Graphene Brillouin Zone
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Graphene () is a
carbon allotrope Carbon is capable of forming many allotropes (structurally different forms of the same element) due to its valency ( tetravalent). Well-known forms of carbon include diamond and graphite. In recent decades, many more allotropes have been disc ...
consisting of a single layer of
atom Atoms are the basic particles of the chemical elements. An atom consists of a atomic nucleus, nucleus of protons and generally neutrons, surrounded by an electromagnetically bound swarm of electrons. The chemical elements are distinguished fr ...
s arranged in a
honeycomb A honeycomb is a mass of Triangular prismatic honeycomb#Hexagonal prismatic honeycomb, hexagonal prismatic cells built from beeswax by honey bees in their beehive, nests to contain their brood (eggs, larvae, and pupae) and stores of honey and pol ...
planar
nanostructure A nanostructure is a structure of intermediate size between microscopic and molecular structures. Nanostructural detail is microstructure at nanoscale. In describing nanostructures, it is necessary to differentiate between the number of dimen ...
. The name "graphene" is derived from "
graphite Graphite () is a Crystallinity, crystalline allotrope (form) of the element carbon. It consists of many stacked Layered materials, layers of graphene, typically in excess of hundreds of layers. Graphite occurs naturally and is the most stable ...
" and the suffix
-ene The suffix -ene is used in organic chemistry to form names of organic compounds where the -C=C- group has been attributed the highest priority according to the rules of organic nomenclature. Sometimes a number between hyphens is inserted before ...
, indicating the presence of double bonds within the carbon structure. Graphene is known for its exceptionally high
tensile strength Ultimate tensile strength (also called UTS, tensile strength, TS, ultimate strength or F_\text in notation) is the maximum stress that a material can withstand while being stretched or pulled before breaking. In brittle materials, the ultimate ...
,
electrical conductivity Electrical resistivity (also called volume resistivity or specific electrical resistance) is a fundamental specific property of a material that measures its electrical resistance or how strongly it resists electric current. A low resistivity in ...
, transparency, and being the thinnest two-dimensional material in the world. Despite the nearly transparent nature of a single graphene sheet, graphite (formed from stacked layers of graphene) appears black because it absorbs all visible light wavelengths. On a microscopic scale, graphene is the strongest material ever measured. The existence of graphene was first theorized in 1947 by Philip R. Wallace during his research on graphite's electronic properties, while the term ''graphene'' was first defined by
Hanns-Peter Boehm Hanns-Peter Boehm (9 January 1928 – 10 May 2022) was a German chemist and professor emeritus at Ludwig-Maximilians-Universität in Munich, Germany. Boehm is considered a pioneer of graphene research. Biography Hanns-Peter Boehm studied chem ...
in 1987. In 2004, the material was isolated and characterized by
Andre Geim Sir Andre Konstantin Geim (; born 21 October 1958; IPA1 pronunciation: ɑːndreɪ gaɪm) is a Russian-born Dutch–British physicist working in England in the School of Physics and Astronomy at the University of Manchester. Geim was awarded th ...
and
Konstantin Novoselov Sir Konstantin Sergeevich Novoselov ( rus, Константи́н Серге́евич Новосёлов, p=kənstɐnʲˈtʲin sʲɪrˈɡʲe(j)ɪvʲɪtɕ nəvɐˈsʲɵləf; born 1974) is a Russian–British physicist. His work on graphene ...
at the
University of Manchester The University of Manchester is a public university, public research university in Manchester, England. The main campus is south of Manchester city centre, Manchester City Centre on Wilmslow Road, Oxford Road. The University of Manchester is c ...
using a piece of graphite and
adhesive tape Adhesive tape is one of many varieties of backing materials coated with an adhesive. Several types of adhesives can be used. Types Pressure-sensitive tape Pressure-sensitive tape, PSA tape, self-stick tape or sticky tape consists of a pre ...
. In 2010, Geim and Novoselov were awarded the
Nobel Prize in Physics The Nobel Prize in Physics () is an annual award given by the Royal Swedish Academy of Sciences for those who have made the most outstanding contributions to mankind in the field of physics. It is one of the five Nobel Prizes established by the ...
for their "groundbreaking experiments regarding the two-dimensional material graphene". While small amounts of graphene are easy to produce using the method by which it was originally isolated, attempts to scale and automate the manufacturing process for mass production have had limited success due to cost-effectiveness and quality control concerns. The global graphene market was $9 million in 2012, with most of the demand from research and development in
semiconductors A semiconductor is a material with electrical conductivity between that of a conductor and an insulator. Its conductivity can be modified by adding impurities (" doping") to its crystal structure. When two regions with different doping levels ...
, electronics,
electric batteries An electric battery is a source of electric power consisting of one or more electrochemical cells with external connections for powering electrical devices. When a battery is supplying power, its positive terminal is the cathode and its nega ...
, and composites. The
IUPAC The International Union of Pure and Applied Chemistry (IUPAC ) is an international federation of National Adhering Organizations working for the advancement of the chemical sciences, especially by developing nomenclature and terminology. It is ...
(International Union of Pure and Applied Chemistry) advises using the term "graphite" for the three-dimensional material and reserving "graphene" for discussions about the properties or reactions of single-atom layers. A narrower definition, of "isolated or free-standing graphene", requires that the layer be sufficiently isolated from its environment, but would include layers suspended or transferred to
silicon dioxide Silicon dioxide, also known as silica, is an oxide of silicon with the chemical formula , commonly found in nature as quartz. In many parts of the world, silica is the major constituent of sand. Silica is one of the most complex and abundan ...
or
silicon carbide Silicon carbide (SiC), also known as carborundum (), is a hard chemical compound containing silicon and carbon. A wide bandgap semiconductor, it occurs in nature as the extremely rare mineral moissanite, but has been mass-produced as a powder a ...
.


History


Structure of graphite and its intercalation compounds

In 1859, Benjamin Brodie noted the highly
lamellar A lamella (: lamellae) is a small plate or flake, from the Latin, and may also refer to collections of fine sheets of material held adjacent to one another in a gill-shaped structure, often with fluid in between though sometimes simply a set of ...
structure of thermally reduced
graphite oxide Graphite oxide (GO), formerly called graphitic oxide or graphitic acid, is a compound of carbon, oxygen, and hydrogen in variable ratios, obtained by treating graphite with strong oxidizers and acids for resolving of extra metals. The maximally o ...
. Pioneers in
X-ray crystallography X-ray crystallography is the experimental science of determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to Diffraction, diffract in specific directions. By measuring th ...
attempted to determine the structure of graphite. The lack of large
single crystal In materials science, a single crystal (or single-crystal solid or monocrystalline solid) is a material in which the crystal lattice of the entire sample is continuous and unbroken to the edges of the sample, with no Grain boundary, grain bound ...
graphite specimens contributed to the independent development of
X-ray powder diffraction Powder diffraction is a scientific technique using X-ray, neutron, or electron diffraction on powder or microcrystalline samples for structural characterization of materials. An instrument dedicated to performing such powder measurements is cal ...
by
Peter Debye Peter Joseph William Debye ( ; born Petrus Josephus Wilhelmus Debije, ; March 24, 1884 – November 2, 1966) was a Dutch-American physicist and physical chemist, and Nobel laureate in Chemistry. Biography Early life Born in Maastricht, Neth ...
and
Paul Scherrer Paul Hermann Scherrer (3 February 1890 – 25 September 1969) was a Swiss physicist. Born in St. Gallen, Switzerland, he studied at Göttingen, Germany, before becoming a lecturer there. Later, Scherrer became head of the Department of Physics ...
in 1915, and
Albert Hull Albert Wallace Hull (19 April 1880 – 22 January 1966) was an American physicist and electrical engineer who made contributions to the development of vacuum tubes, and invented the magnetron. He was a member of the National Academy of Scienc ...
in 1916. However, neither of their proposed structures was correct. In 1918, Volkmar Kohlschütter and P. Haenni described the properties of graphite oxide paper. The structure of graphite was successfully determined from single-crystal X-ray diffraction by J. D. Bernal in 1924, although subsequent research has made small modifications to the
unit cell In geometry, biology, mineralogy and solid state physics, a unit cell is a repeating unit formed by the vectors spanning the points of a lattice. Despite its suggestive name, the unit cell (unlike a unit vector In mathematics, a unit vector i ...
parameters. 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 In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all spin-1/2 massive particles, called "Dirac ...
was separately pointed out in 1984 by Gordon Walter Semenoff, and by David P. Vincenzo and Eugene J. Mele. Semenoff emphasized the occurrence in a magnetic field of an electronic
Landau level In quantum mechanics, the energies of Cyclotron motion#Cyclotron resonance, cyclotron orbits of charged particles in a uniform magnetic field are quantized to discrete values, thus known as Landau levels. These levels are Degenerate energy level, d ...
precisely at the
Dirac point In physics, Dirac cones are features that occur in some electronic band structures that describe unusual electron transport properties of materials like graphene and topological insulators. In these materials, at energies near the Fermi leve ...
. This level is responsible for the anomalous integer
Quantum Hall effect The quantum Hall effect (or integer quantum Hall effect) is a quantized version of the Hall effect which is observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall resistance exhi ...
.


Observations of thin graphite layers and related structures

Transmission electron microscopy Transmission electron microscopy (TEM) is a microscopy technique in which a beam of electrons is transmitted through a specimen to form an image. The specimen is most often an ultrathin section less than 100 nm thick or a suspension on a g ...
(TEM) images of thin
graphite Graphite () is a Crystallinity, crystalline allotrope (form) of the element carbon. It consists of many stacked Layered materials, layers of graphene, typically in excess of hundreds of layers. Graphite occurs naturally and is the most stable ...
samples consisting of a few graphene layers were published by G. Ruess and F. Vogt in 1948. Eventually, single layers were also observed directly. Single layers of graphite were also observed by
transmission electron microscopy Transmission electron microscopy (TEM) is a microscopy technique in which a beam of electrons is transmitted through a specimen to form an image. The specimen is most often an ultrathin section less than 100 nm thick or a suspension on a g ...
within bulk materials, particularly inside soot obtained by chemical exfoliation. From 1961 to 1962,
Hanns-Peter Boehm Hanns-Peter Boehm (9 January 1928 – 10 May 2022) was a German chemist and professor emeritus at Ludwig-Maximilians-Universität in Munich, Germany. Boehm is considered a pioneer of graphene research. Biography Hanns-Peter Boehm studied chem ...
published a study of extremely thin flakes of graphite. The study measured flakes as small as ~0.4 nm, which is around 3 atomic layers of amorphous carbon. This was the best possible resolution for TEMs in the 1960s. However, it is impossible to distinguish between suspended monolayer and multilayer graphene by their TEM contrasts, and the only known method is to analyze the relative intensities of various diffraction spots. The first reliable TEM observations of monolayers are likely given in references 24 and 26 of Geim and Novoselov's 2007 review. In 1975, van Bommel et al.
epitaxially Epitaxy (prefix ''epi-'' means "on top of”) is a type of crystal growth or material deposition in which new crystalline layers are formed with one or more well-defined orientations with respect to the crystalline seed layer. The deposited cry ...
grew a single layer of graphite on top of silicon carbide. Others grew single layers of carbon atoms on other materials. This "epitaxial graphene" consists of a single-atom-thick hexagonal lattice of sp2-bonded carbon atoms, as in free-standing graphene. However, there is significant charge transfer between the two materials and, in some cases, hybridization between the
d-orbital In quantum mechanics, an atomic orbital () is a function describing the location and wave-like behavior of an electron in an atom. This function describes an electron's charge distribution around the atom's nucleus, and can be used to calc ...
s of the substrate atoms and π orbitals of graphene, which significantly alter the electronic structure compared to that of free-standing graphene. Boehm et al. coined the term "graphene" for the hypothetical single-layer structure in 1986. The term was used again in 1987 to describe single sheets of graphite as a constituent of
graphite intercalation compound In the area of solid state chemistry, graphite intercalation compounds are a family of materials prepared from graphite. In particular, the sheets of carbon that comprise graphite can be pried apart by the insertion ( intercalation) of ions. T ...
s, which can be seen as crystalline salts of the intercalant and graphene. It was also used in the descriptions of
carbon nanotube A carbon nanotube (CNT) is a tube made of carbon with a diameter in the nanometre range ( nanoscale). They are one of the allotropes of carbon. Two broad classes of carbon nanotubes are recognized: * ''Single-walled carbon nanotubes'' (''S ...
s by R. Saito and Mildred and Gene Dresselhaus in 1992, and in the description of
polycyclic aromatic hydrocarbon A Polycyclic aromatic hydrocarbon (PAH) is any member of a class of organic compounds that is composed of multiple fused aromatic rings. Most are produced by the incomplete combustion of organic matter— by engine exhaust fumes, tobacco, incine ...
s in 2000 by S. Wang and others. Efforts to make thin films of graphite by mechanical exfoliation started in 1990. Initial attempts employed exfoliation techniques similar to the drawing method. Multilayer samples down to 10 nm in thickness were obtained. 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 . The key to success was the ability to quickly and efficiently identify graphene flakes on the substrate using optical microscopy, which provided a small but visible contrast between the graphene and the substrate. 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. In 2014, inventor Larry Fullerton patented a process for producing single-layer graphene sheets by graphene's strong
diamagnetic Diamagnetism is the property of materials that are repelled by a magnetic field; an applied magnetic field creates an induced magnetic field in them in the opposite direction, causing a repulsive force. In contrast, paramagnetic and ferromagn ...
properties.


Full isolation and characterization

Graphene was properly isolated and characterized in 2004 by
Andre Geim Sir Andre Konstantin Geim (; born 21 October 1958; IPA1 pronunciation: ɑːndreɪ gaɪm) is a Russian-born Dutch–British physicist working in England in the School of Physics and Astronomy at the University of Manchester. Geim was awarded th ...
and
Konstantin Novoselov Sir Konstantin Sergeevich Novoselov ( rus, Константи́н Серге́евич Новосёлов, p=kənstɐnʲˈtʲin sʲɪrˈɡʲe(j)ɪvʲɪtɕ nəvɐˈsʲɵləf; born 1974) is a Russian–British physicist. His work on graphene ...
at the
University of Manchester The University of Manchester is a public university, public research university in Manchester, England. The main campus is south of Manchester city centre, Manchester City Centre on Wilmslow Road, Oxford Road. The University of Manchester is c ...
. They pulled graphene layers from graphite with a common
adhesive tape Adhesive tape is one of many varieties of backing materials coated with an adhesive. Several types of adhesives can be used. Types Pressure-sensitive tape Pressure-sensitive tape, PSA tape, self-stick tape or sticky tape consists of a pre ...
in a process called micro-mechanical cleavage, colloquially referred to as the Scotch tape technique. The graphene flakes were then transferred onto a thin
silicon dioxide Silicon dioxide, also known as silica, is an oxide of silicon with the chemical formula , commonly found in nature as quartz. In many parts of the world, silica is the major constituent of sand. Silica is one of the most complex and abundan ...
layer on a
silicon Silicon is a chemical element; it has symbol Si and atomic number 14. It is a hard, brittle crystalline solid with a blue-grey metallic lustre, and is a tetravalent metalloid (sometimes considered a non-metal) and semiconductor. It is a membe ...
plate ("wafer"). The silica electrically isolated the graphene and weakly interacted with it, providing nearly charge-neutral graphene layers. The silicon beneath the could be used as a "back gate" electrode to vary the charge density in the graphene over a wide range. This work resulted in the two winning the Nobel Prize in Physics in 2010 for their groundbreaking experiments with graphene. Their publication and the surprisingly easy preparation method that they described, sparked a "graphene gold rush". Research expanded and split off into many different subfields, exploring different exceptional properties of the material—quantum mechanical, electrical, chemical, mechanical, optical, magnetic, etc.


Exploring commercial applications

Since the early 2000s, several companies and research laboratories have been working to develop commercial applications of graphene. In 2014, a
National Graphene Institute The National Graphene Institute is a research institute and building at the University of Manchester, England, that is focused on the research of graphene. Construction of the building to house the institute started in 2013 and finished in 2015. ...
was established with that purpose at the University of Manchester, with a £60 million initial funding. In
North East England North East England, commonly referred to simply as the North East within England, is one of nine official regions of England. It consists of County DurhamNorthumberland, , Northumberland, Tyne and Wear and part of northern North Yorkshire. ...
two commercial manufacturers, Applied Graphene Materials and Thomas Swan Limited have begun manufacturing. Cambridge Nanosystems is a large-scale graphene powder production facility in
East Anglia East Anglia is an area of the East of England, often defined as including the counties of Norfolk, Suffolk and Cambridgeshire, with parts of Essex sometimes also included. The name derives from the Anglo-Saxon kingdom of the East Angles, ...
.


