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.     

Simulation of transient banded textures of sheared nematic polymers

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.     

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 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).     

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.     

Twin nematic phenylbenzoates in a.c. electric fields

The orientational behaviour of nematic compounds having twin phenylbenzoate mesogens was examined under a wide range of a.c. electric fields (0-2 V mum-1 and 10Hz-50 kHz). For this study, crossed polarizing optical microscopy (POM) and real-time X-ray diffraction (RTXRD) measurements were employed to investigate optical and orientational response. These nematic compounds have a positive dielectric anisotropy and a relatively low epsilon// relaxation frequency which allowed study in both homeotropic and planar orientations over a controllable frequency range. The optical behaviour and X-ray results corresponded well, providing a tool for understanding the orientational behaviour of these liquid crystals. For homeotropic alignment, an electric field of over 1 V mum-1 was required in order to obtain good orientation. However, homeotropic orientation depended on a delicate balance between thermal fluctuations and dielectric torque imposed by the electric field, which are both strongly related to the elasticity of the LC domains. Due to this effect, the highest orientation parameter achieved for homeotropic orientation was only 0.48, which indicated that this state was still non-equilibrium. On the other hand, for planar orientation, a uniform texture with orientation parameter of 0.65 was easily obtained even at electric fields as low as 0.2 V mum-1. The application of an electric field stronger than 1 V mum-1 induced a distortion in the texture, and reduced the orientation parameter to 0.45 for planar alignment.     

Role of steric factors in the mechanism of separation of structural isomers with nematic sorbents

The model of a nematic binary mixture of rigid biaxial molecules is used to calculate the coefficients of selectivity enhancement S _m/p (the ratio between the activity coefficients ofmeta- andpara-substituted benzenes as sorbates at infinite dilution) in the nematogenic matrix of a nematic liquid-crystal sorbent and the parameters of orientation order of the components. It was found that in systems of particles in which interaction between the particles consists in steric repulsion, the Sm/p coefficient is less than 1 and is practically constant in the isotropic phase, whereas in the nematic phase, S _m/p is greater than 1 and increases in parallel with the order parameter.     

Slow dynamics of thin nematic films in the presence of adsorbed nanoparticles

Recent experiments indicate that liquid crystals can be used to optically report the presence of biomolecules adsorbed at solid surfaces. In this work, numerical simulations are used to investigate the effects of biological molecules, modeled as spherical particles, on the structure and dynamics of nematic ordering. In the absence of adsorbed particles, a nematic in contact with a substrate adopts a uniform orientational order, imposed by the boundary conditions at this surface. It is found that the relaxation to this uniform state is slowed down by the presence of a small number of adsorbed particles. However, beyond a critical concentration of adsorbed particles, the liquid crystal ceases to exhibit uniform orientational order at long times. At this concentration, the domain growth is characterized by a first regime where the average nematic domain size LD obeys the scaling law LDt approximately t1/2; at long times, a slow dynamics regime is attained for which LD tends to a finite value corresponding to a metastable state with a disordered texture. The results of simulations are consistent with experimental observations.     

Thermodynamic model of surfactant adsorption on soft liquid crystal interfaces

The Gibbs adsorption isotherm for planar liquid crystal/fluid interfaces is derived using the anisotropic Gibbs-Duhem equation. The Gibbs adsorption isotherm for planar interfaces is used to analyze the adsorption-driven orientation transition in aqueous solutions of anionic surfactants in contact with rodlike uniaxial nematic liquid crystal films. In qualitative agreement with experiments, the model predicts that, as the surfactant concentration increases, the tangential (planar) average molecular orientation of the liquid crystal with respect to the interface undergoes a transition to a normal (homeotropic) orientation. The anchoring coefficient or strength of anisotropic component of the interfacial tension is shown to depend on the surfactant's concentration. Analyzing the response to addition of a co-cation, the model reveals that, as the fractional coverage of the surfactant's chains increases, the interpenetration of liquid crystal molecules between the adsorbed surfactant tails promotes the orientation transition; at even higher surfactant chain concentrations, interpenetration is hindered because of lack of available space and a random surface orientation emerges. Thus, for aqueous surfactant solutions in contact with nematic liquid crystals, increasing the surfactant concentration leads to the following interfacial liquid crystal orientation transition cascade, planar orientation --> homeotropic orientation --> random orientation, which can lead to new sensor capabilities and surface structuring processes.     

