Director dynamics of uniformly aligned nematic liquid crystals in transient shear flow

We have developed a modular rheo-optical apparatus to study the flow properties of liquid crystals. Its main components are shearing device, strong magnetic field, and optical microscope. We performed experiments on well defined initial morphologies with uniform molecular alignment. The monodomains were achieved with strong magnetic fields (4.7T). Time-resolved conoscopy is the primary optical technique in our investigation. We propose a simple relation between the distribution of alignment angles over the sample thickness and the conoscopically measured angle, to quantitatively measure the alignment angle in shear flow.We followed the relaxation of a shear-induced splay deformation in small molecule model systems (N-(p-methoxybenzylidene) p-butylaniline (MBBA), pentyl-cyano-biphenyl (5 CB) and a commercially available mixture OM14244). We define a rotational director diffusivity (K _s splay elastic constant.i7s splay viscosity) from the relaxation process and devised a model, based on the diffusion equation to determine their values.The director alignment behavior of the small molecule liquid crystals (SMLC's) in shear flow is well described by the two-dimensional Leslie-Ericksen model. The effect of director elasticity can clearly be seen in our experiments, resulting in a decrease of the steady state alignment angle at smaller Ericksen numbers.We found that there is no strain rate dependence of the director vorticity from 0.002/s to 2/s for poly-(-benzyl-D/L-glutamate) (PBG). We determined ₂/₃ = –44 for a 2007o solution of 280000 molecular weight PBG in m-cresol at 20°C. The conoscopic interference pattern vanished after 8 strain units from an initially planar alignment and shearing could be reversed up to 10 strain units to completely recover the initial monodomain.Presented at 4th Meeting of European Rheologists, Sept. 4–9, 1994, Seville, SpainDedicated to Prof. H. Janeschitz-Kriegl at the occasion of his 70th birthday.     

Shear-induced long-range alignment of BCC-ordered block copolymers

Effect of large shear on an asymmetric block copolymer with nanospherical domains has been studied using rheology and small angle X-ray scattering. The material investigated was a triblock copolymer poly[styrene-b-(ethylene-co-butylene)-b-styrene] swollen in a midblock-selective solvent. When cooled below the order–disorder transition temperature (T _ODT), the system forms a locally ordered structure of grains with body-centered cubic (BCC) lattice. Isothermal shearing, either at constant rate or with large amplitude oscillatory shear (LAOS) at low frequencies and strain amplitude greater than or equal to 2.0, leads to the destruction of the BCC lattice (isothermal “shear melting”). Upon cessation of the shear, the BCC structure recovers with kinetics similar to the one after thermal quench from above T _ODT. Under certain experimental conditions, LAOS leads to alignment of the BCC lattice. The lattice orientation depends primarily on shearing frequency. At low frequencies, there exists an upper and lower bound on strain amplitude where monodomain textures can be obtained. Upon alignment, the modulus drops by about 30% of that of the polycrystalline structure. Measurement of rheological properties offers an indirect method for distinguishing between polycrystalline structure (grains) and monodomain texture.     

Conoscopic observations of shear-induced rotations in nematic liquid crystals

Orientational changes in monodomains of flow-aligning liquid crystals, 4-n-pentyl-4′-cyanobiphenyl and N-(4-methoxybenzylidene)-4-butylaniline, were studied during shear and recovery in a linear shearing device fitted to an optical microscope. Planar alignment (director in the shear plane) allows the study of twist effects and was generated by strong planar anchoring at the walls with orientations in a range of 0–90° with the shear direction. While being held back by the anchoring walls, shear caused the bulk director to rotate towards a steady-state alignment angle in the shear direction (Leslie angle θ_L). The transient director rotation was observed with conoscopy. It was found that increasing the initial alignment towards the vorticity direction increased the measured θ_L. Upon stopping the flow, the bulk director returned to its initial state. With initial alignment orientation changing from parallel to perpendicular to the flow direction, the rate of the twist-driven recovery process increases. This rate increase is not seen in the splay-driven recovery which is constant and consistently faster than twist-driven recovery at all orientations studied. Received: 10 December 1998/Accepted: 7 June 1999     

