Order Parameter Of Liquid Crystal Research Articles

Optimization of the Domain Size in Stressed Liquid Crystals

The distributions of orientational and translational order parameters in liquid crystal polymer composites are studied using the methods of molecular-statistical physics. A model is considered in which the composite consists of liquid crystal (LC) domains separated by flat polymer sheets. The perturbation of the orientational and translational order parameters, which is caused by an arbitrary flat polymer sheet in a planar LC layer, is estimated. The effective distance over which this disturbance propagates is estimated. It is shown that it is proportional to the square root of the splay elastic constant of LC. It has been shown that in certain temperature ranges the polymer can induce a more ordered liquid crystal phase near itself (smectic phase inside of nematic phase and nematic phase – inside of isotropic liquid phase). In this case, the orientational order parameter of LC near the polymer can be significantly higher than far from it, and the “perturbation” of the order parameters can propagate over a distance of up to several micrometers with a sharp peak at a distance of the order of one micrometer. Based on the original theory, the methods have been proposed for optimizing the sizes of domains in stressed liquid crystals obtained by mechanical treatment in liquid crystal polymer composites.

Biaxial nematic order in fundamental measure theory.

Liquid crystals consisting of biaxial particles can exhibit a much richer phase behavior than their uniaxial counterparts. Usually, one has to rely on simulation results to understand the phase diagram of these systems since very few analytical results exist. In this work, we apply fundamental measure theory, which allows us to derive free energy functionals for hard particles from first principles and with high accuracy, to systems of hard cylinders, cones, and spherotriangles. We provide a general recipe for incorporating biaxial liquid crystal order parameters into fundamental measure theory and use this framework to obtain the phase boundaries for the emergence of orientational order in the considered systems. Our results provide insights into the phase behavior of biaxial nematic liquid crystals and, in particular, into methods for their analytical investigation.

Enhancement in electrical response of liquid crystals with carbon nanotubes doping

ABSTRACT The Freedericksz transition threshold is investigated in a homogeneously aligned carbon nanotube (CNT) doped liquid crystal (LC) planar cell. By neglecting the aggregate and bundle formation of CNTs in a low concentration of CNT doped LC cell, the reduction in the Freedericksz transition threshold is calculated theoretically. Flexoelectric polarisation tensorial expansion in terms of the order parameter and the generalised Helfrich theory is used to estimate the flexoelectric coefficients in the mixture. Dipolar and quadrupolar polarisations are studied in the flexoelectric coefficients of the mixture. It is shown that doping CNTs changes the flexoelectric coefficients through the order parameter of LCs. According to these calculations, for the LC molecules with a dipole moment parallel to their molecular axis, up to 4-fold increase in flexoelectric coefficient is expected, which is in good accordance with experimental reports. Also, it is shown that in the absence of dipolar flexoelectricity, the quadrupolar polarisation is responsible for the changes of the flexoelectric coefficients.

Dynamics of Nanoparticle Self-Assembly by Liquid Crystal Sorting in Two Dimensions

We study nonlinear dynamical equations for coupled conserved and non-conserved fields describing nanoparticle concentration and liquid crystal order parameter, respectively, and solve them numerically over bidimensional domains. These equations model the rapid segregation of nanoparticles away from nematic domains, which has been observed experimentally in a suspension of gold nanoparticles in 5CB below the isotropic-nematic transition temperature. We contrast the different behaviors obtained when the LC order parameter is treated as a scalar or a tensor, as well as the different rates of evolution observed with each of these. We find, after an instantaneous quench lowering the temperature below the transition one, an initial linear regime where the ordering of the nematic phase proceeds exponentially with time. Only after a lag period the nanoparticle material couples effectively to the LC order parameter and segregates to regions that are less orientationally ordered (extended domain walls for a scalar order parameter, but point disclinations for a tensor one). The lag period is followed by the onset of nonlinear dynamics and saturation of the order parameter. The choice of a scalar or tensor LC order parameter does not change this sequence but results in a clear overshooting of the nonlinear saturation level for the tensor order parameter case. These results are found to be insensitive to weak anchoring due to coupling of gradients of the conserved and non-conserved variables, for the nanoparticle concentrations and anchoring parameters studied. Our modeling approach can be extended in a straightforward manner to cases where the cooling rate is finite and to other systems where a locally conserved concentration is coupled to a orientation field, such as active Langmuir monolayers, and possibly to other examples of nonlinear dynamics in ecological or excitable media problems.