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.     

Viscoelastic theory for nematic polymer interfaces

A macroscopic theory for the dynamics of compressible nematic polymer‐viscous fluid interfaces is developed from first principles. The theory is used to define and characterize the basic interfacial viscoelastic material properties of the ordered interfaces. The theory is based on a decomposition of the kinematic fields and nematic tensor order parameter that takes into account the symmetry breaking of the interface. The interfacial rate of entropy production used to identify the interfacial viscoelastic modes is given in terms of surface rate of deformation tensor and the surface Jaumann derivative of the tangential component nematic tensor order parameter. The derived surface viscous stress tensor is asymmetric and thus describes surface flow‐induced changes in the tensor order parameter. Consistency with the Boussinesq surface fluid appropriate for Newtonian interfaces is established. The interfacial material functions are identified as the dynamic surface tension, the interfacial dilational viscosities, and the interfacial shear viscosities. The interfacial material functions depend on the surface tensor order parameter and as a consequence anisotropy is their characteristic feature. Two characteristic interfacial tensions and two dilational viscosities are predicted depending on the director orientation. In addition six interfacial shear viscosities arise as the directors sample the velocity, velocity gradient, and vorticity directions. Finally the theory provides for the necessary theoretical tools needed to describe the interfacial dynamics of nematic polymer interfaces, such as capillary instabilities, Marangoni flows, and wetting phenomena.     

Experimental study of the director pattern dynamics in the vicinity of the Fréedericksz twist geometry

We present an experimental study of the transient periodic structures appearing in the nematic director field in the magnetically induced reorientation of the director in the vicinity of the twist Fréedericksz geometry. Thin nematic samples (50?µm thick) were exposed to magnetic fields of variable intensity and orientation relative to the surface aligning direction of the sample. The director reorientation was induced by a rapid rotation of the sample in the static magnetic field producing a misalignment between the director and the magnetic field. The director field was optically monitored during the reorientation process and the transient periodic structures were characterized. Two types of periodic structures could be identified, namely bands and walls. Walls grow from bands close to the twist Fréedericksz geometry. The time dependence of the wave length and inclination of the periodic structures was obtained as a function of the magnetic field intensity and orientation relative to the surface aligning direction of the sample. The results for the bands are compared with the predictions of a model that we specifically developed to account for the non-orthogonal field orientations. It is seen that our model can account rather well for the experimental results considering that it uses only the field rotation time as adjustable parameter. All other model parameters are known.     

Electrical orientation behaviour of a nematic liquid crystal with negative dielectric anisotropy above the microelectrodes

Factors for the electrical orientation on interdigitated microelectrodes deposited on a substrate, a microdielectrometric sensor (or a sensor), were discussed experimentally using a model nematic liquid crystal with negative dielectric anisotropy. The electrical orientation behaviour of the nematic liquid crystal was investigated using microdielectrometry and polarised optical microscopy. The experimental results were discussed in relation to electric-field line, surface topology, anchoring of the liquid crystalline molecules to the microelectrodes, and transversal rotation of a rode-like molecule of the liquid crystal with negative dielectric anisotropy.     

Chiral conflict. The effect of temperature on the helical sense of a polymer controlled by the competition between structurally different enantiomers: from dilute solution to the lyotropic liquid crystal state

Helical polymers appended with paired structurally different enantiomers, which have opposing helical sense preferences, yield a new kind of relationship between optical activity and temperature, and also reveal unusual details of the nature of chiral interactions. Consistent with a statistical physical theory developed for these experiments, the proportion of the competing chiral groups, determined by synthesis, fixes the compensation temperature at which the helical senses are equally populated. The lyotropic liquid crystal state formed by these polymers yields therefore a nematic state at any chosen temperature over a very wide range, with a cholesteric state arising with tightening pitch as temperature deviates from this point. Far from the nematic temperature, the pitch reaches the nanometer scale and therefore the reflection of visible light. Before crossing zero at the nematic temperature, the optical activity becomes so large that it may be observed with the unaided eye through crossed polarizers.     

