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7/29/2019 Electrochemistry Encyclopedia -- Electrochemical Capacitors
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Electrochemistry Encyclopedia
(http://electrochem.cwru.edu/encycl/)
ELECTROCHEMICAL CAPACITORS
Their Nature, Function, and Applications
Brian E. Conway
Chemistry Department, University of Ottawa
10 Marie Curie StreetOttawa, Ontario K1N 6N5, Canada
(March, 2003)
Historical introduction
Electrochemical capacitors provide a mode of electrical charge- and energy-storage and delivery,
complementary to that bybatteries. The first electrochemical capacitor device was disclosed in a General
Electric Co. patent in 1957 to Becker but was of a crude nature, employing porous carbon. Later work by
Sohio (1969) described a so-called "electrokinetic capacitor" utilizing porous carbon in a non-aqueous
electrolyte which enabled it to be charged up to about 3 V, though the operation of the device was not
"electrokinetic" in nature, a misnomer. In 1971, Trasatti and Buzzanca recognized that the electrochemical
charging behavior of ruthenium dioxide films was like that ofcapacitors. Between 1975 and 1980, the present
author and his co-workers, under contract with the then Continental Group Inc., carried out extensive
fundamental and development work on the ruthenium oxide type of electrochemical capacitor (Conway, 1997)
which behaves as a surface- redoxpseudocapacitance (seebelow). The whole field has burgeoned since about
1990 and is very active in fundamental, and R&D directions.
A great deal of scientific and technological research has been reported in the scientific literature since about
1990. An extensive and detailed account of this has been given in the author's monograph on "Electrochemical
Supercapacitors: Scientific Fundamentals and Technological Applications" (1999).
Scientific introduction
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Fig. 1. Leyden
Jar, the first
capacitor or
"condenser".
In order to describe "electrochemical capacitors" and to explain their function and applications, it is necessary
first to consider the nature of an ordinary electrostatic capacitor or a "condenser" as it used to be called, and
thence the meaning of the term electrical capacitance.
The nature of electricity took a long time to be understood, from the early experiments on electrostatic electricity
in the mid-18th century, for example by Galvani, through the time of the invention of the first electric battery by
Alessandro Volta (Volta's "Pile") in 1800, on to Faradays's and Davy's monumental discoveries on the
chemical origin of electricity generated by Volta's pile. At first, two "kinds" of electricity were postulated: "animalelectricity", as in the works of Galvani on stimulation of the frog's leg nerve by contact between two dissimilar
metals and later, "Voltaic electricity" generated chemically from a Volta pile of zinc and silver or copper plates
separated by paper wetted with an acid or salt solution (Conway, 2000).
In parallel with these discoveries were extensive works on electrostatic electricity generated for example by the
rubbing of naturally occurring amber or by the so-called Wimshurst machine (a rotating circular plate, containing
insets of amber-like material, rubbing against charge-collector plates connected overall to a Leyden Jar or a
spark-gap). It was from this direction of research on electricity that the invention of the electric condenser arose,
referred to as the "Leyden Jar", and capable of storing electric charge generated by a Wimshurst machine. Such
a jar had the "capacity", depending on its dimensions and materials of construction, of storing electric charge bybringing it together in a condensed way (hence the term "condenser") on the surfaces of a Leyden Jar at a certain
two-dimensional charge density.
The principle of design and operation of the Leyden Jar and all subsequent regular condensers or capacitor
devices, is as follows. Two metal surfaces that constitute electrodes are separated at some small distance either
in air (or vacuum) or on each side of a liquid or solid film, referred to as the "dielectric", a term first used by
Michael Faraday . For a given separation of the electrode plates, the capacitance developed per unit area of the
two plates depends on the properties of the dielectric between the plates characterized by its so-called dielectric
constant.
In the case of the Leyden Jar (Figure 1), the material (glass) of the jar itself serves a the
dielectric medium and the contact plates were metal foils wrapped, inside and out,
around the cylindrical surfaces of the jar. The electrical contact to the inner surface foil
was by means of a conductingelectrolyte solution (or originally by ordinary water itself)
in which was immersed a conducting metal electrode for electrical contact. The device
was charged by joining two wires from the inside electrode and the outside foil to an
electrostatic machine of the Wimshurst type. In later experimentation, the Leyden Jar
capacitor was connected to the electrodes of a Volta's pile orbattery forcharging. This
was the first-generation capacitor forstorage ofelectric charge.
