J. Electrochem. Soc., Vol. 137, No. 6, June 1990 9 The Electrochemical Society, Inc.
mass-transport parameters of the surface layers, such as
their cationic transference numbers, salt diffusion coefficients, and ionic concentrations. The analysis of the values
obtained for these parameters has demonstrated that the
surface layers behave as dilute electrolytes, the ionic concentrations of which are lower than those of their parent
liquid electrolytes. This study has also demonstrated that
the best cycling performances are obtained with the surface layers the characteristic parameters of which are close
to those of the parent liquid electrolytes. Different tests
based on the evaluation of the layer conductivity, the Warburg constant, and the limiting current density inside the
surface layer, have been proposed for the search of more
appropriate liquid electrolytes to be used in secondary
lithium batteries. However, these tests have been established from a quite limited n u m b e r of organic electrolytes.
More data are still to be accumulated to more firmly settle
the conclusions and field of utilization of this exploratory
work.
Manuscript submitted July 18, 1989; revised manuscript
received Jan. 10, 1990.
CNRS assisted in meeting the publication costs of this article.
REFERENCES
1. E. Peled, This Journal, 126, 357 (1981).
2. E. Peled, in "Lithium Batteries," J. P. Gabano, Editor,
p. 43, Academic Press, New York (1983).
3. J. Thevenin, J. Power Sources, 14, 45 (1985).
1665
4. J. Thevenin and R. Muller, This Journal, 134, 273
(1987).
5. (a) J. R. MacDonald, J. Chem. Phys., 58, 4982 (1973); (b)
ibid., 61, 3977 (1974).
6. (a) J. R. MacDonald, J. Electroanal. Chem., 32, 317
(1971); (b) ibid., 47, 182 (1973); (c) ibid., 53, 1 (1974).
7. (a) R. P. Buck, J. Membrane Sci., 17, 1 (1984); (b) R. P.
Buck, J. Electroanal. Chem., 210, 1 (1986).
8. W. I. Archer and R. D. Armstrong, in "Electrochemistry, A Specialist Periodic Report," Vol. 7, H.R.
Thirsk, Editor, p. 157, The Chemical Society, Burlington House, London (1980).
9. C. Dubois, Ph.D. Thesis, University of Paris VI (1987).
10. (a) C. Dubois, A. De Guibert, and J. Thevenin, J. Power
Sources, 26, 571 (1989); (b) Rev. Sci. Tech. D~fense, 2,
73 (1988).
11. J. S. Foos, L. S. Rembetsy, and S. B. Brummer, E.I.C.
Laboratories, Inc., Final Report (1984).
12. S. Panero, P. Prosperi, B. Klaptse, and B. Scrosati,
Electrochim. Acta, 31, 1597 (1986).
13. S. Fouache-Ayoub, Ph.D. Thesis, University of Paris
VI (1988).
14. J. Newman, in "Advances in Electrochemistry and
Electrochemical Engineering," Vol. 6, P. Delahay
and C.W. Tobias, Editors, p. 87, Academic Press,
New York (1967).
15. P. Drossbach and J. Schultz, Electrochim. Acta, 11,
1391 (1964).
16. (a) J. O. Besenhard, J. Gfirtler, and P. Komenda, J.
Power Sources, 20, 253 (1987); (b) ibid., in "Dechema
Monographien," VCH Verlagengesellschaft, Vol.
109, p. 315 (1987).
Assessment of Capacity Loss in Low-Rate Lithium/Bromine
Chloride in Thionyl Chloride Cells by Microcalorimetry and
Long-Term Discharge
E. S. Takeuchi,* S. M. Meyer, and C. F. Holmes*
Wilson Greatbatch, Limited, Clarence, New York 14031
ABSTRACT
Real-time discharge is one of the few reliable methods available for determining capacities of low-rate cells. The utilization of high energy density lithium batteries in low-rate implantable applications has increased the need for more timeefficient methods of predicting cell longevity since cells have been shown to last in excess of eight years. The relationship
between heat dissipation and self-discharge of low-rate lithium/BCX (bromine chloride in thionyl chloride) cells was
studied and allows prediction of cell life prior to the availability of real-time data. The method was verified by real-time
cell discharge data and provided estimates of delivered capacity within 6% of the actual values.
