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

• Applicant: Professor Dr. Thomas Franosch
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: from 2012 to 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 218924699

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.

• DFG Programme: Research Grants
• International Connection: Austria