Impedance concepts can be applied to the analysis of battery electrodes, yielding information about the structure of the electrode and the processes occurring in the electrode. Structural parameters such as the specific area (surface area per gram of electrode) can be estimated. Electrode variables such as surface overpotential, ohmic losses, and diffusion limitations may be studied. Nickel and cadmium electrodes were studied by measuring the ac impedance as a function of frequency, and the specific areas that were determined were well within the range of specific areas determined from BET measurements. Impedance spectra were measured for the nickel and cadmium electrodes, and for a 20 A-hr NiCd battery as functions of the state of charge. More work is needed to determine the feasibility of using frequency response as a nondestructive testing technique for batteries

Thomas, Daniel L.

English

NASA Technical Reports Server

N90-19419
1989
NASA/ASEE SUMMER FACULTY FELLOWSHIP PROGRAM
MARSHALL SPACE FLIGHT CENTER
THE UNIVERSITY OF ALABAMA IN HUNTSVILLE
FREQUENCY RESPONSE OF ELECTROCHEMICAL CELLS
Prepared by:
Academic Rank:
University and Department:
Daniel L. Thomas
Assistant Professor
The University of Alabama
in Huntsville
Chemical Engineering Program
Mechanical Engineering
Department
NASA/MSFC:
Laboratory:
Division:
Branch:
MSFC Colleague:
Date:
Contract No.:
Electronics and Information
Systems
Electrical
Electrical/Electronics Parts
Teddy M. Edge
August ii, 1989
The University of
Alabama in Huntsville
NGT-01-008-021
XXIX
https://ntrs.nasa.gov/search.jsp?R=19900010103 2020-03-19T23:03:53+00:00Z