Structure

Graphene is a single layer 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 R = . The area of a
hexagon In geometry, a hexagon (from Greek , , meaning "six", and , , meaning "corner, angle") is a six-sided polygon. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°. Regular hexagon A regular hexagon is de ...
of side R being \frac2R^2, one hexagonal unit of graphene has an area of \frac20.142^2 = 0.0524 nm2. There are two carbon atoms per unit, together having a mass of 2\frac=.0399\times10^ mg. The (two-dimensional) density of graphene is therefore 0.0399/0.0542 = 0.762 mg per square meter. A kilogram of graphene therefore has an area of 10^6/0.762=1.312\times10^6 m2 or 131.2
hectares The hectare (; SI symbol: ha) is a non-SI metric unit of area equal to a square with 100-metre sides (1 hm2), that is, square metres (), and is primarily used in the measurement of land. There are 100 hectares in one square kilometre. A ...
. In a graphene sheet, each atom is connected to its three nearest carbon neighbors by
σ-bond In chemistry, sigma bonds (σ bonds) or sigma overlap are the strongest type of covalent chemical bond. They are formed by head-on overlapping between atomic orbitals along the internuclear axis. Sigma bonding is most simply defined for diatom ...
s, and a delocalized
π-bond In chemistry, pi bonds (π bonds) are covalent chemical bonds, in each of which two lobes of an orbital on one atom overlap with two lobes of an orbital on another atom, and in which this overlap occurs laterally. Each of these atomic orbitals ...
, which contributes to a
valence band In solid-state physics, the valence band and conduction band are the bands closest to the Fermi level, and thus determine the electrical conductivity of the solid. In nonmetals, the valence band is the highest range of electron energies in ...
that extends over the whole sheet. This type of bonding is also seen in
polycyclic aromatic hydrocarbon A Polycyclic aromatic hydrocarbon (PAH) is any member of a class of organic compounds that is composed of multiple fused aromatic rings. Most are produced by the incomplete combustion of organic matter— by engine exhaust fumes, tobacco, incine ...
s. The valence band is touched by a
conduction band In solid-state physics, the valence band and conduction band are the bands closest to the Fermi level, and thus determine the electrical conductivity of the solid. In nonmetals, the valence band is the highest range of electron energies in ...
, making graphene a
semimetal A semimetal is a material with a small energy overlap between the bottom of the Electrical conduction, conduction Electronic band structure, band and the top of the valence band, but they do not overlap in momentum space. According to Band theory ...
with unusual electronic properties that are best described by theories for massless relativistic particles. Charge carriers in graphene show linear, rather than quadratic, dependence of energy on momentum, and field-effect transistors with graphene can be made that show bipolar conduction. Charge transport is ballistic over long distances; the material exhibits large quantum oscillations and large nonlinear
diamagnetism Diamagnetism is the property of materials that are repelled by a magnetic field; an applied magnetic field creates an induced magnetic field in them in the opposite direction, causing a repulsive force. In contrast, paramagnetic and ferromagnet ...
.


Bonding

Three of the four outer-
shell Shell may refer to: Architecture and design * Shell (structure), a thin structure ** Concrete shell, a thin shell of concrete, usually with no interior columns or exterior buttresses Science Biology * Seashell, a hard outer layer of a marine ani ...
electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...
s 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. Recent quantitative estimates of aromatic stabilization and limiting size derived from the enthalpies of
hydrogenation Hydrogenation is a chemical reaction between molecular hydrogen (H2) and another compound or element, usually in the presence of a catalyst such as nickel, palladium or platinum. The process is commonly employed to redox, reduce or Saturated ...
(ΔHhydro) agree well with the literature reports. Graphene sheets stack to form graphite with an interplanar spacing of . Graphene sheets in solid form usually show evidence in diffraction for graphite's (002) layering. This is true of some single-walled nanostructures. However, unlayered graphene displaying only (hk0) rings have been observed in the core of presolar graphite onions. TEM studies show faceting at defects in flat graphene sheets and suggest a role for two-dimensional crystallization from a melt.


Geometry

The hexagonal lattice structure of isolated, single-layer graphene can be directly seen with transmission electron microscopy (TEM) of sheets of graphene suspended between bars of a metallic grid. Some of these images showed a "rippling" of the flat sheet, with an amplitude of about one nanometer. These ripples may be intrinsic to the material as a result of the instability of two-dimensional crystals, or may originate from the ubiquitous dirt seen in all TEM images of graphene.
Photoresist A photoresist (also known simply as a resist) is a light-sensitive material used in several processes, such as photolithography and photoengraving, to form a patterned coating on a surface. This process is crucial in the electronics industry. T ...
residue, which must be removed to obtain atomic-resolution images, may be the "
adsorbate Adsorption is the adhesion of atoms, ions or molecules from a gas, liquid or dissolved solid to a surface. This process creates a film of the ''adsorbate'' on the surface of the ''adsorbent''. This process differs from absorption, in which a ...
s" observed in TEM images, and may explain the observed rippling. The hexagonal structure is also seen in
scanning tunneling microscope A scanning tunneling microscope (STM) is a type of scanning probe microscope used for imaging surfaces at the atomic level. Its development in 1981 earned its inventors, Gerd Binnig and Heinrich Rohrer, then at IBM Zürich, the Nobel Prize in ...
(STM) images of graphene supported on silicon dioxide substrates The rippling seen in these images is caused by the conformation of graphene to the substrates' lattice and is not intrinsic.


Stability

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 A fullerene is an allotropes of carbon, allotrope of carbon whose molecules consist of carbon atoms connected by single and double bonds so as to form a closed or partially closed mesh, with fused rings of five to six atoms. The molecules may ...
(as within graphite) only for molecules larger than 24,000 atoms.


Electronic properties

Graphene is a zero-gap
semiconductor A semiconductor is a material with electrical conductivity between that of a conductor and an insulator. Its conductivity can be modified by adding impurities (" doping") to its crystal structure. When two regions with different doping level ...
because its conduction and
valence bands In solid-state physics, the valence band and conduction band are the bands closest to the Fermi level, and thus determine the electrical conductivity of the solid. In nonmetals, the valence band is the highest range of electron energies in whi ...
meet at the Dirac points. The Dirac points are six locations in
momentum space In physics and geometry, there are two closely related vector spaces, usually three-dimensional but in general of any finite dimension. Position space (also real space or coordinate space) is the set of all ''position vectors'' r in Euclidean sp ...
on the edge of the
Brillouin zone In mathematics and solid state physics, the first Brillouin zone (named after Léon Brillouin) is a uniquely defined primitive cell in reciprocal space Reciprocal lattice is a concept associated with solids with translational symmetry whic ...
, divided into two non-equivalent sets of three points. These sets are labeled K and K'. These sets give graphene a valley degeneracy of g_ = 2. In contrast, for traditional semiconductors, the primary point of interest is generally Γ, where momentum is zero. If the in-plane direction is confined rather than infinite, its electronic structure changes. These confined structures are referred to as
graphene nanoribbon Graphene nanoribbons (GNRs, also called nano-graphene ribbons or nano-graphite ribbons) are strips of graphene with width less than 100 nm. Graphene ribbons were introduced as a theoretical model by Mitsutaka Fujita and coauthors to examine ...
s. If the nanoribbon has a "zig-zag" edge, the bandgap remains zero. If it has an "armchair" edge, the bandgap is non-zero. Graphene's honeycomb structure can be viewed as two interleaving triangular lattices. This perspective has been used to calculate the band structure for a single graphite layer using a tight-binding approximation.


Electronic spectrum

Electrons propagating through the graphene honeycomb lattice effectively lose their mass, producing quasi-particles described by a 2D analogue of the
Dirac equation In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all spin-1/2 massive particles, called "Dirac ...
rather than the
Schrödinger equation The Schrödinger equation is a partial differential equation that governs the wave function of a non-relativistic quantum-mechanical system. Its discovery was a significant landmark in the development of quantum mechanics. It is named after E ...
for spin- particles.


Dispersion relation

The cleavage technique led directly to the first observation of the anomalous quantum Hall effect in graphene in 2005 by Geim's group and by Philip Kim and Yuanbo Zhang. This effect provided direct evidence of graphene's theoretically predicted
Berry's phase In Classical mechanics, classical and quantum mechanics, geometric phase is a Phase (waves), phase difference acquired over the course of a Period (physics), cycle, when a system is subjected to cyclic adiabatic process (quantum mechanics), adiabat ...
of massless
Dirac fermion In physics, a Dirac fermion is a spin-½ particle (a fermion) which is different from its antiparticle. A vast majority of fermions fall under this category. Description In particle physics, all fermions in the standard model have distinct antipar ...
s and proof of the Dirac fermion nature of electrons. These effects were previously observed in bulk graphite by Yakov Kopelevich, Igor A. Luk'yanchuk, and others, in 2003–2004. When atoms are placed onto the graphene hexagonal lattice, the overlap between the ''p''z(π) orbitals and the ''s'' or the ''p''x and ''p''y orbitals is zero by symmetry. Therefore, ''p''z electrons forming the π bands in graphene can be treated independently. Within this π-band approximation, using a conventional tight-binding model, the
dispersion relation In the physical sciences and electrical engineering, dispersion relations describe the effect of dispersion on the properties of waves in a medium. A dispersion relation relates the wavelength or wavenumber of a wave to its frequency. Given the ...
(restricted to first-nearest-neighbor interactions only) that produces the energy of the electrons with wave vector ''k'' is: :E(k_x,k_y)=\pm\,\gamma_0\sqrt with the nearest-neighbor (π orbitals) hopping energy ''γ''0 ≈ and the
lattice constant A lattice constant or lattice parameter is one of the physical dimensions and angles that determine the geometry of the unit cells in a crystal lattice, and is proportional to the distance between atoms in the crystal. A simple cubic crystal has ...
. The conduction and valence bands correspond to the different signs. With one ''p''z electron per atom in this model, the valence band is fully occupied, while the conduction band is vacant. The two bands touch at the zone corners (the ''K'' point in the Brillouin zone), where there is a zero density of states but no band gap. Thus, graphene exhibits a semi-metallic (or zero-gap semiconductor) character, although this is not true for a graphene sheet rolled into a
carbon nanotube A carbon nanotube (CNT) is a tube made of carbon with a diameter in the nanometre range ( nanoscale). They are one of the allotropes of carbon. Two broad classes of carbon nanotubes are recognized: * ''Single-walled carbon nanotubes'' (''S ...
due to its curvature. Two of the six Dirac points are independent, while the rest are equivalent by symmetry. Near the ''K''-points, the energy depends ''linearly'' on the wave vector, similar to a relativistic particle. Since an elementary cell of the lattice has a basis of two atoms, the
wave function In quantum physics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common symbols for a wave function are the Greek letters and (lower-case and capital psi (letter) ...
has an effective 2-spinor structure. Consequently, at low energies even neglecting the true spin, electrons can be described by an equation formally equivalent to the massless
Dirac equation In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all spin-1/2 massive particles, called "Dirac ...
. Hence, the electrons and holes are called Dirac
fermions In particle physics, a fermion is a subatomic particle that follows Fermi–Dirac statistics. Fermions have a half-integer spin ( spin , spin , etc.) and obey the Pauli exclusion principle. These particles include all quarks and leptons and ...
. This pseudo-relativistic description is restricted to the chiral limit, i.e., to vanishing rest mass ''M''0, leading to interesting additional features: :v_F\, \vec \sigma \cdot \nabla \psi(\mathbf)\,=\,E\psi(\mathbf). Here ''vF'' ~ (.003 c) is the
Fermi velocity The Fermi energy is a concept in quantum mechanics usually referring to the energy difference between the highest and lowest occupied single-particle states in a quantum system of non-interacting fermions at absolute zero temperature. In a Fermi ga ...
in graphene, which replaces the velocity of light in the Dirac theory; \vec is the vector of the
Pauli matrices In mathematical physics and mathematics, the Pauli matrices are a set of three complex matrices that are traceless, Hermitian, involutory and unitary. Usually indicated by the Greek letter sigma (), they are occasionally denoted by tau () ...
, \psi(\mathbf) is the two-component wave function of the electrons, and ''E'' is their energy. The equation describing the electrons' linear dispersion relation is: :E(q)=\hbar v_F q where the
wavevector In physics, a wave vector (or wavevector) is a vector used in describing a wave, with a typical unit being cycle per metre. It has a magnitude and direction. Its magnitude is the wavenumber of the wave (inversely proportional to the wavelength), ...
''q'' is measured from the Brillouin zone vertex K, q=\left, \mathbf-\mathrm\, and the zero of energy is set to coincide with the Dirac point. The equation uses a pseudospin matrix formula that describes two sublattices of the honeycomb lattice.


Single-atom wave propagation

Electron waves in graphene propagate within a single-atom layer, making them sensitive to the proximity of other materials such as
high-κ dielectric In the semiconductor industry, the term high-κ dielectric refers to a material with a high dielectric constant (κ, kappa), as compared to silicon dioxide. High-κ dielectrics are used in semiconductor manufacturing processes where they are usual ...
s, superconductors, and
ferromagnets Ferromagnetism is a property of certain materials (such as iron) that results in a significant, observable magnetic permeability, and in many cases, a significant magnetic coercivity, allowing the material to form a permanent magnet. Ferromagne ...
.


Ambipolar electron and hole transport

Graphene exhibits high
electron mobility In solid-state physics, the electron mobility characterizes how quickly an electron can move through a metal or semiconductor when pushed or pulled by an electric field. There is an analogous quantity for Electron hole, holes, called hole mobilit ...
at room temperature, with values reported in excess of . Hole and electron mobilities are nearly identical. The mobility is independent of temperature between and , showing minimal change even at room temperature (300 K), suggesting that the dominant scattering mechanism is defect scattering. Scattering by graphene's acoustic
phonon A phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, specifically in solids and some liquids. In the context of optically trapped objects, the quantized vibration mode can be defined a ...
s intrinsically limits room temperature mobility in freestanding graphene to at a carrier density of . The corresponding
resistivity Electrical resistivity (also called volume resistivity or specific electrical resistance) is a fundamental specific property of a material that measures its electrical resistance or how strongly it resists electric current. A low resistivity i ...
of graphene sheets is , lower than the resistivity of
silver Silver is a chemical element; it has Symbol (chemistry), symbol Ag () and atomic number 47. A soft, whitish-gray, lustrous transition metal, it exhibits the highest electrical conductivity, thermal conductivity, and reflectivity of any metal. ...
, which is the lowest known at room temperature."Physicists Show Electrons Can Travel More Than 100 Times Faster in Graphene"
University Communications Newsdesk, University of Maryland . Newsdesk.umd.edu (24 March 2008). Retrieved on 12 January 2014.
However, on substrates, electron scattering by optical phonons of the substrate has a more significant effect than scattering by graphene's phonons, limiting mobility to . Charge transport can be affected by the adsorption of contaminants such as
water Water is an inorganic compound with the chemical formula . It is a transparent, tasteless, odorless, and Color of water, nearly colorless chemical substance. It is the main constituent of Earth's hydrosphere and the fluids of all known liv ...
and
oxygen Oxygen is a chemical element; it has chemical symbol, symbol O and atomic number 8. It is a member of the chalcogen group (periodic table), group in the periodic table, a highly reactivity (chemistry), reactive nonmetal (chemistry), non ...
molecules, leading to non-repetitive and large hysteresis I-V characteristics. Researchers need to conduct electrical measurements in a vacuum. Coating the graphene surface with materials such as SiN, PMMA or h-BN has been proposed for protection. In January 2015, the first stable graphene device operation in the air over several weeks was reported for graphene whose surface was protected by
aluminum oxide Aluminium oxide (or aluminium(III) oxide) is a chemical compound of aluminium and oxygen with the chemical formula . It is the most commonly occurring of several aluminium oxides, and specifically identified as aluminium oxide. It is commonly ...
. In 2015,
lithium Lithium (from , , ) is a chemical element; it has chemical symbol, symbol Li and atomic number 3. It is a soft, silvery-white alkali metal. Under standard temperature and pressure, standard conditions, it is the least dense metal and the ...
-coated graphene exhibited
superconductivity Superconductivity is a set of physical properties observed in superconductors: materials where Electrical resistance and conductance, electrical resistance vanishes and Magnetic field, magnetic fields are expelled from the material. Unlike an ord ...
, a first for graphene. Electrical resistance in 40-nanometer-wide
nanoribbon Nanoribbon may refer to: * Graphene nanoribbons * Silicene nanoribbons * Boron nitride nanoribbons * Gallium(III) oxide nanoribbons * titanate nanoribbons - see titanium dioxide Titanium dioxide, also known as titanium(IV) oxide or titania ...
s of epitaxial graphene changes in discrete steps. The ribbons' conductance exceeds predictions by a factor of 10. The ribbons can function more like
optical waveguide An optical waveguide is a physical structure that guides electromagnetic waves in the optical spectrum. Common types of optical waveguides include optical fiber waveguides, transparent dielectric waveguides made of plastic and glass, liquid ligh ...
s or
quantum dot Quantum dots (QDs) or semiconductor nanocrystals are semiconductor particles a few nanometres in size with optical and electronic properties that differ from those of larger particles via quantum mechanical effects. They are a central topic i ...
s, allowing electrons to flow smoothly along the ribbon edges. In copper, resistance increases proportionally with length as electrons encounter impurities. Transport is dominated by two modes: one ballistic and temperature-independent, and the other thermally activated. Ballistic electrons resemble those in cylindrical carbon nanotubes. At room temperature, resistance increases abruptly at a specific length—the ballistic mode at 16 micrometers and the thermally activated mode at 160 nanometers (1% of the former length). Graphene electrons can traverse micrometer distances without scattering, even at room temperature.