Lithium cells have proven to be useful in implantable
medical applications as they have excellent volumetric
energy density and can be hermetically sealed (1). Frequently, medical applications require very long cell lifetimes u n d e r low drain rates which makes predictions of
cell longevity based on real-time data impractical. A useful
tool for the estimation of cell lifetime is microcalorimetry,
in which cell heat dissipation is measured u n d e r load or on
open-circuit voltage (2). The heat dissipation of a cell can
be related to the self-discharge rate of the cell, which then
allows prediction of cell lifetime.
Lithium/bromine chloride in thionyl chloride (BCX)
cells have been used for implantable medical applications
(3-6). This publication presents discharge data from cells
that have been on low-rate discharge for as long as eight
years. The heat dissipation of these cells was intermittently measured and is shown to be related to cell selfdischarge. The measured heat dissipation can thus be used
as a predictive tool to estimate cell longevity. Finally, the
relationship between average rate of self-discharge and the
rate of discharge is addressed with respect to optimizing
* Electrochemical Society Active Member.
anode surface area to minimize cell self-discharge fo," a
particular application.
Experimental
Half-round prismatic (45 • 28 • 7.0 mm) hermetically
sealed Li/BCX cells were used as test vehicles. The cells
employed 304L stainless steel for case and lid construction, were case positive, and were equipped with glass-tometal seals. A sandwich structure was utilized with a centrally located lithium anode made of two pieces of lithium
(0.73g total) pressed on either side of a nickel screen
equipped with leads. The total anode surface area was
14.5 cm 2. The lithium anode was positioned between two
carbon plates composed of Shawinigan acetylene black
and Teflon. Glass fiber separator (Mead Paper, Specialty
Paper Division) was used to envelope the lithium. The
electrolyte consisted of 0.4M lithium tetrachloroaluminate
in a 6:1 molar ratio of thionyl chloride to bromine chloride.
The thionyl chloride was distilled from lithium strips prior
to use. Electrolyte was prepared from lithium chloride and
a l u m i n u m trichloride. The lithium chloride was dried at
120~ and the a l u m i n u m trichloride was used as received.
Bromine chloride was passed through an alumina drying
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J. Electrochem. Soc., Vol. 137, No. 6, June 1990 9 The Electrochemical Society, Inc.
1666
column before being added to the thionyl chloride solution. Dry argon was bubbled through the final electrolyte
solution to remove traces of HC1. The cells were v a c u u m
filled with electrolyte and welded to provide a hermetic
seal. The stoichiometric capacity of these test cells was
2.8 Ah.
Cells were discharged under loads of 1.78, 10, 20, 50, 100,
and 140 kl2, representing average current densities ranging from 0.0018 to 0.14 mA/cm 2. Five cells were discharged
per load. Cell voltage and 1 kHz ac impedance were measured on a regular basis with an in-house semiautomatic
measuring system interfaced with a Prime computer. The
heat dissipation of cells under load (excluding the 1.78 kf~
group) was measured periodically in a Tronac microcalorimeter (Model No. 351RA) or equivalent. The resistor
was inserted into the calorimeter with the cell and thus net
heat dissipation was calculated by subtracting the resistive heat dissipation (V2/R) from the total microcalorimetric heat dissipation of the cell. All measurements
and discharge experiments were conducted at 37~
The analysis and presentation of data were accomplished using a Macintosh IIcx computer. Cricket Graph TM
was utilized for curve fitting and the preparation of
graphic illustrations, while computational data analyses
were performed with the aid of Mathematica TM (7, 8).
<
4000"
30OO
- 14000
120OO
10000
84
Voltage
2000"
..........
Impedance
84
"4000
10~0"
/
-20OO
!
0,
.
,
.
,
0.5
0.0
9
,
1.0
.
,
1.5
.
