Embed Size (px)
Citation preview
NASA
Technical
Memorandum
NASA TM- Io35Bo
P //y
TESTING AND ANALYSES OF ELECTROCHEMICAL
CELLS USING FREQUENCY RESPONSE
Center Director's Discretionary Fund Final Report,
Project No. 90-18
By D.L. Thomas and O.A. Norton Jr.
Information and Electronic Systems LaboratoryScience and Engineering Directorate
March 1992
(NASA-TM-103580) IESTING AND ANALYSES OFELECTROCHFMICAL C_LLS USING FREQUENCY
RESPONSE Final Report, I Feb. - 31 Dec. 1991(NASAl 23 p CSCL 09C
/kSANational Aeronautics andSpace Administration
George C. Marshall Space Flight Center
G _/33
N92-23_31
Unclas
0086858
MSFC - Form 3190 (Rev. May 1983)
REPORT DOCUMENTATION PAGEForm Approved
OMB No, 0704-0188
Public repOrt.ng burden for this collection of information is estimated to average 1 hour Der response, including the time for reviewing Instructions, searching existing data sources,
gathering and maintaining the data needed, and completing and revlewtng the collection of information. Send comments re_arding this burden estimate or any other asl_)ect of this
collection of information, nduding suggestions for reducing this burden, to WashingtOn Headquarters Services, DirectOrate roT information Operations and Reports, 1215 Jefferson
Davis Highway, Suite 1204. A rlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduce on Pro ect (0704-0188), Washington, OC 20503.
1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE | 3. REPORT TYPE AND DATES COVERED
March 1992 J Technical Memorandum
4. TITLE AND SUBTITLE 15. FUNDING NUMBERS
Testing and Analyses of Electrochemical Cells Using Frequency
Response----Centea, Director's Discretionary Fund Final Report, Projec!,,.No. 90-18r. AUTHOR(S)
O.A. Norton, Jr. and D.L. Thomas*
7. PERFORMINGORGANIZATIONNAME(S)AND ADDRESS(ES)
George C. Marshall Space Flight Center
Marshall Space Flight Center, Alabama 35812
9. SPONSORING/MONITORINGAGENCYNAME(S)AND ADDRESS(ES)
National Aeronautics and Space Administration
Washington, DC 20546
8. PERFORMING ORGANIZATIONREPORT NUMBER
10. SPONSORING / MONITORINGAGENCY REPORT NUMBER
NASA TM-I03580
11. SUPPLEMENTARyNOTES
Prepared by Information and Electronic Systems Labom_ry, Science and Engineering Directorate.
*University of Alabama, Huntsville
12a. DISTRIBUTION/AVAILABILITYSTATEMENT
Unclassified-- Unlimited
12b. DISTRIBUTION CODE
13. ABSTRACT (Maximum 200 words)
The feasibility of electrochemical impedance spectroscopy as a method for analyzing battery
state of health and state of charge was investigated. Porous silver, zinc, nickel, and cadmium
electrodes as well as silver/zinc cells were studied. State of charge could be correlated with impedance
data for all but the nickel electrodes. State of health was correlated with impedance data for two silver/
zinc cells, one apparently good and the other dead. The experimental data were fit to equivalent circuit
models.
14. SUBJECTTERMS
Impedance spectroscopy on silver, cadmium, nickel, and zinc electrodes.
17. SECURITYCLASSIFICATION18. SECURITYCLASSIFICATION19. SECURITYCLASSIFICATIONOF REPORT OFTHISPAGE OFABSTRACT
Unclassified Unclas sifted Unclas sifted
15. NUMBER OF PAGES
2316. PRICE CODE
NTIS
20. LIMITATIONOFABSTRACT
Unlimited
Standard Form 298 (Rev 2-89)NSN 7540-01-280-5500
TABLE OF CONTENTS
Page
INTRODUCTION ............................................................. , ........................................................... 1
EXPERIMENTAL ...................................................... , .................................................................. 1
MATHEMATICAL MODELING .............................................................................................. 2
Equivalent Circuit Analysis .............................................................................................. 2Numerical Finite Difference Models ............................................................................... 5
RESULTS AND DISCUSSION .................................................................................................... 5
Silver/Zinc Cells ................................................................................................................ 5
Nickel/Cadmium Cells ....................................................................................................... 6
CONCLUSIONS ............................................................................................................................ 7
REFERENCES ............................................................................................................................ 17
°°,
UlPRIECED_NG PAGE BLANK NOT FILMED
LIST OF ILLUSTRATIONS
Figure
1.
2.
3.
t
.
.
7_
.
.
10.
11.
12.
13.
14.
15.
16.
Title
Diagram of the experimental apparatus ....................................................................
Equivalent circuits used in impedance modeling ........................................................
Bode magnitude plot of porous silver electrode (169 cm 2) impedance as a
function of state of charge ............................................................................................
Bode angle plot of porous silver electrode (169 cm 2) impedance as a
function of state of charge ............................................................................................
Bode magnitude plot of porous zinc electrode (169 cm 2) impedance as a
function of state of charge ............................................................................................
Bode angle plot of porous zinc electrode impedance (169 cm 2) as a
function of state of charge ............................................................................................
Comparison of discharged silver/zinc cell impedance for a good cell and a
dead cell (Bode magnitude plot) ................................................................................
Comparison of discharged silver/zinc cell impedance for a good cell and a
dead cell (Bode angle plot) ..........................................................................................
Comparison of charged silver/zinc cell impedance for a good ceil and a
dead cell (Bode angle plot) ..........................................................................................
Comparison of charged silver/zinc cell impedance for a good cell and a
dead cell (Bode magnitude plot) .................................................................................
Comparison of experimental and equivalent circuit impedance for a (169 cm 2)
charged silver electrode (Bode magnitude plot) .........................................................
Comparison of experimental and equivalent circuit impedance for a (169 cm 2)
discharged silver electrode (Bode angle plot) ............................................................
