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Investigating electro-optical properties of a nematic liquid crystal cell with planar anchoring boundary condition for various thicknesses: A Monte Carlo study
Abstract
Monte Carlo (MC) simulations and the Mueller matrix formalism were applied to investigate electro optical properties of a LC cell with planar boundary conditions for various thicknesses. Field dependent global order parameter and the optical transmissions were analyzed in common. Three characteristic regions of the periodicity of optical transmissions as a function of polarizer angle and the external field were identified.
... In this formalism, all polarisation states of the light beam arriving at optical elements are represented by a 4 × 1 Stokes vector. Many optical elements, such as polarisers and phaseshifting optical retarders, can each be represented by a 4 × 4 Mueller matrix [9][10][11]. ...
... The systematic analysis performed in this study offers insights into the dynamic tuning of optical transmissions as a function of external fields and the cell thicknesses. Compared to a single-stage configuration [10,11], the two-stage LC retarder system provides significantly enhanced tunability, which allows for more precise control over the adjustment of optical properties across different wavelengths. This capability is particularly important in applications where selective or broadband tuning is required, offering superior functionality over single-stage setups. ...
... The third term is called the Rapini-Papoular term [11,[13][14][15][16], which describes the anchoring forces between LCMs and the confining cell walls. The parameters τ and k w represent the anchoring force strength and the indices of nearest neighbouring LCM to the cell walls, respectively. ...
This study employs the Mueller matrix method to analyse the optical properties of a two-stage liquid crystal (LC) retarder system. The system is constructed using planar-aligned nematic LC cell retarders and linear polarisers. The orientation of the LC molecules (LCMs) in the cells are determined through Monte Carlo (MC) simulations by using a lattice Hamiltonian model that includes the Lebwohl-Lasher energy, external field interaction and the Rapini-Papoular term. The analysis focuses on the tunable wavelength range of 400–800 nm. The external field and the thicknesses of both LC cells are used as key parameters for tuning the optical transmission characteristics. The results demonstrate that the interplay between the thickness of the retarders and the applied external field significantly affects the transmission spectra, enabling precise control over wavelength selectivity and broadband transmission. Thinner configurations exhibit sharper wavelength selectivity and higher sensitivity to external fields, while thicker configurations provide broader, more uniform transmission across a wider wavelength range.
We present the concentration and temperature dependent optical textures, and dielectric properties of bismuth titanate (Bi 2 Ti 2 O 7 /Bi 4 Ti 3 O 12) (BT2/BT4) nanocomposite doped 4 0-octyl-4-biphenylcarbonitrile (8CB) liquid crystal (LC) mixtures using polarizing optical microscope and dielectric spectroscopic techniques. The optical textures of pure 8CB and BT2/BT4 nanocomposite doped 8CB mixtures affirm a uniform dispersion of nanocomposite. Interestingly, the value of dielectric permittivity (e 0 ?) is found to be higher for all mixtures as compared to pure 8CB. Moreover, the values of e 0 ? and electrical conductivity are the highest for the 0.1 wt% mixture in the low frequency region (20 to 100 Hz). These changes are attributed to the fact that both concentration and diffusion coefficient of mobile ions collectively control the dielectric parameters in the lower frequency region. The threshold voltage of N phase of 0.1 wt% BT2/BT4 nanocomposite doped 8CB mixture is found to be higher as compared to pure 8CB and the observed change is attributed to the ion releasing effect of the doped nanocomposite in the 8CB matrix.
In this research article, we have investigated the dielectric properties of a nematic liquid crystal (NLC), namely 4 cyano-4′- pentylbiphenyl (which is commonly known as 5CB), in sample cells of variable thickness. The dielectric behaviour has been studied through a LCR meter in the frequency ranging from 20 Hz to 1 MHz. It was observed that the real part of complex dielectric permittivity (ε') decreases and the peak value of the energy dissipated per unit cycle (ε′′) increases on increasing the cell thickness. It has also been noticed that the relaxation frequency of LC material under investigation shifts towards the lower side with the increment in the sample cell thickness. The observed dielectric behaviour has been attributed to the contribution of the ionic species available in the NLC used. The mobilized ions have a significant contribution in influencing the dielectric studies of 5CB in thin cells. Further, all the above mentioned physical attributes of 5CB will play an important role in fabricating a device which is not only cost effective but also has higher transmittance and negligible power consumption.
