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...

We theoretically and experimentally study nematic liquid crystal equilibria within shallow rectangular wells. We model the wells within a two-dimensional Oseen-Frank framework, with strong tangent anchoring, and obtain explicit analytical expressions for the director fields and energies of the 'diagonal' and 'rotated' solutions reported in the literature. These expressions separate the leading-order defect energies from the bulk distortion energy for both families of solutions. The continuum Oseen-Frank study is complemented by a microscopic mean-field approach. We numerically minimize the mean-field functional, including the effects of weak anchoring, variable order and random initial conditions. In particular, these simulations suggest the existence of higher-energy metastable states with internal defects. We compare our theoretical results to experimental director profiles, obtained using two types of filamentous virus particles, wild-type fd-virus and a modified stiffer variant (Y21M), which display nematic ordering in rectangular chambers, as found by confocal scanning laser microscopy. We combine our analytical energy expressions with experimentally recorded frequencies of the different equilibrium states to obtain explicit estimates for the extrapolation length, defined to be the ratio of the nematic elastic constant to the anchoring coefficient, of the fd-virus.

According to the Stokes-Einstein-Debye (SED) relation, the rotational diffusion coefficient of a colloidal tracer sphere scales with the inverse of the solvent viscosity. Here we investigate the generalization of the SED relation to tracer diffusion in suspensions of neutral and charged colloidal host spheres. Rotational diffusion coefficients are measured with dynamic light scattering and phosphorescence spectroscopy, and calculated including two-and three-particle hydrodynamic interactions. We find that rotational tracer diffusion is always faster than predicted by the SED relation, except for large tracer/host size ratios l. In the case of neutral particles this observation is rationalized by introducing an apparent l-dependent slip boundary coefficient. For charged spheres at low ionic strength, large deviations from SED scaling are found due to the strongly hindered host sphere dynamics. Finally, we present some first experiments on tracer sphere diffusion in suspensions of host rods, showing that hydrodynamic hindrance by rods is much stronger than by spheres. We conclude by pointing to some interesting unresolved issues for future research. I IntroductionThe rotational diffusion coefficient of a single colloidal sphere with radius a T suspended in a solvent with shear viscosity Z 0 is given by the familiar Stokes-Einstein-Debye (SED) relationwith k B T the thermal energy and f r 0 the Stokesian friction factor. Eqn. (1) assumes that the particle is large enough for the solvent to behave as a structureless continuum with vanishing response time. Moreover, stick boundary conditions are assumed, i.e. the velocity of the fluid on the tracer surface equals that of the tracer. Eqn. (1) holds quantitatively not only for colloidal particles but,

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.

Diffusion and ionic conduction in liquids.Abstract. -We measure the self-diffusion of colloidal rod-like virus fd in an isotropic and nematic phase. A low volume fraction of viruses are labelled with a fluorescent dye and dissolved in a background of unlabelled rods. The trajectories of individual rods are visualized using fluorescence microscopy from which the diffusion constant is extracted. The diffusion parallel (D ) and perpendicular (D ⊥ ) to the nematic director is measured. The ratio (D /D ⊥ ) increases monotonically with increasing virus concentration. Crossing the isotropic-nematic phase boundary results in increase of D and decrease of D ⊥ when compared to the diffusion in the isotropic phase (D iso ).Introduction. -Suspensions of semi-flexible polymers exhibit a variety of dynamical phenomena, of great importance to both physics and biology, that are still only partially understood. Advances over the past decade include direct visual evidence for a reptation-like diffusion of individual polymers in a highly entangled isotropic solution and shape anisotropy of a single polymer [1][2][3][4]. If the concentration of the polymers is increased, a suspension undergoes a first order phase transition to a nematic phase, which has long range orientational order but no long range positional order. As a result of the broken orientational symmetry it is expected that the diffusion of polymers in the nematic liquid crystals will be drastically different from that in concentrated isotropic solutions. While the static phase behavior of semiflexible nematic polymers is well understood in terms of the Onsager theory and its extensions by Khoklov and Semenov [5,6], the dynamics of semi-flexible polymers in the nematic phase is much less explored [7].In this paper, we determine the concentration dependence of the anisotropic diffusion of semi-flexible viruses in a nematic phase and compare it to the diffusion in the isotropic phase. Experimentally, the only data on the translational diffusion of colloidal rods in the nematic phase was taken in a mixture of labelled and unlabelled polydysperse boehmite rods using fluorescence recovery after photobleaching (FRAP) [8]. Theoretically, molecular dynamics simulations were performed on hard spherocylinder and ellipsoidal systems from which the anisotropic diffusion data was extracted [9][10][11]. The anisotropic diffusion has also been studied in low molecular weight thermotropic liquid crystals using NMR spectroscopy or inelastic scattering of neutrons [12].

