2.5 tft lcd screen for super capasitors quotation

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Each atom in a graphene sheet is connected to its three nearest neighbors by a strong σ-bond, and contributes to a valence band one electron that extends over the whole sheet. This is the same type of bonding seen in carbon nanotubes and polycyclic aromatic hydrocarbons, and (partially) in fullerenes and glassy carbon.conduction band, making graphene a semimetal with unusual electronic properties that are best described by theories for massless relativistic particles.ballistic over long distances; the material exhibits large quantum oscillations and large and nonlinear diamagnetism.

Scientists theorized the potential existence and production of graphene for decades. It has likely been unknowingly produced in small quantities for centuries, through the use of pencils and other similar applications of graphite. It was possibly observed in electron microscopes in 1962, but studied only while supported on metal surfaces.

In 2004, the material was rediscovered, isolated and investigated at the University of Manchester,Andre Geim and Konstantin Novoselov. In 2010, Geim and Novoselov were awarded the Nobel Prize in Physics for their "groundbreaking experiments regarding the two-dimensional material graphene".

The IUPAC (International Union for Pure and Applied Chemistry) recommends use of the name "graphite" for the three-dimensional material, and "graphene" only when the reactions, structural relations, or other properties of individual layers are discussed.silicon dioxide or silicon carbide.

The theory of graphene was first explored by P. R. Wallace in 1947 as a starting point for understanding the electronic properties of 3D graphite. The emergent massless Dirac equation was first pointed out in 1984 separately by Gordon Walter Semenoff,Landau level precisely at the Dirac point. This level is responsible for the anomalous integer quantum Hall effect.

In 1961–1962, Hanns-Peter Boehm published a study of extremely thin flakes of graphite, and coined the term "graphene" for the hypothetical single-layer structure.nm or 3 atomic layers of amorphous carbon. This was the best possible resolution for 1960 TEMs. However, neither then nor today is it possible to argue how many layers were in those flakes. Now we know that the TEM contrast of graphene most strongly depends on focusing conditions.

In 2002, Robert B. Rutherford and Richard L. Dudman filed for a patent in the US on a method to produce graphene by repeatedly peeling off layers from a graphite flake adhered to a substrate, achieving a graphite thickness of 0.00001 inches (2.5×10−7 metres). The key to success was high-throughput visual recognition of graphene on a properly chosen substrate, which provides a small but noticeable optical contrast.

Another U.S. patent was filed in the same year by Bor Z. Jang and Wen C. Huang for a method to produce graphene based on exfoliation followed by attrition.

This work resulted in the two winning the Nobel Prize in Physics in 2010 "for groundbreaking experiments regarding the two-dimensional material graphene."

Graphene is a single layer (monolayer) of carbon atoms, tightly bound in a hexagonal honeycomb lattice. It is an allotrope of carbon in the form of a plane of sp2-bonded atoms with a molecular bond length of 0.142 nanometres.

Carbon orbitals 2s, 2px, 2py form the hybrid orbital sp2 with three major lobes at 120°. The remaining orbital, pz, is sticking out of the graphene"s plane.

Three of the four outer-shell electrons of each atom in a graphene sheet occupy three sp2 hybrid orbitals – a combination of orbitals s, px and py — that are shared with the three nearest atoms, forming σ-bonds. The length of these bonds is about 0.142 nanometers.

The remaining outer-shell electron occupies a pz orbital that is oriented perpendicularly to the plane. These orbitals hybridize together to form two half-filled bands of free-moving electrons, π and π∗, which are responsible for most of graphene"s notable electronic properties.hydro) agree well with the literature reports.

Graphene sheets in solid form usually show evidence in diffraction for graphite"s (002) layering. This is true of some single-walled nanostructures.presolar graphite onions.

Ab initio calculations show that a graphene sheet is thermodynamically unstable if its size is less than about 20 nm and becomes the most stable fullerene (as within graphite) only for molecules larger than 24,000 atoms.

