Highly rotational ${\mathrm{C}}_{60}$ dynamics inside single-walled carbon nanotubes: NMR observations

Rotational dynamics of ${\mathrm{C}}_{60}$ molecules composing a one-dimensional (1D) linear array inside single-walled carbon nanotubes have been investigated by ${}^{13}\mathrm{C}$ NMR in a temperature range from $4.2\text{to}300\mathrm{K}$. The temperature dependence of the NMR lineshape and spin-lattice relaxation time $\left(T_1\right)$ indicate that the encapsulated ${\mathrm{C}}_{60}$ molecules exhibit a quasi-free-rotation with correlation times of $5–10\mathrm{ps}$ at $300\mathrm{K}$. With decreasing temperature, the large amplitude molecular rotation continues to $30\mathrm{K}$ with an activation energy of $467\mathrm{K}$. It is suggested that the ${\mathrm{C}}_{60}$ linear array does not undergo an orientational phase transition, which is associated with its 1D nature. Furthermore, no evidence for the polymerization of ${\mathrm{C}}_{60}$ molecules is found from the ${}^{13}\mathrm{C}$ NMR line shape analysis.

Figure 1

Temperature evolution of ${}^{13}\mathrm{C}$ NMR spectrum for ${\mathrm{C}}_{60}$ molecules encapsulated inside SWCNTs. A calculated powder pattern line shape with CS tensor $({\delta }_{11},{\delta }_{22},{\delta }_{33})=(208,177,-8)\mathrm{ppm}$ is also displayed in the figure (cal. 1). The line shape is convoluted with a Gaussian function with a FWHM value of $70\mathrm{ppm}$. The line shape expected for the $[2+2]$ cycloadditive ${\mathrm{C}}_{60}$ dimers inside SWCNTs is displayed at the bottom of the figure (cal. 2). In this simulation, the signal intensity ratio of $s{p}^2$ and $s{p}^3$ carbons is 2:58 and the line shape from $s{p}^3$ carbon was assumed to be a Gaussian function with a peak at $70\mathrm{ppm}$ and FWHM value of $20\mathrm{ppm}$.

Figure 2

(a) ${}^{13}\mathrm{C}$ NMR spectrum observed at $77\mathrm{K}$. The motionally narrowed component (solid gray line) was deduced by subtracting the broad component (dotted gray line) from the measured spectrum (solid line). (b) A Lorentzian fit to the narrow spectral component at $77\mathrm{K}$. The narrow component (solid gray line) is well fitted by a Lorentzian function with a FWHM value of $35\mathrm{ppm}$ (thin solid line). (c) Simulated line shape for the uniaxial rotation. The motionally averaged line shape was calculated for the rotation along the twofold axis of the ${\mathrm{C}}_{60}$ molecule (thin dotted line) (see text for details). The line shape convoluted by a Lorentzian function with a FWHM value of $7\mathrm{ppm}$ is also displayed (thin solid line).

Figure 3

(Color online) Temperature and frequency dependence of ${}^{13}\mathrm{C}$ nuclear spin-lattice relaxation time $T_1$ of encapsulated ${\mathrm{C}}_{60}$ measured at $4.0\mathrm{T}$ (circles) and $9.4\mathrm{T}$ (squares). The solid and dotted lines represent the best fits to the $T_1$ data at 4.0 and $9.4\mathrm{T}$, respectively.

Figure 4

(Color online) Temperature dependence of rotational correlation time $\tau$ for ${\mathrm{C}}_{60}$ encapsulated inside SWCNTs. The solid line denotes $\tau ={\tau }_0\exp (⟨T_0⟩∕T)$ with ${\tau }_0=1.62\times {10}^{-12}\mathrm{s}$ and $⟨T_0⟩=467\mathrm{K}$. The shaded region in the inset shows the range $\tau ={\tau }_0\exp [(⟨T_0⟩\pm \beta )∕T]$ with $\beta =113\mathrm{K}$. In the figure, $\tau$ values for quasi-free-rotational phase and ratchet phase in the ${\mathrm{C}}_{60}$ bulk crystals (dotted line) and for the ratchet phase below $280\mathrm{K}$ in the ${\mathrm{C}}_{70}$ bulk crystals (dash-dotted line) are also displayed for comparison (Refs. 23, 24, 25, 29). The arrows are those estimated from the NMR spectral broadening (Refs. 23, 24, 29, 33).