Thermodynamic parameters for Nickel-Cadmium (NiCad) and Nickel-Hydrogen (NiH2) batteries are calculated for temperatures ranging from 273.15K (0 C) to 373.15K (100 C). For both systems, we list equilibrium and thermoneutral voltages for the cells, and in the case of the NiH2 battery, these data are provide for hydrogen fugacities ranging from 0.01 to 100 (atm) to simulate the full discharged and charged states. The quality of the input thermodynamic data are assessed and the effect of assuming different cell reactions is analyzed

Challingsworth, Mark L.

Macdonald, Digby D.

English

NASA Technical Reports Server

N94-23349
THERMODYNAMICS OF NICKEL-CADMIUM AND NICKEL-HYDROGEN BATTERIES
Digby D. Macdonald and Mark L. Challingsworth
Center for Advanced Materials
The Pennsylvania State University
517 Deike Building
University Park, PA 16802
ABSTRACT
Thermodynamic parameters for Nickel-Cadmium (NiCad) and Nickel-Hydrogen (NiH2) batteries are calculated for
temperatures ranging from 273.15K (0"C) to 373.15K (100"C). For both systems, we list equilibrium and
thermoneutral voltages for the cells, and in the case of the NiH2 battery, these data are provide for hydrogen
fugacities ranging from 0.01 to 100 (arm) to simulate the full discharged and charged states. The quality of the input
thermodynamic data are assessed and the effect of assuming different cell reactions is analyzed.
INTRODUCTION
Nickel-cadmium (NiCad) and nickel-hydrogen (NiH2) batteries are used extensively in aerospace systems, because
of their relatively high energy and power densities and their excellent cycling capabilities [14]. However, given the
severe demands placed on cycling performance for satellites in low earth orbit (LEO) and recognizing the need to
keep battery weight to an absolute minimum, efforts continue to improve the cycle life particularly to high depths of
discharge. The current standard in this regard for NiH 2 batteries is a cycle life of 30,000 cycles to 50% loss in
capacity (of the nickel electrode) at 50% depth of discharge. The cycle life of NiCad batteries is not as favorable
(generally a few thousand cycles), so that these systems are commonly not employed where cycle life is the key
operational characteristic.
It is well recognized that the cycle lives of NiCad and NiH2 batteries are limited by irreversible s_uctural and
physicochemical changes that occur in the porous nickel electrodes as the batteries are cycled between the charged
and discharged states. Although the mechanistic details of the degradation processes are not well-understood,
various models have been developed that provide a good phenomenological simulation of the loss of capacity [5,6].
However, a complete understanding of the degradation mechanisms requires a careful analysis of the cell
thermodynamics so that the voltage and energy efficiencies can be placed on a rational basis. Thermodynamic data
for a variety of alkaline batteries has been published previously by Pound, Singh, and Macdonald [7] and for sealed
NiCad batteries by Hodge et al [8]. The present work recalculates and expands the thermodynamic database for the
PR6C>_OtNG PAGE BLANK NOT FK.MED
27
https://ntrs.nasa.gov/search.jsp?R=19940018876 2020-06-16T16:06:43+00:00Z
NiCad and NiH2 systems by deriving values for relevant parameters (equilibrium cell and thermoneutral potentials)
over a wide range of temperatcm (0"C- 100"C) and, in the case of NiH2, hydrogen pressure (0.01 - 100 alto).
BATFERY THERMODYNAMICS
Following conventional formalism, the cell reactions for NiCad and NiH2 batteries can be written as
and
CA+ 2 NiOOH + 2H20 = Cd(OI-P/2+ 2Ni(OH)2
1
_H 2 + NiOOH = Ni(OH)2
(1)
(2)
respectively, assuming that the charged nickel active material is NiOOH, or as
and
CA + 2NiOOH. H20 = Cd(OH)2 + 2Ni(OH)2
1
:H 2 + NiOOH. H20 = Ni(OH)2 + H20
(1')
(2")
ffNi0OH • H20 is assumed to be the active material at the nickel posidve electrode [8]. The equilibrium Voltages
for these four reactions are given by the Nemst equation as
Ape u = AEOcelI + 2.303RT
F l°gaH20 (3)
2.303RT
AEeU = AE°II + logfi_/22 (4)
F
and
= o')
AEeU 1= AEOu + 2.303RT logfb/22 2.303RT logaH20 (4')
F F
where fH2 is rite fugacity of hydrogen, all20 is the activity of water, and the standard celi+voltages are given by
.AEOcell o= -AGcell / nF (5)
28 !
