Energetics and packing of fullerenes in nanotube peapods

We use structure-optimization techniques to study the equilibrium packing of fullerenes in carbon nanotube peapods. Our results for nanotubes containing ${\mathrm{C}}_n$ fullerenes with $60⩽n⩽84$ atoms indicate that the fullerenes are more densely packed in the nanotubes than in the bulk crystal, in agreement with experimental data. We find that the reduction of the interfullerene distance, as well as a structural relaxation of fullerenes and nanotubes, results from a high internal pressure within the peapods, suggesting the use of nanotubes as nanoscale autoclaves for chemical reactions.

Figure 1

Energetics of fullerene encapsulation. (a) During its insertion into a nanotube, a fullerene is pulled in by a “capillary” force $F$, which is linked to the energy gain upon axial displacement $\Delta z$. (b) The encapsulation energy $\Delta E$ of isolated ${\mathrm{C}}_{60}$ (엯) and ${\mathrm{C}}_{84}$ (•) fullerenes in single-walled carbon nanotubes with radii ranging from $0.6\mathrm{nm}\lesssim R_{NT}\lesssim 0.8\mathrm{nm}$. (c) The energy change during the fullerene insertion process along the tube axis $z$, with $z=0$ denoting the tube end. ${\mathrm{C}}_{60}$ and ${\mathrm{C}}_{84}$ are pulled into the best fitting (10, 10) and (11, 11) nanotubes by a force $F=-\Delta E∕\Delta z\gtrsim 0.1\mathrm{nN}$ close to the tube end. The high energy cost prevents spontaneous entry of the ${\mathrm{C}}_{84}$ fullerene into the narrow (10, 10) nanotube.

Figure 2

Equilibrium packing structure of fullerenes in peapods. (a) An external capillary force $F$ reduces the axial interfullerene distance $D_z$. An off-axis fullerene displacement $\Delta$ is expected especially if the fullerene radius $R_F$ is much smaller than the nanotube radius $R_{NT}$. (b) The reduction of the axial interfullerene distance $D_z$ in peapods with respect to the equilibrium separation $D_0$ in bulk crystals of ${\mathrm{C}}_n$ fullerenes with 60–84 atoms. The observations for different fullerenes inside a 1.4-nm-wide nanotube, reported in Ref. 7 and given by the data points with error bars, are compared to our analytical results for various applied forces $F$, shown by the dashed lines. (c) The predicted off-axis displacement $\Delta$ inside a 1.4-nm-wide nanotube as a function of the fullerene size, for various applied forces $F$.

Figure 3

Fullerene-induced strain in the nanotube walls of peapods for different packing geometries. (a) In peapods containing fullerenes equal to or smaller than the optimum size, the strain in the nanotube wall is induced by an axial force. (b) The strain distribution on the wall of a (10, 10) nanotube containing ${\mathrm{C}}_{60}$ fullerenes, subject to the axial force of 0.5 nN. (c) In peapods containing fullerenes exceeding the optimum size, the strain is induced even in the absence of an axial force. (d) The strain distribution on the wall of a (10, 10) nanotube containing ${\mathrm{C}}_{84}$ fullerenes. The strain energy is represented by the reduction of the atomic binding energy on a gray scale in (b) and (d).