I wish
Electronics
particular,
ACKNOWLEDGEMENTS
to acknowledgethe staff of the Electronics
and Information Systems Laboratory led by Mr.
I wish to thank Mr. A1 Norton, Jr.,
Divisicn of the
Jim Miller. In
for helping to round up
equipment and fabrication the test cell and reference electrode, Mr. Ted Edge
_nd Mr. Mike Martin for sponsoring me, and Mr. Roy Lanier for supFlying some
of the equipment used.
XXIX-i
FREQUENCYRESPONSEOFPOROUSBATTERYELECTRODES
V
Daniel L. Thomas
Assistant Professor of Chemical Engineering
The University of Alabama in Huntsville
Huntsville, AL 35899
ABSTRACT
Impedance concepts can be applied to the analysis of battery electrodes,
yielding information about the structure of the electrode and the processes
occuring in the electrode. Structural parameters such as the specific area
(surface area per gram of electrode) can be estimated. Electrode variables
such as surface overpotential, ohmic losses and diffusion limitat.ons may be
studied.
Nickel and cadmium electrodes were studied by measuring the A.C. impedance as
a function of frequency, and the specific areas that were determined were
well within the range of specific areas determined from BET measurements by
other workers. Impedance spectra were measured for the nickel and cadmium
electrodes, and for a 20 A-hr NiCd battery as functions of the state of
charge. More work is needed to determine the feasibility of using frequency
response as a non-destructive testing technique for batteries.
XXlX-ii
INTRODUCTION
Electrochemical processes may and have been studied
response techniques and modeled using impedance concepts.
occur at
impedance.
using Irequency
Processes that
electrodes may be modeled as resistance, capacitance or complex
More information may be gained using dynamic techniques than by
using steady-state D.C. techniques. For example, one could study an
electrede by measuring steady D.C. current and potential, or the same system
could be studied using A.C. over a range of frequencies with an increase in
the am_,_nt of information learned. Dynamic techniques have been used to
estimate the specific area of porous lead-acid battery electrodes (Newman and
Tiedemann_ 1976), the kinetics and mechanisms of electrode reactions and a
the rate of mass-transport processes such as diffusion (Bard and Faulkner,
1980). Attempts have been made to correlate cell state of charge with A.C.
impedance spectra (Brodd and DeWane, 1963; Sathyanarayana et al., 1979).
Zimmerman et al. (1982) studied the very low frequency impedance (as low as
0.i Hz) of NiCd cells.
OBJECTIVES
The objective of this work was to examine the feasibility of using
_equency response techniques i) as a tool in destructive physical analysis
of batteries, particularly for estimating electrode structural parameters
such as specific area, porosity and tortuosity and 2) as a non-destructive
testing technique for obtaining information such as state of charge and
acceptability for space flight. It would be desireable to ha_e a non-
destructive battery test that can be run rapidly and as close to launch of
spacecraft as possible. The battery frequency response may be such a test.
XXlX-I
THEORY
This section will briefly review the physical phenomena that contribute
to the _requency response of an electrode.
Electric Double Laey_e_r
The double layer is a thin (about 20 Angstrom) layer of electric charge
that exists at the boundary between two phases, such as an electrode/solution
interface, and can form for several reasons. One of the poles in a polar
solvent molecule may be preferentially oriented toward the surface. Figure I
shows how the negative pole of a water molecule may be oriented toward a
surface and create a separation of charge. Double layers also occur because
positive or negative ions may be preferentially adsorbed by a surface. For
example, chloride ions in a solution of potassium chloride are adsorbed onto
mercury in preference to potassium ions as shown in Figure 2, resulting in a
separation of charge.
Finally, double layers are formed when electrodes are charged. Consider
the situation in Figure 3, where two inert metal surfaces such as gold are
immersed in NaF solution. These ions are not preferentially adsorbed by the
metal. If a potential difference less than the 1.2 V required to decompose
water is placed across the cell no steady state current can flow, yet there
must be a potential drop. The potential drop occurs at the double layers
that exist at each electrode surface. Electrodes which behave in this way
are called ideally polarizable electrodes (IPE).
The double layer can be considered as an electric capacitor since it
acts to store charge. The concept of the double layer was experimentally
verified with mercury which has the advantage of a reproducible liquid
surface and of inhibiting hydrogen evolution and hence approaching IPE
XXIX-2
F!gure [. Double layer formation by solvent molecule orientation.
® @®® ©
Figure 2. Double layer formation by ion adsorption.
Y_XIX- 3
-%
! .................V I
V2
V3
Figure 3. Voltage profile in cell with ideal polarizable electrodes.
3e
34
30
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Figure 4. Double layer capacity of 0.001M NaF/Hg electrode.
XXIX-4
behavior over a wide potential range (Newman, 1973). Figure 4 shows how the
double layer capacitance of mercury in 0.001 M NaF varies with applied
potential. The capacitance was also calculated from the mercury surface
tension (which varies with potential and charge) and from direct measurement
of charge, both of which require liquid metal electrodes. The double layer
capacitance in on the order of 10_F/cm , which corresponds to a parallel
plate capacitor with a plate separation of about 20 A, the double layer
thickness. The double layer capacitance is potential dependent, but can be
treated as constant over small (7 mV) potential range.
Electrochemical Reaction
