Simulation of transient banded textures of sheared nematic polymers

Abstract

Nematic polymers, under certain conditions, develop a transient banded texture after cessation of simple shear flow when observing the sheared sample between crossed polars. Here we present a viscoelastic model that describes the formation mechanism of this well-characterized but yet unexplained phenomenon for a typical uniaxial rigid rod nematic polymer. It predicts that the relaxation of shear-flow enhanced scalar order parameter spatial fluctuations produces spatially periodic torques on the director, thereby producing a transient banded texture when viewing the sample between crossed polars. Our numerical results and digitized optical pattern are in good agreement with reported experimental observations.     

The parabolic focal conic texture in a lyotropic liquid-crystalline polymer

Hydroxypropyl cellulose (HPC) forms liquid-crystalline solutions in both water and methanol. When these solutions are sheared, the banded texture seen in many liquid-crystalline polymers is formed. Detailed optical microscopy of the bands has been carried out, showing that the bands arise from a smooth variation in the orientation of the local extinction directions, and not (as previously suggested in the literature) from sharp kinks. Over a period of time, the bands degenerate to form a new texture, which appears as a square grid pattern of extinction when specimens are viewed between crossed polars. The location of the corners of the squares depends on whether the microscope is focused near the top or bottom surface. When focus is altered to the middle of the sample, the periodicity of the pattern is halved. This texture is identified with the parabolic focal conies previously seen in small molecule smectic and cholesteric materials.     

A study on the relaxation phenomena of nematic polymers after cessation of shear flow

A viscoelastic model, composed of the Ericksen and Landau-de Gennes nematic continuum theories, is used to study numerically the relaxation phenomena after cessation of simple shear flow for a model rigid rod uniaxial nematic polymer. This model predicts that under certain conditions the relaxation of stored molecular and coupling elastic free energies due to periodic fluctuations in the scalar order parameter results in a transient periodic distortion of the director field. These conditions are that: (1) the ratio of the wavelength scales of the initial periodic spatial variation in the scalar order parameter k_s to the initial periodic planar director orientation fluctuation kφ (i.e. k_S/kφ) and the amplitude of the initial S spatial variation exceed certain minimum values, and (2) kφ is not zero. It is shown that the wavelength selection mechanism is controlled by the director reorientation-induced backflows. The digitized optical patterns of the transient periodic director field show transient periodic optical patterns similar to the transient banded texture nematic polymers exhibit after cessation of shear flow when observed between crossed polars. The numerical results and digitized optical patterns replicate frequently reported experimental observations.     

The identification of the sign and strength of disclinations in the schlieren (nucleated domain) texture of the nematic phase,by optical microscopy

ABSTRACT

The optical texture of the nematic phase, variously known as the schlieren, structure à noyuax or nucleated domain texture, was identified over a century ago as being an array of point singularities. When viewed between crossed polars, patterns of dark brushes radiate from each point nucleus. The sign and strength of each nucleus can be uniquely determined from the changes in the orientation of these brushes when either the sample or the crossed polars are rotated, from two formulae given by Chadrasekhar in 1977. However, these were given with little exemplification and have been largely overlooked. Consequently, the majority of the discussions given in current literature are either incomplete and confusing or, in some cases, incorrect. Here, we provide a detailed explanation of the textures and their behaviour as viewed with the most commonly used experimental geometry (i.e. with a rotating sample and stationary polars).     

Effect of the thermal history on the phase transition and the liquid crystalline structure of thermotropic polyesters

A series of triad type thermotropic polyesters based on phenylsulfonyl hydroquinone and α,ω-bis(4-carboxyphenoxy)alkane was prepared, and the effect of the thermal history on the phase transition and the liquid crystalline structure of the polyesters was studied. The phase transition was significantly affected by the thermal history. When annealed at various temperatures, multiple endotherms were observed for all polyesters in DSC thermograms. A phase stability concept was employed to explain the complicated phase transitions. The time evolution of the liquid crystalline structure was investigated by optical microscopy and transmitted light intensity measurement under crossed polars during annealing. The steady decrease in the density of disclinations with accompanying increase of transmitted light intensity was observed. Depending on the surface conditions of the liquid crystal polymer film, two markedly different domain growth patterns and different textures were found on isothermal annealing; the continuous wormlike texture and the discontinuous droplet texture. The structural relaxation of the deformed texture during annealing was also studied. When shear was applied, the characteristic banded texture was formed in all polyesters.     