Addition of Nano rods results change in the dielectric and electro-optical properties of pure Ferroelectric Liquid Crystal (FLC) considerably. The present study is devoted to characterize the dielectric and electro-optical parameters of the FLC nano rods composite system. The size of nano rods is usually much bigger than that of FLC molecules, therefore, when they are doped in different concentrations, in pure FLC, their volume fraction plays considerable role in deciding the molecular dynamics of the resultant composite system. For the lesser concentrations, the nano rods offer mechanical strength to system geometry while at higher concentration of nano rods, they offer additional constraints on the system. In present report both of these aspects have been analyzed and explained.
We review the research on carbon nanotube (CNT) dispersion in liquid crystals (LCs), focusing mainly on the approaches where the aim is to align CNTs along the LC director field, but also covering briefly the proposed possibility to enhance thermotropic LCs by CNT doping. All relevant LC types are considered: thermotropic LChosts allowing dynamic CNT realignment, lyotropic LChosts allowing very high concentration of CNTs uniformly aligned over macroscopic areas and consequent removal of the LC, and LC phases formed by CNTs themselves, used in spinning high-quality carbon nanotube fibres. We also discuss the issue of CNT dispersion in some detail, since successful nanotube separation is imperative for success in this field regardless of the type of LC that is considered. We end by defining a few major challenges for the development of the field over the next few years, critical for reaching the stage where industrially viable protocols for LC-based CNT alignment can be defined.
Monte Carlo studies of the field-induced complex refractive index changes in nano-dispersed nematic liquid crystals (NLCs) exhibiting negative–positive refractive indices have been performed for various cases of applied field strengths and anchoring conditions over a broad spectral regime. The resultant field-induced spatially inhomogeneous molecular order and the corresponding metamaterial properties are obtained for various wavelengths and applied field strengths below and above the Freedericksz transition. In general, the director axis reorientation and the resultant refractive index distribution are spatially inhomogeneous, even under a uniform applied field. The detailed computations have identified parameter sets for obtaining the negative index of refraction and maximal index modulations that can be more than an order of magnitude larger than those obtainable from pure NLC systems.
The Lebwohl-Lasher model of nematogens consists of a system of particles placed at the sites of a cubic lattice and interacting with a pair potential Ui,j = -εijP2(cos betaij), where εij is a positive constant, ε, for nearest neighbours particles i and j and betaij is the angle between the axis of these two molecules. We have investigated this model using Monte Carlo simulations with periodic boundary conditions on a 30 × 30 × 30 lattice while the largest system previously studied was 20 × 20 × 20. The number of simulation runs near the transition is also significantly higher than in previous simulations to allow a more precise determination of the orientational transition temperature T*NI. The transition temperature has been placed at kT/ε = 1·1232 ± 0·0006, refining previous estimates. Orientational order parameters , have been calculated and a new algorithm is proposed for the computation of . Particular attention has been devoted to pretransitional properties. Pair correlations G2(r), G4(r) as well as the second rank g2-factor are reported. g2 is found to diverge at a temperature T*NI* = kT/ε = 1·1201 ± 0·0006 and to fit the Landau-de Gennes behaviour except near the transition. Our results indicate therefore that the Lebwohl-Lasher model can yield the small difference between the nematic-isotropic transition temperature and the isotropic phase limiting instability temperature without the need of introducing additional terms in the potential.
Monte Carlo (MC) simulations based exclusively on nearest-neighbor intermolecular interactions reveal the existence of stable long-range deformations and topological defects in a thin nematic film confined between two surfaces with antagonistic (normal and tangential) molecular orientations. Thus the MC technique allows one to describe a delicate balance of bulk elasticity and surface energy usually treated only with macroscopic theories.
