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.     

S-shaped deformation profiles in sheared liquid-crystalline polymers

A tracer particle technique has been used to investigate the deformation profiles of a liquid-crystalline polymer under shear between parallel plates. The system was an aqueous solution of hydroxypropylcellulose (HPC), the good transparency of which allows for optical observations over thicknesses of the order of millimetres, as used here. The results indicate that the deformation profile deviated considerably from linearity, whereas a linear profile was confirmed for isotropic liquids, including polymeric ones. For the HPC liquid-crystalline solution most of the deformation was concentrated close to the walls.     

Perturbation expansion of polymers in shear flow

The effect of shear flow on the excluded volume properties of bead spring chains is calculated via the perturbation expansion of the mean-square end-to-end distance with respect to the excluded volume parameter z. The coefficient of the series 〈R²〉/〈R²〉₀ = 1 + C₁ · z − … vanishes for large flow rates but shows a strong dependence on the shear rate in the intermediate regime.     

Adhesive liquid-crystalline polymers

The synthesis and characterization of liquid-crystalline polymers with possible good adhesive properties is reported. These polymers are prepared by alternating copolymerization of maleic anhydride and mesogenic alkenes. The spacer length m is varied (m = 2, 3, 4, 6, 8 and 9) and methoxybiphenyl is used as the mesogenic group. The glass transition temperature decreases and the isotropization temperature increases with spacer length. Depending on the spacer length and temperature, S_B and S_Ad mesophases can be observed. After annealing, spin-coated films of these polymers show very regular layered structures with a layer spacing similar to that in the bulk.     

Mixtures of liquid-crystalline polymers

A density-functional expansion method is used to derive the free energy of a polymer mixture. The expression obtained includes the entropy of mixing, the entropy of configuration of the chains and the interactions (both isotropic and anisotropic ones). The chains are modelled as interacting elastic lines (bend curvature). The method is very general, and we only focus our attention on binary mixtures. The phase diagram and the order parameters are calculated. We show some results for two types of mixtures: a nematic polymer in a non-mesomorphic particle (polymer or solvent) and in another nematic liquid crystal (small-molecule or polymer). We discuss the influence of the molecular weights, the persistence length and the interactions on the phase separation.     

Effect of shear history on the steady shear flow behavior of a thermotropic liquid-crystalline polymer

The steady shear stress (σ) and first normal stress difference (N₁) of a thermotropic liquid-crystalline polyester, poly[(phenylsulfonyl)-p-phenylene 1,10-decamethylene-bis(4-oxybenzoate)] (PSHQ10), in both the isotropic and nematic regions were measured as a function of shear rate (γ), using a cone-and-plate rheometer. For the study, PSHQ10 was synthesized via solution polymerization in our laboratory. The PSHQ10 was found to have (a) the weight-average molecular weight of 45,000 relative to polystyrene standards and a polydispersity index of 2, (b) a glass transition temperature of 88°C, (c) a melting point of 115°C, and (d) a nematic-to-isotropic transition temperature of 175°C. For the measurements of σ and N₁ in the nematic region of PSHQ10, its initial conditions for the startup of shear flow was controlled by (a) first heating an as-cast specimen to 190°C, (b) shearing there at γ = 0.085 s^?1 for about 5 min, and then (c) cooling slowly down to a predetermined temperature (130, 140, 150, 160, or 171°C) in the nematic region. For each γ chosen, after start-up of shear flow, we waited for a sufficiently long time until both the shear stress and first normal stress difference leveled off, giving rise to steady-state values of σ and N₁. Emphasis was placed on investigating the effect of shear history on σ and N₁ of PSHQ10 in the nematic region. For this, the following experiments were conducted: (a) a fresh specimen was sheared continuously by increasing the γ stepwise, and (b) a presheared specimen was further sheared continuously by increasing the γ stepwise. We have found that fresh specimens exhibited ‘shear-thinning’ behavior over the entire range of γ (0.008?0.27 s^?1) tested, whereas the presheared specimens exhibited both zero-shear viscosities and shear-thinning behavior. When using fresh specimens, we found that N₁ was positive over the entire range of γ (0.008–0.27 s^?1) tested. However, when using presheared specimens we found that (a) at very low γ, N₁ initially was negative and then became positive as shearing continued, and (b) at higher γ, N₁ was positive over the entire duration of shearing. © 1994 John Wiley & Sons, Inc.     

