Smectic Order Research Articles

Synergistic Investigation of Binary Hydrogen Bond Liquid Crystal Complex: Experimental and Theoretical (DFT) Perspectives of Smectic Molecular Ordering via Molecular Dynamics

Synergistic Investigation of Binary Hydrogen Bond Liquid Crystal Complex: Experimental and Theoretical (DFT) Perspectives of Smectic Molecular Ordering via Molecular Dynamics

Generation of nematic order in itraconazole by cryo-milling

Mechanical milling is a well-known method of solid-state amorphization of crystalline materials. Here, it is revealed that cryo-milling of itraconazole, a model thermotropic liquid-crystalline active pharmaceutical ingredient, leads to a preferred nematic order of molecules in solid particles instead of isotropic disorder − usually observed for most molecules that do not form liquid-crystalline mesophases. While standard quenching of itraconazole isotropic liquid down to room temperature results in the formation of glass with some degree of smectic order, cryo-milling easily destroys not only crystalline order but also smectic organization of molecules into layers, omitting the melting. The cryo-milled itraconazole samples exhibit faster α-relaxation and slightly slower δ-mode above the glass transition temperature. They are also more physically stable, with the stability dependent on the grinding time, below this temperature, with respect to the ordinary glass. The explanation for this behavior is believed to be increased short-range intermolecular disorder. Moreover, the cryo-milled particles with nematic order are better soluble than ordinary glass. Therefore, this work can guide the formulation of stable pharmaceuticals with nematic order/disorder and enhanced solubility.

From Fractional Quantum Anomalous Hall Smectics to Polar Smectic Metals: Nontrivial Interplay Between Electronic Liquid Crystal Order and Topological Order in Correlated Topological Flat Bands.

Symmetry-breaking orders can not only compete with each other, but also be interwined, and the interwined topological and symmetry-breaking orders make the situation more intriguing. This work examines the archetypal correlated flat band model on a checkerboard lattice at filling ν = 2/3 and we find the unique interplay between smectic charge order and topological order gives rise to two novel quantum states. As the interaction strength increases, the system first transitions from a Fermi liquid into FQAH smectic (FQAHS) state, where FQAH topological order coexists cooperatively with smectic charge order with enlarged ground-state degeneracy and interestingly, the Hall conductivity is σxy = ν = 2/3, different from the band-folding or doping scenarios. Further increasing the interaction strength, the system undergoes another quantum phase transition and evolves into a polar smectic metal (PSM) state. This emergent PSM is an anisotropic non-Fermi liquid, whose interstripe tunneling is irrelevant while it is metallic inside each stripe. Different from the FQAHS and conventional smectic orders, this PSM spontaneously breaks the two-fold rotational symmetry, resulting in a nonzero electric dipole moment and ferroelectric order. In addition to the exotic ground states, large-scale numerical simulations are also used to study low-energy excitations and thermodynamic characteristics. We find the onset temperature of the incompressible FQAHS state, which also coincides with the onset of non-polar smectic order, is dictated by the magneto-roton modes. Above this onset temperature, the PSM state exists at intermediate-temperature regime. Although the T = 0 quantum phase transition between PSM and FQAHS is first order, the thermal FQAHS-PSM transition could be continuous. We expect the features of the exotic states and thermal phase transitions could be accessed in future experiments.

Thermodynamic model for electro-optical properties of antiferroelectric phase in mesogen W-330-3 and W-331-3

ABSTRACT A thermodynamic model developed by our group has been employed to explore the electro-optical properties of the chiral antiferroelectric smectic C (Sm C A ∗ ) phase. In the present study, the temperature dependence of tilt angle and spontaneous polarization of binary ferroelectric mixtures represented as W-330-3 and W-331-3 exhibiting ferroelectric Sm C* and antiferroelectric Sm C A ∗ phase has been investigated. Within the framework of this model, the free-energy density characterizing the system featuring the Sm C A ∗ phase is expressed as a series expansion that incorporates all pertinent degrees of freedom: tensor orientational order Q ij , scalar smectic order ψ, polarization vector P, wave vector q of the helix and the resulting coupling terms between these order parameters. The values of Landau coefficients featured in the expansion series are derived from experimental data (tilt angle and spontaneous polarization) of W-330-3 and W-331-3. A substantial agreement between the theoretical predictions and experimental observations has been found.

