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Liquid Crystals 2020

A special issue of Molecules (ISSN 1420-3049). This special issue belongs to the section "Materials Chemistry".

Deadline for manuscript submissions: closed (31 October 2021) | Viewed by 29945

Special Issue Editors


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Guest Editor
Department of Inorganic Chemistry, Faculty of Chemistry, University of Bucharest, Bucharest, Romania
Interests: liquid crystals; metallomesogens; luminescent materials; inorganic and coordination chemistry
Special Issues, Collections and Topics in MDPI journals

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Guest Editor
Department of Physics, Universitatea Politehnica din Bucuresti, Bucharest, Romania
Interests: liquid crystals; polymer-dispersed liquid crystals; nanocomposites; soft matter; dielectric properties; physical properties; optoelectronics; organic solar cells
Special Issues, Collections and Topics in MDPI journals

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Guest Editor
B.I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, Minsk, Belarus
Interests: liquid crystals; polymer-dispersed liquid crystals; composite and smart materials; single and multiple scattering of waves in partially ordered disperse media; electro-optic devices; light propagation in metamaterials; photonic crystals; solar cells
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue on “Liquid Crystals” will address recent progress in both experimental and theoretical aspects of liquid crystals science and technology, including molecular design, synthesis, processing, fabrication, characterization and engineering. With their unique combination of properties related to anisotropic fluids (anisotropy of physical properties and fast orientational response to external fields), liquid crystals are among the most versatile and dynamic soft materials of the present day, and they have found important indispensable applications such as the manufacturing of display devices, molecular sensors and detectors, optical switches, spatial light modulators, and many others not mentioned here. Tremendous research efforts are also dedicated to the exploration of fundamental aspects related to self-assembly and supermolecular organization in thermotropic or lyotropic liquid crystals, contributing to the advancement of knowledge in liquid crystals science. This Special Issue will offer an appropriate opportunity to authors and research groups to make their studies visible to the liquid crystals scientific community. Contributions in the form of original research articles or comprehensive review papers from various fields are welcomed: biological, organic and inorganic liquid crystals; metallomesogens; ionic liquid crystals; and liquid crystalline polymers and liquid crystal composites, concerning both experimental and theoretical studies.

Prof. Dr. Viorel Circu
Prof. Dr. Doina Manaila-Maximean
Prof. Dr. Valery A. Loiko
Guest Editors

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Keywords

  • liquid crystals
  • nanoparticles
  • liquid crystal composites
  • polymer liquid crystals
  • metallomesogens
  • ionic liquid crystals

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Published Papers (11 papers)

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Editorial

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4 pages, 196 KiB  
Editorial
Editorial: Special Issue “Liquid Crystals 2020”
by Viorel Cîrcu, Doina Manaila-Maximean and Valery A. Loiko
Molecules 2023, 28(8), 3359; https://doi.org/10.3390/molecules28083359 - 11 Apr 2023
Cited by 1 | Viewed by 1296
Abstract
This Special Issue, entitled “Liquid Crystals 2020”, is a collection of ten original research papers, including two feature papers, on theoretical and experimental advanced studies of liquid crystal science and technology [...] Full article
(This article belongs to the Special Issue Liquid Crystals 2020)

Research

Jump to: Editorial

10 pages, 2487 KiB  
Article
Multimode Robust Lasing in a Dye-Doped Polymer Layer Embedded in a Wedge-Shaped Cholesteric
by Tatevik M. Sarukhanyan, Hermine Gharagulyan, Mushegh S. Rafayelyan, Sergey S. Golik, Ashot H. Gevorgyan and Roman B. Alaverdyan
Molecules 2021, 26(19), 6089; https://doi.org/10.3390/molecules26196089 - 8 Oct 2021
Cited by 10 | Viewed by 2517
Abstract
Cholesteric liquid crystals (CLCs) with induced defects are one of the most prominent materials to realize compact, low-threshold and tunable coherent light sources. In this context, the investigation of optical properties of induced defect modes in such CLCs is of great interest. In [...] Read more.
Cholesteric liquid crystals (CLCs) with induced defects are one of the most prominent materials to realize compact, low-threshold and tunable coherent light sources. In this context, the investigation of optical properties of induced defect modes in such CLCs is of great interest. In particular, many studies have been devoted to the spectral control of the defect modes depending on their thickness, optical properties, distribution along the CLC, etc. In this paper, we investigate the lasing possibilities of a dye-doped polymer layer embedded in a wedge-shaped CLC. We show that multimode laser generation is possible due to the observed multiple defect modes in the PBG that enlarges the application range of the system. Furthermore, our simulations based on a Berreman 4 × 4 matrix approach for a wide range of CLC thickness show both periodic and continuous generation of defect modes along particular spectral lines inside the PBG. Such a robust spectral behaviour of induced defect modes is unique, and, to our knowledge, is not observed in similar CLC-based structures. Full article
(This article belongs to the Special Issue Liquid Crystals 2020)
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Figure 1

Figure 1
<p>The sketch of the CLC-DDPL wedge-shaped cell.</p>
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<p>Absorption and emission spectra of DDPL.</p>
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<p>Experimental setup for investigation of laser generation in CLC-DDPL wedge-shaped system, where (1) Laser, (2) <math display="inline"><semantics> <mi>λ</mi> </semantics></math>/2 wave plate, (3) Polarizing beam splitter, (4) Lens with 200 <math display="inline"><semantics> <mi>mm</mi> </semantics></math> focus, (5) CLC-DDPL sample, (6) Fibre, (7) Spectrometer.</p>
Full article ">Figure 4
<p>(<b>a</b>) The fluorescence spectrum of the laser dye dissolved in the polymer before and after polymerization. (<b>b</b>) Transmission spectrum from DDPL for left (LCP) and right (RCP) circularly polarized light.</p>
Full article ">Figure 5
<p>The experimentally recorded transmission spectra from CLC-DDPL wedge-shaped system corresponding to the 32.5 <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>, 40.7 <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> and 48.3 <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> thicknesses of the cell, namely close to the edges and the intermediate part of the wedge cell (see <a href="#molecules-26-06089-f001" class="html-fig">Figure 1</a>).</p>
Full article ">Figure 6
<p>The experimentally recorded lasing generation from different thicknesses of the CLC-DDPL wedge-shaped cell. Measurements were carried out with constant 6 kW/pulse pumping energy.</p>
Full article ">Figure 7
<p>The wavelength of the generated laser peaks dependence on the thickness of the CLC-DDPL wedge-shaped cell.</p>
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<p>Lasing (Pulse laser), fluorescence (CW laser) and transmission spectra from the CLC-DDPL wedge-shaped cell.</p>
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<p>(<b>a</b>) The sketch of the CLC-IDL system considered in the theoretical simulations. (<b>b</b>) Distribution of CLC helices around the IDL showing a non-standard boundary conditions of CLC molecules.</p>
Full article ">Figure 10
<p>The defect modes when refractive index of defect layer is (<b>a</b>) n = 1.3, (<b>b</b>) n = 1.4, (<b>c</b>) n = 1.5, (<b>d</b>) n = 1.6 and (<b>e</b>) n = 1.68. Each panel has an inset above showing enlarged 6.1–6.4 <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> region of CLC thicknesses. The CLC thickness changes from 4.3 <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> to 9.5 <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>. The thickness of defect layer is 30 <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>. Panel (<b>f</b>) shows the transmission spectrum for defect thickness change from 30 <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> to 35.8 <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>, and for the CLC thickness 5.8 <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>. An inset for the Panel (f) for 31 <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>–33 <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> is also presented.</p>
Full article ">
11 pages, 3867 KiB  
Article
Defect Structures of Magnetic Nanoparticles in Smectic A Liquid Crystals
by Vladimíra Novotná, Lubor Lejček, Věra Hamplová and Jana Vejpravová
Molecules 2021, 26(18), 5717; https://doi.org/10.3390/molecules26185717 - 21 Sep 2021
Cited by 1 | Viewed by 2310
Abstract
Topological defects in anisotropic fluids like liquid crystals serve as a playground for the research of various effects. In this study, we concentrated on a hybrid system of chiral rod-like molecules doped by magnetic nanoparticles. In textures of the smectic A phase, we [...] Read more.
Topological defects in anisotropic fluids like liquid crystals serve as a playground for the research of various effects. In this study, we concentrated on a hybrid system of chiral rod-like molecules doped by magnetic nanoparticles. In textures of the smectic A phase, we observed linear defects and found that clusters of nanoparticles promote nucleation of smectic layer defects just at the phase transition from the isotropic to the smectic A (SmA) phase. In different geometries, we studied and analysed creation of defects which can be explained by attractive elastic forces between nanoparticles in the SmA phase. On cooling the studied hybrid system, clusters grow up to the critical dimension, and the smectic texture is stabilised. The presented effects are theoretically described and explained if we consider the elastic interaction of two point defects and stabilisation of prismatic dislocation loops due to the presence of nanoparticles. Full article
(This article belongs to the Special Issue Liquid Crystals 2020)
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Figure 1