L
OAGcell, n, and F are the change in standard Gibbs energy for the cell, the number of electrons involved in the cell
reaction, and Faraday's constant, respectively. The change in standard Gibbs energy for the cell is
AGcell =
Products Reactants
where AfG_ is the standard Gibbs energy of formation of component I, n is the stoichiometric coefficient for the
reaction, and subscripts P and R refer to "products"and "reactants,"respectively, in the cell reactions (i.e. Reactions
(1),(2),(l'),and(2')).
A full assessment of the thermodynamics of a battery requires the estimation of the thermoneutral potential of the
cell, defined as
and hence
TAEcell = -/_J-lcell / rib (7)
= AEcell - T
(8)
T
Using standard thermodynamic identifies, we derive expressions for AEcell for the four cells of interest as
and
T R_T 
AEcell'l = 2F F L 3T
(9)
T AH_ (10)
AEcell'2 = F
T AH_, (11)
AEceU'I" = 2F
T AH_, + RT 2 [Olnalt:_O]AEcell'2' =- F F" L 0T
(12)
where AH_ is the change in standard enthalpy for Reaction k. Note that a term involving the fugacity of hydrogen
does not appear in Equations (10) and (11) [corresponding to Reactions (2) and (2")], because we have assumed that
fH2 is a constant, independent of temperature.
29
THERMODYNAMICDATA
Thethermodynamicdataemployedinthisstudy are summarized in Tables 1 and 2, together with the sources from
which they were taken. Heat capacities for Ni(OH)2, Cd(OI02, NiOOH •I-I20, and NiOOH had to be estimated
using C_/S o ratios, which are found to be constant for given classes of compounds [7]. The value adopted for the
Gibbs energy of formation for Cd(OH)2 was adjusted slightly from thatgivenby Naumov et al (Ref. (a), Table 1),
474.5 kJ/mol, so as to yield the observed equilibrium voltage for the NiCad battery [1.45V (2)]. The accuracies of
the various thermodynamic quantifies summarized in Table 1 are largely unknown and are difficult to estimate
without detailed information on the original experiments from which they are derived.
Noting that heat capacities are generally expressed in the form
o = A + BT + CT "2 (13)Cp
we derived expressions for the Gibbs energy and enthalpy of formation of any given compound at temperature T as
¢
follows.
F f "r
tmo)jL
[ ][1 ][(T2-'I"°2 T(T-T o) Cf "i" _ T _oo -1+Bf. _ + _, T 1
(14)
and
AfH'_ = AfH'_° + Af(T- T°) + Bf IT2 - T2]- C(_2t To1)
- -
(15)
(16)
where afS_o and AfH_- o are the enux_py and enthalpy 0f formation at the reference temperature (T O= 298.15K)
and Af, Bf, and Cfare the coefficients in Equation (13) for the formation of the compound of interest.
Thermodynamic parameters of formation calculated using Equations (14) to (16) for various active components in
NiCad and NiH2 batteries are summarized in Table 3 as a function of temperature from 273.15K (0'C) to 373.15K
30
(100'C).NotethatnovaluesaregivenforCd and H2 because, by definition, the parameters of formation are zero at
all temperatures.
Calculation of the equilibrium and thermoneulral cell voltages requires a knowledge of the activity of water, which
for 8 molal KOH can be expressed as (7)
In all20 = -6.345750 + 6.125771 x 103 / T- 2.093874 x 106 / T 2
(17)
+2.324516 x 108/T 3
The activity of water for this electrolyte ranges from 0.514 at 263.15I( to 0.618 at 393.15K.
The data summarized in Table 3 were used to estimate equilibrium and thermoneutral cell voltages for NiCad and
NiH2 batteries as a function of temperature, as given in Tables 4-7. We should note, at this point, that the
thermodynamic data for NiOOH •H20 are poorly known, so that lower confidence should be placed in the
potentials calculated from Reactions (1') and (2') than is those calculated from Reactions (1) and (2). Accordingly,
in this work, we will emphasize the thermodynamic calculations that involve NiOOH as the oxidized, active material
at the positive electrodes ofNiCad and NiH2 batteries.
DISCUSSION
As seen from the data summarized in Tables 4 and 5, the equilibrium potentials for NiCad and NiH2 batteries with
8m KOH electrolyte decrease with increasing temperature and, for the latter system at any given temperature,
increase with increasing hydrogen partial pressure. The dependence of AEell on temperature results directly from
the entropy and heat capacity changes for the cell reactions as well as from the change in water activity in the
electrolyte, whereas the dependence on hydrogen pressure (in the case of NiH2 batteries) results directly from the
thermodynamics of the negative electrode. We also note that much larger changes in AEcell with temperature are
predicted if the oxidized nickel phase is assumed to be NiOOH •H20 rather than NiOOH, but the poor quality of the
data for the former precludes any in-depth analysis of this difference.
