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[[File:Pseudocapacitance-Priciple.png|thumb|right|200px|Simplified view of a double-layer with specifically adsorbed ions which have submitted their charge to the electrode to explain the faradaic charge-transfer of the pseudocapacitance.]]
'''Pseudocapacitance''' stores [[Electric energy|electrical energy]] [[Electrochemistry|electrochemically]] by means of reversible [[Faradaic current|faradaic]] [[Redox|redox reactions]] on the surface of suitable [[electrode]]s in an [[Supercapacitor|electrochemical capacitor]] with a [[Double layer (interfacial)|electric double-layer]].<ref name="conway1">{{Literatur|Autor=B. E. Conway|Titel=Electrochemical Supercapacitors: Scientific Fundamentals and Technological Applications|Verlag=Springer|Ort=Berlin|ISBN=0306457369|Jahr=1999|Seiten=1-8|Online={{Google Buch|BuchID=8yvzlr9TqI0C|Seite=1}}}} see also [http://electrochem.cwru.edu/encycl/art-c03-elchem-cap.htm Brian E. Conway in Electrochemistry Encyclopedia: ''ELECTROCHEMICAL CAPACITORS Their Nature, Function, and Applications'']</ref><ref name="Halper">{{cite techreport|author= Marin S. Halper, James C. Ellenbogen |title= Supercapacitors: A Brief Overview |publisher=MITRE Nanosystems Group|date= March 2006|url= http://www.mitre.org/sites/default/files/pdf/06_0667.pdf ||accessdate=2014-01-20}}</ref><ref name="Frackowiak">E. Frackowiak, F. Beguin: ''Carbon Materials For The Electrochemical Storage Of Energy In Capacitors.'' In: ''CARBON.'' 39, 2001, S. 937–950 ([http://144.206.159.178/ft/145/34337/587733.pdf PDF])  E. Frackowiak, K. Jurewicz, S. Delpeux, F. Béguin: ''Nanotubular Materials For Supercapacitors.'' In: ''Journal of Power Sources.'' Volumes 97–98, Juli 2001, S. 822–825, {{doi|10.1016/S0378-7753(01)00736-4}}.</ref> Pseudocapacitance is accompanied with an [[electron]] [[Charge transfer complex|charge-transfer]] between [[electrolyte]] and electrode coming from a [[Solvation|de-solvated]] and [[Adsorbtion|adsorbed]] [[ion]] whereby only one electron per charge unit is participating. This faradaic charge transfer originates by a very fast sequence of reversible redox, [[Capacitive deionization|elctrosorption]] or [[Intercalation (chemistry)|intercalation]] processes. The adsorbed ion has no [[chemical reaction]] with the [[atom]]s of the electrode. No [[chemical bond]]s arise.<ref name="Garthwaite">{{cite web|last=Garthwaite|first=Josie|title=How ultracapacitors work (and why they fall short)|url=http://gigaom.com/cleantech/how-ultracapacitors-work-and-why-they-fall-short/|work=Earth2Tech|publisher=GigaOM Network|accessdate=23 April 2013|date=12 July 2011}}</ref> Only a charge-transfer take place.

A faradaic pseudocapacitance still only occurs together with a static [[double-layer capacitance]]. Pseudocapacitance and double-layer capacitance both contribute indivisible to the total capacitance value of the chemical capacitor. The amount of pseudocapacitance depends on the surface area, material and structure of the electrodes. The pseudocapacitance may exceed the value of double-layer capacitance for the same surface area by factor 100, depending on the nature and the structure of the electrode.<ref name="conway1" />

The amount of [[electric charge]] stored in a pseudocapacitance is linearly proportional to the applied [[voltage]]. The unit of pseudocapacitance is [[farad]].

== History ==

* Development of the double layer and pseudocapacitance model see [[Double layer (interfacial)]]
* Development of the electrochemical components see [[Supercapacitors]]

== Redox reactions ==

=== Differences ===

==== Rechargeable batteries ====
Redox reactions in [[Rechargeable battery|batteries]] with faradaic charge-transfer between an electrolyte and the surface of an electrode were characterized decades ago. These [[chemical process]]es are associated with [[chemical reaction]]s of the electrode materials usually with attendant [[Phase transition|phase changes]]. Although these chemical processes are relatively reversible, battery charge/discharge cycles often irreversibly produce unreversed chemical reaction products of the reagents. Accordingly, the cycle-life of rechargeable batteries is usually limited. Further, the reaction products lowers [[power density]].  Additionally, the chemical processes are relatively slow, extending charge/discharge times.