Figure 1
<p>Texture of inclusions in a hybrid system of liquid crystalline compound DL10* with magnetic nanoparticles at 5 °C below the isotropic–SmA phase transition temperature. Orientation of the polariser (P) and the analyser (A) is depicted. The width of the picture is 240 μm.</p>
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<p>Microphotographs of the studied hybrid system in a commercial HG cell, thickness—5 μm, in the SmA phase at T = 98 °C (<b>a</b>) under the applied electric field, E, with the intensity of 50 V/μm in the perpendicular direction, and (<b>b</b>) after switching off the field after 10 seconds.</p>
Full article ">Figure 3
<p>Texture of small focal conics and small prismatic dislocation loops in the studied hybrid composite system: (<b>a</b>) in the crossed position of the analyser (A) and the polariser (P) and (<b>b</b>) in depolarised light. The width of the picture is 120 μm. Clusters of nanoparticles are visualised as black dots accompanied by line defects, either focal lines or dislocation lines.</p>
Full article ">Figure 4
<p>Microphotographs of a droplet on a glass plate: (<b>a</b>) under crossed polarisers and (<b>b</b>) the identical part of the sample in depolarised view with a common scale bar for all three figures. The inset in (<b>a</b>) shows the border of the droplet in an enlarged view and (<b>c</b>) presents focal conics in the thicker part of the droplet.</p>
Full article ">Figure 5
<p>Schematic drawing of a prismatic dislocation loop with the Burgers vector 2<span class="html-italic">b</span> in smectic layers. Rod-like molecules in layers are presented as small rods. A vacant volume is designed in the center of the loop where nanoparticles can condense. Orientation of the applied coordinate system is depicted; note that the <span class="html-italic">z</span>-axis is oriented along the layer normal.</p>
Full article ">Figure 6
<p>Schematic drawing in the plane (<span class="html-italic">y</span>,<span class="html-italic">z</span>) shows a nanoparticle cluster incorporated into the smectic layer system. The cluster in this scheme has an ellipsoidal profile along with the layer normal and is covered by a shell of disordered molecules influenced by the molecular interaction with the cluster’s surface. The cluster within the shell is enveloped by prismatic dislocation loops (not included in this figure, for the illustration see <a href="#molecules-26-05717-f005" class="html-fig">Figure 5</a>).</p>
Full article ">
9 pages, 2785 KiB  
Article
Anomalous Lehmann Rotation of Achiral Nematic Liquid Crystal Droplets Trapped under Linearly Polarized Optical Tweezers
by Jarinee Kiang-ia, Rahut Taeudomkul, Pongthep Prajongtat, Padetha Tin, Apichart Pattanaporkratana and Nattaporn Chattham
Molecules 2021, 26(14), 4108; https://doi.org/10.3390/molecules26144108 - 6 Jul 2021
Cited by 5 | Viewed by 2574
Abstract
Continuous rotation of a cholesteric droplet under the heat gradient was observed by Lehmann in 1900. This phenomenon, the so-called Lehmann effect, consists of unidirectional rotation around the heat flux axis. We investigate this gradient heat effect using infrared laser optical tweezers. By [...] Read more.
Continuous rotation of a cholesteric droplet under the heat gradient was observed by Lehmann in 1900. This phenomenon, the so-called Lehmann effect, consists of unidirectional rotation around the heat flux axis. We investigate this gradient heat effect using infrared laser optical tweezers. By applying single trap linearly polarized optical tweezers onto a radial achiral nematic liquid crystal droplet, trapping of the droplet was performed. However, under a linearly polarized optical trap, instead of stable trapping of the droplet with slightly deformed molecular directors along with a radial hedgehog defect, anomalous continuous rotation of the droplet was observed. Under low power laser trapping, the droplet appeared to rotate clockwise. By continuously increasing the laser power, a stable trap was observed, followed by reverse directional rotation in a higher intensity laser trap. Optical levitation of the droplet in the laser beam caused the heat gradient, and a breaking of the symmetry of the achiral nematic droplet. These two effects together led to the rotation of the droplet under linearly polarized laser trapping, with the sense of rotation depending on laser power. Full article
(This article belongs to the Special Issue Liquid Crystals 2020)
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Figure 1