Electrical conductivity and charge transport

Despite zero carrier density near the Dirac points, graphene exhibits a minimum conductivity on the order of 4e^2/h. The origin of this minimum conductivity is still unclear. However, rippling of the graphene sheet or ionized impurities in the substrate may lead to local puddles of carriers that allow conduction. Several theories suggest that the minimum conductivity should be 4e^2/h); however, most measurements are of the order of 4e^2/h or greater and depend on impurity concentration. Near zero carrier density, graphene exhibits positive photoconductivity and negative photoconductivity at high carrier density, governed by the interplay between photoinduced changes of both the Drude weight and the carrier scattering rate. Graphene doped with various gaseous species (both acceptors and donors) can be returned to an undoped state by gentle heating in a vacuum. Even for
dopant A dopant (also called a doping agent) is a small amount of a substance added to a material to alter its physical properties, such as electrical or optics, optical properties. The amount of dopant is typically very low compared to the material b ...
concentrations in excess of 1012 cm−2, carrier mobility exhibits no observable change. Graphene doped with
potassium Potassium is a chemical element; it has Symbol (chemistry), symbol K (from Neo-Latin ) and atomic number19. It is a silvery white metal that is soft enough to easily cut with a knife. Potassium metal reacts rapidly with atmospheric oxygen to ...
in
ultra-high vacuum Ultra-high vacuum (often spelled ultrahigh in American English, UHV) is the vacuum regime characterised by pressures lower than about . UHV conditions are created by pumping the gas out of a UHV chamber. At these low pressures the mean free path of ...
at low temperature can reduce mobility 20-fold. The mobility reduction is reversible on heating the graphene to remove the potassium. Due to graphene's two dimensions, charge fractionalization (where the apparent charge of individual pseudoparticles in low-dimensional systems is less than a single quantum) is thought to occur. It may therefore be a suitable material for constructing
quantum computer A quantum computer is a computer that exploits quantum mechanical phenomena. On small scales, physical matter exhibits properties of both particles and waves, and quantum computing takes advantage of this behavior using specialized hardware. ...
s using
anyon In physics, an anyon is a type of quasiparticle so far observed only in two-dimensional physical system, systems. In three-dimensional systems, only two kinds of elementary particles are seen: fermions and bosons. Anyons have statistical proper ...
ic circuits.


Chiral half-integer quantum Hall effect


Quantum hall effect in graphene

The
quantum Hall effect The quantum Hall effect (or integer quantum Hall effect) is a quantized version of the Hall effect which is observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall resistance exhi ...
is a quantum mechanical version of the
Hall effect The Hall effect is the production of a voltage, potential difference (the Hall voltage) across an electrical conductor that is wikt:transverse, transverse to an electric current in the conductor and to an applied magnetic field wikt:perpendicul ...
, which is the production of transverse (perpendicular to the main current) conductivity in the presence of a
magnetic field A magnetic field (sometimes called B-field) is a physical field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular ...
. The quantization of the
Hall effect The Hall effect is the production of a voltage, potential difference (the Hall voltage) across an electrical conductor that is wikt:transverse, transverse to an electric current in the conductor and to an applied magnetic field wikt:perpendicul ...
\sigma_ at integer multiples (the "
Landau level In quantum mechanics, the energies of Cyclotron motion#Cyclotron resonance, cyclotron orbits of charged particles in a uniform magnetic field are quantized to discrete values, thus known as Landau levels. These levels are Degenerate energy level, d ...
") of the basic quantity ''e''2/''h'' (where ''e'' is the elementary electric charge and ''h'' is the
Planck constant The Planck constant, or Planck's constant, denoted by h, is a fundamental physical constant of foundational importance in quantum mechanics: a photon's energy is equal to its frequency multiplied by the Planck constant, and the wavelength of a ...
). It can usually be observed only in very clean
silicon Silicon is a chemical element; it has symbol Si and atomic number 14. It is a hard, brittle crystalline solid with a blue-grey metallic lustre, and is a tetravalent metalloid (sometimes considered a non-metal) and semiconductor. It is a membe ...
or
gallium arsenide Gallium arsenide (GaAs) is a III-V direct band gap semiconductor with a Zincblende (crystal structure), zinc blende crystal structure. Gallium arsenide is used in the manufacture of devices such as microwave frequency integrated circuits, monoli ...
solids at temperatures around and very high magnetic fields. Graphene shows the quantum Hall effect: the conductivity quantization is unusual in that the sequence of steps is shifted by 1/2 with respect to the standard sequence and with an additional factor of 4. Graphene's Hall conductivity is \sigma_=\pm /h , where ''N'' is the Landau level and the double valley and double spin degeneracies give the factor of 4. These anomalies are present not only at extremely low temperatures but also at room temperature, i.e. at roughly .


Chiral electrons and anomalies

This behavior is a direct result of graphene's chiral, massless Dirac electrons. In a magnetic field, their spectrum has a Landau level with energy precisely at the Dirac point. This level is a consequence of the
Atiyah–Singer index theorem In differential geometry, the Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential operator on a compact manifold, the analytical index (related to the dimension of the space ...
and is half-filled in neutral graphene, leading to the "+1/2" in the Hall conductivity. Bilayer graphene also shows the quantum Hall effect, but with only one of the two anomalies (i.e. \sigma_=\pm /h ). In the second anomaly, the first plateau at is absent, indicating that bilayer graphene stays metallic at the neutrality point. 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, thus the term "''integral'' quantum Hall effect". These oscillations show a phase shift of π, known as
Berry's phase In Classical mechanics, classical and quantum mechanics, geometric phase is a Phase (waves), phase difference acquired over the course of a Period (physics), cycle, when a system is subjected to cyclic adiabatic process (quantum mechanics), adiabat ...
. Berry's phase arises due to chirality or dependence (locking) of the pseudospin quantum number on the momentum of low-energy electrons near the Dirac points. The temperature dependence of the oscillations reveals that the carriers have a non-zero cyclotron mass, despite their zero effective mass in the Dirac-fermion formalism.


Experimental observations

Graphene samples prepared on nickel films, and on both the silicon face and carbon face of
silicon carbide Silicon carbide (SiC), also known as carborundum (), is a hard chemical compound containing silicon and carbon. A wide bandgap semiconductor, it occurs in nature as the extremely rare mineral moissanite, but has been mass-produced as a powder a ...
, show the anomalous effect directly in electrical measurements. Graphitic layers on the carbon face of silicon carbide show a clear Dirac spectrum in angle-resolved photoemission experiments, and the effect is observed in cyclotron resonance and tunneling experiments.


"Massive" electrons

Graphene's unit cell has two identical carbon atoms and two zero-energy states: one where the electron resides on atom A, and the other on atom B. However, if the unit cell's two atoms are not identical, the situation changes. Research shows that placing
hexagonal boron nitride Boron nitride is a thermally and chemically resistant refractory compound of boron and nitrogen with the chemical formula B N. It exists in various crystalline forms that are isoelectronic to a similarly structured carbon lattice. The hexago ...
(h-BN) in contact with graphene can alter the potential felt at atoms A and B sufficiently for the electrons to develop a mass and an accompanying band gap of about 30 meV. 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 Spectroscopy is the field of study that measures and interprets electromagnetic spectra. In narrower contexts, spectroscopy is the precise study of color as generalized from visible light to all bands of the electromagnetic spectrum. Spectros ...
. 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 In physics, topological order describes a state or phase of matter that arises system with non-local interactions, such as entanglement in quantum mechanics, and floppy modes in elastic systems. Whereas classical phases of matter such as gases an ...
and displays much the same physics as topological insulators. If the mass in graphene can be controlled, electrons can be confined to massless regions by surrounding them with massive regions, allowing the patterning of
quantum dot Quantum dots (QDs) or semiconductor nanocrystals are semiconductor particles a few nanometres in size with optical and electronic properties that differ from those of larger particles via quantum mechanical effects. They are a central topic i ...
s, wires, and other mesoscopic structures. It also produces one-dimensional conductors along the boundary. These wires would be protected against
backscatter In physics, backscatter (or backscattering) is the reflection of waves, particles, or signals back to the direction from which they came. It is usually a diffuse reflection due to scattering, as opposed to specular reflection as from a mirror, ...
ing and could carry currents without dissipation.


Interactions and phenomena


Strong magnetic fields

In magnetic fields above 10 tesla, additional plateaus of the Hall conductivity at with are observed. A plateau at and the
fractional quantum Hall effect The fractional quantum Hall effect (fractional QHE or FQHE) is the observation of precisely quantized plateaus in the Hall conductance of 2-dimensional (2D) electrons at fractional values of e^2/h, where ''e'' is the electron charge and ''h'' i ...
at were also reported. These observations with indicate that the four-fold degeneracy (two valley and two spin degrees of freedom) of the Landau energy levels is partially or completely lifted.


Casimir effect

The
Casimir effect In quantum field theory, the Casimir effect (or Casimir force) is a physical force (physics), force acting on the macroscopic boundaries of a confined space which arises from the quantum fluctuations of a field (physics), field. The term Casim ...
is an interaction between disjoint neutral bodies provoked by the fluctuations of the electromagnetic vacuum. Mathematically, it can be explained by considering the normal modes of electromagnetic fields, which explicitly depend on the boundary conditions on the interacting bodies' surfaces. Due to graphene's strong interaction with the electromagnetic field as a one-atom-thick material, the Casimir effect has garnered significant interest.


Van der Waals force

The
Van der Waals force In molecular physics and chemistry, the van der Waals force (sometimes van der Waals' force) is a distance-dependent interaction between atoms or molecules. Unlike ionic or covalent bonds, these attractions do not result from a chemical elec ...
(or dispersion force) is also unusual, obeying an inverse cubic asymptotic
power law In statistics, a power law is a Function (mathematics), functional relationship between two quantities, where a Relative change and difference, relative change in one quantity results in a relative change in the other quantity proportional to the ...
in contrast to the usual inverse quartic law.


Permittivity

Graphene's
permittivity In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter (epsilon), is a measure of the electric polarizability of a dielectric material. A material with high permittivity polarizes more ...
varies with frequency. Over a range from microwave to millimeter wave frequencies, it is approximately 3.3. This permittivity, combined with its ability to function as both a conductor and as an insulator, theoretically allows compact
capacitor In electrical engineering, a capacitor is a device that stores electrical energy by accumulating electric charges on two closely spaced surfaces that are insulated from each other. The capacitor was originally known as the condenser, a term st ...
s made of graphene to store large amounts of electrical energy.


Optical properties

Graphene exhibits unique optical properties, showing unexpectedly high
opacity Opacity is the measure of impenetrability to electromagnetic or other kinds of radiation, especially visible light. In radiative transfer, it describes the absorption and scattering of radiation in a medium, such as a plasma, dielectric, shie ...
for an atomic monolayer in vacuum, absorbing approximately of
light Light, visible light, or visible radiation is electromagnetic radiation that can be visual perception, perceived by the human eye. Visible light spans the visible spectrum and is usually defined as having wavelengths in the range of 400– ...
from visible to infrared wavelengths, where ''α'' is the
fine-structure constant In physics, the fine-structure constant, also known as the Sommerfeld constant, commonly denoted by (the Alpha, Greek letter ''alpha''), is a Dimensionless physical constant, fundamental physical constant that quantifies the strength of the el ...
. This is due to the unusual low-energy electronic structure of monolayer graphene, characterized by electron and hole conical bands meeting at the
Dirac point In physics, Dirac cones are features that occur in some electronic band structures that describe unusual electron transport properties of materials like graphene and topological insulators. In these materials, at energies near the Fermi leve ...
, which is qualitatively different from more common quadratic massive bands. Based on the Slonczewski–Weiss–McClure (SWMcC) band model of graphite, calculations using
Fresnel equations The Fresnel equations (or Fresnel coefficients) describe the reflection and transmission of light (or electromagnetic radiation in general) when incident on an interface between different optical media. They were deduced by French engineer and ...
in the thin-film limit account for interatomic distance, hopping values, and frequency, thus assessing optical conductance. Experimental verification, though confirmed, lacks the precision required to improve upon existing techniques for determining the
fine-structure constant In physics, the fine-structure constant, also known as the Sommerfeld constant, commonly denoted by (the Alpha, Greek letter ''alpha''), is a Dimensionless physical constant, fundamental physical constant that quantifies the strength of the el ...
.


Multi-parametric surface plasmon resonance

Multi-parametric surface plasmon resonance has been utilized to characterize both the thickness and refractive index of chemical-vapor-deposition (CVD)-grown graphene films. At a wavelength of , measured refractive index and extinction coefficient values are 3.135 and 0.897, respectively. Thickness determination yielded 3.7 Å across a 0.5mm area, consistent with the 3.35 Å reported for layer-to-layer carbon atom distance of graphite crystals. This method is applicable for real-time label-free interactions of graphene with organic and inorganic substances. The existence of unidirectional surface plasmons in nonreciprocal graphene-based gyrotropic interfaces has been theoretically demonstrated, offering tunability from THz to near-infrared and visible frequencies by controlling graphene's chemical potential. Particularly, the unidirectional frequency bandwidth can be 1– 2 orders of magnitude larger than that achievable with metal under similar magnetic field conditions, stemming from graphene's extremely small effective electron mass.


Tunable band gap and optical response

Graphene's
band gap In solid-state physics and solid-state chemistry, a band gap, also called a bandgap or energy gap, is an energy range in a solid where no electronic states exist. In graphs of the electronic band structure of solids, the band gap refers to t ...
can be tuned from 0 to (about 5-micrometer wavelength) by applying a voltage to a dual-gate bilayer graphene
field-effect transistor The field-effect transistor (FET) is a type of transistor that uses an electric field to control the current through a semiconductor. It comes in two types: junction FET (JFET) and metal-oxide-semiconductor FET (MOSFET). FETs have three termi ...
(FET) at room temperature. The optical response of
graphene nanoribbons Graphene nanoribbons (GNRs, also called nano-graphene ribbons or nano-graphite ribbons) are strips of graphene with width less than 100 nm. Graphene ribbons were introduced as a theoretical model by Mitsutaka Fujita and coauthors to examine ...
is tunable into the terahertz regime by an applied magnetic fields. Graphene/graphene oxide systems exhibit electrochromic behavior, enabling tuning of both linear and ultrafast optical properties.


Graphene-based Bragg grating

A graphene-based Bragg grating (one-dimensional
photonic crystal A photonic crystal is an optical nanostructure in which the refractive index changes periodically. This affects the propagation of light in the same way that the structure of Crystal structure, natural crystals gives rise to X-ray crystallograp ...
) has been fabricated, demonstrating its capability to excite surface electromagnetic waves in periodic structure using a He–Ne laser as the light source.