The rate of electrochemical reation is an exponential function
potential drop across the double layer
of the
RT RT (i)
where io is the exchange current density,
usually taken to be 0.5, F is Faraday's constant, R is the gas constant,
is the absolute temperature and Vm - V s is the potential drop across
double layer. The first term in brackets is the rate of the f_rward
anodic reaction while the second term is the rate of the reverse or
reaction. When Vm i V s then these two rates are equal (to the
current density) and there is no net current.
Equation I is highly non-linear and must be linearized before using
an impedance analysis:
Pf = d(V m -V,) I
dif (Vm -V, )o
=< is a kinetic symmetry parameter
T
the
or
cathodic
exchange
in
XXIX-5
Linear expressions are valid for potential variations of 7 mV or less.
Combined Reaction and Double Lay__ Charzlnz
Most electrodes, particularly those used in batteries, have combined
reaction and double layer charging. For a bare metal electrode in contact
with solution this can be modeled as a resistor (Rf) and capacitor (Cd ) in
parallel as shown in Figure 5. The solution resistance R s also must be
considered. At very high frequencies the phase angle is 0 and the modulus of
the impedance is R , while at sufficiently low frequencies the phase angle
s
is 0 and the modulus is R s + Rf. Hence Rf and R s can be separately
determined, whZch could not be done readily using a steady D.C. experiment.
Diffusion Effects
Slow diffusion of reactants to the electrode surface or ol reaction
products away from the surface also causes the potential to lag the current.
The Nernst equation, and its linearlzed form, gives the potential drop due to
concentration differences:
C
= nF __s _, nF ,(Cb _ Cs _
Vb - Vs _-_in Cb RT---Cb
(4)
where C is the bulk solution concentration and C is the concentration
b s
adjacent to the electrode. Again, the linearization is valid for a potential
range of 5-7 mV. Hence, as the reaction proceeds and the reactant near the
surface is consumed this potential drop increases.
The Warburg impedance is the impedance due to slow diffusion. For a
planar electrode in a large excess of electrolyte solution
_r
XXIX-6
Electrode
Vm
Double layer
capacitance
Cd
I
Vs Warburg Rs
Rf Impedance Solution
Resistance
Reaction (Mess
(Ohmic)
Resistance Diffusion
(Non-linear) Effect)
Figure 5. Equivalent circuit for electrode with capacitance, reaction,
Warburg impedance and ohmic resistance.
XXIX-7
Z a: (jwD) -05
<5)
The real and imaginary Warburg impedances are equal for this case. The
Warburg impedance is usually manifested at frequencies less than 1 Hz.
Measurments at frequencies as low as 0.0001Hz have been reported. The
period of such a measurement is about as long as a battery cycle, hence
higher frequencies would be needed for state of charge determinations without
substantially changing the state of charge.
Porous Electrodes . .
Most actual battery electrodes are high surface area porous electrodes.
The electrode processes are distributed throughout the electrode volume
instead of at a single surface. One porous electrode model is the idealized
cylindrical pore shown in Figure 6. The pore walls are the solid surface
where the electrode reaction and double layer charging occurs. At the
electrode grid (x-0) all of the current is in the solid phase while at the
electrode/separator boundary (x-L) all of the current is in the liquid phase.
The current is transferred from the liquid to the solid along the pore wall.
Figure 7 shows the model circuit for the pore, which is often called a
transmission line model. The impedance Z can include reaction, double layer
capacitance and Warburg impedance. The impedance of the electrode, assuming
conductivity and no Warburg impedence is
cosh(mL)
Zpo , = krn sinh(mL)
a very large solid
(7)
m 2 _ {I
k + JWCd)
"v"
XXlX-8
SOLID
,, > >
,. > > >--->--> I_=
SEPARATOR
Figure 6. Idealized model of a cylindrical pore.
R
S
RFO
R
P
Figure 7. Equivalent circuit for the model in Figure 6.
XXIX-9
This is a complicated expression to interpret, especially since m is a
complex number, but it can be linearized for small values of mL, and the
Theresulting expression is useful for estimating specific surface area.
important result is
Irn (Zpo,.,) = aWCd L3
45 k 2
Equation 8 is an approximation of Equation 7 that is valid at low
frequencies, providing that the frequency is high enough that Warburg
impedance is not a factor. A plot of Im(Z) vs. frequency is linear in this
range, and the specific area can be determined from the slope of the line.
EXPERIMENTAL
A three electrode cell was made by sandwiching a Cd electrode between
two Ni electrodes. The electrodes were from an Eagle-Picher 50 A-Hr cell
that had undergone destructive physical analysis. Separator material from
the cell was used as separator in this cell. The cell was immersed in 31%
KOH solution. A Ag/AgO reference electrode was placed in a separate
compartment with 31% KOH. The two compartments were connected by a I mm
Teflon tube filled with electrolyte, and the tube was placed near the Cd
electrode at the center of the cell.
A EG&G/PAR model 363 potentiostat was used to control the potential
between the Cd and reference electrode. A Wavetek signal generator supplied
the voltage perturbations that were added to the D.C. offset voltage of the
potentiostat. The potential and current monitors of the potentiostat were
connected to a Tektronics storage oscilloscope, from which the peak current,
XXIX-IO
peak voltage and phase angles were obtained. Impedance spectra were obtaineo
for GE 20 A-Hr cells using similar instrumentation. The reference electrode
lead from the potentiostat was connected directly to the counter electrode
terminal.
Eagle-Picher Electrodes
Figure
discha_ged
right hand
RESULTS
8 shows the experimental Nyqulst plot for a charged and
Eagle Picher Cd electrode in a frequency range of 0.001 Hz on the