Figure 1
<p>Schematic illustration of the optical tweezers setup on an inverted microscope.</p>
Full article ">Figure 2
<p>Microscopic images taken under crossed polarizers and a one-wavelength plate inserted diagonally for director orientation mapping. (<b>a</b>) A 19-μm radial NLC droplet suspended in water. The droplet configuration is spherically symmetric, the so-called ‘radial hedgehog’. (<b>b</b>) By applying the linearly polarized laser onto the droplet, the defect in the middle shifted slightly to the side along the polarization direction of the laser, β = 135° with respect to a horizontal direction. This distorted configuration caused by the alignment of the molecules in the laser beam pointed toward the laser polarization direction, thus pushing the defect to the side.</p>
Full article ">Figure 3
<p>An NLC droplet under linearly polarized laser trap was found rotating clockwise at laser power 298 mW. The laser polarization direction was set at an angle β = 135° with respect to the horizontal (<a href="#app1-molecules-26-04108" class="html-app">Supplementary video available</a>).</p>
Full article ">Figure 4
<p>(<b>a</b>) Plot of the radial hedgehog defect position of 19-μm NLC droplet. The position <span class="html-italic">r</span> was measured with respect to the center of the elliptical trajectory (shown in (<b>b</b>,<b>c</b>)), during clockwise rotation at 298 mW and 338 mW. The period of rotation was 4.54 s and 1.79 s for 298 mW and 338 mW, respectively. (<b>b</b>,<b>c</b>) Tracking of the elliptical trajectory of the defect showing non-uniform angular speed. (<b>d</b>,<b>e</b>) Angular speed of the defect at 298 mW and 338 mW, respectively. The defect rotation was very slow at points P and Q along the direction of laser polarization for 298 mW laser trapping. The effect is less severe for higher laser power.</p>
Full article ">Figure 5
<p>The same 19-μm NLC droplet as in <a href="#molecules-26-04108-f003" class="html-fig">Figure 3</a> rotated in the reverse direction under the same linearly polarized laser trap at a higher laser power of 635 mW (<a href="#app1-molecules-26-04108" class="html-app">Supplementary video available</a>).</p>
Full article ">Figure 6
<p>Schematic illustration of the droplet position at (<b>a</b>) low power and (<b>b</b>) higher power of a laser when slowly increasing the power of the trapping laser. <math display="inline"><semantics> <mrow> <mover accent="true"> <mi mathvariant="normal">G</mi> <mo stretchy="true">⇀</mo> </mover> </mrow> </semantics></math> represents direction of temperature gradient due to laser intensity. The temperature gradient points toward the laser focus. <math display="inline"><semantics> <mrow> <mover accent="true"> <mi mathvariant="normal">n</mi> <mo stretchy="true">⇀</mo> </mover> </mrow> </semantics></math> is the direction of average molecular directors of the distorted radial droplet. <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>τ</mi> <mo stretchy="true">⇀</mo> </mover> </mrow> </semantics></math> is torque direction of the droplet from <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>τ</mi> <mo stretchy="true">⇀</mo> </mover> <mo>=</mo> <mi>ν</mi> <mover accent="true"> <mi mathvariant="normal">n</mi> <mo stretchy="true">⇀</mo> </mover> <mo>×</mo> <mrow> <mo>(</mo> <mrow> <mover accent="true"> <mi mathvariant="normal">n</mi> <mo stretchy="true">⇀</mo> </mover> <mo>×</mo> <mover accent="true"> <mi mathvariant="normal">G</mi> <mo stretchy="true">⇀</mo> </mover> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math>, which resulted in clockwise rotation in (<b>a</b>) and counterclockwise rotation in (<b>b</b>). (<b>c</b>) Particle position with laser power illustrated roughly the observation of Ashkin’s experiment in optical levitation [<a href="#B15-molecules-26-04108" class="html-bibr">15</a>].</p>
Full article ">Figure 7
<p>Plot of threshold laser power for droplet rotation in clockwise and counterclockwise directions with droplet size. Notice that there is no counterclockwise rotation of small droplets at high power since the droplets were too small, so they were pushed off the trap at high power. There is no clockwise rotation of larger droplets at low power because the droplets were too heavy for rotation. The force from a low power laser could be too small to initiate droplet motion.</p>
Full article ">Figure 8
<p>Plot of angular speed with laser power of a radial hedgehog defect under linearly polarized laser tweezers. Notice that we can only record one set of data for counterclockwise rotation for each droplet size since the power range for counterclockwise rotation is very small and by increasing the laser power higher than the last data plotted, the droplet was pushed out of the laser trap. For an 18 μm droplet, no counterclockwise rotation was observed, analogous to the observation in <a href="#molecules-26-04108-f007" class="html-fig">Figure 7</a>.</p>
Full article ">
12 pages, 3729 KiB  
Article
Aptamer Laden Liquid Crystals Biosensing Platform for the Detection of HIV-1 Glycoprotein-120
by Amna Didar Abbasi, Zakir Hussain and Kun-Lin Yang
Molecules 2021, 26(10), 2893; https://doi.org/10.3390/molecules26102893 - 13 May 2021
Cited by 13 | Viewed by 2673
Abstract
We report a label-free and simple approach for the detection of glycoprotein-120 (gp-120) using an aptamer-based liquid crystals (LCs) biosensing platform. The LCs are supported on the surface of a modified glass slide with a suitable amount of B40t77 aptamer, allowing the LCs [...] Read more.
We report a label-free and simple approach for the detection of glycoprotein-120 (gp-120) using an aptamer-based liquid crystals (LCs) biosensing platform. The LCs are supported on the surface of a modified glass slide with a suitable amount of B40t77 aptamer, allowing the LCs to be homeotropically aligned. A pronounced topological change was observed on the surface due to a specific interaction between B40t77 and gp-120, which led to the disruption of the homeotropic alignment of LCs. This results in a dark-to-bright transition observed under a polarized optical microscope. With the developed biosensing platform, it was possible to not only identify gp-120, but obtained results were analyzed quantitatively through image analysis. The detection limit of the proposed biosensing platform was investigated to be 0.2 µg/mL of gp-120. Regarding selectivity of the developed platform, no response could be detected when gp-120 was replaced by other proteins, such as bovine serum albumin (BSA), hepatitis A virus capsid protein 1 (Hep A VP1) and immunoglobulin G protein (IgG). Due to attributes such as label-free, high specificity and no need for instrumental read-out, the presented biosensing platform provides the potential to develop a working device for the quick detection of HIV-1 gp-120. Full article
(This article belongs to the Special Issue Liquid Crystals 2020)
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Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>Schematic illustration of the preparation and sensing strategy of proposed bio-sensing approach: (<b>A</b>) cleaning and preparation of <span class="html-italic">N,N</span>-dimethyl-n-octadecyl-3aminopropyltrimethoxy-silyl chloride (DMOAP)-coated glass slides; (<b>B</b>) dispensing droplets of B40t77 aptamer solution in an array form; (<b>C</b>) after immobilization of B40t77 aptamer, gp-120 protein droplets were dispensed on immobilized B40t77 aptamer; (<b>D</b>) after washing and drying, place spacer (6µm) on left and right edges of slides, followed by covering the slide with another DMOAP–coated glass slide; (<b>E</b>) clip the left and right edges of both slides with clippers to make an optical cell; (<b>F</b>) introduce liquid crystal (LC) 4-cyano-4-pentylbiphenyl (5CB) into the prepared optical cell; (<b>G</b>) visualization under polarized optical microscope with the naked eye, analysis of final results (dark to bright transition in optical appearances).</p>
Full article ">Figure 2
<p>Optical images of LCs supported on DMOAP-coated surface immobilized with B40t77 aptamer solutions made in different MgCl<sub>2</sub> concentrations; MgCl<sub>2</sub> concentrations are 1 M, 100 mM, 10 mM and 0 mM; control is just TE buffer with different concentrations of MgCl<sub>2</sub>.</p>
Full article ">Figure 3
<p>Optical images of LCs supported on a DMOAP-coated slide immobilized with B40t77 aptamer solution with different concentrations; number above each spot is B40t77 aptamer concentration (µg/mL), whereas control is just TE buffer without B40t77 aptamer.</p>
Full article ">Figure 4
<p>Optical images of LCs supported on a DMOAP-coated slide immobilized with B40t77 aptamer solution of different concentrations showing effects of different immobilization times; the B40t77 aptamer concentrations used are 16, 14, 12, 10 and 8 µg/mL.</p>
Full article ">Figure 5
<p>AFM images of different slide surfaces: (<b>A</b>) with DMOAP coating; (<b>B</b>) after B40t77 aptamer (8 µg/mL) immobilization; (<b>C</b>) after addition of gp-120 (8 µg/mL), and the corresponding polarized optical images of LCs supported on different slide surfaces; (<b>D</b>) coated with DMOAP; (<b>E</b>) with B40t77 aptamer (8 µg/mL) modification; (<b>F</b>) after addition of gp-120 (8 µg/mL).</p>
Full article ">Figure 6
<p>Optical images of LCs supported on B40t77 aptamer (8 µg/mL) immobilized DMOAP-coated glass surfaces after addition of different concentrations of gp-120: (<b>A</b>) 8, (<b>B</b>) 6, (<b>C</b>) 4, (<b>D</b>) 2, (<b>E</b>) 1, (<b>F</b>) 0.5, (<b>G</b>) 0.2, (<b>H</b>) 0.1 and (<b>I</b>) 0 µg/mL, respectively.</p>
Full article ">Figure 7
<p>(<b>A</b>–<b>I</b>) are showing mean gray values corresponding to different optical images of LCs given in <a href="#molecules-26-02893-f006" class="html-fig">Figure 6</a>.</p>
Full article ">Figure 8
<p>Calibration curve of the mean gray values of LC optical images and the logarithm of the gp-120 concentration (Y = mean gray value of the optical images and C<sub>gp-120</sub> = concentration of gp-120 (ng/mL)).</p>
Full article ">Figure 9
<p>Optical images of LCs supported on B40t77 immobilized DMOAP decorated glass surfaces after treating with different proteins at concentration (8 µg/mL): (<b>A</b>) Gp-120, (<b>B</b>) BSA, (<b>C</b>) Hep A VP1, (<b>D</b>) IgG and (<b>E</b>–<b>G</b>) optical images with double concentration (16 µg/mL) of IgG, Hep A VP1 and BSA, respectively.</p>
Full article ">
13 pages, 2763 KiB  
Article
Dielectric Spectroscopy Analysis of Liquid Crystals Recovered from End-of-Life Liquid Crystal Displays
by Ana Barrera, Corinne Binet, Frédéric Dubois, Pierre-Alexandre Hébert, Philippe Supiot, Corinne Foissac and Ulrich Maschke
Molecules 2021, 26(10), 2873; https://doi.org/10.3390/molecules26102873 - 12 May 2021
Cited by 19 | Viewed by 3178
Abstract
In the present work, the dielectric properties of recycled liquid crystals (LCs) (non-purified, purified, and doped with diamond nanoparticles at 0.05, 0.1, and 0.2 wt%) were investigated. The studied LC mixtures were obtained from industrial recycling of end-of-life LC displays presenting mainly nematic [...] Read more.
In the present work, the dielectric properties of recycled liquid crystals (LCs) (non-purified, purified, and doped with diamond nanoparticles at 0.05, 0.1, and 0.2 wt%) were investigated. The studied LC mixtures were obtained from industrial recycling of end-of-life LC displays presenting mainly nematic phases. Dielectric measurements were carried out at room temperature on a frequency range from 0.1 to 106 Hz using an impedance analyzer. The amplitude of the oscillating voltage was fixed at 1 V using cells with homogeneous and homeotropic alignments. Results show that the dielectric anisotropy of all purified samples presents positive values and decreases after the addition of diamond nanoparticles to the LC mixtures. DC conductivity values were obtained by applying the universal law of dielectric response proposed by Jonscher. In addition, conductivity of the doped LC mixtures is lower than that of the undoped and non-purified LC. Full article
(This article belongs to the Special Issue Liquid Crystals 2020)
Show Figures

