Uniaxial Nematics Research Articles

Topological interfaces crossed by defects and textures of continuous and discrete point group symmetries in spin-2 Bose-Einstein condensates

We systematically and analytically construct a set of spinor wave functions representing defects and textures that continuously penetrate interfaces between coexisting, topologically distinct magnetic phases in a spin-2 Bose-Einstein condensate. These include singular and nonsingular vortices carrying mass or spin circulation that connect across interfaces between biaxial- and uniaxial nematic, cyclic and ferromagnetic phases, as well as vortices terminating as monopoles on the interface (“boojums”). The biaxial-nematic and cyclic phases exhibit discrete polytope symmetries featuring non-Abelian vortices and we investigate a pair of noncommuting line defects within the context of a topological interface. By numerical simulations, we characterize the emergence of nontrivial defect core structures, including the formation of composite defects. Our results demonstrate the potential of spin-2 Bose-Einstein condensates as experimentally accessible platforms for exploring interface physics, offering a wealth of combinations of continuous and discrete symmetries. Published by the American Physical Society 2024

Proton-decoupled deuterium NMR study of an asymmetric liquid crystal dimer having two nematic phases.

Proton-decoupled deuterium NMR spectra were obtained for an asymmetric liquid crystal dimer 1-(4-cyanobiphenyl-4'-yloxy)-6-(4-cyanobiphenyl-4'-yl)hexane (CB6OCB) containing a single -CD_{2}- group. The sample has two nematic liquid crystal phases: a twist-bend nematic, N_{TB}, at the lowest temperature followed by a uniaxial nematic, N_{U}, on increasing the temperature. Proton decoupling reduces the linewidths of the peaks in the deuterium spectrum from kHz to ∼100Hz, enabling quadrupolar splittings, Δν, to be obtained with enhanced precision as well as the dipolar coupling between deuterium nuclei within the CD_{2} group, hence enhancing the information content.

Evidence of T-type structures of hard square boards in capillary confinement.

We employ Onsager's second virial density functional theory combined with the Parsons-Lee theory within the restricted orientation (Zwanzig) approximation to examine the phase structure of hard square boards of dimensions (L×D×D) uniaxially confined in narrow slabs. Depending on the wall-to-wall separation (H), we predict a number of distinctly different capillary nematic phases, including a monolayer uniaxial or biaxial planar nematic, homeotropic with a variable number of layers, and a T-type structure. We determine that the favored phase is homotropic, and we observe first-order transitions from the homeotropic structure with n layers to n+1 layers as well as from homeotropic surface anchoring to a monolayer planar or T-type structure involving both planar and homeotropic anchoring at the pore surface. By increasing the packing fraction, we further demonstrate a reentrant homeotropic-planar-homeotropic phase sequence in a particular range (i.e., H/D=1.1 and 0.25≤L/D<0.26). We find that the T-type structure is more stable when the pore is wide enough with respect to the planar phase. The enhanced stability of the mixed-anchoring T-structure is unique for square boards and becomes manifest at pore width exceeding L+D. More specifically, the biaxial T-type structure emerges directly from the homeotropic state without intervention of a planar layer structure as observed for other convex particle shapes.

Core structures of vortices in Ginzburg-Landau theory for neutron P23 superfluids

We investigate vortex solutions in the Ginzburg-Landau theory for neutron $^3P_2$ superfluids relevant for neutron star cores in which neutron pairs possess the total angular momentum $J=2$ with spin-triplet and $P$ wave, in the presence of the magnetic field parallel to the angular momentum of vortices. The ground state is known to be in the uniaxial nematic (UN) phase in the absence of magnetic field, while it is in the $D_2$ ($D_4$) biaxial nematic (BN) phase in the presence of the magnetic field below (above) the critical value. We find that a singly quantized vortex always splits into two half-quantized non-Abelian vortices connected by soliton(s) as a vortex molecule with any strength of the magnetic field. In the UN phase, two half-quantized vortices with ferromagnetic cores are connected by a linear soliton with the $D_4$ BN order. In the $D_2$ ($D_4$) BN phase, two half-quantized vortices with cyclic cores are connected by three linear solitons with the $D_4$ ($D_2$) BN order. The energy of the vortex molecule monotonically increases and the distance between the two half-quantized vortices decreases with the magnetic field increases, except for a discontinuously increasing jump of the distance at the critical magnetic field. We also construct an isolated half-quantized non-Abelian vortex in the $D_4$ BN phase.

