Theoretical Study on the Heat Conductivities of Cyclic Molecules in Molecular Machines
Abstract: The formulas for energy flux of atomic vibrations and linewidths of phonons of cyclic molecules in molecular machines were derived based on the lattice dynamics, and then based on those formulas and Green-Kubo formula, the formula for heat conductivities of cyclic molecules was derived. Finally the numerical calculations were carried out. The numerical results show that the heat conductivity of a short cyclic molecule increases when its length increases and will tend to infinity when its length tends to infinity, so there is size effect of the heat conductivity in a cyclic molecule with any length. The numerical results also show that the main contributions to the heat conductivity of a long cyclic molecule are made by phonons with short wave vectors.
文章引用: 黄建平 , 唐 婧 (2017) 分子机器中环状分子热传导性质的理论研究。 现代物理， 7， 169-174. doi: 10.12677/MP.2017.75019
Carina, R.F., Dietrich-Buchecker, C. and Sauvage J.P. (2016) Molecular Composite Knots. Journal of the American Chemical Society, 118, 9110-9116.
Badjic, J.D., Ronconi, C.M., Stoddart, J.F., et al. (2015) Operating Molecular Elevators. Journal of the American Chemical Society, 128, 1489-1499.
Ruangsupapichat, N., Pollard, M.M., Harutyunyan, S.R., et al. (2011) Reversing the Direction in a Light-Driven Rotary Molecular Motor. Nature Chemistry, 3, 53-60.
Wu, G. and Dong, J. (2005) Anomalous Heat Conduction in a Carbon Nanowire: Molecular Dynamics Calculations. Physical Review B, 71, Article ID: 115410.
 李圣怡, 黄建平. 基于晶格动力学的纳米薄膜热特性研究[J]. 微纳电子技术, 2008, 45(5): 249-254.
 Bottger, H. (1983) Principles of the Theory of Lattice Dynamics. Physik-Verlag, Weinheim, 85-90.
Frizzera, W., Viliani, G., Montagna, M., et al. (1997) One-Dimensional Dynamics of Lattice Heat Transport. Journal of Physics: Condensed Matter, 9, 10867-10879.
Wang, J. and Li, B. (2004) Mode-Coupling Theory and Molecular Dynamics Simulation for Heat Conduction in a Chain with Transverse Motions. Physical Review E, 70, Article ID: 021204.
 Wilson, R.S. and Kim, S.K. (1962) Theory of Heat Conductivity of Anharmonic Crystals. Physical Review, 128, 4674-4677.
 Semwal, B.S. and Sharma, P.K. (1972) Heat Conductivity of an Anharmonic Crystal. Physical Review B, 5, 3909-3913.
 Maradudin, A.A. and Fein, A.E. (1973) Scattering of Neutrons by an Anharmonic Crystal. Physical Review B, 7, 2589-2608.
Hyzorek, K. and Tretiakov, K.V. (2016) Thermal Conductivity of Liquid Argon in Nanochannels from Molecular Dynamics Simulations. The Journal of Chemical Physics, 144, Article ID: 194507.