==== Electro-chemical capacitors ====
[[File:Electric double-layer (BMD model) NT.PNG|thumb|right|200px|Schematic representation of a double layer on an electrode (BMD) model. 1. Inner Helmholtz plane, (IHP), 2. Outer Helmholtz plane (OHP), 3. Diffuse layer, 4. Solvated ions (cations) 5. Specifically adsorbed ions (redox ion, which contributes to the pseudocapacitance), 6. Molecules of the electrolyte solvent]]

A fundamental difference between redox reactions in batteries and in electrochemical capacitors ([[Supercapacitor]]s) is that in the latter, the reactions are very a fast sequence of reversible processes with electron transfer without any phase changes of the electrode molecules. They does not involve making or breaking [[chemical bond]]s. The [[Solvation|de-solvated]] atoms or ions contributing the pseudocapacitance simply cling<ref name="Garthwaite" /> to the atomic structure of the electrode and charges are distributed on surfaces by physical [[adsorption]] processes. Compared with batteries, supercapacitor faradaic processes are much faster and much more stable over the time because they leave no or fewer reaction products leading to a degradation of capacitance.

This behavior is the essence of the new class of capacitance, termed “pseudocapacitance”.

Pseudocapacitive processes lead to a charge dependent linear capacitive behavior as well as the accomplishing non-faradaic [[double-layer capacitance]] in contrast to batteries, which have nearly a charge-independent behavior. Pseudocapacitance and double-layer capacitance both contribute indivisible to the total capacitance value of a supercapacitor like the both sides of the same coin. The amount of pseudocapacitance depends on the surface area, material and structure of the electrodes. The pseudocapacitance may exceed the value of double-layer capacitance for the same surface area by factor 100, depending on the nature and the structure of the electrode.<ref name="conway1" />

== Capacitance functionality ==
[[File:Intercalactionrp.png|thumb|right|Intercalated metal atoms between planar graphite layers]]
[[File:Figure5CDC.jpg|thumb|right|Confinement of solvated ions in pores, such as those present in carbide-derived carbon (CDC). As the pore size approaches the size of the solvation shell, the solvent molecules are removed, resulting in larger ionic packing density and increased charge storage capability.]]

Applying a voltage at the capacitor terminals moves the polarized [[ion]]s or charged atoms in the electrolyte to the opposite polarized electrode. Between the surfaces of the electrodes and the adjacent electrolyte an electric [[Double layer (interfacial)|double-layer]] will be generated. One layer of ions on the surface atoms of the electrode and the second layer of adjacent polarized and solvated ions in the electrolyte which have moved to the opposite polarized electrode. The two ion layers are separated by a layer of single solvent molecules of the electrolyte. Between the two electrical separated layers a [[Static electricity|static]] [[electric field]] has formed which results in a [[double-layer capacitance]]. Accompanied with the electric double-layer some [[Solvation|de-solvated]] ions out of the electrolyte pervade the separating solvent layer and will be [[Adsorbtion|adsorbed]] by the surface atoms of the electrode. They will be specifically adsorbed and deliver they charge to the electrode.

With other words: In a Helmholtz double-layer the ions in the electrolyte may also act as [[electron donor]]s transferring with a  [[Charge-transfer complex|charge-transfer]] [[electron]]s to the [[atom]]s of the electrode resulting in a [[faradaic current]]. This faradaic [[Charge-transfer complex|charge transfer]] originates by a very fast sequence of reversible  [[redox]] reactions, electrosorptions or [[Intercalation (chemistry)|intercalation]] processes between electrolyte and the electrode surface is called pseudocapacitance.<ref name="Conway-Pell" />

Depending on the electrode's structure or surface material, pseudocapacitance can originate when specifically adsorbed [[Ion|cations]] pervade the double-layer, proceeding in several one-[[electron]] stages. The electrons involved in the faradaic processes are transferred to or from [[Valence electron|valence-electron]] states ([[Atomic orbital|orbitals]]) of the redox electrode reagent. They enter the negative electrode and flow through the external circuit to the positive electrode where a second double-layer with an equal number of [[Ion|anions]] has formed. But these anions don’t accept the electrons. They remain on the electrode's surface in the charged state, and the electrons remain in the strongly ionized and "electron hungry" transition-metal ions of the electrode. This kind of pseudocapacitance has a linear function within narrow limits and is determined by the [[Electric potential|potential-dependent]] degree of surface coverage of the adsorbed anions. The storage capacity of the pseudocapacitance is limited by the finite quantity of [[reagent]] or of available surface.

