Abstract
We report numeric and analytic calculations of the electrostatic properties for armchair carbon nanotube–graphene junctions. Using a semi-empirical method we first demonstrate that the equilibrium distance between a carbon nanotube and a graphene sheet varies with respect to the diameter of the carbon nanotube. We find significantly reduced values compared to AB-stacked graphene sheets in graphite, while even smaller value is found for a fullerene C60 implying a dimensionality dependence of the equilibrium distance between graphene and the other sp2 carbon allotropes. Then, we use conformal mapping and a charge–dipole model to study the charge distribution of the carbon nanotube–graphene junctions in various configurations. We observe that the charges are accumulated/depleted at and near the vicinity of the junctions and that capped carbon nanotubes induce a significantly smaller charge concentration at their ends than the open-end nanotubes. We demonstrate that the carbon nanotube influence on the graphene sheet is limited to only few atomic rows. Such an influence strongly depends on the distance between carbon nanotube and the graphene sheet and scales with the carbon nanotube radius, while the potential difference does not modify the length over which the charge concentration is disturbed by the presence of the tube. By studying the potential landscape of carbon nanotube–graphene junctions, our work could be used as a starting point to model the charge carrier injection in these unconventional systems.
Highlights
Due to its outstanding physical properties, graphene is seen as a very promising material for many applications ranging from high frequency electronics to energy storage [1,2,3]
We have studied the electrostatic behavior of a carbon nanotube (CNT)–graphene junction
The influence of the CNT on the charge distribution in the graphene sheet has been analyzed by defining the length of influence of the CNT on the graphene sheet l5% max
Summary
Due to its outstanding physical properties, graphene is seen as a very promising material for many applications ranging from high frequency electronics to energy storage [1,2,3]. The van der Waals interaction handling has been improved for it by introducing a specific empirical term to account for the London dispersion energy as described in [90] Such a method has been used successfully to determine the bending of a suspended graphene sheet in a holey graphite structure [91]. The lack of dispersion term as seen in figure 2 leads to a weaker binding (−0.38 eV compared to −4.16 eV for the PM6-D method) and as well as to a higher equilibrium distance, close to the interlayer distance in graphite We confirm this trend by performing similar calculations for a C60 molecule on a graphene sheet (see figure 3). We have used the calculated equilibrium distance (and the extrapolated values for very large diameter CNT, see appendix A) for our study of the charge distribution described
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