Uniaxial Rod Research Articles

Characteristics of Space, Leaky, and Creeping Waves in a Uniaxial Dielectric Rod

The excitation of space wave, leaky wave, and creeping wave in a cylindrical rod with uniaxial anisotropic permittivity and permeability is thoroughly characterized. The closed-form expressions of the space, leaky, and creeping waves in the uniaxial rod are derived for all source polarizations through the rigorous formulation, taking into account all higher order azimuthal harmonics and TE-TM mode coupling for the space and creeping waves. Conditions for obtaining a high space- and leaky-wave directivity are thoroughly examined for all source polarizations with variation in the vertical and horizontal permittivities/permeabilities and the rod radius. The leaky-wave phase and attenuation constants with variation in the rod parameters are investigated to identify the leaky-wave propagation regions of the uniaxial rod. Beam-scanning characteristics for the space and leaky waves are examined with variation in the uniaxial rod parameters. The complex pole loci for the azimuthally propagating creeping waves around the uniaxial rod are also investigated to identify the leaky, the creeping, and the trapped-mode regions.

Helicoidal dynamics of biaxial curved rods in twist-bend nematic phases unveiled by unsupervised machine learning techniques.

Uniaxial rods in a nematic phase diffuse preferentially in the direction parallel to the nematic director n[over ̂]. The nematic director field n[over ̂](r) of a chiral twist-bend nematic (N_{TB}) phase of achiral banana-shaped particles, recently discovered experimentally, displays a heliconical twist of given handedness and periodicity. Using simulations, we investigate the long-time macroscopic diffusion in N_{TB} phases, and find that the predilection of curved rods to diffuse in the direction of the twisting n[over ̂](r) yields a fascinating chiral dynamics along helices, even though achiral curved rods display Brownian motion with a nontrivial rototranslational coupling. We devise a machine learning protocol to characterize the helicoidal particle trajectories, finding that their pitch and radius are determined by the pitch and conical angle of the N_{TB} phase thereby connecting its structural and dynamical properties.

Influence of hydrogen bond on the mesomorphic behaviour in urethane based liquid crystalline compounds: Experimental and computer simulation study

We present a combined experimental and theoretical study on the novel hydrogen-bonded liquid crystalline complex (UR-LC11) exhibiting both nematic and smectic phases upon cooling. The complex was prepared by mixing 2-(2-methoxyethoxy)ethylbutyl carbamate (UR) as H-bond acceptor with calamitic mesogen 4′-((11-hydroxyundecyl)oxy)-[1,1′-biphenyl]-4‑carbonitrile (LC11) as H-bond donor. The complex was characterized by FTIR technique and its liquid crystalline properties were studied by differential scanning calorimetry (DSC) and polarized optical microscope (POM). The experimental IR spectra were compared with theoretically obtained IR spectra by Density Functional Theory (DFT) to suggest the structure of hydrogen-bonded liquid crystal (LC). The molecular dynamics (MD) simulations were performed to understand the impact of hydrogen bonding on the mesomorphic behaviour of the complex and the temperature dependency of the transitions between the mesophases. We determined that UR-LC11 is a stable H-bond acceptor/donor type complex and a single H-bond forms between the carbonyl oxygen atom of the amide moiety of UR and the hydrogen atom of the terminal hydroxyl group of the LC11. Although LC11 is present only in nematic liquid crystalline form, the new complex displayed both nematic and smectic phases during cooling. The reason for the two distinctive LC phases was explained by the presence of hydrogen bond interactions, which provides structural flexibility. Besides, H-bond maintains uniaxial rod shape of the molecule to promote self-assembly behaviour and induces positional ordering in the smectic phase. The enhancement in the self-assembly of the H-bonded chains in the complex is reflected in the increased ΔHfusion values. Due to the intermolecular π-π interactions of the phenyl rings and the formation of strong dipoles on the backbone, especially at the cyanobiphenyl end of the chains, the long-range directional order of the dipoles along their long axes are preserved at elevated temperatures and nematic to isotropic phase transition is observed at around 370 K both experimentally and theoretically.