Ordering effects in shear flows of discotic polymers

The tensorial mechanical model of Farhoudi and Rey (1993) for uniaxial, rodlike, spatially homogeneous and monodomain nematics is modified to describe the microstructural response of discotic nematic network polymers in rectilinear simple shear flow. The particular topological features of the discotic phase are taken into account by a proper modification of the phenomenological parameters. Asymptotic and numerical solutions of the microstructural balance equations indicate the appearance of tumbling, oscillating, and stationary flow regimes as the strength of shear increases, as is the case for rod-like nematic polymers (Marrucci, 1991). The tumbling-oscillating transition is characterized by a diverging tumbling function , while the oscillating-stationary transition is characterized by a single steady value smaller than —1. The stable steady states of the stationary regime are shown to belong to the family of unstable isotropic solutions that exist at small shear rates, and are characterized by a director angle close to, but less than +90° to the flow direction.     

Shear orientation of a lamellar lyotropic liquid crystal

Shear orientation of a lyotropic lamellar liquid crystalline phase of tetra ethyleneglycol mono dodecylether, C₁₂A₄ in water was studied by combined rheo-small-angle light scattering. Shear thinning was observed with a sample of 500 m thickness. The scattering patterns showed that domains were aligned and stretched in flow direction. Shear thinning was also observed with a thinner sample, but caused a strong change in light-scattering pattern. A maximum of scattering intensity was observed at finite scattering vector and shifted to a higher scattering vector with increasing shear stress. This observation can be explained by a fragmentation of domains at high shear stress and is supported by a mosaic texture observed in optical microscopy.     

On the relative magnitudes of viscous,elastic and texture stresses in liquid crystalline PBG solutions

The relative contributions of the viscous, elastic, and texture stresses in flows of modestly concentrated liquid crystalline solutions of poly(-benzyl glutamate) or PBG, at low shear rates are assessed by comparing published experimental rheological and light-scattering data to theoretical predictions. The data considered include ratios of Leslie-Ericksen viscosities, the shear viscosity jump at the transition from the isotropic to the liquid-crystalline state, the dependence of the shear viscosity on concentration, and the fraction of slowly relaxing stress after cessation of shearing flow. We quantify the relative contributions of viscous and elastic stresses by estimating from these data a value for the parameter ß^* _{V str} D ^* _r /kT, where _str , is the solvent-polymer friction coefficient and D _r ^* is the rotary diffusivity in the isotropic phase at the concentration where the isotropic phase becomes unstable to liquid crystalline order. The experimental evidence suggests a value \^* _v 0.03, five times lower than the value, 0.15, for dilute solutions. The relative contributions of elastic and texture stresses can be quantified by a parameter in the mesoscopic theory for polydomain nematics; a value of 0.03 gives reasonable agreement with transient shearing experiments, and predicts that the shear viscosity will show an upturn at high polymer concentrations, in agreement with experiments.Dedicated to Prof. Dr. J. Meissner on the occasion of his retirement from the chair of Polymer Physics at the Eidgenössische Technische Hochschule (ETH) Zürich, Switzerland     

Transient rheological behaviour of poly-para-henylenetherephthalamide (PpPTA) in sulphuric acid

Nearly all the available information on the transient flow behaviour of liquid crystalline polymers has been obtained on model systems, especially on solutions of polybenzylglutamate (PBG) and hydroxypropylcellulose (HPC). The assessment of rheological models has been based almost entirely on these model systems. It is not clear how much of the available theoretical and experimental knowledge can be applied to systems of industrial relevance, which have quite different molecular structures. Here, an industrial lyotropic system, poly(p-phenylenetherephthalamide) (PpPTA) in sulphuric acid (TWARON from AKZO), is investigated. Various techniques to study transient behaviour are used, these include measurements of transient shear and normal stresses after sudden changes in shear rate, dynamic moduli and stress relaxation after cessation of flow and elastic recoil. At all shear rates studied the PpPTA solution is shear thinning, and the first normal stress difference remains positive. For the stress transients a strain scaling applies reasonably well as it did in model systems. The moduli increase with time upon cessation of flow, indicating that the molecules become less oriented in the previous flow direction. This particular behaviour is similar to that of HPC. Transients also resemble more closely those of HPC rather than those of PBG. This latter difference might be attributed to the higher flexibility of HPC and PpPTA chains as compared with PBG molecules.     

