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The Electrochemical Society Interface • Spring 2006 17
Batteries andElectrochemicalCapacitorsby Daniel A. Scherson and Attila Palencsár
The invention of the battery can be attributed to Alessandro
Volta (1745-1827) of Como, Italy, who in 1800 described anassembly consisting of plates of two different metals, such asZn and Cu, placed alternately in a stack-like fashion separatedby paper soaked in an aqueous solution, such as brine orvinegar. As discovered by Volta, this contraption was capable of producing an electrical shock when its ends were touched. Ina broad sense, batteries can be defined as devices that convertchemical into electrical energy using electrodes, immersed inmedia (liquids, gels, and even solids) that support the transportof ions, or electrolyte. This mode of operation is fundamentallydifferent from that associated with conventional solid-state
capacitors, invented about half a century earlier in Leyden,The Netherlands, in which charge is physically stored innonreactive electrodes separated by a dielectric, or insulatingmaterial. However, the latter shares important commonalitieswith yet another class of devices developed much later knownas electrochemical capacitors, which, as described later inthis article, rely on charge separation at electrode|electrolyteinterfaces to store energy.
Automotive, communications,and a host of consumer marketapplications, introduced in the first
quarter of the twentieth century, madebatteries a household term. However,
the technological explosion broughtabout by the advent of the transistorand the concomitant miniaturizationof electronic circuitry (as eloquentlyevidenced by the seemingly ever-evolvingmultifunctional cell phones, portabledigital assistants, laptop computers,digital cameras, games, and, morerecently, portable media devices, such asthe iPod), may be regarded as perhapsthe major factor responsible for batteries
becoming among the most ubiquitousdevices ever invented. Further major
market expansions are expected from the
impending introduction of large fleets of gasoline-electric hybrid vehicles, which
will help alleviate, at least momentarily,the worldwide impact on the economyand the environment induced by theinexorable depletion of fossil fuels andthe release of greenhouse gases intothe atmosphere. Driven primarily bya fast-growing and highly competitivemarket and the support of governments,
scientists and engineers in industry,academia, and national laboratories haveengaged in a frenzied search of means
for maximizing battery performance interms of power and capacity, i.e., theactual charge the device can store, whileminimizing weight and volume andmitigating safety risks.
General Considerations
Batteries consist of single (although
the term defines a collection), or mul-tiple galvanic cells, connected in seriesto generate higher voltages. For example,in a car battery, six individual 2.0 V lead-acid cells provide 12 V. Each such cellconsists of two electrodes: the anode, orsource of electrons, and the cathode, orsink of electrons, labeled, respectively, asnegative and positive in consumer batter-ies. Whereas the voltage of a cell ( E
cell) is
prescribed by the nature of the chemical
reactions at the two electrodes, the powerit can deliver, defined as the product of the voltage ( E) and the current ( I ), aregoverned by much more subtle factors.Some batteries can be used only once,so-called non-rechargeable or primary,and others multiple times, rechargeable
or secondary. The most common primarybattery, i.e., Zn|MnO
2, is depicted in Fig.
1a. For this system, the anode is a collec-tion of Zn metal particles dispersed in a
strongly alkaline aqueous solution mixedwith a polymer, and the cathode is a hol-low molded cylinder made out of MnO
2.
Direct physical (electronic) contactbetween the two electrodes (and, thus,
F IG. 1. (a) Schematic diagram of commercial primary (non-rechargeable) Zn| MnO2 and (b) secondary (rechargable) Ni| MH batteries. Adapted with permission from the manufacturers.
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18 The Electrochemical Society Interface • Spring 2006
a short) is prevented by placing a non-woven fabric or separator between them,which also serves to hold sufficientelectrolyte to establish ionic continuitywithin the battery. The intrinsic elec-tronic conductivity of MnO
2is too low to
sustain high currents; hence, a conduc-
tivity enhancer, most commonly a highsurface area graphitic carbon, must beincorporated into the cathode to improveits performance and a polymeric binderfor mechanical stability. Electrons aregenerated at the anode, via the oxidationof metallic Zn to yield a Zn2+ species, atwo-electron transfer process, and arecollected by a metal pin current collectorinserted in the Zn paste as shown in Fig.1. After flowing through the load, such
as a light bulb, the electrons are deliveredthrough a steel casing current collector,to the MnO
2cathode, where the Mn4+
ions are reduced to a lower valent state.