Thermoneutral potentials for NiCad and NiH2 batteries are listed in Tables 6 and 7. The thermoneutral voltage
corresponds to that voltage that the cell would have to operate at so that the entropic dissipation of energy is zero.
Of course, the data calculated in this work do not include the various irreversible sources of energy dissipation,
associated with heat generation due to the internal cell resistance and arising from the reactions occurring at the
31
electrodeson charging and discharging. These irreversible effects are best la'eated using irreversible thermodynamic
methods of the type proposed by Ratjke et al [9].
For both the NiCad and NiH2 batteries, lhe thermoneutral voltage is greater than the equilibrium cell voltage at
equivalent temperatures and hydrogen pressure (for the Nil 2 system). This relationship arises from the fact that the
entropy changes for the cell reactions on discharge are negative, corresponding to exothermic processes. Likewise,
e T
on charging both cells are endothermic provided that the voltage lies between AI_-Celland AP-cell.
Finally, we note that the equilibrium cell potentials calculated in this work for the NiH2 battery are in good
agreement with our previous calculations and with experimental data [7]. A similar comparison cannot be made
with experimental data for NiCad batteries because we have used these data to adjust the Gibbs energy of formation
of Cd(OI-l)2 used in the calculafionsl However, it is worth noting that our equifibrium cell potential at 25"C (1.45V)
is significantly more positive than that calculated by Hodge et al [8] (1.29V). This difference may be attributed to
the large uncertainty in the Gibbs energy of formation for NiOOH • H20 [8] and to the fact that Hodge et al [8] did
not apply a correction for the activity of water. Clearly, the calculated value of Hodge et al [8] is much lower than
the open circuit voltage of 1.45V quoted by Halpert [2]. Because irreversible processes within the cell are expected
to reduce the measured open circuit voltage below the equilibrium cell voltage, it is evident that the calculations of
Hodge et al (8) are at odds with experiment.
REFERENCES
1. P.C. Milner and U.B. Thomas, in "Advances in Electrochemistry and Electrochemical Engineering," Vol. 5, p. 1
(Interscience, N.Y., 1967).
2. (3. Halpert, J. Power Sources, 15, 119 (1985).
3. J.K. McDermott, J. Power Sources, 18, 265 (1986).
4. L. Miller, J. Brill, and G. Dodson, J. Power Sources, 29, 533 (1990).
5. D.D. Macdonald, B.G. Pound, and S.L l_eahart, J. Power Sources, 29,447 (1990).
6. D.D. Macdonald, M. Urquidi-Macdonald, S.D. Bhatka, and B.G. Pound, J. Electrochem. Soc., _ 1359
(1991).
7. B.G. Pound, R.P. Singh, and D.D. Macdonald, J. Power Sources, 18, 1 (1986).
8. B.LR. Hodge, R. Bonnaterre, and F. Putois, J. Power Sources, 7.,211 (1975).
9. $.K. Ralkje, T. lkeshoji, and K. $yvorad, J. Elocm3chem. So¢., 137, 2088 (1990).
32
F
TABLE 1
Thermodynamic Properties of Components at 298.15K
Component
Ni
Cd
O2
H_
H20
Ni(OH_
NiOOH
NiOOH.H20
Cd(OI-I'D
AfGo
0d/mol)
Ar8°
0d/tool)
Also (0
0/K.mol)
S°
(J/K.mol)
0 0 0 29.87
0 0 0 51.756
0 0 205.030
0 0 0
-163.174
-277.474
-233.207
-219.478
-299.496
130.574
69.915
88D
66.98
(0
(a)
(t)
(a)
(a)
(0
O))
150.6_ (c)
-237.178
-459.070
-321.7
-564.422
-482,347
(a)
(b) .
(b) .
(c)
-285.828 (_
-541.799(_
!-391.231 ((I)
-629.859 (d)
-571.642 ((I) 87.864 (a)
(a) G.B. Namnov, et al, Handbook of Thermodynamic Data, USGS-WRD-74-001, US Geol.
Co)P.G. Pound, R.P. Singh, & D.D. Macdonald, L Powez Sources, 18, 1 (1986).
(c) BJ.R. Hodge et al, L Power Somr, es, 7, 211 (1975).
((1)Esfinmted from AfH ° = At-G ° + TAfS °.
(e) Calculated for the fot'malion reaction from the elements.
(f) D.D. Wagman et al, J. Phys. Chem. Ref. Data, 11, SuppL No. 2 (1982).