Figure 1

Figure 1
<p>Dielectric spectra of a non-purified LC mixture at room temperature (20 °C), using 20 µm cells in (<b>a</b>) homeotropic and (<b>b</b>) homogeneous alignment, for two amplitudes of the oscillating voltage: 0.1 and 1 V.</p>
Full article ">Figure 2
<p>(<b>a</b>) Relative permittivity and (<b>b</b>) dielectric anisotropy of three non-purified LC mixtures as function of frequency. Measurements were taken at 1 V and room temperature (20 °C) with 20 µm cells in homogeneous and homeotropic alignments. NP-M stands for non-purified LCs mixtures.</p>
Full article ">Figure 3
<p>Dielectric permittivity of purified LCs doped with different concentrations of DNPs (0.05, 0.1, and 0.2 wt%): (<b>a</b>) real and (<b>b</b>) imaginary parts in homeotropic alignment, (<b>c</b>) real and (<b>d</b>) imaginary parts in homogeneous alignment, and (<b>e</b>) dielectric anisotropy. The spectra were measured under identical experimental conditions (P stands for purified LC mixtures; P + 0.05D, P + 0.1D, and P + 0.2D correspond to purified LC mixtures doped with 0.05, 0.1, and 0.2 wt% of DNPs, respectively).</p>
Full article ">Figure 4
<p>Real part of the complex conductivity in (<b>a</b>) homeotropic and (<b>b</b>) homogeneous alignments as a function of frequency of non-purified, purified, and DNP-doped (0.05 wt%) LC mixtures. The experimental data are represented by symbols and the red lines show the curves obtained applying Jonscher’s model. NP corresponds to non-purified; P is for purified; and P + 0.05D stands for LC mixtures doped with 0.05 wt% of DNPs.</p>
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<p>Variation of DC conductivity as a function of concentration of DNPs added to a purified LC mixture.</p>
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<p>(<b>a</b>) End-of-life LCD, (<b>b</b>) LCD display composition, (<b>c</b>) Non-purified and (<b>d</b>) purified LCs mixtures, and (<b>e</b>) Texture of purified LC mixtures observed under polarizing optical microscope (POM) Olympus BX60 (Olympus Corporation, Tokyo, Japan), presenting a nematic Schlieren texture. Conditions: LC sample sandwiched between un-aligned glass and coverslip; crossed polarizers; and room temperature.</p>
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<p>Textures of a purified LC mixture in (<b>a</b>) homogeneous and (<b>b</b>) homeotropic alignments. The micrographs are recorded by POM under cross-polarized condition at room temperature.</p>
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12 pages, 3349 KiB  
Article
Liquid Crystals Based on the N-Phenylpyridinium Cation—Mesomorphism and the Effect of the Anion
by Jordan D. Herod and Duncan W. Bruce
Molecules 2021, 26(9), 2653; https://doi.org/10.3390/molecules26092653 - 1 May 2021
Cited by 4 | Viewed by 1990
Abstract
Families of symmetric, ionic, tetracatenar mesogens are described based on a rigid, N-phenylpyridinium core, prepared as their triflimide, octyl sulfate and dodecyl sulfate salts for a range of terminal chain lengths. The mesomorphism of the individual series is described before a comparison [...] Read more.
Families of symmetric, ionic, tetracatenar mesogens are described based on a rigid, N-phenylpyridinium core, prepared as their triflimide, octyl sulfate and dodecyl sulfate salts for a range of terminal chain lengths. The mesomorphism of the individual series is described before a comparison is drawn between the different families and then more broadly with (i) neutral tetracatenar materials and (ii) related bis(3,4-dialkoxystilbazole)silver(I) salts. For the octyl and dodecyl sulfates and the related triflates reported earlier, a SmA phase is seen at shorter chain lengths, giving way to a Colh phase as the terminal chain lengthens. For the alkyl sulfate salts, an intermediate cubic phase is also seen and the terminal chain length required to cause the change from lamellar to columnar mesophase depends on the anion. Furthermore, there is an unexpected and sometime very large mesophase stabilisation seen on entering the columnar phase. All of the triflimide salts show a rectangular columnar (ribbon) phase. Full article
(This article belongs to the Special Issue Liquid Crystals 2020)
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Figure 1
<p>Preparation of the target salts; in all cases <span class="html-italic">n</span> = <span class="html-italic">m</span>. (<b>i</b>) AgOTf, DMF, 70 °C; (<b>ii</b>) 3,4-dialkoxybenzene boronic acid pinacol ester, THF/H<sub>2</sub>O (1:1), Na<sub>2</sub>CO<sub>3</sub>, N<sub>2</sub>, [Pd<sub>3</sub>(OAc)<sub>6</sub>], SPhos, 65 °C; (<b>iii</b>) LiTf<sub>2</sub>N/MeOH/Δ; (<b>iv</b>) 3,4-dialkoxybenzene boronic acid pinacol ester, THF/H<sub>2</sub>O/EtOH (3:3:1), Na<sub>2</sub>CO<sub>3</sub>, [Pd<sub>3</sub>(OAc)<sub>6</sub>], SPhos, N<sub>2</sub>, 65 °C; (<b>v</b>) NaO<sub>3</sub>SOC<span class="html-italic"><sub>p</sub></span>H<sub>2<span class="html-italic">p</span>+1</sub>/MeOH/Δ (<span class="html-italic">p</span> = 8 or 12).</p>
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<p>Phase diagram of the tetracatenar <span class="html-italic">N</span>-phenylpyridinium octyl sulfate salts, <b>3</b>-<span class="html-italic">n</span>.</p>
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<p>Optical textures of (<b>a</b>) the SmA phase formed by compound <b>3</b>-6 at 116 °C, (<b>b</b>) the cubic phase formed by <b>3</b>-10 with polarisers slightly uncrossed at 105 °C, (<b>c</b>) the Col<sub>h</sub> phase formed by compound <b>3</b>-12 at 154 °C.</p>
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<p>Phase diagram of the tetracatenar <span class="html-italic">N</span>-phenylpyridinium dodecyl-sulfates, <b>4</b>-<span class="html-italic">n</span>.</p>
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<p>(<b>a</b>) The cubic phase growing in from Col<sub>h</sub> phase of compound <b>4</b>-10 at 108 °C and (<b>b</b>) the Col<sub>h</sub> phase formed by compound <b>4</b>-12 at 172 °C.</p>
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<p>Diffraction pattern of the Col<sub>h</sub> phase formed by compound <b>4</b>-10 at 105 °C on cooling.</p>
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<p>Structure and phase diagram of the tetracatenar triflimide salts, <b>5</b>-<span class="html-italic">n</span>.</p>
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<p>Photomicrographs of the Col<sub>r</sub> phase formed by compound <b>5</b>-8: (<b>a</b>) cooling from the isotropic liquid at 10 °C min<sup>−1</sup> at 158 °C, (<b>b</b>) slow cooling of the same compound at 0.1 °C min<sup>−1</sup> at 159 °C, (<b>c</b>) miscibility gap between this phase and the Col<sub>h</sub> phase of the OTf compound <b>1</b>-18 (<b>5</b>-8 is bottom left and <b>1</b>-18 is top right) and (<b>d</b>) miscibility gap between the phase of <b>5</b>-8 (top and left) and the SmA phase of the OTf compound <b>1</b>-12 (right).</p>
Full article ">Figure 8 Cont.
<p>Photomicrographs of the Col<sub>r</sub> phase formed by compound <b>5</b>-8: (<b>a</b>) cooling from the isotropic liquid at 10 °C min<sup>−1</sup> at 158 °C, (<b>b</b>) slow cooling of the same compound at 0.1 °C min<sup>−1</sup> at 159 °C, (<b>c</b>) miscibility gap between this phase and the Col<sub>h</sub> phase of the OTf compound <b>1</b>-18 (<b>5</b>-8 is bottom left and <b>1</b>-18 is top right) and (<b>d</b>) miscibility gap between the phase of <b>5</b>-8 (top and left) and the SmA phase of the OTf compound <b>1</b>-12 (right).</p>
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<p>Diffraction pattern of compound <b>5</b>-10 at 139 °C: insert represents the zoomed in region for clarity of the low intensity reflections.</p>
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<p>Phase diagram for <b>1</b>-<span class="html-italic">n</span> (reproduced from reference [<a href="#B15-molecules-26-02653" class="html-bibr">15</a>] with permission from the Royal Society of Chemistry).</p>
Full article ">Figure 11
<p>Structure of the silver complexes <b>5</b>-<span class="html-italic">n</span>.</p>
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12 pages, 3656 KiB  
Article
Effective Permittivity of a Multi-Phase System: Nanoparticle-Doped Polymer-Dispersed Liquid Crystal Films
by Doina Manaila-Maximean
Molecules 2021, 26(5), 1441; https://doi.org/10.3390/molecules26051441 - 7 Mar 2021
Cited by 23 | Viewed by 2561
Abstract
This paper studies the effective dielectric properties of heterogeneous materials of the type particle inclusions in a host medium, using the Maxwell Garnet and the Bruggeman theory. The results of the theories are applied at polymer-dispersed liquid crystal (PDLC) films, nanoparticles (NP)-doped LCs, [...] Read more.
This paper studies the effective dielectric properties of heterogeneous materials of the type particle inclusions in a host medium, using the Maxwell Garnet and the Bruggeman theory. The results of the theories are applied at polymer-dispersed liquid crystal (PDLC) films, nanoparticles (NP)-doped LCs, and developed for NP-doped PDLC films. The effective permittivity of the composite was simulated at sufficiently high frequency, where the permittivity is constant, obtaining results on its dependency on the constituents’ permittivity and concentrations. The two models are compared and discussed. The method used for simulating the doped PDLC retains its general character and can be applied for other similar multiphase composites. The methods can be used to calculate the effective permittivity of a LC composite, or, in the case of a composite in which one of the phases has an unknown permittivity, to extract it from the measured composite permittivity. The obtained data are necessary in the design of the electrical circuits. Full article
