Flow behavior of colloidal rodlike viruses in the nematic phase

Multiscale study of the chiral self-assembly of cellulose nanocrystals during the frontal ultrafiltration process

The structural organization of cellulose nanocrystal (CNC) suspensions at the membrane surface during frontal ultrafiltration has been characterized, for the first time, at the nano- and microscale by in situ small-angle X-ray and light scattering (SAXS and SALS, respectively). During filtration, the particles assembled at the membrane surface and formed the so-called concentration polarization layer (CPL), which contains CNCs arranged in a chiral nematic (cholesteric) helicoidal structure, with the long axis of the CNCs oriented parallel to the membrane surface, and the helical axis of the cholesteric structure oriented perpendicular to the membrane surface. The self-organization of CNCs in the form of oriented cholesteric structures was further characterized by a pitch gradient in the CPL. The structure of the CPL was also investigated upon release of the transmembrane pressure. SAXS data revealed a relaxation process associated with a diffusion of the CNCs from the membrane surface towards the bulk, while SALS measurements revealed a re-organization of the cholesteric phase that was preserved all along the deposit. The preservation of the observed structure after 14 days of continuous filtration followed by air-drying was confirmed using scanning electron microscopy and wide-angle X-ray diffraction, demonstrating the feasibility of the process scale-up.

Structural Color from Cellulose Nanocrystals or Chitin Nanocrystals: Self-Assembly, Optics, and Applications

Widespread concerns over the impact of human activity on the environment have resulted in a desire to replace artificial functional materials with naturally derived alternatives. As such, polysaccharides are drawing increasing attention due to offering a renewable, biodegradable, and biocompatible feedstock for functional nanomaterials. In particular, nanocrystals of cellulose and chitin have emerged as versatile and sustainable building blocks for diverse applications, ranging from mechanical reinforcement to structural coloration. Much of this interest arises from the tendency of these colloidally stable nanoparticles to self-organize in water into a lyotropic cholesteric liquid crystal, which can be readily manipulated in terms of its periodicity, structure, and geometry. Importantly, this helicoidal ordering can be retained into the solid-state, offering an accessible route to complex nanostructured films, coatings, and particles. In this review, the process of forming iridescent, structurally colored films from suspensions of cellulose nanocrystals (CNCs) is summarized and the mechanisms underlying the chemical and physical phenomena at each stage in the process explored. Analogy is then drawn with chitin nanocrystals (ChNCs), allowing for key differences to be critically assessed and strategies toward structural coloration to be presented. Importantly, the progress toward translating this technology from academia to industry is summarized, with unresolved scientific and technical questions put forward as challenges to the community.

How Softness Matters in Soft Nanogels and Nanogel Assemblies

Softness plays a key role in determining the macroscopic properties of colloidal systems, from synthetic nanogels to biological macromolecules, from viruses to star polymers. However, we are missing a way to quantify what the term "softness" means in nanoscience. Having quantitative parameters is fundamental to compare different systems and understand what the consequences of softness on the macroscopic properties are. Here, we propose different quantities that can be measured using scattering methods and microscopy experiments. On the basis of these quantities, we review the recent literature on micro- and nanogels, i.e. cross-linked polymer networks swollen in water, a widely used model system for soft colloids. Applying our criteria, we address the question what makes a nanomaterial soft? We discuss and introduce general criteria to quantify the different definitions of softness for an individual compressible colloid. This is done in terms of the energetic cost associated with the deformation and the capability of the colloid to isotropically deswell. Then, concentrated solutions of soft colloids are considered. New definitions of softness and new parameters, which depend on the particle-to-particle interactions, are introduced in terms of faceting and interpenetration. The influence of the different synthetic routes on the softness of nanogels is discussed. Concentrated solutions of nanogels are considered and we review the recent results in the literature concerning the phase behavior and flow properties of nanogels both in three and two dimensions, in the light of the different parameters we defined. The aim of this review is to look at the results on micro- and nanogels in a more quantitative way that allow us to explain the reported properties in terms of differences in colloidal softness. Furthermore, this review can give researchers dealing with soft colloids quantitative methods to define unambiguously which softness matters in their compound.