Saturable absorption

Graphene exhibits unique saturable absorption, which saturates when the input optical intensity exceeds a threshold value. This nonlinear optical behavior, termed
saturable absorption Saturable absorption is a property of materials where the absorption of light decreases with increasing light intensity. Most materials show some saturable absorption, but often only at very high optical intensities (close to the optical damage ...
, occurs across the visible to
near-infrared Infrared (IR; sometimes called infrared light) is electromagnetic radiation (EMR) with wavelengths longer than that of visible light but shorter than microwaves. The infrared spectral band begins with the waves that are just longer than those of ...
spectrum, due to graphene's universal optical absorption and zero band gap. This property has enabled full-band mode-locking in
fiber laser A fiber laser (or fibre laser in Commonwealth English) is a laser in which the active gain medium is an optical fiber doped with rare-earth elements such as erbium, ytterbium, neodymium, dysprosium, praseodymium, thulium and holmium. They ar ...
s using graphene-based saturable absorbers, contributing significantly to ultrafast
photonics Photonics is a branch of optics that involves the application of generation, detection, and manipulation of light in the form of photons through emission, transmission, modulation, signal processing, switching, amplification, and sensing. E ...
. Additionally, the optical response of graphene/graphene oxide layers can be electrically tuned. Saturable absorption in graphene could occur at the Microwave and Terahertz band, owing to its wideband optical absorption property. The microwave-saturable absorption in graphene demonstrates the possibility of graphene microwaves and terahertz photonics devices, such as a microwave-saturable absorber, modulator, polarizer, microwave signal processing, and broadband wireless access networks.


Nonlinear Kerr effect

Under intense laser illumination, graphene exhibits a nonlinear phase shift due to the optical nonlinear
Kerr effect The Kerr effect, also called the quadratic electro-optic (QEO) effect, is a change in the refractive index of a material in response to an applied electric field. The Kerr effect is distinct from the Pockels effect in that the induced index chan ...
. Graphene demonstrates a large nonlinear Kerr coefficient of , nearly nine orders of magnitude larger than that of bulk dielectrics, suggesting its potential as a powerful nonlinear Kerr medium capable of supporting various nonlinear effects, including
soliton In mathematics and physics, a soliton is a nonlinear, self-reinforcing, localized wave packet that is , in that it preserves its shape while propagating freely, at constant velocity, and recovers it even after collisions with other such local ...
s.


Excitonic properties

First-principle calculations incorporating quasiparticle corrections and many-body effects have been employed to study the electronic and optical properties of graphene-based materials. The approach was described as three stages. With GW calculation, the properties of graphene-based materials were accurately investigated, including bulk graphene, nanoribbons, edge and surface functionalized armchair ribbons, hydrogen saturated armchair ribbons,
Josephson effect In physics, the Josephson effect is a phenomenon that occurs when two superconductors are placed in proximity, with some barrier or restriction between them. The effect is named after the British physicist Brian Josephson, who predicted in 1962 ...
in graphene SNS junctions with single localized defect and armchair ribbon scaling properties.


Spin transport

Graphene is considered an ideal material for
spintronics Spintronics (a portmanteau meaning spin transport electronics), also known as spin electronics, is the study of the intrinsic spin of the electron and its associated magnetic moment, in addition to its fundamental electronic charge, in solid-st ...
due to its minimal
spin–orbit interaction In quantum mechanics, the spin–orbit interaction (also called spin–orbit effect or spin–orbit coupling) is a relativistic interaction of a particle's spin with its motion inside a potential. A key example of this phenomenon is the spin– ...
, the near absence of
nuclear magnetic moment The nuclear magnetic moment is the magnetic moment of an atomic nucleus and arises from the spin of the protons and neutrons. It is mainly a magnetic dipole moment; the quadrupole moment does cause some small shifts in the hyperfine structure ...
s in carbon, and weak hyperfine interaction. Electrical injection and detection of spin current have been demonstrated up to room temperature, with spin coherence length exceeding 1 micrometer observed at this temperature. Control of spin current polarity via electrical gating has been achieved at low temperatures.


Magnetic properties


Strong magnetic fields

Graphene's quantum Hall effect in magnetic fields above approximately 10 tesla reveals additional interesting features. Additional plateaus in Hall conductivity at \sigma_=\nu e^2/h with \nu=0,\pm ,\pm have been observed, along with plateau at \nu=3 and a fractional quantum Hall effect at \nu=1/3. These observations with \nu=0,\pm 1,\pm 3, \pm 4 indicate that the four-fold degeneracy (two valley and two spin degrees of freedom) of the Landau energy levels is partially or completely lifted. One hypothesis proposes that
magnetic catalysis Magnetic catalysis is a physics phenomenon, which is defined as an enhancement of dynamical symmetry breaking by an external magnetic field in quantum field theory, used for the description of quantum ( quasi-)particles in particle physics, nucl ...
of
symmetry breaking In physics, symmetry breaking is a phenomenon where a disordered but Symmetry in quantum mechanics, symmetric state collapses into an ordered, but less symmetric state. This collapse is often one of many possible Bifurcation theory, bifurcatio ...
is responsible for this degeneracy lift.


Spintronic properties

Graphene exhibits spintronic and magnetic properties concurrently. Low-defect graphene Nano-meshes, fabricated using a non-lithographic approach, exhibit significant ferromagnetism even at room temperature. Additionally, a spin pumping effect has been observed with fields applied in parallel to the planes of few-layer ferromagnetic nano-meshes, while a
magnetoresistance Magnetoresistance is the tendency of a material (often ferromagnetic) to change the value of its electrical resistance in an externally-applied magnetic field. There are a variety of effects that can be called magnetoresistance. Some occur in bulk ...
hysteresis loop is evident under perpendicular fields. Charge-neutral graphene has demonstrated magnetoresistance exceeding 100% in magnetic fields generated by standard permanent magnets (approximately 0.1 tesla), marking a record magneto resistivity ''at room temperature'' among known materials.


Magnetic substrates

In 2010, researchers magnetized graphene by producing it via CVD on the Ni(111) substrate and then in 2014 by placing it on an atomically smooth layer of magnetic
yttrium iron garnet Yttrium iron garnet (YIG) is a kind of synthetic garnet, with chemical composition , or Y3Fe5O12. It is a ferrimagnetic material with a Curie temperature of 560  K. YIG may also be known as yttrium ferrite garnet, or as iron yttrium oxide or ...
, maintaining graphene's electronic properties unaffected. Previous methods involved doping graphene with other substances. The dopant's presence negatively affected its electronic properties.


Mechanical properties

As noted
above Above may refer to: *Above (artist) Tavar Zawacki (b. 1981, California) is a Polish, Portuguese - American abstract artist and internationally recognized visual artist based in Berlin, Germany. From 1996 to 2016, he created work under the ...
, the (two-dimensional) density of graphene is 0.762 mg per square meter. Graphene is the strongest material ever tested, with an intrinsic
tensile strength Ultimate tensile strength (also called UTS, tensile strength, TS, ultimate strength or F_\text in notation) is the maximum stress that a material can withstand while being stretched or pulled before breaking. In brittle materials, the ultimate ...
of (with representative engineering tensile strength ~50-60 GPa for stretching large-area freestanding graphene) and a
Young's modulus Young's modulus (or the Young modulus) is a mechanical property of solid materials that measures the tensile or compressive stiffness when the force is applied lengthwise. It is the modulus of elasticity for tension or axial compression. Youn ...
(stiffness) close to . The Nobel announcement illustrated this by saying that a 1 square meter graphene hammock would support a cat but would weigh only as much as one of the cat's whiskers, at (about 0.001% of the weight of of paper). Large-angle bending of graphene monolayers with minimal strain demonstrates its mechanical robustness. Even under extreme deformation, monolayer graphene maintains excellent carrier mobility. The
spring constant In physics, Hooke's law is an empirical law which states that the force () needed to extend or compress a spring (device), spring by some distance () Proportionality (mathematics)#Direct_proportionality, scales linearly with respect to that ...
of suspended graphene sheets has been measured using an
atomic force microscope Atomic force microscopy (AFM) or scanning force microscopy (SFM) is a very-high-resolution type of scanning probe microscopy (SPM), with demonstrated resolution on the order of fractions of a nanometer, more than 1000 times better than the diffr ...
(AFM). Graphene sheets were suspended over cavities where an AFM tip was used to apply stress to the sheet to test its mechanical properties. Its spring constant was in the range 1–5  N/m and the stiffness was , which differs from that of bulk graphite. These intrinsic properties could lead to applications such as NEMS as pressure sensors and resonators. Due to its large surface energy and out of plane ductility, flat graphene sheets are unstable with respect to scrolling, i.e. bending into a cylindrical shape, which is its lower-energy state. In two-dimensional structures like graphene, thermal and quantum fluctuations cause relative displacement, with fluctuations growing logarithmically with structure size as per the
Mermin–Wagner theorem In quantum field theory and statistical mechanics, the Hohenberg–Mermin–Wagner theorem or Mermin–Wagner theorem (also known as Mermin–Wagner–Berezinskii theorem or Mermin–Wagner–Coleman theorem) states that continuous symmetries cann ...
. This 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, and it has been proposed that the ripples are caused by thermal fluctuations in the material. As a consequence of these dynamical deformations, it is debatable whether graphene is truly a 2D structure. These ripples, when amplified by vacancy defects, induce a negative
Poisson's ratio In materials science and solid mechanics, Poisson's ratio (symbol: ( nu)) is a measure of the Poisson effect, the deformation (expansion or contraction) of a material in directions perpendicular to the specific direction of loading. The value ...
into graphene, resulting in the thinnest auxetic material known so far. Graphene-nickel (Ni) composites, created through plating processes, exhibit enhanced mechanical properties due to strong Ni-graphene interactions inhibiting dislocation sliding in the Ni matrix.


Fracture toughness

In 2014, researchers from
Rice University William Marsh Rice University, commonly referred to as Rice University, is a Private university, private research university in Houston, Houston, Texas, United States. Established in 1912, the university spans 300 acres. Rice University comp ...
and the
Georgia Institute of Technology The Georgia Institute of Technology (commonly referred to as Georgia Tech, GT, and simply Tech or the Institute) is a public university, public research university and Institute of technology (United States), institute of technology in Atlanta, ...
have indicated that despite its strength, graphene is also relatively
brittle A material is brittle if, when subjected to stress, it fractures with little elastic deformation and without significant plastic deformation. Brittle materials absorb relatively little energy prior to fracture, even those of high strength. ...
, with a
fracture toughness In materials science, fracture toughness is the critical stress intensity factor of a sharp Fracture, crack where propagation of the crack suddenly becomes rapid and unlimited. It is a material property that quantifies its ability to resist crac ...
of about 4 MPa√m. This indicates that imperfect graphene is likely to crack in a brittle manner like
ceramic materials A ceramic is any of the various hard, brittle, heat-resistant, and corrosion-resistant materials made by shaping and then firing an inorganic, nonmetallic material, such as clay, at a high temperature. Common examples are earthenware, porcelai ...
, as opposed to many metallic materials which tend to have fracture toughness 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. The force was transmitted at .


Polycrystalline graphene

Various methods – most notably,
chemical vapor deposition Chemical vapor deposition (CVD) is a vacuum deposition method used to produce high-quality, and high-performance, solid materials. The process is often used in the semiconductor industry to produce thin films. In typical CVD, the wafer (electro ...
(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. The mechanical properties of polycrystalline graphene are affected by the nature of the defects, such as grain-boundaries (GB) and vacancies, present in the system and the average grain-size. Graphene grain boundaries typically contain heptagon-pentagon pairs. The arrangement of such defects depends on whether the GB is in a zig-zag or armchair direction. It further depends on the tilt-angle of the GB. In 2010, researchers from
Brown University Brown University is a Private university, private Ivy League research university in Providence, Rhode Island, United States. It is the List of colonial colleges, seventh-oldest institution of higher education in the US, founded in 1764 as the ' ...
computationally predicted that as the tilt-angle increases, the grain boundary strength also increases. They showed that the weakest link in the grain boundary is at the critical bonds of the heptagon rings. As the grain boundary angle increases, the strain in these heptagon rings decreases, causing the grain boundary to be stronger than lower-angle GBs. They proposed that, in fact, for sufficiently large angle GB, the strength of the GB is similar to pristine graphene. In 2012, it was further shown that the strength can increase or decrease, depending on the detailed arrangements of the defects. These predictions have since been supported by experimental evidence. In a 2013 study led by James Hone's group, researchers probed the elastic
stiffness Stiffness is the extent to which an object resists deformation in response to an applied force. The complementary concept is flexibility or pliability: the more flexible an object is, the less stiff it is. Calculations The stiffness, k, of a ...
and
strength Strength may refer to: Personal trait *Physical strength, as in people or animals *Character strengths like those listed in the Values in Action Inventory *The exercise of willpower Physics * Mechanical strength, the ability to withstand ...
of CVD-grown graphene by combining nano-indentation and high-resolution TEM. They found that the elastic stiffness is identical and strength is only slightly lower than those in pristine graphene. In the same year, researchers from
University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a Public university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after t ...
and
University of California, Los Angeles The University of California, Los Angeles (UCLA) is a public university, public Land-grant university, land-grant research university in Los Angeles, California, United States. Its academic roots were established in 1881 as a normal school the ...
probed bi-crystalline graphene with TEM and AFM. They found that the strength of grain boundaries indeed tends to increase with the tilt angle. While the presence of vacancies is not only prevalent in polycrystalline graphene, vacancies can have significant effects on the strength of graphene. The consensus is that the strength decreases along with increasing densities of vacancies. Various studies have shown that for graphene with a sufficiently low density of vacancies, the strength does not vary significantly from that of pristine graphene. On the other hand, a 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. In fact, three notable theoretical or computational studies on this topic have led to three different conclusions. First, in 2012, Kolakowski and Myer studied the mechanical properties of polycrystalline graphene with "realistic atomistic model", using molecular-dynamics (MD) simulation. To emulate the growth mechanism of CVD, they first randomly selected
nucleation In thermodynamics, nucleation is the first step in the formation of either a new Phase (matter), thermodynamic phase or Crystal structure, structure via self-assembly or self-organization within a substance or mixture. Nucleation is typically def ...
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, and 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. Second, in 2013, Z. Song et al. used MD simulations to study the mechanical properties of polycrystalline graphene with uniform-sized hexagon-shaped grains. The hexagon grains were oriented in various lattice directions and the GBs consisted of only heptagon, pentagon, and hexagonal carbon rings. The motivation behind such a model was that similar systems had been experimentally observed in graphene flakes grown on the surface of liquid copper. While they also noted that crack is typically initiated at the triple junctions, they found that as the grain size decreases, the yield strength of graphene increases. Based on this finding, they proposed that polycrystalline follows pseudo Hall-Petch relationship. Third, in 2013, Z. D. Sha et al. studied the effect of grain size on the properties of polycrystalline graphene, by modeling the grain patches using Voronoi construction. The GBs in this model consisted of heptagons, pentagons, and hexagons, as well as squares, octagons, and vacancies. Through MD simulation, contrary to the aforementioned study, they found an inverse Hall-Petch relationship, where the strength of graphene increases as the grain size increases. Experimental observations and other theoretical predictions also gave differing conclusions, similar to the three given above. Such discrepancies show the complexity of the effects that grain size, arrangements of defects, and the nature of defects have on the mechanical properties of polycrystalline graphene.