Electronic band structure of graphene. Valence and conduction bands meet at the six vertices of the hexagonal Brillouin zone and form linearly dispersing Dirac cones.

Graphene is a zero-gap semiconductor, because its conduction and valence bands meet at the Dirac points. The Dirac points are six locations in momentum space, on the edge of the Brillouin zone, divided into two non-equivalent sets of three points. The two sets are labeled K and K". The sets give graphene a valley degeneracy of gv = 2. By contrast, for traditional semiconductors the primary point of interest is generally Γ, where momentum is zero.condensed matter systems.

Graphene"s hexagonal lattice can be regarded as two interleaving triangular lattices. This perspective was successfully used to calculate the band structure for a single graphite layer using a tight-binding approximation.

Electrons propagating through graphene"s honeycomb lattice effectively lose their mass, producing quasi-particles that are described by a 2D analogue of the Dirac equation rather than the Schrödinger equation for spin-1/2 particles.

When the atoms are placed onto the graphene hexagonal lattice, the overlap between the pz(π) orbitals and the s or the px and py orbitals is zero by symmetry. The pz electrons forming the π bands in graphene can therefore be treated independently. Within this π-band approximation, using a conventional tight-binding model, the dispersion relation (restricted to first-nearest-neighbor interactions only) that produces energy of the electrons with wave vector k is

As a consequence, at low energies, even neglecting the true spin, the electrons can be described by an equation that is formally equivalent to the massless Dirac equation. Hence, the electrons and holes are called Dirac fermions.chiral limit, i.e., to vanishing rest mass M0, which leads to interesting additional features:

Electron waves in graphene propagate within a single-atom layer, making them sensitive to the proximity of other materials such as high-κ dielectrics, superconductors and ferromagnetics.

Charge transport has major concerns due to adsorption of contaminants such as water and oxygen molecules. This leads to non-repetitive and large hysteresis I-V characteristics. Researchers must carry out electrical measurements in vacuum. The protection of graphene surface by a coating with materials such as SiN, PMMA, h-BN, etc., have been discussed by researchers. In January 2015, the first stable graphene device operation in air over several weeks was reported, for graphene whose surface was protected by aluminum oxide.lithium-coated graphene exhibited superconductivity, a first for graphene.

Transport is dominated by two modes. One is ballistic and temperature-independent, while the other is thermally activated. Ballistic electrons resemble those in cylindrical carbon nanotubes. At room temperature, resistance increases abruptly at a particular length—the ballistic mode at 16 micrometres and the other at 160 nanometres (1% of the former length).

Unlike normal metals, graphene"s longitudinal resistance shows maxima rather than minima for integral values of the Landau filling factor in measurements of the Shubnikov–de Haas oscillations, whereby the term integral quantum Hall effect. These oscillations show a phase shift of π, known as Berry"s phase.

The Casimir effect is an interaction between disjoint neutral bodies provoked by the fluctuations of the electrodynamical vacuum. Mathematically it can be explained by considering the normal modes of electromagnetic fields, which explicitly depend on the boundary (or matching) conditions on the interacting bodies" surfaces. Since graphene/electromagnetic field interaction is strong for a one-atom-thick material, the Casimir effect is of growing interest.

The Van der Waals force (or dispersion force) is also unusual, obeying an inverse cubic, asymptotic power law in contrast to the usual inverse quartic.

The mass can be positive or negative. An arrangement that slightly raises the energy of an electron on atom A relative to atom B gives it a positive mass, while an arrangement that raises the energy of atom B produces a negative electron mass. The two versions behave alike and are indistinguishable via optical spectroscopy. An electron traveling from a positive-mass region to a negative-mass region must cross an intermediate region where its mass once again becomes zero. This region is gapless and therefore metallic. Metallic modes bounding semiconducting regions of opposite-sign mass is a hallmark of a topological phase and display much the same physics as topological insulators.

