Graphene

In term of applications, graphene has enormous potential for use in ultrafast electronic transistors and flexible displays. Moreover, graphene can be used in composite materials and in electric batteries due to its large surface-to-volume ratio and high conductivity, for transparent membranes due to its atomic thickness, in micro-mechanical resonators due to its robustness and light weight, and chemical detectors due to it selective reactivity [11]. 

Graphene is a one-atom-thick planar layer of graphite, where the atoms are packed in a hexagonal ( honeycomb ) crystal lattice. The carbon atoms are sp -bonded with a bond length of 1.42 A. The crystal lattice has two atoms per unit cell, A and B, and it is rotationally symmetric for rotations of 120° around any lattice point. One can view the honeycomb lattice as a triangular Bravais lattice with a basis of two atoms per unit cell. Fig. 2a. 

If we now move from real space into reciprocal space, the Brillouin zone associated with the crystal lattice is also hexagonal and it shows characteristic high-symmetry points the centre is called F point, while two consecutive corners are denoted as K and K points. Fig. 2b. 

As a result, quasi-particles in graphene exhibit the linear dispersion relation E = hvp, where vp is the Fermi velocity ( 10 m/s), as if they were massless relativistic particles. Thus, graphene s quasiparticles behave differently from those in conventional metals and semiconductors, where the energy spectrum can be approximated by a parabolic dispersion relation. Electron transport in all known condensed-matter systems is described by the (non-relativistic) Schrodinger equation and relativistic effects are usually negligible. In contrast, the electrons of graphene are described by the (relativistic) Dirac equation, i.e. they mimic relativistic charged particles with zero rest mass and constant velocity [10]. 

Graphene is found to exhibit a pronounced ambipolar electric field effect, i.e. charge carriers can be tuned continuously between electrons to holes in 

Single planar sheet of sp -bonded carbon atoms corresponds to one hexagonal basal plane of graphite and is termed graphene. Recently, a successful attempt to isolate such a graphene layer has been reported [3], and apparently, it becomes possible to produce 

Each graphene sheet is composed of rings of carbon atoms arranged on a hexagonal 2D tiling. This form of carbon has n bonds in addition to the a bonds, as shown in Fig. 4.6, leading to a bond order of 1.33. 

Therefore, there is a certain equilibrium distance r , at which the dispersive-attractive and the repulsive forces balance and the system achieves minimum energy at the minimum of potential curve y(r ). The van der Walls radius, r, for the C-H interaction can be assumed to be about 0.16 nm. 

The thermal and electrical conductivity is very high, and it can be used as a flexible conductor. Its thermal conductivity is much higher than that of silver. Graphene has a number of properties which makes it interesting for several different applications. It is an ultimately thin, mechanically very strong, transparent, and flexible conductor. Its conductivity can be modified over a large range either by 

The Nobel Prize in Physics 2010 honors two scientists who have made the decisive contributions to this development. They are Andre K. Geim and Konstantin S. Novoselov, both at the University of Manchester, UK. They have succeeded in producing, isolating, identifying, and characterizing graphene [2]. 

A new form of molecular carbon is the so-called fullerenes (see Fig. 16.4). The most common, caUed C60, contains 60 carbon atoms and looks like a football (soccer ball) made up from 20 hexagons and 12 pentagons which allow the surface to form a sphere. The discoverer of fullerenes was awarded the Nobel Prize in Chemistry in 1996 [2]. 

A related quasi-one-dimensional form of carbon, carbon nanotubes, has been known for several decades, and the single-walled nanotubes, since 1993 [1, 2]. These can be formed from graphene sheets which are rolled up to form tubes, and their ends are half spherical in the same way as the fullerenes. The electronic and mechanical properties of metallic single-walled nanotubes have many similarities with graphene. 

the difficulty was not to fabricate the graphene structures, but to isolate sufficiently large individual sheets in order to identify and characterize the graphene and to verify its unique two-dimensional (2D) properties. This is what Geim, Novoselov, and their collaborators succeeded in doing. 

In this chapter, we will introduce some typical carbon materials that are widely studied in electrochemistry. Their properties, not restricted to their electrochemical properties, will be briefly described. Some characterization techniques, including spectroelectrochemistry, will be described when applied to selected carbon materials. A brief overview of the application of various carbon materials to electrochemistry will be included in this chapter, which will be concluded by an outlook to the future. 

Many scientists believed that two-dimensional crystals, which are one atom thick, could not exist. The theory pointed out that a divergent contribution of thermal vi- 

The problem to produce the graphene was solved by A. Geim and K. Novoselov. 

By gently rubbing or pressing a freshly cleaved crystal on an oxidized wafer graphene flakes with the correct thickness of oxide, single atomic layers are visible under an optical microscopy due to thin film interference effects. 

Mechanical properties of graphene have been measured by methods of static deflection using an atomic force microscope [66]. Spring constants ranging from 1 

whereas in compression, there is an indication of flake buckling at about 0.7% strain. 