Melted grain boundaries in smectic A under imposed bend: role of the anisotropy

ABSTRACT The well-known de Gennes analogy between smectics and superconductors predicts two types of smectic A behaviour under imposed bend. In Type I smectics, the smectic order melts, expelling all of the bend in a bulk nematic region (3D ‘defect’). In Type II smectics, the order melts on 1D defects, edge dislocation lines, which form an Abrikosov-like lattice. Here, I discuss how the strong anisotropy of the smectic coherence lengths influence the smectic A behaviour under imposed bend distortion. I show analytically and numerically that, as proposed previously, a third type of behaviour is possible close to a second-order nematic–smectic A transition, with smectic order melting on the plane of the grain boundary (2D defects). This third kind of behaviour, Melted Grain Boundary (MGB), which has been previously reported experimentally in the smectic A material 9CB, is intermediate between the Type I and Type II behaviours and can be considered as Type ‘one-and-a-half’ smectic A. I define the domain of material parameters in which the planar MGB defect is energetically and topologically stable. I discuss also if similar planar defects may exist, or not, in other anisotropic materials, e.g. superconductors, chiral smectic A, cholesterics and twist-bend nematics.

Stability of the chiral crystal phase and breakdown of the cholesteric phase in mixtures of active-passive chiral rods.

In this study, we aim to explore the effect of chirality on the phase behavior of active helical particles driven by two-temperature scalar activity. We first calculate the equation of state of soft helical particles of various intrinsic chiralities using molecular dynamics (MD) simulation. In equilibrium, the emergence of various liquid crystal (LC) phases such as nematic (N), cholesteric , smectic (Sm) and crystal (K) crucially depends on the presence of walls that induce planar alignment. Next, we introduce activity through the two-temperature model: keep increasing the temperature of half of the helical particles (labeled as 'hot' particles) while maintaining the temperature of the other half at a lower value (labeled as 'cold' particles). Starting from a homogeneous isotropic (I) phase, we find the emergence of 2-TIPS: two temperature-induced phase separations between the hot and cold particles. We also observe that the cold particles undergo an ordering transition to various LC phases even in the absence of a wall. This observation reveals that the hot-cold interface in the active system plays the role of a wall in the equilibrium system by inducing an alignment direction for the cold particles. However, in the case of a cholesteric phase, we observe that activity destabilizes the phase by inducing smectic ordering in the cold zone while an isotropic structure in the hot zone. The smectic ordering in the cold zone eventually transforms to a chiral crystal phase with high enough activity.

Splay-induced order in systems of hard tapers.

The main objective of this work is to clarify the role that taper-shaped elongated molecules, i.e., molecules with one end wider than the other, can play in stabilizing orientational order. The focus is exclusively on entropy-driven self-organization induced by purely excluded volume interactions. Drawing an analogy to RM734 (4-[(4-nitrophenoxy)carbonyl]phenyl-2,4-dimethoxybenzoate), which is known to stabilize ferroelectric nematic (N_{F}) and nematic splay (N_{S}) phases, and assuming that molecular biaxiality is of secondary importance, we consider monodisperse systems composed of hard molecules. Each molecule is modeled using six collinear tangent spheres with linearly decreasing diameters. Through hard-particle, constant-pressure Monte Carlo simulations, we study the emergent phases as functions of the ratio between the smallest and largest diameters of the spheres (denoted as d) and the packing fraction (η). To analyze global and local molecular orderings, we examine molecular configurations in terms of nematic, smectic, and hexatic order parameters. Additionally, we investigate the radial pair distribution function, polarization correlation function, and the histogram of angles between molecular axes. The last characteristic is utilized to quantify local splay. The findings reveal that splay-induced deformations drive unusual long-range orientational order at relatively high packing fractions (η>0.5), corresponding to crystalline phases. When η<0.5, only short-range order is affected, and in addition to the isotropic liquid, only the standard nematic and smectic-A liquid crystalline phases are stabilized. However, for η>0.5, apart from the ordinary nonpolar hexagonal crystal, three additional frustrated crystalline polar blue phases with long-range splay modulation are observed: antiferroelectric splay crystal (Cr_{S}P_{A}), antiferroelectric double-splay crystal (Cr_{DS}P_{A}), and ferroelectric double-splay crystal (Cr_{DS}P_{F}). Finally, we employ Onsager-Parsons-Lee local density functional theory to investigate whether any sterically induced (anti)ferroelectric nematic or smectic-A type of ordering is possible for our system, at least in a metastable regime.

