Anisotropic Packing and One-Dimensional Fluctuations of ${\mathrm{C}}_{60}$ Molecules in Carbon Nanotubes

The confinement of a ${\mathrm{C}}_{60}$ molecule encapsulated in a cylindrical nanotube depends on the tube radius. In small tubes with radius $R_{\mathrm{T}}\lesssim 7\AA$, a fivefold axis of the molecule coincides with the tube axis. The interaction between ${\mathrm{C}}_{60}$ molecules in the nanotube is then described by a $O_2$-rotor model on a 1D liquid chain with coupling between orientational and displacive correlations. This coupling leads to chain contraction. The structure factor of the 1D liquid is derived. In tubes with a larger radius the molecular centers of mass are displaced off the tube axis. The distinction of two groups of peapods with on- and off-axis molecules suggests an explanation of the apparent splitting of $A_g$ modes of ${\mathrm{C}}_{60}$ in nanotubes measured by resonant Raman scattering.

Figure 1

Mercator map of nanotube field potential $V(R_{\mathrm{T}};\beta ,\gamma )$, units K, $R_{\mathrm{T}}=6.86\AA$. Energy measured from its minimum.

Figure 2

Variation of nanotube field potential with $\Delta$.

Figure 3

Structure factor $S(q)$, given by Eq. (12), for $T=300\mathrm{K}$. For $q\frac{\overline{a}}{2\pi }\in {\mathbb{Z}}_0$, $S(q)$ reaches local maxima $\frac{1+Z(q)}{1-Z(q)}$.