Bode magnitude plot of porous cadmium electrode (230 cm 2) impedance as a
function of state of charge .............................................................................................
Bode angle plot of porous cadmium electrode (230 cm 2) impedance as a
function of state of charge .............................................................................................
Comparison of experimental and equivalent circuit impedance for a charged
cadmium (230 cm 2) electrode (Bode magnitude plot) ................................................
Comparison of experimental and equivalent circuit impedance for a charged
cadmium (230 cm 2) electrode (Bode angle plot) .........................................................
iv
Page
1
4
9
9
10
10
11
11
12
12
13
13
14
14
LIST OF ILLUSTRATIONS (Continued)
Figure
17.
18.
Title
Comparison of experimental and equivalent circuit impedance for a nickel
electrode (230 cm 2) (Bode magnitude plot) ...............................................................
Comparison of experimental, and equivalent circuit impedance for a nickel
electrode (230 cm 2) (Bode angle plot) ........................................................................
Page
15
15
V
TECHNICAL MEMORANDUM
TESTING AND ANALYSES OF ELECTROCHEMICAL CELLS
USING FREQUENCY RESPONSE
Center Director's Discretionary Fund Final Report, Project No. 90-18
INTRODUCTION
This report presents the research performed for NASA-MSFC during the period from
February 1 to December 31, 1991, under contract No. NAS8-36955-114. The objective of this project
was to investigate the feasibility of using frequency response techniques for enhancing destructive
physical analysis and for nondestructive testing of aerospace battery electrodes. Nickel, cadmium,silver, and zinc electrodes were tested by imposing alternating current upon the electrodes and mea-
suring the magnitude and phase of the response voltage. This yields an impedance spectrum for the
battery electrode from which electrochemical kinetic, double-layer capacitance, and mass transfer
effects can be characterized. Frequencies from 10 kHz to 0.1 mHz were used in the testing.
EXPERIMENTAL
Figure 1 shows a diagram of the experimental apparatus. The centerpiece is a Schlumberger
model 1250 frequency response analyzer (FRA) and model 1286 electrochemical interface (EI). The
FRA contains a signal generator, the output of which can modulate the voltage or current output of
the EI. The FRA also has two signal inputs which are connected to the two analog outputs of the EI,
proportional to the cell current and the electrode potential.
Apple II Cemlmt erand GPIBInterf_©e
T
Counter
Itdaence 2
Reference 1
EI W.T_I
Anelo9
Oetjpet:s
1 fi_mai Sisal
Output lnl_t_
FR.A
Figure 1. Diagram of the experimental apparatus.
Thebatteryelectrodeswereplacedin prismaticcells fabricatedfrom Plexiglas.Thesecellstypically containedoneworking electrodeandone or two counterelectrodes.The working electrodepotentialwasmeasuredrelative to a referenceelectrodethat wasalso in the ceil. Only a smallamountof current,on theorder of microamperes,is drawnfrom the referenceelectrodeduring poten-tial measurements,hencethe working electrodepolarizationcanbe measuredwithout interferencefrom the counterelectrode.A silver referenceelectrodewasusedfor silver and zinc working elec-trodemeasurements,while a nickel referenceelectrodewasusedfor nickel andcadmiumelectrodemeasurements.
TheFRA andEI werecontrolledby anApple II computerthroughaGPIB interface.Programswritten in Applesoft Basicwereusedto control theamplitudeandfrequencyduring logarithmicsweepsof the working electrodeimpedanceversusfrequency,andto control theEI during chargeand dischargeof thecells. The resultsweredisplayedon the computerscreenandrecordedin anotebookfor processing.Bode magnitudeplots (impedancemagnitudeversuslog frequency)andBode angleplots (impedancephaseangleversuslog frequency)were usedto representthe data.
Frequency response analysis is valid only for linear systems, but electrochemical parameters
such as interfacial resistance, double-layer capacitance, and diffusion (Warburg) impedance are
strong functions of potential. Hence, it is important that the amplitude of the voltage response be
small. Each of the above named impedances can be treated as constant if the voltage amplitudedriving current through that impedance does not exceed 5 mV. The computer programs were written
so that the total working electrode voltage amplitude was about 5 mV, thus the amplitude through
the individual impedances would be no larger than this maximum permissible value.
MATHEMATICAL MODELING
This section briefly summarizes the modeling techniques for analyzing impedance data. More
complete presentations can be found in the literature. 1 Two techniques are reported---equivalent
circuit analysis and finite difference numerical analysis. Most of the work in this project used the f'u'st
technique, but work with the second technique was begun.
Equivalent Circuit Analysis
The traditional approach to electrochemical impedance data is to model it in terms of equiva-
lent electrical circuit elements, fitting the experimental data to the circuit with the method of least
squares. Equivalent circuit elements used in this work will be discussed briefly.
The double-layer capacitance (Cd) of the electrode/solution interface is usually modeled as a
pure capacitance. The double layer itself is a solution layer, about 10 to 20/_ thick, adjacent to the
electrode surface which can be charged due to (1) nonrandom alignment of dipoles near or at the
electrode surface or (2) preferential adsorption of either the anion or cation at the electrode surface.
This capacitance is relatively large, on the order of 10 -5 F/cm 2, and is strongly potential dependent,
but can be treated as constant for potential variations of the order of 5 mV or less. 2
There are two electrochemical phenomena that can be modeled as pure resistance with no
reactive component: ohmic electrolyte resistance and Faradaic resistance, the ohmic electrolyte
resistance Rta is usually linear over the entire range of potential and is simple to analyze. In the case
2
of alkaline aerospacebatteries,the electrolyteconductivity is quite high so that R_ is low. The
Faradaic resistance RF is the resistance to charge transfer across the electrode/electrolyte interface
and is also known as the kinetic resistance. It is highly nonlinear since the relationship between
electrode reaction rate (current density) and interfacial potential difference is exponential, but the
exponential relationship can be linearized for potential variations of about 5 mV or less.
