分子動力學模擬應用於聚乙烯之線性黏彈性質預測與非線性行為探討

The Prediction of Linear Viscoelasticity of Polyethylene and the Investigation of Nonlinear Behavior via Molecular Dynamic Simulation

王鎮杰(Chen-Chieh Wang)

指導教授 ： 張榮語

國立清華大學/工學院/化學工程學系/博士(2012年)

摘要

本研究利用分子動力學(molecular dynamics, MD)模擬、結合Rouse理論和蛇行(reptation)理論來預測線型高分子的線性黏彈性質。利用MD模擬來研究極小時間與空間尺度的行為。由於MD目前於可接受的計算時間內只能模擬分子量較小之高分子。因此我們將嘗試使用分子流變學中的理論將分子量小的MD計算結果，轉化成高分子量的參數，並配合Rouse理論、與蛇行理論來預測高分子量材料於大尺度的黏彈性質，並且加入了雙蛇行(double reptation)理論來描述分子量分佈的效應，理論預測高分子量的聚乙烯結果與實驗值有很好的吻合度。
本研究也利用MD計算來研究高分子薄膜系統奈米尺度的特殊現象，以簡諧式剪切流場(oscillatory shear)為研究例題，探討薄膜的表面滑動以及非線性黏彈行為，本研究並利用富利葉轉換(Fourier transform)來分析非線性行為、同時利用Lissajous曲線來研究非線性黏彈行為，我們發現奇數項的富利葉級數與MD模擬結果有很好的吻合度。同時利用MD計算分子的形態參數(分子排向性)與勢能變化(包含凡得瓦爾、鍵結拉伸、扭轉及鍵角等能量)，來研究微觀分子結構的變化與巨觀黏彈行為的關聯性。同時我們發現薄膜於高剪切頻率時將受到shear wave propagation的影響。經由不同頻率下的模擬發現黏彈性的線性範圍會隨著頻率增加而變小，本研究引入應力分解法解析彈性與黏性對總應力的貢獻，藉此分析我們找出線性範圍隨著頻率改變而變化的原因。

關鍵字

分子動力學模擬 ； 奈米薄膜 ； 分子流變學 ； 蛇行理論 ； 非線性黏彈

並列摘要

In this study, we combine molecular dynamics (MD) simulation and molecular theory such as Rouse and reptation theory to develop a method for predicting the viscoealstic properties. Reptation theory can be used to descrie phenomenon of entangled polymer and analyze it quantitatively. However, some material parameters in these models are difficult to obtain. MD simulation is based on atomic level which can simulate material properties with less assumption. But for large systems it is time consuming and inefficiency. Hence, we take advantage of the strong points of the two methods. i.e. we used MD simulation to calculate the material parameters in the reptation model then applied it to the reptation model to predict the viscoelastic properties of material. In this work, double reptation theory was also appled to describe the effect of molecular weight distribution. The prediction of high molecular weight polyethylene are agree with the experimental results by applying double reputation theory
MD simulation was also used to investigate the viscoelastic properties of short chain PE under oscillatory shear flow. Rheometric simulations of an ultra-thin molecular film are studied and compared with the results of a bulk simulation. Strain amplitude sweep tests at a fixed frequency show that strain thinning (the dynamic modulus monotonically decreases with increasing strain amplitude) exists at extreme strain for both bulk and thin film systems. Fourier analysis is performed to characterize the nonlinear behavior of the viscoelasticity. No even harmonic was found in our study even though wall slip occurs. Furthermore, we show that a Fourier series with odd harmonics can be used to perfectly describe the simulation results by plotting Lissajous loops. Shear wave propagation appears when the frequency is larger than a certain value. Moreover, the molecular orientation and molecular potential energies, including those for bonding potential, intra- and intermolecular van der Waals interactions are plotted against the strain amplitude to examine the changes in the microscopic structures with respect to the macroscopic thermodynamic states.
In addition, we found that the linear region is decreaseing with the increase of frequency. By stress decomposition the individual contribution of elastic or viscous effect is determined. Therefore, the origin of decrase of linear region could be investigated.

參考文獻

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