Graphene"s unique optical properties produce an unexpectedly high opacity for an atomic monolayer in vacuum, absorbing πα ≈ 2.3% of light, from visible to infrared.α is the fine-structure constant. This is a consequence of the "unusual low-energy electronic structure of monolayer graphene that features electron and hole conical bands meeting each other at the Dirac point... [which] is qualitatively different from more common quadratic massive bands."Fresnel equations in the thin-film limit.

Multi-Parametric Surface Plasmon Resonance was used to characterize both thickness and refractive index of chemical-vapor-deposition (CVD)-grown graphene films. The measured refractive index and extinction coefficient values at 670 nm (6.7×10−7 m) wavelength are 3.135 and 0.897, respectively. The thickness was determined as 3.7Å from a 0.5mm area, which agrees with 3.35Å reported for layer-to-layer carbon atom distance of graphite crystals.

A graphene-based Bragg grating (one-dimensional photonic crystal) has been fabricated and demonstrated its capability for excitation of surface electromagnetic waves in the periodic structure by using 633 nm (6.33×10−7 m) He–Ne laser as the light source.

Such unique absorption could become saturated when the input optical intensity is above a threshold value. This nonlinear optical behavior is termed saturable absorption and the threshold value is called the saturation fluence. Graphene can be saturated readily under strong excitation over the visible to near-infrared region, due to the universal optical absorption and zero band gap. This has relevance for the mode locking of fiber lasers, where fullband mode locking has been achieved by graphene-based saturable absorber. Due to this special property, graphene has wide application in ultrafast photonics. Moreover, the optical response of graphene/graphene oxide layers can be tuned electrically.

First-principle calculations with quasiparticle corrections and many-body effects are performed to study the electronic and optical properties of graphene-based materials. The approach is described as three stages.nanoribbons,Josephson effect in graphene SNS junctions with single localized defect

Graphene is claimed to be an ideal material for spintronics due to its small spin–orbit interaction and the near absence of nuclear magnetic moments in carbon (as well as a weak hyperfine interaction). Electrical spin current injection and detection has been demonstrated up to room temperature.

Thermal transport in graphene is an active area of research, which has attracted attention because of the potential for thermal management applications. Following predictions for graphene and related carbon nanotubes,thermal conductivity of suspended graphene reported an exceptionally large thermal conductivity up to 5300 W⋅m−1⋅K−1,graphite of approximately 2000 W⋅m−1⋅K−1 at room temperature.1500 – 2500 W⋅m−1⋅K−1 for suspended single layer graphene.500 – 600 W⋅m−1⋅K−1 at room temperature as a result of scattering of graphene lattice waves by the substrate,500 – 600 W⋅m−1⋅K−1 for bilayer graphene.

It has been suggested that the isotopic composition, the ratio of 12C to 13C, has a significant impact on the thermal conductivity. For example, isotopically pure 12C graphene has higher thermal conductivity than either a 50:50 isotope ratio or the naturally occurring 99:1 ratio.Wiedemann–Franz law, that the thermal conduction is phonon-dominated.Fermi energy shift much larger than kBT can cause the electronic contribution to increase and dominate over the phonon contribution at low temperatures. The ballistic thermal conductance of graphene is isotropic.

Potential for this high conductivity can be seen by considering graphite, a 3D version of graphene that has basal plane thermal conductivity of over a 1000 W⋅m−1⋅K−1 (comparable to diamond). In graphite, the c-axis (out of plane) thermal conductivity is over a factor of ~100 smaller due to the weak binding forces between basal planes as well as the larger lattice spacing.

Despite its 2-D nature, graphene has 3 acoustic phonon modes. The two in-plane modes (LA, TA) have a linear dispersion relation, whereas the out of plane mode (ZA) has a quadratic dispersion relation. Due to this, the T2 dependent thermal conductivity contribution of the linear modes is dominated at low temperatures by the T1.5 contribution of the out of plane mode.Grüneisen parameters.thermal expansion coefficient (which is directly proportional to Grüneisen parameters) negative. The lowest negative Grüneisen parameters correspond to the lowest transverse acoustic ZA modes. Phonon frequencies for such modes increase with the in-plane lattice parameter since atoms in the layer upon stretching will be less free to move in the z direction. This is similar to the behavior of a string, which, when it is stretched, will have vibrations of smaller amplitude and higher frequency. This phenomenon, named "membrane effect," was predicted by Lifshitz in 1952.