The Warburg impedance is caused by concentration gradients in the mass transfer boundary
layer (thickness of 100 l.tm order of magnitude) adjacent to an electrode, has both resistive andreactive components, and increases as frequency decreases. This impedance becomes appreciable
when the frequency is low enough that significant depletion of reactants or accumulation of products
occurs during the anodic or cathodic half of a sinusoid. The Warburg impedance for an electrode in a
large excess (semi-infinite) of solution is
Zw = cr/(J'ogD) °'5 , (1)
where D is the diffusion coefficient, o9 is the frequency, and cr is the Warburg coefficient,
cr= RT/Cb(nF) 2 , (2)
R is the gas constant, T the absolute temperature, Co the bulk concentration, n the stoiciometricnumber of electrons transferred, and F is Faraday's constant (96,487 Coulombs/mole electrons). The
phase of the Warburg impedance is -45% and the magnitude is proportional to the inverse square
root of frequency. More complex expressions are required when there is not excess solution or whenthere is more than one diffusing species contributing to the impedance. An exponential relation
between concentration and potential (the Nernst equation or something similar) means that this
impedance is also highly nonlinear but can be linearized for voltage amplitudes less than 5 mV.
Another circuit element has gained popularity in recent years, especially when the data to be
analyzed does not fit simple circuit elements, is the constant phase element (CPE). It has themathematical form
Zcpe = A(jw) m , (3)
where A and n are constants that can be fit to experimental data. The impedances Ru, RF, Cd, and Z_
can be thought of as CPE's where m is a theoretical value. The CPE can be used to account for com-
plex phenomena such as coupled diffusion effects or porosity fluctuations. It is often used as an
empirical fitting device and has the disadvantages associated with such tools. However, if the alter-native is an equivalent circuit with an excessive number of elements (circuits with 15 or 20 elements
have been proposed in some systems without physical explanations of the elements) then the CPE
may be an attractive alternative.
Figure 2a shows a simple equivalent circuit that has been used often. Ca is considered paral-
lel to R/and Zw, forming _in equivalent interfacial impedance that is in series with the R_. The justifi-cation cited is that the first three can only be determined by measurements at an interface. However,
since Rf and Ca are double-layer phenomena while Zw is a diffusion layer phenomena (orders ofmagnitude thicker than the double-layer), the circuit of figure 2b seems more physically realistic.
3
a)
C d
Electrode Reference
Su__ r°de
R R_
f Z = ,_(ju) -°-5
b)
C dElect rode Reference
Z = o (ju)-°-s R ORf
c)
Electrode
Surface
_'__'___ Reference
RQ RO R( T RO
d)
CfElectrode . Reference
Z = A(jw) n R QRf
Figure 2. Equivalent circuits used in impedance modeling.
4
The two preceding equivalent circuits are for smooth planar electrodes. Battery electrodes
usually are porous electrodes in which there is pore electrolyte resistance as well as the interfacial
impedances discussed in the preceding paragraphs. Figure 2c shows the transmission line modelthat is often used to model porous electrodes, where R_ is the pore electrolyte resistance and Z1
represents the collective interfacial impedances. The impedance of this electrode, where there is nodirect current bias current and no concentration gradients along the pore axis, 3 is
Zp = cosh (mL)lOcegm sinh (mL)) , (4)
where
m 2 = aDCerfZi , (5)
a is the interfacial surface area per unit volume and _¢e.rfis the effective conductivity of the electrolyte.
In the limit of small mL
Zp = ZllaL , (6)
while in the limit of large mL
Zp = llregm . (7)
At this latter limit, the phase angle of Z1 is halved so that the double-layer capacitance has an
apparent phase angle of -45 ° while semi-infinite Warburg impedance has an angle of-22.5 °
The equivalent circuit for Z1 used most in this study is shown in figure 2d, and is similar to
figure 2b except that the Warburg impedance was replaced by a CPE and the ohmic resistance wasdeleted. Also, almost all the phase angles measured were less than zero (capacitive reactance),
and, when it is said that a phase angle increases, it is referring to the magnitude of the angle.
Numerical Finite Difference Models
The physics and chemistry that govern battery electrode operation can be expressed in theform of coupled differential equations with much greater clarity and flexibility than is possible using
equivalent circuit techniques. In particular, complicated phenomena that would otherwise get lumpedinto CPE's can be modeled in this way. Numerical finite difference solutions for models of charging or
discharging batteries abound in the literature. However, these techniques have not been widely
utilized to analyze impedance data.
RESULTS AND DISCUSSION
Silver/Zinc Cells
A cell consisting of one silver and one zinc electrode from a Yardney 50-Ah battery wasassembled and tested. The reference electrode was an anodized silver wire that was connected to
the silver working electrode during cycling. The cell was cycled twice, with discharge at 100 percent
5
of measuredcapacity,andthe impedancespectrumof eachelectrodewasmeasuredat 100,75, 50,25, and 0 percentstatesof charge(SOC).
Figures3 and4, respectively,are theBode magnitudeandangleplots for the silver electrodeduring dischargeon the secondcycle. It showsa trendof decreasingmagnitudeandphaseanglewithincreasingstateof chargeat low frequency,reflecting increasedmasstransfer impedance,althoughmost of the lines crossat 3 mHz. Thesegeneraltrendswereobservedin both cycles.Figures 5 and6 aretheplots for the zincelectrodeduringdischargeon the secondcycle. In this case,the fullychargedstatehas the highestimpedancemagnitudeandphaseangle.In both electrodesit seemsthat thebaremetal in contactwith solutionhasthehigherimpedance,while themetal with the fullyoxidized surfacehasthe lowest impedance.
Testswere also madewith two Yardney 150-Ahcells.Thesecells had beencycled at least100 times, and, as received, had rest potentials of 1.6 V (cell No. 1) and 0.3 V (cell No. 2).
