Soft-matter labyrintine structures: Bicontinuous mesophases, capillary condensation and tomographic image analysis

采用纳米级迷宫几何构型作为空间结构的物理体系，如嵌段共聚物或脂类/表面活性剂自组装，具有重要的技术和生物学意义。此外，在迷宫内发生的物理过程，如多孔介质中的催化和毛细凝聚，受到这种限制的关键影响，是目前科学感兴趣的问题。对这些系统的物理描述依赖于对迷宫结构可能的几何特征的全面(但尚未完全开发)的理解。这个项目通过研究最近在两个特定系统中应用的中间表面(MS)的几何概念来促进这一理解。对于迷宫，MS是以通道为中心的曲面骨架，同时表示拓扑和几何体。首先，我们利用密度泛函理论中的自由能几何模型分析了具有高空间复杂性的受限几何结构中的流体相图。其次，我们研究了双连续中间相在脂类/表面活性剂或嵌段共聚体系中的自组装。基于前人对单分散体系的研究结果，我们对多分散体系进行了分析，以期为中间相组装找到更广泛的几何构型。第三，针对海量数据集，提出了一种噪声不敏感的并行MS算法。这将成为X射线、电子和纳米层析成像应用中结构识别的有效工具，远远超过通常使用的通道图。

Physical systems that adopt nanometre-scale labyrinthine geometries as their spatial structure, such as block-copolymer or lipid/surfactant self-assembly, are of technological and biological importance. Furthermore, physical processes that take place inside a labyrinth and are crucially influenced by that confinement, such as catalysis and capillary condensation in porous media, are of current interest to science. The physical description of these systems relies on a comprehensive (and not yet fully developed) understanding of the wealth of possible geometric features of labyrinthine structures. This project contributes to that understanding by investigating the recent geometric concept of medial surfaces (MS), applied in the context of two specific systems. For a labyrinth, the MS is a surface skeleton centered in the channels that represents both topology and geometry. First, we analyse the phase diagram of fluids in confined geometries with high spatial complexity using a geometric model with free energy derived from density functional theory. Second, we study self-assembly of bicontinuous mesophases in lipid/surfactant or block-copolymer systems. Based on previous results for monodisperse systems, we analyse polydisperse systems expecting to find a wider spectrum of geometries for mesophase assembly. Third, we develop a parallel noise-insensitive MS algorithm for massive data sets. This will constitute an efficient tool for structure-recognition in X-ray-, electron- and nano-tomography applications far exceeding the commonly used channel graphs.