parichehr
29th November 2010, 10:55 AM
Graphene is a one-atom-thick planar (http://njavan.com/wiki/Plane_(geometry)) sheet of sp2-bonded (http://njavan.com/wiki/Orbital_hybridisation#sp2_hybrids) carbon (http://njavan.com/wiki/Carbon) atoms that are densely packed in a honeycomb crystal lattice. The term graphene was coined as a combination of graphite (http://njavan.com/wiki/Graphite) and the suffix -ene (http://njavan.com/wiki/-ene) by Hanns-Peter Boehm (http://njavan.com/wiki/Hanns-Peter_Boehm), who described single-layer carbon foils in 1962. Graphene is most easily visualized as an atomic-scale chicken wire (http://njavan.com/wiki/Chicken_wire_(chemistry)) made of carbon atoms and their bonds. The crystalline or "flake" form of graphite consists of many graphene sheets stacked together.
http://upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Graphen.jpg/300px-Graphen.jpg (http://njavan.com/wiki/File:Graphen.jpg)
Epitaxial growth on silicon carbide
Another method of obtaining graphene is to heat silicon carbide to high temperatures (>1100 °C) to reduce it to graphene. This process produces epitaxial graphene with dimensions dependent upon the size of the SiC substrate (wafer). The face of the silicon carbide used for graphene formation, silicon- or carbon-terminated, highly influences the thickness, mobility and carrier density of the graphene.
Many important graphene properties have been identified in graphene produced by this method. For example, the electronic band-structure (so-called Dirac cone structure) has been first visualized in this material. Weak anti-localization is observed in this material and not in exfoliated graphene produced by the pencil trace method. Extremely large, temperature independent mobilities have been observed in SiC epitaxial graphene. They approach those in exfoliated graphene placed on silicon oxide but still much lower than mobilities in suspended graphene produced by the drawing method. It was recently shown that even without being transferred graphene on SiC exhibits the properties of massless Dirac fermions such as the anomalous quantum Hall effect (http://njavan.com/wiki/Quantum_Hall_effect).
The weak van der Waals force that provides the cohesion of multilayer graphene stacks does not always affect the electronic properties of the individual graphene layers in the stack. That is, while the electronic properties of certain multilayered epitaxial graphenes are identical to that of a single graphene layer, in other cases the properties are affected as they are for graphene layers in bulk graphite. This effect is theoretically well understood and is related to the symmetry of the interlayer interactions.
Electronic properties
http://upload.wikimedia.org/wikipedia/commons/thumb/3/35/Cnt_zz_v3.gif/350px-Cnt_zz_v3.gif (http://njavan.com/wiki/File:Cnt_zz_v3.gif) http://bits.wikimedia.org/skins-1.5/common/images/magnify-clip.png (http://njavan.com/wiki/File:Cnt_zz_v3.gif)
GNR band structure for zig-zag type. Tightbinding calculations show that zigzag type is always metallic.
http://upload.wikimedia.org/wikipedia/commons/thumb/f/fb/Cnt_gnrarm_v3.gif/350px-Cnt_gnrarm_v3.gif (http://njavan.com/wiki/File:Cnt_gnrarm_v3.gif) http://bits.wikimedia.org/skins-1.5/common/images/magnify-clip.png (http://njavan.com/wiki/File:Cnt_gnrarm_v3.gif)
GNR band structure for arm-chair type. Tightbinding calculations show that armchair type can be semiconducting or metallic depending on width (chirality).
Graphene differs from most conventional three-dimensional materials. Intrinsic graphene is a semi-metal (http://njavan.com/wiki/Semi-metal) or zero-gap semiconductor (http://njavan.com/wiki/Semiconductor). Understanding the electronic structure of graphene is the starting point for finding the band structure of graphite. It was realized early on that the E-k relation is linear for low energies near the six corners of the two-dimensional hexagonal Brillouin zone (http://njavan.com/wiki/Brillouin_zone), leading to zero effective mass (http://njavan.com/wiki/Effective_mass) for electrons and holes. Due to this linear (or “conical (http://njavan.com/wiki/Conical_intersection)") dispersion relation at low energies, electrons and holes near these six points, two of which are inequivalent, behave like relativistic (http://njavan.com/wiki/Theory_of_relativity) particles described by the Dirac equation (http://njavan.com/wiki/Dirac_equation) for spin 1/2 particles. Hence, the electrons and holes are called Dirac fermions (http://njavan.com/wiki/Fermions), and the six corners of the Brillouin zone are called the Dirac points. The equation describing the E-k relation is http://upload.wikimedia.org/math/d/6/5/d65cc73fc84497a6bca1529feebe93be.png; where the Fermi velocity (http://njavan.com/wiki/Fermi_velocity) vF ~ 106 m/s.