Graphene is the strongest material ever tested,tensile strength of 130 GPa (19,000,000 psi) (with representative engineering tensile strength ~50-60 GPa for stretching large-area freestanding graphene) and a Young"s modulus (stiffness) close to 1 TPa (150,000,000 psi). The Nobel announcement illustrated this by saying that a 1 square meter graphene hammock would support a 4 kg cat but would weigh only as much as one of the cat"s whiskers, at 0.77 mg (about 0.001% of the weight of 1 m2 of paper).

Large-angle-bent graphene monolayer has been achieved with negligible strain, showing mechanical robustness of the two-dimensional carbon nanostructure. Even with extreme deformation, excellent carrier mobility in monolayer graphene can be preserved.

The spring constant of suspended graphene sheets has been measured using an atomic force microscope (AFM). Graphene sheets were suspended over SiO2 cavities where an AFM tip was used to apply a stress to the sheet to test its mechanical properties. Its spring constant was in the range 1–5 N/m and the stiffness was 0.5 TPa, which differs from that of bulk graphite. These intrinsic properties could lead to applications such as NEMS as pressure sensors and resonators.

As is true of all materials, regions of graphene are subject to thermal and quantum fluctuations in relative displacement. Although the amplitude of these fluctuations is bounded in 3D structures (even in the limit of infinite size), the Mermin–Wagner theorem shows that the amplitude of long-wavelength fluctuations grows logarithmically with the scale of a 2D structure, and would therefore be unbounded in structures of infinite size. Local deformation and elastic strain are negligibly affected by this long-range divergence in relative displacement. It is believed that a sufficiently large 2D structure, in the absence of applied lateral tension, will bend and crumple to form a fluctuating 3D structure. Researchers have observed ripples in suspended layers of graphene,Poisson"s ratio into graphene, resulting in the thinnest auxetic material known so far.

Graphene nanosheets have been incorporated into a Ni matrix through a plating process to form Ni-graphene composites on a target substrate. The enhancement in mechanical properties of the composites is attributed to the high interaction between Ni and graphene and the prevention of the dislocation sliding in the Ni matrix by the graphene.

In 2014, researchers from Rice University and the Georgia Institute of Technology have indicated that despite its strength, graphene is also relatively brittle, with a fracture toughness of about 4 MPa√m.ceramic materials, as opposed to many metallic materials which tend to have fracture toughnesses in the range of 15–50 MPa√m. Later in 2014, the Rice team announced that graphene showed a greater ability to distribute force from an impact than any known material, ten times that of steel per unit weight.

Various methods – most notably, chemical vapor deposition (CVD), as discussed in the section below - have been developed to produce large-scale graphene needed for device applications. Such methods often synthesize polycrystalline graphene.grain-boundaries (GB) and vacancies, present in the system and the average grain-size. How the mechanical properties change with such defects have been investigated by researchers, theoretically and experimentally.

While the presence of vacancies is not only prevalent in polycrystalline graphene, vacancies can have significant effects on the strength of graphene. The general consensus is that the strength decreases along with increasing densities of vacancies. In fact, various studies have shown that for graphene with sufficiently low density of vacancies, the strength does not vary significantly from that of pristine graphene. On the other hand, high density of vacancies can severely reduce the strength of graphene.