Pre-Smectic Ordering and the Unwinding Helix in Monte Carlo Simulations of Cholesteric Liquid-Crystals.

In this paper, molecular chirality is studied for liquid-crystal fluids represented by hard rods with the addition of an attractive chiral dispersion term. Chiral forces between molecular pairs are assumed to be long-ranged and are described in terms of the pseudotensor of Goossens [W. J. A. Goossens, Mol. Cryst. Liq. Cryst. 1971, 12, 237-244]. Following Varga and Jackson [S. Varga and G. Jackson, Chem. Phys. Lett. 2003, 377, 6-12], this is combined with a hard-spherocylinder core. We investigate the relationship between molecular chirality and the helical pitch of the system, which occurs in the absence of full three-dimensional periodic boundary conditions. The dependence of the wavenumber of this pitch on the thermodynamic variables, temperature, and density is measured. We also explore the use of a novel surface boundary interaction model. As a result of this approach, we are able to lower the temperature of the system without the occurrence of nematic droplets, which would interfere with the formation of a uniaxial pitch. Regarding the theoretical predictions of Wensink and Jackson [H. H. Wensink and G. Jackson, J. Chem. Phys. 2009, 130, 234911], on the one hand, we have qualitative agreement with the observed non-monotonic density dependence of the wavenumber. Initially increasing with density, the wavenumber reaches a maximum, before falling as the density moves toward the point of phase transition from cholesteric to smectic. However, further analysis for shorter rods, in the presence of novel boundary conditions, reveals some disagreement with the theory, at least in this case; the unwinding of the cholesteric helix in the cholesteric phase occurs simultaneously with subtle increases in smectic ordering. These pre-smectic fluctuations have not been accounted for so far in theories on cholesterics but turn out to play a key role in controlling the pitch of cholesteric phases of rod-shaped mesogens with a small to moderate aspect ratio.

Smectic pair-density-wave order in EuRbFe4As4.

The pair density wave (PDW) is a superconducting state in which Cooper pairs carry centre-of-mass momentum in equilibrium, leading to the breaking of translational symmetry1-4. Experimental evidence for such a state exists in high magnetic field5-8 and in some materials that feature density-wave orders that explicitly break translational symmetry9-13. However, evidence for a zero-field PDW state that exists independent of other spatially ordered states has so far been elusive. Here we show that such a state exists in the iron pnictide superconductor EuRbFe4As4, a material that features co-existing superconductivity (superconducting transition temperature (Tc) ≈ 37 kelvin) and magnetism (magnetic transition temperature (Tm) ≈ 15 kelvin)14,15. Using spectroscopic imaging scanning tunnelling microscopy (SI-STM) measurements, we show that the superconducting gap at low temperature has long-range, unidirectional spatial modulations with an incommensurate period of about eight unit cells. Upon increasing the temperature above Tm, the modulated superconductor disappears, but a uniform superconducting gap survives to Tc. When an external magnetic field is applied, gap modulations disappear inside the vortex halo. The SI-STM and bulk measurements show the absence of other density-wave orders, indicating that the PDW state is a primary, zero-field superconducting state in this compound. Both four-fold rotational symmetry and translation symmetry are recovered above Tm, indicating that the PDW is a smectic order.

What promotes smectic order: Applying mean-field theory to the ends.

Not every particle that forms a nematic liquid crystal makes a smectic. The particle tip is critical for this behavior. Ellipsoids do not make a smectic, but spherocylinders do. Similarly, only those N-CB alkylcyanobiphenyls with sufficiently long (N≥8 carbons) alkane tails form smectics. We understand the role of the particle tip in the smectic transition by means of a simple two-dimensional model. We model spherocylinders by "boubas" with rounded tips, and ellipsoids by "kikis" with pointed tips. The N-CB molecules are modeled by a small body with a polymer tail. We find that rounded tips and longer polymer tails lead to a smectic at lower densities by making the space between layers less accessible, destabilizing the nematic.

