We treat the ballistic heat conduction of cup-stacked carbon nanofibers (CSCNF) by a nonequilibrium molecular dynamics simulation. The CSCNF consist of numerous tiny graphene cups linked in line by weak intermolecular forces. The simulation results show that the thermal conductivity varies with the fiber length in a power law fashion with an exponent as large as 0.7. The calculated phonon density of states revealed that a low frequency oscillation in the radial and axial directions dominates the heat conduction in CSCNF. The atomic motions indicate that these low frequency oscillations are quasi-one-dimensional (1D) where each cup moves axially like a rigid body and radially with a breathing motion. This quasi-1D oscillation occurs due to the unique structure of a CSCNF that resembles a 1D harmonic chain. Our investigations show that treating a CSCNF as a 1D chain with three-dimensional oscillations explains why this material has the highest ballistic phonon transport ever observed.
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