Nematic Phase Transition Research Articles

Monte Carlo study with reweighting of uniaxial nematic liquid crystals composed of biaxial molecules.

We present a high accuracy Monte Carlo simulation study of the uniaxial nematic (N_{U}) to isotropic (I) phase transition of a lattice dispersion model of uniaxial nematics composed of biaxial molecules. The N_{U}-I coexistence curve terminating at the Landau critical point has been determined using the multiple histogram reweighting technique. A close investigation reveals a sharp departure in the nature of the N_{U}-I coexistence curve in the temperature-biaxiality parameter phase diagram in comparison to the earlier theoretical (either mean-field or computer simulation) predictions. The coexistence curve shows a change in curvature with increasing value of the degree of molecular biaxiality.

Mean-field theory of isotropic-uniaxial nematic-biaxial nematic phase transitions in an external field

We present a simple mean-field theory to study the effects of an external magnetic field on biaxial nematic liquid crystals. Isotropic-uniaxial nematic-biaxial nematic phase sequence in an external magnetic field is described. We determine the temperature-field phase diagrams. The model predicts two new phase diagrams. It is shown that in the presence of the magnetic field, the first order uniaxial nematic to biaxial nematic and isotropic to uniaxial nematic phase transitions become second order transition at a tricritical point.

Threshold voltage decrease in a thermotropic nematic liquid crystal doped with graphene oxide flakes.

We report a threshold voltage decrease in a nematic liquid crystal compound, 4-cyano-4′-pentylbiphenyl (5CB), doped with graphene oxide (GO) flakes at a concentration of 0.05–0.3 wt %. The threshold voltage decrease was observed at the same concentration in electro-optic and dielectric spectroscopy measurements. The effect is related to the disrupted planar alignment due to the strong π–π stacking between the 5CB’s benzene rings and the graphene oxide’s structure. Additionally, we present the GO concentration dependence on the isotropic–nematic phase transition temperature, electric anisotropy, splay elastic constant, switch-on time, and switch-off time. The shape and dimensions of the GO flakes were studied using atomic force microscopy (AFM) and scanning electron microscopy (SEM). The influence of the GO concentration on the physical properties and switching process in the presence of the electric field was discussed.

Evolution of the low-temperature Fermi surface of superconducting FeSe1\u2212xSx across a nematic phase transition

The existence of a nematic phase transition in iron-chalcogenide superconductors poses an intriguing question about its impact on superconductivity. To understand the nature of this unique quantum phase transition, it is essential to study how the electronic structure changes across this transition at low temperatures. Here, we investigate the evolution of the Fermi surfaces and electronic interactions across the nematic phase transition of FeSe1−xSx using Shubnikov-de Haas oscillations in high magnetic fields up to 45 T in the low temperature regime down to 0.4 K. Most of the Fermi surfaces of FeSe1−xSx monotonically increase in size except for a prominent low frequency oscillation associated with a small, but highly mobile band, which disappears at the nematic phase boundary near x ~ 0.17, indicative of a topological Lifshitz transition. The quasiparticle masses are larger inside the nematic phase, indicative of a strongly correlated state, but they become suppressed outside it. The experimentally observed changes in the Fermi surface topology, together with the varying degree of electronic correlations, will change the balance of electronic interactions in the multi-band system FeSe1−xSx and promote different kz-dependent superconducting pairing channels inside and outside the nematic phase.

Pretransitional behavior of viscoelastic parameters at the nematic to twist-bend nematic phase transition in flexible n-mers.