Impedance measurements were first made for the two cells as received and shown in figures 7 and 8.
Cell No. 2 had a much higher low-frequency impedance. It is thought that the zinc electrode morphol-
ogy in this cell had deteriorated, reducing the zinc active surface area and increasing the mass
transfer limitations. The cells were then charged to 1.8 V rest potential, and spectra were again runand are shown in figures 9 and 10. Charging increased the magnitude of the impedance for both cells
but caused the phase angles to become less negative at low frequency. The work reported in theprevious paragraph showed that impedance magnitude is highest for bare metal electrodes (the zinc
electrode in this case), hence the zinc electrode impedance increases more than the silver electrode
impedance decreases during charge. It is also interesting to note that the charged cell has positive
phase angles at high frequency. It has been shown in other systems 14 5 that this can result from
nonelementary electrochemical reactions. This most likely occurs at the zinc electrode in which the
reaction product, zincate ion, is quite soluble in the electrolyte solution.
Figures I 1 and 12 compare the experimental results for the impedance of a discharged silver
electrode with the best fit to the equivalent shown in figure 2d at the limit given by equation (6). The
circuit seems capable of following the trends in the magnitude, while the maximum angle discrepancy
is about 0.25". Table 1 gives values for the equivalent circuit parameters. The parameter aC, which is
the capacitance per unit volume, is a figure of merit that characterizes the electrochemically activesurface area.
Nickel/Cadmium Cells
Impedance spectroscopy was used by Armstrong et al. 6 and Armstrong and Edmondson 7 to
study cadmium electrodes while Lenhart et al. 8 have studied porous nickel electrodes. Ni-Cd cell
studies have been performed by Sathyanarayana et oal. 9 and Zimmerman et al.lo
A cell consisting of a nickel electrode sandwiched between cadmium electrodes was con-
structed, and impedance spectra for the nickel and cadmium electrodes were obtained. Figures 13
and 14 compare the spectra for charged and discharged cadmium electrodes. As with the zinc and
silver electrodes, the low-frequency impedance magnitude and phase angles for the bare metal
(charged cadmium) are higher than for the oxidized metal. There was little observed dependance of
impedance with SOC for the nickel electrode, which is always in an oxidized state.
Figures 15 and 16 compare the cadmium electrode experimental impedance (fig. 2d) with the
equivalent circuit best fit. Of all the electrodes studied, this one seemed to fit the equivalent circuit
6
best.Figures 17 and 18 compare the results for the nickel electrodes, which give a fairly reasonable
agreement between experiment and equivalent circuit. There is some discrepancy in the angle plot
although the trends are comparable. The results are markedly different from Lenhart et al., s who
reported all positive phase angles for porous nickel electrodes over approximately the same fre-
quency range. This may be due to the presence of Li-Oh in the electrolyte and to differences in elec-trode manufacture.
It should be emphasized that the fit of equivalent circuits to experiments were obtained by
replacing the Warburg impedance, which is based on fundamental electrochemical transport princi-
ples, with the empirical constant phase element. Replacement of equivalent circuit models withcoupled differential equation models is recommended for future studies. While this approach is much
more difficult to implement, it is expected to provide a more rigorous understanding of porous batteryelectrodes.
It is also interesting to note the wide variation in aC values in table 1. It is possible that the
CPE is also accounting for some or most of the double-layer capacitance effects, and that a morefundamental modeling approach will yield double-layer capacitances that do not differ by so many
orders of magnitude. However, other workers have also observed order of magnitude differences in
capacitance effects between electrodes. For instance, Tiedemann and Newman, 11 using models
without empirical components, observed that capacitance effects for porous lead electrodes are two
orders of magnitude higher than for porous lead dioxide electrodes. This is because double layer
capacitance is a chemical and not purely an electrical effect.
CONCLUSIONS
1. State of charge estimations can be made using electrochemical impedance techniques. In
particular, the low-frequency impedance of metal electrodes is higher in the fully reduced state than
in the fully oxidized state.
2. Comparisons between healthy and unhealthy Ag-Zn cells show that, at least in some
instances, state of health can be correlated with impedance data. The "dead cell," which presumablyfailed because of decreased active zinc content and decreased active zinc surface area, had a signifi-
cantly higher low frequency impedance.
3. Semi-empirical equivalent circuit models were able to fit the experimental data. It is
recommended that models incorporating the fundamental coupled-differential equations describing
the electrodes be solved in future work. Such an approach will be more difficult, and will require sig-
nificant time and resources to initiate, but the results will be more fundamentally satisfying.
7
0.35
._. 0.3]
.-_ 0.25-o
v
o 0.2"
_0.15 !"t3
_- 0.1-
0.05-
o_
Porous Ag ElectrodeBode Magnitude Plot
itA iLiAiii&LiA jiiA !Hj&IViiiLjLiiii
:_`_`_`_t!!=-_`r.tt_!_._i_=_=N_..i_:_.:`_;_;. _;_="_*._i_i_="_1_ F_
__-___
_01' '0.001_;ii;i_i ; ; i _;;;_0.01;i ;;;;;;0.1i ; ;;;it.;1 i ; 10_ ii'lO0;;_ ; ;_i;;i_1000;i ;;;;ii,10000
Frequency (Hz)
"-="- 100% Charged --4"- 75% _ 50*
-e.- 25% -t.F- Fully Discharged
Figure 3. Bode magnitude pitt of porous silver electrode (169 cm _) impedanceas a function of state of charge.
8
0-
Porous Ag ElectrodeBode Angle Plot
0 ................................................................................................................
20 ........................................... " ..................................................................
o:........---"---------_-'::-:=--==---"- _-:_ =-_==:_-----......°=-1o-__.-._i.i .....................§ -_o--j-__ .........................................< __o-;=........ _¢........................................................................................
.40 _ ...........................................................................................................