Temperature-Dependent Circularly Polarized Luminescence of a Cholesteric Copolymer Doped with a Europium Complex

The design of new materials for non-contact temperature sensors is an important task for scientists working in the fields of chemistry, physics, and materials science. In the present paper, a novel cholesteric mixture based on a copolymer doped with a highly luminescent europium complex was prepared and studied. It was found that the spectral position of the selective reflection peak strongly depends on temperature and a shift towards shorter wavelengths is observed upon heating with an amplitude of more than 70 nm, from the red to green spectral range. This shift is associated with the existence and melting of clusters of smectic order, as confirmed by X-ray diffraction investigations. The extreme temperature dependence of the wavelength of selective light reflection provides a high thermosensitivity of the degree of circular polarization of the europium complex emission. The highest values of the dissymmetry factor are observed when the peak of selective light reflection fully overlaps with the emission peak. As a result, the highest sensitivity of 65%/K for luminescent thermometry materials was obtained. In addition, the ability of the prepared mixture to form stable coatings was demonstrated. The obtained experimental results, i.e., the high thermosensitivity of the degree of circular polarization, and the ability to form stable coatings allow us to consider the prepared mixture as a promising material for luminescent thermometry.

Colorful patterned polyacrylate films prepared using cholesteric liquid-crystalline mixtures with a smectic order

ABSTRACT Polymer-stabilised cholesteric liquid crystal (PSCLC) films with selective circularly polarised light reflection have attracted much attention for their applications as polarisers, energy-saving windows and for displays. Herein, CLC mixtures were prepared using a nematic LC LC242 and a chiral compound S-6 with enantiotropic SmA and SmC* phases, which exhibited a cholesteric phase with a smectic order. After photopolymerisation, the PSCLC films with fingerprint structure at the surfaces and supramolecular helical structure inside were obtained. Due to the existence of short-range smectic order in the cholesteric structure, the Bragg reflection bands were broadened. For a CLC mixture, with increasing temperature, the short-range smectic order was suppressed, and the selective Bragg reflection band shifted to the short wavelength. Based on this thermochromic behaviour, colourful PSCLC patterns and gratings were prepared, which were able to be applied in decoration and anti-counterfeiting. Since the PSCLC films can be obtained within several seconds under air, large-area films can be prepared on coating lines at low-cost.

The smectic ZA phase: Antiferroelectric smectic order as a prelude to the ferroelectric nematic

We have structurally characterized the liquid crystal (LC) phase that can appear as an intermediate state when a dielectric nematic, having polar disorder of its molecular dipoles, transitions to the almost perfectly polar-ordered ferroelectric nematic. This intermediate phase, which fills a 100-y-old void in the taxonomy of smectic LCs and which we term the "smectic ZA," is antiferroelectric, with the nematic director and polarization oriented parallel to smectic layer planes, and the polarization alternating in sign from layer to layer with a 180 Å period. A Landau free energy, originally derived from the Ising model of ferromagnetic ordering of spins in the presence of dipole-dipole interactions, and applied to model incommensurate antiferroelectricity in crystals, describes the key features of the nematic-SmZA-ferroelectric nematic phase sequence.

Main‐Chain Nematic Side‐Chain Smectic Composite Liquid Crystalline Elastomers

AbstractA composite liquid crystalline elastomer is designed, combining main‐chain and side‐chain mesogenic polymers in the network, and resulting in micro‐phase separated regions of nematic and smectic ordering in the macroscopically homogeneous elastomer. A range of different fractions of the components is explored, from fully nematic main‐chain system, across to fully smectic side‐chain elastomer. Thermal phase transitions of both phases coexisting in the material are detected by calorimetry, and the nematic/smectic structure investigated by X‐ray scattering. The tensile stress–strain data reveal the key effect of such a multi‐phase composite, where the nematic fraction adds ductility while the smectic fraction increases the modulus and mechanical stiffness. Varying the composition, the authors are able to optimize the mechanical properties of this material type.