Ordering behavior and electric response of a ferroelectric nano-doped liquid crystal with ion impurity effects

We present a theoretical study of the simultaneous effects of ferroelectric nanoparticles and ion impurities on the order parameter of liquid crystals. We have focused on the effect of ion impurities on the ordering behavior and electrical response of a ferroelectric nano-doped liquid crystal near the nematic-isotropic phase transition. In this study, a statistical theory based on the orientational distribution of the nanoparticle dopants is used. We have performed the calculations using the Poisson–Boltzmann equation and a modified Landau-De Gennes model. The total density of free energy of the system is obtained within the framework of this theory, and the changes in the concentration of mobile ions due to the presence of ferroelectric nanoparticles are investigated. It is shown that the screening effect of the ion impurities plays a dominant role in the ordering behavior and electrical response of a ferroelectric nano-doped liquid crystal. The ion generation and the consequent changes are also described in some physical properties of a nano-doped system under an applied electric field.

Thermoelectric signature of the nematic phase in hole-doped iron-based superconductors

Studies of the copper-based superconductors demonstrate how their phase diagram becomes more complex as experimental probes improve, able to distinguish among subtly different electronic phases. One of those phases, nematicity, has become the matter of great interest also in the iron-based superconductors, where it is detected deep in the tetragonal state. Here we present the evolution of the in-plane Nernst effect anisotropy in the strain detwinned Ca(Fe1-xCox)2As2 single crystals, whose behaviour can be explained within the approach developed to describe the nematic order parameter in liquid crystals [1,2]. Furthermore, the employed method turns out to be universally applicable to data from other superconductors: Ba(Fe1-xCox)2As2 [3] as well as YBa2Cu3Oy [4]. We conclude the observed broken rotational symmetry of the electronic system is a consequence of the emerging thermodynamic electronic nematic order at a temperature much higher than onset of the magnetic and structural transitions.

Understanding liquid crystal order parameters deduced from different vibrations in polarised Raman spectroscopy

ABSTRACTPolarised Raman Spectroscopy (PRS) has been used to measure order parameters in liquid crystalline materials for decades. However, it is well known that different values of the order parameters are deduced for the same material when different vibrational modes are used in the analysis. This is an undesirable discrepancy that has somewhat hindered the use of the technique. Here we use two Raman active bands namely the phenyl (1606 cm−1) and cyano (2220 cm−1) stretching modes in the nematic phase of 5CB (4-cyano-4ʹ-pentylbiphenyl) as the example to explore the origin of such discrepancy. Two approaches are proposed in the data a nalysis taking either non-axial or non-cylindrical symmetric vibration into consideration. Together with a systematic discussion based on experimental data, we can conclude that whether or not the vibration satisfies the conditions associated with cylindrical symmetry is the correct physical explanation for the discrepancy in the order parameters.

Measuring order in disordered systems and disorder in ordered systems: Random matrix theory for isotropic and nematic liquid crystals and its perspective on pseudo-nematic domains.

Surprisingly long-ranged intermolecular correlations begin to appear in isotropic (orientationally disordered) phases of liquid crystal forming molecules when the temperature or density starts to close in on the boundary with the nematic (ordered) phase. Indeed, the presence of slowly relaxing, strongly orientationally correlated, sets of molecules under putatively disordered conditions ("pseudo-nematic domains") has been apparent for some time from light-scattering and optical-Kerr experiments. Still, a fully microscopic characterization of these domains has been lacking. We illustrate in this paper how pseudo-nematic domains can be studied in even relatively small computer simulations by looking for order-parameter tensor fluctuations much larger than one would expect from random matrix theory. To develop this idea, we show that random matrix theory offers an exact description of how the probability distribution for liquid-crystal order parameter tensors converges to its macroscopic-system limit. We then illustrate how domain properties can be inferred from finite-size-induced deviations from these random matrix predictions. A straightforward generalization of time-independent random matrix theory also allows us to prove that the analogous random matrix predictions for the time dependence of the order-parameter tensor are similarly exact in the macroscopic limit, and that relaxation behavior of the domains can be seen in the breakdown of the finite-size scaling required by that random-matrix theory.