A small-volume microcapillary rheometer

We demonstrate a capillary device used to measure the shear rate-dependent viscosity of microliter scale volumes. Liquid samples are driven pneumatically through a microcapillary and partially fill a larger glass capillary. The glass capillary is mounted on an optical linear sensor to track the air-liquid meniscus in real time and trigger the reversal of flow direction by switching a pneumatic valve. Each transit provides a volumetric flow rate measurement, which is used with the pressure drop to determine viscosity as a function of shear rate. A given sample of at least 50 μL can be measured over at least 2 to 3 decades in shear rate, in the range of 10 to 10⁵ s^-1, and be essentially fully recovered. Validation by comparison to reference measurements is performed using samples of Newtonian and non-Newtonian fluid, with viscosity ranging from 1 to 100 mPa s. The range of operation and uncertainty arising from instrumentation, meniscus effects, and inertial effects are discussed. The performance of this rheometer is advantageous, especially for use and reuse of small volumes.

Cellulose nanocrystals suspensions: Liquid crystal anisotropy, rheology and films iridescence

The properties of aqueous suspensions of cellulose nanocrystals (CNC) and their casted films are revised. The bio-nanoparticles are briefly introduced, including modifications of the crystals and the suspending media. The formation of CNC-derived liquid crystals (LC) and their resulting rheological behavior are presented. The effects of different variables are addressed: CNC aspect ratio, surface chemistry, concentration, time required for the appearance of an anisotropic phase and addition of other components to the suspension media. The changes on the structure induced by alignment, and by conditions of the drying process are also reported. The optical properties of the films are considered, and the effect of the above variables on the final transparency, iridescence and overall optical response of these bio-inspired photonic materials. Control of the reviewed variables is needed to achieve reliable materials in applications such as sensors, smart inks and papers, transparent flexible supports for electronics, decorative coatings and films.

Shear-Induced Isotropic-Nematic Transition in Poly(ether ether ketone) Melts

In a previous work on a poly(ether ether ketone) (PEEK) melt, above its nominal melting temperature (T_m ≅ 335 °C), a severe Cox-Merz rule failure was observed. The abrupt decrease in the apparent shear viscosity was ascribed to the formation of flow-induced crystallization precursors. Here shear rheology and reflection polariscope experiments are utilized to unravel the structural changes occurring under shear on a similar PEEK melt above T_m. Three regimes of the flow curve were identified from low (0.01 s^-1) to high shear rates (1000 s^-1): (I) an isotropic structure with weak birefringence due to polymer chain orientation and mild shear thinning for γ̇ < 1 s^-1, (II) an isotropic-nematic transition accompanied by strong birefringence, two steady-state viscosities, and large nematic polydomain director fluctuations, and (III) shear-thinning behavior with an η ∼ γ̇^-0.5 dependence for γ̇ > 20 s^-1, typically found in nematic fluids. The findings reported in this experimental work suggest that the nematic phase may represent the early stage of the formation of shear-induced crystallization precursors.

Rheological and rheo-birefringence features of semidilute ethyl cellulose dispersions under steady shear flow

We have conducted comprehensive rheological and rheo-birefringence characterizations of a series of semidilute ethyl cellulose (EC)/α-terpineol dispersions under steady shear flow. The EC dispersions investigated have commonly been utilized as a binder agent in fabricating metal/metal-oxide pastes for a number of industrial applications, and were recently demonstrated to foster nearly monodisperse spherical aggregates under dilute conditions. Herein, semidilute EC dispersions are shown to exhibit rheological features practically no different from those known for standard entangled polymer solutions. The corresponding rheo-birefringence responses, however, reveal microstructural features that are reminiscent of general colloidal systems. The steady-state feature reveals a universal stress-birefringence relationship at various EC concentrations, along with a common critical stress (∼200 Pa) at which the EC network breaks into smaller clusters. The transient feature displays prominent and long-persisting periodic oscillations that have previously been observed only for nearly monodisperse rod-like colloids or liquid crystals. The overall findings shed new light on the role of EC serving as a commonplace polymer binder in industry and, from a scientific perspective, raise interesting questions related to the characteristic rheological and microstructural features of general polymer dispersions in overlapped regimes.

