noted. A sensitivity coefficient (SC) is defined as follows
n
~[hE(tj)l
SCi-
a steady state b e f o r e t h e o x y g e n p r e s s u r e builds up significantly. F i g u r e 10 s h o w s t h e c h a r g e c u r r e n t density as a
f u n c t i o n of time. I f t h e o x y g e n reactions [B] and [D] are not
i n c l u d e d in t h e m o d e l , t h e charge c u r r e n t d e n s i t y will drop
to zero d u r i n g voltage control charge. This is a p u r e hypothetical case. I f the o x y g e n reactions on b o t h the positive
and t h e n e g a t i v e e l e c t r o d e s are i n c l u d e d in the model, the
c h a r g e c u r r e n t d e n s i t y d u r i n g voltage control charge app r o a c h e s a n o n z e r o a s y m p t o t i c value, w h i c h indicates that
o x y g e n generation, diffusion, and r e d u c t i o n reach a steady
state in t h e cell. T h e o x y g e n c o n c e n t r a t i o n in the positive
e l e c t r o d e for this c h a r g i n g t e c h n i q u e is s h o w n in Fig. 11.
C o m p a r i s o n of Fig. 11 to Fig. 8 s h o w s that t h e o x y g e n
b u i l d u p d u r i n g the v o l t a g e control c h a r g e is m u c h less
t h a n that d u r i n g t h e c o n s t a n t rate charge.
15.0 . . . .
, ....
, ....
+ ....
, ....
Wit.___hhOxylea Rxn~
Without OxyKen Rxn
13.0
, ....
, 9
~=1
[46]
AE(tj) = E(tj) - E*(tj)
[47]
hpari = par, - par i
[48]
nlhpar, I/par~
where
parj and par: are the p e r t u r b e d values of p a r a m e t e r i and
t h e r e f e r e n c e v a l u e of p a r a m e t e r i, respectively. E(tj) is the
v a l u e of t h e cell voltage at t i m e t~ w h e n u s i n g par~; and,
E*(~) is t h e v a l u e of t h e cell voltage at t i m e tj w h e n u s i n g
par,. In Eq. [46], n is t h e n u m b e r of t i m e s o v e r w h i c h the
voltage v a l u e s are c o m p a r e d , and its v a l u e is c h o s e n so
that 80% of t h e d i s c h a r g e or c h a r g e t i m e is i n c l u d e d in the
analysis.
The results of the sensitivity analysis are s h o w n in
Fig. 12 and 13. F i g u r e 12 s h o w s sensitivity of the cell voltage to t h e e l e c t r o d e kinetic p a r a m e t e r s d e s c r i b i n g the dis-
]
12.0
II.O
10.0
9.0
~
B.O
~
7.O
~
6.O
~
5.0
I
~
~t
Y,
4.11
t~
t~
3.O
2.O
1.0
0.0
,
0.0
,
t
t
i
t.O
,
,
,
,
i
,
2.0
,
t
i
i
. . . .
3.0
Charge Time
,
4.0
9
,
,
,
I
5.0
,
,
,
,
I
,
e.o
(hre)
Fig. 10. Charge current density as a function of time for the voltage
control charge mode (i.e., first constant current charge at 10 mA/cm2
until the voltage reaches 1.35, then constant voltage charge and current falls off).
0.0
0.2
Dimensionless
0.4
0.6
Spatial Coordinance
0.8
(X)
1.0
Fig. 11. Oxygen concentration profiles during the voltage control
charge mode.
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24
J. Electrochem. Soc., Vol. 138, No. 1, January 1991 9 The Electrochemical Society, Inc.
85.0
. . . . . . . . .
,
. . . . . . . . .
,
. . . . . . . . .
,
. . . . . . . . .
45.0
~~o
'~
/
40.0
3'5,0
~0.0
8
'~.
"~
zo.O
m
1~.o
A ......
-5.0
. . . . . . . . .
o.o
'
...
& ...... A
. . . . . . . . .
-5.0
Applied
'
.........
. . . . . . . . .
-1o.o
Discharge
Current
'
. . . . . . . . .
