Phase field crystal model for patchy colloids

该项目的目标是开发和应用片状胶体的平均场理论。片状胶体是溶液中微米大小的颗粒，上面装饰着斑块，吸引着相邻的胶体斑块。因此，可以通过自组装来实现各种不同的周期甚至非周期的相位。我们想要确定这些相，研究它们的性质，并探索它们是如何生长的。我们的平均场方法是由已知的由轴对称或极对称的粒子组成的液晶的静态和动态相场模型所推动的。因此，自由能将取决于与密度场相关的序参数，以及给出粒子取向的大小和方向的附加复序参数。在第一步中，对称性考虑被用来构造二维自由能展开。稍后，我们的模型将与通过适当的经典密度泛函方法获得的展开有关。在项目的最后，我们希望将我们的考虑扩展到三维系统。通过最小化自由能来确定相。我们期望找到密度结构和定向场结构不一定重合的复杂相。此外，甚至可能出现具有独特附加自由度的非周期结构。所有主要结果都将通过静态计算的蒙特卡罗模拟和动态现象的布朗动力学模拟来验证。我们的项目不仅将揭示片状胶体的复杂相行为，而且将导致对如何从总体上稳定复杂结构的更深层次的洞察：例如，对于金属体系，原子之间的相互作用可能非常复杂，涉及多个长度尺度和偏爱特定的键角。当胶体被视为金属的模型体系时，到目前为止，通常已经研究了多个长度尺度的各向同性相互作用。我们的结果将提高我们对作为替代成分的键合角度如何影响复杂结构的稳定性、静态性质以及生长过程的了解。

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.