We report dynamic light scattering measurements of the orientational (Frank) elastic constants and associated viscosities among a homologous series of a liquid crystalline dimer, trimer, and tetramer exhibiting a uniaxial nematic (N) to twist-bend nematic (NTB) phase transition. The elastic constants for director splay (K11), twist (K22) and bend (K33) exhibit the relations K11 > K22 > K33 and K11/K22 > 2 over the bulk of the N phase. Their behavior near the N-NTB transition shows dependency on the parity of the number (n) of the rigid mesomorphic units in the flexible n-mers. Namely, the bend constant K33 in the dimer and tetramer turns upward and starts increasing close to the transition, following a monotonic decrease through most of the N phases. In contrast, K33 for the trimer flattens off just above the transition and shows no pretransitional enhancement. The twist constant K22 increases pretransitionally in both even and odd n-mers, but more weakly so in the trimer, while K11 increases steadily on cooling without evidence of pretransitional behavior in any n-mer. The viscosities associated with pure splay, twist-dominated twist-bend, and pure bend fluctuations in the N phase are comparable in magnitude to those of rod-like monomers. All three viscosities increase with decreasing temperature, but the bend viscosity in particular grows sharply near the N-NTB transition. The N-NTB pretransitional behavior is shown to be in qualitative agreement with the predictions of a coarse-grained theory, which models the NTB phase as a "pseudo-layered" structure with the symmetry (but not the mass density wave) of a smectic-A* phase.

Symmetric and antisymmetric strain as continuous tuning parameters for electronic nematic order

We report the separate response of the critical temperature of the nematic phase transition ${T}_{\mathrm{S}}$ to symmetric and antisymmetric strains for the prototypical underdoped iron pnictide $\mathrm{Ba}{({\mathrm{Fe}}_{0.975}{\mathrm{Co}}_{0.025})}_{2}{\mathrm{As}}_{2}$. This decomposition is achieved by comparing the response of ${T}_{\mathrm{S}}$ to in-plane uniaxial stress and hydrostatic pressure. In addition to quantifying the two distinct linear responses to symmetric strains, we find a quadratic variation of ${T}_{\mathrm{S}}$ as a response to antisymmetric strains ${\ensuremath{\varepsilon}}_{{\mathrm{B}}_{1\mathrm{g}}}=\frac{1}{2}({\ensuremath{\varepsilon}}_{\mathrm{xx}}\ensuremath{-}{\ensuremath{\varepsilon}}_{\mathrm{yy}})$, exceeding the nonlinear response to symmetric strains by at least two orders of magnitude. These observations establish orthogonal antisymmetric strain as a powerful tuning parameter for nematic order.

Thermally-induced nonlinear spatial shaping of infrared femtosecond pulses in nematic liquid crystals

An optically-induced thermal non-linear effect in a nematic liquid-crystal (E7) cell is evidenced through weak light-absorption by the ITO coating of an infrared pulsed femtosecond laser (m). Strong spatial self-phase modulation is generated, thus a multiple-ring pattern is observed in the far-field. The sign of the nonlinearity is changed depending on the laser polarization. The refractive index and thermal gradients are measured as a function of the laser intensity and we observe that the temperature can increase close to the nematic phase transition. The fidelity and stability of the process open new prospects for spatial shaping devices and delimits the operating wavelength range for ultrafast liquid-crystal based electro-optic application.

Critical behavior of the optical birefringence at the nematic to twist-bend nematic phase transition

The critical behavior at the transition from uniform nematic to twist-bend modulated nematic phase is revealed and shown to be well explained by the mean field approximation. The study was performed on a group of materials that exhibit an unusually broad temperature range of the nematic phase above the twist-bend modulated nematic phase, so the critical range in which the order parameter fluctuations are strong and can be experimentally observed is wide. The formation of instantaneous helices is observed already several degrees above the transition temperature, strongly influencing the birefringence of the system. The analysis of a critical part of the birefringence changes provides a set of critical exponents that are consistent with the mean field approximation, indicating a large correlation length of helical fluctuations in the nematic phase.

