分子机器中环状分子热传导性质的理论研究

Theoretical Study on the Heat Conductivities of Cyclic Molecules in Molecular Machines

运用晶格动力学理论推导了分子机器中环状分子振动的能量通量公式,在此基础上再应用格林-久保公式推导了环状分子的热传导系数公式。由于环状分子的热传导系数与声子的谱线宽度有关,因此还推导了其声子谱线宽度公式。数值计算结果表明,环状分子的热传导系数随着环状分子长度的增加而增加,并且在环状分子无限增长时趋于无限,因此任何长度的环状分子其热传导性质都存在尺寸效应。数值计算结果还表明,长环状分子的热传导系数主要来自于短波矢声子的贡献。

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.