The nature of electric charge remained elusive until much later (1897) when J.J.
Thomson identified and characterized the fundamental entity of electric charge as the
"electron", present ubiquitously in all atoms of the Universe and identified, in his
experiments, by means of experiments on gases at low pressures in gas-discharge tubes
(Crookes tubes or neon lights). The electron charge was determined independently by
Townsend and by Millikan (Glasstone, 1940), and was shown to be equivalent to
Faraday's constant for the relation between extent of passage of charge and extent of
chemical change (as related by Faraday's Laws) caused by electrolysis of conducting
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solutions, when calculated on a "pergram-atom" or "gram-equivalent" basis.
Relation of capacitance to geometry and dielectric constant of a capacitor
The capacitance of a capacitor is proportional to the area of the contact plates and the dielectric constant of the
medium between the plates, and it is inversely proportional to the separation between the plates (see the
Appendix). In relation to electrochemical capacitors, to be discussed below, the capacitance of small dielectriccapacitors is very small being on the order of microfarads or nanofarads (millionth or billionth of a farad,
respectively) for small devices on the order ofmm orcm in dimensions. By having very thin insulating films, on
the order of 10 to 100 nanometers, formed anodically on the plate of a two-electrode capacitor, substantially
larger specific capacitances (that is per cm2) can be attained. Such devices are called "electrolytic capacitors"
because the thin dielectric oxide films are formed on the plates by an anodic electrolysis procedure applied at
metals such as aluminum, tantalum, titanium, niobium, etc. Such capacitors are still of the dielectric type (the
dielectric medium being here the thin, insulating oxide film, usually having a relatively high dielectric constant) and
should not be confused with the "electrochemical" capacitor type of device which is the topic of this article.
Electrochemical capacitors are a special kind of capacitor based on charging and discharging the interfaces of
high specific-area materials such as porous carbon materials or porous oxides of some metals. They can store
electric charge and corresponding energy at high densities in an highly reversible way, as does a regular
capacitor, and hence can be operated at specificpower densities (in watts/kg) substantially higher than can most
batteries. Their capacitance for a given size of the device is thus much higher, by a factor of 10,000 or so, than
those achievable with regular capacitors. For this reason proprietary names such as "Supercapacitors" or
"Ultracapacitors" have been coined to describe their performance.
While they function formally like rechargeable batteries in storing or delivering electric charge, their mechanisms
of charge storage are quite different, in most cases, from those operating in batteries. Thus, electrochemical
capacitors are not substitutes for batteries but rather are to be regarded as complementary to them for charge
storage or delivery. They can offer advantageously fast charging or discharging rates over most batteries of
comparable volume but their energy density is usually less, by a factor of 3 to 4, than that of batteries. Their high
power or power densities, however, enables them to be employed in interesting complementary ways in hybrid
systems with batteries.
An important difference between charging a capacitor and charging a battery is that there is always an intrinsic
increase of voltage on charge (or decrease on discharge) of a capacitor as the charge per cm2 is increased or
decreased. In contrast, an ideal battery has a constant voltage during discharge or recharge except as the state o
charge approaches 0 or 100%. Although practical batteries exhibitsome dependence of cell voltage on state ofcharge, especially lithium-intercalation batteries, the latter for fundamental reasons arising from intercalation. (See
the Appendix for further details.)
The double-layer capacitance at electrode interfaces
Nature of electrical double layers
An important class of electrochemical
capacitors utilizes the co-called
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Fig. 2. Models of the double layer as historically developed: a)
Helmholtz model b) Gouy-Chapman model of the diffuse layer
c) Stern's model, combining (a) and (b) d) Grahame's later
double-layercapacitance that arises at
all electrode interfaces with electrolyte
solutions orionic melts. The concept
and model of the double layer arose in
the work of von Helmholtz (1853) on
the interfaces ofcolloidal suspensions
and was subsequently extended to
surfaces of metal electrodes by Gouy,Chapman, and Stern, and later in the
notable work of Grahame around
1947. Models of the double layer are
shown in Figure 2, with their
capacitor-like structures.