Elastic and electro-optical properties of flexible fluorinated dimers with negative dielectric anisotropy

ABSTRACT We report the synthesis and the temperature dependencies of optical, dielectric, and elastic properties of four homologous dimeric mesogens in the uniaxial nematic (N) phase. The studied dimers are derived from 2ʹ,3ʹ-difluoroterphenyl units connected via flexible alkyl chains. The compounds differ in the length of either the flexible alkyl chain or the terminal groups. These achiral bimesogens exhibit the twist-bend nematic (NTB) phase with a nanoscale pitch of the modulated nematic director, as established by the freeze-fracture transmission electron microscopy. All four homologs have negative dielectric anisotropy owing to the permanent dipole oriented normal to the long molecular axes. A longer flexible bridge length yields an expanded temperature range of the N phase, stronger dielectric anisotropy, larger birefringence and bend elastic constant . Longer alkyl terminal chains increase birefringence but decrease the absolute value of dielectric anisotropy and . All four bimesogens show a dramatic decrease of down to ~0.5 pN on approaching the N-NTB transition. A longer bridge yields a longer period of twist-bend modulation in the NTB phase.

Switching in a Biaxial Smectic A - like Phase

ABSTRACT Comments and the work presented in this paper aim at initiating discussion within the liquid crystalline community about the nature of different biaxial phases and their switching mechanisms. The mechanisms have the potential for applications in switching devices for displays and photonics. Claire Meyer et. al. interestingly report recently a fast Freedericksz-like transition of the secondary director in the biaxial Smectic Ab phase of a mixture of two compounds. Fast switching in liquid crystals occurs through a coupling of the biaxiality with the electric field. To realise this potential, one of the major goals of the liquid crystal community had been to discover biaxial nematic liquid crystals. In a biaxial liquid crystalline phase, the refractive indices along the three orthogonal axes are all different [n11≠ n22 ≠ n33] as opposed to these being different only along the two orthogonal directions n11 ≠ n22 = n33 in uniaxial nematics. In this notation 1, 2 and 3 are the three orthogonal axes that coincide with the major and the two minor directors. The biaxial nematic phase has been elusive for over half a Century. It has therefore proven to be almost impossible to meet the goal of achieving fast switching using biaxial nematics. Ferroelectric and antiferroelectric liquid crystals were discovered in 1975 and 1989 by R. Meyer in the USA and Atsuo Fukuda in Japan, respectively, for fast switching. These have been used in devices for niche but limited high-resolution applications as the devices using these liquid crystals suffered not only from achieving proper alignment at surfaces but also showed poor recovery of alignment following repeated cycles of switching.

Phase transitions in a high magnetic field of an odd, symmetric liquid crystal dimer having two nematic phases, N_{U} and N_{TB}, studied by NMR spectroscopy.

Both ^{1}H and ^{13}C NMR spectra have been obtained in a static magnetic field of 23.5 T on a bent-shaped dimer molecule, 1^{''},7^{''}-bis(4-cyanobiphenyl-4'-yl) nonane (CB9CB), which shows the sequence of liquid crystal phases twist-bend nematic, N_{TB}, and uniaxial nematic, N_{U}, before entering the isotropic phase. The ^{1}H spectra are used to locate the temperature at which the sample melts to form a twist-bend nematic, T_{CrN_{TB}}, and then T_{N_{U}I} when the isotropic phase is entered, both in a magnetic field of 23.5 T, and to compare these with those measured at the Earth's field. The differences between these transition temperatures are found to be zero within the error in their measurement, in stark contrast to previous measurements by Salili et al. [Phys. Rev. Lett. 116, 217801 (2016)10.1103/PhysRevLett.116.217801]. In the isotropic phase in the presence of the field the sample exists in a paranematic phase in which the molecules of CB9CB are partially ordered. The ^{1}H and ^{13}C NMR spectra in the paranematic phase are used to measure the critical temperature T* below which this phase is unstable. The spectra are also used to study the structure, molecular orientational order, and distribution of molecular conformations in the paranematic phase.