(This article belongs to the Special Issue Liquid Crystals 2020)
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<p>Auxiliary sphere around a molecule for determining the local electric field.</p>
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<p>Schematic presentation of a nanoparticles (NPs) polymer-dispersed liquid crystal (PDLC)-doped film between two indium tin oxide (ITO) glass coated plates: LC droplets are spherical.</p>
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<p>Representation of PDLC permittivity in the Maxwell Garnett model, for different LC fractions: (<b>a</b>) <span class="html-italic">f<sub>LC,a</sub></span> = 0.2; (<b>b</b>) <span class="html-italic">f<sub>LC,b</sub> =</span> 0.3; (<b>c</b>) <span class="html-italic">f<sub>LC,c</sub></span> = 0.4. Ox: LC permittivity <math display="inline"><semantics> <mrow> <msub> <mi>ε</mi> <mrow> <mi>L</mi> <mi>C</mi> </mrow> </msub> </mrow> </semantics></math>, Oy: polymer permittivity <math display="inline"><semantics> <mrow> <msub> <mi>ε</mi> <mrow> <mi>p</mi> <mi>l</mi> <mi>y</mi> </mrow> </msub> </mrow> </semantics></math>; vertical color bar: PDLC film effective permittivity using the Maxwell Garnet model, symbol @ stands for “at”.</p>
Full article ">Figure 3 Cont.
<p>Representation of PDLC permittivity in the Maxwell Garnett model, for different LC fractions: (<b>a</b>) <span class="html-italic">f<sub>LC,a</sub></span> = 0.2; (<b>b</b>) <span class="html-italic">f<sub>LC,b</sub> =</span> 0.3; (<b>c</b>) <span class="html-italic">f<sub>LC,c</sub></span> = 0.4. Ox: LC permittivity <math display="inline"><semantics> <mrow> <msub> <mi>ε</mi> <mrow> <mi>L</mi> <mi>C</mi> </mrow> </msub> </mrow> </semantics></math>, Oy: polymer permittivity <math display="inline"><semantics> <mrow> <msub> <mi>ε</mi> <mrow> <mi>p</mi> <mi>l</mi> <mi>y</mi> </mrow> </msub> </mrow> </semantics></math>; vertical color bar: PDLC film effective permittivity using the Maxwell Garnet model, symbol @ stands for “at”.</p>
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<p>Representation of PDLC film effective permittivity in the Bruggeman model for different LC fractions: (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mrow> <mi>L</mi> <mi>C</mi> <mo>,</mo> <mi>a</mi> </mrow> </msub> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mrow> <mi>L</mi> <mi>C</mi> <mo>,</mo> <mi>b</mi> </mrow> </msub> <mo>=</mo> <mn>0.3</mn> </mrow> </semantics></math>, (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mrow> <mi>L</mi> <mi>C</mi> <mo>,</mo> <mi>c</mi> </mrow> </msub> <mo>=</mo> <mn>0.4</mn> </mrow> </semantics></math>. Ox: LC permittivity <math display="inline"><semantics> <mrow> <msub> <mi>ε</mi> <mrow> <mi>L</mi> <mi>C</mi> </mrow> </msub> </mrow> </semantics></math>, Oy: polymer permittivity <math display="inline"><semantics> <mrow> <msub> <mi>ε</mi> <mrow> <mi>p</mi> <mi>l</mi> <mi>y</mi> </mrow> </msub> </mrow> </semantics></math>; vertical color bar: PDLC film effective permittivity using the Bruggeman model, symbol @ stands for “at”.</p>
Full article ">Figure 4 Cont.
<p>Representation of PDLC film effective permittivity in the Bruggeman model for different LC fractions: (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mrow> <mi>L</mi> <mi>C</mi> <mo>,</mo> <mi>a</mi> </mrow> </msub> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mrow> <mi>L</mi> <mi>C</mi> <mo>,</mo> <mi>b</mi> </mrow> </msub> <mo>=</mo> <mn>0.3</mn> </mrow> </semantics></math>, (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mrow> <mi>L</mi> <mi>C</mi> <mo>,</mo> <mi>c</mi> </mrow> </msub> <mo>=</mo> <mn>0.4</mn> </mrow> </semantics></math>. Ox: LC permittivity <math display="inline"><semantics> <mrow> <msub> <mi>ε</mi> <mrow> <mi>L</mi> <mi>C</mi> </mrow> </msub> </mrow> </semantics></math>, Oy: polymer permittivity <math display="inline"><semantics> <mrow> <msub> <mi>ε</mi> <mrow> <mi>p</mi> <mi>l</mi> <mi>y</mi> </mrow> </msub> </mrow> </semantics></math>; vertical color bar: PDLC film effective permittivity using the Bruggeman model, symbol @ stands for “at”.</p>
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<p>The difference between the Maxwell Garnett (MG) and Bruggeman effective permittivity, <math display="inline"><semantics> <mrow> <msub> <mi>ε</mi> <mrow> <mi>e</mi> <mi>f</mi> <mi>f</mi> <mo>,</mo> <mi>M</mi> <mi>G</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>ε</mi> <mrow> <mi>e</mi> <mi>f</mi> <mi>f</mi> <mo>,</mo> <mi>B</mi> </mrow> </msub> </mrow> </semantics></math>, (<b>a</b>) <span class="html-italic">f<sub>LC,a</sub></span> = 0.2; (<b>b</b>) <span class="html-italic">f<sub>LC,b</sub> =</span> 0.3; (<b>c</b>) <span class="html-italic">f<sub>LC,c</sub></span> = 0.4.. Ox: LC permittivity <math display="inline"><semantics> <mrow> <msub> <mi>ε</mi> <mrow> <mi>L</mi> <mi>C</mi> </mrow> </msub> </mrow> </semantics></math>, Oy: polymer permittivity <math display="inline"><semantics> <mrow> <msub> <mi>ε</mi> <mrow> <mi>p</mi> <mi>l</mi> <mi>y</mi> </mrow> </msub> </mrow> </semantics></math>; vertical color bar: the difference between the MG and Bruggeman effective permittivity of the PDLC film, <math display="inline"><semantics> <mrow> <msub> <mi>ε</mi> <mrow> <mi>e</mi> <mi>f</mi> <mi>f</mi> <mo>,</mo> <mi>M</mi> <mi>G</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>ε</mi> <mrow> <mi>e</mi> <mi>f</mi> <mi>f</mi> <mo>,</mo> <mi>B</mi> </mrow> </msub> </mrow> </semantics></math> symbol @ stands for “at”.</p>
Full article ">Figure 6
<p>Representation of effective permittivity for NPs-doped LC versus NP permittivity, <math display="inline"><semantics> <mrow> <msub> <mi>ε</mi> <mrow> <mi>N</mi> <mi>P</mi> </mrow> </msub> </mrow> </semantics></math>, for three NP volume fractions: 0.01; 0.001; and 0.0001, (<b>a</b>) MG model (Equation (14)); (<b>b</b>) Bruggeman model (Equation (15)), and (<b>c</b>) the difference of the effective permittivity obtained using these models.</p>
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<p>(<b>a</b>) Effective permittivity for the NPs-doped PDLC, versus NP permittivity, <math display="inline"><semantics> <mrow> <msub> <mi>ε</mi> <mrow> <mi>N</mi> <mi>P</mi> </mrow> </msub> </mrow> </semantics></math>, (Equation (18)) at a constant LC volume fraction <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mrow> <mi>L</mi> <mi>C</mi> </mrow> </msub> <mo>=</mo> <mn>0.4</mn> </mrow> </semantics></math> and for different NP volume fractions <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mrow> <mi>N</mi> <mi>P</mi> </mrow> </msub> </mrow> </semantics></math>: 0.01; 0.001; and 0.0001. LC permittivty <math display="inline"><semantics> <mrow> <msub> <mi>ε</mi> <mrow> <mi>L</mi> <mi>C</mi> </mrow> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, polymer permittivity <math display="inline"><semantics> <mrow> <msub> <mi>ε</mi> <mrow> <mi>p</mi> <mi>l</mi> <mi>y</mi> </mrow> </msub> <mo>=</mo> <mn>8</mn> </mrow> </semantics></math>; (<b>b</b>) representation of undoped PDLC effective permittivity in the Bruggeman model versus LC volume fractions, equation (14), at constant LC permittivty <math display="inline"><semantics> <mrow> <msub> <mi>ε</mi> <mrow> <mi>L</mi> <mi>C</mi> </mrow> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, polymer permittivity <math display="inline"><semantics> <mrow> <msub> <mi>ε</mi> <mrow> <mi>p</mi> <mi>l</mi> <mi>y</mi> </mrow> </msub> <mo>=</mo> <mn>8</mn> </mrow> </semantics></math>.</p>
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14 pages, 3940 KiB  
Article
Phase Transitions and Hysteresis for a Simple Model Liquid Crystal by Replica-Exchange Monte Carlo Simulations
by Akie Kowaguchi, Paul E. Brumby and Kenji Yasuoka
Molecules 2021, 26(5), 1421; https://doi.org/10.3390/molecules26051421 - 5 Mar 2021
Cited by 6 | Viewed by 2473
Abstract
In this work, the advantages of applying the temperature and pressure replica-exchange method to investigate the phase transitions and the hysteresis for liquid-crystal fluids were demonstrated. In applying this method to the commonly used Hess–Su liquid-crystal model, heat capacity peaks and points of [...] Read more.
In this work, the advantages of applying the temperature and pressure replica-exchange method to investigate the phase transitions and the hysteresis for liquid-crystal fluids were demonstrated. In applying this method to the commonly used Hess–Su liquid-crystal model, heat capacity peaks and points of phase co-existence were observed. The absence of a smectic phase at higher densities and a narrow range of the nematic phase were reported. The identity of the crystalline phase of this system was found to a hexagonal close-packed solid. Since the nematic-solid phase transition is strongly first order, care must be taken when using this model not to inadvertently simulate meta-stable nematic states at higher densities. In further analysis, the Weighted Histogram Analysis Method was applied to verify the precise locations of the phase transition points. Full article
(This article belongs to the Special Issue Liquid Crystals 2020)
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Figure 1

