星狀共聚高分子溶液之自洽場理論

Abstract

近年來，可溶性塊狀共聚高分子自組裝而成的精緻結構形態受到廣泛的研究與討論，對於奈米材料的製備與應用開啟了一條新途徑。此種塊狀共聚物的雙親性質與一般生活中常見的界面活性劑非常相似，然而，塊狀共聚高分子的碳鏈長度卻是一般界面活性劑數百倍長，這使得塊狀共聚高分子將會比界面活性劑更適用於自洽平均場理論(self-consistent mean field theory ; SCFT)的計算；在本篇論文中，我們利用自洽平均場理論來計算並分析可溶性塊狀共聚高分子在不同的溶劑系統下的相行為。 本文的第一個部份利用典型的配分函數(partition function)推導出用於AnBm共聚高分子混合不同溶劑的自洽平均場理論。我們將Matsen在1994年發表的自洽平均場計算方案做延伸，此演算在當時是用於研究雙鏈段線性高分子在熔融狀態的相行為並利用光譜法來解配分函數，在本文中我們發表的演算法特別適用於計算多臂塊狀共聚物在加入溶劑之後的相行為。 在本文的第二個部份我們計算出ABm星狀共聚物在弱選擇性溶劑中的相行為。藉由改變B高分子的手臂數目以及溶劑對高分子之濃度，我們利用數值方法計算出ABm星狀共聚物之相圖並且找出其相變濃度；我們將主要探討溶劑濃度與高分子本身的結構對於ABm塊狀共聚高分子微結構所造成的影響，並且比較其與典型界面活性劑相行為的異同處；在此我們也試著建構出類似介面活性劑的臨界堆疊參數(critical packing parameter)來解釋星狀高分子之相行為；另外，我們亦發現高分子溶解度會隨著高分子手臂數目增加而上升。

Lyotropic block copolymers have become new approaches for preparing nano-materials with delicate, accessible self-assembled morphologies. Their amphiphilic property is very similar to surfactants’. However, the chain length of the polymers could be hundred times more than the surfactants. So that it is much easier to develop the self-consistent field theory (SCFT) to calculate the copolymer phase diagram than the surfactants. In this thesis, SCFT is employed to analyze the phase behavior of lyotropic star copolymers with different solvent systems. In the first part of this thesis, we present the theoretical derivation of the SCFT for AnBm copolymers with solvent from the full classical partition function of this system. We extend the recent SCFT scheme of Matsen, which was developed to study the polymer phase behavior of melts, to solve the partition function by spectral method. We present an algorithm for the SCFT of block copolymers within a specific class of multiple arms chain architecture. In the second part of this thesis, we calculate the common mesophases for the ABm star copolymers. Interestingly, we also find a new mesostructure for the ABm star copolymers. By changing the arm number of solvophilic B, we construct numerically the phase diagrams and try to locate the precision phase boundary between the lamellar, the hexagonal and the micelle phases. We discuss the microstructures of star copolymers, which are affected by the copolymer architecture, and the solvent concentration. We try to explain the results for phase transitions by the idea comes from the surfactant packing parameter. The ratio of the ABm copolymer volume to the cross-section of the B-head and the height of the copolymer is similar to the critical packing parameter of surfactants. We study the micelle melting in the dilute region and find that the single polymer solubility is increased as the arm number of B increases.