Twisted nematic (TN) liquid crystal (LC) cells doped with carbon nanotubes (CNTs) were fabricated and their electro-optic characteristics were studied. The CNTs with a minute amount of doping did not disturb the liquid crystal orientation in the off and on state. Effects of CNTs on voltage-dependent transmittance curves and voltage holding ratio were not found to be so strong. The response time however was improved as compared to pure LC.
We have developed a high performance liquid crystal (LC) alignment layer of ultra-thin single wall carbon nanotubes (SWNTs) and a conjugated block copolymer nanocomposite that is solution-processible for conventional twisted nematic (TN) LC cells. The alignment layer is based on the non-destructive solution dispersion of nanotubes with a poly(styrene-b- paraphenylene) (PS-b-PPP) copolymer and subsequent spin coating, followed by conventional rubbing without a post-annealing process. Topographically grooved nanocomposite films with two dimensionally (2D) networked SWNTs embedded in a block copolymer matrix were created using a rubbing process in which bundles of SWNTs on the composite surface were effectively removed. The LCs were well aligned with a stable pre-tilt angle of approximately 2° on our extremely transparent nanocomposite, which gave rise to superfast switching of the TN LC molecules that was approximately 3.8 ms, or four times faster than that on a commercial polyimide layer. Furthermore, the TN LCD cells containing our SWNT nanocomposite alignment layers exhibited low power operation at an effective switching voltage amplitude of approximately 1.3 V without capacitance hysteresis.
This paper describes effect of electro-optic memory in the carbon nanotubes (CNTs) doped liquid crystals (LCs) and recent trends in optimization of these composites for practical use. The memory effect consists in irreversible increase of light transmittance through the homeotropically aligned layers of LC-CNTs composites placed between two crossed polarizers due to the electric field application cycle. The irreversibility of electro-optic response is caused by stabilization of LC planar alignment realized in the electric field by a network of CNTs acting as a spatially distributed aligning surface. This network reveals itself in percolation behavior of electric conductivity of LC-CNTs samples. By using nematic mixtures MLC6608 and MLC6609 from Merck developed for vertical alignment, a number of essential improvements of the LC-CNTs composites are obtained such as a room temperature operation, reduced controlling voltage and switching time. Efficiency of electro-optic memory of these composites was further doubled by doping LC with small amount of chiral agent. The developed samples give real application prospect to the memory type LC-CNTs composites, especially in the information displaying and storage systems based on the LC materials.
The electro-optical response and the microstructure of multiwalled carbon nano-tubes dispersed in nematic liquid crystals with negative dielectric anisotropy are investigated. In contrast to undoped liquid crystals, the liquid crystal dispersions of carbon nanotubes are characterized by the irreversible electro-optic response or the so-called electro-optical memory effect. This effect is that the light transmittance through the sandwiched layer of the dispersion placed between two crossed polarizers considerably increases after the electric field application cycle. The state of memory persisted over months of our observation. The memory is caused by the incomplete relaxation of liquid crystal molecules from the random planar to the initial homeotropic state after the field is off. It is pointed out that the stabilization of the planar state is due to the network of small nanotube aggregates formed in the liquid crystal disturbed by electro-hydrodynamic flows. It is revealed that the efficiency of electro-optical memory depends on the network morphology and the efficiency of electro-hydrodynamic flows in a liquid crystal.
We investigated the properties of nematic liquid crystal device (NLC) doped with titanium (Ti) nanoparticle (~100nm). The electro-optic (EO) properties of LCs changed according to Ti nanoparticle doping concentration. Ti nanoparticles in the NLC cells focused the electric field flux and strengthened the electric field. Further, Ti nanoparticles in NLC molecules may trap charged ionic impurities and suppress the screen effect, leading to a stronger electric field and the van der Waals dispersion interactions between NLC molecules and the alignment layers. We also simulated the boundary conditions of the Ti nanoparticles in the electric field using Ansoft Maxwell software. Our experimental results agreed with the phenomenon predicted by software simulation based on general physical theory. Synthetically, at a 1.0 wt. % Ti nanoparticle doping concentration, the NLC cells showed the best EO properties, such as a low threshold voltage (1.25V), fast response time (13.2ms), and low pretilt angle (3.90°).