On the Isotropic–Nematic Phase Transition for the Liquid Crystal

In this paper, we study the isotropic–nematic phase transition for the nematic liquid crystal based on the Landau–de Gennes $$\mathbf {Q}$$ -tensor theory. We justify the limit from the Landau–de Gennes flow to a sharp interface model: in the isotropic region, $$\mathbf {Q}\equiv 0$$ ; in the nematic region, the $$\mathbf {Q}$$ -tensor is constrained on the manifolds $$\mathcal {N}=\{s_+(\mathbf {n}\otimes \mathbf {n}-\frac{1}{3}\mathbf {I}), \mathbf {n}\in {\mathbb {S}^2}\}$$ with $$s_+$$ a positive constant, and the evolution of alignment vector field $$\mathbf {n}$$ obeys the harmonic map heat flow, while the interface separating the isotropic and nematic regions evolves by the mean curvature flow. This problem can be viewed as a concrete but representative case of the Rubinstein–Sternberg–Keller problem introduced in Rubinstein et al. (SIAM J. Appl. Math. 49:116–133, 1989; SIAM J. Appl. Math. 49:1722–1733, 1989).

Magnetic fluctuations under pressure on S-doped FeSe studied via 77Se NMR

FeSe1-xSx has attracted much attention among iron-based superconductors because the pure sample undergoes nematic and superconducting (SC) phase transitions without magnetism. A pressure-induced antiferromagnetic (AFM) phase emerges upon applying pressure. In the pressure (P)-temperature (T) phase diagram for the 12%-S doped sample, the AFM phase is separated from the nematic phase at around 3.0 GPa, and SC transition temperature (Tc) takes a maximum (∼30 K). We measured T1 of 77Se for the 12%-S doped FeSe at 3.0 GPa. We found from 1/T1T that low-energy AFM fluctuations are not so much enhanced under pressure compared with those at ambient pressure. The result suggests changes of topology and nesting of Fermi surfaces during pressurizing process.

Smeared nematic quantum phase transitions due to rare-region effects in inhomogeneous systems

The concept of a vestigial nematic order emerging from a "mother" spin or charge density-wave state has been applied to describe the phase diagrams of several systems, including unconventional superconductors. In a perfectly clean system, the two orders appear simultaneously via a first-order quantum phase transition, implying the absence of quantum criticality. Here, we investigate how this behavior is affected by impurity-free droplets that are naturally present in inhomogeneous systems. Due to their quantum dynamics, finite-size droplets sustain long-range nematic order but not long-range density-wave order. Interestingly, rare droplets with moderately large sizes undergo a second-order nematic transition even before the first-order quantum transition of the clean system. This gives rise to an extended regime of inhomogeneous nematic order, which is followed by a density-wave quantum Griffiths phase. As a result, a smeared quantum nematic transition, separated from the density-wave quantum transition, emerges in moderately disordered systems.

Nonperturbative renormalization group for the Landau–de Gennes model

We studied the nematic isotropic phase transition by applying the functional renormalization group to the Landau-de Gennes model. We derived the flow equations for the effective potential as well as the cubic and quartic "couplings" and the anomalous dimension. We then solved the coupled flow equations on a grid using Newton Raphson method. A first order phase transition is observed. We also investigated the nematic isotropic puzzle (the NI puzzle) in this paper. We obtained the NI transition temperature difference ${T_c-T^*}=5.85K$ with sizable improvement over previous results.

Fractional quantum Hall systems near nematicity: Bimetric theory, composite fermions, and Dirac brackets

We perform a detailed comparison of the Dirac composite fermion and the recently proposed bimetric theory for a quantum Hall Jain states near half filling. By tuning the composite Fermi liquid to the vicinity of a nematic phase transition, we find that the two theories are equivalent to each other. We verify that the single mode approximation for the response functions and the static structure factor becomes reliable near the phase transition. We show that the dispersion relation of the nematic mode near the phase transition can be obtained from the Dirac brackets between the components of the nematic order parameter. The dispersion is quadratic at low momenta and has a magnetoroton minimum at a finite momentum, which is not related to any nearby inhomogeneous phase.