,
2.0
9
2.5
,0
3.0
D E L I V E R E D C A P A C I T Y (All)
Results and Discussion
Cell discharge results.--Discharge tests at average current densities of 0.14mA/cm 2 (1.78k~), 0.025mA/cm 2
(10 kfD, 0.012 mA/cm 2 (20 k~), 0.005 mA/cm 2 (50 k~), and
0.0025 mA/cm 2 (100 k~) are complete. Cells discharged at
0.0018 mA/cm 2 (140 k~) are still on test after approximately
eight years and have delivered 1.82 Ah to date. Figures la
and b present the discharge performance of typical lithium/BCX cells discharged under loads of 20 and 100 k~,
respectively. Cell voltage and 1 kHz ac impedance are depicted. At both drain rates, the cells experience an initial
high-voltage region from 3.9 to 3.65V and a subsequent
plateau at approximately 3.6V. The initial high-voltage region has been shown to result from the reduction of the interhalogen BrC1 and halogens chlorine and bromine with
w hi ch it is in equilibrium (9). As the cells approach end of
life, cell voltage decreases gradually from 3.6 to 3.0V followed by a rapid drop to 0 V. Table I lists average current
density (mA/cm2), average time on test (years), average delivered capacity (Ah to 0 V), and the standard deviation of
delivered capacity (Ah) for each of the groups noted above.
The capacities and times on test shown are averages based
on four to five cells.
Figure 2 is a Selim-Bro plot which provides a graphical
representation of average delivered capacity as a function
of the logarithm of average current density (mA/cm2). Cells
discharged at a rate of 0.14 mA/cm 2 delivered more capacity (152mAh) than cells discharged at a rate of
0.025 mA/cm 2. Delivered capacity is not greatly affected by
a decrease in the rate of discharge from 0.025 to
0.012 mA/cm 2. As the rate of discharge is further decreased
from 0.012 to 0.005 mA/cm 2, delivered capacity increases
significantly (739 mAh). As the rate of discharge is further
decreased beyond 0.005 mA/cm 2, delivered capacity decreases slightly (167 mAh). These results indicate that
m a x i m u m attainable capacity is achieved under m e d i u m
drain rates (i.e., 0.005 mA/cm2).
Table I. Discharge of lithium/BrCI in thionyl chloride cells at 37~
Standard
deviation
Delivered of delivered
Load Current density Time on test capacity
capacity
(kf2)
(mA/cm2)
(years)
(Ah)
(Ah)
1.8
10
20
50
100
140a
0.14
0.025
0.012
0.005
0.0025
0.0018
0.1
0.6
1.1
4.1
7.1
8.0
a Still on test (3.6V under load).
1.844
1.692
1.649
2.388
2.221
1.821
0.077
0.018
0.016
0.002
0.006
0.001
4000"
" 14000
3000'
10000
~o
- -
Voltage
..........
Impedance
2000'
4(]oo
1000
'20oo
......... ~.,.o~
O,
{kO
9
,
0.5
9
,
1.0
9
,
1.5
.
,
2.0
-
,
9
2.5
0
3.0
D E L I V E R E D C A P A C I T Y (All)
Fig. 1. (a, top) Voltage and 1 kHz impedance of I.i/BCX cells discharged under 20 k~ loads. (b, bottom) Voltage and 1 kHz impedance
of I.i/BCX cells discharged under 100 k~ loads.
Cells that reached 0 V were destructively analyzed and
residual lithium was determined. Virtually no lithium remained, which indicated that corrosion of the lithium
anode was the reason for cell depletion rather than polarization or passivation. Since the capacity not used for
faradaic discharge was lost due to anode corrosion (selfdischarge), capacity loss due to self-discharge can be calculated by subtracting actual delivered capacity from the
stoichiometric capacity of 2.BAh. The average selfdischarge rate was calculated by dividing the capacity loss
due to self-discharge by the total time on test and dividing
the resultant value by the anode surface area. Figure 3 illustrates the relationship between average self-discharge
rate (~A/cm 2) and current density. It can be seen that the
rate of self-discharge increases significantly as current
density is increased beyond 0.005 mA/cm 2.
This information can thus be used to predict the selfdischarge rate if the current density of discharge is known.
Based on this, it may be possible to optimize anode surface
area in an attempt to minimize self-discharge for an application where the discharge rate is accurately known. For
Downloaded on 2016-09-17 to IP 130.203.136.75 address. Redistribution subject to ECS terms of use (see ecsdl.org/site/terms_use) unless CC License in place (see abstract).
J. Electrochem. Soc., Vol. 137, No. 6, June 1990 9 The Electrochemical Society, Inc.
3.0"
whereas the cell with a surface area of 6 cm 2 would lose an
estimated 1292 mAh.
