Teiresias algorithm

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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 electrical energy electrochemically by means of reversible faradaic redox reactions on the surface of suitable electrodes in an electrochemical capacitor with a electric double-layer. Pseudocapacitance is accompanied with an electron charge-transfer between electrolyte and electrode coming from a de-solvated and adsorbed ion whereby only one electron per charge unit is participating. This faradaic charge transfer originates by a very fast sequence of reversible redox, elctrosorption or intercalation processes. The adsorbed ion has no chemical reaction with the atoms of the electrode. No chemical bonds arise. 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.

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 batteries with faradaic charge-transfer between an electrolyte and the surface of an electrode were characterized decades ago. These chemical processes are associated with chemical reactions of the electrode materials usually with attendant 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

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 (Supercapacitors) 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 bonds. The de-solvated atoms or ions contributing the pseudocapacitance simply cling 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.

Capacitance functionality

Intercalated metal atoms between planar graphite layers

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 ions 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 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 electric field has formed which results in a double-layer capacitance. Accompanied with the electric double-layer some de-solvated ions out of the electrolyte pervade the separating solvent layer and will be 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 donors transferring with a charge-transfer electrons to the atoms of the electrode resulting in a faradaic current. This faradaic charge transfer originates by a very fast sequence of reversible redox reactions, electrosorptions or intercalation processes between electrolyte and the electrode surface is called pseudocapacitance.

Depending on the electrode's structure or surface material, pseudocapacitance can originate when specifically adsorbed 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 states (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 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 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:

• Redox system: Ox + ze‾ ⇌ Red and Template:Chem + Template:Chem ⇌ in lattice
• Intercalation system: Liˡ in "Template:Chem"
• Electrosorption, underpotential deposition of metal adatoms: Template:Chem + S + ze‾ ⇌ SM (S = surface lattice sites) or Template:Chem e‾ + S ⇌ SH

All three types of electrochemical processes giving rise to pseudocapacitance have been utilized in supercapacitors.

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 are electrodes out of transition metal oxides for high amount of pseudocapacitance. Many oxides of transition metals like ruthenium (Template:Chem), iridium (Template:Chem), iron (Template:Chem), manganese (Template:Chem) or sulfides such as titanium sulfide (Template:Chem) or their combinations are able to generate many faradaic electron–transferring reactions combined with low conducting resistance. Ruthenium dioxide in combination with Template:Chem 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 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 orbitals 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:

$\mathrm {RuO_{2}+xH^{+}+xe^{-}\leftrightarrow RuO_{2-x}(OH)_{x}}$ where $0\leq x\leq 2$

During charging and discharging in this charge-transfer transition H+ protons are incorporated into or removed from the 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 polymers 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. 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 carbons (CDCs) or carbon nanotubes /CNTs for electrodes provides a network of very small pores formed by nanotube entanglement. These nanoporous materials have diameters in the range of <2 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 Template:Chem adsorption treatment. Occupation of these pores by de-solvated ions from the electrolyte solution occurs according to (faradaic) intercalation.

Verification of pseudocapacitance

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 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.

Applications

Pseudocapacitance arises in supercapacitors

Literature

• Template:Literatur
• 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
• Template:Literatur
• Template:Literatur
• 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
• Template:Literatur