Other properties


Thermal conductivity

Thermal transport in graphene is a burgeoning area of research, particularly for its potential applications in thermal management. Most experimental measurements have posted large uncertainties in the results of thermal conductivity due to the limitations of the instruments used. Following predictions for graphene and related
carbon nanotubes A carbon nanotube (CNT) is a tube made of carbon with a diameter in the nanometre range (nanoscale). They are one of the allotropes of carbon. Two broad classes of carbon nanotubes are recognized: * ''Single-walled carbon nanotubes'' (''SWC ...
, early measurements of the
thermal conductivity The thermal conductivity of a material is a measure of its ability to heat conduction, conduct heat. It is commonly denoted by k, \lambda, or \kappa and is measured in W·m−1·K−1. Heat transfer occurs at a lower rate in materials of low ...
of suspended graphene reported an exceptionally large thermal conductivity up to , compared with the thermal conductivity of pyrolytic
graphite Graphite () is a Crystallinity, crystalline allotrope (form) of the element carbon. It consists of many stacked Layered materials, layers of graphene, typically in excess of hundreds of layers. Graphite occurs naturally and is the most stable ...
of approximately at room temperature. However, later studies primarily on more scalable but more defected graphene derived by Chemical Vapor Deposition have been unable to reproduce such high thermal conductivity measurements, producing a wide range of thermal conductivities between – for suspended single-layer graphene. The large range in the reported thermal conductivity can be caused by large measurement uncertainties as well as variations in the graphene quality and processing conditions. In addition, it is known that when single-layer graphene is supported on an amorphous material, the thermal conductivity is reduced to about – at room temperature as a result of scattering of graphene lattice waves by the substrate, and can be even lower for few-layer graphene encased in amorphous oxide. Likewise, polymeric residue can contribute to a similar decrease in the thermal conductivity of suspended graphene to approximately – for bilayer graphene. Isotopic composition, specifically the ratio of 12C to 13C, significantly affects graphene's thermal conductivity. Isotopically pure 12C graphene exhibits higher thermal conductivity than either a 50:50 isotope ratio or the naturally occurring 99:1 ratio.
''Lay summary'':
It can be shown by using the
Wiedemann–Franz law In physics, the Wiedemann–Franz law states that the ratio of the electronic contribution of the thermal conductivity (''κ'') to the electrical conductivity (''σ'') of a metal is proportional to the temperature (''T''). : \frac \kappa ...
, that the thermal conduction is
phonon A phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, specifically in solids and some liquids. In the context of optically trapped objects, the quantized vibration mode can be defined a ...
-dominated. However, for a gated graphene strip, an applied gate bias causing a
Fermi energy The Fermi energy is a concept in quantum mechanics usually referring to the energy difference between the highest and lowest occupied single-particle states in a quantum system of non-interacting fermions at absolute zero temperature. In a Fermi ga ...
shift much larger than ''k''B''T'' can cause the electronic contribution to increase and dominate over the
phonon A phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, specifically in solids and some liquids. In the context of optically trapped objects, the quantized vibration mode can be defined a ...
contribution at low temperatures. The ballistic thermal conductance of graphene is isotropic. Graphite, a 3D counterpart to graphene, exhibits a
basal plane In crystallography, crystal structure is a description of ordered arrangement of atoms, ions, or molecules in a crystalline material. Ordered structures occur from intrinsic nature of constituent particles to form symmetric patterns that repeat a ...
thermal conductivity The thermal conductivity of a material is a measure of its ability to heat conduction, conduct heat. It is commonly denoted by k, \lambda, or \kappa and is measured in W·m−1·K−1. Heat transfer occurs at a lower rate in materials of low ...
exceeding (similar to
diamond Diamond is a Allotropes of carbon, solid form of the element carbon with its atoms arranged in a crystal structure called diamond cubic. Diamond is tasteless, odourless, strong, brittle solid, colourless in pure form, a poor conductor of e ...
), 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. In addition, the ballistic thermal conductance of graphene is shown to give the lower limit of the ballistic thermal conductance, per unit circumference, length of carbon nanotubes. Graphene's thermal conductivity is influenced by its three acoustic phonon modes: two linear
dispersion relation In the physical sciences and electrical engineering, dispersion relations describe the effect of dispersion on the properties of waves in a medium. A dispersion relation relates the wavelength or wavenumber of a wave to its frequency. Given the ...
dispersion relation in-plane modes (LA, TA) and one quadratic dispersion relation out-of-plane mode (ZA). At low temperatures, the dominance of the T1.5 thermal conductivity contribution of the out-of-plane mode supersedes the ''T''2 dependence of the linear modes. Some graphene phonon bands exhibit negative Grüneisen parameters, resulting in negative
thermal expansion coefficient Thermal expansion is the tendency of matter to increase in length, area, or volume, changing its size and density, in response to an increase in temperature (usually excluding phase transitions). Substances usually contract with decreasing temp ...
at low temperatures. The lowest negative Grüneisen parameters correspond to the lowest transverse acoustic ZA modes, whose frequencies increase with in-plane
lattice parameter A lattice constant or lattice parameter is one of the physical dimensions and angles that determine the geometry of the unit cells in a crystal lattice, and is proportional to the distance between atoms in the crystal. A simple cubic crystal has ...
, akin to a stretched string with higher frequency vibrations.


Chemical properties

Graphene has a theoretical
specific surface area Specific surface area (SSA) is a property of solids defined as the total surface area (SA) of a material per unit mass, (with units of m2/kg or m2/g). Alternatively, it may be defined as SA per solid or bulk volume (units of m2/m3 or m−1). I ...
(SSA) of . This is much larger than that reported to date for carbon black (typically smaller than ) or for carbon nanotubes (CNTs), from ≈100 to and is similar to
activated carbon Activated carbon, also called activated charcoal, is a form of carbon commonly used to filter contaminants from water and air, among many other uses. It is processed (activated) to have small, low-volume pores that greatly increase the surface ar ...
. Graphene is the only form of carbon (or solid material) in which every atom is available for chemical reaction from two sides (due to the 2D structure). Atoms at the edges of a graphene sheet have special chemical reactivity. Graphene has the highest ratio of edge atoms of any
allotrope Allotropy or allotropism () is the property of some chemical elements to exist in two or more different forms, in the same physical state, known as allotropes of the elements. Allotropes are different structural modifications of an element: the ...
. Defects within a sheet increase its chemical reactivity. The onset temperature of reaction between the basal plane of single-layer graphene and oxygen gas is below . Graphene burns at very low temperatures (e.g., ). Graphene is commonly modified with oxygen- and nitrogen-containing
functional group In organic chemistry, a functional group is any substituent or moiety (chemistry), moiety in a molecule that causes the molecule's characteristic chemical reactions. The same functional group will undergo the same or similar chemical reactions r ...
s and analyzed by
infrared spectroscopy Infrared spectroscopy (IR spectroscopy or vibrational spectroscopy) is the measurement of the interaction of infrared radiation with matter by absorption, emission, or reflection. It is used to study and identify chemical substances or functio ...
and
X-ray photoelectron spectroscopy X-ray photoelectron spectroscopy (XPS) is a surface-sensitive quantitative spectroscopic technique that measures the very topmost 50-60 atoms, 5-10 nm of any surface. It belongs to the family of photoemission spectroscopies in which electro ...
. However, the determination of structures of graphene with oxygen- and nitrogen- functional groups require the structures to be well controlled. In 2013,
Stanford University Leland Stanford Junior University, commonly referred to as Stanford University, is a Private university, private research university in Stanford, California, United States. It was founded in 1885 by railroad magnate Leland Stanford (the eighth ...
physicists reported that single-layer graphene is a hundred times more chemically reactive than thicker multilayer sheets. Graphene can self-repair holes in its sheets, when exposed to molecules containing carbon, such as
hydrocarbon In organic chemistry, a hydrocarbon is an organic compound consisting entirely of hydrogen and carbon. Hydrocarbons are examples of group 14 hydrides. Hydrocarbons are generally colourless and Hydrophobe, hydrophobic; their odor is usually fain ...
s. Bombarded with pure carbon atoms, the atoms perfectly align into
hexagon In geometry, a hexagon (from Greek , , meaning "six", and , , meaning "corner, angle") is a six-sided polygon. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°. Regular hexagon A regular hexagon is de ...
s, filling the holes.


Biological properties

Despite the promising results in different cell studies and proof of concept studies, there is still incomplete understanding of the full biocompatibility of graphene-based materials. Different cell lines react differently when exposed to graphene, and it has been shown that the lateral size of the graphene flakes, the form and surface chemistry can elicit different biological responses on the same cell line. There are indications that graphene has promise as a useful material for interacting with neural cells; studies on cultured neural cells show limited success. Graphene also has some utility in osteogenesis. Researchers at the Graphene Research Centre at the
National University of Singapore The National University of Singapore (NUS) is a national university, national Public university, public research university in Singapore. It was officially established in 1980 by the merging of the University of Singapore and Nanyang University ...
(NUS) discovered in 2011 the ability of graphene to accelerate the osteogenic differentiation of human
mesenchymal stem cell Mesenchymal stem cells (MSCs), also known as mesenchymal stromal cells or medicinal signaling cells, are multipotent stromal cells that can Cellular differentiation, differentiate into a variety of cell types, including osteoblasts (bone cells), ...
s without the use of biochemical inducers. Graphene can be used in biosensors; in 2015, researchers demonstrated that a graphene-based sensor can be used to detect a cancer risk biomarker. In particular, by using epitaxial graphene on silicon carbide, they were repeatedly able to detect 8-hydroxydeoxyguanosine (8-OHdG), a DNA damage biomarker.


Support substrate

The electronic 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. The Si(100)/H surface does not perturb the electronic properties of graphene, whereas the interaction between the clean Si(100) surface and graphene changes the electronic states of graphene significantly. This effect results from the covalent bonding between C and surface Si atoms, modifying the π-orbital network of the graphene layer. The local density of states shows that the bonded C and Si surface states are highly disturbed near the Fermi energy.


Graphene layers and structural variants


Monolayer sheets

In 2013 a group of Polish scientists presented a production unit that allows the manufacture of continuous monolayer sheets. The process is based on graphene growth on a liquid metal matrix. The product of this process was called High Strength Metallurgical Graphene. In a new study published in Nature, the researchers have used a single-layer graphene electrode and a novel surface-sensitive non-linear spectroscopy technique to investigate the top-most water layer at the electrochemically charged surface. They found that the interfacial water response to the applied electric field is asymmetric concerning the nature of the applied field.


Bilayer graphene

Bilayer graphene displays the anomalous quantum Hall effect, a tunable
band gap In solid-state physics and solid-state chemistry, a band gap, also called a bandgap or energy gap, is an energy range in a solid where no electronic states exist. In graphs of the electronic band structure of solids, the band gap refers to t ...
and potential for excitonic condensation –making it a promising candidate for
optoelectronic Optoelectronics (or optronics) is the study and application of electronic devices and systems that find, detect and control light, usually considered a sub-field of photonics. In this context, ''light'' often includes invisible forms of radia ...
and
nanoelectronic Nanoelectronics refers to the use of nanotechnology in electronic components. The term covers a diverse set of devices and materials, with the common characteristic that they are so small that inter-atomic interactions and quantum mechanical p ...
applications. Bilayer graphene typically can be found either in twisted configurations where the two layers are rotated relative to each other or graphitic Bernal stacked configurations where half the atoms in one layer lie atop half the atoms in the other. Stacking order and orientation govern the optical and electronic properties of bilayer graphene. One way to synthesize bilayer graphene is via
chemical vapor deposition Chemical vapor deposition (CVD) is a vacuum deposition method used to produce high-quality, and high-performance, solid materials. The process is often used in the semiconductor industry to produce thin films. In typical CVD, the wafer (electro ...
, which can produce large bilayer regions that almost exclusively conform to a Bernal stack geometry. It has been shown that the two graphene layers can withstand important strain or doping mismatch which ultimately should lead to their exfoliation.


Turbostratic

Turbostratic graphene exhibits weak interlayer coupling, and the spacing is increased with respect to Bernal-stacked multilayer graphene. Rotational misalignment preserves the 2D electronic structure, as confirmed by
Raman spectroscopy Raman spectroscopy () (named after physicist C. V. Raman) is a Spectroscopy, spectroscopic technique typically used to determine vibrational modes of molecules, although rotational and other low-frequency modes of systems may also be observed. Ra ...
. The D peak is very weak, whereas the 2D and G peaks remain prominent. A rather peculiar feature is that the I2D/IG ratio can exceed 10. However, most importantly, the M peak, which originates from AB stacking, is absent, whereas the TS1 and TS2 modes are visible in the Raman spectrum. The material is formed through conversion of non-graphenic carbon into graphenic carbon without providing sufficient energy to allow for the reorganization through annealing of adjacent graphene layers into crystalline graphitic structures.


Graphene superlattices

Periodically stacked graphene and its insulating isomorph provide a fascinating structural element in implementing highly functional superlattices at the atomic scale, which offers possibilities for designing nanoelectronic and photonic devices. Various types of superlattices can be obtained by stacking graphene and its related forms. The energy band in layer-stacked superlattices is found to be more sensitive to the barrier width than that in conventional III–V semiconductor superlattices. When adding more than one atomic layer to the barrier in each period, the coupling of electronic wavefunctions in neighboring potential wells can be significantly reduced, which leads to the degeneration of continuous subbands into quantized energy levels. When varying the well width, the energy levels in the potential wells along the L-M direction behave distinctly from those along the K-H direction. 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). Furthermore, superlattices of graphene-HBN are ideal model systems for the realization and understanding of coherent (wave-like) and incoherent (particle-like) phonon thermal transport.


Nanostructured graphene forms


Graphene nanoribbons

Graphene nanoribbons Graphene nanoribbons (GNRs, also called nano-graphene ribbons or nano-graphite ribbons) are strips of graphene with width less than 100 nm. Graphene ribbons were introduced as a theoretical model by Mitsutaka Fujita and coauthors to examine ...
("nanostripes" in the "zig-zag"/"zigzag" orientation), at low temperatures, show spin-polarized metallic edge currents, which also suggests applications in the new field of
spintronics Spintronics (a portmanteau meaning spin transport electronics), also known as spin electronics, is the study of the intrinsic spin of the electron and its associated magnetic moment, in addition to its fundamental electronic charge, in solid-st ...
. (In the "armchair" orientation, the edges behave like semiconductors.)


Graphene quantum dots

A
graphene quantum dot Graphene quantum dots (GQDs) are graphene nanoparticles with a size less than 100 nm. Due to their exceptional properties such as low toxicity, stable photoluminescence, chemical stability and pronounced quantum confinement effect, GQDs are co ...
(GQD) is a graphene fragment with a size lesser than 100 nm. The properties of GQDs are different from bulk graphene due to the quantum confinement effects which only become apparent when the size is smaller than 100 nm.


Modified and functionalized graphene


Graphene oxide

Graphene oxide is usually produced through chemical exfoliation of graphite. A particularly popular technique is the improved Hummers' method. Using paper-making techniques on dispersed, oxidized and chemically processed graphite in water, the monolayer flakes form a single sheet and create strong bonds. These sheets, called
graphene oxide paper Graphene oxide paper or graphite oxide paper is a material fabricated from graphite oxide. Micrometer thick films of graphene oxide paper are also named as graphite oxide membranes (in the 1960s) or (more recently) graphene oxide membranes. The me ...
, have a measured tensile modulus of 32
GPa Grading in education is the application of standardized measurements to evaluate different levels of student achievement in a course. Grades can be expressed as letters (usually A to F), as a range (for example, 1 to 6), percentages, or as num ...
. The chemical property of graphite oxide is related to the functional groups attached to graphene sheets. These can change the
polymerization In polymer chemistry, polymerization (American English), or polymerisation (British English), is a process of reacting monomer molecules together in a chemical reaction to form polymer chains or three-dimensional networks. There are many fo ...
pathway and similar chemical processes. Graphene oxide flakes in
polymers A polymer () is a substance or material that consists of very large molecules, or macromolecules, that are constituted by many repeating subunits derived from one or more species of monomers. Due to their broad spectrum of properties, b ...
s display enhanced photo-conducting properties. Graphene is normally
hydrophobic In chemistry, hydrophobicity is the chemical property of a molecule (called a hydrophobe) that is seemingly repelled from a mass of water. In contrast, hydrophiles are attracted to water. Hydrophobic molecules tend to be nonpolar and, thu ...
and impermeable to all gases and liquids (vacuum-tight). However, when formed into a graphene oxide-based capillary membrane, both liquid water and water vapor flow through as quickly as if the membrane were not present. In 2022, researchers evaluated the biological effects of low doses on graphene oxide on larvae and imago of ''
Drosophila melanogaster ''Drosophila melanogaster'' is a species of fly (an insect of the Order (biology), order Diptera) in the family Drosophilidae. The species is often referred to as the fruit fly or lesser fruit fly, or less commonly the "vinegar fly", "pomace fly" ...
''. Results show that oral administration of graphene oxide at concentrations of 0.02-1% has a beneficial effect on the developmental rate and hatching ability of larvae. Long-term administration of a low dose of graphene oxide extends the lifespan of Drosophila and significantly enhances resistance to environmental stresses. These suggest that graphene oxide affects carbohydrate and lipid metabolism in adult Drosophila. These findings might provide a useful reference to assess the biological effects of graphene oxide, which could play an important role in a variety of graphene-based biomedical applications.