2.5
~o
v
~
O
1.5-
0.0025m A / c m 2
0.14 mA/cm2
(100 KQ)
~.~
1667
L0"
(1.8K.Q)
0.5'
0.0
.001
.01
.1
C u r r e n t D e n s i t y (mA/cm2)
Fig. 2. Relationship between average delivered capacity and average
current density of Li/BCX cells.
example, consider a Li/BCX cell whose application drain
rate will be 0.075 mA. If the cell is designed with an anode
surface area of 15 c m 2, the average self-discharge rate of
the cell will be about 0.81 ~A/cm2 according to the data
shown in Fig. 3. If, for the same drain rate, the cell is designed with an anode surface area of 6 cm 2, the selfdischarge rate of the cell will be about 8.2 ~A/cm 2. After
three years, the cell with a surface area of 15 cm 2 would
lose approximately 319mAh due to self-discharge,
20"
"
A
...... ~ ....
S
Microcalorimetry results.--The heat dissipation of cells
on loads ranging from 10 to 140 kl2 was monitored under
dynamic conditions. Resistive heat dissipation (V2/R) was
subtracted from total microcalorimetric heat dissipation to
obtain a value for net heat dissipation. Figure 4 shows a
schematic of the microcalorimetry data for the various discharge groups. Net heat dissipation is shown to increase as
the rate of discharge increases. Cells discharged at average
rates of 0.025 and 0.012 mA/cm 2 exhibit increasing followed by decreasing heat dissipation with m a x i m u m net
microcalorimetric values of 1420 and 760 ~W, respectively.
For both groups, net heat dissipation is shown to peak at
approximately 1.2 Ah. This same p h e n o m e n o n has been
observed in the low-rate discharge of thionyl chloride cells
(1). Heat dissipation at current densities of 0.005 mA/cm 2
and below remains fairly constant. Figure 5 presents voltage and net heat dissipation as a function of delivered capacity for a typical Li/BCX cell discharged under a 50 kt2
load. Heat dissipation was monitored throughout the first
1600 m A h of discharge and indicates stable dissipation at a
level of approximately 100 ~W. Net heat dissipation of
cells discharged at lower current drains is considerably
lower and was found to remain stable throughout discharge.
As previously noted, microcalorimetry has been used in
the past to relate heat dissipation to self-discharge (2). In
order to relate microcalorimetric heat dissipation to selfdischarge, the following thermodynamic relationship was
utilized
Qt = Qr + Qp + Q~p + Q~d
[1]
where Qt is the total dissipated heat as measured by the
microcalorimeter, Q~ is the total heat dissipated by the resistor on the cell (IR heat), Qp is the heat dissipation attributed to polarization, Q~p is the dissipation attributed to entropy, and Qsd is the heat dissipation attributed to
self-discharge. Heat flow attributed to polarization is calculated from the loaded voltage of the cell and is equal to
(Voc- V)(V/R). The entropic heat output contribution is
equal to OV/OT(-TV/R). Values of OV/OTat various depths of
discharge were extrapolated from published data on the
voltage vs. temperature dependence of BrC1 cells (10).
Table II presents average Qt, Qr, Qp, Q,p, and Q,d values
at selected depths of discharge for cells tested under 50 kfl
loads. The standard deviation of Qt at each depth of discharge is noted as well. For cells discharged under 50 kt%
loads, resistive heat dissipation accounts for approximately 78-86% of the total cell heat dissipation, while en-
16
I
0.025 mAJe.m2
(10KQ)
<
1600-
1400-
12
,.r
1200"
8
.(! <
0.012
Vem2
~20~s~)
10K
1000'
r~
g
0.0025mA/cm$
8oo-
4
600 -
1] 0 " - - ~
0 |
.001
........
400 -
0`~5
mAIc~2
(~o~1
<
, ~
.01
........
,
.1
........
Current Density (mAlcm2)
Fig. 3. Relationship between average self-discharge rate and average current density of Li/BCX cells: A
calculated from actual delivered capacity, and B .... microcalorimetry estimates of self-discharge
rote.
200 -
0
2 0
400
600
800
10 0
1
0 1400
1600
1600
2000
Capacity(mAh)
Fig. 4. Comparison of the relationship between net heat output and
discharge state of Li/BCX cells at various discharge rates.
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d. Electrochem. Soc., Vol. 137, No. 6, June 1990 9 The Electrochemical Society, Inc.
