Self-Diffusion of Rodlike Viruses through Smectic Layers

Abstract

We report the direct visualization at the scale of single particles of mass transport between smectic layers, also called permeation, in a suspension of rod-like viruses. Self-diffusion takes place preferentially in the direction normal to the smectic layers, and occurs by quasi-quantized steps of one rod length. The diffusion rate corresponds with the rate calculated from the diffusion in the nematic state with a lamellar periodic ordering potential that is obtained experimentally.Since the pioneering work of Onsager on the entropy driven phase transition to a liquid crystalline state [1], the structure and the phase behavior of complex fluids containing anisotropic particles with hard core interactions has been a subject of considerable interest, both theoretically [2] and experimentally [3]. Understanding of the particle mobility in the different liquid crystalline phases is more recent [4]. In experiments various methods have been applied to obtain the ensemble averaged selfdiffusion coefficients in thermotropic [5] and amphiphilic [6] liquid crystals, block copolymer [7] and colloidal systems [8]. Only a few studies have been done where dynamical phenomena are probed at the scale of a single anisotropic particle: the Brownian motion of an isolated colloidal ellipsoid in confined geometry [9] and the selfdiffusion in a nematic phase formed by rod-like viruses [10] represent two recent examples. In the latter case, the diffusion parallel (D ) and perpendicular (D ⊥ ) to the average rod orientation (the director) has been measured, showing an increase of the ratio D /D ⊥ with particle concentration. Knowledge of the dynamics at the single particle level is fundamental for understanding the physics of mesophases with spatial order like the smectic (lamellar) phase of rod-like particles. In this mesophase the particle density is periodic in one dimension parallel to the long axis of the rods, while the interparticle correlations perpendicular to this axis are short-ranged (fluid-like order). For parallel diffusion to take place, the rods need to jump between adjacent smectic layers, overcoming an energy barrier related to the smectic order parameter [11]. This process of interlayer diffusion, or permeation, was first predicted by Helfrich [12]. In this Letter, we use video fluorescence microscopy to monitor the dynamics of individual labeled colloidal rods in the background of a smectic mesophase formed by identical but unlabeled rods. In this way we directly observe permeation of single rods in adjacent layers. As in the nematic phase, self-diffusion in a smectic phase is anisotropic: the diffusion through the smectic layers is shown here to be much faster than the diffusion within each liquid-like layer, i.e. D /D ⊥ ≫ 1, in contrast to thermotropic systems. Moreover, since the individual rod positions within the layer are monitored, the potential barrier for permeation is straightly determined for the first time. The permeation can then be . The layer spacing is L ≃ 0.9 µm. (b) Displacement of a given particle...

Entropy driven self-assembly of nonamphiphilic colloidal membranes

“…It is also of interest to compare the properties of colloidal membranes to single layers in a bulk smectic phase. For example, the dynamics of rods in these two structures is very different (18), and the concentration of the rods in the colloidal membranes is significantly smaller than the concentration of rods in a smectic layer formed at comparable ionic strength (19). In addition, light scattering experiments on the bulk smectic phase also indicate a very large bending rigidity in agreement with our real space analysis of isolated membranes (19).…”

Confinement Induced Splay-to-Bend Transition of Colloidal Rods

“…We use the fd -virus, which is an excellent model liquid crystal system for both static and dynamic behaviour [13][14][15][16]. The virus' contour length and diameter are 0.88 µm and 6.6 nm, respectively.…”

“…We introduce a new method for estimating elastic constants suitable to colloidal and biological systems, as an alternative to previous methods using magnetic fields [11] or light scattering [12]. Specifically, we determine the transition from a splay to a bend director field, with increasing wedge angle.We use the fd -virus, which is an excellent model liquid crystal system for both static and dynamic behaviour [13][14][15][16]. The virus' contour length and diameter are 0.88 µm and 6.6 nm, respectively.…”

Molecular Dynamics Simulations of One-, Two-, Three-dimensional Hopping Dynamics

“…Recently, experimental observation of hopping-like diffusion among smectic layers were reported in systems of viruses [4]. This stimulated investigations of hopping dynamics in other systems including thermotropic LC phases, which consists of much shorter molecules compared to viruses ( [1] and references therein).…”