以分子模擬分析奈米材料之溫度效應與熱性質

本研究經由修正模型的體積與能量，將溫度效應加入分子靜力學模擬當中，得以在各種勢能函數中求得模型在具有溫度時的力學性質，並與分子動力學模擬相互比對，修正的模擬結果在溫度400K以下可以正確地預測楊氏係數與帕松比，而在700K以下楊氏係數誤差小於7.5%、帕松比誤差小於1.3%，綜合這些結果，提出一個改良式分子靜力學模擬流程，與分子動力學模擬相較，可以快速的計算特定溫度下材料的彈性力學性質。本研究第二個主題為使用平衡式分子動力學模擬法計算奈米碳管的熱傳導係數，透過Einstein及Green-Kubo關係式的推導找出正確的Green-Kubo關係式，並利用已知訊號對正確的Green-Kubo關係式進行系統性的測試，觀察計算結果是否與Einstein關係式結果一致並收斂，了解各種訊號形式對計算結果的影響，並以此方法計算奈米碳管的熱傳導係數，發現奈米碳管在週期性長度為5至12nm之間仍具有尺寸效應。

關鍵字

溫度效應；改良式分子靜力學；分子動力學；奈米碳管；熱傳導係數； Green-Kubo關係式

並列摘要

This research was composed of two parts. First, we proposed a modified molecular statics method, which focused on incorporating effect into molecular static simulation by adjusting the volume of the atomic model. The volume justification was based on the thermal expansion coefficient and the potential energy at that temperature. The elasticity properties was calculated and compared with the ones using molecular dynamics simulation. The simulation result showed that Young’s modulus and Poisson’s ratio can be correctly predicted under temperature 400K, and the errors was less than 7.5% and 1.3% for Young’s modulus and Poisson’s ratio under temperature 700K. It is concluded that the proposed methodology is much more time efficient than molecular dynamics simulation and could apply to molecular statics simulation irrespective to the potential function. The second part is on the investigation of thermal conductivity of carbon nanotube using both Green-Kubo and Einstein relation. The correct expression of Green-Kubo relation was derived and examined using various given signals. Through the examination of different time signal, the result consistence between Green-Kubo and Einstein relation was checked and the effect of the signal pattern on the results was fully understood. The thermal conductivity of an infinite long carbon nanotube was calculated using equilibrium molecular dynamics simulation and correct Green-Kubo relation, it was found that the calculated thermal conductivity coefficient would depend on the periodic axial length within 5-12 nm.

並列關鍵字

temperature effect ； modified molecular static ； molecular dynamic ； nanotube ； thermal conductivity ； Green-Kubo relation

參考文獻

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[3] B.J. Alder and T.E. Wainwright, “Studies in Molecular Dynamics in General Method,” Journal of Chemical Physics, Vol. 31, pp. 459-466, 1959

[4] D. Chen, “Structural Modeling of Nanocrystalline Materials,” Computational Materials Science, Vol. 3, pp. 327-333, 1995

[5] P. Villain, P. Beauchamp, K.F. Badawi, P. Goudeau, P.O. Renault, “Atomistic Calculation of Size Effects on Elastic Coefficients in Nanometre-Sized Tungsten Layers and Wires,” Scripta Materialia, Vol. 50, pp. 1247–1251, 2004

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以分子模擬分析奈米材料之溫度效應與熱性質

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