We present here the dielectric and electro-optical studies of cadmium telluride quantum dots (CdTe QDs) doped ferroelectric liquid crystals (FLCs). It has been observed that the doping of CdTe QDs not only induced a pronounced memory effect but also affected the physical parameters of FLC material (LAHS19). The modifications in the physical parameters and memory effect of LAHS19 are found to depend on the concentration ratio of CdTe QDs. The lower concentration of CdTe QDs (1-3 wt%) enhanced the values of spontaneous polarization and rotational viscosity of LAHS19 material but did not favor the memory effect, whereas a higher concentration of CdTe QDs (>5 wt%) degraded the alignment of LAHS19 material. The doping of ∼5 wt% of CdTe QDs is found to be the most suitable for achieving good memory effect without significantly affecting the material parameters.
The electrical Freedericksz transition characteristics of planar aligned liquid crystal cells doped with harvested single ferroelectric domain 9 nm nanoparticles of BaTiO3 have been measured. We demonstrate for the first time that the electrical pre-history of the cells imparts significant polarity sensitivity to the Freedericksz characteristics. The presence of harvested single domain ferroelectric nanoparticles enables cells to be programmably semi-permanently polarized. This reduces or increases the Freedericksz transition threshold by 0.8 V, depending on the polarity of the applied voltage, giving a net 1.6 V Freedericksz threshold asymmetry for 8 μm thick cells filled with TL205 liquid crystal.
We present Monte Carlo computer simulations of model nematic droplets that mimic polymer dispersed liquid crystals (PDLC's) with bipolar boundary conditions. We investigate the orientational order and the molecular organization in these systems for various anchoring strengths and for external applied fields of different magnitude both for positive and negative susceptivity anisotropy. We report a number of simulations for system sizes from 304 to 11 752 particles and calculate powder deuterium NMR spectra and polarizing microscope textures for the various cases.
Liquid crystals constitute a fascinating class of soft condensed matter characterized by the counterintuitive combination of fluidity and long-range order. Today they are best known for their exceptionally successful application in flat panel displays, but they actually exhibit a plethora of unique and attractive properties that offer tremendous potential for fundamental science as well as innovative applications well beyond the realm of displays. Today this full breadth of the liquid crystalline state of matter is becoming increasingly recognized and numerous new and exciting lines of research are being opened up. We review this exciting development, focusing primarily on the physics aspects of the new research thrusts, in which liquid crystals – thermotropic as well as lyotropic – often meet other types of soft matter, such as polymers and colloidal nano- or microparticle dispersions. Because the field is of large interest also for researchers without a liquid crystal background we begin with a concise introduction to the liquid crystalline state of matter and the key concepts of the research field. We then discuss a selection of promising new directions, starting with liquid crystals for organic electronics, followed by nanotemplating and nanoparticle organization using liquid crystals, liquid crystal colloids (where the liquid crystal can constitute either the continuous phase or the disperse phase, as droplets or shells) and their potential in e.g. photonics and metamaterials, liquid crystal-functionalized polymer fibers, liquid crystal elastomer actuators, ending with a brief overview of activities focusing on liquid crystals in biology, food science and pharmacology.
Monte Carlo simulations were used for modeling of optical transmission in twisted nematic liquid crystals containing metal nanoparticles interacting resonantly with pump polarized laser light. This method allows for tuning of the interaction strength: light-nanoparticle (parameter τ), anchoring at the surface (parameter α) and gives profile of angular molecular distribution within the LC layer thickness. We supplemented this method by a classic description of the optical Kerr effect in the TNLC between crossed polarizer system and compare results of transmittance changes of the system with measurements.
