Phase field crystal model for patchy colloids

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The goal of the project is to develop and employ a mean field theory for patchy colloids. Patchy colloids are micrometer-sized particles in solution that are decorated with patches that attract patches of neighboring colloids. As a consequence, a huge variety of different periodic and even aperiodic phases is expected that can be achieved by self-assembly. We want to determine these phases, study their properties and explore how they grow.Our mean field approach is motivated by the known static and dynamical phase field models for liquid crystals consisting of particles with axial or polar symmetry. Therefore, the free energy will depend on an order parameter related to the density field and an additional complex order parameter that gives the magnitude as well as the direction of the orientation of the particles. In a first step symmetry considerations are used to construct the free energy expansion in two dimensions. Later our model will be related to expansions obtained by appropriate classical density functional approaches. At the end of the project we want to extend our considerations to three-dimensional systems.The phases are determined by minimizing the free energy. We expect to find complex phases where the structure of the density and that of the orientational field not necessarily have to coincide. Furthermore, even aperiodic structures might occur that possess unique additional degrees of freedom. All major results will be verified by Monte Carlo simulations in case of the static calculations and by Brownian dynamics simulations in case of dynamical phenomena.Our project will not only reveal the complex phase behavior of patchy colloid but also will lead to deeper insights into how complex structures can be stabilized in general: For example, in case of metallic systems, the interactions between atoms might be very complicated involving multiple length scales and preferring specific bond angles. When colloids are considered as model systems for metals, usually isotropic interactions with multiple lengths scales have been studied so far. Our results will improve our knowledge on how bindings angles as an alternative ingredient influences the stability, the static properties, as well as the growth processes of complex structures.