以球諧函數展開分析共聚合高分子在溶劑軟性限制下的微胞曲面

Abstract

我們利用自洽平均場理論，探討高分子交替嵌段共聚物在溶劑軟性限制下，改變嵌段間的作用力 與交替鏈段的次數n如何影響微結構衍變，並以球諧函數的展開定量化分析微胞曲面的形狀。在交替嵌段系統中，隨著 的增加微胞內開始產生小尺寸的分離，形成一維的有序層狀排列。在溶劑逐漸進入層間緩衝嵌段間的不相容性時，也改變了微胞的形狀，微胞曲面上有溶劑聚集而形成的不規則凹陷。我們以球諧函數展開曲面方程式，能得知在微胞內未分離成層時，展開至二階球諧係數已足以近似曲面，此時曲面的形狀像是往一個維度延伸的橢圓球面。而我們感興趣的是當結構內形成層狀分離時，需展開至更高階的球諧係數來描述曲面開始上的層狀特徵。當溶劑進入層間的量變多時，曲面形狀更不規則，以較低階的球諧展開足以近似曲面。反之若溶劑在層間的量不多，曲面形狀較為平滑，則需用到更高階的球諧係數才能描述曲面上的些微凹陷。

We use self-consistent mean field theory to investigate changing Flory-Huggins parameter XBC and alternating block number(n) affect the structure under soft confinement by poor solvent, and analyze the micelles surface shape by spherical harmonics. In alternating block copolymer system, increase of XBC gives rise to one dimension ordered lamellar arrangement. The solvent will diffuse into the lamellar region to buffer repulsive force and cave in the surface. The second order spherical harmonics is sufficient to describe the surface shape when two blocks mixed in the micelle. Thus surface shape is similar to one dimension extended ellipsoids. What we are interesting is that the higher order spherical harmonic coefficient is needed when two block separated into lamellar structure inside the micelles. When more solvent molecular diffuse into the lamellar structure, the more irregular surface shape the micelles will be, and lower order spherical harmonics is enough to fit. The less solvent in lamellar structure the less cavity on the surface of micelles, and higher order spherical harmonics coefficient is necessary to describe the delicate cavity.