Twist-Bend Nematic Phase from the Landau-de Gennes Perspective.

Generalized Landau–de Gennes theory is proposed that comprehensively explains currently available experimental data for the heliconical twist–bend nematic (NTB) phase observed in liquid crystalline systems of chemically achiral bent-core-like molecules. A bifurcation analysis gives insight into possible structures that the model can predict and guides in the numerical analysis of relative stability of the isotropic (I), uniaxial nematic (NU), and twist–bend nematic phases. An estimate of constitutive parameters of the model from temperature variation of the nematic order parameter and the Frank elastic constants in the nematic phase enables us to demonstrate quantitative agreement between the calculated and experimentally determined temperature dependence of the pitch and conical angle in NTB. Properties of order parameters also explain a puzzling lack of a half-pitch band in resonant soft X-ray scattering. Other key findings of the model are predictions of I–NTB and NU–NTB tricritical points and insight into biaxiality of NTB.

Topological defects at the boundary of neutron P23 superfluids in neutron stars

We study surface effects of neutron $^{3}P_{2}$ superfluids in neutron stars. $^{3}P_{2}$ superfluids are in uniaxial nematic (UN), D$_{2}$ biaxial nematic (BN), or D$_{4}$ BN phase, depending on the strength of magnetic fields from small to large. We suppose a neutron $^{3}P_{2}$ superfluid in a ball with a spherical boundary. Adopting a suitable boundary condition for $^{3}P_{2}$ condensates, we solve the Ginzburg-Landau equation to find several surface properties for the neutron $^{3}P_{2}$ superfluid. First, the phase on the surface can be different from that of the bulk, and symmetry restoration or breaking occurs in general on the surface. Second, the distribution of the surface energy density has an anisotropy depending on the polar angle in the sphere, which may lead to the deformation of the geometrical shape of the surface. Third, the order parameter manifold induced on the surface, which is described by two-dimensional vector fields induced on the surface from the condensates, allows topological defects (vortices) on the surface, and there must exist such defects even in the ground state thanks to the Poincar\'{e}-Hopf theorem: although the numbers of the vortices and antivortices depend on the bulk phases, the difference between them is topologically invariant (the Euler number $\chi=2$) irrespective of the bulk phases. These vortices, which are not extended to the bulk, are called boojums in the context of liquid crystals and helium-3 superfluids. The surface properties of the neutron $^{3}P_{2}$ superfluid found in this paper may provide us useful information to study neutron stars.

Probing molecular ordering in the nematic phases of para-linked bimesogen dimers through NMR studies of flexible prochiral solutes

ABSTRACT The quadrupolar splittings of perdeuteriated n-decane dissolved in nematic phases formed by mesogenic dimers of the CBnCB series, for n = 7,9,10,11, are measured throughout the entire temperature range of these phases. These results are reported together with related measurements using the common nematic phase of 5CB as a solvent for n-decane. The data obtained from the 13C spectra of the cyanobiphenyl mesogenic units of the monomeric and dimeric solvent molecules yield the order parameter of those units. The information obtained from this set of experiments is used to elucidate the structure of the low temperature (NX) and the high temperature (N) nematic phases of CBnCB dimers with n = 7,9,11. The polar twisted nematic (NPT) model is found to provide a consistent description not only of our experimental results but also of NMR measurements previously reported in the literature for these phases. These findings suggest that the high temperature nematic (N) is not a common, locally uniaxial and apolar nematic, but rather a nematic phase consisting of NPT clusters. The twist-bend (NTB) model, often identified with the NX phase, is shown to be inadequate to account even qualitatively for crucial features of the experimental findings. NMR studies of perduteriated n-decane dissolved in mesogenic dimers of the CBnCB series elucidate the structure of the low and high temperature nematic phases of the odd-n dimers.