-50 i i 1111111 I I t111111 I I lllllll i t illllll i I I It1111 I I iiiiiii i t 1111111 i i iltlll
0.0001 0.001 0.01 0.1 1 10 100 1000 10000
Frequency (Hz)
Figure 4.
lO0%Charged _ 75% + 50°1° I
--e- 25% _ Fully Discharged I
Bode angle plot of porous silver electrode (169 cm2) impedanceas a function of state of charge.
O
Porous Zn ElectrodeBode Magnitude Plot
i!# i -iiii i i Hiiil i i;iiiiJl i iH41iJ. . ........... , ............... ,.:._.| • . :...:;. . ; ':%;:
-._.;4-qii_,..-4-.$-i4;,.'&'.4--...l-.&'_._;_.:41..... ;-4.44-,_ ....._..4-+_.,_0....._--,-_-,4m
,°,,o . , ,, . . • .•.,.• , o. i , ,,H.o: :::::': : :::::::' : :::::m : :::::::: : ::;::::: : :::::':--_---:--t-_¢-:+:+---+-+-_-_.+:_.....o--_--_+H4......_--_--:-_-_H......H-_-,-m,
..... : : :::: : :::::: : ::::::: : ::::: :::::::__ |o , .'' o ,o , • ..• , • ,o,,o•. _ . o,H.,_, ,_,._ _,,,:_.....,._:_,:_....._._,:,_......_,_:_,_
..... .:._":',i_ ' ,:'_,.,L._.._....;...:..L." ;; -'*'-'..... ;.._..'_:,,,¢. ............ _,, ....... _-.,.,-,-, ..... : ,. '" ' :: '" : : ::::':; , : ::::::, : : :::t::: : ,' ::"::
_!__.,'.__-,_!_.._.._._._._,_._.=,:__!._' i ; ;;;;;;; i i iiiiiii ; i iiiiii; i i iiiiii; ; ; ;;iiiii ; i i;il;;)1 0.1 1 10 100 1000 10000
Frequency (Hz)
[...___ 100% Charged _ 75% _ 50%25% _ Fully Discharged
Figure 5. Bode magnitude plot of porous zinc electrode (169 cm:) impedanceas a function of state of charge.
Porous Zn ElectrodeBode Angle Plot
6O
t.............................................................................................................._'_ 30 ......................................................................................... ' ...........
& _o%..........................................................................................._ ....._ot_..........................................................__ .........
-10; .......................
-30 ........................................................................................
4°ob_.......6'_.........i ....... {b ...... i'6o..... i'6bo.... _''_oooFrequency (Hz)
lO0% Charged _ 75% _ 50% I
25% _ Fully Discharged I
Figure 6. Bode angle plot of porous zinc electrode impedance (169 cm 2)as a function of state of charge.
9
Impedance of Discharged Ag-Zn CellBode Magnitude Plot
0.025,
A 0.02,¢O
Et"
,_o 0.015.
8-_ 0.01-
_ 0.005 !
8.1ol
• i i ; ' " ,t:l I : I I = I:=: -' -' : : -' ;-"I_ i i I I ; ;I-'! : = I I I I'-'-' : I : ; " :=
' ' " I lllll I i i i i I I .... I i1 I I '
........ •r ..... ,r---_---r-T-i-l-iT........ T.... r'"i"T'_"_,'r,'r,T......... _.....T'"r,"i'I"T'r,T"
I I I I I IIII I I I I IIIII I I I I II:I
-i---i--.:--i-i.i$.....<...i...... '_-..i...!-.i..i._4 J,.......... i..... ._...i.._..i.-:,..'_.!.,i
......... i. ...... "...'._i-i.i,i. ......... i...... "..-i.-$.L.';.';.:,,_......... i.....$...t..'.J.'7:_
....... 011 _ : :I : i : ; 1:: 110
Frequency (Hz)
Figure 7,
-i- "Good Cell" --+-- "Dead Cell" I
Comparison of discharged silver/zinc cell impedance for a good celland a dead cell (Bode magnitude plot).
Impedance of Discharged Ag-Zn CellBode Angle Plot
O- . , , ..... -i'-- ¢ : : : - ::J. _ .......... ! ...... l---.i-- • _ _.:-_ .......... 4- ..... .:'-.-+:. _.i-_.l-i .......... ,i...... i,-...i...i..;..i..:.--lO i ! i i i_ii! i _ I TI:--'_' , [: i_
I / i : ::l:: : ill: : : : : ::::
I_) , : I :ill: I i : i llli i i : : I ill:l i : : i ii!!: i i i i i!iii _ i i ! ii!!_ I : : .... . ...... .' ..... "....'...' .-' .:.'.l.: .......... " ...... _...A..l..:.A._.',-30 .......... ! ...... ""'I"'T'_'- ii"'" i i i :::: : : _ : i :::
: _ ! ' =ii'! l i ! i iiii! ! i ! ! !!!!,==================================================================< ! , i i !i!!! ! ! i ! i!!!! ! i i i ii!!o.1 : { J ._ .LILt,: .......... i ..... J.;..L.I.I.J.J.LI.......... J...... L..I..LJ.A.'.L03"50 .............. l'"l"l'l gill : I l I lllll l : ; : I l:"I : l : I : :Ill l : : : illii I : : : : :::
I I l:ll I : i I ll:l I l : l l ; Ill
.01 0.1 1 10
Frequency (Hz)
--_- "Good Cell":--_-:= "Dead Cell" ]
Figure 8. Comparison of discharged silver/zinc cell impedance for a good celland a--dead cell (Bode angle pl0t).