Emerging Ferroelectric Uniaxial Lamellar (Smectic AF) Fluids for Bistable In-Plane Polarization Memory.

The emerging matter category of liquid-matter ferroelectrics, i.e., ferroelectric nematics, demonstrates an unprecedented combination of fluidity and spontaneous polarization. However, unlike traditional ferroelectrics, the field-switched polarization at zero-field cannot be conserved, so the memory effect remains challenging. Here we report another new type of ferroelectric liquid crystal state, dubbed the ferroelectric smectic A phase, where the polarization is longitudinally coupled to the smectic quasi-layer order. With higher packing density, the phase exhibits higher values of refractive anisotropy and spontaneous polarization compared to the ferroelectric nematics. A delicate balance between the liquid crystal elasticity and flow viscosity enables both the switching and memory of the polarization field, thus opening the door toward realizing liquid-matter ferroelectric memory devices.

Thermodynamic model to study the ferroelectric behaviour of lactic acid derivatives with keto linkage group

ABSTRACT The electro-optical and structural properties of chiral lactic acid derivatives with keto linkage group ((S)-4-((1-alkoxy-1-oxopropan-2-yloxy) carbonyl)phenyl4’-alkyloylbiphenyl-4-carboxylates denoted as KL n/m) exhibiting Sm C* phase and Sm A*−Sm C* phase transition have been studied by using a thermodynamic model based on Landau-de-Gennes theory. The free-energy density of the system is expanded in terms of three degrees of freedom – tensor orientational order , the scalar smectic order , the polarisation vector P, the wave vector q, and the couplings between these order parameters. The values of the Landau coefficients involved in the free-energy density have been calculated by comparing the experimental data of tilt angle, spontaneous polarisation, and pitch of KL n/m. The theoretical and experimental data have been analysed, and a close agreement has been found between the two.

Diverse Exotic Orders and Fermiology in Fe-Based Superconductors: A Unified Mechanism for B1g/B2g Nematicity in FeSe/(Cs,Rb)Fe2As2 and Smectic Order in BaFe2As2

A rich variety of nematic/smectic orders in Fe-based superconductors is an important unsolved problem in strongly correlated electron systems. A unified understanding of these orders has been investigated for the last decade. In this study, we explain the B1g symmetry nematic transition in FeSe1−xTex, the B2g symmetry nematicity in AFe2As2 (A = Cs, Rb), and the smectic state in BaFe2As2 based on the same framework. We investigate the quantum interference mechanism between spin fluctuations by developing the density wave equation. The observed rich variety of nematic/smectic orders is naturally understood in this mechanism. The nematic/smectic orders depend on the characteristic shape and topology of the Fermi surface (FS) of each compound. 1) In FeSe1−xTex (nd = 6.0), each FS is very small and the dxy-orbital hole pocket is below the Fermi level. In this case, the small spin fluctuations on three dxz, dyz, and dxy orbitals cooperatively lead to the B1g nematic (q = 0) order without magnetization. The experimental Lifshitz transition below the nematic transition temperature (TS) is naturally reproduced. 2) In BaFe2As2 (nd = 6.0), the dxy-orbital hole pocket emerges around the M point, and each FS is relatively large. The strong spin fluctuations due to the dxy-orbital nesting give rise to the B1g nematic (q = 0) order and the smectic [q = (0, π)] order, and the latter transition temperature (T* ∼ 170K) exceeds the former one (TS ∼ 140K). 3) In heavily hole-doped AFe2As2 (nd = 5.5), the large dxy-orbital hole pocket and the four tiny Dirac pockets appear due to the hole-doping. The B2g nematic bond order emerges on the dxy-orbital hole pocket because of the same interference mechanism. The present paramagnon interference mechanism provides a unified explanation of why the variety of nematic/smectic orders in Fe-based superconductors is so rich, based on the well-established fermiology of Fe-based superconductors.

Equilibrium phases and domain growth kinetics of calamitic liquid crystals.