Domain walls in neutron P23 superfluids in neutron stars

We work out domain walls in neutron $^{3}P_{2}$ superfluids realized in the core of neutron stars. Adopting the Ginzburg-Landau (GL) theory as a bosonic low-energy effective theory, we consider configurations of domain walls interpolating ground states, i.e., the uniaxial nematic (UN), ${\mathrm{D}}_{2}$-biaxial nematic (${\mathrm{D}}_{2}$-BN), and ${\mathrm{D}}_{4}$-biaxial nematic $({\mathrm{D}}_{4}$-BN) phases in the presence of zero, small and large magnetic fields, respectively. We solve the Euler-Lagrange equation from the GL free energy density, and calculate surface energy densities of the domain walls. We find that one extra Nambu-Goldstone mode is localized in the vicinity of a domain wall in the UN phase while a U(1) symmetry restores in the vicinity of one type of domain wall in the ${\mathrm{D}}_{2}$-BN phase and all domain walls in the ${\mathrm{D}}_{4}$-BN phase. Considering a pile of domain walls in the neutron stars, we find that the most stable configurations are domain walls perpendicular to the magnetic fields piled up in the direction along the magnetic fields in the ${\mathrm{D}}_{2}$-BN and ${\mathrm{D}}_{4}$-BN phases. We estimate the energy released from the deconstruction of the domain walls in the edge of a neutron star, and show that it can reach an astrophysical scale such as glitches in neutron stars.

Twist-bend nematic phases of banana-shaped molecules with an axial chirality

ABSTRACTWe present a mean field theory to describe uniaxial () and biaxial twist-bend nematic () phases of banana-shaped liquid crystalline molecules with an axial chirality. We first derive a tensor order parameter for the banana-shaped molecules as a function of a bend angle (), a torsion angle for the axial chirality, and four orientational order parameters, which describe uniaxial and biaxial nematic phases. Depending on the bend angle and the strength of an oblique twisting power of the banana-shaped molecules, we calculate phase diagrams on the temperaturebend angle plane. We derive the analytical formulas for two Landau points (LPs): one is at the bend angle and the other is at , which depends on the torsion angle. We also find that the phase appears outside the two LP angles and the phase diagrams show a rich variety of phase transitions, such as the second-order uniaxial nematic ( and the second-order phase transitions, etc.

Identification of low-symmetry phases in nematic liquid crystals

Mesophases of nematic liquid crystals (NLC) are traditionally identified by building a second-rank ordering tensor that efficiently describes the average orientation of nematogenic molecules with respect to a fixed laboratory/reference frame. In general, both in experiments and in simulations, the symmetry group of the molecules is known a-priori, contrary to the symmetry group of the phase; this latter has to be determined by analysing the numerical realisation of possibly affected by numerical errors. Furthermore, when a mesophase has a simple symmetric structure, as is the case of uniaxial nematics, the identification of the preferred direction is relatively an easy task. However, this task becomes less straightforward when the symmetry group of a mesophase is more complex. There is no generally accepted procedure to perform this analysis, but we have provided in a previous paper a new algorithm suited to identifying the symmetry group of the phase. We implement here such algorithm which gives a canonical representation of for each of the classes that can be distinguished with a second-rank ordering tensor, and determines the nearest tensor of the assigned symmetry by group averaging.

Phase structure of neutron P23 superfluids in strong magnetic fields in neutron stars

We discuss the effect of a strong magnetic field on neutron $^{3}P_{2}$ superfluidity. Based on the attraction in the $^{3}P_{2}$ pair of two neutrons, we derive the Ginzburg-Landau equation in the path-integral formalism by adopting the bosonization technique and leave the next-to-leading order in the expansion of the magnetic field $B$. We determine the $(T,B)$ phase diagram with temperature $T$, comprising three phases: the uniaxial nematic (UN) phase for $B=0$, D$_{2}$-biaxial nematic (BN) and D$_{4}$-BN phases in finite $B$ and strong $B$ such as magnetars, respectively, where D$_{2}$ and D$_{4}$ are dihedral groups. We find that, compared with the leading order in the magnetic field known before, the region of the D$_{2}$-BN phase in the $(T,B)$ plane is extended by the effect of the next-to-leading-order terms of the magnetic field. We also present the thermodynamic properties, such as heat capacities and spin susceptibility, and find that the spin susceptibility exhibits anisotropies in the UN, D$_{2}$-BN, and D$_{4}$-BN phases. This information will be useful to understand the internal structures of magnetars.