-15.0
-20,0
(mA/em z)
Fig. 12. Sensitivities of the predicted cell voltage to changes in the
electrode kinetic parameter and separator property during the discharge processes.
85.0
.........
~
. . . . . . . . .
, .........
,
.
.
.
.
.
.
.
.
Future Model Refinement
T h e results p r e s e n t e d h e r e are s o m e p r i m a r y s i m u l a t i o n
results. M a n y o t h e r i m p o r t a n t features n e e d to be incorporated into t h e m o d e l in o r d e r to h a v e a b e t t e r u n d e r s t a n d ing of t h e e l e c t r o c h e m i c a l p h e n o m e n a in a nickel-cadm i u m ceil. S o m e future r e f i n e m e n t s to the m o d e l m a y
include: (i) solid i n t e r c a l a t i o n properties of the nickel electrode; (ii) s e m i c o n d u c t o r properties of t h e nickel electrode; (iii) p r o t o n diffusion in t h e nickel electrode (iv) twop h a s e t r a n s p o r t of o x y g e n ; (v) porosity distribution across
t h e e l e c t r o d e section; a n d (vi) d e g r a d a t i o n effects.
Conclusions
A m a t h e m a t i c a l s i m u l a t i o n for the d i s c h a r g e and charge
p e r f o r m a n c e of a sealed n i c k e l - c a d m i u m battery has
s h o w n t h a t t h e m o d e l can b e u s e d to p r e d i c t cell p e r f o r m ance. Thus, it can serve as a useful tool for cell designers
and e n g i n e e r s in s t u d y i n g t h e effect of various design par a m e t e r s on t h e d i s c h a r g e and c h a r g e p e r f o r m a n c e of the
cell. T h e sensitivity analyses indicate that the p r o d u c t of
e x c h a n g e c u r r e n t d e n s i t y and specific surface area is the
m o s t influential factor to cell p e r f o r m a n c e .
Acknowledgments
T h e authors a c k n o w l e d g e gratefully that this w o r k was
s u p p o r t e d by the J e t P r o p u l s i o n L a b o r a t o r y (NASA)
u n d e r C o n t r a c t No. 958344. We w o u l d also like to t h a n k
G e r a l d Halpert, P a u l T i m m e r m a n , Karla Clark, Sal DiStefano, a n d P e t e r G l u c k for t h e i r helpful discussions and for
p r o v i d i n g m a n y of t h e p a r a m e t e r v a l u e s u s e d in our
model. Finally, w e w o u l d like to t h a n k J e t P r o p u l s i o n Laboratory for use of t h e i r s u p e r c o m p u t e r and Cray Research,
Inc., for t i m e on t h e Cray Y M P at T e x a s A & M University.
M a n u s c r i p t s u b m i t t e d Dec. 18, 1989; revised m a n u s c r i p t
r e c e i v e d Aug. 7, 1990.
Texas A & M University assisted in meeting the publication costs of this article.
LIST OF SYMBOLS
a . . . . j m a x i m u m specific active surface area of region j,
cm2/cm 3 (j = 1, 3)
C
c o n c e n t r a t i o n of t h e b i n a r y electrolyte, KOH, mol/
45.0
~-
4o.o
cm 3
Cref
35,0
Iv
~-~
(o'ma:r" 'to,r..f )
/ 0
Co 2
30.0
#
zs.o
~,
so.o
Co2,ref
DKOH
o/
Do s
ex]
15.0
exmj
I0.0
fsat
6.0
( f , at" ~.,p)
F
...... A
ioj,ref
o.o
5.0
Applied
Charge
1o.o
Current
15.o
(rnA~evn s)
2o.o
Fig. 13. Sensitivities of the predicted cell voltage to changes in the
electrode kinetic parameter and separator property during the charge
processes.