1668
4OOO
\
1~00
,
1600"
14.00
3OOO
1200
I'
v
&
'
r
Minivolts
2OO0
9
8{]0
- -
~
"(~
..~
Microwatts
[] mm
u ~
r
600 9
1000
~
400
mm
'
a
I:
0
0
Z
[]
1000
2.0
Capacity (mAh)
C a p a c i t y (Ah)
Fig. 5. Voltage and net heat dissipation as a function of delivered capacity for a Li/BCX cell discharged under a SO k~ load.
t r o p i c h e a t d i s s i p a t i o n a c c o u n t s for o n l y 1-7%, a n d h e a t
d i s s i p a t i o n d u e to p o l a r i z a t i o n a c c o u n t s for less t h a n 0.5%
of t h e t o t a l h e a t d i s s i p a t i o n . H e a t d i s s i p a t i o n d u e to selfd i s c h a r g e is e s t i m a t e d to b e 7-23% of t h e t o t a l h e a t dissip a t i o n . Cells d i s c h a r g e d u n d e r 10, 20, 100, a n d 140 k ~ exhibit similar trends, with polarization and entropy contribu t i n g s m a l l a m o u n t s of h e a t flow c o m p a r e d to h e a t
d i s s i p a t i o n d u e to s e l f - d i s c h a r g e a n d t h e resistor. I n particular, cells d i s c h a r g e d u n d e r 10 a n d 20 k ~ e x h i b i t r e l a t i v e l y
l a r g e Qr values, t h u s l e a d i n g t o a g r e a t e r d e g r e e o f e r r o r i n
n e t h e a t d i s s i p a t i o n values. F i g u r e 6 p r e s e n t s m i c r o c a l o r i m e t r y d a t a for t w o cells d i s c h a r g e d u n d e r 20 k ~ loads.
F o r t h o s e cells t h a t w e r e d i s c h a r g e d c o m p l e t e l y , h e a t
d i s s i p a t i o n d u e to s e l f - d i s c h a r g e (Qsd) w a s p l o t t e d v s . del i v e r e d c a p a c i t y a n d a fitted e q u a t i o n w a s c o m p u t e d b y t h e
u s e o f C r i c k e t G r a p h TM (7). A n e x a m p l e is p r o v i d e d i n
Fig. 6, w h e r e m i c r o c a l o r i m e t r y d a t a for cells d i s c h a r g e d
Fig. 6. Net heat dissipation as a function of delivered capacity for
two Li/BCX cells discharged under 20 k~ loads.
u n d e r 20 k ~ l o a d s are p r e s e n t e d a l o n g w i t h t h e o b t a i n e d
r e g r e s s i o n curve. T h e e q u a t i o n u s e d to fit t h e r e g r e s s i o n
c u r v e w a s Y = 80.718 + 164.51X + 1324.9X 2 - 878.47X 3.
T h e m o d e l e d e q u a t i o n w a s t h e n i n t e g r a t e d o v e r t h e life o f
t h e cell. M a t h e m a t i c a TM w a s utilized as t h e c o m p u t a t i o n a l
tool for i n t e g r a t i o n (8). T h e r e s u l t a n t v a l u e (Watt A h ) w a s
d i v i d e d b y V 2 / R to o b t a i n a n e s t i m a t e of t o t a l c a p a c i t y loss
d u e to s e l f - d i s c h a r g e as m e a s u r e d b y m i c r o c a l o r i m e t r y .