Observation of transition cascades in sheared liquid crystalline polymers

We report on the shear rheology of liquid crystalline solutions composed of charged, rodlike polymers that form supramolecular assemblies dispersed in water. Under steady shear, we observe shear thickening behavior, followed by a hesitation in the viscosity accompanied by an extremely narrow range of negative first normal stress difference. The Peclet number (Pe, shear rate normalized by rod rotational diffusivity) for the onset of shear thickening is in agreement with previous, high-resolution numerical simulations of the Doi-Edwards-Hess kinetic theory. We interrogate these dynamic responses through shear step-down experiments, revealing a complex evolution of transient responses. Detailed analysis of the stress transients provides compelling evidence that the principal axis of the rod orientational distribution, the nematic director, undergoes a cascade of transitions and coexistence of periodic states known as kayaking, tumbling, and wagging, before transitioning to steady flow alignment above a critical shear rate.

Axisymmetric spheroidal squirmers and self-diffusiophoretic particles

We study, by means of an exact analytical solution, the motion of a spheroidal, axisymmetric squirmer in an unbounded fluid, as well as the low Reynolds number hydrodynamic flow associated to it. In contrast to the case of a spherical squirmer-for which, e.g. the velocity of the squirmer and the magnitude of the stresslet associated with the flow induced by the squirmer are respectively determined by the amplitudes of the first two slip ('squirming') modes-for the spheroidal squirmer each squirming mode either contributes to the velocity, or contributes to the stresslet. The results are straightforwardly extended to the self-phoresis of axisymmetric, spheroidal, chemically active particles in the case when the phoretic slip approximation holds.

Role of particle orientational order during shear thickening in suspensions of colloidal rods

Rheology of dense anisotropic colloidal suspensions often exhibits unsteady flow at constant imposed shear stress and/or shear rate. Using simultaneous high-resolution confocal microscopy and rheology, we find that the temporal behavior arises due to a strong coupling between shear flow and particle orientation. At smaller applied stresses, the orientation of rods fluctuates around the flow direction. A transition to an intermittent disordered state is observed at higher stresses when the angle between the flow and the rod orientation reaches a critical value. This disordered state is associated with transient drop in shear rate and an increase in viscosity. Simultaneous visualization of boundary stresses and orientation shows that the disordered regions lead to heterogeneous stresses and positive normal forces at the boundary, indicating the formation of systems spanning disordered particle contact networks.

Short and Soft: Multidomain Organization, Tunable Dynamics, and Jamming in Suspensions of Grafted Colloidal Cylinders with a Small Aspect Ratio

The yet virtually unexplored class of soft colloidal rods with a small aspect ratio is investigated and shown to exhibit a very rich phase and dynamic behavior, spanning from liquid to nearly melt state. Instead of the nematic order, these short and soft nanocylinders alter their organization with increasing concentration from isotropic liquid with random orientation to small domains with preferred local orientation and eventually a multidomain arrangement with a local orientational order. The latter gives rise to a kinetically suppressed state akin to structural glass with detectable terminal relaxation, which, on further increasing concentration, reveals features of hexagonally packed order as in ordered block copolymers. The respective dynamic response comprises four regimes, all above the overlapping concentration of 0.02 g/mL:(I) from 0.03 to 0.1 g/mol, the system undergoes a liquid-to-solidlike transition with a structural relaxation time that grows by 4 orders of magnitude. (II) From 0.1 to 0.2 g/mL, a dramatic slowing-down is observed and is accompanied by an evolution from isotropic to a multidomain structure. (III) Between 0.2 and 0.6 g/mol, the suspensions exhibit signatures of shell interpenetration and jamming, with the colloidal plateau modulus depending linearly on concentration. (IV) At 0.74 g/mL, in the densely jammed state, the viscoelastic signature of hexagonally packed cylinders from microphase-separated block copolymers is detected. These properties set short and soft nanocylinders apart from long colloidal rods (with a large aspect ratio) and provide insights for fundamentally understanding the physics in this intermediate soft colloidal regime and for tailoring the flow properties of nonspherical soft colloids.