Chemical modification

Soluble fragments of graphene can be prepared in the laboratory through chemical modification of graphite. First, microcrystalline graphite is treated with an acidic mixture of sulfuric acid and
nitric acid Nitric acid is an inorganic compound with the formula . It is a highly corrosive mineral acid. The compound is colorless, but samples tend to acquire a yellow cast over time due to decomposition into nitrogen oxide, oxides of nitrogen. Most com ...
. A series of oxidation and exfoliation steps produce small graphene plates with
carboxyl In organic chemistry, a carboxylic acid is an organic acid that contains a carboxyl group () attached to an R-group. The general formula of a carboxylic acid is often written as or , sometimes as with R referring to an organyl group (e.g. ...
groups at their edges. These are converted to
acid chloride In organic chemistry, an acyl chloride (or acid chloride) is an organic compound with the functional group . Their formula is usually written , where R is a side chain. They are reactive derivatives of carboxylic acids (). A specific example o ...
groups by treatment with
thionyl chloride Thionyl chloride is an inorganic compound with the chemical formula . It is a moderately Volatility (chemistry), volatile, colourless liquid with an unpleasant acrid odour. Thionyl chloride is primarily used as a Halogenation, chlorinating reagen ...
; next, they are converted to the corresponding graphene
amide In organic chemistry, an amide, also known as an organic amide or a carboxamide, is a chemical compound, compound with the general formula , where R, R', and R″ represent any group, typically organyl functional group, groups or hydrogen at ...
via treatment with octadecyl amine. The resulting material (circular graphene layers of thickness) is soluble in
tetrahydrofuran Tetrahydrofuran (THF), or oxolane, is an organic compound with the formula (CH2)4O. The compound is classified as heterocyclic compound, specifically a cyclic ether. It is a colorless, water- miscible organic liquid with low viscosity. It is ...
,
tetrachloromethane Carbon tetrachloride, also known by many other names (such as carbon tet for short and tetrachloromethane, also IUPAC nomenclature of inorganic chemistry, recognised by the IUPAC), is a chemical compound with the chemical formula CCl4. It is a n ...
and
dichloroethane Dichloroethane can refer to either of two isomeric organochloride Organochlorine chemistry is concerned with the properties of organochlorine compounds, or organochlorides, organic compounds that contain one or more carbon–chlorine bonds. The c ...
. Refluxing single-layer graphene oxide (SLGO) in
solvent A solvent (from the Latin language, Latin ''wikt:solvo#Latin, solvō'', "loosen, untie, solve") is a substance that dissolves a solute, resulting in a Solution (chemistry), solution. A solvent is usually a liquid but can also be a solid, a gas ...
s 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 In organic chemistry, an acyl chloride (or acid chloride) is an organic compound with the functional group . Their formula is usually written , where R is a side chain. They are reactive derivatives of carboxylic acids (). A specific example o ...
groups result, which can then form aliphatic and aromatic amides with a reactivity conversion of around 70–80%.
Hydrazine Hydrazine is an inorganic compound with the chemical formula . It is a simple pnictogen hydride, and is a colourless flammable liquid with an ammonia-like odour. Hydrazine is highly hazardous unless handled in solution as, for example, hydraz ...
reflux is commonly used for reducing SLGO to SLG(R), but
titration Titration (also known as titrimetry and volumetric analysis) is a common laboratory method of Quantitative research, quantitative Analytical chemistry, chemical analysis to determine the concentration of an identified analyte (a substance to be ...
s 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
hydrochloric acid Hydrochloric acid, also known as muriatic acid or spirits of salt, is an aqueous solution of hydrogen chloride (HCl). It is a colorless solution with a distinctive pungency, pungent smell. It is classified as a acid strength, strong acid. It is ...
(< 1.0 M) leads to around 60% loss of COOH functionality. Room temperature treatment of SLGO with
carbodiimide In organic chemistry, a carbodiimide (systematic IUPAC name: methanediimine) is a functional group with the formula RN=C=NR. On Earth they are exclusively synthetic, but in interstellar space the parent compound HN=C=NH has been detected by its ...
s 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). It is apparent that conventional chemical treatment of carboxylic groups on SLGO generates morphological changes of individual sheets that leads to a reduction in chemical reactivity, which may potentially limit their use in composite synthesis. Therefore, chemical reaction types have been explored. SLGO has also been grafted with polyallylamine, cross-linked through
epoxy Epoxy is the family of basic components or Curing (chemistry), cured end products of epoxy Resin, resins. Epoxy resins, also known as polyepoxides, are a class of reactive prepolymers and polymers which contain epoxide groups. The epoxide fun ...
groups. When filtered into graphene oxide paper, these composites exhibit increased stiffness and strength relative to unmodified graphene oxide paper. Full
hydrogenation Hydrogenation is a chemical reaction between molecular hydrogen (H2) and another compound or element, usually in the presence of a catalyst such as nickel, palladium or platinum. The process is commonly employed to redox, reduce or Saturated ...
from both sides of the graphene sheet results in Graphane, but partial hydrogenation leads to hydrogenated graphene. Similarly, both-side fluorination of graphene (or chemical and mechanical exfoliation of graphite fluoride) leads to fluorographene (graphene fluoride), while partial fluorination (generally
halogenation In chemistry, halogenation is a chemical reaction which introduces one or more halogens into a chemical compound. Halide-containing compounds are pervasive, making this type of transformation important, e.g. in the production of polymers, drug ...
) provides fluorinated (halogenated) graphene.


Graphene ligand/complex

Graphene can be a
ligand In coordination chemistry, a ligand is an ion or molecule with a functional group that binds to a central metal atom to form a coordination complex. The bonding with the metal generally involves formal donation of one or more of the ligand's el ...
to
coordinate In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine and standardize the position of the points or other geometric elements on a manifold such as Euclidean space. The coordinates are ...
metals and metal ions by introducing functional groups. Structures of graphene ligands are similar to e.g. metal-
porphyrin Porphyrins ( ) are heterocyclic, macrocyclic, organic compounds, composed of four modified pyrrole subunits interconnected at their α carbon atoms via methine bridges (). In vertebrates, an essential member of the porphyrin group is heme, w ...
complex, metal-
phthalocyanine Phthalocyanine () is a large, aromatic, macrocyclic, organic compound with the formula and is of theoretical or specialized interest in chemical dyes and photoelectricity. It is composed of four isoindole units linked by a ring of nitrogen ato ...
complex, and metal-
phenanthroline 1,10-Phenanthroline (phen) is a heterocyclic organic compound. It is a white solid that is soluble in organic solvents. The 1,10 refers to the location of the nitrogen atoms that replace CH's in the hydrocarbon called phenanthrene. Abbreviated " ...
complex. Copper and nickel ions can be coordinated with graphene ligands.


Advanced graphene structures


Graphene fiber

In 2011, researchers reported a novel yet simple approach to fabricating graphene fibers from chemical vapor deposition-grown graphene films. The method was scalable and controllable, delivering tunable morphology and pore structure by controlling the evaporation of solvents with suitable
surface tension Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension (physics), tension is what allows objects with a higher density than water such as razor blades and insects (e.g. Ge ...
. Flexible all-solid-state supercapacitors based on these graphene fibers were demonstrated in 2013. 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. The resulting fibers offered better thermal and electrical conductivity and mechanical strength. Thermal conductivity reached , while tensile strength reached . In 2016, kilometer-scale continuous graphene fibers with outstanding mechanical properties and excellent electrical conductivity were produced by high-throughput wet-spinning of graphene oxide liquid crystals followed by
graphitization Graphitization is a process of transforming a carbonaceous material, such as coal or the carbon in certain forms of iron alloys, into graphite. Process The graphitization process involves a restructuring of the molecular structure of the carbon ...
through a full-scale synergetic defect-engineering strategy. The graphene fibers with superior performances promise wide applications in functional textiles, lightweight motors, microelectronic devices, etc.
Tsinghua University Tsinghua University (THU) is a public university in Haidian, Beijing, China. It is affiliated with and funded by the Ministry of Education of China. The university is part of Project 211, Project 985, and the Double First-Class Constructio ...
in Beijing, led by Wei Fei of the Department of Chemical Engineering, claims to be able to create a carbon nanotube fiber that has a tensile strength of .


3D graphene

In 2013, a three-dimensional
honeycomb A honeycomb is a mass of Triangular prismatic honeycomb#Hexagonal prismatic honeycomb, hexagonal prismatic cells built from beeswax by honey bees in their beehive, nests to contain their brood (eggs, larvae, and pupae) and stores of honey and pol ...
of hexagonally arranged carbon was termed 3D graphene, and self-supporting 3D graphene was also produced. 3D structures of graphene can be fabricated by using either CVD or solution-based methods. A 2016 review by Khurram and Xu et al. provided a summary of then-state-of-the-art techniques for fabrication of the 3D structure of graphene and other related two-dimensional materials. In 2013, researchers at
Stony Brook University Stony Brook University (SBU), officially the State University of New York at Stony Brook, is a public university, public research university in Stony Brook, New York, United States, on Long Island. Along with the University at Buffalo, it is on ...
reported a novel radical-initiated crosslinking method to fabricate porous 3D free-standing architectures of graphene and carbon nanotubes using nanomaterials as building blocks without any polymer matrix as support. These 3D graphenes (all-carbon) scaffolds/foams have applications in several fields such as energy storage, filtration, thermal management, and biomedical devices and implants. Box-shaped graphene (BSG)
nanostructure A nanostructure is a structure of intermediate size between microscopic and molecular structures. Nanostructural detail is microstructure at nanoscale. In describing nanostructures, it is necessary to differentiate between the number of dimen ...
appearing after mechanical cleavage of pyrolytic graphite was reported in 2016. The discovered nanostructure is a multilayer system of parallel hollow nanochannels located along the surface and having quadrangular cross-section. The thickness of the channel walls is approximately equal to 1 nm. Potential fields of BSG application include ultra-sensitive
detector A sensor is often defined as a device that receives and responds to a signal or stimulus. The stimulus is the quantity, property, or condition that is sensed and converted into electrical signal. In the broadest definition, a sensor is a devi ...
s, high-performance catalytic cells, nanochannels for
DNA Deoxyribonucleic acid (; DNA) is a polymer composed of two polynucleotide chains that coil around each other to form a double helix. The polymer carries genetic instructions for the development, functioning, growth and reproduction of al ...
sequencing In genetics and biochemistry, sequencing means to determine the primary structure (sometimes incorrectly called the primary sequence) of an unbranched biopolymer. Sequencing results in a symbolic linear depiction known as a sequence which succ ...
and manipulation, high-performance heat sinking surfaces,
rechargeable batteries A rechargeable battery, storage battery, or secondary cell (formally a type of energy accumulator), is a type of electrical battery which can be charged, discharged into a load, and recharged many times, as opposed to a disposable or prima ...
of enhanced performance, nanomechanical resonators, electron multiplication channels in emission Nano-electronic devices, high-capacity
sorbent A sorbent is an insoluble material that either absorbs or adsorbs liquids or gases. They are frequently used to remove pollutants and in the cleanup of chemical accidents and oil spills. Besides their uses in industry, sorbents are used in comm ...
s for safe
hydrogen storage Several methods exist for storing hydrogen. These include mechanical approaches such as using high pressures and low temperatures, or employing chemical compounds that release H2 upon demand. While large amounts of hydrogen are produced by variou ...
. Three dimensional bilayer graphene has also been reported.


Pillared graphene

Pillared graphene is a hybrid carbon structure, consisting of an oriented array of carbon nanotubes connected at each end to a sheet of graphene. It was first described theoretically by George Froudakis and colleagues at the
University of Crete The University of Crete (UoC; Greek: Πανεπιστήμιο Κρήτης) is a multi-disciplinary, research-oriented institution in Crete, Greece, located in the cities of Rethymno (official seat) and Heraklion. There are 16 main undergraduate ...
in Greece in 2008. Pillared graphene has not yet been synthesized in the laboratory, but it has been suggested that it may have useful electronic properties, or as a hydrogen storage material.


Reinforced graphene

Graphene reinforced with embedded
carbon nanotube A carbon nanotube (CNT) is a tube made of carbon with a diameter in the nanometre range ( nanoscale). They are one of the allotropes of carbon. Two broad classes of carbon nanotubes are recognized: * ''Single-walled carbon nanotubes'' (''S ...
reinforcing bars ("rebar") is easier to manipulate, while improving the electrical and mechanical qualities of both materials. Functionalized single- or multi-walled 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 group The carbon group is a group (periodic table), periodic table group consisting of carbon (C), silicon (Si), germanium (Ge), tin (Sn), lead (Pb), and flerovium (Fl). It lies within the p-block. In modern International Union of Pure and Applied Ch ...
s decompose into graphene, while the nanotubes partially split and form in-plane
covalent bond A covalent bond is a chemical bond that involves the sharing of electrons to form electron pairs between atoms. These electron pairs are known as shared pairs or bonding pairs. The stable balance of attractive and repulsive forces between atom ...
s 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 In materials science, a grain boundary is the interface between two grains, or crystallites, in a polycrystalline material. Grain boundaries are two-dimensional crystallographic defect, defects in the crystal structure, and tend to decrease the ...
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 Indium tin oxide (ITO) is a ternary composition of indium, tin and oxygen in varying proportions. Depending on the oxygen content, it can be described as either a ceramic or an alloy. Indium tin oxide is typically encountered as an oxygen-saturate ...
(ITO) used in displays and
photovoltaic cell A solar cell, also known as a photovoltaic cell (PV cell), is an electronic device that converts the energy of light directly into electricity by means of the photovoltaic effect.
s.


Molded graphene

In 2015, researchers from the
University of Illinois at Urbana–Champaign The University of Illinois Urbana-Champaign (UIUC, U of I, Illinois, or University of Illinois) is a public land-grant research university in the Champaign–Urbana metropolitan area, Illinois, United States. Established in 1867, it is the f ...
(UIUC) developed a new approach for forming 3D shapes from flat, 2D sheets of graphene. A film of graphene that had been soaked in solvent to make it swell and become malleable was overlaid on an underlying substrate "former". The solvent evaporated over time, leaving behind a layer of graphene that had taken on the shape of the underlying structure. In this way, they were able to produce a range of relatively intricate micro-structured shapes. Features vary from 3.5 to 50 μm. Pure graphene and gold-decorated graphene were each successfully integrated with the substrate.


Specialized graphene configurations


Graphene aerogel

An
aerogel Aerogels are a class of manufacturing, synthetic porous ultralight material derived from a gel, in which the liquid component for the gel has been replaced with a gas, without significant collapse of the gel structure. The result is a solid wit ...
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.


Graphene nanocoil

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 In mathematics, particularly in complex analysis, a Riemann surface is a connected one-dimensional complex manifold. These surfaces were first studied by and are named after Bernhard Riemann. Riemann surfaces can be thought of as deformed vers ...
, 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. The nano-solenoids analyzed through computer models at
Rice University William Marsh Rice University, commonly referred to as Rice University, is a Private university, private research university in Houston, Houston, Texas, United States. Established in 1912, the university spans 300 acres. Rice University comp ...
should be capable of producing powerful magnetic fields of about 1 tesla, about the same as the coils found in typical loudspeakers, according to Yakobson and his team – and about the same field strength as some MRI machines. They found the magnetic field would be strongest in the hollow, nanometer-wide cavity at the spiral's center. A
solenoid upright=1.20, An illustration of a solenoid upright=1.20, Magnetic field created by a seven-loop solenoid (cross-sectional view) described using field lines A solenoid () is a type of electromagnet formed by a helix, helical coil of wire whos ...
made with such a coil behaves as a quantum conductor whose current distribution between the core and exterior varies with applied voltage, resulting in nonlinear
inductance Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The electric current produces a magnetic field around the conductor. The magnetic field strength depends on the magnitude of the ...
.


Crumpled graphene

In 2016,
Brown University Brown University is a Private university, private Ivy League research university in Providence, Rhode Island, United States. It is the List of colonial colleges, seventh-oldest institution of higher education in the US, founded in 1764 as the ' ...
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 In chemistry and materials science, ultrahydrophobic (or superhydrophobic) surfaces are highly hydrophobic, i.e., extremely difficult to wet. The contact angles of a water droplet on an ultrahydrophobic material exceed 150°. This is also ref ...
, and when used as a battery electrode, the material was shown to have as much as a 400% increase in
electrochemical Electrochemistry is the branch of physical chemistry concerned with the relationship between electrical potential difference and identifiable chemical change. These reactions involve electrons moving via an electronically conducting phase (typi ...
current density In electromagnetism, current density is the amount of charge per unit time that flows through a unit area of a chosen cross section. The current density vector is defined as a vector whose magnitude is the electric current per cross-sectional ...
.