Analysis of transient periodic textures in nematic polymers

A numerical solution of the Leslie-Ericksen equations for nematic liquid crystals is obtained for in-plane rotation of a strong magnetic field. A transient periodic orientation develops as a result of in-plane director motion and the induced shear flow. At long times the in-plane director orientation results in steady splay-bend inversion walls. A linear stability analysis shows that the inversion walls are unstable to perturbations out of the plane for elastic coefficients characteristic of nematic polymers. Calculations of transmitted light intensity through crossed polarizers for the computed orientation development predict the evolution of a banded texture, as observed experimentally.     

Crystallization and morphology of melt-solidified poly(vinylidene fluoride)

Crystallization of poly(vinylidene fluoride) (PVF₂) from the melt yields two types of spherulites. The first consists of large, highly birefringent, and tightly banded spherulites of the α-form, which are seen at all temperatures. The second type, termed mixed, crystallizes with a newly reported unit cell which appears to be the correct one for γ-PVF₂, but may contain inclusions of a different form (probably α-PVF₂); it is seen only at relatively high temperatures and frequently exhibits irregular or disorganized birefringent and morphological features. In thin films, some mixed spherulites contain regions of single-crystal-like aggregates which are grown parallel to the substrate and appear essentially nonbirefringent between crossed polars. Mixed spherulites frequently undergo transformations at their growth fronts leading to initiation of α-growth. These transformations are associated with the generally higher growth rate of α-spherulites which may exceed that of their mixed counterparts by almost seven times. However, with increasing temperature this difference in growth rates is progressively reduced and ultimately reversed.     

Quenched disorder in a liquid-crystal biosensor: adsorbed nanoparticles at confining walls

We analyze the response of a nematic liquid-crystal film, confined between parallel walls, to the presence of nanoscopic particles adsorbed at the walls. This is done for a variety of patterns of adsorption (random and periodic) and operational conditions of the system that can be controlled in experimental liquid-crystal-based devices. We compute simulated optical textures and the total optical output of the sensor between crossed polars, as well as the correlation function for the liquid-crystal tensor order parameter; we use these observables to discuss the gradual destruction of the original uniform orientation. For large concentrations of particles adsorbed in random patterns, the liquid crystal at the center of the sensor adopts a multidomain state, characterized by a small correlation length of the tensor order parameter, and also by a loss of optical anisotropy under observation through crossed polars. In contrast, for particles adsorbed in periodic patterns, the nematic at the center of the cell can remain in a monodomain orientation state, provided the patterns in opposite walls are synchronized.     

Structure development of fibers from liquid-crystalline PET/60PHB copolyester

Effect of extrusion conditions, particularly temperature, on the structure development of fibers from poly(ethylene terephthalate) modified with 60 mol% p-hydroxybenzoic acid was investigated. Light microscopy revealed that the structure of the liquid-crystalline fiber was highly dependent on the extrusion temperature: low-temperature-spun fibers exhibited a structure with domains or clusters of crystallites randomly oriented, whereas the fibers spun at high temperatures had a well-developed fibrillar texture. Anisotropy of the fibers, as evidenced by dichroism and by the variation of brightness or darkness of the fibers between crossed polars, was significantly higher for those spun at relatively high temperatures. Scanning electron microscopy revealed that the fibers spun at relatively low temperatures had poorly oriented, nonuniform morphology. Those produced at relatively high temperatures, on the other hand, consisted of well-developed fibrils. X-ray diffraction patterns showed that the molecular orientation increased with increasing extrusion temperature. A model for the development of fiber structure from thermotropic liquid-crystalline polymers is proposed.     