Compared to the fairly well-understood nature of the effect that grain boundary and vacancies have on the mechanical properties of graphene, there is no clear consensus on the general effect that the average grain size has on the strength of polycrystalline graphene.molecular-dynamics (MD) simulation. To emulate the growth mechanism of CVD, they first randomly selected nucleation sites that are at least 5A (arbitrarily chosen) apart from other sites. Polycrystalline graphene was generated from these nucleation sites and was subsequently annealed at 3000K, then quenched. Based on this model, they found that cracks are initiated at grain-boundary junctions, but the grain size does not significantly affect the strength.Hall-Petch relationship.Voronoi construction. The GBs in this model consisted of heptagon, pentagon, and hexagon, as well as squares, octagons, and vacancies. Through MD simulation, contrary to the fore-mentioned study, they found inverse Hall-Petch relationship, where the strength of graphene increases as the grain size increases.

Graphene has a theoretical specific surface area (SSA) of 2630 m2/g. This is much larger than that reported to date for carbon black (typically smaller than 900 m2/g) or for carbon nanotubes (CNTs), from ≈100 to 1000 m2/g and is similar to activated carbon.allotrope. Defects within a sheet increase its chemical reactivity.

In 2013, Stanford University physicists reported that single-layer graphene is a hundred times more chemically reactive than thicker multilayer sheets.

There are indications that graphene has promise as a useful material for interacting with neural cells; studies on cultured neural cells show limited success.

The electronics property of graphene can be significantly influenced by the supporting substrate. Studies of graphene monolayers on clean and hydrogen(H)-passivated silicon (100) (Si(100)/H) surfaces have been performed.

One way to synthesize bilayer graphene is via chemical vapor deposition, which can produce large bilayer regions that almost exclusively conform to a Bernal stack geometry.

Periodically stacked graphene and its insulating isomorph provide a fascinating structural element in implementing highly functional superlattices at the atomic scale, which offers possibilities in designing nanoelectronic and photonic devices. Various types of superlattices can be obtained by stacking graphene and its related forms.

A superlattice corresponds to a periodic or quasi-periodic arrangement of different materials, and can be described by a superlattice period which confers a new translational symmetry to the system, impacting their phonon dispersions and subsequently their thermal transport properties.

Recently, uniform monolayer graphene-hBN structures have been successfully synthesized via lithography patterning coupled with chemical vapor deposition (CVD).

Refluxing single-layer graphene oxide (SLGO) in solvents leads to size reduction and folding of individual sheets as well as loss of carboxylic group functionality, by up to 20%, indicating thermal instabilities of SLGO sheets dependent on their preparation methodology. When using thionyl chloride, acyl chloride groups result, which can then form aliphatic and aromatic amides with a reactivity conversion of around 70–80%.

Boehm titration results for various chemical reactions of single-layer graphene oxide, which reveal reactivity of the carboxylic groups and the resultant stability of the SLGO sheets after treatment.

Hydrazine reflux is commonly used for reducing SLGO to SLG(R), but titrations show that only around 20–30% of the carboxylic groups are lost, leaving a significant number available for chemical attachment. Analysis of SLG(R) generated by this route reveals that the system is unstable and using a room temperature stirring with HCl (< 1.0 M) leads to around 60% loss of COOH functionality. Room temperature treatment of SLGO with carbodiimides leads to the collapse of the individual sheets into star-like clusters that exhibited poor subsequent reactivity with amines (c. 3–5% conversion of the intermediate to the final amide).polyallylamine, cross-linked through epoxy groups. When filtered into graphene oxide paper, these composites exhibit increased stiffness and strength relative to unmodified graphene oxide paper.

In 2015, intercalating small graphene fragments into the gaps formed by larger, coiled graphene sheets, after annealing provided pathways for conduction, while the fragments helped reinforce the fibers.W/m/K (1,290 watts per metre per kelvin), while tensile strength reached 1,080 MPa (157,000 psi).

Box-shaped graphene (BSG) nanostructure appearing after mechanical cleavage of pyrolytic graphite was reported in 2016.detectors, high-performance catalytic cells, nanochannels for DNA sequencing and manipulation, high-performance heat sinking surfaces, rechargeable batteries of enhanced performance, nanomechanical resonators, electron multiplication channels in emission nanoelectronic devices, high-capacity sorbents for safe hydrogen storage.