Advances in Biological Liquid Crystals

Biological liquid crystals, a rich set of soft materials with rod-like structures widely existing in nature, possess typical lyotropic liquid crystalline phase properties both in vitro (e.g., cellulose, peptides, and protein assemblies) and in vivo (e.g., cellular lipid membrane, packed DNA in bacteria, and aligned fibroblasts). Given the ability to undergo phase transition in response to various stimuli, numerous practices are exercised to spatially arrange biological liquid crystals. Here, a fundamental understanding of interactions between rod-shaped biological building blocks and their orientational ordering across multiple length scales is addressed. Discussions are made with regard to the dependence of physical properties of nonmotile objects on the first-order phase transition and the coexistence of multi-phases in passive liquid crystalline systems. This work also focuses on how the applied physical stimuli drives the reorganization of constituent passive particles for a new steady-state alignment. A number of recent progresses in the dynamics behaviors of active liquid crystals are presented, and particular attention is given to those self-propelled animate elements, like the formation of motile topological defects, active turbulence, correlation of orientational ordering, and cellular functions. Finally, future implications and potential applications of the biological liquid crystalline materials are discussed.

Dynamics of Cellulose Nanocrystal Alignment during 3D Printing

The alignment of anisotropic particles during ink deposition directly affects the microstructure and properties of materials manufactured by extrusion-based 3D printing. Although particle alignment in diluted suspensions is well described by analytical and numerical models, the dynamics of particle orientation in the highly concentrated inks typically used for printing via direct ink writing (DIW) remains poorly understood. Using cellulose nanocrystals (CNCs) as model building blocks of increasing technological relevance, we study the dynamics of particle alignment under the shear stresses applied to concentrated inks during DIW. With the help of in situ polarization rheology, we find that the time period needed for particle alignment scales inversely with the applied shear rate and directly with the particle concentration. Such dependences can be quantitatively described by a simple scaling relation and qualitatively interpreted in terms of steric and hydrodynamic interactions between particles at high shear rates and particle concentrations. Our understanding of the alignment dynamics is then utilized to estimate the effect of shear stresses on the orientation of particles during the printing process. Finally, proof-of-concept experiments show that the combination of shear and extensional flow in 3D printing nozzles of different geometries provides an effective means to tune the orientation of CNCs from fully aligned to core-shell architectures. These findings offer powerful quantitative guidelines for the digital manufacturing of composite materials with programmed particle orientations and properties.

Chiral twist drives raft formation and organization in membranes composed of rod-like particles

Lipid rafts are hypothesized to facilitate protein interaction, tension regulation, and trafficking in biological membranes, but the mechanisms responsible for their formation and maintenance are not clear. Insights into many other condensed matter phenomena have come from colloidal systems, whose micron-scale particles mimic basic properties of atoms and molecules but permit dynamic visualization with single-particle resolution. Recently, experiments showed that bidisperse mixtures of filamentous viruses can self-assemble into colloidal monolayers with thermodynamically stable rafts exhibiting chiral structure and repulsive interactions. We quantitatively explain these observations by modeling the membrane particles as chiral liquid crystals. Chiral twist promotes the formation of finite-sized rafts and mediates a repulsion that distributes them evenly throughout the membrane. Although this system is composed of filamentous viruses whose aggregation is entropically driven by dextran depletants instead of phospholipids and cholesterol with prominent electrostatic interactions, colloidal and biological membranes share many of the same physical symmetries. Chiral twist can contribute to the behavior of both systems and may account for certain stereospecific effects observed in molecular membranes.

Shear banding in nematogenic fluids with oscillating orientational dynamics

We investigate the occurrence of shear banding in nematogenic fluids under planar Couette flow, based on mesoscopic dynamical equations for the orientational order parameter and the shear stress. We focus on parameter values where the sheared homogeneous system exhibits regular oscillatory orientational dynamics, whereas the equilibrium system is either isotropic (albeit close to the isotropic-nematic transition) or deep in its nematic phase. The numerical calculations are restricted to spatial variations in shear gradient direction. We find several new types of shear-banded states characterized by regions with regular oscillatory orientational dynamics. In all cases shear banding is accompanied by a non-monotonicity of the flow curve of the homogeneous system; however, only in the case of the initially isotropic system this curve has the typical S-like shape. We also analyze the influence of different orientational boundary conditions and of the spatial correlation length.