The anisotropic shape of calamitic liquid crystal (LC) particles results in distinct values of energy when the nematogens are placed side by side or end to end. This anisotropy in energy which is governed by a parameter κ^{'} has deep consequences on equilibrium and nonequilibrium properties. Using the Gay-Berne (GB) model, which exhibits the nematic (Nm) as well as the low-temperature smectic (Sm) order, we undertake large-scale Monte Carlo and molecular dynamics simulations to probe the effect of κ^{'} on the equilibrium phase diagram and the nonequilibrium domain growth following a quench in the temperature T or coarsening. There are two transitions in the GB model: (i) isotropic to Nm at T_{c}^{1} and (ii) Nm to Sm at T_{c}^{2}<T_{c}^{1}. κ^{'} decreases T_{c}^{1} significantly but has relatively little effect on T_{c}^{2}. Domain growth in the Nm phase exhibits the well-known Lifshitz-Allen-Cahn (LAC) law, L(t)∼t^{1/2} and the evolution is via annihilation of string defects. The system exhibits dynamical scaling that is also robust with respect to κ^{'}. We find that the Sm phase at the quench temperatures T (T>T_{c}^{1}→T<T_{c}^{2}) that we consider has SmB order with a hexatic arrangement of the LC molecules in the layers (SmB-H phase). Coarsening in this phase exhibits a striking two-timescale scenario: First, the LC molecules align and develop orientational order (or nematicity), followed by the emergence of the characteristic layering (or smecticity) along with the hexatic bond-orientational-order within the layers. Consequently, the growth follows the LAC law L(t)∼t^{1/2} at early times and then shows a sharp crossover to a slower growth regime at later times. Our observations strongly suggest that L(t)∼t^{1/4} in this regime. Interestingly, the correlation function shows dynamical scaling in both the regimes and the scaling function is universal. The dynamics is also robust with respect to changes in κ^{'}, but the smecticity is more pronounced at larger values. Further, the early-time dynamics is governed by string defects, while the late-time evolution is dictated by interfacial defects. We believe this scenario is generic to the Sm phase even with other kinds of local order within the Sm layers.

Structures of glasses created by multiple kinetic arrests.

X-ray scattering has been used to characterize glassy itraconazole (ITZ) prepared by cooling at different rates. Faster cooling produces ITZ glasses with lower (or zero) smectic order with more sinusoidal density modulation, larger molecular spacing, and shorter lateral correlation between the rod-like molecules. We find that each glass is characterized by not one, but two fictive temperatures Tf (the temperature at which a chosen order parameter is frozen in the equilibrium liquid). The higher Tf is associated with the regularity of smectic layers and lateral packing, while the lower Tf with the molecular spacings between and within smectic layers. This indicates that different structural features are frozen on different timescales. The two timescales for ITZ correspond to its two relaxation modes observed by dielectric spectroscopy: the slower δ mode (end-over-end rotation) is associated with the freezing of the regularity of molecular packing and the faster α mode (rotation about the long axis) with the freezing of the spacing between molecules. Our finding suggests a way to selectively control the structural features of glasses.

Comparative study of electrooptic, dielectric, and structural properties of two glassforming antiferroelectric mixtures with a high tilt angle.

Vitrification of the antiferroelectric smectic-C_{A}^{*} phase is reported for the orthoconic mixture W-1000 and its new derivative W-356. The crystallization is not observed even upon slow cooling and the cold crystallization on subsequent heating is also absent. Molecular dynamics in the smectic phases of both mixtures is investigated down to 173K and the fragility parameters are determined from the temperature behavior of the α-process. X-ray diffraction is applied to compare the structural parameters of W-356 and W-1000 as well as to study the structural changes during the glass transition of the Sm-C_{A}^{*} phase. The evolution of the smectic layer order within the Sm-C_{A}^{*} glass is reported, while the correlation length of the short-range order in the smectic layers is shown to be almost constant below the glass transition temperature. Electrooptic properties of W-356: spontaneous polarization, tilt angle and switching time are determined and compared with these of W-1000. The observed differences between the properties of W-356 and W-1000 might be explained by the dimer formation of components with the -C≡N terminal group, present only in the W-356 mixture, and by the different structure of the aromatic molecular core in one of the W-356 components.