Graphene reinforced with embedded carbon nanotube reinforcing bars ("rebar") is easier to manipulate, while improving the electrical and mechanical qualities of both materials.

Functionalized single- or multiwalled carbon nanotubes are spin-coated on copper foils and then heated and cooled, using the nanotubes themselves as the carbon source. Under heating, the functional carbon groups decompose into graphene, while the nanotubes partially split and form in-plane covalent bonds with the graphene, adding strength. π–π stacking domains add more strength. The nanotubes can overlap, making the material a better conductor than standard CVD-grown graphene. The nanotubes effectively bridge the grain boundaries found in conventional graphene. The technique eliminates the traces of substrate on which later-separated sheets were deposited using epitaxy.

Stacks of a few layers have been proposed as a cost-effective and physically flexible replacement for indium tin oxide (ITO) used in displays and photovoltaic cells.

In 2015, researchers from the University of Illinois at Urbana-Champaign (UIUC) developed a new approach for forming 3D shapes from flat, 2D sheets of graphene.

An aerogel made of graphene layers separated by carbon nanotubes was measured at 0.16 milligrams per cubic centimeter. A solution of graphene and carbon nanotubes in a mold is freeze dried to dehydrate the solution, leaving the aerogel. The material has superior elasticity and absorption. It can recover completely after more than 90% compression, and absorb up to 900 times its weight in oil, at a rate of 68.8 grams per second.

In 2015, a coiled form of graphene was discovered in graphitic carbon (coal). The spiraling effect is produced by defects in the material"s hexagonal grid that causes it to spiral along its edge, mimicking a Riemann surface, with the graphene surface approximately perpendicular to the axis. When voltage is applied to such a coil, current flows around the spiral, producing a magnetic field. The phenomenon applies to spirals with either zigzag or armchair patterns, although with different current distributions. Computer simulations indicated that a conventional spiral inductor of 205 microns in diameter could be matched by a nanocoil just 70 nanometers wide, with a field strength reaching as much as 1 tesla.

In 2016, Brown University introduced a method for "crumpling" graphene, adding wrinkles to the material on a nanoscale. This was achieved by depositing layers of graphene oxide onto a shrink film, then shrunken, with the film dissolved before being shrunken again on another sheet of film. The crumpled graphene became superhydrophobic, and, when used as a battery electrode, the material was shown to have as much as a 400% increase in electrochemical current density.

Isolated 2D crystals cannot be grown via chemical synthesis beyond small sizes even in principle, because the rapid growth of phonon density with increasing lateral size forces 2D crystallites to bend into the third dimension. In all cases, graphene must bond to a substrate to retain its two-dimensional shape.

Shear exfoliation is another method which by using rotor-stator mixer the scalable production of the defect-free Graphene has become possible.turbulence is not necessary for mechanical exfoliation,ball milling is shown to be effective in the production of High-Yield and water-soluble graphene.

Another approach sprays buckyballs at supersonic speeds onto a substrate. The balls cracked open upon impact, and the resulting unzipped cages then bond together to form a graphene film.

Electrochemical synthesis can exfoliate graphene. Varying a pulsed voltage controls thickness, flake area, number of defects and affects its properties. The process begins by bathing the graphite in a solvent for intercalation. The process can be tracked by monitoring the solution"s transparency with an LED and photodiode.

Epitaxial graphene growth on silicon carbide is wafer-scale technique to produce graphene. Epitaxial graphene may be coupled to surfaces weakly enough (by the active valence electrons that create Van der Waals forces) to retain the two dimensional electronic band structure of isolated graphene.

A normal silicon wafer coated with a layer of germanium (Ge) dipped in dilute hydrofluoric acid strips the naturally forming germanium oxide groups, creating hydrogen-terminated germanium. CVD can coat that with graphene.

