用于C-C共价键力能关系表征的等效C-C键合单元  

AN EQUIVALENT C-C BONDING ELEMENT FOR REPRESENTING THE FORCE-ENERGY RELATION OF CARBON-CARBON COVALENT BOND

作　　者：曾攀[1] 杜婧[1] 杨学贵[1] 

机构地区：[1]清华大学机械工程系先进成形制造教育部重点实验室,北京100084

出　　处：《固体力学学报》2007年第4期325-332,共8页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金(10172054)资助

摘　　要：基于Born-Oppenheimer近似的二次函数形式的势能关系,研究了C-C键沿键轴伸缩、在σ平面和π平面内旋转的力学表征.在原子的平衡位置附近和线弹性的范围内,得到了基于原子核位移表达的平衡关系.在定义一个C-C共价键上两个原子的6个位移自由度的基础上,构建了完整的等效C-C键合单元.当对构成晶形碳的C-C共价键的六环结构进行建模时,等效C-C键合单元方法能够反映出共价键中的键长、键角和键能这三大特征.通过对石墨片和C60分子振动的计算分析和实验比较,得到等效C-C键单元中的力常数,并讨论了力常数的变化状况.该文还对单壁碳纳米管的拉伸弹性模量进行了计算分析,取得较好的效果.等效C-C键合单元可以为碳材料的大规模分子力学计算提供一种实用方法.Based on the quadratic potential function of C-C bond from the Born-Oppenheimer approximation,the stretching along the bond axis and the rotating in the σ or π plane of C-C bond are analyzed. With the linearly elastic theory near the origin equilibrium position, the balance equations are expressed through the displacements of atomic nuclei. Based on the defined six degree of freedoms of two atoms on a C-C covalent bond, an equivalent C-C bonding element is constructed. The C-C bonding element can characterize the three properties of covalent bond： length, angle and energy, when it is used to model the hexagonal structure of crystal carbon. The force constants of C-C bonding element have been obtained through calculation and comparison with the experimental results of the graphite and C60 molecular vibration （Raman spectrum）. The tensile modulus of carbon nanotube is investigated by the C-C bonding element, and reasonable results have been obtained, which implies that the C-C bonding element can provide an effective method for large-scale calculations of molecular mechanics.

关 键 词：等效C-C键合单元 分子结构表征 力常数 石墨 碳纳米管 

分 类 号：O641.4[理学—物理化学]