掌性雙嵌段共聚高分子的密度泛函理論和數值模擬

Density Functional Theory and Numerical Simulations of Chiral Diblock Copolymer Melts

王世豪(Shih-Hao Wang)

指導教授 ： 陸駿逸

國立臺灣大學/理學院/物理研究所/博士(2013年)

https://doi.org/10.6342/NTU.2013.10670

摘要

在軟物質系統中，掌性及自組裝行為是兩種頗受注目的特性。包含掌性成分的兩親性共聚高分子是個可用來檢視掌性作用於自組裝結構的理想系統。近年來，在由掌性及非掌性兩嵌段所組成的掌性共聚高分子實驗系統中發現一個新穎的奈米螺旋結構相，本論文的主旨為發展一個理論方法來分析此有趣的系統。
論文的第一部分主要為建構一個適用於由掌性及非掌性雙嵌段所組成之掌性共聚高分子的密度泛函理論。我們分別引進了兩個序參數，一個為用來描述鏈段密度分佈的純量序參數，另一個則是用來描述掌性嵌段鏈結之局部指向的向量序參數。在此我們假設掌性作用力為成對存在於向量序參數之間的形式。藉由使用隨機相位近似法推導出自由能相對於以上序參數的展開二次項，我們確認了有序-無序相轉變的離相點。從此理論模型的安定性分析我們觀察到添加掌性作用力所造成的有序無序相轉換之偏移。
在論文的第二部分，我們引入自由能展開的高次項來進行一系列的數值模擬。藉由數值迭代的方法去找出自由能的局部極小值，我們檢視了六角圓柱相的掌性效應。在掌性作用力的存在下，我們獲得了相似前述實驗系統所發現的半穩態螺旋圓柱結構。同時也觀察到另一個類似此半穩態螺旋圓柱的鋸齒狀轉型結構。在切斷掌性作用力的條件下，此鋸齒和螺旋狀結構隨即消失。因此，我們了解上述掌性結構的驅動力來自於掌性作用力的效應。

關鍵字

掌性 ； 共聚高分子 ； 密度泛函理論

並列摘要

Chirality and self-assembly are two of the fascinating properties in the soft matter systems. The amphiphilic block copolymer with chiral components is an ideal system to examine the chirality effect on self-assembly structure. In recent years, a novel nanohelical phase was observed experimentally in chiral diblock copolymer system constituting both achiral and chiral blocks. The objective of this thesis was to develop a theoretical method to analyze the interesting system.
In the first part of this thesis, a density functional theory is developed for the chiral diblock copolymer composed of a chiral block and an achiral block. We introduce two order parameters, one is a scalar order parameter that describes the segment density distribution and the other is a vector order parameter that describes the local alignment of the bonds in the chiral block. We assume a pairwise chiral interaction between the vector order parameters. The random phase approximation is used to obtain the quadratic terms in the expansion of the free energy in terms of the order parameters, with which we identify the spinodal point for the order-disorder transition. From the stability analysis of this model we find that the additional chiral interaction shifts the order-disorder transition.
In the second part of this thesis, we introduce the higher-order terms into the expansion of the free energy to perform a series of numerical simulations. Using the numerical iterative method to find the local minima of the free energy, we examine the chiral effect on the hexagonal cylinder phase. In the presence of chiral interactions, we obtain a metastable helical cylinder structure, which is similar to the structure found in experimental system. Another similar metastable helical cylinder structure but with zigzag modulation is also observed. When the chiral interaction is switched off, the zigzag and helical structure disappears. Therefore, we understand that the chiral effect is the driving force for the formation of these chiral metastable structures.

並列關鍵字

chirality ； copolymer ； density functional theory

參考文獻

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