Figure 1
<p>Plots of nematic order <math display="inline"><semantics> <msub> <mi>S</mi> <mn>2</mn> </msub> </semantics></math> (<b>top</b>) and number density <math display="inline"><semantics> <msup> <mi>ρ</mi> <mo>∗</mo> </msup> </semantics></math> (<b>bottom</b>) versus pressure <math display="inline"><semantics> <msup> <mi>P</mi> <mo>∗</mo> </msup> </semantics></math> for upward and downward branches using conventional MC at <math display="inline"><semantics> <mrow> <msup> <mi>T</mi> <mo>∗</mo> </msup> <mo>=</mo> <mn>1.0</mn> </mrow> </semantics></math>.</p>
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<p>Plots of nematic order <math display="inline"><semantics> <msub> <mi>S</mi> <mn>2</mn> </msub> </semantics></math> versus pressure <math display="inline"><semantics> <msup> <mi>P</mi> <mo>∗</mo> </msup> </semantics></math> for upward (<b>top</b>) and downward (<b>bottom</b>) branches using replica-exchange MC at temperatures (<math display="inline"><semantics> <msup> <mi>T</mi> <mo>∗</mo> </msup> </semantics></math>) as indicated by the legend.</p>
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<p>Plots of nematic order <math display="inline"><semantics> <msub> <mi>S</mi> <mn>2</mn> </msub> </semantics></math> (<b>top</b>) and number density <math display="inline"><semantics> <msup> <mi>ρ</mi> <mo>∗</mo> </msup> </semantics></math> (<b>bottom</b>) versus pressure <math display="inline"><semantics> <msup> <mi>P</mi> <mo>∗</mo> </msup> </semantics></math> for upward and downward branches using replica-exchange MC at <math display="inline"><semantics> <mrow> <msup> <mi>T</mi> <mo>∗</mo> </msup> <mo>=</mo> <mn>1.0</mn> </mrow> </semantics></math>.</p>
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<p>Snapshot of a nematic phase at <math display="inline"><semantics> <mrow> <msup> <mi>T</mi> <mo>∗</mo> </msup> <mo>=</mo> <mn>1.0</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msup> <mi>P</mi> <mo>∗</mo> </msup> <mo>=</mo> <mn>3.0</mn> </mrow> </semantics></math> from three different angles.</p>
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<p>Snapshot of a solid phase at <math display="inline"><semantics> <mrow> <msup> <mi>T</mi> <mo>∗</mo> </msup> <mo>=</mo> <mn>1.0</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msup> <mi>P</mi> <mo>∗</mo> </msup> <mo>=</mo> <mn>7.0</mn> </mrow> </semantics></math> from three different angles. To help with the visualisation of the structure of this phase, all molecules have been rendered as small spherically symmetric spheres.</p>
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<p>Plots of heat capacity <math display="inline"><semantics> <msup> <mrow> <msub> <mi>c</mi> <mi>p</mi> </msub> </mrow> <mo>∗</mo> </msup> </semantics></math> versus pressure <math display="inline"><semantics> <msup> <mi>P</mi> <mo>∗</mo> </msup> </semantics></math> for upward (<b>top</b>) and downward (<b>bottom</b>) branches using conventional MC and replica-exchange MC at <math display="inline"><semantics> <mrow> <msup> <mi>T</mi> <mo>∗</mo> </msup> <mo>=</mo> <mn>1.0</mn> </mrow> </semantics></math>.</p>
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<p>Phase diagram plots for phase transition lines predicted from replica-exchange MC for the upward (<b>top</b>) and downward (<b>bottom</b>) branches.</p>
Full article ">Figure 7 Cont.
<p>Phase diagram plots for phase transition lines predicted from replica-exchange MC for the upward (<b>top</b>) and downward (<b>bottom</b>) branches.</p>
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<p>Replica-exchange energy histograms for the upward branch.</p>
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<p>Plots of the free-energy surfaces for the nematic-solid phase transition for the upward (<b>top</b>) and downward (<b>bottom</b>) branches using replica-exchange MC at <math display="inline"><semantics> <mrow> <msup> <mi>T</mi> <mo>∗</mo> </msup> <mo>=</mo> <mn>1.0</mn> </mrow> </semantics></math>.</p>
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<p>A plot of <math display="inline"><semantics> <msub> <mi>B</mi> <mn>4</mn> </msub> </semantics></math> versus <math display="inline"><semantics> <msub> <mi>B</mi> <mn>6</mn> </msub> </semantics></math> for the Hess–Su liquid-crystal model studied in this work using the upward branch of the replica-exchange method simulations. The phase of each point is denoted in the legend. For comparison, data points for perfect FCC and HCP crystals are also included.</p>
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12 pages, 599 KiB  
Article
Ferroelectric Particles in Nematic Liquid Crystals with Soft Anchoring
by Cristina Cirtoaje
Molecules 2021, 26(4), 1166; https://doi.org/10.3390/molecules26041166 - 22 Feb 2021
Cited by 3 | Viewed by 2382
Abstract
A theoretical evaluation of the electric Freedericksz transition threshold and saturation field is proposed for a liquid crystals composite with ferroelectric particles. Existing models consider a strong anchoring of nematic molecules on the glass support of the cell, but in this paper a [...] Read more.
A theoretical evaluation of the electric Freedericksz transition threshold and saturation field is proposed for a liquid crystals composite with ferroelectric particles. Existing models consider a strong anchoring of nematic molecules on the glass support of the cell, but in this paper a soft molecular anchoring of molecules on the glass support and also on the ferroelectric nanoparticle’s surface is assumed. Thus, a finite saturation field was obtained in agreement with real systems. Calculations are made for planar configuration of positive dielectric anisotropy liquid crystals. The results are compared with data obtained on similar systems from different publications and the differences are discussed. Full article
(This article belongs to the Special Issue Liquid Crystals 2020)
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Graphical abstract

