A modified molecular structural mechanics method, based on molecular mechanics and similar to the finite element method, was developed. The energy of a system was expressed by the force field functions of the molecula...A modified molecular structural mechanics method, based on molecular mechanics and similar to the finite element method, was developed. The energy of a system was expressed by the force field functions of the molecular mechanics. Under the small deformation assumption and by the principle of minimum potential energy, the system function was established. The properties of tension and bending of single-walled carbon nanotubes were analyzed. The Young＇s modulus is about 0.36 TPa nm, which agrees perfectly with the results of previous analysis by other researchers. It is found, for the first time, that the Young＇s moduli, for Zigzag nanotubes, are different from each other when the system energy was expressed as the sum of two or three individual energy terms in molecular mechanics. Whereas, the Young＇s moduli were the same for the Armchair nanotubes. It is found, when simulating the bending, that the deflections are closer to the theoretical ones, of the classical elasticity, when the diameter of the carbon nanotube increases.展开更多
Based on molecular mechanics and the deformation characteristics of the atomic lattice structure of graphene, a modifi ed molecular structure mechanics method was developed to improve the original one, that is, the se...Based on molecular mechanics and the deformation characteristics of the atomic lattice structure of graphene, a modifi ed molecular structure mechanics method was developed to improve the original one, that is, the semi-rigid connections were used to model the bond angle variations between the C-Cbonds in graphene. The simulated results show that the equivalent space frame model with semi-rigid connections for graphene proposed in this article is a simple, efficient, and accurate model to evaluate the equivalent elastic properties of graphene. Though the present computational model of the semi-rigid connected space frame is only applied to characterize the mechanical behaviors of the space lattices of graphene, it has more potential applications in the static and dynamic analyses of graphene and other nanomaterials.展开更多
Density functional theory （DFT） calculations, at the B3LYP/6-311G＊＊ level of theory, were performed to study the reaction mechanism and potenti4the potential energy surface of the studied reactions was investigate...Density functional theory （DFT） calculations, at the B3LYP/6-311G＊＊ level of theory, were performed to study the reaction mechanism and potenti4the potential energy surface of the studied reactions was investigated. Our calculation results show that [2 ＋ 2] and [4 ＋ 4] reactions are concerted and synchronous processes; while [4 ＋ 2] reactions proceed via a concerted but asynchronous way in general. [2 ＋ 2] and [4 ＋ 2] reactions of germabenzenes and 1-germana- phthalene proceed much more easily than the corresponding [4 ＋ 4] reaction, both thermo- dynamically and kinetically; while most [4 ＋ 2] paths have lower activation barrier than the corres- ponding [2 ＋ 2] ones. As the number of six-membered aromatic rings in reactant molecules becomes larger, [2 ＋ 2], [4 ＋ 2] and [4 ＋ 4] reactions become easier to proceed. The influence of substituents at the Ge atom of germabenzenes on the potential energy surface of [2 ＋ 2] and [4 ＋ 2] reactions correlates with their electronic properties and volume. Solvent effect is not crucial for the potential energy surfaces of the studied reactions.展开更多
文摘A modified molecular structural mechanics method, based on molecular mechanics and similar to the finite element method, was developed. The energy of a system was expressed by the force field functions of the molecular mechanics. Under the small deformation assumption and by the principle of minimum potential energy, the system function was established. The properties of tension and bending of single-walled carbon nanotubes were analyzed. The Young＇s modulus is about 0.36 TPa nm, which agrees perfectly with the results of previous analysis by other researchers. It is found, for the first time, that the Young＇s moduli, for Zigzag nanotubes, are different from each other when the system energy was expressed as the sum of two or three individual energy terms in molecular mechanics. Whereas, the Young＇s moduli were the same for the Armchair nanotubes. It is found, when simulating the bending, that the deflections are closer to the theoretical ones, of the classical elasticity, when the diameter of the carbon nanotube increases.
基金Funded by the Talent Foundation and Youth Foundation of Xi’an University of Architecture and Technology(Nos.DB12062 and QN1239)
文摘Based on molecular mechanics and the deformation characteristics of the atomic lattice structure of graphene, a modifi ed molecular structure mechanics method was developed to improve the original one, that is, the semi-rigid connections were used to model the bond angle variations between the C-Cbonds in graphene. The simulated results show that the equivalent space frame model with semi-rigid connections for graphene proposed in this article is a simple, efficient, and accurate model to evaluate the equivalent elastic properties of graphene. Though the present computational model of the semi-rigid connected space frame is only applied to characterize the mechanical behaviors of the space lattices of graphene, it has more potential applications in the static and dynamic analyses of graphene and other nanomaterials.
基金Henan Provincial Fundamental and Frontier Technological Research Program (No. 092300410207)
文摘Density functional theory （DFT） calculations, at the B3LYP/6-311G＊＊ level of theory, were performed to study the reaction mechanism and potenti4the potential energy surface of the studied reactions was investigated. Our calculation results show that [2 ＋ 2] and [4 ＋ 4] reactions are concerted and synchronous processes; while [4 ＋ 2] reactions proceed via a concerted but asynchronous way in general. [2 ＋ 2] and [4 ＋ 2] reactions of germabenzenes and 1-germana- phthalene proceed much more easily than the corresponding [4 ＋ 4] reaction, both thermo- dynamically and kinetically; while most [4 ＋ 2] paths have lower activation barrier than the corres- ponding [2 ＋ 2] ones. As the number of six-membered aromatic rings in reactant molecules becomes larger, [2 ＋ 2], [4 ＋ 2] and [4 ＋ 4] reactions become easier to proceed. The influence of substituents at the Ge atom of germabenzenes on the potential energy surface of [2 ＋ 2] and [4 ＋ 2] reactions correlates with their electronic properties and volume. Solvent effect is not crucial for the potential energy surfaces of the studied reactions.
