Graphene

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Figure 1. This image was captured using a Digital Multimode AFM (atomic force microscope). Notice the step from the substrate at zero height to a graphene flake about 8 angstroms high, which is on the order of a monolayer.

Graphene is a single planar sheet of sp²-bonded carbon atoms. It is not an allotrope of carbon because the sheet is of finite thickness. Graphenes are the 2-D counterparts of 3-D graphite. They are aromatic.

1 Description
2 Chemical modification
3 Properties
- 3.1 Absence of localization
- 3.2 Electron transport
4 References
5 See also
6 External links

[edit] Description

Perfect graphenes consist exclusively of hexagonal cells; pentagonal and heptagonal cells constitute defects. If an isolated pentagonal cell is present, then the plane warps into a cone shape; insertion of 12 pentagons would create a fullerene. Likewise, insertion of an isolated heptagon causes the sheet to become saddle-shaped. Controlled addition of pentagons and heptagons would allow a wide variety of shapes to be made.

Single walled Carbon nanotubes may be considered to be graphene cylinders; some have a hemispherical graphene cap (that includes 6 pentagons) at each end. Graphenes have also attracted the interest of technologists who see them as a way of constructing ballistic transistors. In March 2006, Georgia Tech researchers announced that they had successfully built an all-graphene planar field-effect transistor and a quantum interference device. ^[1]

The IUPAC compendium of technology states: "previously, descriptions such as graphite layers, carbon layers, or carbon sheets have been used for the term graphene...it is not correct to use for a single layer a term which includes the term graphite, which would imply a three-dimensional structure. The term graphene should be used only when the reactions, structural relations or other properties of individual layers are discussed".

Writing in Science ^[2] , physicist Konstantin Novoselov and coworkers from the University of Manchester and the Institute of Microelectronics Technology and High Purity Materials at Chernogolovka state:

Graphene is the name given to a single layer of carbon atoms densely packed into a benzene-ring structure, and is widely used to describe properties of many carbon-based materials, including graphite, large fullerenes, nanotubes, etc. (e.g., carbon nanotubes are usually thought of as graphene sheets rolled up into nanometer-sized cylinders). Planar graphene itself has been presumed not to exist in the free state, being unstable with respect to the formation of curved structures such as soot, fullerenes, and nanotubes.

The researchers went on to construct graphenes by mechanical exfoliation (repeated peeling) of small "mesas" of highly oriented pyrolytic graphite; their motivation was to study the electrical properties of graphene. Mobilities of up to 10⁴ cm²V^-1s^-1 were reported; this value was almost independent of temperature. In addition, graphene has been shown to exhibit quantum Hall effect properties.

Similar work is ongoing at Princeton University in Professor Ali Yazdani's laboratory by three researchers: Dan Kuncik, Josh Moskowitz, and Patrick Ho. Many of the results obtained by the Novoselov group in their PNAS paper "Two-dimensional atomic crystals" ^[3] have been confirmed by the Yazdani group's work. For an example of a sample on the order of a monolayer, see figure 1.

Although theory and experiment suggest that perfect two-dimensional structures cannot exist in the free state, single-atom thick graphite has been produced. These are possible due to intrinsic microscopic roughening on the scale of 1nm ^[4].

[edit] Chemical modification

Soluble fragments of graphene can be prepared in the laboratory ^[5] through chemical modification of graphite. First, microcrystalline graphite is treated with a strongly acidic mixture of sulphuric acid and nitric acid. A series of steps involving oxidation and exfoliation result in small graphene plates with carboxyl groups at their edges. These are converted to acid chloride groups by treatment with thionyl chloride; next, they are converted to the corresponding graphene amide via treatment with octadecylamine. The resulting material (circular graphene layers of 5.3 angstrom thickness ) is soluble in tetrahydrofuran, tetrachloromethane, and dichloroethane.

[edit] Properties

[edit] Absence of localization

The tunneling anomalies in single- and bilayer graphene systems are expected to play an important role in their transport properties, especially in the regime of low carrier concentrations where disorder induces significant potential barriers and the systems are likely to split into a random distribution of p-n junctions. In conventional two-dimensional systems, sufficiently strong disorder results in electronic states that are separated by barriers with exponentially small transparency. This is known to lead to Anderson localization. In contrast, in both graphene materials, all potential barriers are rather transparent, at least for some angles. This means that charge carriers cannot be confined by potential barriers that are smooth on the atomic scale. Therefore, different electron and hole puddles induced by disorder are not isolated but effectively percolate, thereby suppressing localization. This is important in understanding the minimal conductivity $\sim e^2/\hbar$ observed experimentally in both single and bilayer graphene. Further discussion of this minimal conductivity phenomenon in terms of quantum relativistic effects can be found elsewhere.

[edit] Electron transport

Electron transport in condensed matter physics is governed by Schrodinger equation, due to its non-relativistic nature. But graphene is unusual in this respect. Electrons effectively obey massless relativistic Dirac equation with a different coefficient (~10⁶ m/s) in the place of speed of light. ^[6]

[edit] References

^ Carbon-Based Electronics: Researchers Develop Foundation for Circuitry and Devices Based on Graphite March 14, 2006 gtresearchnews.gatech.edu Link
^ Novoselov, K.S. et al. "Electric Field Effect in Atomically Thin Carbon Films", Science, Vol 306 (5696), p. 666-669, 2004 DOI:10.1126/science.1102896
^ Novoselov, K.S. et al. "Two-dimensional atomic crystals", PNAS, Vol 102 (30), p. 10451-10453, January 26, 2005 DOI:10.1073/pnas.0502848102
^ Nature 446, 60-63 (1 March 2007)DOI:10.1038/nature05545
^ Solution Properties of Graphite and Graphene Sandip Niyogi, Elena Bekyarova, Mikhail E. Itkis, Jared L. McWilliams, Mark A. Hamon, and Robert C. Haddon J. Am. Chem. Soc.; 2006; 128(24) pp 7720 - 7721; (Communication) DOI:10.1021/ja060680r
^ Two-Dimensional Gas of Massless Dirac Fermions in Graphene, Novoselov, K.S. et al, cond-mat/0509330, 2005