Graphical abstract
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<p>Molecular orientation in nematic liquid crystal with ferroparticles insertion (<b>a</b>) without an applied field and (<b>b</b>) with an electric field applied. The molecules and ferroparticles are oversized compared to the glass cell for a better understanding of orientation.</p>
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<p>Freedericksz transition threshold versus anchoring strength energy for different interaction energies.</p>
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<p>Saturation voltage versus interaction energy density between molecules and particles.</p>
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<p>Saturation voltage versus anchoring energy of molecules on the substrate.</p>
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<p>Saturation voltage versus anchoring anisotropy parameter for two different anchoring energies on the support surface.</p>
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19 pages, 5285 KiB  
Article
Impact of Substitution Pattern and Chain Length on the Thermotropic Properties of Alkoxy-Substituted Triphenyl-Tristriazolotriazines
by Thorsten Rieth, Natalie Tober, Daniel Limbach, Tobias Haspel, Marcel Sperner, Niklas Schupp, Philipp Wicker, Stefan Glang, Matthias Lehmann and Heiner Detert
Molecules 2020, 25(23), 5761; https://doi.org/10.3390/molecules25235761 - 7 Dec 2020
Cited by 7 | Viewed by 3746
Abstract
Tristriazolotriazines (TTTs) with a threefold alkoxyphenyl substitution were prepared and studied by DSC, polarized optical microscopy (POM) and X-ray scattering. Six pentyloxy chains are sufficient to induce liquid-crystalline behavior in these star-shaped compounds. Thermotropic properties of TTTs with varying substitution patterns and a [...] Read more.
Tristriazolotriazines (TTTs) with a threefold alkoxyphenyl substitution were prepared and studied by DSC, polarized optical microscopy (POM) and X-ray scattering. Six pentyloxy chains are sufficient to induce liquid-crystalline behavior in these star-shaped compounds. Thermotropic properties of TTTs with varying substitution patterns and a periphery of linear chains of different lengths, branching in the chain and swallow-tails, are compared. Generally, these disks display broad and stable thermotropic mesophases, with the tangential TTT being superior to the radial isomer. The structure–property relationships of the number of alkyl chains, their position, length and structure were studied. Full article
(This article belongs to the Special Issue Liquid Crystals 2020)
Show Figures