Direct observation of spin excitation anisotropy in the paramagnetic orthorhombic state of BaFe2−xNixAs2

We use transport and inelastic neutron-scattering measurements to investigate single crystals of iron pnictide ${\mathrm{BaFe}}_{2\ensuremath{-}x}{\mathrm{Ni}}_{x}{\mathrm{As}}_{2}\phantom{\rule{0.28em}{0ex}}(x=0,0.03)$, which exhibit a tetragonal-to-orthorhombic structural transition at ${T}_{s}$ and stripe antiferromagnetic order at ${T}_{N}\phantom{\rule{0.28em}{0ex}}({T}_{s}\ensuremath{\ge}{T}_{N})$. Using a tunable uniaxial pressure device, we detwin the crystals and study their transport and spin excitation properties at antiferromagnetic wave-vector ${S}_{1}(1,0)$ and its ${90}^{\ensuremath{\circ}}$ rotated wave-vector ${S}_{2}(0,1)$ under different pressure conditions. We find that uniaxial pressure necessary to detwin and maintain the single domain orthorhombic antiferromagnetic phase of ${\mathrm{BaFe}}_{2\ensuremath{-}x}{\mathrm{Ni}}_{x}{\mathrm{As}}_{2}$ induces resistivity and spin excitation anisotropy at temperatures above zero pressure ${T}_{s}$. In the uniaxial pressure-free detwinned sample, spin excitation anisotropy between ${S}_{1}(1,0)$ and ${S}_{2}(0,1)$ first appears in the paramagnetic orthorhombic phase below ${T}_{s}$. These results are consistent with predictions of spin nematic theory, suggesting the absence of structural or nematic phase transition above ${T}_{s}$ in iron pnictides.

Isotropic-Nematic Transition and Demixing Behavior in Binary Mixtures of Hard Spheres and Hard Spherocylinders Confined in a Disordered Porous Medium: Scaled Particle Theory.

We develop the scaled particle theory to describe the thermodynamic properties and orientation ordering of a binary mixture of hard spheres (HS) and hard spherocylinders (HSC) confined in a disordered porous medium. Using this theory, the analytical expressions of the free energy, the pressure, and the chemical potentials of HS and HSC have been derived. The improvement of obtained results is considered by introducing the Carnahan-Starling-like and Parsons-Lee-like corrections. Phase diagrams for the isotropic-nematic transition are calculated from the bifurcation analysis of the integral equation for the orientation singlet distribution function and from the conditions of thermodynamic equilibrium. Both the approaches correctly predict the isotropic-nematic transition at low concentrations of hard spheres. However, the thermodynamic approach provides more accurate results and is able to describe the demixing phenomena in the isotropic and nematic phases. The effects of porous medium on the isotropic-nematic phase transition and demixing behavior in a binary HS/HSC mixture are discussed.

Dynamics of liquid crystalline phase transition in sedimenting platelet-like particles.

When a suspension of platelet-like particles sediment in a closed container, the particles undergo isotropic-nematic phase transition (I-N transition), and there appears a clear interface between the isotropic phase and the nematic phase. Usually the interface moves from bottom to top since the nematic phase appears and grows at the bottom, but it has been observed that in some situations the interface moves from top to bottom. Here, we study the dynamics of the interface by solving the non-equilibrium diffusion equation for the concentration of platelet-like particles, and show that the I-N interface can move upward (rising interface) or downward (falling interface) depending on whether the initial concentration is less than the critical concentration of I-N transition or more than it. We give a simple analysis theory for the motion of the interface in each case, which agrees well with the numerical calculations. We also show that the numerical results are in reasonable agreement with existing experimental measurements.

Dynamic calorimetry and XRD studies of the nematic and twist-bend nematic phase transitions in a series of dimers with increasing spacer length.

