分子机器中链状分子热传导性质的理论研究

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

摘要: 运用晶格动力学理论推导了分子机器中链状分子振动的能量通量公式，在此基础上再应用格林–久保公式推导了链状分子的热传导系数公式。由于计算链状分子的热传导系数时需要声子的谱线宽度，因此还推导了声子谱线宽度公式。数值计算结果表明，链状分子的热传导系数随着其长度的增加而增加，并且在其长度趋于无限时而趋于无限；等长的链状分子热传导系数与环状分子热传导系数有很大的差异。数值计算结果还表明，长链状分子的热传导系数主要来自于短波矢声子的贡献。

Abstract: The formula for energy flux of chain molecule vibrations in molecular machines was derived based on the lattice dynamics, and then the formula for heat conductivities of chain molecules was derived based on energy flux formula and Green-Kubo formula. In view of the fact that the linewidths of all phonons should be needed during the calculations of the heat conductivities of chain molecules, the formula for phonons’ linewidths was derived based on lattice dynamics and Green’s function theory. Finally the numerical calculations were carried out, and the results show that the heat conductivities of chain molecules increase and tend to infinity when their lengths increase and tend to infinity, and there is a big difference between the heat conductivities of a chain molecule and a cyclic molecule with the same length. The numerical results also show that the main contributions to the heat conductivities of long chain molecules were made by phonons with short wave vectors.