Helmholtz envisaged a capacitor-like
separation ofanionic and cationic
charges across the interface of
colloidal particles with an electrolyte.For electrode interfaces with an
electrolyte solution, this concept was
extended to model the separation of
"electronic" charges residing at the
metal electrode surfaces (manifested
as an excess of negative charge
densities under negativepolarization
with respect to the electrolyte solution
or as a deficiency of electron charge
density under positive polarization),
depending in each case, on the
correspondingpotential difference
between the electrode and the solution
boundary at the electrode. For zero
net charge, the corresponding potentia
is referred to as the "potential of zero
charge".
In response to positive or negativeelectric polarization of the electrode
relative accumulations of cations or
anions develop, respectively, at the
solution side of the charged electrode.
If, for energetic reasons, the ions of
the electrolyte are not faradaically
dischargeable (that is no electron
transfercan occur across the interface
("ideally polarizable electrode", for
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model and e) Model of Bockris, Devanathan and Muller
showing presence and orientation of solvent dipoles.
example a mercury electrode,
Grahame 1947 and Parsons 1954),
then an electrostatic electrical
equilibrium is established at the
interface resulting in a "double layer" of separated charges (electrons or electron deficiency at the metal side and
cations oranions at the solution side of the interface boundary), negative and positive, across the interface.
The difference of potential extends beyond the immediate layer ofsolvatedions in the compact, capacitor-like
(Helmholtz) region, out into solution, so that a furtherdiffuse region capacitance (the diffuse-layer capacitance
"Cdiff") arises. It combines with that of Helmholtz's region "CH" in series. (See the Appendix for further details.)
The Helmholtz region capacitance "CH" is of special significance for electrochemical capacitors since it is directly
dependent on accessible electrode area and has large values (relative to those for regulardielectric capacitors)
between about 16 F/cm2 and about 40-50 F/cm2, depending on electrode potential, the chemical nature of the
metal surface, chemical nature of the solvent, and the types of ions (and their solvation by the solvent) present in
the electrolyte solution.
The most extensively studied metal surface, with respect to its double-layer capacitance, is that of mercury in
various solvent media, especially water.
It was mentioned that the specific capacitances of electrode double layers are very large, some 10,000 times
those of ordinary dielectric capacitors, per cm2 area. The reason for this is that the separation ofcharges in
electrochemical double layers is on the order of 0.3-0.5 nminstead of 10 to 100 nm with oxide-film dielectrics
(electrolytic capacitors) or 1000 nm with very thin mica or polystyrene dielectric-film hardware capacitors.
Hence, it is seen that with large specific-area porous electrodes, for example at carbons having say 1000 m2/g
of material and exhibiting, say, 15 F/(real cm2) of double-layer capacitance in some suitable electrolyte solution
the accessible capacitance "C" is 1000 (m2/g) 10,000 (cm2/m2) 15 (F/cm2) = 150 million F/g, that is 150
farads/g, a very large capacitance! Hence the term "supercapacitors" or "ultracapacitors" for devices based on
double-layer capacitance at high-area substrates.
The high degree of reversibility of charge acceptance and delivery, and hence capability for excellent operating
powerlevels compared withbatteries of comparable size arises because no slow chemical processes or phase
changes take place between charge and discharge as they do in most battery-type electrical charge generating
devices.
It is the essence of battery-type charge/discharge processes that faradaic processes take place leading to major
chemical and structural changes of the electrochemical reactive materials, for example conversions of lead
dioxide to lead sulfate and lead metal to lead sulfate in discharge of the lead-acid battery which, as is well
known, limits charge/discharge to a cycle life of 1000 to 3000, depending on rates of charge and discharge, and
temperature. By contrast, electrochemical double-layer and oxide-type (seebelow) capacitors can exhibit cycle
lives up to one million under suitable conditions. This is because, ideally at least, only storage and delivery of
electrostatic charge takes place at the extended two-dimensional interface of high-area materials and no
irreversible or slow chemical phase changes take place as they do between three-dimensional chemical materials
in rechargeable batteries. This is a fundamental difference between the electrochemical behavior and properties
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Fig. 3. Hierarchy of equivalent circuits for capacitors and
electrochemical capacitors showing " transmission-line"
circuit for the latter, in the case of a porous carbon electrode.
of electrochemical capacitors relative to those of batteries.