Dynamics of relaxation of entangled polymers in shear flow

The application of shear flow to entangled polymer melts can strongly modify its rheological and physicochemical behaviors, giving rise to an acceleration of several chemical processes such as diffusion-controlled reactions. In the present work, we investigate the modification of conformational and diffusive properties of an entangled polymer in shear flow by numerical methods. The flow affects both the conformational and diffusive properties of the system, giving rise to a quasinematic ordering of the macromolecules which take prolate spheroid shape with the main axis aligned to the shear direction. The shear flow is found to accelerate the overall diffusion of the chains in all directions at times longer than the polymer relaxation time. The polymer chains display a quite peculiar displacement behavior in direction parallel to the flow. At the same conditions, the linear relation between the diffusion constant in direction perpendicular to the flow and the inverse of the relaxation time, usually adopted in equilibrium regimes, is shown to hold even in the presence of flow.     

Coalescence in semiconcentrated emulsions in simple shear flow

The coalescence frequency in emulsions containing droplets with a low viscosity (viscosity ratio approximately 0.005) in simple shear flow has been investigated experimentally at several volume fractions of the dispersed phase (2%-14%) and several values of the shear rate (0.1-10 s(-1)). The evolution of the size distribution was monitored to determine the average coalescence probability from the decay of the total number of droplets. Theoretically models for two-droplet coalescence are considered, where the probability is given by P(c)=exp(-tau(dr)tau(int)). Since the drainage time tau(dr) depends on the size of the two colliding droplets, and the collision time tau(int) depends on the initial orientation of the colliding droplets, the calculated coalescence probability was averaged over the initial orientation distribution and the experimental size distribution. This averaged probability was compared to the experimentally obtained coalescence frequency. The experimental results indicate that (1) to predict the average coalescence probability one has to take into account the full size distribution of the droplets; (2) the coalescence process is best described by the "partially mobile deformable interface" model or the "fully immobile deformable interface" model of Chesters [A. K. Chesters, Chem. Eng. Res. Des. 69, 259 (1991)]; and (3) independent of the models used it was concluded that the ratio tau(dr)tau(int) scales with the coalescence radius to a power (2+/-1) and with the rate of shear to a power (1.5+/-1). The critical coalescence radius R(o), above which hardly any coalescence occurs is about 10 microm.     

Rheology of rodrun liquid-crystalline polymers

The rheological characterization of two commercial thermotropic liquid crystalline polymers based on poly(ethylene terephthalate) (PET) and para-hydroxybenzoic acid (PHB) is carried out. The thermal transitions determined by DMTA are explained by the random character of these copolyesters, in comparison with non-random copolyesters synthesized by Jackson and Kuhfuss. The evolution of the dynamic viscoelastic functions with time in the nematic state is concave in shape for the 20%PET/80%PHB copolymer, a result that leads us to treat this system as a suspension of solid spheres (unmolten crystals) where the volume fraction of crystals increases with time according to an Avrami equation. The response of 40%PET/60%PHB copolymer is similar to a chemical or physical gelation and the hypothesis that the polydomain structure gives rise to a network is considered. Continuous flow, time-independent viscosity results reveal the existence of a three-region flow curve for 40%PET/60%PHB copolymer, but a Newtonian zone followed by a shear thinning region for 20%PET/80%PHB sample. At high temperatures the isotropization of the samples leads to a very strong decrease of the activation energy of flow, which becomes zero for 40%PET/60%PHB. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36 : 253–263, 1998     

Interactions between colloidal particles in simple shear flow

Recent progress in experimental and theoretical developments dealing with colloidal. interactions between two spheres in shear flow is reviewed. A systematic comparison is made between spheres suspended in simple electrolyte and in cationic polyelectrolye solutions. Microrheological observations, performed with the traveling microtube, make an in-depth investigation possible of the colloidal forces and the mechanisms of polymer bridge formation. Reasons are discussed for the often-observed aging of colloidal aggregates. Finally, coagulation rates are presented for systems with weak and strong Brownian motion. It is shown that the often-used assumption of additivity of the ortho- and perikinetic coagulation rates is incorrect.     

