Graphene Review

Engineering Materials

Graphene is an allotrope of carbon, whose structure is one-atom-thick planar sheets of sp2-bonded carbon atoms that are densely packed in a honeycomb crystal lattice. The term graphene was coined as a combination of graphite and the suffix -ene by Hanns-Peter Boehm, who described single-layer carbon foils in 1962. Graphene is most easily visualized as an atomic-scale chicken wire made of carbon atoms and their bonds. The crystalline or "flake" form of graphite consists of many graphene sheets stacked together.

The carbon-carbon bond length in graphene is about 0.142 nanometers. Graphene sheets stack to form graphite with an interplanar spacing of 0.335 nm, which means that a stack of three million sheets would be only one millimeter thick. Graphene is the basic structural element of some carbon allotropes including graphite, charcoal, carbon nanotubes and fullerenes. It can also be considered as an indefinitely large aromatic molecule, the limiting case of the family of flat polycyclic aromatic hydrocarbons.

One definition given in a recent review on graphene is:

Graphene is a flat monolayer of carbon atoms tightly packed into a two-dimensional (2D) honeycomb lattice, and is a basic building block for graphitic materials of all other dimensionalities. It can be wrapped up into 0D fullerenes, rolled into 1D nanotubes or stacked into 3D graphite.

A previous definition is:

A single carbon layer of the graphitic structure can be considered as the final member of the series naphthalene, anthracene, coronene, etc. and the term graphene should therefore be used to designate the individual carbon layers in graphite intercalation compounds. Use of the term "graphene layer" is also considered for the general terminology of carbons.

Thermal properties:

The near-room temperature thermal conductivity of graphene was recently measured to be between (4.84±0.44) ×103 to (5.30±0.48) ×103 Wm−1K−1. These measurements, made by a non-contact optical technique, are in excess of those measured for carbon nanotubes or diamond. It can be shown by using the Wiedemann-Franz law, that the thermal conduction is phonon-dominated. However, for a gated graphene strip, an applied gate bias causing a Fermi energy shift much larger than kBT can cause the electronic contribution to increase and dominate over the phonon contribution at low temperatures. The ballistic thermal conductance of graphene is isotropic.

Potential for this high conductivity can be seen by considering graphite, a 3D version of graphene that has basal plane thermal conductivity of over a 1000 Wm−1K−1 (comparable to diamond). In graphite, the c-axis (out of plane) thermal conductivity is over a factor of ~100 smaller due to the weak binding forces between basal planes as well as the larger lattice spacing. In addition, the ballistic thermal conductance of a graphene is shown to give the lower limit of the ballistic thermal conductances, per unit circumference, length of carbon nanotubes.

Despite its 2-D nature, graphene has 3 acoustic phonon modes. The two in-plane modes (LA, TA) have a linear dispersion relation, whereas the out of plane mode (ZA) has a quadratic dispersion relation. Due to this, the T2 dependent thermal conductivity contribution of the linear modes is dominated at low temperatures by the T1.5 contribution of the out of plane mode. Some graphene phonon bands display negative Grüneisen parameters. At low temperatures (where most optical modes with positive Grüneisen parameters are still not excited) the contribution from the negative Grüneisen parameters will be dominant and thermal expansion coefficient (which is directly proportional to Grüneisen parameters) negative. The lowest negative Grüneisen parameters correspond to the lowest transversal acoustic ZA modes. Phonon frequencies for such modes increase with the in-plane lattice parameter since atoms in the layer upon stretching will be less free to move in the z direction. This is similar to the behavior of a string which is being stretched will have vibrations of smaller amplitude and higher frequency. This phenomenon, named "membrane effect", was predicted by Lifshitz in 1952.

Mechanical properties:

As of 2009, graphene appears to be one of the strongest materials ever tested. Measurements have shown that graphene has a breaking strength 200 times greater than steel, with a tensile strength of 130 GPa (19,000,000 psi). However, the process of separating it from graphite, where it occurs naturally, will require some technological development before it is economical enough to be used in industrial processes, though this may be changing soon.

Graphene paper or GP has recently been developed by a research department from the University of Technology Sydney by Guoxiu Wang, that can be processed, reshaped and reformed from its original raw material state. Researchers have successfully milled the raw graphite by purifying and filtering it with chemicals to reshape and reform it into nano-structured configurations which are then processed into sheets as thin as paper, according to a university statement. Lead researcher Ali Reza Ranjbartoreh said: 'Not only is it lighter, stronger, harder and more flexible than steel, it is also a recyclable and sustainably manufacturable product that is eco-friendly and cost effective in its use.' Ranjbartoreh said the results would allow the development of lighter and stronger cars and planes that use less fuel, generate less pollution, are cheaper to run and ecologically sustainable. He said large aerospace companies have already started to replace metals with carbon fibres and carbon-based materials, and graphene paper with its incomparable mechanical properties would be the next material for them to explore.

Using an atomic force microscope (AFM), the spring constant of suspended graphene sheets has been measured. Graphene sheets, held together by van der Waals forces, were suspended over SiO2 cavities where an AFM tip was probed to test its mechanical properties. Its spring constant was in the range 1–5 N/m and the Young's modulus was 0.5 TPa, which differs from that of the bulk graphite. These high values make graphene very strong and rigid. These intrinsic properties could lead to using graphene for NEMS applications such as pressure sensors and resonators.

As is true of all materials, regions of graphene are subject to thermal and quantum fluctuations in relative displacement. Although the amplitude of these fluctuations is bounded in 3D structures (even in the limit of infinite size), the Mermin-Wagner theorem shows that the amplitude of long-wavelength fluctuations will grow 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.

Modified from materials by Wikipedia under the Creative Commons Attribution License

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