Thermal properties
The near-room temperature thermal conductivity (http://njavan.com/wiki/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 (http://njavan.com/wiki/Wiedemann-Franz_law), that the thermal conduction is phonon (http://njavan.com/wiki/Phonon)-dominated However, for a gated graphene strip, an applied gate bias causing a Fermi energy (http://njavan.com/wiki/Fermi_energy) shift much larger than kBT can cause the electronic contribution to increase and dominate over the phonon (http://njavan.com/wiki/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 (http://njavan.com/wiki/Basal_plane) thermal conductivity (http://njavan.com/wiki/Thermal_conductivity) of over a 1000 Wm−1K−1 (comparable to diamond (http://njavan.com/wiki/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 (http://njavan.com/wiki/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 (http://njavan.com/wiki/Acoustic_phonon) modes. The two in-plane modes (LA, TA) have a linear dispersion relation (http://njavan.com/wiki/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 (http://njavan.com/wiki/Gr%C3%BCneisen_parameter). 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 (http://njavan.com/wiki/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 (http://njavan.com/wiki/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 (http://njavan.com/wiki/Ilya_Mikhailovich_Lifshitz) in 1952.
Graphene biodevices
Graphene's modifiable chemistry, large surface area, atomic thickness and molecularly-gatable structure make antibody-functionalized graphene sheets excellent candidates for mammalian and microbial detection and diagnosis devices.
http://upload.wikimedia.org/wikipedia/commons/thumb/0/0b/GrapheneE2.png/220px-GrapheneE2.png (http://njavan.com/wiki/File:GrapheneE2.png) http://bits.wikimedia.org/skins-1.5/common/images/magnify-clip.png (http://njavan.com/wiki/File:GrapheneE2.png)
Energy of the electrons with wavenumber k in graphene, calculated in the Tight Binding (http://njavan.com/wiki/Tight_Binding)-approximation. The unoccupied (occupied) states, colored in blue-red (yellow-green), touch each other without energy gap (http://njavan.com/wiki/Energy_gap) exactly at the above-mentioned six k-vectors.
The most ambitious biological application of graphene is for rapid, inexpensive electronic DNA sequencing. Integration of graphene (thickness of 0.34 nm) layers as nanoelectrodes into a nanopore can solve one of the bottleneck issues of nanopore-based single-molecule DNA sequencing.
Anti-bacterial
The Chinese Academy of Sciences (http://njavan.com/wiki/Chinese_Academy_of_Sciences) has found that sheets of graphene oxide are highly effective at killing bacteria such as Escherichia coli (http://njavan.com/wiki/Escherichia_coli). This means graphene could be useful in applications such as hygiene products or packaging that will help keep food fresh for longer
www.science (http://www.science) direct
http://upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Graphen.jpg/300px-Graphen.jpg (http://njavan.com/wiki/File:Graphen.jpg)
Epitaxial growth on silicon carbide
Another method of obtaining graphene is to heat silicon carbide to high temperatures (>1100 °C) to reduce it to graphene. This process produces epitaxial graphene with dimensions dependent upon the size of the SiC substrate (wafer). The face of the silicon carbide used for graphene formation, silicon- or carbon-terminated, highly influences the thickness, mobility and carrier density of the graphene.
Many important graphene properties have been identified in graphene produced by this method. For example, the electronic band-structure (so-called Dirac cone structure) has been first visualized in this material. Weak anti-localization is observed in this material and not in exfoliated graphene produced by the pencil trace method. Extremely large, temperature independent mobilities have been observed in SiC epitaxial graphene. They approach those in exfoliated graphene placed on silicon oxide but still much lower than mobilities in suspended graphene produced by the drawing method. It was recently shown that even without being transferred graphene on SiC exhibits the properties of massless Dirac fermions such as the anomalous quantum Hall effect (http://njavan.com/wiki/Quantum_Hall_effect).
The weak van der Waals force that provides the cohesion of multilayer graphene stacks does not always affect the electronic properties of the individual graphene layers in the stack. That is, while the electronic properties of certain multilayered epitaxial graphenes are identical to that of a single graphene layer, in other cases the properties are affected as they are for graphene layers in bulk graphite. This effect is theoretically well understood and is related to the symmetry of the interlayer interactions.