Electrical irreversibility in electrochemical capacitor charging and discharge:
rate effects
It was stated earlier in this article that charging and discharging of electrochemical capacitors has commonly been
perceived as a process much more reversible than that for batteries and hence being capable of operation at high
power densities. While, in practice, this is largely true, charging of the high-area, porous-electrode structures thatare required for achieving large capacitance densities (farads/g or farads/cm3) encounters limitations of rate due
to the distributed electrolytic and contact resistances within the pore structure of such materials.
In the simplest analysis, any practical
capacitor device behaves as if an
ohmic resistance is in series with it, the
so-called equivalent (or real) series
resistance (Figure 3).
The presence of real or equivalentseries resistance in the operating
equivalent circuit of any capacitor
introduces an ir potential drop in the
process ofcharging ordischarging and
this drop depends, of course, on the
charging rate (current) leading to
distortion of the charging curve of
accumulated charge against voltage, in
time. When the distributed resistanceeffect also operates, as it normally
does, the distortion effect becomes
more complex but has been
experimentally and computationally
evaluated (de Levie, 1963).
The above effect causes limitation of
rates at which the capacitor can be
charged or discharged and, forac
modulated charging, it also introducesa frequency-dependent phase angle
(normally -90o) between the
modulated applied voltage and the
resultant charging current. This also
applies to other, non-constant charging
modes.
In practice, with a porous electrode,
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Fig. 4. de Levie transmission-line model forresistance/capacitance matrix in an high-area porous
electrode.
Fig. 5. Complex-plane impedance plots
(imaginary capacitive component against realohmic component) for a porous electrode
according to de Levie.
the situation is much more complex
since the matrix of microscopic pores
within the macroscopic electrode
structure offers a complex,
series/parallel equivalent circuit
comprised of a distribution ofohmic
(resistive) and capacitive elements
which leads to the whole electrodehaving a non-uniform effective
resistance and capacitance, dependent
on frequency (in ac modulation) or on
the time-scale of pulsed or non-
constant rates of charging. As shown
in the classical work of de Levie
(1963), the equivalent circuit for such
electrodes is that of a transmission line
(Figure 4) having a -45o phase angle
(Figure 5) characterizing its impedance
behavior.
This situation leads to limitation of the rates of which
charging ordischarging of porous capacitor electrodes
can be conducted and is additional to any equivalent
series resistance effects a practical cell may experience
due to cell design and electrolyteresistance.
de Levie has pointed out that the distributed R/C effect
in porous electrodes is equivalent to restrictions of
power due to ohmic ir drop (that is the potential drop
due to current passing through resistive elements in the
matrix). Thus there is a "penetration effect" into the
electrode matrix due to attenuation of for example a
modulation or time-dependent transient charging
voltage so that not all of the depth or width, or
diameter of the electrode structure is subject to a
uniform charging rate. This introduces a non-chemical
irreversibility in the charge/discharge behavior of the
electrochemical capacitor device which is electrically
demonstrable.
It must be stated, however, that in state-of-the-art developments of electrochemical capacitors, using aqueous-
solution electrolytes, the above distributed-resistance effect has been substantially minimized so that devices
having high operating power have been successfully engineered and marketed. Nevertheless, with non-aqueous
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electrolyte capacitors, which have higher operating voltages up to 3.0 to 3.5 V (hence 9 to 12 times energy
density which depends on thesquare of maximum operating voltage), the distributed ohmic effects are more
significant so that achievable operating power levels are less than those attainable with aqueous electrolyte
devices.
Electrochemical capacitors based on pseudocapacitance
A different kind ofcapacitance can arise at electrodes of certain kinds, for example ruthenium dioxide, when the
extent offaradaically admitted charge depends linearly, or approximately linearly, on the applied voltage. For
such a situation, the electrode behavior is equivalent to, and measurable as, a capacitance. This capacitance can
be large but it isfaradaic and not electrostatic (that is non-faradaic) in origin. This is hence an important
difference from the nature ofdouble-layer capacitance, so it is called "pseudocapacitance". This kind of
pseudocapacitance can originate when an electrochemical charge-transfer process takes place to an extent
limited by a finite quantity of reagent or of available surface. Several examples of pseudocapacitance can arise,
but the capacitance function is usually not constant and, in fact, is usually appreciably dependent onpotential or
state of charge.
