分子机器中环状分子热膨胀性质的理论研究

Theoretical Study on Thermal Expansions of Cyclic Molecules in Molecular Machines

摘要: 运用晶格动力学理论推导了分子机器中环状分子的原子间距热膨胀和热膨胀系数公式，并在此基础上进行了数值计算。数值计算结果表明，在低温下，当短的环状分子的长度增加时，其原子间距热膨胀快速减小而热膨胀系数快速增加，并分别快速趋近于无限长的环状分子的原子间距热膨胀及热膨胀系数，即短环状分子热膨胀性质呈现明显的尺寸效应；随温度升高，环状分子的热膨胀性质的尺寸效应明显减弱，直至在高温极限下消失。因此必须考虑低温下短环状分子的热膨胀性质的尺寸效应。

Abstract: The formulas for thermal expansions of interatomic distances and thermal expansion coefficients of cyclic molecules in molecular machines were derived based on the lattice dynamics, and then the numerical calculations were carried out. The numerical results show that at the low temperature, the thermal expansions of interatomic distances in short cyclic molecules increase and thermal expansion coefficients of short cyclic molecules decrease rapidly, and they tend to these values of cyclic molecules with infinite lengths respectively when the lengths of cyclic molecules increase, therefore there are size effects of the thermal expansion properties in short cyclic molecules; the size effects of thermal expansion properties in cyclic molecules are weakened obviously when temperature increases and almost disappear at high temperature. It is concluded that the size effects of thermal expansion properties in short cyclic molecules of molecular machines must be considered at low temperature.