In 2010, Japanese researchers at Ehime University together with Sumitomo Electric Co. developed another method to produce large diamond crystals (shown in the right hand side of Eig. 11.1) named as HIME diamond.  

11 Diamond, Graphite, Graphene, Bucky Baii and Nanotube (Fun with Carbon) 

HIERARCHICAL MATERIALS ARCHITECTURES EOR ENZYMATIC FUEL CELLS 

Wang et al. showed that certain Shewanella sp. including Shewanella oneidensis MR-1 can use graphene oxide as a terminal electron acceptor, ultimately yielding conductive graphene [43]. 

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The circumference of any carbon nanotube is expressed in terms of the chiral vector = nai ma2 which connects two crystallographically equivalent sites on a 2D graphene sheet [see Fig. 16(a)] [162]. The construction in... 

Structurally, carbon nanotubes of small diameter are examples of a onedimensional periodic structure along the nanotube axis. In single wall carbon nanotubes, confinement of the stnreture in the radial direction is provided by the monolayer thickness of the nanotube in the radial direction. Circumferentially, the periodic boundary condition applies to the enlarged unit cell that is formed in real space. The application of this periodic boundary condition to the graphene electronic states leads to the prediction of a remarkable electronic structure for carbon nanotubes of small diameter. We first present... 

The ID electronic energy bands for carbon nanotubes [170, 171, 172, 173, 174] are related to bands calculated for the 2D graphene honeycomb sheet used to form the nanotube. These calculations show that about 1/3 of the nanotubes are metallic and 2/3 are semiconducting, depending on the nanotube diameter di and chiral angle 6. It can be shown that metallic conduction in a (n, m) carbon nanotube is achieved when... 

These surprising results can be understood on the basis of the electronic structure of a graphene sheet which is found to be a zero gap semiconductor [177] with bonding and antibonding tt bands that are degenerate at the TsT-point (zone corner) of the hexagonal 2D Brillouin zone. The periodic boundary... 

Closely related to the ID dispersion relations for the carbon nanotubes is the ID density of states shown in Fig. 20 for (a) a semiconducting (10,0) zigzag carbon nanotube, and (b) a metallic (9,0) zigzag carbon nanotube. The results show that the metallic nanotubes have a small, but non-vanishing 1D density of states, whereas for a 2D graphene sheet (dashed curve) the density of states... 

Fig. 20. Electronic 1D density of states per unit cell of a 2D graphene sheet for two (n, 0) zigzag nanotubes (a) the (10,0) nanotube which has semiconducting behavior, (b) the (9, 0) nanotube which has metallic behavior. Also shown in the figure is the density of states for the 2D graphene sheet (dotted line) [178].

Compared to PAN and pitch-based carbon fiber, the morphology of VGCF is unique in that the graphene planes are more preferentially oriented around the axis... 

In graphitic carbon, the in-plane stnrcture of graphene layers is almost the same as in graphite except the lateral extent of the layers inereases with heat-treatment... 

Figure 8 shows plotted versus P for all the carbons listed in Table 1 and for many others. There is a linear relationship betw cen g , and P which is well described by Q, =312(i-P) mAh/g. This implies that little or no lithium is able to intercalate between randomly stacked parallel layers [2]. Therefore we call the space between these adjacent randomly stacked graphene layers, blocked galleries . 

Fig. 24. Adsorption of lithium on the internal surfaces of micropores formed by single, bi, and trilayers of graphene sheets in hard carbon.

Powder X-ray diffraction and SAXS were employed here to explore the microstructure of hard carbon samples with high capacities. Powder X-ray diffraction measurements were made on all the samples listed in Table 4. We concentrate here on sample BrlOOO, shown in Fig. 27. A weak and broad (002) Bragg peak (near 22°) is observed. Well formed (100) (at about 43.3°) and (110) (near 80°) peaks are also seen. The sample is predominantly made up of graphene sheets with a lateral extension of about 20-30A (referring to Table 2, applying the Scherrer equation to the (100) peaks). These layers are not stacked in a parallel fashion, and therefore, there must be small pores or voids between them. We used SAXS to probe these pores. 

F ig. 29. Schematic graph showing the definition of the parameter, R, used to empirically estimate the fraction of single graphene layers in hard carbon samples. 

Fig. 32. Reversible capacity of microporous carbon prepared from phenolic resins heated between 940 to 1 I00°C plotted as a function of the X-ray ratio R. R is a parameter which is empirically correlated to the fraction of single-layer graphene sheets in the samples.

Interest has rapidly focused on the single-walled, capped tubes, as shown in Figure 11.7. They can currently be grown up to 100 pm in length, i.e., about 100,000 times their diameter. As the figure shows, there are two ways of folding a graphene sheet in such a way that the resultant tube can be seamlessly closed with a Cfto hemisphere... one way uses a cylinder axis parallel to some of the C—C bonds in... 

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