10
Impedance of Discharged Ag-Zn CellBode Angle Plot
01 ...... ,., , , ...... * , i ,,,,=. i ,,=1=,=, i ; _illill i i iiii;_ i I ,,..,, . = .*lP,,
: :::::1'; : :::|1::: : : It':'=: ' :::::::' I "-'|::::: , I,|,,,= .... ,,,i, , ,,,,,.,
: ' |.':'::: | : ;|H,o, , o ,aHm, 0 I:,,tl°: , I o,.I.• * _ ,,a,=: , ,•,.m• , ,,,.°.o
_, 4o ...i..!.k:iiiii...i..!._i!!!...!..F.H!!.1i...{.._`...!iii_{....H...qi!H...÷.!.i!_!Lw...*...i.iii{i_..._.i!{!!..
_um_ _iiiiiii! !i!!iiii i i!!!!!!! !_i!!!!!! !iiiiii_ i!!i!!iii_ iiiiill
A =oe-{+mN{-lt_,m_ttttti!!"tmlm-T[Tii_--ti_!i!,,T_ _'m
"_ = ' :::::=: : : :=::_" i ,'T."_I_.I iI I::::: = : :i!!!" ! i!i_llil| __F!.:I.204-..÷.-'+L-','{...{.+_+_N÷..-'.÷÷'_..q..'+,iiN. m_,_.W.'+.',--+.'-'qli:-..=-..r:;_=.--'-..:4.=
1 .::::::: :|1":: .... :ill,.=| Ill:If:,: I:::::,.| :I|i;qi_ i iiii!_i! i ii_Hii-4oi i!!!!!!!!!!!!!E ii:',:k:i:iiiii_ii_i_! !::::=::',:::::::::=::::::0.0001 0.001 0.01 0.1 1 10 100 1000 10
Frequency (Hz)
O0
• "Dead Cell" .- "Good Cell" J
Figure 9. Comparison of charged silver/zinc ceU impedance for a good cell
and a dead cell (Bode angle plot).
Impedance of Discharged Ag-Zn CellBode Magnitude Plot
....' '"""'""°""' "'""!'iE 0 07.... _:_._'_ii;--_"`_"_'_L-_`_-L_;-'_-_'__ _'''L_&_o 0 06 ....i._.H._i_._....i._.i_ii|_..._.._._d..._.÷i_..i.qÈ..._._.._.¢....H."_...+._+"È_..._..._+È_:_v • : '' ::: ; :::::;_ I Ill|If I IIIIIP.I ;11":I." I l;;lll: : l,I'll. " I , ::::::
0.05 .... ;" :': _ ,'_', °"';':'; ::: :='"_";_' ;:'f'":'@ :_"_";'_ ":" ;': _ .'''': ";;:;::'''_'; '_: t :_°'':° '_¢;:'_': ::::::: ::::::': '|=u::, |,:=|:= =|:m._ _!!!!!!'_ !i!!!!!" !!iHi!!
"o .v ::T]_:: :::_H.: !!!iiiii i i!iii=! i!!Hil. = _!ili!.: i i{i}ii.: !iiii!_i_. 0 03 ..... i_i_ii_.i_i_i_iiii.._i_-i_iiiii_4_i,_'_ik_..i_i_i&_ii|_._|.!_i_i_.i_:_'_i!_
" l i !i_i.:i _!!i_i i !iiiiii i i!iii=i i iii!!i. _ _ !:i: ! _!!!]!.= ! !!H}il- o.o_+-.._i.ii_..iiiiiilt-i-lfii_i.-i-fi._B_..ii.i_..iiiiii_,_-iii_--i--._
O_ i!!!ii_,! iii!!!!_ !
Porous Silver Electrode - Bode Mag.Discharged-Zero Cycles
0"281 i iiiiHil [ ii[iiii[ i iiiiiiii i ilHiill i iii_iiii _ ji_iii_
o.26_---i--+-i+!iiii----+--H-i{+_----H--÷ii{{F-i--H-iiii{!.....H-Hi-iN----i--_-÷i-i!iilkli !il}!ll! ! !!!!i!!! ! !i!l!!ll :ii!!!!i! ! !!ii!!!i i:_:}_{}
0.24l-_g--:m_..................................................................................;--_.....;;;'::_: : ::i=i:l: i :i::;::l ; :::Iiiii i _{_iiii_ _ _}I_H:
: ! '::;::' : ; : ,;,;,: • ' ,;":', [ ' ' ',,,,................. :
R 994 ----_" -_-"_'!"I___ "-""':"""H -[_$_ .....[--_-$_4[I_[----_--$-[-[|}_.....[--_-_-[_-[[{-._----i--_-$_4_
{+i}i{{{i.................................'..........= '. -_ I_N i i iiiiiii i }4iiiiii-i iiiiiN i i4iiiii0 0.18 ...........................................
N 0.16......4-,-,,,-:-,....,-.,-,.4-:44..... _.°-'-4-4-"$Z,----4--4--$4,$444_ ..... _--_-4-_4-:444-----8-.4-4.4-_-::;=====================================
o.,,......o 12_-_i,_!il,..,,!-;.+-:--._g",.l:----'--i-_-.;'-_----i--'-+_.-h;;.;
014 ; ' ':::::: . ,::.................ooo_ " o.oo_' ' 'b:bl ...... iJh ' ':;::;:i :,: ::;:;i:5 : ;;;:;iieFrequency (Hz)
,.. Experimental -- Model j
Figure 11. Comparison of experimental and equivalent circuit impedancefor a (169 cm 2) charged silver electrode (Bode magnitude plot).
12
¢0
<
mt-O_
Porous Silver Electrode - Bode AngleDischarged-Zero Cycles
I :I
ot ":L'T: :::::::: : :_:,,:.m ; ;;:;::::".. ........ :;::::;: : :;:::::
05"_ "_' _ ........ ' .... :-.o ..._i i_,,i_--:i---_t_ii_i----t-+-i-lii_------H-iiiiii----_--Hili_.....i--i-i-_i_
o,, z?::i giiiiii:: i eetee :i:iiiiiii::c:i::i:i:[iiiii::::i::i fe .....-o.z.....! !!.:.,i!ii!i_i i_|.iHi__ _iiiiiiii_i',,---_-.,'_..'_----_-q{{i{{F-+-+-}+{{{{F--+--i-{-i{{{{F-i--i-Fi{{_{.....i--F{-H_.....