Description of the systems that give rise to pseudocapacitance:<ref name="Conway-Pell" />
* [[Redox]] system: Ox + ze‾ ⇌ Red and {{chem|O|2|‾}} +  {{chem|H|1}} ⇌ in lattice
* [[Intercalation (chemistry)|Intercalation]] system: Liˡ in "{{chem|Ma|2}}"
* [[Capacitive deionization|Electrosorption]], underpotential deposition of metal adatoms: {{chem|M|꞊|1}} + S + ze‾ ⇌ SM  (S = surface lattice sites) or {{chem|H|ˡ}} e‾ + S ⇌ SH

All three types of electrochemical processes giving rise to pseudocapacitance have been utilized in supercapacitors.<ref name="Conway-Pell">B.E. Conway, W.G. Pell, [http://www.springerlink.com/content/tvbpuql70x5uetay/ Double-layer and pseudocapacitance types of electrochemical capacitors and their applications to the development of hybrid components]</ref><ref name="Conway-Birss">B. E. Conway, V. Birss, J. Wojtowicz, [http://www.sciencedirect.com/science/article/pii/S0378775396024743 The role and the utilization of pseudocapacitance for energy storage by supercapacitors], Journal of Power Sources, Volume 66, Issues 1–2, May–June 1997, Pages 1–14</ref>

When discharging pseudocapacitance, the charge transfer is reversed and the ions or atoms leave the double-layer and distribute randomly into the electrolyte.

=== Pseudocapacitive materials ===

The ability of electrodes to accomplish pseudocapacitance effects by redox reactions of electroactive species, electrosorption of H or metal ad-atoms or intercalation strongly depends on the chemical affinity of electrode materials to the ions adsorbed on the electrode surface as well as on the structure and dimension of the electrode pores. Materials exhibiting redox behavior for use as electrodes in pseudocapacitors are transition-metal oxides inserted by doping in the conductive electrode material such as active carbon, as well as conducting polymers such as [[polyaniline]] or derivatives of [[polythiophene]] covering the electrode material.

==== Transition metal oxides ====

The best researched and understood by the research of B. E. Conway <ref name="conway1"  /><ref name="Conway Transition">{{Literatur|Autor=B. E. Conway|Titel=Transition from ‘Supercapacitor’ to ‘Battery’ Behavior in Electrochemical Energy Storage|Sammelwerk=Journal of The Electrochemical Society|Band=138|Nummer=6|Jahr=1991|Monat=Mai|Seiten=1539–1548|url=http://jes.ecsdl.org/content/138/6/1539.full.pdf+html |DOI=10.1149/1.2085829}}</ref> are electrodes out of transition metal oxides for high amount of pseudocapacitance. Many oxides of transition metals like [[ruthenium]] ({{chem|RuO|2}}), [[iridium]] ({{chem|IrO|2}}), [[iron]] ({{chem|Fe|3|O|4}}), [[manganese]] ({{chem|MnO|2}}) or sulfides such as [[titanium sulfide]] ({{chem|TiS|2}}) or their combinations are able to generate many faradaic electron–transferring reactions combined with low conducting resistance.<ref>M. Jayalakshmi, K. Balasubramanian, Simple Capacitors to Supercapacitors - An Overview, Int. J. Electrochem. Sci., 3 (2008) 1196 – 1217, [http://www.electrochemsci.org/papers/vol3/3111196.pdf PDF]</ref> Ruthenium dioxide in combination with {{chem|H|2|SO|4}} electrolyte provides one of the best examples of pseudocapacitance. Charge/discharge takes place with electron charge transfer or removal and occurs over a window of about 1.2&nbsp;V per electrode. In addition for these transition metal electrodes, its reversibility is excellent, with a cycle life over several hundred-thousand cycles.

Here the pseudocapacitance originates out of a coupled, reversible redox reaction with several oxidation steps with overlapping potential. The electrons mostly come from the [[valence orbital]]s of the electrode. The electron transfer reaction is very fast, and can be accompanied with high currents.

