Structure of Graphene

Graphene is defined as a single, infinite monolayer of sp2 bonded carbon atoms arranged in a hexagonal lattice. The thickness of an individual graphene sheet is 0.35 nm, whilst the interatomic distance between adjacently bonded carbon atoms within the lattice is 1.42 Å.19 Each of the carbon atoms within a pristine graphene lattice possess a single s orbital and two in-plane p orbitals which hybridise to form three sp2 orbitals and one p orbital, giving rise to the planar arrangement of graphene. These orbitals also define the highly conjugated, aromatic structure of graphene through  bonds which exist between each carbon atom and three of its nearest neighbours in the lattice. Additionally, each carbon atom also possesses a  orbital which contributes to a system of delocalised  electrons both above and below the basal plane. Therefore, although graphene is three dimensional, it is commonly considered a two dimensional particle due to its ultra-high aspect ratio.

Despite the unique two dimensional structure of graphene, it also exhibits a strong relationship with carbon materials of other dimensionalities, in particular, graphite (Figure 3.1). Graphene sheets occur naturally in three-dimensional bulk graphite as stacked layers held together by long-range van der Waals intermolecular forces. The van der Waals interaction energy between adjacent graphene layers in graphite is 2 eV/nm2, while the interlayer spacing between these layers is 0.34 nm. As the number of graphene layers in a sample increases from a single layer the mechanical, electrical and

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thermal properties of the graphene deteriorate, so that at 10 layers of graphene, the material exhibits an electronic structure that is indistinguishable from bulk graphite.20 However, as the screening length of pristine graphene is only 0.5 nm, equivalent to two sheets of graphene, it is important to recognise that layered graphene sheets of as little as five layers exhibit distinct surface and bulk properties.21 Consequently, it is important that graphene samples are produced with as few carbon layers as possible in order to take full advantage of the superior properties of graphene.

Figure 3.1: Graphene is a 2D building material for carbon materials of all other dimensionalities. It can be wrapped up into 0D buckyballs, rolled into 1D nanotubes or stacked into 3D graphite. (Reprinted by permission from Macmillan Publishers Ltd: Nature Materials, Geim, A. K.; Novoselov, K. S., The rise of graphene. Nat. Mater. 2007, 6, (3), 183-191., Copyright 2007).

3.2.1

Properties of Graphene

The unique, two-dimensional structure of graphene gives rise to a material which showcases a combination of impressive properties. Indeed, many of these properties are

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the highest ever recorded for a material, with some even approaching their theoretical limit. For instance, the excellent electronic properties exhibited by pristine monolayer graphene originate from extensive delocalisation of -electrons along the graphene basal plane. Consequently, defect-free monolayer graphene has been shown to possess charge carrier mobilities of 2.5 × 105 cm2 V-1 at room temperature22, along with current capacities several orders of magnitude higher than copper.23 Similarly, the strength of the C=C bonds in the graphene lattice is responsible for the superior mechanical features displayed by graphene, with the single carbon layers having a Young’s modulus of 1 TPa and tensile strength of 130 GPa.24 In addition to electronic and mechanical properties, graphene also demonstrates a remarkable thermal conductivity of 5300 W m-1 K-1, the highest of any known material.25 Due to the two dimensional nature of graphene, the material is also predicted to possess a high specific surface area of 2630 m2/g 26. Furthermore, several studies have shown the effective gas barrier properties27, high flexural strength28 and exceptional optical transparency29 characteristic to single layer graphene. Together, these features occur as a direct result of the unique planar structure of pristine graphene.

3.2.2

Surface Charge and Intermolecular Forces Present on Graphene

The unique planar structure of graphene also dictates the surface forces demonstrated by the graphene surface. The conjugated structure present along the graphene basal plane gives rise to a system of delocalised -electrons which can allow dispersion forces to occur. As result, the extended conjugation present in graphene has been shown to facilitate intermolecular interactions with polycyclic aromatic compounds, which can interact with the graphene surface through - stacking.30 Cationic species are also

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able to interact with the delocalised -electron system on graphene through cation- interactions.31

Graphene exfoliated from natural sources of graphite typically exhibits defects within the lattice due to the formation of grain boundaries and imperfect crystal lattices. At these boundaries and along the edges of graphene, the most common types of defect functional groups that exist are oxygenated functional groups such as ether, carbonyl, carboxylic acid and alcohol groups.32 As a result, hydrogen bonding interactions can occur depending on the type of edge group and pH. A small negative charge is also typically exhibited within the vicinity of these groups. Conversely, the presence of defects within the lattice not only has a detrimental effect on the electronic and mechanical properties of graphene, but also acts as a weak point in the lattice. Consequently, defects are known to cause unzipping of the conjugated lattice structure.30 This effect can be reduced through either synthetic, highly ordered graphitic precursors where applicable, or carefully selected graphene production methods.