Mechanical synthesis

A rapidly increasing list of production techniques have been developed to enable graphene's use in commercial applications. Isolated 2D crystals cannot be grown via chemical synthesis beyond small sizes even in principle, because the rapid growth of
phonon A phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, specifically in solids and some liquids. In the context of optically trapped objects, the quantized vibration mode can be defined a ...
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.


Bottom-up and top-down methods

Small graphene structures, such as graphene quantum dots and nanoribbons, can be produced by "bottom-up" methods that assemble the lattice from organic molecule monomers (e. g. citric acid, glucose). "Top-down" methods, on the other hand, cut bulk graphite and graphene materials with strong chemicals (e. g. mixed acids).


Micro-mechanical cleavage

The most famous, clean and rather straight-forward method of isolating graphene sheets, called micro-mechanical cleavage or more colloquially called the scotch tape method, was introduced by Novoselov et al. in 2004, which uses
adhesive tape Adhesive tape is one of many varieties of backing materials coated with an adhesive. Several types of adhesives can be used. Types Pressure-sensitive tape Pressure-sensitive tape, PSA tape, self-stick tape or sticky tape consists of a pre ...
to mechanically cleave high-quality
graphite Graphite () is a Crystallinity, crystalline allotrope (form) of the element carbon. It consists of many stacked Layered materials, layers of graphene, typically in excess of hundreds of layers. Graphite occurs naturally and is the most stable ...
crystal A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macros ...
s into successively thinner platelets. Other methods do exist like exfoliation.


Exfoliation techniques


Mechanical exfoliation

Geim and Novoselov initially used
adhesive tape Adhesive tape is one of many varieties of backing materials coated with an adhesive. Several types of adhesives can be used. Types Pressure-sensitive tape Pressure-sensitive tape, PSA tape, self-stick tape or sticky tape consists of a pre ...
to pull graphene sheets away from graphite. Achieving single layers typically requires multiple exfoliation steps. After exfoliation, the flakes are deposited on a silicon wafer. Crystallites larger than 1 mm and visible to the naked eye can be obtained. As of 2014, exfoliation produced graphene with the lowest number of defects and highest electron mobility. One specific exfoliation technique involved using a sharp single-crystal diamond wedge to penetrate the graphite source and precisely cleave individual layers. That same year, researchers also developed liquid-phase methods, creating defect-free, unoxidized graphene-containing liquids from graphite using mixers that generate extremely high local shear rates greater than . A 2014 study published in ''Nature Materials'' demonstrated that scalable production of defect-free graphene is possible through shear exfoliation using a
high-shear mixer A high-shear mixer disperses, or transports, one phase or ingredient (liquid, solid, gas) into a main continuous phase (liquid), with which it would normally be immiscible. A rotor or impeller, together with a stationary component known as a stat ...
. This technique can produce large quantities of few-layer graphene in solution while preserving structural integrity. As turbulence is not necessary for mechanical exfoliation, resonant acoustic mixing or low-speed
ball milling A ball mill is a type of grinder filled with grinding balls, used to grind or blend materials for use in mineral dressing processes, paints, pyrotechnics, ceramics, and selective laser sintering. It works on the principle of impact and attri ...
can also be effective in the production of high-yield and water-soluble graphene.


Liquid phase exfoliation

Liquid phase exfoliation (LPE) is a relatively simple method that involves dispersing graphite in a liquid medium to produce graphene by
sonication image:Sonicator.jpg, A sonicator at the Weizmann Institute of Science during sonicationSonication is the act of applying sound energy to agitate particles in a sample, for various purposes such as the extraction of multiple compounds from plants, ...
or high shear mixing, followed by
centrifugation Centrifugation is a mechanical process which involves the use of the centrifugal force to separate particles from a solution according to their size, shape, density, medium viscosity and rotor speed. The denser components of the mixture migrate ...
. Restacking is an issue with this technique unless solvents with appropriate surface energy are used (e.g. NMP). Adding a
surfactant Surfactants are chemical compounds that decrease the surface tension or interfacial tension between two liquids, a liquid and a gas, or a liquid and a solid. The word ''surfactant'' is a Blend word, blend of "surface-active agent", coined in ...
to a solvent prior to sonication prevents restacking by adsorbing to the graphene's surface. This produces a higher graphene concentration, but removing the surfactant requires chemical treatments. LPE results in nanosheets with a broad size distribution and thicknesses roughly in the range of 1-10 monolayers. However, liquid cascade centrifugation can be used to size-select the suspensions and achieve monolayer enrichment. Sonicating graphite at the interface of two
immiscible Miscibility () is the property of two chemical substance, substances to mix in all mixing ratio, proportions (that is, to fully dissolution (chemistry), dissolve in each other at any concentration), forming a homogeneity and heterogeneity, homoge ...
liquids, most notably
heptane Heptane or ''n''-heptane is the straight-chain alkane with the chemical formula H3C(CH2)5CH3 or C7H16. When used as a test fuel component in anti-knock test engines, a 100% heptane fuel is the zero point of the octane rating scale (the 100 poi ...
and water, produced macro-scale graphene films. The graphene sheets are adsorbed to the high-energy interface between the materials and are kept from restacking. The sheets are up to about 95% transparent and conductive. With definite cleavage parameters, the box-shaped graphene (BSG)
nanostructure A nanostructure is a structure of intermediate size between microscopic and molecular structures. Nanostructural detail is microstructure at nanoscale. In describing nanostructures, it is necessary to differentiate between the number of dimen ...
can be prepared on
graphite Graphite () is a Crystallinity, crystalline allotrope (form) of the element carbon. It consists of many stacked Layered materials, layers of graphene, typically in excess of hundreds of layers. Graphite occurs naturally and is the most stable ...
crystal A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macros ...
. A major advantage of LPE is that it can be used to exfoliate many inorganic 2D materials beyond graphene, e.g. BN, MoS2, WS2.


Exfoliation with supercritical carbon dioxide

Liquid-phase exfoliation can also be done by a less-known process of intercalating
supercritical carbon dioxide Supercritical carbon dioxide (s) is a fluid state of carbon dioxide where it is held at or above its critical temperature and critical pressure. Carbon dioxide usually behaves as a gas in air at standard temperature and pressure (STP), or a ...
(scCO2) into the interstitial spaces in the graphite lattice, followed by rapid depressurization. The scCO2 intercalates easily inside the graphite lattice at a pressure of roughly 100 atm. Carbon dioxide turns gaseous as soon as the vessel is depressurized and makes the graphite explode into few-layered graphene. This method may have multiple advantages: being non-toxic, the graphite does not have to be chemically treated in any way before the process, and the whole process can be completed in a single step as opposed to other exfoliation methods.


Splitting monolayer carbon allotropes

Graphene can be created by opening
carbon nanotube A carbon nanotube (CNT) is a tube made of carbon with a diameter in the nanometre range ( nanoscale). They are one of the allotropes of carbon. Two broad classes of carbon nanotubes are recognized: * ''Single-walled carbon nanotubes'' (''S ...
s by cutting or etching. In one such method, multi-walled carbon nanotubes were cut open in solution by action of
potassium permanganate Potassium permanganate is an inorganic compound with the chemical formula KMnO4. It is a purplish-black crystalline salt, which dissolves in water as K+ and ions to give an intensely pink to purple solution. Potassium permanganate is widely us ...
and
sulfuric acid Sulfuric acid (American spelling and the preferred IUPAC name) or sulphuric acid (English in the Commonwealth of Nations, Commonwealth spelling), known in antiquity as oil of vitriol, is a mineral acid composed of the elements sulfur, oxygen, ...
. In 2014, carbon nanotube-reinforced graphene was made via spin coating and annealing functionalized carbon nanotubes. 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.


Chemical synthesis


Graphite oxide reduction

P. Boehm reported producing monolayer flakes of reduced graphene oxide in 1962. Rapid heating of graphite oxide and exfoliation yields highly dispersed carbon powder with a few percent of graphene flakes. Another method is the reduction of graphite oxide monolayer films, e.g. by
hydrazine Hydrazine is an inorganic compound with the chemical formula . It is a simple pnictogen hydride, and is a colourless flammable liquid with an ammonia-like odour. Hydrazine is highly hazardous unless handled in solution as, for example, hydraz ...
with annealing in
argon Argon is a chemical element; it has symbol Ar and atomic number 18. It is in group 18 of the periodic table and is a noble gas. Argon is the third most abundant gas in Earth's atmosphere, at 0.934% (9340 ppmv). It is more than twice as abu ...
/
hydrogen Hydrogen is a chemical element; it has chemical symbol, symbol H and atomic number 1. It is the lightest and abundance of the chemical elements, most abundant chemical element in the universe, constituting about 75% of all baryon, normal matter ...
with an almost intact carbon framework that allows efficient removal of functional groups. Measured
charge carrier In solid state physics, a charge carrier is a particle or quasiparticle that is free to move, carrying an electric charge, especially the particles that carry electric charges in electrical conductors. Examples are electrons, ions and holes. ...
mobility exceeded 1,000 cm/Vs (10 m/Vs). Burning a graphite oxide coated
DVD The DVD (common abbreviation for digital video disc or digital versatile disc) is a digital optical disc data storage format. It was invented and developed in 1995 and first released on November 1, 1996, in Japan. The medium can store any ki ...
produced a conductive graphene film (1,738 siemens per meter) and specific surface area (1,520 square meters per gram) that was highly resistant and malleable. A dispersed reduced graphene oxide suspension was synthesized in water by a hydrothermal dehydration method without using any surfactant. The approach is facile, industrially applicable, environmentally friendly, and cost-effective. Viscosity measurements confirmed that the graphene colloidal suspension (graphene nanofluid) exhibits Newtonian behavior, with the viscosity showing a close resemblance to that of water.


Molten salts

Graphite particles can be corroded in molten salts to form a variety of carbon nanostructures including graphene. Hydrogen cations, dissolved in molten lithium chloride, can be discharged on cathodically-polarized graphite rods, which then intercalate, peeling graphene sheets. The graphene nanosheets produced displayed a single-crystalline structure with a lateral size of several hundred nanometers and a high degree of crystallinity and thermal stability.


Electrochemical synthesis

Electrochemical synthesis can exfoliate graphene. Varying a pulsed voltage controls thickness, flake area, and 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.


Hydrothermal self-assembly

Graphene has been prepared by using a sugar like
glucose Glucose is a sugar with the Chemical formula#Molecular formula, molecular formula , which is often abbreviated as Glc. It is overall the most abundant monosaccharide, a subcategory of carbohydrates. It is mainly made by plants and most algae d ...
,
fructose Fructose (), or fruit sugar, is a Ketose, ketonic monosaccharide, simple sugar found in many plants, where it is often bonded to glucose to form the disaccharide sucrose. It is one of the three dietary monosaccharides, along with glucose and gal ...
, etc. This substrate-free "bottom-up" synthesis is safer, simpler and more environmentally friendly than exfoliation. The method can control the thickness, ranging from monolayer to multilayer, which is known as the "Tang-Lau Method".


Sodium ethoxide pyrolysis

Gram-quantities were produced by the reaction of
ethanol Ethanol (also called ethyl alcohol, grain alcohol, drinking alcohol, or simply alcohol) is an organic compound with the chemical formula . It is an Alcohol (chemistry), alcohol, with its formula also written as , or EtOH, where Et is the ps ...
with
sodium Sodium is a chemical element; it has Symbol (chemistry), symbol Na (from Neo-Latin ) and atomic number 11. It is a soft, silvery-white, highly reactive metal. Sodium is an alkali metal, being in group 1 element, group 1 of the peri ...
metal, followed by
pyrolysis Pyrolysis is a process involving the Bond cleavage, separation of covalent bonds in organic matter by thermal decomposition within an Chemically inert, inert environment without oxygen. Etymology The word ''pyrolysis'' is coined from the Gree ...
and washing with water.


Microwave-assisted oxidation

In 2012, microwave energy was reported to directly synthesize graphene in one step. This approach avoids use of potassium permanganate in the reaction mixture. It was also reported that by microwave radiation assistance, graphene oxide with or without holes can be synthesized by controlling microwave time. Microwave heating can dramatically shorten the reaction time from days to seconds. Graphene can also be made by
microwave Microwave is a form of electromagnetic radiation with wavelengths shorter than other radio waves but longer than infrared waves. Its wavelength ranges from about one meter to one millimeter, corresponding to frequency, frequencies between 300&n ...
assisted hydrothermal pyrolysis.


Thermal decomposition of silicon carbide

Heating
silicon carbide Silicon carbide (SiC), also known as carborundum (), is a hard chemical compound containing silicon and carbon. A wide bandgap semiconductor, it occurs in nature as the extremely rare mineral moissanite, but has been mass-produced as a powder a ...
(SiC) to high temperatures () under low pressures (c. 10−6 torr, or 10−4 Pa) reduces it to graphene.


Vapor deposition and growth techniques


Chemical vapor deposition


Epitaxy

Epitaxial graphene growth on silicon carbide Epitaxial graphene growth on silicon carbide, silicon carbide (SiC) by thermal decomposition is a method to produce large-scale few-layer graphene (FLG). Graphene is one of the most promising nanomaterials for the future because of its various chara ...
is a wafer-scale technique to produce graphene.
Epitaxial Epitaxy (prefix ''epi-'' means "on top of”) is a type of crystal growth or material deposition in which new crystalline layers are formed with one or more well-defined orientations with respect to the crystalline seed layer. The deposited cry ...
graphene may be coupled to surfaces weakly enough (by the active valence electrons that create
Van der Waals force In molecular physics and chemistry, the van der Waals force (sometimes van der Waals' force) is a distance-dependent interaction between atoms or molecules. Unlike ionic or covalent bonds, these attractions do not result from a chemical elec ...
s) to retain the two-dimensional
electronic band structure In solid-state physics, the electronic band structure (or simply band structure) of a solid describes the range of energy levels that electrons may have within it, as well as the ranges of energy that they may not have (called ''band gaps'' or '' ...
of isolated graphene. A normal
silicon wafer In electronics, a wafer (also called a slice or substrate) is a thin slice of semiconductor, such as a crystalline silicon (c-Si, silicium), used for the fabrication of integrated circuits and, in photovoltaics, to manufacture solar cells. The ...
coated with a layer of
germanium Germanium is a chemical element; it has Symbol (chemistry), symbol Ge and atomic number 32. It is lustrous, hard-brittle, grayish-white and similar in appearance to silicon. It is a metalloid or a nonmetal in the carbon group that is chemically ...
(Ge) dipped in dilute
hydrofluoric acid Hydrofluoric acid is a solution of hydrogen fluoride (HF) in water. Solutions of HF are colorless, acidic and highly corrosive. A common concentration is 49% (48–52%) but there are also stronger solutions (e.g. 70%) and pure HF has a boiling p ...
strips the naturally forming germanium oxide groups, creating hydrogen-terminated germanium. CVD can coat that with graphene. The direct synthesis of graphene on insulator TiO2 with high-dielectric-constant (high-κ). A two-step CVD process is shown to grow graphene directly on TiO2 crystals or exfoliated TiO2 nanosheets without using any metal catalyst.


Metal substrates

CVD graphene can be grown on metal substrates including
ruthenium Ruthenium is a chemical element; it has symbol Ru and atomic number 44. It is a rare transition metal belonging to the platinum group of the periodic table. Like the other metals of the platinum group, ruthenium is unreactive to most chem ...
,
iridium Iridium is a chemical element; it has the symbol Ir and atomic number 77. This very hard, brittle, silvery-white transition metal of the platinum group, is considered the second-densest naturally occurring metal (after osmium) with a density ...
,
nickel Nickel is a chemical element; it has symbol Ni and atomic number 28. It is a silvery-white lustrous metal with a slight golden tinge. Nickel is a hard and ductile transition metal. Pure nickel is chemically reactive, but large pieces are slo ...
and
copper Copper is a chemical element; it has symbol Cu (from Latin ) and atomic number 29. It is a soft, malleable, and ductile metal with very high thermal and electrical conductivity. A freshly exposed surface of pure copper has a pinkish-orang ...
.


Roll-to-roll

In 2014, a two-step roll-to-roll manufacturing process was announced. The first roll-to-roll step produces the graphene via chemical vapor deposition. The second step binds the graphene to a substrate.


Cold wall

Growing graphene in an industrial resistive-heating cold wall CVD system was claimed to produce graphene 100 times faster than conventional CVD systems, cut costs by 99%, and produce material with enhanced electronic qualities.