The voltage of an off-the-shelf Zn|MnO
2cell, as measured with a high
impedance voltmeter (which drawsonly a miniscule current) is E
cell~ 1.5 V.
This value corresponds to the sum of the individual half-cell potentials of the two electrodes, as predicted by
the corresponding Nernst equations,although the precise nature of theelectrochemical reactions involved havebeen the subject of much heated debate.During operation, E
cellis always smaller
than its open-circuit value (no load) anda function of both the demands imposedby the device it powers and the depth towhich the battery has been discharged.
An example of a popular rechargeablesystem is the Ni metal hydride (Ni|MH)battery, E
cell~ 1.2 V, shown schematically
in Fig. 1b. Its active cathode material isnickel hydroxide, Ni(OH)
2, which has
a layered-type crystal lattice, and the
anode, denoted as MH, consists of analloy incorporating an array of mainly
rare earth elements (or mischmetal).During charging, the metal sites inNi(OH)
2undergo oxidation to yield
NiOOH, whereas the anode reduceswater to elemental hydrogen, whichcombines with the metal to form ahydride, a virtual hydrogen storage. Theconstruction of this battery differs from
that of Zn|MnO2 in that the electrodesare sandwiched with the separator inbetween and wound to form a cylinder,
resembling a jellyroll.
Selection of a battery for a specific
device is often made based primarilyon its performance characteristics. Onesuch figure of merit is obtained byapplying a constant current ( I ), whilemonitoring E
cellas a function of time.
Shown in Fig. 2 is a plot of Ecell
vs. timefor various I for an AA Ni|MH battery.As indicated therein, for I = 250 mA (seepurple curve, top), E
celldecreases slowly
during the first 2 h to reach a fairlyconstant plateau. After about 6 h, Ecell
once again drops first slowly and thensuddenly at about 10 h signaling the endof the battery useful life. Based on theobserved lifetime, the charge or capacitythe battery can deliver under theseconditions, is 10 h × 3600 s/h × 0.25 A =9000 coulombs (denoted C), or in batterytechnology units, 2500 mAh (250 mA× 10 h). If I is increased, for example,to meet the demands of a more power
hungry device, the observed useful lifeof the battery is obviously shorter, asillustrated by the blue curve, Fig. 2 top,
for I = 500 mA. Nevertheless, based onthe same calculation presented above,the useful capacity of the battery remainsvirtually unchanged. Manufacturersoften quote discharge rates in units of C (which, although it bears the samesymbol, is not to be confused with thatfor coulombs) where C/1 corresponds to
the current at which the useful capacityof the battery is consumed in 1 h. For theresults shown in Fig. 2 top, the capacityof the battery for I = 250 and 500 mAwas exhausted in 10 (purple curve) and5 h (blue curve), which corresponds todischarge rates of 0.1 C (or C/10) and 0.2C (or C/5), respectively.
As the C rate is increased beyonda certain limit, however, the capacityof the battery can no longer be fullyutilized. This is clearly illustrated forthe AA Ni|MH battery discharged at 2
C (see magenta curve, Fig. 2 bottom),for which the lifetime falls short of the0.5 h predicted based on the resultsobtained at the lower C rates. A fractionof valuable electrode material remainedunused, an effect found for all batterysystems for sufficiently high C rates. Itis a challenge faced by scientists and
engineers to find means of avoiding this
F IG. 2. Cell voltage ( Ecell ) vs. time (in hours) for the discharge of a AA
Ni| MH battery at various constant currents as indicated. Adapted with permission from the manufacturer.
0.1 1 10 1000
50
100
150
Ni|Cd
Ni|MH
S p e c i f i c e n e r g y , W h / k g
Specific power, W/kg
Li-ion
F IG. 3. Specific energy vs. specific power or Ragone plots, for three commonrechargeable batteries. Ref: Handbook of batteries, D. Linden, T. B. Reddy,
Eds., McGraw-Hill, New York (2002), 3rd Edition.
Batteries andElectrochemical Capacitors(continued from previous page)
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The Electrochemical Society Interface • Spring 2006 19
undesirable and wasteful phenomenon.This task requires a deep understanding
of the underlying processes involved,which are almost always linked tohindrances in the transport of chargedspecies.
