Phase field crystal model for patchy colloids

该项目的目标是开发和应用斑片状胶体的平均场理论。斑块状胶体是溶液中微米大小的颗粒，其表面装饰有斑块，可以吸引邻近的斑块状胶体。因此，期望通过自组装可以实现各种不同的周期甚至非周期相。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性对称粒子组成的液晶的静态和动态相场模型驱动的。因此，自由能将取决于与密度场相关的阶参数和一个附加的复阶参数，该参数给出了粒子的大小和方向。在第一步中，对称性被用来构造二维的自由能展开。稍后，我们的模型将与适当的经典密度泛函方法得到的展开有关。在项目的最后，我们想把我们的考虑扩展到三维系统。相是通过最小化自由能来确定的。我们期望找到复杂的相，其中密度的结构和方向场的结构不一定要重合。此外，即使是非周期结构也可能具有独特的附加自由度。所有主要结果将通过蒙特卡罗模拟对静态计算进行验证，并通过布朗动力学模拟对动态现象进行验证。我们的项目不仅将揭示斑块胶体的复杂相行为，而且还将深入了解复杂结构如何在一般情况下稳定：例如，在金属系统的情况下，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好特定的键角。当胶体被认为是金属的模型系统时，迄今为止研究的通常是多长度尺度的各向同性相互作用。我们的研究结果将提高我们对结合角度作为一种替代成分如何影响稳定性、静态性能以及复杂结构生长过程的认识。

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.