The self-discharge capacity was subtracted from the total
s t o i c h i o m e t r i c c a p a c i t y of t h e cell to o b t a i n a n e s t i m a t e o f
d e l i v e r e d capacity. T h e a c t u a l c a p a c i t i e s a n d t h o s e estim a t e d f r o m m i c r o c a l o r i m e t r y d a t a are d e p i c t e d s i m u l t a n e o u s l y i n Fig. 7 as a f u n c t i o n of c u r r e n t d e n s i t y . T a b l e III
p r e s e n t s t h e d a t a i n n u m e r i c a l format. T h e a c t u a l delivered capacities and the capacities estimated from the
m i c r o c a l o r i m e t r i c d a t a a g r e e d w i t h i n 6%. T h i s c o n f i r m s
Table II. Heat dissipation of Li/BrCI in thionyl chloride cells discharged under 50 k~q laods
Depth of discharge
(mAh)
Total heat, Qt
(~W)
Standard
deviation of Qt
(~W)
Resistive
heat, Qr
(~W)
Entropic
heat, Q~p
(t~W)
Polarization
heat, Qp
(~W)
Self-discharge
heat, Q~o
(~W)
40
290
410
680
800
1090
1330
1500
1710
1900
395
358
328
322
324
335
325
323
313
315
10
10
2
6
4
8
14
10
1
3
310
285
277
268
267
268
269
268
266
262
6
10
13
14
14
15
17
17
20
22
<1
<1
<1
<1
<1
<1
<1
<1
<1
<1
79
63
38
40
43
52
39
38
27
31
Table III. Self-discharge of lithium/BrCI in thionyl chloride cells under low-rate discharge
Load
(kn)
10
20
50
100
140
Time on test
(years)
Capacity lost due to
self-discharge (Ah)
actual vs. predicted
Delivered
capacity (Ah)
actual vs. predicted
percent
0.6
1.1
4.1
7.1
8.0a
1. ] 1/1.21
1. ] 5/1.25
0.41/0.48
0.58/0.46
NA
1.69/1.59
1.65/1.55
2.39/2.32
2.22/2.34
NA/2.08
6
6
3
5
NA
Error
a Still on test.
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J. Electrochem. Soc., Vol. 137, No. 6, June 1990 9 The Electrochemical Society, Inc.
1669
1600'
2~
1400'
2.4
o....
1200.
2.0
-....,
0.0018m~dcm2
1.6-
,-o
0
1000"
r~
800.
~,~
600-
1.2"
0.8"
0.4
"t
0.0
.001
.01
9
A
...... ~ ....
B
400 "
.1
Current Density (mA/cm2)
Fig. 7. Relationship between average delivered capacity and average
current density of Li/BCX cells: A - calculated from actual delivered capacity, and B .... microcalorimetry estimates of self-discharge
rate.
the assumption stated earlier that the measured heat flow
was due to self-discharge resulting from anode corrosion.
As further evidence that microcalorimetry is useful in
estimating cell life for lithium/BCX cells, the average rate
of self-discharge at each current drain was calculated
based on the microcalorimetric estimates of capacity loss.
These values are presented in Fig. 3 along with the values
derived from discharge data. Actual and estimated values
are in very close agreement, as would be expected in view
of the close agreement between actual and estimated delivered capacities. This further demonstrates that selfdischarge can be estimated from microcalorimetry measurements and that integration of the heat dissipation of a
cell accurately accounts for capacity loss due to nonfaradalc processes.
Since microcalorimetry accurately accounts for nonfaradaic capacity loss, it should be possible to use measured heat dissipation as a predictive tool for applications
where the current density is 0.005 mA/cm 2 or below, since
at those discharge rates, the heat dissipation is relatively
constant throughout the discharge of the cell. In order to
use microcalorimetry as a predictive tool, a different
method must be used to project the delivered capacity of
cells w h e n the total time on test is unknown. As an example, the delivered capacity of cells under discharge at
140 k ~ loads was predicted. An iterative process was employed to predict the total amount of time on test. Predictions were made assuming that the self-discharge rate
would remain constant throughout the life of the cell.
F r o m the available microcalorimetry data depicted in
Fig. 4, it can be seen that at current densities of
0.005 mA/cm 2 or less, the heat dissipation is constant
throughout discharge. For the cells on test, the fitted Qsd
vs. capacity curve depicted in Fig. 8 was integrated over
the interval of available microcalorimetry data to obtain an
estimate of self-discharge over a given time period (8). The
regression curve equation assigned by Cricket Graph was
Y = 16.987- 25.846 (lOgl0X) (7). From this estimate, the
average self-discharge rate was calculated by the methods
described above. The rate at which the cells were discharged (0.0018 mA/cm 2) was then added to the predicted
rate of self-discharge to obtain the total rate of discharge.
The theoretical capacity was divided by the predicted total
rate of discharge to obtain an estimate of the total time on
test. This value was multiplied by the rate of discharge to
obtain a projected delivered capacity value of 2.08 Ah. As
verification of this method, the delivered capacity of cells
00.0
0.2
0.4
0,6
0.8
Capacity (Ah)
Fig. 8. Net heat dissipation as a function of delivered capacity for
three Li/BCX cells discharged under 140 k ~ loads.
under discharge at 100 k~2 was also predicted based on microcalorimetry data collected over the first half of discharge. The method estimated delivered capacity of these
cells within 3.5%.