Likelihood and expected-time statistics of monodomain attractors in sheared discotic and rod-like nematic polymers

Employing a mesoscopic Doi tensor model, we develop transient statistical properties of sheared nematic polymer monodomains consistent with typical experimental protocols. Our goal is to convey to the experimentalist a list of expected outcomes, based not only on properties of the nematic liquid and imposed flow rate, but also on the timescale of the experiment and variability in the initial conditions. Step 1 is deterministic: we solve the model equations completely, then compile the flow-phase diagram of all monodomain attractors and phase transitions versus nematic concentration and Peclet number (shear rate normalized by molecular relaxation rate). Step 2 is to overlay on the phase diagram a statistical diagnostic of the expected time, t_A, to reach a small neighborhood of every attractor A. The statistics are taken over the arbitrary quiescent director angle on the sphere, modeling experiments that begin from rest. Step 3 is to explore parameter regimes with multiple attractors, where we statistically determine the likelihood of convergence to each attractor. These statistical properties are critical for any application of theoretical models to the interpretation of experimental data. If t_A is longer than the timescale of the experiment, attractor A is never fully resonated and the relevant stress and scattering predictions are those of the transients, not the attractor. In bi-stable and tri-stable parameter regimes, which are typical of nematic polymers, a distribution of monodomains of each type will populate the sample, so experimental data must be compared with weighted averages based on the likelihood of each attractor (see Grosso et al (2003) Phys Rev Lett 90:098304). The final step is to give statistics of shear stress and normal stress differences during the approach to each attractor type, as well as typical paths of the major director that are contrasted with the results of Van Horn et al (Rheol Acta (2003) 42(6):585–589) with Leslie-Ericksen theory.     

The flow-phase diagram of Doi-Hess theory for sheared nematic polymers II: finite shear rates

The purpose of this paper is to extend the rheological predictions of the Doi-Hess kinetic theory for sheared nematic polymers from the anomalous weak shear regime (Forest et al. 2004a) to arbitrary shear rates, and to associate salient rheological and optical properties with the solution space of kinetic theory. Using numerical bifurcation software (AUTO), we provide the phase diagram of all stable monodomain orientational probability distribution functions (PDFs) and their phase transitions (bifurcations) vs nematic concentration (N) and normalized shear rate (Peclet number, Pe) for Pe1. Shear stresses, normal stress differences, the peak direction of the orientational distribution, and birefringence order parameters are calculated and illustrated for each type of PDF attractor: steady flow-aligning, both in and out of the flow deformation plane and along the vorticity axis; unsteady limit cycles, where the peak orientation direction rotates in-plane or around the vorticity axis or in bi-stable orbits tilted between them; and chaotic attractors first observed in kinetic simulations by Grosso et al. (2001). We pay particular attention to correlations between rheological features and the variety of monodomain phase transitions. Together with the weak flow regime, these results provide a nearly complete picture of the rheological consequences of the Doi-Hess kinetic theory for sheared monodomains of rigid, extreme aspect ratio, nematic rods or platelets.     

Orthogonal and parallel superposition measurements on lyotropic liquid crystalline polymers

 Mechanical spectroscopy is used to probe the structure of lyotropic liquid crystalline polymers during flow and after the cessation of flow. The oscillatory flow is either parallel or perpendicular to the steady-state flow. The resulting moduli provide information about the time- and shear-dependent microstructure, including anisotropy. Two different concentrations of poly(benzylglutamate) (PBG) in m-cresol and a concentrated hydroxypropylcellulose (HPC) solution, also in m-cresol, are investigated. In all cases, the orthogonal superposition moduli evolve differently from the parallel ones. The former are less sensitive to the flow-induced changes in structure than the latter ones. Together with the lack of sensitivity of the superposition moduli to texture refinement during flow, this suggests a strong relation between director orientation and superposition moduli. After the cessation of flow the parallel moduli decrease for the PBG solutions, whereas the opposite is observed in the HPC solutions. A comparison with the orthogonal moduli provides a direct measure of anisotropy. At rest, the PBG solutions tend toward a higher degree of anisotropy while the HPC solutions become more isotropic. In the latter systems, all moduli are much larger, reflecting a larger contribution from the texture. Received: 8 July 1999/Accepted: 1 October 1999     