Figure 1

Figure 1
<p>Tangential tristriazolotriazines (<span class="html-italic">t</span>-TTTs) (<b>a</b>) and propeller tristriazolotriazines (<span class="html-italic">r</span>-TTTs) (<b>b</b>) and the substitution pattern.</p>
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<p>Phase behavior of 3,4-di- (<b><span class="html-italic">t</span>-13</b>–<b><span class="html-italic">t</span>-25</b>), 3,5-di- (<b><span class="html-italic">t</span>-26</b>–<b><span class="html-italic">t</span>-32</b>) and 3,4,5-trialkoxyphenyl (<b><span class="html-italic">t</span>-33</b>–<b><span class="html-italic">t</span>-37</b>)-substituted <span class="html-italic">t</span>-TTTs depending on chain length.</p>
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<p>Model of a supercell (2<span class="html-italic">a</span> × 2<span class="html-italic">a</span> × 4<span class="html-italic">c</span>) of <b><span class="html-italic">t</span>-33</b>. (<b>a</b>,<b>b</b>) Top and side view, where hexyl chains are omitted; (<b>c</b>,<b>d</b>) side and top view, including hexyl chains.</p>
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<p>(<b>a</b>): Homeotropic growth of <b><span class="html-italic">t</span>-60</b> at 135 °C (cooling rate: 1 °C/min); (<b>b</b>): fan textures at 137 °C (cooling rate: 1 °C/min).</p>
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<p>Modeled liquid crystal (LC) phase of <b><span class="html-italic">t</span><span class="html-italic">-60</span></b>: (<b>a</b>,<b>b</b>): top and side view on columns in the c-direction, where alkyl chains are omitted; (<b>c</b>,<b>d</b>) top and side view.</p>
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<p>POM of <b><span class="html-italic">t</span>-66</b>: (<b>a</b>): at 84 °C; (<b>b</b>): fan and homeotropic orientation at 65 °C.</p>
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<p>(<b>a</b>) Simulated structure of <b><span class="html-italic">t</span>-66</b>: aromatic part of dimer; (<b>b</b>) view on 3 × 3 × 6 unit cells.</p>
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<p>Model of a supercell (2<span class="html-italic">a</span> × 2<span class="html-italic">a</span> × 4<span class="html-italic">c</span>) of <b><span class="html-italic">r</span>-33</b>. (<b>a</b>,<b>b</b>) Top view, where hexyl chains are omitted; (<b>c</b>,<b>d</b>) top and side view, including hexyl chains; (<b>e</b>) side view, where hexyl chains are omitted.</p>
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<p>Synthesis of <span class="html-italic">t</span>-TTTs and thermal rearrangement to <span class="html-italic">r</span>-TTTs.</p>
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<p>Synthesis of TTTs with chains of different lengths. i: R<sup>1</sup>Br, K<sub>2</sub>CO<sub>3</sub>; ii: R<sup>2</sup>Br, K<sub>2</sub>CO<sub>3</sub>; iii: NaOH, iv: HCl; v: SOCl<sub>2</sub>; vi: NH<sub>3</sub> aq; vii: ClSi(N<sub>3</sub>)<sub>3</sub>; viii: mCPBA; ix: CuCN; x: Et<sub>3</sub>NHN<sub>3.</sub></p>
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