A comprehensive review of the recent developments regarding the phenomenon of reentrant phase transitions (RPT) in liquid crystals is presented. In addition to liquid crystals this phenomenon has been observed in amazingly diverse systems. A critical assessment of the experimental investigations concerning single and multiple reentrances is given. A brief account of the theoretical efforts is also given. The article ends with the identification of the factors which impede the proper understanding of the phenomenon.
We study the effect of spatial inhomogeneity of anchoring forces on real part of effective refractive index in nanosphere dispersed liquid crystal (NDLC) metamaterial at infrared frequencies using the approach of Khoo et al. [1] and Monte Carlo modeling proposed recently in Ref. [2]. Local and global characterization is made using 2D maps of spatial distribution of the index, its gradients and its modulation amplitude below and above Freedericksz threshold. We find that NDLC with step-wise modulation of anchoring forces gives rise to much larger gradients and absolute values of the effective index than NDLC with modulated external electric field as well as pure nematic liquid crystal (NLC) with inhomogeneous anchoring. This indicates that the filling factor of coated spheres in NDLC is an important design parameter which tunes the effective refractive index. We find that the results are strongly dependent on wavelength in the infrared interval 2800–2900 nm. Some potential applications to molding the flow of light are briefly mentioned.
The lattice version of the Maier-Saupe model of a nematic liquid crystal, in which all molecules are restricted to be on a simple-cubic lattice with periodic boundary conditions and to interact only with their nearest neighbors through the interaction energy Eij=-ε(3/2cos2θij-1/2), is investigated using a Monte Carlo technique. The lattice is found to undergo a first-order phase transition at ε/kT=0.890±0.005 with a spontaneous order of 〈P2(cosθ)〉=0.33±0.04 at the transition.
We present a Monte Carlo simulation of a model of a twisted nematic
display on a lattice starting from purely microscopic interactions. We
visualize the simulated display calculating optical textures under
crossed polarizers corresponding to the Monte Carlo microscopic
configurations. We also investigate the orientational order and the
molecular organizations in the different regions of the lattice,
introducing and calculating suitable order parameters.
We investigate nematic-isotropic transition in liquid crystal elastomers employing a variant of Wang–Landau sampling. This technique facilitates calculation of the density of states from which other thermodynamic properties can be obtained. We consider a lattice model of a liquid crystal elastomer and a Hamiltonian which accounts for interactions among liquid crystalline units and interaction of local nematics with global strain. We investigate the effect of varying the strength of coupling between nematic and orientational degrees of freedom. When the local director is coupled strongly to the global strain, the transition is strongly first order. When the strength of the coupling decreases the transition becomes weakly first order. The transition temperature decreases when the coupling becomes weaker. We also report for the first time results on variation of free energy as a function of average energy at different temperatures and coupling constants.
We report electro-optical effects in planar-aligned liquid-crystal cells of pristine and doped calamitics in the presence of dc voltage. The doped cells comprise both a nematic host and a minute amount of either buckminsterfullerene or multiwalled carbon nanotubes. The voltage–transmittance and voltage–capacitance hystereses were observed from the sample cells in the range of applied dc voltage up to 8 V. Experimental evidence indicates that a nanoscale carbon dopant can affect the behavior of a nematic in terms of ion-charge effects and that doping with nanotubes can effectively reduce the driving voltage.
We study the influence of a spatially modulated light intensity on the refractive index of a nematic liquid crystal, using Monte–Carlo simulations with a generalized version of the Lebwohl–Lasher hamiltonian. We have considered a model of 2D liquid crystal cell in which one of the electrodes is covered by a photoconducting polymeric layer. The index profiles along the cell thickness are calculated and compared with experimental data.
Preface; 1. Introduction; 2. Some necessary background; 3. Simple
sampling Monte Carlo methods; 4. Importance sampling Monte Carlo
methods; 5. More on importance sampling Monte Carlo methods of lattice
systems; 6. Off-lattice models; 7. Reweighting methods; 8. Quantum Monte
Carlo methods; 9. Monte Carlo renormalization group methods; 10.
