How Confinement Affects the Dynamics of ${\mathrm{C}}_{60}$ in Carbon Nanopeapods

The dynamics of confined systems is of major concern for both fundamental physics and applications. In this Letter, the dynamics of ${\mathrm{C}}_{60}$ fullerene molecules inside single walled carbon nanotubes is studied using inelastic neutron scattering. We identify the ${\mathrm{C}}_{60}$ vibrations and highlight their sensitivity to temperature. Moreover, a clear signature of rotational diffusion of the ${\mathrm{C}}_{60}$ is evidenced, which persists at lower temperature than in 3D bulk ${\mathrm{C}}_{60}$. It is discussed in terms of confinement and of reduced dimensionality of the ${\mathrm{C}}_{60}$ chain.

Figure 1

Generalized density of states of the peapod sample (top spectrum) and of the SWNT sample (middle spectrum) measured at 10 K using the IN1BeF spectrometer compared with the Raman spectrum of the peapod sample (full line spectrum). The Raman active $A_g$ and $H_g$ modes are marked with a star and a cross symbol, respectively. Note that the Raman spectrum is plotted on a logarithmic scale for the $y$ axis.

Figure 2

Generalized density of states of the peapod sample measured on the IN4C spectrometer at 10 K (a), 150 K (b), 300 K (c), and the one calculated using the model developed in the text (d). The GDOS of a pure ${\mathrm{C}}_{60}$ sample measured at 10 K (e) is also shown for comparison. Inset: the GDOS calculated for a NPP model (squares and triangles) and for a SWNT model (labeled “SWNT,” full line). The GDOS were folded with a Gaussian function (2 meV FWHM) to account for the instrument resolution. The curve with triangles symbols has its part originating from the ${\mathrm{C}}_{60}$ vibrations further folded with a Lorentzian having a FWHM of 6 meV to mimick the effect of the ${\mathrm{C}}_{60}$ rotations (see text).

Figure 3

Bottom right: the scattering function $S(Q,\omega )$ measured for the NPP sample at 280 K. Intensity is given by the classical thermal color scale. The intense elastic line centered at 0 meV is saturating the image (dark horizontal line). (a) and (b) Temperature dependence of the NPP susceptibility ${\omega }^{-1}{\chi }^{\prime \prime }(Q,\omega )$ ($\mathrm{\text{triangles}}=200\mathrm{K}$; $\mathrm{\text{circles}}=100\mathrm{K}$; $\mathrm{\text{squares}}=50\mathrm{K}$) measured at two wave vector transfers (a) $Q=1.8{\AA }^{-1}$; (b) $Q=5.4{\AA }^{-1}$). The susceptibility of “bulk” ${\mathrm{C}}_{60}$ is also drawn in (b) (bottom spectrum line, $T=200\mathrm{K}$) showing the librations peaks at $\sim \pm 2.5\mathrm{meV}$. (c) Integrated intensity of the quasielastic signal measured at 280 K (squares) and calculated for a free rotation model of the ${\mathrm{C}}_{60}$ (full line) and for 1D rotation models in the pentagonal orientation (long dashes) and the standard orientation (dots).