Bookshelf Geometry Research Articles

Strain and vorticity analyses using rotated porphyroclasts in the Tanbour metamorphic rocks: Evidence of transpressional deformation along the Sanandaj-Sirjan metamorphic belt, SW Iran

The Tanbour Metamorphic Complex (TMC) is located within the Sanandaj-Sirjan Metamorphic Belt, SW Iran, along the northeastern margin of the Afro-Arabian plate. Detailed kinematic and strain analyses were combined with vorticity estimates on rocks from the TMC to document patterns and geometry of deformation. The strain parameter measurements including strain ratio in the XZ principal plane of strain ellipsoid (RXZ), strain ellipsoid shape (K) and strain intensity (D), highlight the deformed gneissic rocks in the TMC exhibit constrictional to approximately plane-strain shape of the strain ellipsoids. Several kinematic shear sense indicators including S/C fabrics, mantled porphyroclasts, oblique grain shape, micro-shears with bookshelf geometry and mineral fish show top-to-the-SE sense of shear. The quantitative kinematic analyses highlight that Wk varies between 0.64 and 0.78, implying a general shear flow with 44% < simple shear <58% and 42% < pure shear <57%. The exhumation of TMC is attributed to the exhumation-controlled transpressive tectonic process during oblique convergence between the Afro-Arabian continent and the Central-Iranian microcontinent which started since Upper Cretaceous.

Structural styles, hydrocarbon prospects, and potential of Miano and Kadanwari fields, Central Indus Basin, Pakistan

The main purpose of this paper is to evaluate the structural styles of Miano and Kadanwari Fields, located in the Central Indus Basin, Sindh province, Pakistan. Discovered in 1989 and 1993, Kadanwari and Miano Fields are located on the Pano Aqil graben and Kadanwari High, in between two extensive NW-SE-oriented regional highs, i.e., Jacobabad-Khairpur and Mari-Kandhkot High. The Central Indus Basin is an extensional basin exhibiting normal faulting. Fourteen seismic lines were interpreted to understand the presence, trend, and development of the fault system in the Central Indus Basin along with the assessment of the Petroleum system based on the analysis of seismic reflection data and well logs across the Cretaceous clastic reservoirs. The tectonics of Miano and Kadanwari Fields has been interpreted with the presence of normal faults, strike-slip faults, and inverted structures leading to ambiguities about the structural framework of the area. However, with this detailed study, an extensional fault system has been interpreted in the Cretaceous and lower Tertiary sections over a detachment in the incompetent Sembar Formation. In Miano Field, the faults are dominantly recognized to have NNW-SSE trend due to NW-SE-oriented extension related to northward drift of Indian Plate from Madagascar. Resultantly tilted fault blocks of half grabens geometry have developed in the area depicting bookshelf geometry of an extensional system Wrench fault system is found to be absent with exception of a probable strike-slip fault in the Kadanwari Field. The fields are interpreted to have significant recoverable reserves of 1662 (bcf) equivalents to 280 (mmboe) in tilted fault blocks having an average displacement of about 50 m.

Weak anchoring effects in smectic-A Fréedericksz transitions

In smectic-A (SmA) liquid crystals, rod-like molecules are organized into layers with their optical axis oriented along the normal to these layers. When subject to an external field and for a certain critical threshold, these layers can buckle into a new different configuration. Here, we consider SmA liquid crystals which are confined between two parallel plates aligned in the so-called bookshelf geometry and subject to an external magnetic field. By assuming that instability is induced by a uniform field, we investigate the influence of the anchoring strength on the critical threshold field and on the layers shape by a perturbative analysis to the equilibrium equations. Main differences with respect to the standard Fréedericksz transition of nematics are highlighted. The behavior of this threshold effect suggests a new way to measure geometrical and constitutive parameters of a SmA sample.

Casimir-like interactions and surface anchoring duality in bookshelf geometry of smectic-A liquid crystals.

We analyze the transverse intersubstrate Casimir-like force, arising as a result of thermal fluctuations of the liquid crystalline layers of a smectic-A film confined between two planar substrates in a bookshelf geometry, in which the equidistant smectic layers are placed perpendicular to the bounding surfaces. We discuss the variation of the interaction force as a function of the intersubstrate separation in the presence of surface anchoring to the substrates, showing that the force induced by confined fluctuations is attractive and depends on the penetration length as well as the layer spacing. The strongest effect occurs for tightly confined fluctuations, in which the surface anchoring energy is set to infinity, where the force per area scales linearly with the thermal energy and inversely with the fourth power of the intersubstrate separation. By reducing the strength of the surface anchoring energy, the force first becomes weaker in magnitude but then increases in magnitude as the surface anchoring strength is further reduced down to zero, in which case the force tends to that obtained in the limit of strong anchoring.