Influence of the flow history on stress growth and structure changes in the thermotropic liquid crystalline polymer Vectra B950

The structure changes in the start-up flow of the thermotropic liquid crystalline polymer Vectra 8950 are probed by performing transient experiments after various flow histories. The shear and normal stress growth curves of a squeezed sample and of a randomly oriented sample show a pronounced overshoot at low strains, whereas the stress growth curve of a sample pre-sheared until steady state shows a gradual increase. This first peak is associated with the re-orientation of the director into the shearing plane. All stress transients show a second broad maximum at large strains that results from the generation of a steady defect network. The effect of varying the relaxation period after pre-shearing is reflected in the appearance of two peaks in the subsequent stress growth curves. One of these peaks shifts linearly with re laxation period and the other is more or less fixed in position. The orientation of the molecules during steady shear flow is on average in the flow direction. Intermediate orientation levels may exist in the transient depending on the amount of strain. The material is able to maintain the flow-induced orientation distribution for a long time after cessation of flow. This is reflected in a similar fashion in the initial magnitudes of the stresses and the dynamic moduli after various preshear strains. Moreover, the dynamic moduli decrease with time after cessation of steady shear flow, indicating that the orientation increases during relaxation.     

DNA molecular configurations in flows near adsorbing and nonadsorbing surfaces

We investigate experimentally -phage and T2-coliphage DNA molecules near both non-adsorbing glass and adsorbing 3-aminopropyltriethoxysilane (APTES)-coated glass surfaces in a simple steady shearing flow generated by a torsional flow cell. The DNA molecular deformations near the surface are found to be considerably weaker than in bulk flow at the same shear rate. This affects the DNA molecules deposition and stretching on the adsorbing surface. Surprisingly, for a simple shearing flow in the torsional shearing device, the observed stretch, for molecules both near (<10 µm) the surface and adsorbed to it, is much less than predicted by simulations.     

Molecular orientation in sheared molten thermotropic random copolyester

The macromolecular alignment and texture orientation in sheared thermotropic copolyester were investigated using in situ wide-angle X-ray scattering (WAXS) and polarizing optical microscopy (POM). The molecular behavior was correlated with viscoelastic properties. The polymer is a random copolyester based on 60 mol% 1,4-hydroxybenzoic acid (B) and 40 mol% ethylene terephthalate (ET) units. X-ray scattering showed that the molecular chains were aligned along the flow direction. The degree of molecular orientation, , is an increasing function of the applied shear rate. However, rheo-optics showed that shear flow could not orient the polydomain texture, i.e., neither defect stretching nor elimination of defects was observed. Instead, shear compressed the microdomains and gave rise to long-range orientation correlations. Rheology showed that the nematic melt is viscoelastic, the loss modulus G″ dominates the elastic modulus G′, and the dynamic viscosity η* is shear thinning. Moreover, the steady shear viscosity, η, also behaved shear thinning, while the first normal stress difference N ₁ remained positive. The empirical Cox–Merz rule did not hold, , within the shear rate range studied. The microscopic and rheological properties suggest that B–ET is a flow-aligning nematic polymer.     

The effect of particle size and migration on the formation of flow-induced structures in viscoelastic suspensions

Flow-induced structures in suspensions containing spheres in viscoelastic suspending media were investigated by microscopy and rheo-optical methods. Suspensions of monodisperse polystyrene spheres with diameters ranging from 1.2 to 2.8 μm and dispersed in aqueous solutions of hydroxypropylcellulose were studied in simple shear flows. Optical microscopy observations as well as small-angle light-scattering (SALS) experiments were performed using a parallel plate geometry. In agreement with previous work, necklaces of particles aligned in the flow direction were observed when shearing faster then a critical shear rate, which was found to be independent of particle size. In contrast to earlier work, however, the role of particle migration was found to be of prime importance. Particles were shown to migrate toward the plates where the particles assembled and aligned in strings running in the flow direction. For the smallest particles (1 μm diameter), the formation of particle doublets or short strings along the vorticity direction was observed at low shear rates, which flipped to an orientation into the flow direction and grew into longer strings at higher shear rates. SALS experiments were used to quantify the degree of alignment and its dependence on particle size, shear rate, and gap. For the system under investigation, the degree of alignment was found to increase with increasing shear rate and particle size and with decreasing gap. The present results suggest that, depending on the details of the suspending medium and the size and nature of the suspended particles, the formation of aligned structures is affected by the relative magnitude of the colloidal and hydrodynamic forces and the kinetics of string formation versus the kinetics of migration.     