Biaxial nematic stability in the rod-plate mixture with a dopant: The restricted-orientation model on the 3rd virial level

We analyze the effect of doping a binary mixture of uniaxial rod(R)- and plate(P)-like hard parallelepipeds having equal volumes and conjugated aspect ratios γR=1/γP=5. Uniaxial rods (L) or plates (T) with greater elongations γL=1/γT=10 were used as an admixture. The aim of the work is to examine this effect as a possible tool to stabilize the biaxial (Nb) phase in the P–R mixture, where Nb is known to be unstable with respect to demixing into two uniaxial nematics. The formalism to study orientational phase transitions is the off-lattice restricted-orientation (Zwanzig) model of a multi-component mixture of rectangular parallelepipeds with the EOS on the 3rd virial level. The phase biaxiality parameters of components and the second-order transition lines are located by direct minimization of the Gibbs energy. The results obtained by the examples of ternary systems show that introducing of small amounts of L or T into the reference P–R system promotes broadening of the Nb domain and may induce its stabilization. The case of L admixtures shows that an increase of the dopant particle volume results in a trend towards enhancement of the Nb phase relative stability.

Equivalence principle algorithm using characteristic basis functions with application to finite periodic arrays including uniaxial dielectrics and conducting objects

In this paper, an equivalence principle algorithm combined with the characteristic basis function (CBF) method has been developed to efficiently analyze the finite periodic arrays composed of uniaxial dielectric materials and conducting objects. Three kinds of the CBFs for each equivalent surface and its surrounding object are simultaneously constructed using multiple plane wave illuminations and singular value decomposition technique, and thus memories related to the scattering and translation operators are significantly saved, while retaining good computational accuracy. Numerical results of a frequency selective conducting array, a uniaxial dielectric cube array, and a periodic array of the composite object including a uniaxial rod and a split ring resonator are given to illustrate good performance of proposed method.

Critical strains and necking phenomena for different steel sheet specimens under uniaxial loading

When defining ultimate loads or failure criteria for shells, vessels and containment liners, for instance, reference will be made to critical strains of the material under consideration. In general the critical strains are derived from uniaxial tensile test results obtained with rods. The actual deformation behaviour of sheets (plate and shell type structures), however, differs considerably from the uniaxial rod behaviour. From various tests – along with theoretical investigations – it was found that for membrane or even bending stressed sheets higher ultimate strains are reached. The typical strain behaviour caused by increasing load starts with uniform strain distribution over the specimen length and finally ends with localized necking. As “critical strains” the well known uniform elongation strain and the ultimate strain are defined. For sheets in addition the quasi uniform elongation strain has been introduced in this paper. Whereas for rods under tension localized necking is directly following the uniform straining, tests with sheets show a so-called diffuse necking behaviour before localized necking starts. As a consequence the deformation capacity of steel sheets turns out to be significantly higher than relying on the data from standard tension tests with rods.

Biaxial nematic phases in fluids of hard board-like particles

We use density-functional theory, of the fundamental-measure type, to study the relative stability of the biaxial nematic phase, with respect to non-uniform phases such as smectic and columnar, in fluids made of hard board-like particles with sizes σ(1) > σ(2) > σ(3). A restricted-orientation (Zwanzig) approximation is adopted. Varying the ratio κ(1) = σ(1)/σ(2) while keeping κ(2) = σ(2)/σ(3), we predict phase diagrams for various values of κ(2) which include all the uniform phases: isotropic, uniaxial rod- and plate-like nematics, and biaxial nematic. In addition, spinodal instabilities of the uniform phases with respect to fluctuations of the smectic, columnar and plastic-solid types are obtained. In agreement with recent experiments, we find that the biaxial nematic phase begins to be stable for κ(2)≳ 2.5. Also, as predicted by previous theories and simulations on biaxial hard particles, we obtain a region of biaxiality centred at κ(1)≈κ(2) which widens as κ(2) increases. For κ(2)≳ 5 the region κ(2)≈κ(1) of the packing-fraction vs. κ(1) phase diagrams exhibits interesting topologies which change qualitatively with κ(2). We have found that an increasing biaxial shape anisotropy favours the formation of the biaxial nematic phase. Our study is the first to apply FMT theory to biaxial particles and, therefore, it goes beyond the second-order virial approximation. Our prediction that the phase diagram must be asymmetric in the neighbourhood of κ(1)≈κ(2) is a genuine result of the present approach, which is not accounted for by previous studies based on second-order theories.