ChemInform Abstract: Smectic Layer Instabilities in Liquid Crystals

AbstractReview: 111 refs.

Smectic layer instabilities in liquid crystals.

Scientists aspire to understand the underlying physics behind the formation of instabilities in soft matter and how to manipulate them for diverse investigations, while engineers aim to design materials that inhibit or impede the nucleation and growth of these instabilities in critical applications. The present paper reviews the field-induced rotational instabilities which may occur in chiral smectic liquid-crystalline layers when subjected to an asymmetric electric field. Such instabilities destroy the so-named bookshelf geometry (in which the smectic layers are normal to the cell surfaces) and have a detrimental effect on all applications of ferroelectric liquid crystals as optical materials. The transformation of the bookshelf geometry into horizontal chevron structures (in which each layer is in a V-shaped structure), and the reorientation dynamics of these chevrons, are discussed in details with respect to the electric field conditions, the material properties and the boundary conditions. Particular attention is given to the polymer-stabilisation of smectic phases as a way to forbid the occurrence of instabilities and the decline of related electro-optical performances. It is also shown which benefit may be gained from layer instabilities to enhance the alignment of the liquid-crystalline geometry in practical devices, such as optical recording by ferroelectric liquid crystals. Finally, the theoretical background of layer instabilities is given and discussed in relation to the experimental data.

Boundary Layers in Pressure-driven Flow in Smectic A Liquid Crystals

This article examines the steady flow of a smectic A liquid crystal sample that is initially aligned in a classical bookshelf geometry confined between parallel plates and is then subjected to a lateral pressure gradient which is perpendicular to the initial local smectic layer arrangement. The nonlinear dynamic equations are derived. These equations can be linearized and solved exactly to reveal two characteristic length scales that can be identified in terms of the material parameters and reflect the boundary layer behavior of the velocity and the director and smectic layer normal orientations. The asymptotic properties of the nonlinear equations are then investigated to find that these length scales apparently manifest themselves in various aspects of the solutions to the nonlinear steady state equations, especially in the separation between the orientations of the director and smectic layer normal. Non-Newtonian plug-like flow occurs and the solutions for the director profile and smectic layer normal share features identified elsewhere in static liquid crystal configurations. Comparisons with numerical solutions of the nonlinear equations are also made.

An Azo-Bridged Ferroelectric Liquid Crystal with Highly Enhanced Second and Third Harmonic Generation

A laterally azo-bridged trimer ferroelectric liquid crystal (FLC) incorporating a strong chromophore along its polar axis was synthesized and characterized by polarized-light optical microscopy, differential scanning calorimetry, two-dimensional X-ray diffraction analysis, electro-optical measurements, and nonlinear optical (NLO) investigations. This mesogen exhibits a thermodynamically stable enantiotropic SmC* phase and a bistable ferroelectric switching in a surface stabilized cell with bookshelf geometry. It gives the resonance-enhanced d(22) coefficient of 28 pm V(-1) (λ = 1.369 μm) for second harmonic generation (SHG), the largest NLO susceptibility reported to date for all FLCs. At the same wavelength, a new type of helicoidal phase matching assisted by the helical SmC* structure was identified. When the second harmonic wavelength of 780 nm is far away from the resonance wavelength (λ(max) = 572 nm), the d(22) coefficient is reduced to 6.8 pm V(-1) (λ = 1.56 μm). In addition to a strong SHG activity, the trimer also shows a strong third harmonic generation (THG) with an estimated third-order nonlinear susceptibility of χ((3)) = ~3 × 10(-11) esu (λ = 1.56 μm), among the largest χ((3)) value reported from THG measurements for liquid crystals. This work enables viable applications of FLCs in nonlinear optics and offers an innovative approach to develop new FLCs with larger NLO strength.