Phases and phase transitions in a nematic lyotropic system with a biaxial phase

NMR spectroscopy and optical microscopy have been used to study phase transitions and structure in nematic lyotropic mesophases formed by potassium laurate, decylammonium hydrochloride and water. The different mesophases obtained in a well-defined composition range have been characterized, by deuterium NMR, following the evolution of the D₂O spectra as a function of temperature and of the orientation of the samples with respect to the magnetic field. Wide ranges of biaxiality have been found and the asymmetry parameter of the averaged electrical field gradient tensor on the deuterium of the D₂O molecule has been determined. The presence of the different mesophases has always been confirmed by observing oriented samples under the polarizing optical microscope.     

Texture formation under phase ordering and phase separation in polymer-liquid crystal mixtures

Computational modeling of texture formation in coupled phase separation-phase ordering processes in polymer/liquid crystal mixtures is performed using a unified model based on the nematic tensor order parameter and gradient orientation elasticity. The computational methods are able to resolve defect nucleation, defect-defect interactions, and defect-particle interactions, as well as global and local morphological features in the concentration and order parameter spatiotemporal behavior. Biphasic structures corresponding to polymer dispersed liquid crystals (PDLCs), crystalline filled nematic (CFNs), and random filled nematics (RFNs) are captured and analyzed using liquid crystal defect physics and structure factors. Under spinodal decomposition due to concentration fluctuations, the PDLC structure emerges, and the nucleation and repulsive interaction of defects within nematic droplets leads to bipolar nematic droplets. Under spinodal decomposition due to ordering fluctuations, the CFNs structure emerges, and the stable polymer droplet crystal is pinned by a lattice of topological defects. For intermediate cases, where the mixture is unstable to both concentration and nematic order fluctuations, the RFN structure emerges, and polymer droplets and fibrils are pinned by a defect network, whose density increases with the curvature of the polymer-liquid crystal interface. The simulations provide an information of the role of topological defects on phase separation-phase ordering processes in polymer-liquid crystal mixtures.     

条带织构装饰技术观察含T─型液晶基元的热致性聚芳酯液晶态的向错

采用条带织构装饰新技术研究了含Ｔ─型液晶基元的热致性聚芳酯液晶态的向错形态．经过培养的液晶样品无需剪切，淬火后便可呈现出围绕向错点取向排列的条带织构，而条带织构长轴的垂直方向正代表了液晶基元的指向矢方向，这样，在普通偏光显微镜下就能直接观察到这些条带织构装饰的强度Ｓ＝±１／２和Ｓ＝±１的向错，并观察到Ｓ＝－３／２的高强度向错和闭环状的反转壁．     

Dynamic behaviour at a nematic liquid crystal-rubbednylon interface using evanescent wave photon correlation spectroscopy

Photon correlation spectroscopy of light scattered by director fluctuations from an evanescent optical wave propagating in the nematic liquid crystal 5CB is used to study the interfacial dynamic behaviour of the liquid crystal. The intensity correlation function of light scattered by interfacial orientation fluctuations is measured by illuminating to give a short optical penetration depth within the nematic. These surface scattering correlation functions strongly differ from the bulk correlation function and are interpreted in terms of a nematic surface orientation mode arising from the coupling between the director field and the fluid velocity. It is shown that the analysis of the surface mode gives a method for measuring anchoring energies in liquid crystals. The anchoring energy obtained for rotation of the director away from the rubbing direction about an axis normal to the surface for 5CB at a rubbed nylon surface is 7.14±0.7 × 10-² ergcm-².     

Guided-wave liquid-crystal photonics

In this paper we review the state of the art in the field of liquid-crystal tunable guided-wave photonic devices, a unique type of fill-once, molecular-level actuated, optofluidic systems. These have recently attracted significant research interest as potential candidates for low-cost, highly functional photonic elements. We cover a full range of structures, which span from micromachined liquid-crystal on silicon devices to periodic structures and liquid-crystal infiltrated photonic crystal fibers, with focus on key-applications for photonics. Various approaches on the control of the LC molecular orientation are assessed, including electro-, thermo- and all-optical switching. Special attention is paid to practical issues regarding liquid-crystal infiltration, molecular alignment and actuation, low-power operation, as well as their integrability in chip-scale or fiber-based devices.