Fast switching ferroelectric liquid-crystalline polymers

Ferroelectric liquid-crystalline side chain polymers containing polyacrylate or polysiloxane main chains, a mesogenic unit of three aromatic cores and chiral end groups were synthesized and characterized by D.S.C., optical microscopy, and X-ray diffraction. Polyacrylates with a flexible spacer of eleven methylene groups exhibit fast bistable switching in oriented samples (2 to 4μm cells) with response times of some ms at low D.C. voltages, making these polymers interesting for the fabrication of electrooptical devices. Somewhat longer response times were found for the first switchable polysiloxanes. In this case some problems in obtaining well orientated samples have to be solved.     

Fast switching ferroelectric liquid-crystalline polymers

The principles of ferroelectricity, especially in liquid crystals (FLC) and polymers, are briefly presented. In a liquid-crystalline side chain polyacrylate electro-optical switching with response times of 200–400 μs was measured. Besides the ferroelectric switching an even shorter electroclinic switching process was detected. The influence of the spacer length and the molecular weight on the ferroelectric properties is discussed. The kind and number of chiral centers and their location in the side group strongly affects the electrooptical properties. In one polymer a change of the optical contrast caused by a sign reversal of the spontaneous polarization was found. In another FLC polymer three switching states (antiferroelectric behaviour) were detected. With coloured and fluorescent FLC polymers, obtained by mixing or by copolymerization new promising applications in electrooptical devices are expected.     

Ideal rate of collision of cylinders in simple shear flow

The collision of particles influences the behavior of suspensions through the formation of aggregates for adhesive particles or through the contributions of solid-body contacts to the stress for nonadhesive particles. The simplest estimate of the collision rate, termed the ideal collision rate, is obtained when particles translate and rotate with the flow but have no hydrodynamic or colloidal interactions. Smoluchowski calculated the ideal collision frequency of spherical particles in 1917. So far, little work has been done to understand rate of collision for nonspherical particles. In this work, we calculate the ideal collision rate for cylindrical particles over a broad range of particle aspect ratios r defined as the ratio of length to diameter. Monte Carlo simulations are performed with initial relative positions and orientations that model the rate of approach of noninteracting particles following Jeffery orbits with several choices of the orbit distribution. The role of rotational motion of particles on collision frequency is elucidated by comparing the ideal collision rate calculations with similar calculations for nonrotating particles. It is shown that the ratio of the collision rate of cylinders to that of spheres that circumscribe the cylinders is proportional to 1/rr(e) for r ? 1 and r(e) for r ? 1. Here, r(e) is the effective aspect ratio defined as the aspect ratio of a spheroid having the same period of rotation as the cylinder. The effective aspect ratio of the cylindrical particles was determined using finite element calculations of the torque on nonrotating cylinders with their axes parallel to the velocity and velocity gradient directions. In addition to deriving the total collision rate, we categorize collisions as side-side, edge-side, and face-edge based on the initial point of contact. Most collisions are found to be side-edge for r ? 1 and face-edge for r ? 1, suggesting that nonlinear aggregates will develop if particles stick at the point of first contact.     

New liquid-crystalline polymers with chiral phases

Liquid-crystalline polyesters with cholesteric and probably chiral smectic C* phases were prepared using combined liquid-crystalline polymers (that is polymers with the mesogenic groups in the main chain as well as in the side groups). Copolyesters of these polymers and polymers with olefinic double bonds could be cross-linked retaining the liquid-crystalline phases. This resulted in cross-linked polymers with elastic properties.     

Phenomenological transient shear behavior of liquid crystalline polymers after the start-up of shear flow

Transient stresses of liquid crystalline polymers appear as damped oscillatory patterns after the start-up of shear flow. They are examined by using the constitutive equations which were modified to include the idea of an initial domain state in the Larson-Doi polydomain equation set. In order to be consistent with the phenomenological transient shear stress after the start-up in the region of low shear rates, the Hinch-Leal closure approximations were adopted for the domain-averaged (mesoscopic) fourth-order tensors of the director field. It is predicted as an important result that the amplitude of the first overshoot in the transient stress increases with an increase in the shear rate imposed at the start-up, which was found to be largely in agreement with phenomenology. In addition, the effects of parameters such as molecular concentration, initial domain size, and intensities of viscous and elastic contributions on the transient stress under the start-up process were also evaluated.