The pumping phenomenon in smectic C* liquid crystals

It is known from experiments that smectic C* liquid crystals arranged in a bookshelf geometry between two parallel glass plates can exhibit a pumping phenomenon under the application of an electric field when the lower plate is fixed and the upper plate is allowed the possibility of some movement. This phenomenon, which reflects a change in the cell thickness via mechanical vibrations of the top plate, is known to occur when the direction of an applied electric field is suddenly reversed. An elementary model is developed that describes some of the key features of this effect and is directly relevant to the observations reported in the literature. Two aspects are considered: first, the effect of a simple field reversal, and secondly, the frequency-induced effects of an alternating electric field. A steady increase in the cell thickness occurs under alternating fields and this reflects a pumping phenomenon as the director orientation couples to the flow.

The synthesis and mesomorphic properties of liquid crystals with bulky terminal groups designed for bookshelf geometry ferroelectric mixtures

The synthesis and mesomorphic properties of a systematic range of ortho difluoroterphenyls with a bulky terminal chain are detailed. The bulky terminal chain consists of either a tertiarybutyl group or a trimethylsilyl unit, each separated from the core by a short (dimethylene) chain, with the other terminal chain being either octyloxy or heptyl. The synthesis of the materials was affected efficiently using a combination of low temperature lithiations and palladium-catalysed cross-coupling reactions. Unusually for liquid crystals with bulky terminal chains, the smectic phase stability (particularly smectic C) is upheld by more than the nematic phase stability, and in most cases the smectic C phase stability is actually higher than comparable analogues with conventional unbranched terminal chains. It is postulated that the surprisingly high smectic C phase stability results from a phase separation effect due to the incompatibility of the spherical bulky group and the conventional unbranched terminal chain, hence implying that the smectic ‘layers’ are well defined, and such definition of the layers bodes well for bookshelf geometry in ferroelectric mixtures.

On smectic-A liquid crystals in an electrostatic field

Smectic-A liquid crystals are layered anisotropic materials with anisotropic dielectric features. In this paper we propose a non-linear model describing the static finite deformations induced in a smectic-A by an electrostatic field. In the classical approach, the electric field is considered partially coupled with the mechanical system in the sense that it can induce layer distortions, but it is not affected by these distortions. In our model, the momentum balance equation is fully coupled with Maxwell's electrostatic equations. We study the phase transition induced by an electric field for a simple planar cell of smectic-A in two undistorted configurations: a homeotropic texture and a bookshelf geometry, both with strong anchoring boundary conditions.

Bidimensional distortion in ferroelectric liquid crystals with strong anchoring in bookshelf geometry

In the last decade, it has been experimentally found that in certain conditions a periodic domain pattern arises in ferroelectric liquid crystals (FLC) in bookshelf geometry. Such a periodic texture appears after switching-off an external electric field, even in strong anchoring conditions. It has a static character and is bidimensional, being dependent on directions normal to both the smectic planes and the cell plates. Here a new model explaining this phenomenon is proposed, valid in the case of FLC with strong anchoring. The model is based on the coupling between the spontaneous polarization field in the first semi-period of its modulation along the cell plates and the same field in the second semi-period. This coupling competes with the FLC medium elasticity and is trapped by the anchoring. According to our model, in the ferroelectric state the biperiodic texture is favored by increasing the values of spontaneous polarization. The critical value of the spontaneous polarization for which the undeformed state becomes unstable is found. It is shown to be proportional to the square root of the ratio between the FLC elastic constant and the cell thickness. Moreover, it is inversely proportional to the sinus of the pre-tilt angle with respect to the cell walls.

Integrated Electro-Optic Switches Based on Ferroelectric Liquid Crystal Waveguides

Two integrated electro-optic switches based on smectic C * ferroelectric liquid crystal (FLC) planar waveguides oriented in the bookshelf geometry have been designed and realized. In order to test the first switch, a particular waveguide structure consisting of a three-stage device, having a thin FLC film middle stage and two glass waveguides as other stages, has been designed and realized. The second one is realized by a planar waveguide with a smectic C * ferroelectric liquid crystal overlayer. In this article the design, the realization, and the experimental characterization of electro-optical switches are reported. The electro-optical behavior and the response time of both devices have been studied for different configurations for both TE and TM polarization. Our main aim was to demonstrate the feasibility of an integrated electro-optic device based on a FLC waveguide, and our experimental results provide a number of interesting indications about device optimization and practical applications.