Thermotropic Biaxial Liquid Crystalline Phases in a Mixture of Attractive Uniaxial Rod and Disk Particles

We present the first examples of thermotropic biaxial mesophases in mixtures of model attractive uniaxial molecules. Nematic and smectic biaxial phases are identified. The nematic biaxial phase has remained a key challenge in the science of liquid crystals since it was first proposed almost 40 years ago. Very recently the first experimental evidence of stable biaxial nematic phases has been obtained in thermotropic liquid crystals of single component biaxial mesogens. Still elusive is the possibility of stabilizing biaxial nematic phases in mixtures of uniaxial particles. We use Monte Carlo molecular simulations to study model mixtures of rodlike and disklike molecules interacting through two intermolecular potential models: one incorporating spherically symmetric (isotropic) attractive interactions; another with anisotropic attractive interactions. These models exhibit nematic and smectic biaxial phases.

A general nonlocal microplane concrete material model for dynamic finite element analysis

A method for properly including the effect of crack formation for both fine and coarse finite element meshes for a microplane concrete material model is described. For fine meshes, a weighted integral strain averaging approach is used to ensure that the softening is nonlocal and that the energy that is dissipated at failure is correctly modeled. For coarse meshes, an enriched strain field is employed in which localized and nonlocalized strain tensors are defined at each point within an element. The difference between the two strain tensors depends upon the characteristic crack width and the strain softening modulus of the material. This approach is particularly straightforward for the microplane model because a one-dimensional relationship is assumed for each microplane and the responses are integrated naturally to obtain the effect of crack width on the strain and stress tensors. The method is implemented within an explicit, dynamic, finite element program. Several simple finite element models are analyzed. A single element is loaded uniaxially in tension and compression for a variety of crack width values and the results show that the softening portion of the stress-strain curve varies in an appropriate manner. A uniaxial rod model is analyzed for an impulse load and the response is shown to be consistent for both fine and coarse meshes.

Finite elements for dynamic modeling of uniaxial rods with frequency-dependent material properties

New developments in a method of modeling frcquency-depedent material damping and modulus in structural dynamics analysis are reported. The fundamental feature of the general method is the introduction of augmenting thermodynamic fields (ATF) to interact with the mechanical displacement field of continuum mechanics. These ATF are directly motivated by the “internal state variables” of materials science. The coupled partial differential equations which govern the dynamic behavior of a uniaxial rod are numerically solved within the computational framework of the finite element method, resulting in “ATF-damped” finite elements. Previous work in the development of this modeling technique is characterised by the use of a single augmenting field, with application to lightly-damped rods, bourns and truss structures. New developments include : (1) demonstration of the ability to model the behavior of high-damping materials; and (2) the use of multiple augmenting fields to model materials whose behavior departs significantly from that of standard anelastic solids.

Light Scattering and Contrast in Thermally Addressed Liquid Crystal Displays

Abstract The effects of structural order on the light scattering characteristics of liquid crystal display cells containing smetic p-n-octyl-p′-cyanobiphenyl have been investigated. The scattering characteristics of different structures in the cell due to surface treatments are qualitatively analyzed for their effects on the contrast ratio when used in the thermally addressed liquid crystal display (TALC). Of the four structures investigated, i.e., homeotropic, fan-like, uniaxial rods and spherulites, the spherulitic structure has been found to exhibit the scattering profile best suited for high contrast because of the near-zero scattering near the incident beam. Based on the light scattering theory for spherulites, optimization of structural parameters such as size and order of spherulites, and device design such as collecting angle of projection lens for maximum display contrast has been predicted. Methods to improve contrast have also been discussed.