Orientation of ${\mathrm{C}}_{70}$ molecules in peapods as a function of the nanotube diameter

Encapsulated ${\mathrm{C}}_{70}$ molecules packed in single-walled carbon nanotubes display different orientations depending on the nanotube radius. We present x-ray scattering data obtained on a powder of nanotubes filled with ${\mathrm{C}}_{70}$ molecules. Analytical expressions for calculating the diffraction diagram taking into account fullerene orientations are developed. The comparison between calculations and experiments allows us to conclude that the change from the lying to standing orientation—corresponding to the molecule long axis parallel and perpendicular to the tube axis, respectively—takes place when nanotubes reach a diameter of about $1.42\mathrm{nm}$. Energy calculations are performed using a Lennard-Jones (6-12) potential, leading to a calculated reorientation diameter in good agreement with that determined experimentally.

Figure 1

(Left-hand side) Transmission electron microscopy images of SWNTs. Low magnification, SWNT bundles are shown along with empty polyaromatic carbon shells. (Right-hand side) High resolution transmission electron microscopy image of a ${\mathrm{C}}_{70}$ @SWNT peapod bundle. The resolution is not sufficient to distinguish between lying and standing ${\mathrm{C}}_{70}$ molecules.

Figure 2

Room temperature diffraction patterns of SWNTs (upper curve, open circles) and ${\mathrm{C}}_{70}$ peapods (lower curve, open circles). The curves are translated vertically for the sake of clarity. Diffuse scattering from the glass capillary—centered around $1.7{\mathrm{\AA }}^{-1}$—has been measured on empty capillaries and substracted to both SWNT and peapod diagrams. Below each experimental curves are represented the simulation (black thick line) and the background used for the fit (small circles). Doublets of Miller indices refer to diffraction peaks of the two-dimensional hexagonal bundle lattice. “Gr 002” refers to scattering by graphene-based impurities. The positions of the first order diffraction peaks of the periodic chains of lying and standing ${\mathrm{C}}_{70}$ molecules are indicated by the indexation $L$ and $S$, respectively. Inset: representation of the lying and standing orientations for the ${\mathrm{C}}_{70}$ molecules inside nanotube.

Figure 3

The ${\mathrm{C}}_{70}$ molecule: atomic model and homogeneous approximation.

Figure 4

Representation of the coordinates used in the calculation: (a) in the molecule system $(R^{\prime }=0x^{\prime }{y}^{\prime }{z}^{\prime })$ and (b) in the nanotube system $(R=0XYZ)$. In (b), the orientation of the molecular long axis $0z^{\prime }$ and of the molecule system of coordinates $\left(0x^{\prime }{y}^{\prime }{z}^{\prime }\right)$ in the standing case is drawn.

Figure 5

Scattered intensity calculated: up, for standing (line) and spherical (crosses) ${\mathrm{C}}_{70}$ molecules inside nanotubes, the interfullerenes distance being $L=1\mathrm{nm}$; down, for lying (open circles) and spherical (crosses) molecules with $L=1.1\mathrm{nm}$. $L$ values are taken from experiments (Sec. 2B). Other parameters are ${\Phi }_T=1.4\mathrm{nm}$, $N_f=19$, $p=1$.

Figure 6

The three components of the intensity and their sum. They have been translated vertically for the sake of clarity; the background function $\mathrm{BG}\left(Q\right)$ is not taken into account here. Arrows point toward the diffraction peaks from chains of lying or standing molecules.

Figure 7

Interaction between two ${\mathrm{C}}_{70}$ molecules as a function of the distance $L$ between their centers. Open squares correspond to parallel standing molecules and open circles to lying molecules.

Figure 8

Energy of a ${\mathrm{C}}_{70}$ molecule inside a nanotube as a function of the tube diameter (open circle, lying molecule; open square, standing one).

Figure 9

Total energy per molecule in the lying case (open circles) and in the standing case (open squares, $\psi =0$).