分子動力學模擬聚乙烯分子鍊之熱傳

Abstract

本研究之目標在探討聚乙烯分子鍊之熱傳機制。之前的研究顯示聚乙烯在超拉伸之後形成之奈米纖維之熱傳導率大幅高於其塊材之值，其原因可能為在拉伸時造成晶格的重組，但確切的熱傳增強機制尚未被完全了解。本研究利用波茲曼傳輸方程式結合分子動力學模擬計算聚乙烯分子鍊熱傳導率。波茲曼傳輸方程式所需之聲子群速度、比熱和鬆弛時間則利用分子動力學模擬得到。本研究首先以晶格動力學分析分子軌跡得到聲子色散關係，再由此聲子色散關係求得聲子群速度與比熱，而聲子的鬆弛時間則由簡振模式的自相關函數得到，最後將這些物理量帶入波茲曼傳輸方程式而得到單根聚乙烯分子鍊之熱傳導率。 結果顯示聚乙烯分子鍊之熱傳導率隨長度增長而增加並趨近一定值，此值即被定義為無窮長聚乙烯分子鍊之熱傳導率。此外，較長之聚乙烯分子鍊之熱傳導率隨著溫度增加而到達一峰值，且在高溫區段隨溫度上升而下降。但在較短之聚乙烯分子鍊之熱傳導率隨溫度變化較不明顯。本研究所得之熱傳導率與單根低瑕疵聚乙烯纖維實驗相當吻合。此外，非平衡式分子動力學模擬由於採用古典統計方法，故在低溫下會高估聚乙烯分子鍊之熱傳導率。在室溫下，長聚乙烯分子鍊之熱傳導率可高達45 W/m-K，此值相較於塊材聚乙烯之熱傳導率(0.3~0.5 W/m-K)約提升了100倍，此提升主因是由於此單根聚乙烯分子鍊有較快的聲子群速度以及較長的聲子平均自由徑。

This study aims to investigate the heat transfer on polyethylene (PE) chains. Previous studies have shown that an ultra-drawn PE nanofiber has a thermal conductivity much larger than its bulk counterpart. The enhancement in the nanofiber was speculated as a result of lattice-reconstructing during the ultra-drawing process; however, the exact mechanism causing such enhancement has not been fully understood yet. In this work, thermal conductivity was determined using the Boltzmann transport equation (BTE), where the phonon group velocity, heat capacity and relaxation time were obtained from molecular dynamics (MD) simulations. The phonon group velocity and heat capacity in the chain were determined from the phonon dispersion relation derived from Lattice dynamics using trajectories from MD simulations. Meanwhile, the phonon relaxation time was found from the phonon normal mode autocorrelation function. These properties were adopted as inputs in BTE to determine the thermal conductivities of single PE chains. The thermal conductivity of PE chains increases with increasing chain length and saturates to a constant value. The constant value was taken as the thermal conductivity of an infinite PE chain. For longer chains, the thermal conductivity increases with increasing temperatures, reaches a maximum at a certain temperature and decreases with temperature afterwards. However, for shorter chains, the temperature dependence is not significant. The thermal conductivity for a chain with an infinite length from the BTE agrees well with the experimental result of a near ideal PE fibril. It is also found that the non-equilibrium molecular dynamics method over-predicts the thermal conductivity at low temperature as a result of the classical statistics in MD simulation. At room temperature, the thermal conductivity of the PE chain could be as high as 45 W/m-K, about 100 times that of the bulk PE (0.3~0.5 W/m-K). The enhancement is due to the higher group velocity and longer mean free path in the chain.