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

采用纳米尺度的几何构型作为其空间结构的物理系统，例如嵌段共聚物或脂质/表面活性剂自组装，具有技术和生物学重要性。此外，发生在迷宫内部并受到这种限制的关键影响的物理过程，例如多孔介质中的催化和毛细冷凝，是当前科学的兴趣所在。这些系统的物理描述依赖于对可能的几何特征的丰富的全面（尚未完全开发）的理解。该项目有助于通过调查最近的几何概念的内侧表面（MS）的理解，在两个特定的系统中应用。对于迷宫来说，MS是以通道为中心的表面骨架，代表拓扑结构和几何结构。首先，我们分析了具有高空间复杂性的受限几何中的流体的相图，使用的几何模型与自由能来自密度泛函理论。第二，我们研究了在脂质/表面活性剂或嵌段共聚物体系中双连续中间相的自组装。基于以前的单分散体系的结果，我们分析了多分散体系，期望找到一个更广泛的中间相组装的几何形状。第三，我们开发了一个并行的噪声不敏感的MS算法的海量数据集。这将构成一个有效的工具，结构识别的X射线，电子和纳米层析成像应用远远超过常用的通道图。

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.