Electrochemistry Encyclopedia -- Electrochemical Capacitors

7/29/2019 Electrochemistry Encyclopedia -- Electrochemical Capacitors

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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


12/14

[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

Bibliography

Power Limitations of Supercapacitor OperationAssociated with Resistance and Capacitance

Distribution in porous Electrode Devices, W. G. Pell and B. E. Conway, "Journal of Power Sources" Vol

105, pp 169-181, 2002.

Advances in Electrochemical Capacitors and Hybrid Power Systems, R. J. Brodd, D. H. Doughty, K.

Naoi, M. Morita, C. Nanjundiah, J. H. Kim, and G. Nagasubramanian (editors), The Electrochemical

Society Proceedings, Vol. 2002-7, Pennington, NJ, 2002.

Bicentennial of Alessandro Volta's Invention of the "Electric Pile", B. E. Conway, "Canadian Chemical

News" Vol. 52, No. 1, pp 15-17, January 2000.Available at: http://www.accn.ca/accn2000/january2000/pg12-22.pdf (the second article in the file).

Electrochemical Supercapacitors: Scientific Fundamentals and Technological Applications, B. E. Conway

Kluwer Academic/Plenum Publishing, New York, 1999.

The Role and Utilization of Pseudocapacitance for Energy Storage by Supercapacitors, B. E. Conway, V

Birss, and J. Wojtowicz, "Journal of Power Sources" Vol. 66, pp 1-14, 1997.

Ruthenium Dioxide: a New Interesting Electrode Material, Solid State Structure and Electrochemical


14/14

Behavior, S. Trasatti and G. Buzzanca, "Journal of Electroanalytical Chemistry" Vol. 29, pp A1-A5,

1971.

Michael Faraday, a Biography, L. Pearce Williams, Chapman and Hall, London, 1965.

On Porous Electrodes in Electrolyte Solutions, R. de Levie, "Electrochimica Acta" Vol. 8, pp 751-780,

1963.

Low Voltage Electrolytic Capacitor, H. L. Becker, U.S. Patent 2,800,616, 1957.

Equilibrium Properties of Electrified Interfaces, R. Parsons, in "Modern Aspects of Electrochemistry" Vol.

1, pp 103-179, J. O'M. Bockris (editor), Butterworths, London, 1954.

The Electrical Double Layer and the Theory of Electrocapillarity, D. C. Grahame, "Chemical Reviews"

Vol. 41, pp 441-501, 1947.

Physical Chemistry, (Chapter 1) S. Glasstone, MacMillan, London, 1940.

Leyden Jar, "Encyclopaedia Britannica" Vol. 13, p 989, 1929.

The Electron in Chemistry, J. J. Thomson, Chapman and Hall, London, 1923.

On the Charge of Electricity Carried by Gaseous Ions, J. J. Thomson, "Philosophical Magazine" Vol. 5,

pp 346-355, 1903.

Ueber einige Gesetze der Vertheilung elektrischer Strme in krperlichen Leitern mit Anwendung auf die

thierisch-elektrischen Versuche (in German), H. von Helmholtz, "Annalen der Physik und Chemie,

Leipzig" Vol. 89, pp 211-233, 1853. Available on the WWW.

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 ( [email protected] ), Department of Chemistry , The University of North Carolina at Chapel Hill .

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