The electron transfer reaction take place according to:

:<math>\mathrm{RuO_2 + xH^+ + xe^- \leftrightarrow RuO_{2-x}(OH)_x}</math> where <math>0 \le x \le 2 </math><ref name="Simon-Gogotsi">P. Simon, Y.Gogotsi,  [http://www.ifc.dicp.ac.cn/library/cailiao/pdf1/Materials%20for%20electrochemical%20capacitors.pdf Materials for electrochemical capacitors,  nature materials], VOL 7, NOVEMBER 2008</ref>

During charging and discharging in this [[Charge-transfer complex|charge-transfer transition]]  H+ [[proton]]s are incorporated into or removed from the [[Crystal structure|crystal lattice]] of ruthenium. This generates storage of electrical energy without chemical transformation. The OH groups are deposited as a molecular layer on the electrode surface and remain in the region of the Helmholtz layer. Since the measurable voltage from the redox reaction is proportional to the charged state, the reaction behaves like a capacitor rather than a battery, whose voltage is largely independent of the state of charge.

==== Conducting polymers ====
Another type of material with a high amount of pseudocapacitance is electron-conducting polymers. [[Conductive polymer]]s electrodes include [[polyaniline]], [[polythiophene]], [[polypyrrole]] and [[polyacetylene]] have a lower reversibility of the redox reaction processes with faradaic charge transfer than electrodes with transition metal oxides and suffer from a limited stability during cycling.<ref name="Volfkovich">Yu.M. Volfkovich, A.A. Mikhailin, D.A. Bograchev, V.E. Sosenkin and V.S. Bagotsky, [http://cdn.intechopen.com/pdfs/26963/InTech-Studies_of_supercapacitor_carbon_electrodes_with_high_pseudocapacitance.pdf Studies of Supercapacitor Carbon Electrodes with High Pseudocapacitance], A. N. Frumkin Institute of Physical Chemistry and Electrochemistry, Russian Academy of Sciences, Moscow, Russia, Dr. Ujjal Kumar Sur (Ed.), ISBN 978-953-307-830-4</ref> Such electrodes employ electrochemical doping or dedoping of the polymers with anions and cations. The greatest capacitance and power density have the n/p-type polymer configuration, with one negatively charged (n-doped) and one positively charged (p-doped) electrode.

===Pseudocapacitive structures===
Pseudocapacitance may also originate from the structure and especially from the pore size of the electrodes. The use of [[carbide-derived carbon]]s (CDCs) or [[carbon nanotube]]s /CNTs for electrodes provides a network of very small pores formed by nanotube entanglement. These [[nanoporous]] materials have diameters in the range of <2&nbsp;nm that can be referred to as intercalated pores. Solvated ions in the electrolyte can’t enter these small pores but de-solvated ions which have reduced their ion dimensions are able to enter, resulting in larger ionic packing density and increased charge storage. The tailored sizes of pores in nano-structured carbon electrodes can maximize ion confinement, increasing specific capacitance by faradaic {{chem|H|2}} adsorption treatment. Occupation of these pores by de-solvated ions from the electrolyte solution occurs according to (faradaic) intercalation.<ref name="Pandolfo">A.G. Pandolfo,  A.F. Hollenkamp, [http://www.demar.eel.usp.br/eletronica/artigos/Carbon_in_supercapacitors.pdf Carbon properties and their role in supercapacitors], Journal of Power Sources 157 (2006) 11–27</ref><ref name="Bakhmatyuk">B.P. Bakhmatyuk, B.Ya. Venhryn, I.I. Grygorchak, M.M. Micov and S.I. Mudry, [http://www.ipme.ru/e-journals/RAMS/no_21407/bakhmatyuk.pdf INTERCALATION PSEUDO-CAPACITANCE IN CARBON SYSTEMS OF ENERGY STORAGE]</ref><ref name="Simon-Burke">P. Simon, A. Burke, [http://www.electrochem.org/dl/interface/spr/spr08/spr08_p38-43.pdf Nanostructured carbons: Double-Layer capacitance and more]</ref>

===Verification of pseudocapacitance===
[[File:Voltagram-Engl.png|thumb|right|200px|A cyclic voltammogram shows the fundamental difference of the current curves between static capacitors and pseudocapacitors]]

