拓扑结构耦合液晶基元的高分子链构象及相变问题研究

We develope the self-consistent field theory (SCFT) for liquid crystalline polymers with complex chain architecture, based upon worm-like chain model. A universal model is developed for investigating such as comb-like polymers with liquid crystal mesogens by combining Maier-Saupe orientational interactions between rigid segments with local couplings for hinge effects. Furthermore, the local coupling effect between backbone and side chains and the connectivity of each side groups are all incorporated into the modified diffusion equation of the wormlike main chain. We will introduce real-space finite volume algorithm and the second order pseudospectral numerical method for solving the diffusion equation of the wormlike chain model. At the same time, density functional theory is modified to deal with the excluded volume of segments and thus more detailed chain properties and especially the chain rigidity in origin can be considered. This will will provide a guide to understanding the physical mechanism and essence of biological system and to design materials in desirable application prospects such as the fabrication of organic light emitting devices and high performance polymeric materials.

本项目基于蠕虫状链模型描述半刚性高分子链的构象，发展不同拓扑结构高分子中耦合液晶基元的场论方法。除了引入刚性链段之间的Maier-Saupe各向异性取向相互作用，还考虑表示主/侧链之间连接性的局部耦合作用，结合可以精确考虑链的几何拓扑结构的场论方法，发展蠕虫状链和刚棒高分子自洽场理论的普适模型。采用具有二阶精度的准谱数值解法求解蠕虫状链的构象微分方程，研究含液晶基元的梳型高分子如主/侧链液晶高分子体系的链构象统计及相转变问题。同时，借鉴密度泛函理论方法，引入链段之间的排除体积效应描述链构象，在现有自洽场理论的基础上考虑一些更为精细的链结构细节，以期进一步理解链刚性效应的本源。这些理论工作的开展，有助于深刻理解半刚性高分子体系（如生命体系及结晶高分子等）的链构象及相行为的物理本质及机理，对于制备具有特殊光电物理性能材料及增强高分子复合材料等具有重要指导意义。

本项目基于蠕虫状链模型描述半刚性高分子链的构象，发展了不同拓扑结构高分子中耦合液晶基元的场论方法。相比于易于数学表达的Gaussian链模型，由于增加了链段的取向自由度，求解蠕虫状链的构象微分方程要困难许多，我们通过采用三角网格化离散的单位球面描述链段的取向，直接在3D实空间用有限体积法数值求解了基于刚性链模型的自洽场理论方程，并且易于推广至复杂拓扑结构高分子链如侧链液晶及刚-柔多嵌段高分子等。同时，为了在现有广泛运用的自洽场理论基础上考虑更为细致的化学结构细节，引入密度泛函理论处理链段之间的体积排除效应来描述链构象，以空间拥挤效应显著的相互压缩的高分子刷和树枝状高分子体系为模型，分析了排除体积效应所致的链刚性，从而理解了链刚性产生的本源。这些理论工作的开展，有助于发展高分子结晶相关理论，对于制备光电材料及增强高分子复合材料等具有重要指导意义。

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