Simultaneous optical observation of anisotropic texture for a concentrated solution of poly(γ-benzyl-l-glutamate) under transient stress response in shear flow

Simultaneous optical observation of anisotropic texture was performed under transient stress response in shear flow for a concentrated solution of poly(γ-benzyl-l-glutamate) (PBLG). Transient stress of the PBLG solution immediately after the onset of the shear flow showed a remarkable stress overshoot and damping oscillation behavior, followed by a steady state. On the other hand, simultaneous observation of the polarized optical microscopy showed the remarkable distortion of the banded texture immediately after the onset of the shear flow and the periodical changes in the retardation followed by a steady texture of the PBLG solution. The remarkable stress overshoot and the damping oscillation are closely related to the distortion of the banded texture and to the changes in the orientation of the rod-like molecules of the PBLG, respectively. Received: 15 December 1999/Accepted: 12 July 2000     

Banded texture in sheared a semiflexible thermotropic liquid-crystalline polyester and its graft copolymers with polyolefins

The formation of banded texture both in a semiflexible thermotropic liquid-crystalline polyester (SBH 112, synthesized from sebacic acid, 4,4′-dihydroxybiphenyl and 4-hydroxybenzoic acid, from Eniricerche, Milan) and in a blend of SBH with graft copolymers, consisting of a polyolefin (polyethylene or polypropylene) backbone and SBH grafts (COPPE, COPPP) has been studied by polarization microscopy and by scanning electron microscopy. The influence of the preparation conditions upon the perfection, characteristics and thermal stability of the banded texture has been investigated. The results show that the banded texture formed in SBH sheared films possesses greater perfection, smaller band width and larger angle of deviation, and higher thermal stability than the banded texture formed in COPPE and COPPP prepared under similar conditions. It has been assumed that the chain rigidity of the macromolecules of the system is mainly responsible for the formation and perfection of the banded texture. Received: 17 March 2000 Accepted: 26 July 2000     

BANDED TEXTURE FORMATION IN NEMATIC SOLUTION OF POLY (1,4-BENZAMIDE) IN SULFURIC ACID

The banded texture in films prepared from nematic poly (1,4-benzamide) (PBA)/H_2SO_4 solution by shearing and without shearing has been studied by using microscopy techniques. The kinetic parameters of banded texture formation γ_c and τ_b were measured for nematic solution of PBA by using parallel-plate shearing apparatus. The banded texture was also observed in randomly packed domains for nematic solution of PBA on standing without shearing. The properties of banded texture show no difference between the two samples with or without shearing.     

Band formation in HPC solutions by consecutive shears along orthogonal directions

Experiments of banded texture formation in lyotropic HPC aqueous solutions are reported. A parallel plate apparatus is used, which allows for consecutive shears along mutually orthogonal directions. In the double shear experiment, the effects of the following variables have been explored: first and second deformation shear units, shear rate of the second movement, delay time between the two deformations. The results show that the formation of a banded texture oriented orthogonally to the first shear is strongly enhanced by introducing the second shear motion. The mechanisms of formation of the texture are discussed.     

EVIDENCE FOR THERMOTROPIC LIQUID CRYSTALLINITY OF A FUSIBLE POLYDIACETYLENE

The thermotropic liquid crystalline behavior of a fusible polydiacetylene has beenstudied by using polarizing optical microscopy and wide angle X-ray diffraction. It wasfound that the typical threaded texture can exhibit in the melt and the banded texture canbe observed when applied a gentle shear to the melt. The results indicate that thispolydiacetylene is really a thermotropic liquid crystalline polymer.     