Conclusions
Residual lithium analyses have shown that nonfaradaic
capacity loss in Li/BCX cells under low rate discharge is
due to self-discharge. The study presented here furnishes
further evidence that microcalorimetry can be used to estimate self-discharge rates of Li/BCX cells, thus enabling
the prediction of cell lifetimes prior to the availability of
real-time discharge data. Knowledge of the heat output vs.
discharge rate relationship may also be useful for optimizing anode surface area of a cell. In particular, selfdischarge rates have been shown to decrease as the rate of
discharge is reduced. Microcalorimetry data collected thus
far indicate that heat dissipation of cells discharged at
average current densities below 0.005 mA/cm 2 remains relatively constant throughout life. This enables the extrapolation of total heat output from existing data. Thus, by relating heat evolution to self-discharge, microcalorimetry
can be used to predict low-rate cell longevity prior to the
availability of real-time data. The accuracy of selfdischarge estimates based on microcalorimetry has been
validated through real-time discharge data. Estimates
have been obtained that are within 6% of the actual values.
Delivered capacity projections for cells still on test after
eight years under loads of 140 k~2 will be verified upon
completion of discharge.
Acknowledgments
Much of the work leading to the design, development,
and testing of the cell described in this paper was conducted by Dr. R. M. McLean and Mr. M. J. Brookman.
Manuscript submitted Sept. 5, 1989; revised manuscript
received Jan. 5, 1990.
Wilson Greatbatch, Limited, assisted in meeting the publication costs of this article.
REFERENCES
1. P. M. Skarstad, in "Batteries for Implantable Biomedical Devices," B . B . Owens, Editor, p. 215, P l e n u m
Press, New York (1986).
2. D. Untereker, This Journal, 125, 1907 (1978).
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1670
J. Electrochem. Soc., Vol. 137, No. 6, June 1990 9 The Electrochemical Society, Inc.
3. C. F. Holmes and P. Keister, Abstract 39, p. 61, The
Electrochemical Society Extended Abstracts,
Vol. 86-2, San Diego, CA, Oct. 19-24, 1986.
4. C. F. Holmes, R. L. McLean, and C. C. Liang, in "Cardiac Pacing," G. A. Feruglio, Editor, p. 1193, Piccin
Medical Books, Padua, Italy (1982).
5. M. J. Brookman and R. L. McLean, Abstract 303,
p. 489, The Electrochemical Society E x t e n d e d Abstracts, Vol. 82-2, Oct. 17-21, 1982.
6. M. J. Brookman and R. L. McLean, Abstract 90, p. 142,
7.
8.
9.
10.
The Electrochemical Society Extended Abstracts,
Vol. 83-2, Washington, DC, Oct. 9-14, 1983.
Cricket Graph, Version 1.3, Cricket Software, Inc.,
Malvern, PA (1988).
Mathematica, Version 1.1, Wolfram Research, Inc.,
Champaign, IL (1988).
K.M. Abraham and M. Alamgir, This Journal, 134, 2112
(1987).
E. S. Takeuchi, K. J. Takeuchi, C. Bessel, and E. Cads,
J. Power Sources, 24, 229 (1988).
Nucleation of Lead Sulfate in Porous Lead-Dioxide Electrodes
Dawn M. Bernardi*
Physical Chemistry Department, General Motors Research Laboratories, Warren, Michigan 48090-9055
ABSTRACT
A one-dimensional mathematical model of a porous lead-dioxide electrode is described and used to investigate leadsulfate nucleation and growth during discharge. Derivation of a nucleation rate expression that is based on classical, heterogeneous nucleation theory is outlined. An electrochemical kinetic expression is derived based on a reaction mechanism involving elementary steps, and concentrated ternary electrolyte theory is used in formulating material-transport
equations. Nucleation and electrochemical kinetic parameters are estimated by comparison of model results with experimental results available in the literature. The interplay of nucleation and growth kinetics of lead sulfate is responsible for
the initial m i n i m u m in the voltage-time curve that is c o m m o n l y observed during constant-current discharge. The model
simulates the voltage minimum, which is referred to as the coup defouet, and calculates the degree of lead-ion supersaturation, the n u m b e r density of lead-sulfate particles, and the free energy of formation as well as the size of critical nuclei. The
model also predicts a disappearance of the voltage m i n i m u m with the addition of seed particles for lead-sulfate nucleation, which is experimentally observed. The satisfactory agreement between model and experimental results confirms
that the voltage dip is caused by a temporary oversaturation of lead ions during discharge and supports the proposed
theoretical approach.