Electronic properties
http://upload.wikimedia.org/wikipedia/commons/thumb/3/35/Cnt_zz_v3.gif/350px-Cnt_zz_v3.gif (http://njavan.com/wiki/File:Cnt_zz_v3.gif) http://bits.wikimedia.org/skins-1.5/common/images/magnify-clip.png (http://njavan.com/wiki/File:Cnt_zz_v3.gif)
GNR band structure for zig-zag type. Tightbinding calculations show that zigzag type is always metallic.
http://upload.wikimedia.org/wikipedia/commons/thumb/f/fb/Cnt_gnrarm_v3.gif/350px-Cnt_gnrarm_v3.gif (http://njavan.com/wiki/File:Cnt_gnrarm_v3.gif) http://bits.wikimedia.org/skins-1.5/common/images/magnify-clip.png (http://njavan.com/wiki/File:Cnt_gnrarm_v3.gif)
GNR band structure for arm-chair type. Tightbinding calculations show that armchair type can be semiconducting or metallic depending on width (chirality).
Graphene differs from most conventional three-dimensional materials. Intrinsic graphene is a semi-metal (http://njavan.com/wiki/Semi-metal) or zero-gap semiconductor (http://njavan.com/wiki/Semiconductor). Understanding the electronic structure of graphene is the starting point for finding the band structure of graphite. It was realized early on that the E-k relation is linear for low energies near the six corners of the two-dimensional hexagonal Brillouin zone (http://njavan.com/wiki/Brillouin_zone), leading to zero effective mass (http://njavan.com/wiki/Effective_mass) for electrons and holes. Due to this linear (or “conical (http://njavan.com/wiki/Conical_intersection)") dispersion relation at low energies, electrons and holes near these six points, two of which are inequivalent, behave like relativistic (http://njavan.com/wiki/Theory_of_relativity) particles described by the Dirac equation (http://njavan.com/wiki/Dirac_equation) for spin 1/2 particles. Hence, the electrons and holes are called Dirac fermions (http://njavan.com/wiki/Fermions), and the six corners of the Brillouin zone are called the Dirac points. The equation describing the E-k relation is http://upload.wikimedia.org/math/d/6/5/d65cc73fc84497a6bca1529feebe93be.png; where the Fermi velocity (http://njavan.com/wiki/Fermi_velocity) vF ~ 106 m/s.
Thermal properties
The near-room temperature thermal conductivity (http://njavan.com/wiki/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 (http://njavan.com/wiki/Wiedemann-Franz_law), that the thermal conduction is phonon (http://njavan.com/wiki/Phonon)-dominated However, for a gated graphene strip, an applied gate bias causing a Fermi energy (http://njavan.com/wiki/Fermi_energy) shift much larger than kBT can cause the electronic contribution to increase and dominate over the phonon (http://njavan.com/wiki/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 (http://njavan.com/wiki/Basal_plane) thermal conductivity (http://njavan.com/wiki/Thermal_conductivity) of over a 1000 Wm−1K−1 (comparable to diamond (http://njavan.com/wiki/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 (http://njavan.com/wiki/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 (http://njavan.com/wiki/Acoustic_phonon) modes. The two in-plane modes (LA, TA) have a linear dispersion relation (http://njavan.com/wiki/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 (http://njavan.com/wiki/Gr%C3%BCneisen_parameter). 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 (http://njavan.com/wiki/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 (http://njavan.com/wiki/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 (http://njavan.com/wiki/Ilya_Mikhailovich_Lifshitz) in 1952.
Graphene biodevices
Graphene's modifiable chemistry, large surface area, atomic thickness and molecularly-gatable structure make antibody-functionalized graphene sheets excellent candidates for mammalian and microbial detection and diagnosis devices.
http://upload.wikimedia.org/wikipedia/commons/thumb/0/0b/GrapheneE2.png/220px-GrapheneE2.png (http://njavan.com/wiki/File:GrapheneE2.png) http://bits.wikimedia.org/skins-1.5/common/images/magnify-clip.png (http://njavan.com/wiki/File:GrapheneE2.png)
Energy of the electrons with wavenumber k in graphene, calculated in the Tight Binding (http://njavan.com/wiki/Tight_Binding)-approximation. The unoccupied (occupied) states, colored in blue-red (yellow-green), touch each other without energy gap (http://njavan.com/wiki/Energy_gap) exactly at the above-mentioned six k-vectors.
The most ambitious biological application of graphene is for rapid, inexpensive electronic DNA sequencing. Integration of graphene (thickness of 0.34 nm) layers as nanoelectrodes into a nanopore can solve one of the bottleneck issues of nanopore-based single-molecule DNA sequencing.
Anti-bacterial
The Chinese Academy of Sciences (http://njavan.com/wiki/Chinese_Academy_of_Sciences) has found that sheets of graphene oxide are highly effective at killing bacteria such as Escherichia coli (http://njavan.com/wiki/Escherichia_coli). This means graphene could be useful in applications such as hygiene products or packaging that will help keep food fresh for longer
www.science (http://www.science) direct