The Connection between Biaxial Orientation and Shear Thinning for Quasi-Ideal Rods

The complete orientational ordering tensor of quasi-ideal colloidal rods is obtained as a function of shear rate by performing rheo-SANS (rheology with small angle neutron scattering) measurements on isotropic fd-virus suspensions in the two relevant scattering planes, the flow-gradient (1-2) and the flow-vorticity (1-3) plane. Microscopic ordering can be identified as the origin of the observed shear thinning. A qualitative description of the rheological response by Smoluchowski, as well as Doi⁻Edwards⁻Kuzuu theory is possible, as we obtain a master curve for different concentrations, scaling the shear rate with the apparent collective rotational diffusion coefficient. However, the observation suggests that the interdependence of ordering and shear thinning at small shear rates is stronger than predicted. The extracted zero-shear viscosity matches the concentration dependence of the self-diffusion of rods in semi-dilute solutions, while the director tilts close towards the flow direction already at very low shear rates. In contrast, we observe a smaller dependence on the shear rate in the overall ordering at high shear rates, as well as an ever-increasing biaxiality.

Binary mixtures of rod-like colloids under shear: microscopically-based equilibrium theory and order-parameter dynamics

This paper is concerned with the dynamics of a binary mixture of rod-like, repulsive colloidal particles driven out of equilibrium by means of a steady shear flow (Couette geometry). To this end we first derive, starting from a microscopic density functional in Parsons-Lee approximation, a mesoscopic free energy functional whose main variables are the orientational order parameter tensors. Based on this mesoscopic functional we then explore the stability of isotropic and nematic equilibrium phases in terms of composition and rod lengths. Second, by combining the equilibrium theory with the Doi-Hess approach for the order parameter dynamics under shear, we investigate the orientational dynamics of binary mixtures for a range of shear rates and coupling parameters. We find a variety of dynamical states, including synchronized oscillatory states of the two components, but also symmetry breaking behavior where the components display different in-plane oscillatory states.

X-ray scattering in the vorticity direction and rheometry from confined fluids

An X-ray flexure-based microgap rheometer (X-FMR) has been designed for combining rheology and in situ small-angle X-ray scattering from the vorticity plane. The gap distance can be varied continuously from 500 μm down to several μm, which provides the unique possibility to generate a strong confinement for many complex fluids. A singular advantage of this setup is the possibility to directly probe the vorticity direction of the flow field with a microfocus X-ray beam and to probe the structural response of the fluid to combined shear and confinement in the vorticity plane. The sliding-plate setup operates over a wide range of shear rates of γ = 10(-3)-10(3) s(-1) and strains in the range of 10(-4)-10(2). The flexure-based bearing maintains the plate parallelism within 10(-5) rad. The X-FMR requires very small sample volumes on the order of 10 μl. The applicability of the device is demonstrated here with limited examples of a nematic suspension of fd virus (rods), and a crystalline suspension containing sterically stabilized polystyrene-butylacrylate latex particles.

Feedback control of flow alignment in sheared liquid crystals

Based on a continuum theory, we investigate the manipulation of the nonequilibrium behavior of a sheared liquid crystal via closed-loop feedback control. Our goal is to stabilize a specific dynamical state, that is, the stationary "flow alignment," under conditions where the uncontrolled system displays oscillatory director dynamics with in-plane symmetry. To this end we employ time-delayed feedback control (TDFC), where the equation of motion for the ith component q(i)(t) of the order parameter tensor is supplemented by a control term involving the difference q(i)(t)-q(i)(t-τ). In this diagonal scheme, τ is the delay time. We demonstrate that the TDFC method successfully stabilizes flow alignment for suitable values of the control strength K and τ; these values are determined by solving an exact eigenvalue equation. Moreover, our results show that only small values of K are needed when the system is sheared from an isotropic equilibrium state, contrary to the case where the equilibrium state is nematic.

