Energetics of carbon peapods: Elliptical deformation of nanotubes and aggregation of encapsulated ${\text{C}}_{60}$

The energetics of large diameter carbon nanotubes encapsulating ${\text{C}}_{60}$ molecules (peapods) have been studied by using the local density approximation in the density-functional theory (DFT). We find that the energy gain ascribed to the encapsulation of ${\text{C}}_{60}$ increases under the elliptical deformation of the nanotubes compared to that for the nanotubes with circular cross section. The energy cost of the deformation of nanotubes is found to be less than 10 meV per atom and is found to be the largest for the (20,20) nanotube. We also explore the energetics of the aggregation of encapsulated ${\text{C}}_{60}$ in the nanometer-scale space of the (10,10) nanotube. The total energy of the dimerized ${\text{C}}_{60}$ encapsulated in the (10,10) nanotube is lower by 0.2 eV per atom than that of the isolated ${\text{C}}_{60}$ indicating that the dimerization reaction is exothermic. The activation barrier for the dimerization of ${\text{C}}_{60}$ is about 1.4 eV, so that the spontaneous dimerization of ${\text{C}}_{60}$ is unlikely to take place without any external stimuli such as electron irradiation.

Figure 1

Optimized geometries of peapods having walls that consist of (a) (20,20), (b) (18,18), (c) (16,16), (d) (14,14), and (e) (12,12) nanotubes. In each figure, upper and lower structures correspond to nanotubes with the same circumference lengths in elliptical and circular cross sections, respectively.

Figure 2

(Color online) Reaction energies $\Delta E$ (see text) per ${\text{C}}_{60}$ in the encapsulation reaction for the (12,12), (14,14), (16,16), (18,18), and (20,20) armchair nanotubes with circular (blue squares) and elliptical (red circles) cross sections.

Figure 3

Total energies of ${\text{C}}_{60}@\left(12,12\right)$ peapods per unit cell for the various radial positions of the ${\text{C}}_{60}$ in the (12,12) nanotube with (a) circular and (b) deformed cross sections. The energies are measured from those of the ${\text{C}}_{60}@\left(12,12\right)$, in which the ${\text{C}}_{60}$’s are located at the center of the nanotube.

Figure 4

(Color online) Total energies of (a) empty and (b) ${\text{C}}_{60}$-filled carbon nanotubes as a function of nanotube circumference length. In each panel, the red circles and blue squares denote the nanotubes with circular and elliptically deformed cross sections, respectively. The energies are measured from that of the graphite monolayer.

Figure 5

Total energy of the ${\text{C}}_{60}$ encapsulated within the (10,10) nanotube as a function of the intermolecular distance. The energy is measured from that obtained in the ${\text{C}}_{60}$ arrangement when the ${\text{C}}_{60}$ are equidistantly aligned at $x=9.824\text{Å}$ [E2].

Figure 6

(Color online) Optimized structures of dimerized ${\text{C}}_{60}$ encapsulated within the (10,10) nanotube. Red and gray circles denote the atoms belonging to the ${\text{C}}_{60}$ dimer and the nanotube, respectively.

Figure 7

Total energies of the ${\text{C}}_{60}$ (a) encapsulated within the (10,10) nanotube and (b) unwrapped as a function of the intermolecular distance. The energy is measured from that obtained from the equidistance ${\text{C}}_{60}$ arrangement. The lines are provided as a visual guide.