利用兩相熱力學模型與分子動力學模擬估算純物質之絕對熵與自由能

本研究主要以分子動力學模擬並以兩相熱力學模型（Two-Phase Thermodynamic Model; 2PT）分析計算估算純物質的熱力學性質如自由能、絕對熵、系統內能、熱容等。2PT方法為一高效率的估算方式，僅需相當短的模擬取樣時間（20 ps）即可得到物性的收斂值。2PT方法透過對Density of State之加權積分取得熱力學性質，其加權函數可由統計力學理論推導。另外，透過Density of State，可以用來分析流體或固體的動力學行為，例如解釋分子運動模式與計算擴散係數。在本研究中我們估算水與二氧化碳氣液平衡的相邊界，與在該條件下對應的熱力學性質如自由能與絕對熵，計算溫度範圍涵蓋三相點至臨界點。從計算結果來看，2PT方法具有相當高的準確度，與其他較嚴謹的模擬方法如Free-Energy Perturbation相當，由此可以認定2PT方法為一相當成熟的理論計算方式，並具有應用於不同領域的潛力。

關鍵字

能態密度；熵；自由能；相圖；分子動力學模擬

並列摘要

Presented in this thesis is a novel approach for calculating the free energy and absolute entropy of pure substances from molecular dynamic (MD) simulations based on the two-phase thermodynamic (2PT) method. This efficient method provides converged properties from a very short (20 ps) MD trajectory. The 2PT method determines thermodynamic properties by weighed integral of the density of state (velocity spectrum); the applied weighing functions are obtained from the statistical mechanical theories. The contribution of the density of state from its components, which are associated with their corresponding molecular motions, allows for the evaluation of the dynamical behaviors of fluids or solids. In this study, the accuracy of 2PT thermodynamic properties (absolute entropy, internal energy, heat capacity, etc.) is investigated from the triple point to the critical point along the vapor-liquid coexisting curve for water and carbon dioxide. Also presented are the prediction of coexistence curves of water and carbon dioxide through free energy equalities. Our results show that the 2PT properties are highly accurate, with its results comparable to other rigorous methods, such as the free energy perturbation method. It can be concluded that 2PT method is a matured way that is applicable to various fields and more complicated systems in the near future.

並列關鍵字

Density of State ； Entropy ； Free Energy ； Phase Diagram ； Molecular Dynamics Simulations

參考文獻

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利用兩相熱力學模型與分子動力學模擬估算純物質之絕對熵與自由能

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