Oscillatory motion of sheared nanorods beyond the nematic phase

We study the role of the control parameter triggering nematic order (temperature or concentration) on the dynamical behavior of a system of nanorods under shear. Our study is based on a set of mesoscopic equations of motion for the components of the tensorial orientational order parameter. We investigate these equations via a systematic bifurcation analysis based on a numerical continuation technique, focusing on spatially homogeneous states. Exploring a wide range of parameters we find, unexpectedly, that states with oscillatory motion can exist even under conditions where the equilibrium system is isotropic. These oscillatory states are characterized by a wagging motion of the paranematic director, and they occur if the tumbling parameter is sufficiently small. We also present full nonequilibrium phase diagrams in the plane spanned by the concentration and the shear rate.

Optically anisotropic thin films by shear-oriented assembly of colloidal nanorods

Device-scale thin films of highly oriented (in-plane) colloidal nanorods are made available by using a simple coating process involving thixotropic rod gel suspensions. Application of this process to LaPO₄ nanorods leads to films exhibiting outstanding anisotropic optical properties, such as a remarkably large birefringence (Δn = 0.13) associated with high transparency, and sharply polarized fluorescence spectra when doped with europium.

Nonlinear behavior of nematic platelet dispersions in shear flow

Dispersions of platelets in the nematic phase are submitted to large amplitude oscillatory shear flow and probed by high temporal resolution small angle x-ray scattering. The response displays rich dynamic and structural behavior. Under small amplitude deformations we observe an elastic response, while structurally symmetry is broken: a preferential direction of deformation is selected which induces off-plane orientation of the platelets. We associate the elastic responses with the tilting director of the platelets towards the flow direction at all strain amplitudes. At large strain amplitudes there is a yielding transition between elastic and plastic deformation, accompanied by a flipping of the director. At intermediate strain amplitudes the director has a rich dynamic behavior, illustrating the complex motion of platelets in shear flow. These observations are confirmed by steady-shear flow reversal experiments, which underline the unique character of sheared nematic platelet dispersions.

Confinement induced splay-to-bend transition of colloidal rods

We study the nematic phase of rodlike f d-virus particles confined to channels with wedge-structured walls. Using laser scanning confocal microscopy we observe a splay-to-bend transition at the single particle level as a function of the wedge opening angle. Lattice Boltzmann simulations reveal the underlying origin of the transition and its dependence on nematic elasticity and wedge geometry. Our combined work provides a simple method to estimate the splay-to-bend elasticity ratios of the virus and offers a way to control the position of defects through the confining boundary conditions.

Orientational order and alignment of elongated particles induced by shear

Shear induced alignment of elongated particles is studied experimentally and numerically. We show that shear alignment of ensembles of macroscopic particles is comparable even on a quantitative level to simple molecular systems, despite the completely different types of particle interactions. We demonstrate that for dry elongated grains the preferred orientation forms a small angle with the streamlines, independent of shear rate across three decades. For a given particle shape, this angle decreases with increasing aspect ratio of the particles. The shear-induced alignment results in a considerable reduction of the effective friction of the granular material.

Rheology and DWS microrheology of concentrated suspensions of the semiflexible filamentous fd virus

Microrheology measurements were performed on suspensions of bacteriophage fd with diffusive wave spectroscopy in the concentrated regime, at different values of ionic strength. Viscosity vs. shear rate was also measured, and the effect of bacteriophage concentration and salt addition on shear thinning was determined, as well as on the peaks in the viscosity vs. shear curves corresponding to a transition from tumbling to wagging flow. The influence of concentration and salt addition on the mean square displacement of microspheres embedded in the suspensions was determined, as well as on their viscoelastic moduli up to high angular frequencies. Our results were compared with another microrheology technique previously reported where the power spectral density of thermal fluctuations of embedded micron-sized particles was evaluated. Although both results in general agree, the diffusive wave spectroscopy results are much less noisy and can reach larger frequencies. A comparison was made between measured and calculated shear modulus. Calculations were made employing the theory for highly entangled isotropic solutions of semiflexible polymers using a tube model, where various ways of calculating the needed parameters were used. Although some features are captured by the model, it is far from the experimental results mainly at high frequencies.

