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

• Applicant: Privatdozent Gerd Elmar Schröder-Turk, Ph.D.
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: from 2007 to 2012
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 35696276

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.

• DFG Programme: Research Grants