In this joint experimental-theoretical work we study hydrodynamic interaction effects in dense suspensions of charged colloidal spheres. Using x-ray photon correlation spectroscopy we have determined the hydrodynamic function Hq, for a varying range of electrosteric repulsion. We show that Hq can be quantitatively described by means of a novel Stokesian dynamics simulation method for charged Brownian spheres, and by a modification of a many-body theory developed originally by Beenakker and Mazur. Very importantly, we can explain the behavior of Hq for strongly correlated particles without resorting to the controversial concept of hydrodynamic screening, as was attempted in earlier work by Riese et al. [Phys. Rev. Lett. 85, 5460 (2000)]. DOI: 10.1103/PhysRevLett.96.138303 PACS numbers: 82.70.Dd, 83.10.Mj, 87.15.Vv Suspensions of colloidal particles undergoing Brownian motion in a low-molecular-weight solvent are ubiquitous in chemical industry, biology, food science, and in medical and cosmetic products. For polar solvents like water, the particles are usually charged. At long to intermediate distances these particles interact electrostatically by an exponentially screened Coulomb repulsion originating from the overlap of the neutralizing electric double layers. A considerable effort has been devoted over the past years to study the dynamics of colloidal model suspensions of charged spheres at the microscopic level [1,2]. The dynamics is determined by a subtle interplay of direct interactions and solvent-flow mediated hydrodynamic interaction (HI). The latter dynamic interaction plays a pivotal role not only in unconfined colloidal systems, but also in microfluidic devices where narrow wall confinements or channels are present [3], and in sedimenting dispersions of large nonBrownian particles [4]. HI in unconfined suspensions is very long ranged. It decays with interparticle distance r like 1=r. An account of HI effects in theoretical and computer simulation studies is quite challenging due to its many-body nature, which must be accounted for in nondilute suspensions.An important measure of the strength of HI with regard to short-time particle diffusion caused by local density gradients is given by the hydrodynamic function [2]which is the sum of a wave-number-independent self-part and a q-dependent distinct part. Here, D s is the short-time self-diffusion coefficient, and D 0 is the particle diffusion coefficient at infinite dilution. In the limit of large q, Hq reduces to D s =D 0 . Without HI, Hq 1 and any variation in Hq is a hallmark of HI. It has a direct physical meaning [5] as the (reduced) mean particle sedimentation velocity for a suspension subject to a weak periodic force field, collinear to the wave vector q, and oscillating like cosq r. Experimentally, Hq can be determined as a function of wave number through a combination of static and dynamic scattering experiments [6,7]. Experimental findings [6] for the Hq of highly charged colloidal spheres at low volume fractions (typically <0:05) are in e...

The interplay between shear band (SB) formation and boundary conditions (BC) is investigated in wormlike micellar systems (CPyCl-NaSal) using ultrasonic velocimetry coupled to standard rheology in Couette geometry. Time-resolved velocity profiles are recorded during transient strain-controlled experiments in smooth and sand-blasted geometries. For stick BC standard SB is observed, although depending on the degree of micellar entanglement temporal fluctuations are reported in the highly sheared band. For slip BC wall slip occurs only for shear rates larger than the start of the stress plateau. At low entanglement, SB formation is shifted by a constant ∆γ, while for more entangled systems SB constantly "nucleate and melt." Micellar orientation gradients at the walls may account for these original features.PACS numbers: 83.80.Qr, 83.50.Rp, During the past two decades, shear banding (SB), i.e. the shear-induced coexistence of macroscopic bands with widely different viscosities, has been evidenced in a large range of complex fluids [1]. Sheared dispersions of surfactant wormlike micelles have attracted considerable attention due to their practical use in industry, but also because they challenged the physicists to address a non-equilibrium problem with concepts from thermodynamics [1][2][3]. Indeed, rheological measurements show that the flow curve of shear-banding systems, i.e. the measured shear stress σ vs. the applied shear rateγ, presents a plateau at a well-defined shear stress σ over a given range of shear rates [4], very similar to the plateau in pressure as a function of overall concentration of a demixed system. As for equilibrium phase transitions, it has been suggested that the flow can be either metastable or unstable for SB formation, depending on the applied shear rate [2,[5][6][7]. The formation of two coexisting SB, bearing the local shear ratesγ 1 andγ 2 that mark respectively the lower and upper limits of the stress plateau, constitutes a pathway for the relaxation of the excess stress in the initially linear flow. Stress relaxation can, however, also occur through apparent wall slip. Slip phenomena are ubiquitous in polymers [8,9] and soft glassy materials [10]. Wall slip has also been reported in shearthinning wormlike micellar systems [11,12] but its connection with SB has been underexposed. Still, information on the interplay between wall slip and a flow instability like SB are essential for fully understanding the behavior of complex fluids.In this Letter, wall slip is shown to compete with SB formation by offering an alternative route for stress relaxation. We use tunable boundary conditions (BC) at the walls as an experimental tool to probe the effect of wall slip on the flow behavior of cetylpyridinium chloride/sodium salicylate (CPyCl-NaSal) micellar solutions at 6 and 10 wt. % in 0.5 M NaCl brine at 23 • C. We enforce "stick" BC by using a rough sand-blasted Plexiglas Couette cell and partial "slip" BC by using a smooth Plexiglas cell [13]. The competition between SB formation and wall s...

We present experimental evidence of an instability in the shear flow of transient networks formed by telechelic associative polymers. Velocimetry experiments show the formation of shear bands, following a complex pattern upon increasing the overall shear rate. The chaotic nature of the stress response in transient flow is indicative of spatiotemporal fluctuations of the banded structure. This is supported by time-resolved velocimetry measurements.