Wafer scale CVD graphene

CVD graphene is scalable and has been grown on deposited Cu thin film catalyst on 100 to 300 mm standard Si/SiO2 wafers on an Axitron Black Magic system. Monolayer graphene coverage of >95% is achieved on 100 to 300 mm wafer substrates with negligible defects, confirmed by extensive Raman mapping.


Solvent interface trapping method (SITM)

As reported by a group led by D. H. Adamson, graphene can be produced from natural graphite while preserving the integrity of the sheets using the solvent interface trapping method (SITM). SITM uses a high-energy interface, such as oil and water, to exfoliate graphite to graphene. Stacked graphite delaminates, or spreads, at the oil/water interface to produce few-layer graphene in a thermodynamically favorable process in much the same way as small molecule surfactants spread to minimize the interfacial energy. In this way, graphene behaves like a 2D surfactant. SITM has been reported for a variety of applications such conductive polymer-graphene foams, conductive polymer-graphene microspheres, conductive thin films and conductive inks.


Carbon dioxide reduction

A highly exothermic reaction combusts
magnesium Magnesium is a chemical element; it has Symbol (chemistry), symbol Mg and atomic number 12. It is a shiny gray metal having a low density, low melting point and high chemical reactivity. Like the other alkaline earth metals (group 2 ...
in an oxidation-reduction reaction with carbon dioxide, producing carbon nanoparticles including graphene and
fullerene A fullerene is an allotropes of carbon, allotrope of carbon whose molecules consist of carbon atoms connected by single and double bonds so as to form a closed or partially closed mesh, with fused rings of five to six atoms. The molecules may ...
s.


Supersonic spray

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


Laser

In 2014, a infrared laser was used to produce patterned porous three-dimensional laser-induced graphene (LIG) film networks from commercial polymer films. The resulting material exhibits high electrical conductivity and surface area. The laser induction process is compatible with roll-to-roll manufacturing processes. A similar material, laser-induced graphene fibers (LIGF), was reported in 2018.


Flash Joule heating

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. More recent works demonstrated the use of mixed
plastic waste Plastic pollution is the accumulation of plastic objects and particles (e.g. plastic bottles, bags and microbeads) in the Earth's environment that adversely affects humans, wildlife and their habitat. Plastics that act as pollutants are cate ...
, waste rubber tires, and pyrolysis ash as carbon feedstocks. The graphenization process is kinetically controlled, and the energy dose is chosen to preserve the carbon in its graphenic state (excessive energy input leads to subsequent graphitization through annealing).


Ion implantation

Accelerating carbon ions inside an electrical field into a semiconductor made of thin nickel films on a substrate of SiO2/Si, creates a wafer-scale () wrinkle/tear/residue-free graphene layer at a relatively low temperature of 500 °C.


CMOS-compatible graphene

Integration of graphene in the widely employed
CMOS fabrication process Complementary metal–oxide–semiconductor (CMOS, pronounced "sea-moss ", , ) is a type of metal–oxide–semiconductor field-effect transistor (MOSFET) fabrication process that uses complementary and symmetrical pairs of p-type and n-type ...
demands its transfer-free direct synthesis on
dielectric In electromagnetism, a dielectric (or dielectric medium) is an Insulator (electricity), electrical insulator that can be Polarisability, polarised by an applied electric field. When a dielectric material is placed in an electric field, electric ...
substrates at temperatures below 500 °C. At the IEDM 2018, researchers from
University of California, Santa Barbara The University of California, Santa Barbara (UC Santa Barbara or UCSB) is a Public university, public Land-grant university, land-grant research university in Santa Barbara County, California, United States. Tracing its roots back to 1891 as an ...
, demonstrated a novel CMOS-compatible graphene synthesis process at 300 °C suitable for back-end-of-line (
BEOL Back end of the line or back end of line (BEOL) is a process in semiconductor device fabrication that consists of depositing metal interconnect layers onto a wafer already patterned with devices. It is the second part of IC fabrication, after f ...
) applications. The process involves pressure-assisted solid-state
diffusion Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical p ...
of
carbon Carbon () is a chemical element; it has chemical symbol, symbol C and atomic number 6. It is nonmetallic and tetravalence, tetravalent—meaning that its atoms are able to form up to four covalent bonds due to its valence shell exhibiting 4 ...
through a
thin-film A thin film is a layer of materials ranging from fractions of a nanometer (monolayer) to several micrometers in thickness. The controlled synthesis of materials as thin films (a process referred to as deposition) is a fundamental step in many a ...
of metal catalyst. The synthesized large-area graphene films were shown to exhibit high quality (via Raman characterization) and similar
resistivity Electrical resistivity (also called volume resistivity or specific electrical resistance) is a fundamental specific property of a material that measures its electrical resistance or how strongly it resists electric current. A low resistivity i ...
values when compared with high-temperature CVD synthesized graphene films of the same cross-section down to widths of 20 nm.


Simulation

In addition to experimental investigation of graphene and graphene-based devices, numerical modeling and simulation of graphene has also been an important research topic. The
Kubo formula The Kubo formula, named for Ryogo Kubo who first presented the formula in 1957, is an equation which expresses the linear response of an observable quantity due to a time-dependent perturbation. Among numerous applications of 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. Moreover, a surface conductivity model, which describes graphene as an infinitesimally thin (two-sided) sheet with a local and isotropic conductivity, has been proposed. This model permits the derivation of analytical expressions for the electromagnetic field in the presence of a graphene sheet in terms of a dyadic Green function (represented using Sommerfeld integrals) and exciting electric current. Even though these analytical models and methods can provide results for several canonical problems for benchmarking purposes, many practical problems involving graphene, such as the design of arbitrarily shaped electromagnetic devices, are analytically intractable. With the recent advances in the field of computational electromagnetics (CEM), various accurate and efficient numerical methods have become available for analysis of electromagnetic field/wave interactions on graphene sheets and/or graphene-based devices. A comprehensive summary of computational tools developed for analyzing graphene-based devices/systems is proposed.


Graphene analogs

Graphene analogs (also referred to as "artificial graphene") are two-dimensional systems which exhibit similar properties to graphene. Graphene analogs have been studied intensively since the discovery of graphene in 2004. People try to develop systems in which the physics is easier to observe and manipulate than in graphene. In those systems, electrons are not always the particles that are used. They might be optical photons, microwave photons, plasmons, microcavity polaritons, or even atoms. Also, the honeycomb structure in which those particles evolve can be of a different nature than carbon atoms in graphene. It can be, respectively, a
photonic crystal A photonic crystal is an optical nanostructure in which the refractive index changes periodically. This affects the propagation of light in the same way that the structure of Crystal structure, natural crystals gives rise to X-ray crystallograp ...
, an array of metallic rods, metallic
nanoparticle A nanoparticle or ultrafine particle is a particle of matter 1 to 100 nanometres (nm) in diameter. The term is sometimes used for larger particles, up to 500 nm, or fibers and tubes that are less than 100 nm in only two directions. At ...
s, a lattice of coupled microcavities, or an
optical lattice An optical lattice is formed by the Interference (wave propagation), interference of counter-propagating laser beams, creating a spatially periodic intensity pattern. The resulting periodic scalar potential, potential may trap neutral atoms via ...
.


Applications

Graphene is a transparent and flexible conductor that holds great promise for various material/device applications, including solar cells, light-emitting diodes (LED), integrated photonic circuit devices, touch panels, and smart windows or phones. Smartphone products with graphene touch screens are already on the market. In 2013, Head announced their new range of graphene tennis racquets. As of 2015, there is one product available for commercial use: a graphene-infused printer powder. Many other uses for graphene have been proposed or are under development, in areas including electronics,
biological engineering Biological engineering or bioengineering is the application of principles of biology and the tools of engineering to create usable, tangible, economically viable products. Biological engineering employs knowledge and expertise from a number ...
,
filtration Filtration is a physical separation process that separates solid matter and fluid from a mixture using a ''filter medium'' that has a complex structure through which only the fluid can pass. Solid particles that cannot pass through the filte ...
, lightweight/strong
composite materials A composite or composite material (also composition material) is a material which is produced from two or more constituent materials. These constituent materials have notably dissimilar chemical or physical properties and are merged to create a ...
,
photovoltaic Photovoltaics (PV) is the conversion of light into electricity using semiconducting materials that exhibit the photovoltaic effect, a phenomenon studied in physics, photochemistry, and electrochemistry. The photovoltaic effect is commercially ...
s and
energy storage Energy storage is the capture of energy produced at one time for use at a later time to reduce imbalances between energy demand and energy production. A device that stores energy is generally called an Accumulator (energy), accumulator or Batte ...
. Graphene is often produced as a powder and as a dispersion in a polymer matrix. This dispersion is supposedly suitable for advanced composites, paints and coatings, lubricants, oils and functional fluids, capacitors and batteries, thermal management applications, display materials and packaging, solar cells, inks and 3D-printer materials, and barriers and films. On 2 August 2016, Briggs Automative Company's new Mono model is said to be made out of graphene as the first of both a street-legal track car and a production car. In January 2018, graphene-based spiral
inductor An inductor, also called a coil, choke, or reactor, is a Passivity (engineering), passive two-terminal electronic component, electrical component that stores energy in a magnetic field when an electric current flows through it. An inductor typic ...
s exploiting
kinetic inductance Kinetic inductance is the manifestation of the inertial mass of mobile charge carriers in alternating electric fields as an equivalent series inductance. Kinetic inductance is observed in high carrier mobility conductors (e.g. superconductors) and ...
at room temperature were first demonstrated at the
University of California, Santa Barbara The University of California, Santa Barbara (UC Santa Barbara or UCSB) is a Public university, public Land-grant university, land-grant research university in Santa Barbara County, California, United States. Tracing its roots back to 1891 as an ...
, led by Kaustav Banerjee. These inductors were predicted to allow significant miniaturization in
radio-frequency Radio frequency (RF) is the oscillation rate of an alternating electric current or voltage or of a magnetic, electric or electromagnetic field or mechanical system in the frequency range from around to around . This is roughly between the ...
integrated circuit An integrated circuit (IC), also known as a microchip or simply chip, is a set of electronic circuits, consisting of various electronic components (such as transistors, resistors, and capacitors) and their interconnections. These components a ...
applications. The potential of epitaxial graphene on
SiC The Latin adverb ''sic'' (; ''thus'', ''so'', and ''in this manner'') inserted after a quotation indicates that the quoted matter has been transcribed or translated as found in the source text, including erroneous, archaic, or unusual spelling ...
for
metrology Metrology is the scientific study of measurement. It establishes a common understanding of Unit of measurement, units, crucial in linking human activities. Modern metrology has its roots in the French Revolution's political motivation to stan ...
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 the encapsulation and doping of epitaxial graphene have led to the commercialization of epitaxial graphene quantum resistance standards. Novel uses for graphene continue to be researched and explored. One such use is in combination with water-based epoxy resins to produce anticorrosive coatings. The van der Waals nature of graphene and other two-dimensional (2D) materials also permits van der Waals heterostructures and integrated circuits based on Van der Waals integration of 2D materials. Graphene is utilized in detecting gasses and chemicals in environmental monitoring, developing highly sensitive biosensors for medical diagnostics, and creating flexible, wearable sensors for health monitoring. Graphene's transparency also enhances optical sensors, making them more effective in imaging and spectroscopy.


Toxicity

One review on graphene toxicity published in 2016 by Lalwani et al. summarizes the
in vitro ''In vitro'' (meaning ''in glass'', or ''in the glass'') Research, studies are performed with Cell (biology), cells or biological molecules outside their normal biological context. Colloquially called "test-tube experiments", these studies in ...
,
in vivo Studies that are ''in vivo'' (Latin for "within the living"; often not italicized in English) are those in which the effects of various biological entities are tested on whole, living organisms or cells, usually animals, including humans, an ...
, antimicrobial and environmental effects and highlights the various mechanisms of graphene toxicity. Another review published in 2016 by Ou et al. focused on graphene-family nanomaterials (GFNs) and revealed several typical mechanisms such as physical destruction,
oxidative stress Oxidative stress reflects an imbalance between the systemic manifestation of reactive oxygen species and a biological system's ability to readily detoxify the reactive intermediates or to repair the resulting damage. Disturbances in the normal ...
,
DNA Deoxyribonucleic acid (; DNA) is a polymer composed of two polynucleotide chains that coil around each other to form a double helix. The polymer carries genetic instructions for the development, functioning, growth and reproduction of al ...
damage, inflammatory response,
apoptosis Apoptosis (from ) is a form of programmed cell death that occurs in multicellular organisms and in some eukaryotic, single-celled microorganisms such as yeast. Biochemistry, Biochemical events lead to characteristic cell changes (Morphology (biol ...
,
autophagy Autophagy (or autophagocytosis; from the Greek language, Greek , , meaning "self-devouring" and , , meaning "hollow") is the natural, conserved degradation of the cell that removes unnecessary or dysfunctional components through a lysosome-depe ...
, and
necrosis Necrosis () is a form of cell injury which results in the premature death of cells in living tissue by autolysis. The term "necrosis" came about in the mid-19th century and is commonly attributed to German pathologist Rudolf Virchow, who i ...
. A 2020 study showed that the toxicity of graphene is dependent on several factors such as shape, size, purity, post-production processing steps, oxidative state, functional groups, dispersion state, synthesis methods, route and dose of administration, and exposure times. In 2014, research at
Stony Brook University Stony Brook University (SBU), officially the State University of New York at Stony Brook, is a public university, public research university in Stony Brook, New York, United States, on Long Island. Along with the University at Buffalo, it is on ...
showed that
graphene nanoribbon Graphene nanoribbons (GNRs, also called nano-graphene ribbons or nano-graphite ribbons) are strips of graphene with width less than 100 nm. Graphene ribbons were introduced as a theoretical model by Mitsutaka Fujita and coauthors to examine ...
s, 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 cell In multicellular organisms, stem cells are undifferentiated or partially differentiated cells that can change into various types of cells and proliferate indefinitely to produce more of the same stem cell. They are the earliest type of cell ...
s towards
osteoblast Osteoblasts (from the Greek combining forms for " bone", ὀστέο-, ''osteo-'' and βλαστάνω, ''blastanō'' "germinate") are cells with a single nucleus that synthesize bone. However, in the process of bone formation, osteoblasts fu ...
s (bone) or
adipocyte Adipocytes, also known as lipocytes and fat cells, are the cell (biology), cells that primarily compose adipose tissue, specialized in storing energy as fat. Adipocytes are derived from mesenchymal stem cells which give rise to adipocytes through ...
s (fat), suggesting that at low doses, graphene nanoparticles are safe for biomedical applications. In 2013, research at
Brown University Brown University is a Private university, private Ivy League research university in Providence, Rhode Island, United States. It is the List of colonial colleges, seventh-oldest institution of higher education in the US, founded in 1764 as the ' ...
found that 10 μm few-layered graphene flakes can pierce
cell membrane The cell membrane (also known as the plasma membrane or cytoplasmic membrane, and historically referred to as the plasmalemma) is a biological membrane that separates and protects the interior of a cell from the outside environment (the extr ...
s in solution. They were observed to enter initially via sharp and jagged points, allowing graphene to be internalized in the cell. The physiological effects of this remain unknown, and this remains a relatively unexplored field.


See also

* * * * * *


References

Bor Z. Jang and Wen C. Huang (2002):
Nano-scaled graphene plates
". US Patent 7071258. Filed on 2002-10-21, granted on 2006-07-04, assigned to Global Graphene Group Inc; to expire on 6 January 2024.
Robert B. Rutherford and Richard L. Dudman (2002):
Ultra-thin flexible expanded graphite heating element
". US Patent 6667100. Filed on 2002-05-13, granted on 2003-12-23, assigned to EGC Operating Co LLC; expired.


External links


Manchester's Revolutionary 2D Material
at ''
The University of Manchester The University of Manchester is a public university, public research university in Manchester, England. The main campus is south of Manchester city centre, Manchester City Centre on Wilmslow Road, Oxford Road. The University of Manchester is c ...
''
Graphene
at ''
The Periodic Table of Videos ''Periodic Videos'' (also known as ''The Periodic Table of Videos'') is a video project and YouTube channel on chemistry. It consists of a series of videos about chemical elements and the periodic table, with additional videos on other topics i ...
'' (University of Nottingham)
Graphene: Patent surge reveals global race

'Engineering Controls for Nano-scale Graphene Platelets During Manufacturing and Handling Processes' (PDF)

Band structure of graphene (PDF).
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