Bidimensional instability in antiferroelectric liquid crystals

In the last decade it has been experimentally found a periodic domain pattern arising in smectic C* liquid crystals in surface stabilized bookshelf geometry. Such a periodic texture appears after switching-off an external electric field, even in strong anchoring conditions. It has a static character and can be bidimensional, being dependent on both directions normal to the smectic planes and normal to the cell plates. In the present work an explanation to this phenomenon is proposed. According to our model in the antiferroelectric phase the biperiodic texture is a threshold phenomenon, appearing for values of the spontaneous polarization greater than a critical value, whereas in the ferroelectric phase this type of bidimensional instability is hindered.

Observations of the Ferroelectric Deformed Helix Mode in a Large Pitch Smectic C* Sample

Display devices making use of the deformed helix mode normally employ a smectic C* phase whose pitch is smaller than a wavelength of visible light. Here we study the opposite case, where the pitch is large. Our samples are aligned in the usual bookshelf geometry and the electric field is applied perpendicular to the helix. When the sample is viewed between crossed polarizers with the helix parallel to one of the polarization axes, we observe two stages of response to the application of the electric field. Initially, the transmitted intensity decreases quadratically with the field. This is then followed by a discontinuous jump to a high transmission state at some threshold field. We present evidence that the initial decrease in intensity is due to a diffraction phenomenon.

Integrated Electro-Optic Switch Based on a Ferroelectric Liquid Crystal Waveguide

An electro-optic switch based on a planar, ferroelectric liquid crystal waveguide oriented in the bookshelf geometry has been realized and tested. The waveguide device consists of three stages: two glass waveguides and an FLC waveguide in between, permitting coupling and decoupling of the light into and out of the glass waveguides with prisms. The refractive indices of the FLC used were determined with a total internal reflection method. The time characteristics of the ON-OFF switch and the OFF-ON switch have been studied. Our main aim was the experimental demonstration of previous theoretical studies and no attempt was made up to now to optimize the device performance.

A backflow effect in smectic C liquid crystals

This paper discusses the influence upon a smectic C liquid crystal cell of backflow induced by the relaxation of alignment following the removal of a strong electric or magnetic field. Our study, based upon a recently proposed continuum theory, concentrates upon the homeotropic configuration in which the smectic layers are parallel to the boundary plates, but some consideration is also given to the bookshelf geometry. Although the governing equations prove to be rather complex, some progress is possible analytically by repeating an approximation made in the corresponding problem for a nematic.

Preparation and characterization of side-chain liquid crystalline polymer thin films aligned on PTFE friction-transferred layers

Annealing of a side-chain LC polymer (SC-LCP) and a fluorescent dye containing copolymer deposited on friction-transferred PTFE substrates is found to yield macroscopically aligned glassy films. The results obtained by electron diffraction, u.v.-visible and FTi.r. spectroscopy clearly demonstrate that the mesogenic side-groups as well as the fluorescence dye orient with their long axes parallel to the PTFE chain axis. Thus, the SC-LCP aligned thin films adopt a near perfect bookshelf geometry in which the smectic layers are oriented edge-on and perpendicular to the alignment direction. The order parameter P2 increases from 0.60 to as high as 0.85 when the annealing temperature in the smectic mesophase approaches the smectic to nematic phase transition temperature.

Multiplexing performance of a FLC with high spontaneous polarization in the bookshelf structure

The bistability and multiplexing performance of a Ferroelectric Liquid Crystal with high spontaneous polarization in the bookshelf geometry has been investigated. Such an approach allows for a high contrast switching. The bistability sticking effect is found to be predominant in the static properties but is negligible in the multiplexing regime.

Threshold Properties of SSFLC in Terms of Polarization Structures

Bistability of the surface stabilized ferroelectric liquid crystal (SSFLC) is one of the most important factors of display perfomances. The electrooptical switching is based on the bistability which provides threshold characteristics to the SSFLC display device. The threshold properties of the SSFLC device which has a layer structure of liquid crystal molecules and provides an in-plane molecular switching are assumed to be governed by not only a surface anchoring but also a bulk structure itself. We show some experimental results which suggest a contribution of ferroelectric liquid crystal's bulk structure to the electrooptical threshold properties. Layer structures: the bookshelf and the chevron geometries are one of the main bulk factors. Our experimental results clarified that the polarization switching behavior was intrinsically different between the bookshelf and the chevron structures. The bookshelf geometry also shows a possibility of gray shades.