Diffusion of spheres in crowded suspensions of rods

Abstract

Translational tracer diffusion of spherical macromolecules in crowded suspensions of rodlike colloids is investigated. Experiments are done using several kinds of spherical tracers in fd-virus suspensions. A wide range of size ratios L/2a of the length L of the rods and the diameter 2a of the tracer sphere is covered by combining several experimental methods: fluorescence correlation spectroscopy for small tracer spheres, dynamic light scattering for intermediate sized spheres, and video microscopy for large spheres. Fluorescence correlation spectroscopy is shown to measure long-time diffusion only for relatively small tracer spheres. Scaling of diffusion coefficients with a/ , predicted for static networks, is not found for our dynamical network of rods ͑with the mesh size of the network͒. Self-diffusion of tracer spheres in the dynamical network of freely suspended rods is thus fundamentally different as compared to cross-linked networks. A theory is developed for the rod-concentration dependence of the translational diffusion coefficient at low rod concentrations for freely suspended rods. The proposed theory is based on a variational solution of the appropriate Smoluchowski equation without hydrodynamic interactions. The theory can, in principle, be further developed to describe diffusion through dynamical networks at higher rod concentrations with the inclusion of hydrodynamic interactions. Quantitative agreement with the experiments is found for large tracer spheres, and qualitative agreement for smaller spheres. This is probably due to the increasing importance of hydrodynamic interactions as compared to direct interactions as the size of the tracer sphere decreases.

Self-diffusion of a sphere in an effective medium of rods

“…we represent I 0 as a sum of two integrals, with f (x) replaced by f (0) +f (1) x and f (x)−f (0) − f (1) x, respectively. The first integral is carried out explicitly and then the dominant terms for small ǫ are kept.…”

“…[1,2,3], this process has been used to determine the structure of such networks, in isotropic and nematic phases. A theoretical model of the screened hydrodynamic interactions between a tracer sphere and motionless rods has been constructed, by adding an effective friction force to the hydrodynamic equations.…”

“…In Refs. [1,2,3], diffusion of spheres in isotropic and nematic networks of rods has been modelled, based on the isotropic Debye-BuecheBrinkman equation. The model allows to use the measured values of the self-diffusion coefficients to determine the hydrodynamic screening length 1/κ of the network of rods.…”

“…[1,2,3], the medium velocity v and pressure p are described by the DebyeBüche-Brinkman equation [4,5],…”

“…In Refs. [1,2,3], these integrals have been carried out numerically for a specific value of Γ = L/ā. In this paper, we will carry out explicitly three of these integrations, giving much simpler expressions for the hydrodynamic coefficients.…”