Nonlinear rheology of active particle suspensions: insights from an analytical approach

We consider active suspensions in the isotropic phase subjected to a shear flow. Using a set of extended hydrodynamic equations we derive a variety of analytical expressions for rheological quantities such as shear viscosity and normal stress differences. In agreement to full-blown numerical calculations and experiments we find a shear-thickening or -thinning behavior depending on whether the particles are contractile or extensile. Moreover, our analytical approach predicts that the normal stress differences can change their sign in contrast to passive suspensions.

Shear-stress-controlled dynamics of nematic complex fluids

Based on a mesoscopic theory we investigate the nonequilibrium dynamics of a sheared nematic liquid, with the control parameter being the shear stress σ xy (rather than the usual shear rate, γ). To this end we supplement the equations of motion for the orientational order parameters by an equation for γ, which then becomes time dependent. Shearing the system from an isotropic state, the stress-controlled flow properties turn out to be essentially identical to those at fixed γ. Pronounced differences occur when the equilibrium state is nematic. Here, shearing at controlled γ yields several nonequilibrium transitions between different dynamic states, including chaotic regimes. The corresponding stress-controlled system has only one transition from a regular periodic into a stationary (shear-aligned) state. The position of this transition in the σ xy-γ plane turns out to be tunable by the delay time entering our control scheme for σ xy. Moreover, a sudden change in the control method can stabilize the chaotic states appearing at fixed γ.

Towing, breathing, splitting, and overtaking in driven colloidal liquid crystals

The nonequilibrium response of a colloidal liquid-crystalline nematic phase to an external aligning field, which rotates in a plane, is explored by dynamical fundamental measure density-functional theory. Depending on the drive frequency, different dynamical states are found, which are characterized by towing and overtaking of the nematic director by the field as well as by breathing and dynamical splitting of the orientational distribution peak. This complex response can be exploited for smart optical switching and mixing devices.

Shear-induced dynamic polarization and mesoscopic structure in suspensions of polar nanorods

We investigate the spatiotemporal behavior of sheared suspensions of rodlike particles with permanent dipole moments. Our calculations are based on a self-consistent hydrodynamic model including feedback effects between orientational motion and velocity profile. The competition between shear-induced tumbling motion and the boundary conditions imposed by plates leads to oscillatory alignment structures. These give rise to a spontaneous time-dependent polarization generating, in turn, magnetic fields. This novel shear-induced effect is robust against varying the boundary conditions. The field strengths are of a measurable magnitude for a broad parameter range.

Attractive colloidal rods in shear flow

The effect of shear flow on the isotropic-nematic phase transition of attractive colloidal rods is investigated by a combination of simulations and experiments. The isotropic phase aligns with the flow, while the nematic phase undergoes a collective rotational motion which frustrates the merging of the coexisting regions. The location of binodals, spinodals, and the tumbling-to-aligning transition line in the shear-rate versus concentration plane are investigated. The phase diagrams in the shear-concentration plane for the various strengths of attractions can be mapped onto a master curve by appropriate scaling.

Polar nano-rods under shear: from equilibrium to chaos

The orientational dynamics of rod-like particles with permanent (electric or magnetic) dipole moments in a plane Couette shear flow is investigated using mesoscopic relaxation equations combined with a generalized Landau free energy. The free energy contribution due to the coupling between average alignment and dipole orientation is derived on a microscopic basis. Numerical results of the resulting eight-dimensional dynamical system are presented for the case of longitudinal dipoles and thermodynamic conditions where the equilibrium state is a (polar or non-polar) nematic. Solution diagrams reveal presence of a large variety of periodic, transient chaotic, and chaotic dynamic states of the average alignment and dipole moment, respectively, appearing as a function of Deborah number and tumbling parameter. Compared to rods without dipoles we observe a significant preference of out-of-plane kayaking-tumbling states and, generally, a higher sensitivity to the initial conditions including bistability. We also demonstrate that the average (electric) dipole moment characterizing most of the observed states yields electrodynamic (magnetic) fields of measurable strength.

