The free thermal vibration of single-walled carbon nanotubes (SWCNT) has shown the recurrence of the same motion state repeatedly. Recently, this nonlinearity is replicated in coarse-grained model with internal heat diffusion by Koh et al.\[PRB 2015, arXiv:1910.02880, 2019\], whose energy source is induced by the cross correlated momentum between bending and bond length energy. This internal heat diffusion, which is composed as second order partial differential of the momentum and which is incorporated as a part of the equation of motion, has shown the capability as new strategy as the thermostat in coarse grained model for SWCNT and single stranded DNA.

Another interesting aspect of this trial is that the modified equation of motion by heat diffusion with the bending strain, which is the fourth order of partial differential of displacement, is showing the characteristic of Fermi-Pasta-Ulam (FPU)-beta model, the reappearance of the initial condition in repetition. Although the phase of these differential orders is not exactly matched to the FPU-beta with another discrepancy that the internal heat diffusion incorporated in the equation of motion is supposed to be occurred in THz \[arXiv:1910.02880, 2019\] from the cross-correlation plots, the assumption that the internal heat diffusion is the one of the main causes of nonlinearity of the proposed material SWCNT with fixed boundary seems worthy for further considerations using configurational temperature, \[Pierangeli et al. PRX 8, 041017, 2018 and Liu, & He, PRE, 100, 2019\] to connects to its exceptional thermal conductivity of SWCNT which has been studied as FPU-beta model.

From this approach, quantitative study on the mode-mode interaction at THz will be introduced and the bounded condition between different types of momenta in the level of configurational temperature will be discussed. As the target system, the free thermal vibration at 300 K and nonequilibrium simulation of SWCNT are analyzed. Yet, proper description for cross correlation and its heat diffusion in free thermal vibration of SWCNT have not reached to the unknown principle of high thermal conductivity of SWCNT. Instead, the contour plot of the internal heat diffusion has shown that the rapid exchange rate of the energy level in internal heat diffusion can be one channel to make the thermal transport. The trend that those two different types of short wavelength modes are explained from the necessary condition for the conservative force in mechanics in macroscopic description. It is more quantitatively investigated and will be presented in this talk.


Role of Internal Heat Diffusion on the Nonlinear Dynamic Characteristic Recurrence in SWCNTS Free Thermal Vibration: FPU-Beta Model

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Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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