Considerations in the determination of orientational order parameters from X-ray scattering experiments

ABSTRACTAn assessment of the data processing and analysis methods used to obtain the second- and fourth-rank orientational order parameters of liquid crystals from X-ray scattering experiments has been carried out, using experimental data from four extensively studied alkyl-cyanobiphenyls and calculated data generated from two general types of theoretical orientational distribution function. The application of a background subtraction and two different baseline correction methods to the scattering profiles is assessed, along with three different methods to analyse the processed data. The choice of baseline correction method is shown to have a significant effect: an offset to zero overestimates the order parameters from the experimental and calculated data sets, particularly for lower order parameters arising from broad distributions, whereas an offset to a value estimated from regions of low scattering intensity provides experimental values close to those reported from other experimental techniques. By contrast, the three different analysis methods are shown generally to result in relatively small absolute differences between the order parameters. We outline a straightforward general approach to experimental X-ray scattering data processing and analysis for uniaxial phases that results in order parameters that match well with those reported using other experimental techniques.

Molecular engineering of step-growth liquid crystal elastomers

Liquid crystal elastomers (LCEs) are shape-responsive materials that combine the elastic properties of a polymer network with the molecular ordering and responsiveness of liquid crystals. Recent work has relied on step-growth chemistries to produce LCEs with remarkable diversity and functionality. However, the connection between molecular structure and macroscopic properties such as shape responsiveness and phase behavior are poorly understood. Here, we demonstrate general molecular design principles for increasing shape-responsiveness and reducing the glass-transition temperature of LCEs produced through step-growth chemistries. We systematically investigate the phase behavior, liquid crystal ordering, mechanical properties and shape-responsiveness of a series of model polyester LCE networks using a combination of two-dimensional X-ray diffraction and dynamic mechanical analysis. We demonstrate that tailoring the length and composition of the linking group can reduce the glass-transition temperature with little impact on the liquid crystal order parameter, resulting in LCEs with a large shape-response near room temperature. Furthermore, the incorporation of a chain extending unit can significantly increase shape-responsiveness, from 35 up to 78% reversible strain, and the network crosslink density can be controlled by variation of the network stoichiometry. This work establishes generally applicable molecular design principles applicable to LCEs prepared through step-growth chemistries.

Electric field effects on phase transitions in the 8CB liquid crystal doped with ferroelectric nanoparticles.

The influence of a low ac electric field on phase transitions is discussed in the case of a nematic liquid crystal 4-n-octyl-4^{'}-cyanobiphenyl (8CB) doped with Sn_{2}P_{2}S_{6} ferroelectric nanoparticles. The phase-transition temperatures obtained from temperature-dependent dielectric measurements were higher than those determined by the calorimetric method. This difference is explained by the presence of the measuring electric field which induces two effects. The first one is the amplification of the interactions between the nanoparticle polarization and the liquid-crystal order parameter. The second one is the field-induced disaggregation or aggregation process at high nanoparticle concentrations.

Liquid Crystalline Compositions as Gas Sensors

Droplets and films of liquid crystalline mixtures were studied as promising detectors of volatile organic compounds (VOCs) in the air. Under increasing concentration of VOC in the air the detection may rely on each of the following effects sequentially observed one after the other: i. slight changes in orientation and order parameter of liquid crystal, ii. formation of bubbles on the top of the liquid crystalline droplet, iii. complete isotropisation of the liquid crystal. All three stages can be easily monitored by optical microscopy. Detection limits corresponding to the first stage are typically lower by a factor of 3–6 than detection limits corresponding to isotropisation. The qualitative model is presented to account for the observed changes.

Rebirth of Liquid Crystals for Sensoric Applications: Environmental and Gas Sensors

Films and droplets of liquid crystals may soon become an essential part of sensitive environmental sensors and detectors of volatile organic compounds (VOCs) in the air. In this paper a short overview of recent progress in the area of sensors based on liquid crystals is presented, along with the studies of low molar mass liquid crystals as gas sensors. The detection of VOCs in the air may rely on each of the following effects sequentially observed one after the other: (i) slight changes in orientation and order parameter of liquid crystal, (ii) formation of bubbles on the top of the liquid crystalline droplet, and (iii) complete isotropisation of the liquid crystal. These three stages can be easily monitored by a photo camera and/or optical microscopy. Detection limits corresponding to the first stage are typically lower by a factor of at least 3–6 than detection limits corresponding to isotropisation. The qualitative model taking into account the reorientation of liquid crystals is presented to account for the observed changes.