The properties of pseudocapacitance can be expressed in a [[Cyclic voltammetry|cyclic voltammogram]]. For an ideal double-layer capacitor the sign of the current changes immediately after reversing the potential and the shape of the voltammetry is rectangular. For this electrostatic energy storage the current is independent on potential of the electrode. For double-layer capacitors with resistive losses, the shape changes into a [[parallelogram]]. For electrodes with faradaic pseudocapacitance the electrical charge stored in the capacitor is strongly dependent on the potential. Therefore the voltammetry characteristics deviate from the parallelogram, caused by a delay while reversing the potential, coming from kinetic processes during charging.<ref name="Frackowiak1">Elzbieta Frackowiak, Francois Beguin, PERGAMON, Carbon 39 (2001) 937–950, [http://www.sciencedirect.com/science/article/pii/S0008622300001834 Carbon materials for the electrochemical storage of energy in Capacitors]</ref><ref>[http://electronics.stackexchange.com/questions/36546/why-does-an-ideal-capacitor-give-rise-to-a-rectangular-cyclic-voltammogram-cv Why does an ideal capacitor give rise to a rectangular cyclic voltammogram]</ref>

== Applications ==
Pseudocapacitance arises in [[supercapacitors]]

== Literature ==
<!--alphabetische Sortierung nach dem Nachnamen des ersten Autors-->
*{{Literatur |Autor=Héctor D. Abruña, Yasuyuki Kiya, Jay C. Henderson|Titel=Batteries and electrochemical capacitors|Sammelwerk=[[Physics Today]] |Band=|Nummer=12|Jahr=2008|Seiten=43–47|Online=[https://ecee.colorado.edu/~ecen4555/SourceMaterial/ElectricalEnerStor1208.pdf PDF]}}
*F. Béguin, E. Raymundo-Piñero, E. Frackowiak, Carbons for Electrochemical Energy Storage and Conversion Systems, Chapter 8. Electrical Double-Layer Capacitors and Pseudocapacitors, CRC Press 2009, Pages 329–375, Print ISBN 978-1-4200-5307-4, eBook ISBN 978-1-4200-5540-5, DOI0.1201/9781420055405-c8
*{{Literatur|Autor=J. O'M. Bockris, M. A. V. Devanathan and K. Muller|Titel= On the Structure of Charged Interfaces | Sammelwerk=Proceedings of the Royal Society|Seiten=55-79|Band=274|Nummer=1356|Jahr=1963|DOI=10.1098/rspa.1963.0114 }}
*{{Literatur|Autor=B. E. Conway|Titel=Electrochemical Supercapacitors: Scientific Fundamentals and Technological Applications|Verlag=Springer|Ort=Berlin|ISBN=0306457369|Jahr=1999|Online={{Google Buch|BuchID=8yvzlr9TqI0C|Seite=1}}}}
*K. W. Leitner, M. Winter, J. O. Besenhard, Composite supercapacitor electrodes, Journal of Solid State Electrochemistry, Publisher Springer-Verlag, Volume 8, Issue 1, pp 15–16, Date 2003-12-01, DOI 10.1007/s10008-003-0412-x, Print ISSN1432-8488, Online ISSN1433-0768, |url=http://link.springer.com/article/10.1007%2Fs10008-003-0412-x?LI=true |title=Composite supercapacitor electrodes - Springer |publisher=Link.springer.com |date=2003-12-01 |accessdate=2013-05-24
*Yu. M. Volfkovich, T. M. Serdyuk, Electrochemical Capacitors,  Russian Journal of Electrochemistry, September 2002, Volume 38, Issue 9, pp 935–959, 2002-09-01, DOI 10.1023/A:1020220425954, Print ISSN 1023-1935, Online ISSN 1608-3342, Publisher Kluwer Academic Publishers-Plenum Publishers 
*{{Literatur|Autor=Jiujun Zhang, Lei Zhang, Hansan Liu, Andy Sun, Ru-Shi Liu|Titel=Electrochemical Technologies for Energy Storage and Conversion, Band 1|Verlag=Wiley-VCH|Ort=Weinheim|ISBN=978-3-527-32869-7|Jahr=2011|Seiten=317-376|Online = {{Google Buch|BuchID=AN3B3L5RtqUC|Seite=317}}|Kommentar=Kapitel 8 - ''Electrochemical Supercapacitors''}}

== References ==
<references/>

[[Category:Capacitors]]

[[de:Pseudokapazität]]