However, when the process is surface limited, and is proceeding in several one-electron stages, a broad range of
significant capacitance values arises as is found with ruthenium dioxide electrodes where the pseudocapacitance
is almost constant (within 5%) over the full operating voltage range. Some other metal oxides behave similarly but
only over smaller operating voltage ranges. The ruthenium dioxide pseudocapacitance provides one of the best
examples of electrochemical (pseudo)capacitance as, in addition to the almost constant capacitance over a wide
voltage range, its reversibility is excellent, with a cycle life over several hundred-thousand cycles. Furthermore,
the pseudocapacitance can increase the capacitance of an electrochemical capacitor by as much as an order of
magnitude over that of the double-layer capacitance. However, its cost prevents its large-scale use so that it has
been employed mainly in military applications.
Another type of material exhibiting pseudocapacitive behavior that is highly reversible is the family ofconducting
polymers such as polyaniline or derivatives of polythiophene. These are cheaper than ruthenium dioxide but are
less stable, giving only thousands of cycles (still quite attractive) over a wide voltage range. (See the Appendix
for a more detailed discussion of the pseudocapacitance.)
Applications and technology
Fabrication of electrochemical capacitors
General industrial production of electrochemical capacitors follows that of battery cell procedures with automatic
production-line machinery. Cell designs are of various kinds including cylindrical,prismatic, button, or coin types
with some larger embodiments being of cake-tin sizes or larger, and some multi-cell series for higher voltage with
bipolarelectrodes having edge seals. In series configurations for high-voltage applications, balancing of unit cell
performance and behavior is a technological challenge.
Hybrid systems
The highpower-density capability of electrochemical capacitors has led them to be employed in hybrid
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configurations withbatteries andfuel cells in a load-leveling function, for example in electric vehicles. The
capacitor component, suitably coupled with a battery or fuel cell, provides the necessary power density for up-
hill or accelerative driving while regenerative braking provides a certain extent of recharging.
Another type of hybrid system is where ruthenium dioxide is used as a second oxide component, acting as a
pseudocapacitance in electrolytic capacitors (the Evans Hybrid Capacitor). This gives indirectly, an improved
capacitance density for the overall two-electrode device.
Another interesting hybrid type, currently under investigation in our own and other laboratories, is a combination
of a double-layercarbon (electrochemical capacitor) electrode combined to work against a rechargeable battery
electrode, for example a lead-acid positiveplate (acidic solution) or a nickel battery positive plate (alkaline
solution). This type of device (called an asymmetric capacitor) enables almost all of the charge residing on the
capacitor-type electrode to be utilized on discharge in contrast to the battery-type electrode while, with a
symmetrical capacitor made with two similardouble-layer capacitance electrodes, each electrode is only half
discharged from its initial voltage, relative to the other electrode, when the cell discharge voltage reaches zero,
therefore delivering less electrical energy than the hybrid.
Another application is in electrical research experiments where very high energy and high-rate discharges arerequired, for example through gases for high-energy spark or arc generation.
A variety of other applications has been envisaged in the literature (Conway, 1999). Examples are: cold-start
assist for diesel locomotives; emergency back-up power for computer systems; stationary power-system load
leveling or bridging for short-period power outages; energy source for initial heating of catalytic converter units;
energy collection and storage from windmill dynamos.
For society at large, the use of capacitor/battery hybrid systems for improvement of electric-vehicle (EV)
performance will assist the adoption of EV transportation systems with zero or diminished nitrogen oxide and
carbon dioxide atmospheric contamination. However, such a transition to an "EV lifestyle" will probably notbecome substantial for another one to two decades.
Appendix
Relation of capacitance to geometry and dielectric constant of a capacitor
The capacitance "C" of a capacitor depends on a) the area "A" of the contact plates, b) the separation "d"
between the plates (when parallel), and c) the dielectric constant "" of the medium between the plates (limitingly
vacuum, for which "" is taken as 1; for all other materials, including gases, > 1). The relationship between "C"
and the above quantities is given by the simple equation (Conway 1999)
[1] C = A / 4 d
or, in terms of so-called rationalized units,
[2] C = A o / d
where o (= 8.84 10-12 farads/m) is the dielectric permittivity of free space. The units of "C" are in farads or
coulombs pervolt, that is coulombs stored by the capacitor per volt across its two electrodes.
