纳米管力学ppt.ppt

* * * * * * * * * Buckling – Multi-Walled Nanotube Being sandwiched between the outer and inner layer, when the multi-three-wall carbon nanotube starts to buckle, the atoms at the middle layer will have more nearest-neighbours than those of the outer and inner layer. This causes the reformation of more chemical bonds from sp2 to sp3 configuration Buckling – Multi-Walled Nanotube A larger increase in the empirical bond order function and consequently the binding energy for the middle layer. And hence the middle layer has the highest strain energy per atom for each layer after buckling. Buckling – Multi-Walled Nanotube Being a layer with wider diameter of the multi-three-wall carbon nanotube, the first layer has the highest bucking load at about 1.2 x 10-27 N However, it also tends to buckle faintly earlier than the other two layers after a displacement of 5.8??. Buckling – Multi-Walled Nanotube The multi-four-wall nanotube buckles first even though it has the highest buckling load at 3.2 x 10-27 ?N. The buckling load decreases as the number of layers in a multi-wall nanotube increase. Hence the more layers a nanotube has, the higher buckling load it has although its critical strain will be lower. Continuum model continuum cylindrical shell van der Waals interaction Elastic cylindrical shell theory A multi-walled CNT consists of two or more single CNTs of radius, thickness h, and modulus of elasticity E, which can be modelled as a multi-layer cylindrical shell. The interaction between layers are described by the van der Waals force. RI RO vdW forces h Nx Nx L The governing equations of a circular cylindrical shell is: where Expressions of vdW interaction: To model vdW interaction that exists between any two layers of multi-walled CNTs, the Lennard-Jones pair potential: The vdW force F is obtained from taking the derivative of the Lennard-Jones pair potential The pressure due to the vdW interaction between layers, p, is expressed as where Pre-buc