Contributions of different degrees of freedom to thermal transport in the ${\mathrm{C}}_{60}$ molecular crystal

Three models of the ${\mathrm{C}}_{60}$ molecular crystal are studied using molecular dynamics simulations to resolve the roles played by intermolecular and intramolecular degrees of freedom (DOF) in its structural, mechanical, and thermal properties at temperatures between 35 and 400 K. In the full DOF model, all DOF are active. In the rigid body model, the intramolecular DOF are frozen, such that only center of mass (COM) translations and molecular rotations/librations are active. In the point mass model, the molecule is replaced by a point mass, such that only COM translations are active. The zero-pressure lattice constants and bulk moduli predicted from the three models fall within ranges of 0.15 and 20%. The thermal conductivity of the point mass model is the largest across the temperature range, showing a crystal-like temperature dependence (i.e., it decreases with increasing temperature) due to the presence of phonon modes associated with the COM translations. The rigid body model thermal conductivity is the smallest and follows two distinct regimes. It is crystal-like at low temperatures and becomes temperature invariant at high temperatures. The latter is typical of the behavior of an amorphous material. By calculating the rotational diffusion coefficient, the transition between the two regimes is found to occur at the temperature where the molecules begin to rotate freely. Above this temperature, phonons related to COM translations are scattered by the rotational DOF. The full DOF model thermal conductivity is larger than that of the rigid body model, indicating that intramolecular DOF contribute to thermal transport.

Figure 1

Our three models for the ${\mathrm{C}}_{60}$ molecule each have a different number of DOF. The full DOF has 180, the rigid body has six, and the point mass has three.

Figure 2

Effective potential energy and force for the point mass model.

Figure 3

(a) Lattice constants of the full DOF and point mass models plotted as a function of temperature along with experimental data [55]. (b) Bulk moduli of the three MD models and from experiments [56, 57] plotted as a function of temperature. (c) Rotational diffusion coefficient of the full DOF and rigid body models plotted as a function of temperature. The vertical dot-dashed line indicates a temperature of 100 K. The dashed lines in (b) and (c) are to guide the eye.

Figure 4

(a) Integration of the HCACF (i.e., thermal conductivity) for the three ${\mathrm{C}}_{60}$ models at a temperature of 300 K. (b) HCACF for the full DOF model over a shorter time range. $k_{\mathrm{short}}$ and $k_{\mathrm{long}}$ can be distinguished.

Figure 5

(a) Thermal conductivity of the three ${\mathrm{C}}_{60}$ models plotted as a function of temperature. (b) Full DOF model thermal conductivity decomposition into $k_{\mathrm{short}}$ and $k_{\mathrm{long}}$ and comparison with the rigid body model. The error bars are smaller than the marker size. The vertical dash-dot line denotes a temperature of 100 K.