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Some important differences between capacitors and batteries
An important difference between charging a capacitor and charging abattery is that there is always an intrinsic
increase ofvoltage "V" on charge (or decrease on discharge) of a capacitor as the charge percm2 is increased
or decreased, according to Equation [3] which defines the relation between capacitance "C" and the inter-plate
voltage "V" that arises from accumulation of a charge "q":
[3] C = q/V or q = CV
In contrast, an ideal battery has a constant voltage during discharge or recharge except as the state of charge
approaches 0 or 100%. (Practically, most batteries exhibit some dependence ofcell voltage on state of charge,
especially lithium-intercalation batteries, the latter for fundamental reasons arising from intercalation).
The consequence of the above difference, based on Equation [3], is that the energy stored by a capacitor is 1/2
CV2 or 1/2 qV while, for a battery, the corresponding stored energy (orenergy density) is qV, twice as much
as that for a capacitor charged to the same cell voltage "V". Thus, the stored energy in a capacitor device
increases as thesquare of the cell voltage "V" as charge is accumulated. This is an important difference between
capacitor and battery cell behavior and affects the interfacing between such systems in hybrid devices.
It was noted above that the energy stored in a capacitor cell, charged to a voltage "V" is 1/2 CV 2 and "V"
increases as charge "q" accumulates on its plates determined by "C". The charging energy 1/2 CV2 arises in the
following way. For a capacitor being charged from an initial voltage V = 0 to a final value "V f" the energy "E"
stored will be a free-energy "G" (charge times voltage):
[4]
At any state of charge, q = CV (Equation [3]), so that
[5]
[6] G = 1/2CVf2
Double-layer capacitance
The charge density "q" (coulomb/cm2) ofelectrons and ions at the interface is dependent on thepotential
difference, , across this double layer so that a differential capacitance "Cdl" arises determined by
[7] Cdl = dq/d() or q/
The difference of potential extends beyond the immediate layer ofsolvated ions in the compact, capacitor-like
(Helmholtz) region, out into solution, so that a furtherdiffuse-layer capacitance "Cdiff" arises. It combines with
the capacitance of Helmholtz region "CH" in series, electrically, so that
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[8]
Pseudocapacitance
A different kind of capacitance can arise at electrodes of certain kinds, for example ruthenium dioxide, when the
extent offaradaically admitted charge "q" depends linearly, or approximately linearly, on the applied voltage "V".For such a situation, there is a mathematical derivative, dq/dV that would be constant, which is equivalent to, and
measurable as, a capacitance (see Equation [3]). This capacitance, denoted by "C", can be large but it is
faradaic and not electrostatic (that is non-faradaic) in origin. This is hence an important difference from the
nature of double-layer capacitance "C" or "Cdl" so it is called "pseudocapacitance". The pseudocapacitance can
increase the capacitance of an electrochemical capacitor by as much as an order of magnitude over that of the
double-layer capacitance.
This kind of pseudocapacitance can originate when an electrochemical charge-transfer process takes place to an
extent limited by a finite quantity of reagent or of available surface, the latter in the case ofadsorption (forexample of hydrogen), with charge transfer. Several examples of pseudocapacitance can arise as follows, but the
"C" function is usually not constant and, in fact, is usually appreciably dependent onpotential orstate of charge
a) When an electrochemical adsorption process, arising from charge transfer, takes place at an electrode surface
for example in the process ofelectrosorption of H atomsdischarged at Pt electrode surfaces in aqueousacid
solution by the process:
[9] H3O+ + Pt + e- ==> H2O + Pt/H
so-called underpotential deposition since the above reaction takes place over a potential range "V" of about0.35 V positive to the equilibrium potential forH2 gas evolution in the electrolysis of water.
Fractional H coverages "" at Pt can increase continuously, over the above electrode potential range, from 0 to
1, prior to evolution of H2 and each atom of H deposited requires passage of one electron of electric charge.
Hence, a pseudocapacitance "C" arises from the relation between charge passed "q" and "V", and "q" is
faradaically related to the coverage fraction "" of electrodeposited H. A full monolayer ( ==> 1) of H
requires passage of about 210 C of charge "q1" percm2 of a smooth Pt surface.