A useful means of representing theoperational performance of batteriesand other energy storage and energyconversion devices is a graph of specific
energy (A × V × h/kg = W × h/kg) vs. specific power (W/kg). This graph isknown as a Ragone plot, and is shownin semilog form for three commonrechargeable batteries including Ni|MH
in Fig. 3, derived from measurementsof the type shown in Fig. 2. It becomesevident from these data, that the Li-ionbattery has twice the specific energycompared to Ni|MH, and four timesthat of Ni|Cd, a system expected tobe gradually displaced by Ni|MH, andLi-ion, due to environmental impactconcerns. Although specific energy and
specific power are important, otherfactors must also be considered when
selecting a battery system for a specificapplication, including reliability (criticalfor pacemakers), safety, self-discharge,temperature, and even humidity (key forZn|air hearing aid battery). This latterdevice is a cross between a battery and afuel cell, in that the reaction at the (gaspermeable) cathode is the reduction of oxygen from the atmosphere.
From an overall perspective, Li-ionbatteries, today’s canonical power sourcefor portable electronics, undoubtedlyrepresent the most promising energy
storage system for a host of otherapplications, including transportation;hence, certain aspects of its principles of operation deserve particular attention.
Li-Ion Batteries
The discovery of transition metaloxides, LiMO
2(where M = Ni or Co) as
reversible lithium-ion cathodes display-
ing very positive operating potentials wasmade by J. Goodenough (then at Oxford,and currently at the University of Texas,Austin) in the 1970s. In particular,LiCoO
2proved a key to the development
and commercialization of secondaryLi-ion batteries by Sony Corp. (a non-tra-ditional battery company) as powersources for many of their own electronicdevices. A schematic representation of the elementary redox processes associ-
ated with the operation of the Li-ion bat-tery is shown in Fig. 4. During charging,lithium ions, Li+, are released from theLiCoO
2lattice to the electrolyte solu-
tion incorporating a suitable salt, suchas LiPF
6in an organic (aprotic) solvent,
commonly a mixture of alkyl carbonates.At the same time, Li+ ions are insertedinto the layered graphite structure fromthe electrolyte solution. These reactions
are reversed during battery discharge(see Fig. 5), which led to the coining of such terms as rocking chair or shuttlecock to describe more graphically its modeof operation. The actual electrodes aremade of micrometer-size particles of graphite (anode) or LiCoO
2(cathode),
mixed with relatively high surface area
carbon as a conductivity enhancer, aswell as an organic binder to providestructural integrity.
A technique commonly used togain insight into the properties of electrode materials, involves scanning
F IG. 4. Schematic diagram of the mode of operation of a LiCoO2|graphite
battery. During charge Li+ ions are released from LiCoO2
and injected into the graphite lattice. The reverse processes occur during discharge.
� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � x � �x � �x �
�
� �x � �x � � � � � � � � � � � � � � � � � � � � � � � � x � �
�
� � � � � � � � � � � � � � � � � � � � � � � x � � x
�
�
�
�
�
�
F IG. 5. Single electrode and net reactions for the LiCoO2|graphite Li ion battery.
0.0 0.5 1.0 3.0 3.5 4.0 4.5
0
C u r r e n t D e n s i t y ,
a . u .
���
F IG. 6. Composite, semiquantitative (arbitrary current scale) cyclic voltammograms for natural graphite and LiMn
2O
4recorded independently at
very slow scan rates. Data were obtained in a LiPF 6
solution in a mixture of alkyl carbonates. The arrows indicate the direction of the potential scans and the blue and magenta represent charge and discharge, respectively. Refs: H.Wang and M. Yoshio, Journal of Power Sources 93, 123-129 (2001), and Dana
A. Totir, Boris D. Cahan and Daniel A. Scherson, Electrochimica Acta 45, 161-166 (1999)
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20 The Electrochemical Society Interface • Spring 2006
the potential of a single electrode (half-cell) in a linear fashion between twoprescribed limits first in one directionand then in reverse, while monitoring the
current, known as cyclic voltammetry.This method can be implemented withrelative ease and provides an expedientmeans of screening new materials, asit requires very small quantities, evendown to a single microparticle. Shownin Fig. 6 are cyclic voltammograms of natural graphite and LiCoO
2recorded
independently in a solution of LiPF6
in amixture of alkyl carbonates. The current
axes in these plots are normalized for
didactic purposes and the arrows indicate
the direction of the potential scan, whereblue and magenta represent charge anddischarge, respectively. These data wereacquired at very low scan rates, on the
order of a few tens of microvolts persecond, to offset the sluggish diffusionof Li+ through solid lattices, which areorders of magnitude smaller than thoseof ions in liquid solutions, and allowfor quasi-equilibrium conditions to beachieved over the entire potential rangeexplored.