A modulated and conventional DSC study of the transitions between the twist-bend nematic (Ntb), regular nematic (N) and isotropic liquid (Iso) phases was performed on a series of difluoroterphenyl-based dimers with (CH2)n spacers; n = 5, 7, 9, 11. The enthalpy of Ntb-N transition decreases steeply with increasing n, while that of the N-Iso transition increases with n; hence, the greatest effect of increasing n is a lowering N phase enthalpy. Based on past and present X-ray scattering experiments, we estimate the average molecular conformation in the Ntb phase and perform torsion energy calculations on the spacer. From this, the lowering enthalpy of the N phase is attributed to the decreasing torsional energy cost of bringing the two terphenyls from an inclined twisted conformation in the Ntb phase, to almost parallel in the N phase. With increasing n the C-C bonds of the spacers twist less away from their trans conformation, thereby reducing the overall torsion energy of the N phase. It is speculated that the nearly continuous nature of the Ntb-N transition in n = 11 dimer is associated with the divergence of the helical pitch toward infinity which is intercepted by a final jump at the very weak (0.01 J g-1) first-order transition. Small-angle X-ray scattering results suggest similar local cybotactic layering in both nematic phases, with four sublayers, i.e. tails, mesogens, spacers, mesogens.

Computational modelling of tactoid dynamics in chromonic liquid crystals

ABSTRACTMotivated by recent experiments, the isotropic–nematic phase transition in chromonic liquid crystals is studied. As temperature decreases, nematic nuclei nucleate, grow and coalesce, giving rise to tactoid microstructures in an isotropic liquid. These tactoids produce topological defects at domain junctions (disclinations in the bulk or point defects on the surface). We simulate such tactoid equilibria and their coarsening dynamics with a model using degree of order, a variable length director and an interfacial normal as state descriptors. We adopt Ericksen’s work and introduce an augmented Oseen–Frank energy, with non-convexity in both interfacial energy and the dependence of the energy on the degree of order. A gradient flow dynamics of this energy does not succeed in reproducing some simple expected feature of tactoid dynamics. Therefore, a strategy is devised based on continuum kinematics and thermodynamics to represent such features. The model is used to predict tactoid nucleation, expansion and coalescence during the process of phase transition. We reproduce observed behaviours in experiments and perform an experimentally testable parametric study of the effect of bulk elastic and tactoid interfacial energy parameters on the interaction of interfacial and bulk fields in the tactoids.

An electro‐elastic phase‐field model for nematic liquid crystal elastomers based on Landau‐de‐Gennes theory

AbstractThe present contribution proposes a continuum‐mechanical phase‐field approach to model the electro‐elastic behavior of nematic liquid crystal elastomers. The nemato‐electro‐elastic model is embedded into the fundamental Landau‐de‐Gennes theory for isotropic–nematic phase transition and employs a tensorial order parameter as the phase field. Nematic deformations are incorporated through a constitutive ansatz in terms of the order parameter. The phase‐field formulation is implemented into the finite element method, so that the microstructure evolution of nematic elastomers under different boundary conditions can be studied. We show that the model is capable to capture characteristic features of nematic elastomers including mechanically and electrically induced microstructure evolution as well as the occurrence of stripe domains.

Elementary lattice models for the nematic transitions in liquid-crystalline systems

ABSTRACTThe Maier-Saupe theory of the nematic phase transitions, with the requirement that the molecular directors are restricted to the Cartesian axes, can be formulated as a fully-connected lattice problem, which is amenable to standard statistical-mechanics calculations. A simple three-state Maier-Saupe-Zwanzig (MSZ) model describes the weak first-order transition between uniaxial nematic and isotropic phases in liquid crystals, and provides a framework for several investigations. We describe calculations for a disordered MSZ model, which has been conceived to represent a binary mixture of rods and discs. Conflicting results in the literature about the stability of a long searched for biaxial phase are shown to be related to distinct treatments of disorder degrees of freedom. Effects of intrinsic biaxiality can be accounted for by analyzing a six-state MSZ model. We then used this model to investigate the phase diagrams of a mixture of uniaxial and intrinsically biaxial molecules, which is shown to display several nematic phases, reentrant regions, and a Landau multicritical point. We finally point out the connections of the elementary statistical models with a recent proposal of a mean-field two-tensor formalism.