AlCp. (a,b,f)
0dlmol)
16.987 + 0.02946T
22.217 + 0.012301T
29.957 + 0,00414T - 1.674 x 105 T"2
27,2797 + 0.0032635T + 0.50208 x 105 "1`-2
10.669 + 0. ,04.T2.84T-6.90308 x 105T "2
18.106 - 0.03686T + 1.1719 x 10-5T 2
30.186 - 0.03523T + 1.423 x 105"1`.2
87.388- 0.082844T + 8.661 x 105T "2
12.726 - 0.0197T + 1A7192 x 105T "2
Survey, 1974.
TABLE 2
Heat Capacidcs of Active Compounds (a,b,f, Table 1)
o0d/tool)Compound Cp
H20
Ni(OH)2
NiOOH
NiOOH.H20
Cd(OI-I) 2
52.928+ 47,614x I0"3T - 7.238x 105 T -2
92.33
90.77
200.09
92.18
33
TABLE 3
Thermodynamic Parameters of Formation for Active Components in NiCad
and NiH 2 Batteries as a Function of Temperature
Temperaaa'e G_bs Energy Enthalpy Enlropy
(K) (J/tool) (J/tool) (J/K-tool)
Ni(OI-_2
273.15 -466014.9 -541988.4 -278.1382
283.15 -463234.9 -541909.9 -277.8557
293.15 -460457.7 -541835.1 -277.5959
298.15 -459070 -541799 -277.474
303.15 -457682.9 -541763.9 -277.3572
313.15 -454910.5 -54 1696.4 -277.1382
323.15 -452140.1 -541632.6 -276.9376
333.15 -449371.7 -541572.5 -276.7544
343.15 -446605 -541516.1 -276.5875
353. i 5 -443839.8 -541463.4 -276.436
363.15 -441076.2 -541414.3 -276.299
373.15 -438313.8 -541368.9 -276.1758
NiOOH
273.15 -327593.5 -391776.8 -234.9745
283.15 -325230.3 -391554.5 -234.237
293.15 -322874.9 -391337 -233.5396
298.15 -321700 -391230 -233.205
303,15 -320526.8 -391124.2 -232.8793
313.15 -318185.7 -390915.9 -232.2536
323.15 -315851.2 -390712 -231.66
333.15 -313522.9 -390512.6 -231.0964
343.15 -311200.5 -390317.4 -230.5608
353.15 -308883.8 -390126.4 -230.0517
363.15 -306572.3 -389939.7 -229.5673
373.15 -304266 -389757 -229.1063
NiOOH.H20
273.15 -570232.1 -631718.9 -225.1038
283.15 -567888A -630963.5 -222.763
293,15 -565571.2 -630224 -220.5461
298.15 -564422 -629860 -219.48 l
303.15 -563278.9 -629499.7 -218.4432
313.15 -561010.3 -628789.9 -216.4453
323.15 -558764.1 -628093.9 -214,5448
333.15 -556539.2 -627411.5 -212.7346
343.15 -554334.6 -626742 -211.0085
353.15 -552149A -626085.1 -209.3611
363.15 -549982.6 -625440.3 -207.7873
373.15 -547833A -624807.5 -206.2827
z
34 b_
E
TABLE 3 (continued)
Tcmperatm-e
(K)
Gibbs Energy
(J/tool)
Enthalpy
(J/rooD
Entropy
(J/K-mo0
273.15
283.15
293.15
298.15
303.15
313.15
323.15
333.15
343.15
353.15
363.15
373.15
273.15
283.15
293.15
298.15
303.15
313.15
323.15
333.15
343.15
353.15
363.15
373.15
.489876.4
.486862.4
.483851.4
.482347
.480843.3
-477837.8
.474834.8
.471834
.468835.5
.465839
.462844A
.459851.5
-241078.8
-239514.8
-237955.6
-237178
-236401.7
-234852.9
-233309.6
-231771.8
-230239.5
-228712.8
-227191.8
-225676.6
Cd(OH)2
H20
-571855A
-571767.8
-571683.2
-571642
-571601.5
-571522.6
-571446A
-571372.9
-571302.1
-571233.7
-571167.9
-571104.5
-286186.8
-286051.7
-285906A
-285830
-285751.3
-285587
-285414
-285232.7
-285043A
-284846.5
-284642.2
-284430.8
-300.1235
-299.8593
-299.6129
-299A96
-299.383
-299.1684
-298.9677
-298.7802
-298.6049
-298.441
-298.2878
-298.1446
-165.1239
-164.3391
-163.5557
-163.165
-162.7751
-161.9981
-161.2256
-160A58