: : : :::::: : : : :::::: : : ::::':: : : : :::::: : : : :::::: : : : :::::
%'o ......Frequency (Hz)
- Experimental -- Model j
Figure 12. Comparison of experimental and equivalent circuit impedancefor a (169 cm 2) discharged silver electrode (Bode angle plot).
IPorous Cadmium ElectrodeBode Magnitude Plot
i _i!iiiii i ii,iiiii J _,iiiiii i iiii_iii i i!!iiiiJ i!o.og_iiH......i--i-i-i-iiiV-i--+i-!_!iii......h-i-i-iii_.....hi-iiiii'::i_ !!!! i i_ i : ' "::: ':'::::
oo85__N .....i-...-i-i-ii-iii-:,--i,--i4,i,!iii......i--!--i-i-ii_ii.....i---i4-i-'-iii_ " i iiiiiill i iiiilii. : :iiiiiH _ _ii_
E'_0.075 .... ":'"_'t'tS"ii';'_......
oo_....._H_+!III......I_I_-IHH......i_H_i;_i.....{ i-!-i_iiiII _, ,;;,i _'.---' _ ; i "!UL,' .,' J._ "!,':!_I ___!!_ '_ '_- .... = _ ;'"-
Frequency (Hz)
Figure 13.
--_- Discharged _ Charged I
Bode magnitude plot of porous cadmium electrode (230 cm _) impedanceas a function of state of charge.
Porous Cadmium ElectrodeBode Angle Plot
O/ .............. _ .... , , ,;'_'; _ . . ....
_" -64 .i.....i_::: :::ii ...... ii"i'Li:iiii ...... i"_'iii'iiii ..... iiH'iiii! ...... i'"i'_ii!
-o -_0T_.',_._iik
-_-,_t.....i--i-i-i4-iiii--/---i---i--i-i-ii-!ii------!--i-!!i-!i!!.....i---i--i-i-i!!H......!---i-!!!!ii= : :::::::: : :::::':" : i iii!!l! ! !!it:!:! : :::::::
?_.!_TT!_f_!I!!f_!f?HI......f22i..TTI.!?I_....i...io.i.i.g._....g...g.TTTI?!_Frequency (Hz)
Figure 14.
---_- Discharged + Charged J
Bode angle plot of porous cadmium electrode (230 cm 2) impedanceas a function of state of charge.
13
Porous Cadmium Electrode lBode Magnitude Plot- 05/17/91_ t_CllZ
o.o.......i.--'..i,_-i!-i_......".-._-.)-!-_)-!_.....-J..'.)-!.!.!!_......!--.-i..-.Li-i-ii i iiiiiii i iiiiiiii i iiiiiiii i i iiiiii: i [ili!il i ! '_;:;_ ; _ : _:I_:: _ : ::::::: i I I |Ill; , .........
o o.o8 ........ MI!II .......+i -._h':::+......._----!'--+.'-H-i-!i!.......!----F-H-H-I-!
0.08,......i..4--i-,q.:.;_-....+'.-.,i--H-'_ii-......,_...i--,q-i-i-!i).-.....i----!-'-i-).!-i
"- 0.075" i ....... __.''---+...................... =m....... =, .....+...,_ ) ))i);):I...............i i :':'1;;;ii i ii;m E i iiiiiii i )!ii}ill i .'l'._mi,q_mmm mimm!ii!m I I I Illll( I ) I IlllIl I I I IIIlll I I I IIItl
0.071 i i i!ill)! i i!!!!!!! ! ii!ii)if ! 11!1"410.01 0.1 1 10 100
Frequency (Hz)
I • Experimental- Model J
Figure 15. Comparison of experimental and equivalent circuit impedancefor a charged cadmium (230 cm2) electrode (Bode magnitude plot).
lPorous Cadmium ElectrodeIBode Angle Plot- 05/17/91
o _ _ili _ i_i_ii_ _" T i_iiii1-I........L.--..LiJ._.ii.i.......L..L.I..Li-U_....+...._..i..L.:'.L:_:.......L..._...Li.i.i.iiI IIIlII I I I ' :]i_._I_ I I I I IIIII I I I IIIII]
, + ,+r++o I ' II_IIlI ' • I I I IIIIIl I I I I IIIIi i i iiiill : _m: ::..:: : : : :::::: : : : :::::........) -i::=.;, = , iiiiiii i i iiiiiii ( ) _+i_
-3 ........ +---'i .... l'l'l'l":"....... +---+--{'-H-H- ....... _---+--:'--)-l-l-'l+....... ".-------÷--'-i-'-r"1"I: i iiii)il i i iiiiill i i iiliii! : : :::::: l+ +tii!!++'i!iiii!'!!i!i!ii++++..............ii!................i!ii..................iii.......++-+i++++
-g ......... kt__!_-'_ ....... 4----;---i--I.-i-i-H4
- !++++++++! ++.)+!+++!!+++++++++++++++/&Ol :; ;"::;o;.i ; :_";';;i " '"";""i;o ;; ;::'%
Frequency (Hz)
= Experimental- Model J
Figure 16. Comparison of experimental and equivalent circuit impedancefor a charged cadmium (230 cm 2) electrode (Bode angle plot).
14
0.18
Porous Nickel ElectrodeBode Magnitude Plot- 05/17/91
, : :,::::: : :: ...... : :;':;'"' i i:ilill{ i _ _i_{ !0.17 ...... -.-i.J-_.i..::: ...... :'":";'!":f_.:!...... h"hf ;T_!._.:..... T"_.",_Tr,';:;...... :'":",'rrT:;!