side to i Hz on the left hand side. The Warburg impedance
dominated this part of the diagram,
electrode than the charged electrode.
the electrode reaction
Cd + 2OH- - Cd(OH)
which produces Cd(OH)2upon discharge.
and it is much larger for the discharged
This can be explained by considering
+ 2e
2
A solid film of reaction product would
be a mass transfer barrier that would increase the electrode impedance.
Figure 9 shows the Nyquist diagram for the Ni electrode in the same
frequency range as Figure 8. Re(Z) is an order of magnitude smaller than for
the Cd, while Im(Z) is two orders of magnitude smaller. The primary mass
transport process in the Ni electrode is thought to be proton (H) diffusion
in the solid as the electrode reaction occurs:
NiOOH + H20 + e - Ni(OH) 2 + OH
Proton diffusion occurs rapidly since the hydrogen atom is small and easily
moves between larger atoms in the solid lattice, hence the Warburg impedance
of the Ni electrode is smaller. The curves for the charged and discharged
electrodes are the same, indicating that a film does not grow during a cycle
XXIX-!I
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XXIX-12
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XXIX-13
was 0.04 cm,
conductivity
equation
Figure i0 shows a plot of Im(Z) vs. frequency in a range from i00 - 3000
Hz for the Cd electrode. The plot is linear and the interfaclal area can be
estimated from the slope of the line. The double layer capacitance was
assumed to be 80/_F/cm (Latham and Hampson, 1973), the electrode thickness
-I -i
the solution conductivity 0.5 ohm cm and the effective
in the porous electrode was estimated using the Bruggemann
keff" k(porosity) 1.5
with a porosity of 0.25 to 0.3. The interfacial area was estimated to be 8
to 15 m2/g, which compares with results of 2 to 50 m2/g determined by Pickett
(1975) from BET (hydrogen adsorption) measurements. The BET technique
determines total area, while the present technique measures only the
electrochemically active area.
G.E. Cell
Some impedance spectra were measured for a G.E. 20 A-Hr cell. The cell
had been on the shelf for about 14 years with the terminals shorted. It was
cycled several times and a capacity of 21 A-Hr was obtained, however, the
cell did not retain charge- it lost about half its capacity during overnight
stand. The impedance spectra was measured in the low frequency range (0.001
to i Hz) in the following conditions: I) discharged and overnight stand, 2)
fresh charge, 3) fresh discharge, and 4) recharged and overnight stand. At I
Hz the phase angle was zero, while at frequencies of about I00 Hz and larger
the potential led rather than lagged the current, indicating that induction
effects, which do not have an electrochemical explanation, dominated the
capacitance effects.
Figure ii _ompares the spectra of conditions I and 2. The impedance of
the discharged cell is larger than the charged cell due to the Cd(OH)2 film
v
XXIX-14
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XXIX-15
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XXIX-16
that hinders diffusion. Figure 12 compares conditions i and 3, both of which
are discharged conditions and yield similar spectra. Figure 13 compares the
two recharged conditions, and there is a clear difference between the two
results. The spectra for condition 4 are unlike the others observed. More
data are needed to conclusively determine whether it is a bad set of
measureme__ts or if it represents reality. The dotted line shows how two
humps, r_presentlng two time constants (one for each electrode) may be
This would indicate that the recharged nickel electrode degrades
CONCLUSIONS AND RECOMMENDATIONS
The following conclusions are made concerning this study: i) the
specific area of battery electrodes can be estimated using frequency response
techniques during DPA. The results are consistent with those obtained by
2) Attempts to correlate cell state of charge are
It seemed to work better for individual electrodes during DPA
other workers.
inconclusive.
than for cells.
It is recommended that i) methods for evaluating other electrode
structural parameters such as porosity and tortuosity be developed, 2) a long
t_rm study of frequency response as a non-destructive battery test be
undertaken. Ten weeks is insufficient time for such a study. The results of
such a study would be a correlation of state of charge and of battery
acceptability for space flight. 3) Develop quantitative data analysis of
impedance in the low frequency (mass-transfer dominated) range.
frequency response techniques outlined in this report to Ni/H 2
cells.
4) Apply
and Ag/Zn
XXIX-17
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XXIX-18
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XXIX-19
REFERENCES
R.D. Armstrong and K. Edmondson, Electroanal. Chem. and Interfac.
Electrochem, vol 53, pp 371-387, 1974.
R.D. Armstrong, K. Edmondson and J.A. Lee, J. Electroanal. Chem_____.,vol 63,
pp. 287-302, 1975.
A.J. Bard and L.R. Faulkner, Electrochemical Methods, J. Wiley and Sons,
New York, 1980.
R.J. Brodd and H.J. DeWane, J. Electrochem. Soc., vol Ii0, p. 1091, 1963.
R. Haak, C. Ogden and D. Tench, J. Power Sources, vol 12, pp 289-303, 1984.
R.J. Latham and N.A. Hampson, in Encyclopedia of Electrochemistry of the
Elements, vol I, A.J. Bard, ed., Marcel Dekker, New York, 1973.
J. Newman, Electrochemical Systems, Prentice Hall, Englewood Cliffs, NJ,
1973.
D.F. Pickett, Air Force Aero. Propulsion Lab., Report No. AFL-TR-75-34, 1975.
S. Sathyanarayana, S. Venugopalan and M.L. Gopikanth, J___.Appl. Electrochem.,
vol 9, pp. 125-139, 1979.
W. Tiedemann and J. Newman, J. Electrochem. Soc_____.,vol 122, pp 70-74 1975.
A.H. Zimmerman, M.R. Martinelli, M.C. Janecki and C.C. Badcock, ibid,
pp. 289-298, 1982.
XXIX-20


Frequency response of electrochemical cells

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