-159.6957
-158.939
-158.188
-157.4429
35
TABLE 4
Calcuhted Equih_rium Cell Voltages for NiCad Battcri_ as a Function of Temperature
T/K Reaction (1) Reaction(1")
273.15 1.461 1.459
283.15 1.457 1.438
293.15 1.453 1.418
298.15 1.450 1.408
303.15 1.448 1.397
313.15 1.444 1.377
323.15 1.439 1.356
333.15 1.435 1.334
343.15 1.430 1.313
353.15 1.425 1.292
363.15 1.420 1.270
373.15 1.415 1.248
36
TABLE 5
Calculated Equifibrium Cell Voltages for NiH2 Batteries as a Function
of Temperatm_ and Hydrogen Pressure
PH21atm
T/K 0.01 0.1 1.0 10.0 100.0
Reaction 2
273.15 1.380 1.408 1.435 1.462 1.489
283.15 1.374 1.402 1.430 1.458 1.487
293.15 1.368 1.397 1.426 1.455 1.484
298.15 1.365 1.394 1.424 1.453 1.483
303.15 1.361 1.391 1.422 1.452 1.482
313.15 1.355 1.386 1.417 1.448 1.479
323.15 1.348 1.381 1.413 1.445 1.477
333.15 1.342 1.375 1.408 1.44 1 1.474
343.15 1.335 1.369 1.403 1.437 1.471
353.15 1.329 1.364 1.399 1.434 1.469
363.15 1.322 1.358 1.394 1.430 1.466
373.15 1.315 1.352 1.389 1.426 1.463
Reaction f2_)
273.15 1.459 1.432 1.405 1.378 1.351
283.15 1.440 1.412 1.384 1.356 1.327
293.15 1.420 1.391 1.362 1.333 1.304
298.15 1.410 1.381 1.351 1.322 1.292
303.15 1.401 1.371 1.341 1.311 1.281
313.15 1.382 1.351 1.320 1.289 1.258
323.15 1.362 1.330 1.298 1.266 1.234
333.15 1.342 1.309 1.276 1.243 1.210
343.15 1.322 1.288 1.254 1.220 1.186
353.15 1.302 1.267 1.232 1.197 1.162
363.15 1.282 1.246 1.210 1.174 1.138
373.15 1.262 1.225 1.188 1.151 1.114
37
T/K
TABLE 6
Calculated ThermoneuWal Cell Voltages for NiCad BaRcfies as a
Function of Te_npcrature
T
Reacdon (1) Reaction (1')
273.15
283.15
293.15
298.15
303.15
313.15
323.15
333.15
343.15
353.15
363.15
373.15
1.580
1.574
1.570
1.569
1.568
1.568
1.569
1.572
1.575
1.580
1.585
1.591
2.033
2.040
2.046
2.050
2.053
2.059
2.065
2.071
2.077
2.083
2.089
2.095
E
38
TABLE 7
CalculatedThermoneutralCellVoltagesforNiH 2 Bauericsasa Functionof
Temperatureand Hydrogen Pressure
PH2/atm
T/K 0.01 0.1 1.0 10.0 100.0
Rc_on 2
273.15 1.611 1.584 1.557 1.530 1.503
283.15 1.615 1.586 1.558 1.530 1.502
293.15 1.618 1.589 1.560 1.531 1.502
298.15 1.620 1.590 1.561 1.531 1.501
303.15 1.621 1.591 1.561 1.531 1.501
313.15 1.625 1.594 1.563 1.532 1.501
323.15 1.628 1.596 1.564 1.532 1.500
333.15 1.632 1.599 1.566 1.533 1.500
343.15 1.635 1.601 1.567 1.533 1.499
353.15 1.639 1.604 1.569 1.533 1.498
363.15 1.642 1.606 1.570 1.534 1.498
373.15 1.645 1.608 1.571 1.534 1.497
273.15 2.065 2.038 2.011 1.983 1.956
283.15 2.081 2.053 2.025 1.997 1.969
293.15 2.094 2.065 2.036 2.007 1.978
298.15 2.100 2.071 2.041 2.012 1.982
303.15 2.106 2.076 2.046 2.016 1.986
313.15 2.116 2.085 2.054 2.023 1.992
323.15 2.124 2.092 2.060 2.028 1.996
333.15 2.131 2.098 2.065 2.032 1.999
343.15 2.137 2.103 2.069 2.035 2.001
353.15 2.142 2.107 2.072 2.037 2.002
363.15 2.156 2.110 2.074 2.038 2.002
373.15 2.149 2.112 2.075 2.038 2.001
39



Thermodynamics of nickel-cadmium and nickel-hydrogen batteries

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