During constant-current discharge of a fully charged
lead-acid cell, a m i n i m u m in voltage at the beginning of
the voltage-time curve is observed (1), which is often referred to as the coup de fouet. The shape of the discharge
curve has led to this French terminology, which translates
to English as "stroke of a whip." The coup de fouet is believed to be caused by a supersaturated solution of lead
ions occurring temporarily in the lead-dioxide electrode
during discharge. The duration of this voltage transient is
rather short in comparison to the full discharge time of the
battery, and the magnitude of the dip is small compared to
the terminal voltage. The effect, however, is of consequence in the design of batteries for the operation of sensitive switches (2), and a better understanding of the phenomena will fill one of the gaps in our knowledge about
these batteries.
The observation of a voltage dip during the discharge of
lead-acid batteries was first recorded in the open literature
in the early 1900's and soon after postulated to be caused
by a temporary supersaturation of lead ions of u n k n o w n
origin (2). The mechanism associated with this phenomenon has since been subject to several other explanations.
In 1955, Vinal (3) attributed it to ohmic resistance and a
sudden drop in acid concentration, which would reduce
the electrode potential. Later, in a series of papers, the
coup de fouet was shown to be associated with PbO2 electrode (4) and in particular the B-modification of the oxide
(5). Voltage minima were also demonstrated in the discharge of MnO~ and T1203 electrodes, and the coup de fouet
was suggested as being connected with expansion of the
oxide lattice (6). B6rndt and Voss (2) in 1965 presented a
relatively detailed study of the voltage dip observed in the
discharge of porous, commercial-size PbO2 electrodes,
with the supposition that the effect is associated with leadion supersaturation and PbSO4 nucleation and crystal
growth, which is now the generally accepted mechanism
(1). Slowness in the elucidation of the cause of the coup de
fouet was closely associated with uncertainties in the discharge mechanism of the PbO2 electrode; for example, solution-phase lead ions must be a reaction intermediate if
* Electrochemical Society Active Member.
their supersaturation is the cause of the voltage dip. A
solid-state diffusion discharge mechanism has been proposed (7) which would conflict with the aforementioned
cause of the coup de fouet. Recently, H~meenoja et. al. (8)
reported rotating ring-disk electrode measurements that
proved the existence of solution-phase lead ions and substantiated that they were an intermediate in the PbO2 discharge mechanism and the cause of the coup de fouet.
The reason that a voltage drop should be the consequence of an oversaturated solution of lead ions can be
seen through simple thermodynamic arguments. During
normal discharge and charge conditions, there are two
solid phases present in the lead-dioxide electrode system
(PbSO4 and PbO2, see Fig. 1) along with the electrolytic solution phase. The Gibbs phase rule can be applied at constant temperature, pressure, and H2SO4 composition to
show that the state of the system is fixed under these conditions; that is, the thermodynamic open-circuit potential
(relative to a reference electrode such as Hg/Hg2SO4) is a
constant. In a system without any PbSO4 present, one degree of freedom exists and we can expect the potential to
vary with the lead-ion concentration in the electrolyte. Of
course, our model is not formulated as an equilibrated system, but the basic principles apply in understanding the
phenomena. Early in the discharge of a PbO2 electrode
which contains virtually no lead sulfate, the acid ,concentration remains relatively constant, while lead ions, which
are the product of the overall electrochemical reaction
PbO2(~) + 4H + + 2e- --> Pb 2+ + 2H20
[I]
can reach large concentrations within the pores of the electrode. We expect the electrode potential (relative to a reference electrode) to fall in accordance with this concentration increase until the PbSO4 nucleation and growth
processes
Pb 2+ + HSO4 ---->PbSO4cs) + H +
[II]
(which are accelerated by increases in Pb z+ concentration)
can overcome the electrochemical reaction process and
thereby stabilize potential by reducing the Pb 2+ concentration. In the formulation of a mathematical description of
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