Large-area Raman mapping of CVD graphene on deposited Cu thin film on 150 mm SiO2/Si wafers reveals >95% monolayer continuity and an average value of ~2.62 for I2D/IG. The scale bar is 200 μm.

Supersonic acceleration of droplets through a Laval nozzle was used to deposit reduced graphene-oxide on a substrate. The energy of the impact rearranges that carbon atoms into flawless graphene.

In 2019, flash Joule heating (transient high-temperature electrothermal heating) was discovered to be a method to synthesize turbostratic graphene in bulk powder form. The method involves electrothermally converting various carbon sources, such as carbon black, coal, and food waste into micron-scale flakes of graphene.

Integration of graphene in the widely employed CMOS fabrication process demands its transfer-free direct synthesis on dielectric substrates at temperatures below 500 °C. At the IEDM 2018, researchers from University of California, Santa Barbara, demonstrated a novel CMOS-compatible graphene synthesis process at 300 °C suitable for back-end-of-line (BEOL) applications.diffusion of carbon through a thin-film of metal catalyst. The synthesized large-area graphene films were shown to exhibit high-quality (via Raman characterization) and similar resistivity values when compared with high-temperature CVD synthesized graphene films of same cross-section down to widths of 20 nm.

In addition to experimental investigation of graphene and graphene-based devices, their numerical modeling and simulation have been an important research topic. The Kubo formula provides an analytic expression for the graphene"s conductivity and shows that it is a function of several physical parameters including wavelength, temperature, and chemical potential.

(a) The typical structure of a touch sensor in a touch panel. (Image courtesy of Synaptics, Incorporated.) (b) An actual example of 2D Carbon Graphene Material Co.,Ltd"s graphene transparent conductor-based touchscreen that is employed in (c) a commercial smartphone.

As of 2015, there is one product available for commercial use: a graphene-infused printer powder.biological engineering, filtration, lightweight/strong composite materials, photovoltaics and energy storage.

In January 2018, graphene based spiral inductors exploiting kinetic inductance at room temperature were first demonstrated at the University of California, Santa Barbara, led by Kaustav Banerjee. These inductors were predicted to allow significant miniaturization in radio-frequency integrated circuit applications.

The potential of epitaxial graphene on SiC for metrology has been shown since 2010, displaying quantum Hall resistance quantization accuracy of three parts per billion in monolayer epitaxial graphene. Over the years precisions of parts-per-trillion in the Hall resistance quantization and giant quantum Hall plateaus have been demonstrated. Developments in encapsulation and doping of epitaxial graphene have led to the commercialisation of epitaxial graphene quantum resistance standards.

In 2014, research at Stony Brook University showed that graphene nanoribbons, graphene nanoplatelets and graphene nano–onions are non-toxic at concentrations up to 50 μg/ml. These nanoparticles do not alter the differentiation of human bone marrow stem cells towards osteoblasts (bone) or adipocytes (fat) suggesting that at low doses graphene nanoparticles are safe for biomedical applications.

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Super-capacitors are energy storage devices similar to secondary batteries. Unlike batteries, which use chemical reactions to store energy, super-capacitors generally store energy through the physical separation of electrical charges.

All super-capacitors consist of two electrodes immersed in a conductive liquid or conductive polymer called the electrolyte. The electrodes are separated by an ionic-conducting separator that prevents shorts.

Many applications use a super-capacitor in parallel with a battery, a combination with a better cycle-life and higher power than the battery alone. For more information read Brian Conway’s book on super-capacitor technology1.

This application note is the first part of a two-part overview of the electrochemical techniques used to test a super-capacitor device or technology. Part 1 discusses techniques familiar to electrochemists, while Part 2 discusses techniques familiar to battery technologists.

A traditional Electrical Double-Layer Capacitor (EDLC) uses electrostatic charge storage to store energy. Electrons in each electrode and ions in the electrolyte form a double-layer capacitor. Typical capacitance of an electrochemical double layer is 20 µF/cm2. Capacitance of micro-porous carbon with a surface area of 1000 m2/g can be as high as 200 F/g.