含氧化偶氮苯介晶基元共聚醚的合成与液晶行为

以1,6-二溴己烷(A)和1,10-二溴癸烷(B)为共缩聚单体,按不同摩尔配比与4,4'-二羟基氧化偶氮苯经相转移催化共聚醚化反应,合成了一系列主链上含有氧化偶氮苯介晶基元的共聚醚,它们均有好的液晶性,其取向膜观察到条带织构,当A/B的摩尔比为1时液晶态范围最宽。     

Development of orientation and texture during shearing of liquid-crystalline polymers

Using polarizing microscopy, we study the development of orientation and texture during slow shearing of liquid-crystalline solutions of poly(γ-benzyl-L-glutamate). Shearing of high molecular weight samples that are initially coarsely textured, or are uniformly oriented over regions of 1 mm², produces a steady state striped texture, for each of three different initial average orientations. The director field in the striped texture is on average aligned parallel to the flow direction, but with misalignment that varies periodically as we move in a direction orthogonal to flow, thus giving the sample a striped appearance under crossed polarizers, with stripes parallel to flow. After the stripes form, they become finer with increased shearing, or with increased shear rate. Along with the birefringent stripes, there are defect lines, parallel to the flow direction with a spacing similar to that of the stripes, i.e. 10 μm or less at steady state. The existence of separate time scales for the development of steady state orientation, and for the shrinkage of the texture length scale to a steady state, is consistent with a phenomenological scaling theory that had been postulated to explain the rheological behaviour of these fluids. Although the steady state striped texture is independent of initial orientation, transient textures during start-up of shearing are highly dependent on initial orientation; for some initial orientations, bands perpendicular to flow occur temporarily during shearing.     

UV-initiated solidification of liquid crystalline ethylcellulose/acrylic acid films and bands formed in this process

Solidification of liquid crystalline ethylcellulose/acrylic acid films was realized by UV-initiated polymerization of the solvent acrylic acid. It has been found that the original textures were immobilized to a great extent, and a novel “banded texture” formed at the same time. The optical properties of this texture were different from the banded texture formed by shearing lyotropic or thermotropic polymer liquid crystals. Formation of such bands is assumed to be related to an uncompleted phase separation.     

A simple method for the assessment of molecular orientation in transparent plastics mouldings

A simple practical method for assessing the principal birefringences of a transparent or translucent moulding as a function of depth has been developed. The results obtained on a number of poly(ethylene terephthalate) and polycarbonate mouldings have been used to characterise and quantify the optical anisotropy and hence the molecular orientation or residual stresses. The results are largely free from the distorting effects of optical dispersion of birefringence and specimen preparation. They highlight the hazards of estimating stresses or orientation from the observation of an unprepared moulding between crossed polars. They also agree with the published data on the distribution of birefringence through injection moulded plaques.     

THE MORPHOLOGY AND STRUCTURE OF POLYETHYLENE TEREPHTHALATE SPHERULITES

The morphology and structure of three types of normal and abnormal spherulites of polyethylene terephthalate cast from solution in dimethylphthalate were studied by polarizing microscopy, transmission electron microscopy and electron diffraction techniques. In the normal negative spherulites the [0]~* direction is parallel to the radius direction. In the normal positive spherulites the radius direction is parallel to the [6]~*. In the abnormal PET spherulites the Maltese cross extinction pattern in the polarizing microscope under crossed polars is oriented at 45°to the polars and there are concentric extinction rings around the center of the spherulite. Electron diffraction pattern indicates that [2]~* is parallel to the radius of the spherulite and this explains the observed extinction pattern, in the abnormal spherulite.     

Optical properties of a shear-deformed thermotropic cellulose derivative

The band texture of a thermotropic cellulose derivative, trifluoroacetoxypropylcellulose, was studied by optical microscopy. The texture consists of parallel, long, thin, black lines when viewed between crossed polarizers with one polarizer parallel to the shear direction. These lines are perpendicular to the shear direction. Their optical properties indicate that the molecules are cooperatively oriented and this orientation director alternates from 0° to ±45° from the shear direction, with most of them at ±45°. This band phenomenon is identical to that observed with thermotropic nematic copolyesters.