探討石墨板與奈米碳管之機械性質

Abstract

本研究利用分子動力學理論分析( Molecular Mechanics Analytical Solution )與分子動力學( Molecular Dynamics )探討石墨板與奈米碳管的機械性質，碳-碳原子間的力場則引用AMBER勢能[1]描述之。在石墨板分析中，比較解析解與分子動力學兩種方法分析的結果。另外在分子動力學的模擬中，將石墨板施以平面方向的應力或應變來求得楊氏模數( Young’s modulus )以及浦松比(Poisson ratio)。分析結果顯示，利用解析解與分子動力學所求得之平面方向材料模數，均符合G=E/(1+2υ)等向材料之特性。出平面方向機械性質主要利用Lennard - Jones勢能[2]來探討剪力模數，對石墨板施以出平面方向剪應力，產生層與層間相對位移，而得到出平面方向剪力模數。比較平面方向與出平面方向之機械性質，發現出平面方向之機械性質均比平面方向機械性質要低許多。最後討論不同文獻所引用凡得瓦勢能的參數對於石墨板理論結果的影響。 奈米碳管的研究中，則利用分子動力學模擬並分析單壁碳管和雙壁碳管的楊氏模數及浦松比，研究鋸齒形(zigzag)與扶手椅形(armchair)兩種不同原子排列結構，以及不同管徑下對於機械性質之影響。發現在管徑較小時，鋸齒型(zigzag)碳管的楊氏模數會比扶手椅形(armchair)碳管要來的低；而在管徑較大時，則不會受到原子結構排列的影響。接著利用雙壁碳管內管與外管相互滑動時，所產生的層間原子作用力(atomstic interlayer force)，模擬方法分為兩種，(1) 將雙壁奈米碳管的內管拉出，並計算內管所需之合力。(2) 利用兩種不同平衡條件的雙壁碳管，使內外管相對旋轉後，計算碳管的內管在旋轉時所需之扭轉力，再觀察扭轉力與能量的變化。並藉由層間作用力的分析，解釋在奈米複合材料的應用中，雙壁奈米碳管層間應力傳遞的能力。

This study aims to investigate the mechanical properties of graphene and single/multi-walled carbon nanotubes(S/MWCNT) by analytical molecular structural mechanics and molecular dynamics (MD). The interatomic covalent bond of carbon-carbon is represented by AMBER force field which was employed in the analytical molecular mechanics and MD simulations as well, and the non-bonded interaction was described by Lennard-Jones potential. In particular, in-plane elastic properties of MD graphene model obtained from applying stress or strain were compared with analytical solutions. Results indicated that in-plane properties, predicted by analytical solution demonstrate a good agreement with MD solution. It was found that in-plane properties of graphene basically satisfied the relation, , and thus it can be regarded as a transverse isotropic material. Applying stress on the graphene model in the out-of-plane direction and calculating the relative displacement between graphene layers interacted by van der Waals potential, out-of-plane shear modulus could be derived. Because of the weak Lennard-Jones potential, the in-plane mechanical properties are higher than out-of-plane shear modulus. Since van der Waals potential may affect the mechanical properties of the graphene model, the effect of van der Waals on graphene mechanical properties was also investigated in the study. The axial Young’s modulus and Poisson ratio of S/DWCNTs is predicted by the MD method. In this article, elastic properties of unchiral (zigzag and armchair) S/DWCNTs of different diameters are studied and discussed. The results indicated that Young’s modulus of CNTs varies with the tube diameter and is affected by their helicity. With increasing the tube diameter, the Young’s modulus of both armchair and zigzag CNTs increases. The Young’s modulus of zigzag CNTs is lower than that of armchair at smaller diameters, however, at larger diameters there is no significant difference observed between armchair and Zigzag CNTs. The interlayer atomistic force of between the neighboring graphene layers in DWCNTs was examined by performing inner tube pullout and rotation tests with respective to the outer tube at stationary position. The pullout force corresponding to the pullout distance was measured in the pullout test and the torque of inner tube and interlayer VDW energy variation associated with the rotation angle was calculated in the rotational tests. This information is very essential for understanding the load transfer efficiency between the graphene layers in DWCNTs when they was considered an reinforcement in the nanocomposites.