The clearly defined voltammetricfeatures are ascribed to changes inthe oxidation state of species within
the electrode materials, which are
counterbalanced by the migration of Li+ in and out of the corresponding
lattices. It thus follows from these data,and also confirmed experimentally,that the operating potential of theLiCoO
2|graphite battery is close to theseparation between the peaks associatedwith reactions at the cathode and theanode, ca. 3.7 and 0.1 V vs. Li+/Li,respectively. Furthermore, that the peaks
found in the scans in the positive andnegative directions are nearly mirrorimages is indicative that the reactions
are energetically reversible, i.e., about thesame potential difference, in principle,nominally required to recharge thebattery.
Despite their extraordinary sensitivity,electrochemical measurements do notprovide insight into the structural andelectronic changes associated with theredox processes involved, for example,those responsible for the multiplicityof peaks found in the voltammetry in
Fig. 6. Hence, other techniques must beused to gain access to such information.
A better understanding of these factorsmay be regarded as critical to therational design of materials displayingoptimum performance characteristics.One approach involves a systematicstructural and spectroscopic study of agroup of lithium intercalation materialsprepared individually spanning the entirerange of Li content of relevance to theelectrode operation, e.g., 0 ≤ x ≤ 1, for
LixCoO2, where x = 0 and 1 corresponds
to fully charged and fully dischargedforms, respectively. Serendipitously,
this laborious endeavor can be avoidedby combining electrochemistry, asan expedient and highly accuratesynthetic tool to prepare such group of materials, with X-ray based techniques,such as X-ray diffraction (XRD) orX-ray absorption spectroscopy (XAS)as structural and electronic probes.
Furthermore, advantage can be takenof the high transparency to X-rays of carbon and other low-Z elements presentin the main electrode constituents toperform such measurements in situ. Forsuch experiments, charge is injectedinto the electrodes in small incrementsand the system allowed to reachequilibrium before data are acquired.Once completed, an additional chargeis injected, and the whole procedure
repeated until the desired Li+ range iscovered. Alternatively, and dependingon the time required for XRD or XASdata acquisition, charge can be injectedat a constant and small enough (low C)rate for the system to maintain quasi-equilibrium conditions, while monitoringthe potential and recording the desireddata. These principles were fully exploitedfor studies involving the cubic spinel
LiMn2O4, a “green” cathode material that
0 20 40 60 80 100
8.10
8.15
8.20
8.25
0.0 0.5 1.0 1.5 2.0 2.5
3.6
3.8
4.0
4.2
3.2 3.6 4.0 4.4
0 20 40 60 80 100
L a t t i c e P a r a m
e t e r ,
�
E
�
E ���
��
F IG. 7. Lattice parameter extracted from X-ray diffractionmeasurements collected in situ vs. SOD (%) for Li
x Mn
2O
4 , in the
range 0 (fully charged) ≤ x ≤ 1 (fully discharged). The presence of twodistinct phases are represented by the blue and magenta circles. Topinset: Cyclic voltammetry of LiMn
2O
4in the potential region in which
the redox transitions occur. Bottom inset: Potential (V vs. Li/Li+ ) vs. Charge (mAh) during the C/10 discharge of the electrode. Refs: T.
Eriksson, A-K. Hjelm, G. Lindbergh and T. Gustafsson, Journal of The Electrochemical Society, 149 (9) A1164-A1170 (2002) and Dana
A. Totir, Boris D. Cahan and Daniel A. Scherson, Electrochimica Acta45, 161-166 (1999).
F IG. 8. Series of in situ Mn K-edge X-ray absorption spectra(normalized absorbance vs. energy in keV) for Li
x Mn
2O
4for x values
specified. Ref: Youhei Shiraishi, Izumi Nakai, Toshio Tsubata,Takuhiro Himeda and Fumishige Nishikawa, Journal Of Solid StateChemistry, 133, 587- 590 (1997).
