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

Abstract

Self-diffusion of a sphere in a network of rods is analyzed theoretically. Hydrodynamic interactions are taken into account according to the model of Dhont et al., under the assumption that κā << 1 andā/L << 1, where 1/κ is the network hydrodynamic screening length,ā = a + D/2, and a is the sphere radius, while D and L are the diameter and length of a rod, respectively. Simple expressions for the diffusion coefficients are derived and shown to be independent of L.

Transport of spherical colloids in layered phases of binary mixtures with rod-like particles

“…Some fruitful incursions into the transport properties of this limiting case, in which the spheres can essentially be considered to be a tracer, have been performed in previous studies. [25][26][27][28][29][30][31] On the other hand, at the highest molar fraction of spheres included in our study (x s ¼ 0.5), a lamellar phase is formed that is characterized by alternate layers of rods and spheres, and the uid presents novel features with respect to the pure rod uid. Several rod elongations are as well explored in order to evaluate the inuence of the layer thickness on the efficiency of the diffusion of the colloids across them.…”

“…On the one hand, at a low molar fraction of spheres (x s = 0.01) the study basically explores the diffusion of isolated spheres in the smectic fluid of rods. Some fruitful incursions into the transport properties of this limiting case, in which the spheres can essentially be considered to be a tracer, have been performed in previous studies [25][26][27][28][29][30][31]. On the other hand, at the highest molar fraction of spheres included in our study (x s = 0.5), a lamellar phase is formed that is characterized by alternate layers of rods and spheres, and the fluid presents novel features with respect to the pure rod fluid.…”

The structure of cellulose nanofibril networks at low concentrations and their stabilizing action on colloidal particles

“…One way of investigating the structure of such a network is by measuring the diffusion of spherical tracer particles in the network. Tracer diffusion in a matrix of rod-shaped particles has been studied both theoretically (Cichocki & Ekiel-Jeżewska, 2009;Guzowski et al, 2008;Philipse & Kluijtmans, 1999;Pryamitsyn & Ganesan, 2008a, 2008bSchmidt & Brader, 2003) and experimentally in systems of, for example, filamentous actin (Apgar et al, 2000;Jones & Luby-Phelps, 1996;Wong et al, 2004), viruses (Holmqvist et al, 2008;Kang et al, 2005;Kang et al, 2006;Kang et al, 2007), silica rods (Kluijtmans et al, 2000;Koenderink et al, 2000), and DNA (Mangenot et al, 2003). The diffusion is commonly interpreted using the Langevin-Rondelez approach (Langevin & Rondelez, 1978), which describes two dominating diffusion modes depending on the ratio of the tracer sphere diameter to the network mesh size (a/ξ) (Pryamitsyn & Ganesan, 2008a, 2008b.…”