c h a r g e r e a c t i o n o v e r a range of d i s c h a r g e rates. F i g u r e 13 is
an a n a l o g o u s plot for the c h a r g i n g process. T h e kinetic par a m e t e r is r e p r e s e n t e d b y t h e p r o d u c t of e x c h a n g e c u r r e n t
d e n s i t y and t h e m a x i m u m specific surface area. The s a m 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 y and specific surface
area are u s e d for b o t h t h e positive and n e g a t i v e e l e c t r o d e
(i.e., io 9 amax = iol,r~f" am~i = io3,~f ' amax3)- T h e t r a n s p o r t par a m e t e r is c h a r a c t e r i z e d by t h e p r o d u c t of saturation level,
f~,t, and t h e p o r o s i t y of t h e separator, %~p. The sensitivity
analyses i n d i c a t e t h a t the m o s t influential factor by far is
t h e e l e c t r o d e k i n e t i c s (io - ama~), especially at h i g h disc h a r g e or c h a r g e c u r r e n t density. T h e p a r a m e t e r s characterizing t h e t r a n s p o r t of t h e electrolyte t h r o u g h the separator h a v e m u c h less influence on t h e cell voltage d u r i n g
b o t h t h e c h a r g e and d i s c h a r g e period. This indicates that
t h e n i c k e l - c a d m i u m cell o p e r a t e s u n d e r activation control.
i'oj,ref
i2
icen
d
JNi
Jca
Jo2
l
12
Mi
nj
pari
R
t
t ~-
r e f e r e n c e c o n c e n t r a t i o n of the b i n a r y electrolyte,
KOH, m o l / c m 3
effective o x y g e n concentration, m o l / c m 3
effective r e f e r e n c e o x y g e n concentration, m o l / c m 3
diffusion coefficient for KOH, cm2/s
a p p a r e n t diffusion coefficient of oxygen, cm2/s
t o r t u o s i t y factors of p o r o u s m e d i a in r e g i o n j for liquid p r o p e r t i e s (diffusion coefficients and conductivities) (j = 1, 2, 3)
t o r t u o s i t y factors of r e g i o n j for solid properties
(conductivity) (j = 1, 3)
level of electrolyte saturation in the separator
F a r a d a y ' s constant, 96,487 C/tool
e x c h a n g e c u r r e n t d e n s i t y of the reactions in region
j at cref, A / c m 2 (J = 1, 3)
e x c h a n g e c u r r e n t d e n s i t y of o x y g e n reaction in reg i o n j at Co2,ref,A / c m 2
c u r r e n t d e n s i t y in solution b a s e d on t h e p r o j e c t e d
e l e c t r o d e area, A / c m 2
a p p l i e d c u r r e n t d e n s i t y based on the p r o j e c t e d elect r o d e area, A / c m 2
r e a c t i o n c u r r e n t per unit v o l u m e of p o r o u s electrode, A / c m ~
n i c k e l r e a c t i o n c u r r e n t per unit v o l u m e of positive
electrode, A / c m 3
c a d m i u m r e a c t i o n c u r r e n t p e r unit v o l u m e of negative electrode, A / c m 3
o x y g e n r e a c t i o n c u r r e n t p e r u n i t v o l u m e of p o r o u s
electrode, A / c m 3
total t h i c k n e s s of a cell unit, c m
h a l f t h i c k n e s s o f t h e p o s i t i v e electrode, c m
t h i c k n e s s of the s e p a r a t o r matrix, c m
m o l e c u l a r w e i g h t of solid species i, g/mol i =
NiOOH, Ni(OH)2, Cd, Cd(OH)2)
n u m b e r of e l e c t r o n s i n v o l v e d in t h e e l e c t r o d e reaction j
perturbed values of parameter i
u n i v e r s a l gas constant, 8.3143 J / m o l - K
time, s
t r a n s f e r e n c e n u m b e r of a n i o n O H - w i t h r e s p e c t to
the solvent velocity
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J. Electrochem. Soc., Vol. 138, No. 1, January 1991 9 The Electrochemical Society, Inc.