6.54 6.56 6.58
�LiMn2O4
Li0.67 Mn2O4�Li0.34 Mn2O4
Li0.09 Mn2O4
N o r m a l i z e d A b s o r b a n c e
Energy, keV
Mn K-edge
Batteries andElectrochemical Capacitors(continued from previous page)
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The Electrochemical Society Interface • Spring 2006 21
displays two well-defined voltammetricpeaks at about 4.0 V vs. Li/Li+ (top
inset, Fig. 7). Analysis of a series of X-ray diffractograms for the (111) peak of LiMn
2O
4collected in situ during the C/10
discharge of the fully charged (λ -MnO2)
cathode (bottom inset, Fig. 7), yielded, asshown in Fig. 7, evidence for the presenceof one single phase (blue circles) forstates of discharge (SOD), defined as the
percent of the total capacity consumed,higher than 35%, and another singlephase (magenta circles) for SOD < 10%,
for which the lattice parameter variedlinearly with SOD. As indicated in thefigure, these two phases coexist for 10 <SOD < 35%.
Information regarding the oxidationstate of the Mn sites as a function of SOD can be obtained from in situ XASspectra, a technique in which theenergy of the radiation is scanned overthe range embracing the excitation of core, e.g., 1s, electrons to higher lying
levels, including photoionization, orK-edge. Shown in Fig. 8 are a series of
Mn K-edge XAS spectra in the form of normalized absorbance vs. energy (keV)for Li
xMn
2O
4for x in the range 0 ≤ x ≤ 1
recorded in situ in a specially designedspectroelectrochemical cell. As theelectronic density of the metal decreases,by virtue of an increase in the oxidationstate, the nucleus becomes more effectivein attracting the remaining electrons,making it more difficult for electrons in
the same orbital to be removed. Hence,as the experimental data shows, thecharging of the material leads to a shift
in the energy required to photoexcitethe 1s electrons toward higher energies,providing evidence that the electronsinvolved have predominantly metalcharacter.
Electrochemical Capacitors
Batteries (and also fuel cells) rely onchemical reactions at the electrodes togenerate electrical energy. The behaviorof certain electrode-electrolyte interfaces,however, resembles that of a conven-tional capacitor in that charge transferacross the interface over a limited voltage
range, up to ca. 3 V, is greatly impaired.Even though the potential should bethermodynamically sufficient to drive
one or more electron transfer processes,the rates at which such reactions proceedare negligibly small rendering the inter-face as effectively charged. Exceedinglycareful experiments performed byGrahame toward the middle of this pastcentury laid the foundations of our cur-rent knowledge of electrified interfaces.Key to the success of his experiments wasthe use of Hg electrodes, for which thesurface could be renewed thereby avoid-
ing problems with impurities. According
to theory, one plate of the capacitor is
F IG. 9. (top) Schematic representation of a charged electrochemicalcapacitor and double layers at both electrode|electrolyte interfaces. Note that the device is two double layers in series, one at each electrode|electrolyteinterface. Blue and magenta shades refer to net negative and positivecharges. (bottom) Schematic representation of a charged high area carbon
capacitor. The lines around the carbon (gray) particles represent either positive (magenta) or negative (blue) charges. Positive and negative ions(circles) are in pink and light blue, respectively.
0 100 200 300 400 500
0.0
0.5
1.0
1.5
2.0
2.5
3.0
E
c e l l ,
�
� F IG. 10. Voltage profiles for the constant current charge (light blue) and discharge(pink) of a high area carbon electrochemical capacitor incorporating an organic solvent.
the electrode and the other is a collec-
tion of ions present in the electrolyte,forming a diffuse double layer of only afew nanometers thick (see Fig. 9 top for aschematic representation of a completlycharged double layer capacitor). To pre-
serve interfacial electroneutrality, thetotal charge of this diffuse layer mustbe equal and opposite to that whichresides on the electrode. The actual spe-cific double layer capacitance of solidelectrode|aqueous solution interfaces, C
dl,
is on the order of a few tens of µF/cm 2,and thus much higher than those foundfor conventional capacitors, and a func-tion of the nature of both the electrodeand the electrolyte solution.