! i i _ _ : : : : :,l::: : :, : :: : : ::':::' 4. ...... - ..... '---'--'-;-' ' " '- ..... _....'. ' -' 4-14-_4. ..... 4.-. 4.-_-4-.;.t.¢ _"...... ,_.--,}--;4.-'4-';_
0.16 ...... T'" ":'_._'" : " ::;TIt; . rr'.,:::: =, :::, : :: :'- : : :_.."i:=F*h;'_-':iii i ,::::h ...... i ,,,::,-': ..... : , :::;.:. : l :::::'- _ ! !!ill:: " : ::::::: : ::::_::: : :::::::: ...'...L.i.'.'2":J.O 0.15 ...... T"T'i"T]'[!_i "n-*** r7T[Ti_ TT.rTi[[ii , ,,,,,i,
i i i_i i :_'i{[_ _ _ :::'::: j. : ::j:jjj j j ]j[j'[
=o0.14...... !---..----:-!-i-_iiiH-HiF----i--]--_!ii-!---i.... ..T_.... ! i_ii:. : : ....._ _i::,. : ;::,'"' = .:=:":= : i lilliH i iaiiiii_. " i ii_iiii.._ i ill!i!!! i iiiiiiii i iiiiiii
o 12...... -:,.-_.._--__---N_.--4--_-FI_ .....+---.H-+!-!{!i......H--H-i÷!!i i_iiUi i i i_[Hil ; :'!!U_ ! _ lllilli _ : ::::i_
• ; ':l:':i : i::i::i: : i!'i=:ii i i==iihT TTiTi,3i
%Ol" _o!1 __iii_ i :_:_% __ : ::::i:iFrequency (Hz)
I - Experimental _ Equivalent Circuit ]
Figure 17. Comparison of experimental and equivalent circuit impedancefor a nickel electrode (230 cm 2) (Bode magnitude plot).
=orousNickel ElectrodeBode Angle Plot- 05/17/91
0 i _i_ _ , ,_._ _ _I!U_ :_" _iTi_i'--
-'t...... iiiiiii......i!iiiiiii......i i ::-i iiiiiii......-2ff ...... i---i--i-i-ii-[ii ...... i---i--i-[-ii-iii ...... i--]--_l) _.'-..q ...... i---.!-_-+'i-iii
_.__......,...,..,.,.,,,,......,...,..,.,.;,.,,,......,...,..,_,,, ......,..._..,...,.,,,/ : .:,:::_, : ::::::;: : :__i...;!_ : :::.:::
-4_......_---i--i-i-ii-i::....:_---i--i-i-ii.t_....._--_.;; ......ht_fii_
o -5] ......i---i--H-i'.'_T---[_:.!i -iiii! ......_.-_/Hi[i.Tii[.iil]il][]]]i[H]iiii[r.r.-iT...r......_.-._--m-:.-t:._........--,-_.:hq.:< _I _ : :: ':::h_ , _ ::::::= : i i!ili!i i { _ii_i_
.7I......i-.._-._-: _-_i-_i{....{---i--i-'{+i_......H--H-_-_{I_......I---'-I-'I-HI-8_:|...... F--'--'-'_!I[I[:_',,: • : : : ..q: : : : :.::,:: • ._..:.'.-.u_ ...... _...,xq.¢_..,qI,:; l:::;
-.q/ : : ::_:;;: ; : :;',:::: " : ::;;;_; ; : :;:::;; ; ; ::',:::0.01 0.1 1 10 100 1000
Frequency (Hz)
• Experimental _ Equivalent Circuit I
Figure 18. Comparison of experimental and equivalent circuit impedancefor a nickel electrode (230 cm 2) (Bode angle plot).
15
aC
nl
A
m
Table 1. Equivalent circuit parameters.
Silver
212 F 0.021 F
0.083 _ 0.0062 fl
2.2×10 -6 fl s-m 2.4x10 -5 if2 s-m
-1.1 -1.7
Cadmium
13.25 F
0.044
1.7x10 -5 fl s -m
-1.9
16
=
APPROVAL
TESTING AND ANALYSES OF ELECTROCHEMICAL CELLS
USING FREQUENCY RESPONSE
Center Director's Discretionary Fund Final Report, Project No. 90-18
By D.L. Thomas and O.A. Norton Jr.
The information in this report has been reviewed for technical content. Review of any
information concerning Department of Defense or nuclear energy activities or programs has been
made by the MSFC Security Classification Officer. This report, in its entirety, has been determinedto be unclassified.
ector, Information and Electronic Systems Laboratory
'_ U. S. GOVERNMENT PRINTING OFFICE 1992 -- 631- 060/60104
18
REFERENCES
1. MacDonald, D.D.: "Techniques for Characterization of Electrodes and Electrode Processes."
R. Varma and J.R. Selman, ed., John Wiley and Sons, New York, 1991.
2. Newman, J.: "Electrochemical Systems." Second edition, Prentice-Hall, Englewood Cliffs, NJ,1991.
3. De Levie, R.: "Electrochemica Acta," vol. 8, 1963, p. 751.
4. Missing
5. Missing
6. Armstrong, R.D., and Edmondson, K.: "J. Electroanal. Chem. and Interfacial Electrochem.," vol.
53, 1974, p. 371.
7. Armstrong, R.D., Edmondson, K., and Lee, J.A.: "J. Electroanal. Chem.," vol. 63, 1975, p. 287.
8. Lenhart, S.J., MacDonald, D.D., and Pound, B.G.: "J. Electrochem. Soc.," vol. 135, 1988, p.
1063.
9. Sathyanarayana, S., Venugopalan, S., and Gopikanth, M.L.: "J. Appl. Electrochem.," vol. 9,
1979, p. 125.
10. Zimmerman, A.H., Martinelli, M.R., Janecki, M.C., and Babcock, C.C.: ibid, vol. 129, 1982, p.289.
11. Tiedemann, W., and Newman, J.: "J. Electrochem. Soc.," vol. 122, 1975, p. 70.
17
