Collaborative Research: Numerical Simulation of the Morphosynthesis of Polycrystalline Biominerals

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Polycrystalline biominerals are thermodynamically stable crystal polymorphs of biogenic minerals featuring stacked layers of crystals with mineral bridges between adjacent layers. The unique crystal texture gives rise to specific material properties such as toughness, corrosion resistance, and temperature resistance, which makes these crystals highly attractive for optical nanostructures (photonic band gaps, diffraction gratings) and for special coatings (e.g., in semiconductor device technology). Therefore, many material scientists are currently trying to realize the synthesis of such biominerals. The aim of this project is to provide both a mathematical model for the crystallization process and algorithmic tools for numerical simulations in order to understand the mechanisms of the process, to enable the experimentalists to optimize their laboratory settings, and thus to pave the way for an industrially relevant production line.The morphosynthesis of polycrystalline biominerals follows a multistage crystallization process including a polymer-induced liquid-precursor (PILP) phase, the occurrence of spherulites due to nucleation, and the recrystallization of mosaic mesocrystal thin structures. The PILP phase consists of an aqueous solution of the biomineral and an anionic polymer mixed with ethanol and features a liquid-liquid phase separation in terms of polymer-rich PILP droplets in the liquid mixture. The mixing is taken care of by a surface acoustic waves (SAWs) manipulated fluid flow where the SAWs are generated by two tapered interdigital transducers operating in dual mode. The polycrystallization sets in with the formation of spherulites that spread across the substrate to form a uniform spherulitic thin film. Continuous cooling leads to a recrystallization of the spherulitic thin film into a mosaic polycrystalline thin structure. The liquid-liquid phase separation characterizing the PILP phase can be described by a coupled system consisting of the incompressible Navier-Stokes equations and a Cahn-Hilliard equation. For the numerical simulation, the project will use a splitting scheme based on an implicit discretization in time and C0 Interior Penalty Discontinuous Galerkin (C0-IPDG) methods for discretization in space with respect to simplicial triangulations of the computational domain. The research will study the convergence of the splitting method and realize space-time adaptivity by the goal oriented dual weighted approach. As a mathematical model for the polycrystallization the project investigates a phase field model consisting of the dynamic equations for the measure of local crystallinity, the concentration field for the biomineral, the orientation field, and a heat equation for the evolution of the temperature during the cooling process. The equation for the concentration field is a fourth order Cahn-Hilliard type equation. Again, discretizing implicitly in time and by C0-IPDG methods in space, the project will use a splitting method and dual weighted residuals for space-time adaptivity featuring a desired crystallinity at final time as the objective functional. A model validation will be based on experimental data provided by cooperating laboratories and a systematic parameter study will be performed to investigate the influence of various process parameters.