Superposition principles for small amplitude oscillatory shearing of nematic mesophases

The linear viscoelasticty of Leslie-Ericksen monodomain liquid crystals subjected to a bend distortion through a small amplitude oscillatory shear flow driven by harmonic wall stress is analyzed, using numerical and asymptotic methods. The viscoelastic material functions were derived using a new scaling approach that extracts the material parameters that control superposition. Small and high frequency superposition schemes for linear viscoleasticity were derived. The schemes were successfully applied to collapse the predicted loss and storage linear viscoelastic moduli of seven experimental data sets. Comparisons between different shear flows (simple shear and capillary Poiseuille) and different director distortion modes (splay and bend) shows that the superposition schemes are applicable to shear flows in any single director distortion mode.     

Theory of linear viscoelasticity of chiral liquid crystals

The governing equations of monodomain isothermal cholesteric liquid crystals subjected to small amplitude oscillatory rectilinear shear have been derived for three representative helix orientations. The imposition of oscillatory flow excites splay-bend-twist deformations when the helix is aligned along the flow direction, splay-bend deformations when the helix is along the vorticity gradient, and twist deformations when aligned along the velocity axis. The different nature of the excited elastic modes as well as the anisotropic viscosities are reflected in the anisotropy of the linear viscoelastic material functions for small amplitude rectilinear oscillatory shear. When the helix is aligned along the flow direction, cholesteric viscoelasticity is strongest, and exists in a relatively narrow band of intermediate frequencies. When the helix is aligned along the vorticity direction cholesteric viscoelasticity is significant in a relatively broad range of intermediate frequencies. Finally, when the helix is aligned along the velocity gradient direction, cholesteric viscoelasticity is relatively insignificant and only exists in a narrow band of frequencies. The cholesteric pitch controls the location of viscoelastic region on the frequency spectrum, but only when the helix is not oriented along the vorticity axis.     

“Fracture” phenomena in shearing flow of viscous liquids

In start-up of steady shearing flow of two viscous unentangled liquids, namely low-molecular-weight polystyrene and -D-glucose, the shear stress catastrophically collapses if the shear rate is raised above a value corresponding to a critical initial shear stress of around 0.1–0.3 MPa. The time dependence of the shear stress during this process is similar for the two liquids, but visualization of samples in situ and after quenching reveals significant differences. For -D-glucose, the stress collapse evidently results from debonding of the sample from the rheometer tool, while in polystyrene, bubbles open up within the sample, as occurs in cavitation. Some similarities are pointed out between these phenomena and that of lubrication failure reported in the tribology literature.     

The origin of stress-oscillation damping during startup and reversal of torsional shearing of nematics

Using a controlled-temperature shear cell mounted on a polarizing microscope, we observe the behavior of nematic 4,4-n-octyl-cyanobiphenyl (8CB) during start-up and reversal of shearing in a torsional parallel-plate geometry and correlate this behavior with rheological measurements. During the start-up, a sequence of birefringent rings, or twist walls, are observed that originate at the sample edge and propagate radially inward. Each twist wall is a thin region in which the director is twisted out of the plane of the velocity and velocity-gradient directions. The radial variation of in-plane orientation can be explained by the variation of strain in the parallel-plate device. A high Ericksen-number solution of the Leslie-Ericksen equations predicts a damped oscillatory shear stress response which agrees quantitatively with the measured stress oscillations out to an edge strain of around 50. The damping of the stress oscillations is due to the nonuniformity of strain in the parallel-plate geometry. On reversal of the flow, if the strain, , is smaller than about 500 units, the damping of stress oscillations is reversed; this correlates with an outward radial migration of twist walls. When > 500, disclinations nucleate and spoil the reversibility of stress damping.Deceased