Pseudocapacitance

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 lower power density. Additionally, the chemical processes are relatively slow, extending charge/discharge times.

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 electrolyte ions (cations) 5. Specifically adsorbed ions (redox ion, which contributes to the pseudocapacitance), 6. Molecules of the solvent

A fundamental difference between redox reactions in batteries and in electrochemical capacitors (supercapacitors) is that in the latter, the reactions are a very fast sequence of reversible processes with electron transfer without any phase changes of the electrode molecules. They do not involve making or breaking chemical bonds. The de-solvated atoms or ions contributing the pseudocapacitance simply cling[4] 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 more stable over time, because they leave only traces of reaction products. Despite the reduced amount of these products, they cause capacitance degradation. This behavior is the essence of pseudocapacitance.

Pseudocapacitive processes lead to a charge-dependent, linear capacitive behavior, as well as the accomplishment of non-faradaic double-layer capacitance in contrast to batteries, which have a nearly charge-independent behavior. 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 100x.[1]

Electrodes' ability to produce pseudocapacitance strongly depends on the electrode materials' chemical affinity to the ions adsorbed on the electrode surface as well as on the electrode pore structure and dimension. Materials exhibiting redox behavior for use as pseudocapacitor electrodes 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.

These materials provide high pseudocapacitance and were thoroughly studied by Conway.[1][7] Many oxides of transition metals like ruthenium (RuO
₂), iridium (IrO
₂), iron (Fe
₃O
₄), manganese (MnO
₂) or sulfides such as titanium sulfide (TiS
₂) or their combinations generate faradaic electron–transferring reactions with low conducting resistance.

Ruthenium dioxide (RuO
₂) in combination with sulfuric acid (H
₂SO
₄) electrolyte provides one of the best examples of pseudocapacitance, with a charge/discharge over a window of about 1.2 V per electrode. Furthermore, the reversibility on these transition metal electrodes is excellent, with a cycle life of more than several hundred-thousand cycles. Pseudocapacitance originates from a coupled, reversible redox reaction with several oxidation steps with overlapping potential. The electrons mostly come from the electrode's valence orbitals. The electron transfer reaction is very fast and can be accompanied with high currents.

The electron transfer reaction takes place according to:

${\displaystyle \mathrm {RuO_{2}+xH^{+}+xe^{-}\leftrightarrow RuO_{2-x}(OH)_{x}} }$ where ${\displaystyle 0\leq x\leq 2}$[8]

During charge and discharge, H⁺
(protons) are incorporated into or removed from the RuO
₂ crystal lattice, which 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.

Another type of material with a high amount of pseudocapacitance is electron-conducting polymers. Conductive polymer such as polyaniline, polythiophene, polypyrrole and polyacetylene have a lower reversibility of the redox processes involving faradaic charge transfer than 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. Highest capacitance and power density are achieved with a n/p-type polymer configuration, with one negatively charged (n-doped) and one positively charged (p-doped) electrode.

Pseudocapacitance may originate from the electrode structure, especially from the material pore size. The use of carbide-derived carbons (CDCs) or carbon nanotubes (CNTs) as electrodes provides a network of 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 are unable to enter these small pores, but de-solvated ions that 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 H
₂ adsorption treatment. Occupation of these pores by de-solvated ions from the electrolyte solution occurs according to (faradaic) intercalation.[9][10][11]

A cyclic voltammogram shows the fundamental difference of the current curves between static capacitors and pseudocapacitors

Pseudocapacitance properties can be expressed in a cyclic voltammogram. For an ideal double-layer capacitor, the current flow is reversed immediately upon reversing the potential yielding a rectangular-shaped voltammogram, with a current independent of the electrode potential. For double-layer capacitors with resistive losses, the shape changes to a parallelogram. In faradaic electrodes the electrical charge stored in the capacitor is strongly dependent on the potential, therefore, the voltammetry characteristics deviate from the parallelogram due to a delay while reversing the potential, ultimately coming from kinetic charging processes.[12][13]