Non-equilibrium and irreversible processes; 11. Lattice gauge models: a
brief introduction; 12. A brief review of other methods of computer
simulation; 13. Monte Carlo simulations at the periphery of physics and
beyond; 14. Monte Carlo studies of biological molecules; 15. Outlook;
Appendix; Index.
In this paper, mathematical models are developed to correlate the time-resolved optical transmission experiments of liquid crystals dispersion devices under the influence of an electric field. The dispersion of liquid crystal in the confining matrices is supposed to be composed of identical spherical microdroplets containing the nematic liquid crystal phase. It is proposed that the confining surface induces the formation of a gradient of the torsional molecular velocities (switching velocities) in the response to an electric field or relaxation by the removal of an electric field, along the radius of the liquid crystal microdroplets. A method is proposed to determine the probability density function of the switching velocities. Applying the Laplace transform, the time-dependent functions for the optical transmission behavior of the liquid crystal dispersions are obtained. The model was applied to the study of the dynamics of glass dispersed liquid crystals devices, showing good correlation with the experimental data.
On étudie l'influence sur la transition de Freedericks des conditions d'ancrage : 1) Angle fini d'ancrage ; 2) Energie d'ancrage finie. Cette influence se traduit par une diminution des constantes d'élasticité apparentes. The effect of loose boundary condition on the Freedericks transition is discussed : 1) Finite clamp angle ; 2) Finite clamp energy. Such conditions would decrease the apparent elascity coefficients.
Using polarization microscopy, we have investigated the director configurations of droplets of a nematic liquid crystal with negative dielectric anisotropy and perpendicular boundary conditions subjected to electric fields. The droplets were suspended in liquid poly(dimethyl siloxane) and electric fields were applied both parallel and perpendicular to the viewing direction. The resulting director pattern is deduced by comparing the experimental transmission patterns with patterns calculated from various director models. For low fields, we observe a director field which is essentially radial, but with some azimuthal twist superimposed and a radial point (hedgehog) defect at the center. At intermediate fields, the hedgehog defect moves away from the center along the electric-field direction, while at the highest fields a line defect appears which lies along the diameter parallel to the field. Comparison of the transmission patterns with model calculations yields good agreement for the low- and intermediate-field cases, and reasonable agreement for the high-field case.
We report the results of simulations of the three-dimensional Lebwohl-Lasher model of the nematic-isotropic transition using a single cluster Monte Carlo algorithm. The algorithm, first introduced by Kunz and Zumbach to study two-dimensional nematics, is a modification of the Wolff algorithm for spin systems, and greatly reduces critical slowing down. We calculate the free energy in the neighborhood of the transition for systems up to linear size 70. We find a double well structure with a barrier that grows with increasing system size. We thus obtain an upper estimate of the value of the transition temperature in the thermodynamic limit.
It has long been appreciated that liquid-crystal (LC) devices in which the LC molecules adopt multiple stable orientations could drastically reduce the power consumption required for high-information-content displays. But for the commonly used nematic LCs, which are intrinsically uniaxial in symmetry, no industrially feasible multi-stable LC device has been realized. Recently we demonstrated how bistability can be robustly engineered into a nematic LC device, by patterning a substrate with an orientational chequerboard pattern that enforces orthogonal LC alignment in neighbouring square domains. As a result of the four-fold symmetry of the pattern, the two diagonal axes of the chequerboard become equally stable macroscopic orientations. Here we extend this symmetry approach to obtain a tristable surface-aligned nematic LC. A microscopic pattern exhibiting six-fold symmetry is inscribed on a polyimide surface using the stylus of an atomic force microscope. The hexagonal symmetry of the microscopic orientational domains in turn gives rise to three stable macroscopic LC orientations, which are mutually switchable by an in-plane electric field. The resulting switching mode is surface driven, and hence should be compatible with demanding flexible display applications.
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