Vorticity banding in rodlike virus suspensions

Vorticity banding under steady shear flow is observed in a suspension of semiflexible colloidal rods (fd virus particles) within a part of the paranematic-nematic biphasic region. Banding occurs uniformly throughout the cell gap within a shear-rate interval (.gamma-, .gamma+) , which depends on the fd concentration. For shear rates below the lower-border shear rate .gamma- only shear elongation of inhomogeneities, which are formed due to paranematic-nematic phase separation, is observed. Within a small region just above the upper-border shear rate .gamma+ , banding occurs heterogeneously. An essential difference in the kinetics of vorticity banding is observed, depending on the morphology of inhomogeneities formed during the initial stages of the paranematic-nematic phase separation. Particle tracking and polarization experiments indicate that the vorticity bands are in a weak rolling flow, superimposed on the applied shear flow. We propose a mechanism for the origin of the banding instability and the transient stability of the banded states. This mechanism is related to the normal stresses generated by inhomogeneities formed due to the underlying paranematic-nematic phase transition.

Periodic orientational motions of rigid liquid-crystalline polymers in shear flow

The collective periodic motions of liquid-crystalline polymers in a nematic phase in shear flow have, for the first time, been simulated at the particle level by Brownian dynamics simulations. A wide range of parameter space has been scanned by varying the aspect ratio L/D between 10 and 60 at three different scaled volume fractions Lphi/D and an extensive series of shear rates. The influence of the start configuration of the box on the final motion has also been studied. Depending on these parameters, the motion of the director is either characterized as tumbling, kayaking, log-rolling, wagging, or flow-aligning. The periods of kayaking and wagging motions are given by T=4.2(Lphi/D)gamma(-1) for high aspect ratios. Our simulation results are in agreement with theoretical predictions and recent shear experiments on fd viruses in solution. These calculations of elongated rigid rods have become feasible with a newly developed event-driven Brownian dynamics algorithm.

Diffusion of spheres in isotropic and nematic suspensions of rods

Diffusion of a small tracer sphere (apoferritin) in isotropic and nematic networks [of fd virus] is discussed. For a tracer sphere that is smaller than the mesh size of the network, screened hydrodynamic interactions between the sphere and the network determine its diffusion coefficient. A theory is developed for such interactions as well as their relation to the long-time self-diffusion coefficient. Fluorescence correlation spectroscopy measurements on mixtures of apoferritin and fd virus are presented. The long-time self-diffusion coefficient of apoferritin is measured as a function of the fd-virus concentration, both in the isotropic and nematic state, in directions parallel and perpendicular to the nematic director. The hydrodynamic screening length of the fd-virus network as a function of fd concentration is obtained by combining these experimental data with the theory. Surprisingly, the screening length increases with increasing concentration in nematic networks. This is due to the increase in the degree of alignment, which apparently leads to a strong increase of the screening length. Hydrodynamic screening is thus strongly diminished by alignment. A self-consistent calculation of the screening length does not work at higher concentrations, probably due to the strong variation of the typical incident flow fields over the contour of a rod.

Kayaking and wagging of rods in shear flow

For the first time, we have simulated the periodic collective orientational motions performed by rigid liquid-crystalline polymers with large aspect ratio in the nematic state in shear flow. In order to be able to do so, we developed a new, event-driven Brownian dynamics technique. We present the results of simulations of rods with aspect ratios L/d ranging from 20 to 60 at volume fractions phi given by Lphi/d = 3.5 and 4.5. By studying the path of the director, i.e., the average direction of the rods, we observe kayaking, wagging, flow aligning, and log-rolling type of orbits, depending on the parameters of the simulation and the initial orientation. We find that the tumbling periods depend on Lphi/d and the shear rate but not on the type of motion. Our simulation results qualitatively confirm theoretical predictions and are in good agreement with the experimental measurements of tumbling times of fd viruses.