Colloidal Mikado: Self-motion of a stiff slender rod in a maze of linelike obstacles

高度细长的微米和亚微米尺寸的物体的强受阻运输是从纯理论的角度以及从食品工业中的乳液、病毒的稠密溶液到生物网络的复杂粘弹性响应的各种应用的基本兴趣。由于与溶剂的流体动力学耦合，溶液中的针状物体如纤维、生物丝或纳米管的自由运动已经是各向异性的，然而，沿着和垂直于轴的扩散比永远不会超过2。相反，在稠密的针状液体中，单个棒状物体的运动几乎完全沿着其轴，这意味着各向异性可以变得任意大。棒的强相互作用引起了独特的复杂的动力学的解决方案，其特征在于由一个明显的旋转-平移耦合。本项目的目标是发展一个完整的理论表征的细长杆的高纵横比的自动力学在半细长悬浮杆。输运的统计特性将根据广义货车霍韦相关函数来表征，即假设其初始位置和方向已知，则杆在规定的滞后时间内重新定向到新方向时已经行进了一定距离的概率分布。从这个条件概率可以计算所有的两次相关函数，如均方位移，均四次位移，取向相关函数，或中间散射函数。该理论将基于有效介质方法，其中针在均匀介质中移动，但周围针的存在引起该介质的特殊材料性质。理论预测将通过大量的计算机模拟来验证，这两种模拟都是针对简化模型，其中只允许示踪剂移动，以及针对针液体，其中所有粒子都被平等对待。我们相信，这种理论进步和计算机模拟研究相结合的方法将有助于理解更复杂的传输现象发生在悬浮丝或网络。

Strongly hindered transport of highly elongated micron- and submicron-sized objects is of fundamental interest both from a purely theoretical point of view as well for various applications ranging from emulsions in the food industry, dense solutions of viruses to the complex viscoelastic response of biological networks. Already the free motion of needle-like objects such as fibers, biofilaments, or nanotubes in solution is anisotropic due to hydrodynamic coupling to the solvent, however the ratio of the diffusion along and perpendicular to the axis can never exceed the value of 2. In contrast in dense needle liquids, the motion of a single rodlike objects is almost entirely along its axis implying that anisotropies can become arbitrarily large. The strong mutual interactions of the rods give rise to peculiar complex dynamics of the solution characterized by a pronounced rotation-translation coupling. The goal of the project is to delevelop a complete theoretical characterization of the selfdynamics of slender rod of high aspect ratio in a semidilute suspension of rods. The statistical properties of transport will be characterized in terms of a generalized van Hove correlation function, i.e. the probability distribution that the rod has travelled a certain distance while reorienting to a new direction in a prescribed lagtime, provided its initial position and orientation was known. From this conditional probability all two-time correlation functions such as the mean-square displacements, mean-quartic displacements, the orientational correlation function, or the intermediate scattering functions can calculated. The theory will be based on an effective medium approach, where the needle moves in a homogeneous medium, yet the presence of the surrounding needles gives rise to peculiar material properties of this medium. The theoretical predictions will be validated by extensive computer simulations both for a simplified model, where only the tracer is allowed to move, as well as for a liquid of needles, where all particles are treated on equal footing. We believe that such a combined approach of theoretical advancement and computer simulation study will be useful to understand even more complex transport phenomena occuring in suspension of filaments or networks.