T
absolute temperature, K
UN~Cd open-circuit potential of nickel-cadmium battery at
Cref = 7.1 mol/1, V
Vo2/Cd open-circuit potential of oxygen reaction with respect to c a d m i u m electrode, V
equilibrium potential for half reaction i at the referU,
ence state, V
X
spatial distance from the center of the positive electrode, cm
X
dimensionless distance from the center of the positive electrode, X = x/l
Greek letters
anodic and cathodic transfer coefficients for the
electrode reactions
O/'a, O~'c anodic and cathodic transfer coefficients for the oxygen reaction
exponents for the concentration dependence of reaction rate
ej
porosities of solid materials of region j, (j = 1, 2, 3)
porosities of solid materials of region j at zero
~oj
charge, (j = 1, 3)
porosities of solid material of region j at full charge,
~maxj
( j = 1,3)
porosity of the separator matrix
Esep
exponents for the active material dependence of reaction rate
K
electrolyte conductivity, S/cm
densities of the solid material i, g/cm 3 (i = NiOOH,
Pi
Ni(OH)2, Cd, and Cd(OH)2)
conductivities of the solid material, S/cm (i =
O"i
NiOOH, Cd)
~bl
potential in the solid phase, V
~2
potential in the liquid phase, V
Ota, Otc
Subscripts
1
positive electrode region
2
separator region
3
negative electrode region
02
oxygen or oxygen reaction
Ni
positive electrode reaction [A]
Cd
negative electrode reaction [C]
25
REFERENCES
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Nche, "Secondary Aerospace Batteries and Battery
Materials," NASA SP-7044, July 1976.
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(1969).
3. W. R. Scott and D. W. Rusta, "Sealed-Cell Nickel-Cadm i u m Battery Application Manual," NASA Reference Publication No. 1052, December 1979.
4. F.V. Sturm, "Comprehensive Treatise of Electrochemistry," Vol. 3, J. O'M. Bockris, B.E. Conway, E.
Yeager, and R. E. White, Editors, Chap. 13, P l e n u m
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Princeton, NJ (1979).
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134, 2953 (1987).
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709 (1984).
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135, 887 (1988).
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13. D. F. Pickett, H. S. Lim, S. J. Krause, and S. A. Verzwyvelt, J. Power Sources, 22, 243 (1988).
14. J. Van Zee, G. Kleine, R. E. White, and J. S. Newman,
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(1964).
Effect of Benzotriazole on Surface Processes during Copper
Electrodissolution in Sulfuric Acid
Claude Clerc 1 and Richard Alkire*
Department of Chemical Engineering and Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801
ABSTRACT
Impedance spectra were obtained during anodic dissolution of copper in 0.5M H2SO4 and 40 mM benzotriazole (BTA)
at 25~ The spectra were evaluated according to the hypothesis that the electrode is covered with a barrier film having a
stoichiometric composition through which the current is transported by ionic conduction. This barrier film is itself
covered with an outer porous film of corrosion products. The experimental impedance spectra were fit to the model with a
nonlinear least squares program. A detailed analysis of the physical parameters obtained with this procedure suggested
that the metallic ions transfer through the barrier film, which is likely to be hydrated copper sulfate or contains a nonnegligible a m o u n t of BTA, u n d e r high-field conduction. Experiments carried out at the mass-transfer limiting current in
the absence of BTA suggested that the electrode was also covered with a similar dual salt film, the inner layer of which,
however, has a different chemical composition than in the presence of BTA.
The presence of a surface film is a significant feature in
virtually all cases of high-rate electrodissolution of a metal.
Important practical applications of such p h e n o m e n a include pitting corrosion (1-3), passivity (4), corrosion inhibition (5), electropolishing (6), and battery operations (7). Improved fundamental u n d e r s t a n d i n g of such surface films
is therefore of widespread interest. Since such surface
films respond to the u n i q u e conditions of the electrochemical e n v i r o n m e n t in which they exist, in situ methods of
characterization are strongly preferred. In the present
work impedance spectroscopy was used.
* Electrochemical Society Active Member.
1Present address: Medinvent SA, Lausanne, Switzerland.
In a recent study of copper dissolution in sulfuric acid,
Alkire and Cangellari (8) showed that a small amount of
benzotriazole (BTA), an organic inhibitor, promotes the
precipitation of a surface film having a dual structure. According to this view, presented in Fig. la, there is a thin
barrier film next to the metal which is covered by an outer
porous film. From a series of potential step measurements
at a rotating disk electrode, they concluded that the metallic ions transferred through the barrier film under highfield conduction, and that deviation from the masstransfer rate predicted by the Levich equation was due to
the porous film. A theoretical model was developed to describe the transport of the electrochemical species, assuming molecular diffusion and migration across the porous
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