Effect of molecular-scale surface morphology on the surface melting of liquid crystals on self-assembled monolayers

We devised liquid crystal cell substrates with different surface roughnesses at the molecular scale by controlling the density of two types of trichlorosilanes with different alkyl chain lengths. We investigated surface melting of liquid crystals on these surfaces by observing the anchoring transition (change in the direction of alignment) that usually accompanies surface melting. Surface melting was observed only on substrates that had undulating surface morphologies due to either a low molecular density or interspersed arrangement of the two types of trichlorosilanes. We attributed the surface melting to the influence of molecular-level surface roughness on liquid crystal order parameters near the surface.

Eight types of symmetrically distinct vectorlike physical quantities.

The Letter draws the attention to the spatiotemporal symmetry of various vectorlike physical quantities. The symmetry is specified by their invariance under the action of symmetry operations of the nonrelativistic space-time rotation group O(3)×(1,1') = O'(3), where 1' is a time-reversal operation, the symbol × stands for the group direct product, and O(3) is a group of proper and improper rotations. It is argued that along with the canonical polar vector, there are another seven symmetrically distinct classes of stationary physical quantities, which can be--and often are--denoted as standard three-component vectors, even though they do not transform as a static polar vector under all operations of O'(3). The octet of symmetrically distinct "directional quantities" can be exemplified by two kinds of polar vectors (electric dipole moment P and magnetic toroidal moment T), two kinds of axial vectors (magnetization M and electric toroidal moment G), two kinds of chiral "bidirectors" C and F (associated with the so-called true and false chirality, respectively) and still another two bidirectors N and L, achiral ones, transforming as the nematic liquid crystal order parameter and as the antiferromagnetic order parameter of the hematite crystal α-Fe(2)O(3), respectively.

Fast response time of fringe-field switching liquid crystal mode devices with reactive mesogens in a planar alignment layer

We report the response time of fringe-field switching (FFS) liquid crystal (LC) mode devices using an ultraviolet-curable reactive mesogen (RM) mixed in a planar alignment layer. The RM polymers within the alignment layer increase the surface azimuthal anchoring energy and the order parameter of the LC molecules. As a result, the falling time and the rising time in the FFS mode are improved by the enhanced azimuthal anchoring energy and the increased dielectric torque induced by higher order parameter of LCs.

Symmetry Adapted Molecular-Field Theory for Thermotropic Biaxial Nematic Liquid Crystals and Its Expansion at Low Temperature

We have analyzed some properties of mean field theories of thermotropic biaxial liquid crystals with ($D_{2h}$) symmetry. The study consists of two parts. In the first part we reexamine the standard theory due to Virga and coworkers. We introduce a convenient symmetry-adapted parameterization which allows the phase diagram to be displayed in an explicitly symmetry-preserving triangle. In the second part we use the Laplace approximation to examine the low temperature properties of the liquid crystal order parameters. Two of these (conventionally, $D,P$) are identically zero at zero temperature in a biaxially ordered phase and nonzero at low temperatures in the liquid crystalline phases but are again zero at higher temperatures in the isotropic phase. We use a low temperature expansion to derive an expression for the dominant terms in the free energy. This functional is minimized to obtain the low temperature properties of the order parameters $D,P$.

Ordering dynamics of nematic liquid crystals: Monte Carlo simulations

We present comprehensive results from Monte Carlo (MC) simulations of ordering dynamics in d = 2 nematic liquid crystals. We compare our MC results with an analytic form obtained for the correlation function of the liquid crystal order parameter. The numerical and analytical results are in excellent agreement. The domain growth law is consistent with L(t) ∼ (t/ln t)1/2.

Colorless Molecular Dopants for Low-Operating-Voltage Nematic Liquid Crystals

ABSTRACT In this paper we present a study of two similar, colorless molecular dopants designed to decrease the operating voltages of nematic liquid crystals by increasing the dielectric anisotropy. Experimental analysis shows that these materials reduced the threshold voltage (voltage associated with the Freedericksz transition) by up to 20%, but via a reduction in the liquid crystal order parameter. To gain insight into the decrease of the order parameter, we used density-functional and single-point MP2 theory to investigate the conformational preferences of our dopants; the calculations suggest that, because of steric interactions, the conformations adopted are rather rigid.

Photoinduced anisotropy of the refractive index of an azopolymer with liquid-crystal properties

The formation of a photoinduced refractive-index grating in a photosensitive azopolymer with liquid-crystal (LC) properties is theoretically studied. Equations for photoinduced additions to the refractive index of the LC and amorphous polymers are obtained from balance equations for the distribution densities of trans- and cis-isomers of azodyes. The frequency characteristics of the response of the refractive index to a harmonic perturbation are calculated for different values of the LC order parameter.