[10] C = q1 d/dV
"" is related to electrode potential "V" by the relation
[11] /(1 - ) = Kexp (VF/RT)
b) A number ofelectrochemical reactions involving species in solution, such as Fe+++/Fe++ or
[Fe(CN)6]3-/[Fe(CN)6]
4-, known as redox processes, take place at inert electrodes, for example Au or Pt, with
a logarithmic relation (theNernst equation) between the extents ofoxidation/reduction between the redox couple
pair of ions. Thus, for example
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[12] E = Eo + (RT/F) ln a[Fe(CN)6]3-/a[Fe(CN)6]
4-
where "a" represents the respective activities of the two ions of the redox couple. The above Equation [11] can
be rearranged in terms of the fractions of a given chemical quantity of the redox ions in the reversible reaction
[13] [Fe(CN)6]3- + e- [Fe(CN)6]
4-
that exist in the course of reduction (or reoxidation) as a function of the potential "E" in relation to its so-calledstandard value "Eo" in Equation [12]. E = Eo when the reagent ion activities (concentrations) are equal so that the
ln function is zero. The rearranged form of Equation [11] is in terms of the molar quantities "Qox" and "Qred" in
relation to the total reagents Qox + Qred (= Q) and reads
[14]
with Qred
/Q = 1 - Qox
/Q. Then it is seen that Equation [14] has thesame form as that of Equation [11] (after
taking logarithms) forelectrosorption and its derivative is a capacitance quantity.
c) A similar logarithmic relation in X / (1 - X) applies to absorption of Li+ ions into Li-intercalation hosts in Li-ion
battery electrochemistry where "X" is the fractional occupancy of available intercalation sites in the intercalation
host material, for example TiS2, CoO2, etc. Hence, Li+ ion intercalation formally exhibits a pseudocapacitance,
though the Li+ ion systems are normally referred to as battery devices.
In each of the three types of pseudocapacitance
systems, "C" is substantially dependent on potential,
having a large maximum of about 2200 F/cm2 at "",
"Qox/Q", or "X" equal to 0.5, but with appreciable
values of "C" arising only over a potential range of
about 120 mV which is too narrow to be of value for
practical applications.
However, when the redox process is a surface one,
proceeding in several one electron stages, a much
broader range (1.4 V) of significant "C" values arises
as is found with RuO2 electrodes where "C" is almost
constant within 5% over that voltage range. Some othe
transition-metal oxides behave similarly but only over
smaller operating voltage ranges, about 0.6 to 0.8 V
(Conway, 1997).
The case of RuO2 pseudocapacitance provides one of
the best examples of electrochemical
(pseudo)capacitance as its "C" is almost constant
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Fig. 6. Comparison of cyclic voltammetry
behavior of a reversibly chargeable
electrochemical capacitor material (RuO2)
and a battery-type (Pb/PbCl2) like in the lead-
acid battery.
over a 1.4 V voltage (Figure 6) range and its
reversibility is excellent, with a cycle life over several
hundred-thousand cycles. However, its cost prevents
its large-scale use so that it has been employed mainly
in military applications.
Another type of material exhibiting quasi-redox
behavior that is highly reversible is the family of
conducting polymers such as polyaniline or derivatives
of polythiophene. These are cheaper than ruthenium
dioxide but are less stable, giving only thousands of
cycles (still quite attractive) over a voltage range
between 0.8 V and up to 3.0 V for some materials.
Figure 6 shows the contrast between a reversibly
charged electrochemical capacitor material (RuO2) and
an irreversibly chargeable battery-type material
(Pb/PbCl2).
Related article
Electrolytic capacitors
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Listings of electrochemistrybooks, review chapters,proceedings volumes, and full text of some historical
publications are also available in the Electrochemistry Science and Technology Information Resource (ESTIR).
(http://electrochem.cwru.edu/estir/)
The Encyclopedia is hosted by the Ernest B. Yeager Center for Electrochemical Sciences (YCES) and the Chemical
Engineering Department , Case Western Reserve Univers ity , Cleveland, Ohio.
Copyright Notice.
Edited by Zoltan Nagy ( nagyz@email.unc.edu ), Department of Chemistry , The University of North Carolina at Chapel Hill .
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