Some devices, which we call pseudo-capacitors, store charge via reversible Faradaic reactions on the surface of one or both electrodes. When electrode voltage is proportional to surface coverage and surface coverage is proportional to state-of-charge, these devices behave identically to capacitors. See Conway’s book for details concerning these devices.

Unfortunately, technical papers and commercially available products have used many names for EDLCs and pseudo-capacitors. These include:Super-capacitors

An ideal capacitor loses no power or energy during charge or discharge, so the equation above can also be used to describe the charge process. An ideal capacitor with no current flow will store energy and charge forever.

The ideal capacitor does not exist, for real capacitors have limitations and imperfections. The tests in this application note measure these limitations.

When this was written, commercial single-cell super-capacitors have an upper voltage limit below 3.5 V. High-voltage devices have multiple cells in series.

All commercial super-capacitors are specified to be unipolar: the voltage on the plus (+) terminal must be more positive than the voltage on the minus (–) terminal. The lower voltage limit is therefore zero.

Real capacitors suffer power-loss during charge and discharge. The loss is caused by resistance in the electrodes, contacts, and in the electrolyte. The standard term for this resistance is Equivalent Series Resistance (ESR). ESR is specified on the data sheet for most commercial capacitors.

One of the simplest models for a real capacitor is ESR in series with an ideal capacitor. The power loss, Ploss, during charge or discharge is ESR times the current squared:

Note that a leakage current of 1 µA on a 1 F capacitor held at 2.5 V implies a 2.5 MΩ leakage resistance. The time constant for the self-discharge process on this capacitor is 2.5 × 106 seconds—nearly a month.

Commercial super-capacitors do not show this simple behavior. As seen below, commercial capacitors held at constant potential often take days to reach their specified leakage current. The time needed is much greater than predicted by τ.

Time effects may be caused by slow Faradaic reactions occurring at imperfections on the surface of the electrode material. The carbon surfaces used for most super-capacitors have oxygen-containing groups (hydroxyl, carbonyl, and so on) that are plausible reaction sites.

Time effects might also be a side effect of the porosity inherent in high-capacity electrodes. Electrolyte resistance increases with distance into a pore. Different areas of the electrode surface therefore see different resistances. As discussed below, this complicates the simple-capacitor-plus-ESR model into a distributed-element or transmission-line model.

An ideal capacitor can be charged and discharged for an infinite number of cycles. Many commercial super-capacitors approach this idea: they are specified for 105 or even 106 charge/discharge cycles. Secondary battery cycle-life specifications are typically hundreds of cycles.

The cycle life for all rechargeable devices depends on the exact conditions under which cycling occurs. Currents, voltage limits, device history, and temperature are all important.

Cyclic Voltammetry (CV) is a widely-used electrochemical technique. Early in a capacitor development project, CV yields basic information about a capacitive electrochemical cell including:Voltage window

Figure 1 presents a CV experiment as a plot of capacitor voltage and current versus time. The darker-colored, saw-toothed waveforms are the voltage applied to the cell; the lighter-colored waveforms are measured current. This graph shows a CV test with three and one-half cycles. Each cycle is shown in a different color.

Voltage scan rates for super-capacitor testing are usually between 0.1 mV/s and 1 V/s. Scan rates at the lower end of this range allow slow processes to occur, but take a lot of testing time. Fast scans often show lower capacitance than slower scans. This effect is discussed below.

The voltage limits entered in Setup were +5 and –3 V. The scan was manually reversed when the current started to increase dramatically. The scan rate was slow enough that a user has time to react to the increased current. The reversal occurred at 3.5 volts, well beyond the 2.7 V specification for this capacitor. The negative going sweep was also manually reversed.In Gamry’s Framework software, selecting F2-Skip reverses a sweep.

Integrating a segment of this curve shows calculation of capacitance from CV data. The integrated region (between 1.5 and 2.5 V) is highlighted in pink shading.Select the integration range using the software Select Range Using