Carbon is an unusual material inthat forms displaying very high specificareas, up to 2000 m2/g, can be producedinexpensively. Assuming a C
dl
of ca. 10µF/cm2, a gram of such high-area carbon
should provide a capacity of 200 F, which
could be matched only by a conventionalcapacitor of much larger dimensions.Advantage has been taken of thisphenomenon to develop electrochemicalcapacitors based purely on carbon and
suitable electrolytes with exceedinglyhigh capacitances per unit weight orvolume (see Fig. 9 bottom for a schematicrepresentation of a charged carbonbased capacitor). Note that the storagedevice is comprised of two (interfacial)
capacitors connected in series. As ameans of illustration, constant currentcharging (or discharging) of a high areacarbon capacitor incorporating identicalelectrodes immersed in an organicelectrolyte elicits a linear increase (ordecrease) in the cell potential, E
cell,
with time (see Fig. 10), as expectedfor a conventional capacitor. The very
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22 The Electrochemical Society Interface • Spring 2006
F IG. 11. Ragone plots for an array of energy storage and energy conversion devices. Ref: Venkat Srinivasan and John Newman: http://berc.lbl.gov/venkat/Ragone-construction.pps.
small vertical traces that are observedimmediately following application orreversal of the current are due to voltagelosses attributed to the internal resistanceof the device or IR loss.
An appreciation of the advantagesuch an electrochemical capacitor,often referred to in the popular press assupercapacitor or ultracapacitor, offers
compared to batteries can be gleanedfrom the Ragone plot. As shown in Fig.11, electrochemical capacitors havesuperb specific power compared tobatteries, but modest specific energies.This translates, in transportationterms, as good acceleration but poorrange, which is precisely opposite tobatteries or fuel cells, which are yetanother type of electrochemical device
in which the reactants are added to theelectrodes to generate electricity (seecontribution in this Interface issue fromthe Energy Technology Division). Frompractical and technological viewpoints,electrochemical capacitors are robustdevices with excellent cycle life that canimprove the effectiveness of battery-
based systems by shrinking the volumeof batteries required and reducing thefrequency of their replacement.
Whether a battery, an electrochemicalcapacitor, a fuel cell, or a judicious
combination of two or more of these,the level of sophistication involvedin the design and manufacturingof a power source for a specificapplication, including microelectronics,transportation, and larger scalestationary stacks over the next few yearsmay well approach the same degreeof complexity as the devices they will
power. A particularly intriguing prospectis the possibility of constructing three
dimensional batteries incorporatingcomponents of nanometric dimensionsarranged in interpenetrating networks,to take advantage of short diffusionalpaths and thus higher currentsthan those achievable with present
technologies. The advent of noveltheoretical approaches and powerfulcomputers is expected to deepenfurther our understanding of the factorsthat control both the energetics andtransport dynamics of ions withinwell defined lattices. Such efforts are
being complemented by ingenioustactics in combinatorial chemistry andsimultaneous high-throughput screeningof multiple electrodes that could well
lead to the discovery of materialsdisplaying unsuspected properties.
Acknowledgments
The authors express their deepappreciation to N. Dudney, G. Blomgren,K. M. Abraham, B. Miller, R. Middaugh,R. Brodd, G. Amatucci, J. Miller,
S. Sarangapani, and R. Corn for a criticalreading of the manuscript.
Suggested Readings
1. Handbook of Batteries, 3rd ed.,D. Linden and T. B. Reddy, Editors,McGraw-Hill, New York (2002).
2. B. E. Conway, ElectrochemicalSupercapacitors: Scientific Fundamentalsand Technological Applications, KluwerAcademic/Plenum Publishing, NewYork (1999).
About the Authors
D ANIEL SCHERSON is the Director of the Ernest B.Yeager Center for Electrochemical Sciences and the Charles F. Marbery Professor of Research in
Chemistry at Case Western Reserve University. Heis currently the chair of the ECS Battery Division
Batteries andElectrochemical Capacitors(continued from previous page)
and an Associate Editor for the Journal of The Electrochemical Society. He may be reached at [email protected].
ATTILA P ALENCSÁR is a native of Romania and received his BS in chemistry at Babes-BolyaiUniversity in Cluj Napoca, Romania. He iscurrently pursuing his PhD at Case Western
Reserve University under the supervision of DanielScherson. He may be reached at [email protected].