Connectivity, Not Density, Dictates Percolation in Nematic Liquid Crystals of Slender Nanoparticles.

We show by means of continuum theory and simulations that geometric percolation in uniaxial nematics of hard slender particles is fundamentally different from that in isotropic dispersions. In the nematic, percolation depends only very weakly on the density and is, in essence, determined by a distance criterion that defines connectivity. This unexpected finding has its roots in the nontrivial coupling between the density and the degree of orientational order that dictate the mean number of particle contacts. Clusters in the nematic are much longer than wide, suggesting the use of nematics for nanocomposites with strongly anisotropic transport properties.

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.

Splay Nematic Phase

Different liquid crystalline phases with long-range orientational but not positional order, so-called nematic phases, are scarce. It rarely occurs that a new nematic phase is discovered and such event is inevitably accompanied by a great interest. Here, we describe a transition from uniaxial to novel nematic phase characterized by a periodic splay modulation of the director. In this new nematic phase, defect structures not present in the uniaxial nematic are observed, which indicates that the new phase has lower symmetry than the ordinary nematic phase. The phase transition is weakly first order with a significant pretransitional behavior, which manifests as strong splay fluctuations. When approaching the phase transition, the splay nematic constant is unusually low and goes towards zero. Analogously to the transition from the uniaxial nematic to the twist-bend nematic phase, this transition is driven by instability towards splay orientational deformation, resulting in a periodically splayed structure. And, similarly, a Landau-de Gennes type of phenomenological theory can be used to describe the phase transition. The modulated splay phase is biaxial and antiferroelectric.

Effects of Zeeman field on the dynamical instability of flat states for spin-2 Bose–Einstein condensates in an optical lattice

We investigate the effects of Zeeman field on the dynamical instability of flat states for F=2 spinor Bose–Einstein condensates in an optical lattice. The instability criteria for the ferromagnetic, uniaxial nematic, biaxial nematic-like and cyclic-like states are obtained analytically. It is shown that the linear Zeeman splitting shift only changes the dynamical instability of the biaxial nematic-like phase, but the quadratic Zeeman splitting shift can stabilize or induce additional dynamical instability to all the phases except the first-type ferromagnetic phase. The interaction strength of the spin–singlet pair term can change the dynamical instability of the cyclic-like state only when the quadratic Zeeman splitting is included. We also provide the experimental parameters to observe these interesting phenomena in future experiments.

Frank elasticity of composite colloidal nematics with anti-nematic order.

Mixing colloid shapes with distinctly different anisotropy generates composite nematics in which the order of the individual components can be fundamentally different. In colloidal rod-disk mixtures or hybrid nematics composed of anisotropic colloids immersed in a thermotropic liquid crystal, one of the components may adopt so-called anti-nematic order while the other exhibits conventional nematic alignment. Focussing on simple models for hard rods and disks, we employ Onsager-Straley's second-virial theory to derive scaling expressions for the elastic moduli of rods and disks in both nematic and anti-nematic configurations and identify their explicit dependence on particle concentration and shape. We demonstrate that the splay, bend and twist elasticity of anti-nematically ordered particles scale logarithmically with the degree of anti-nematic order, with the bend-splay ratio for anti-nematic discotic nematics being far greater than for conventional nematic systems. The impact of surface anchoring on the elastic properties of hybrid nematics will also be discussed in detail. We further demonstrate that the elasticity of mixed uniaxial rod-disk nematics depends exquisitely on the shape of the components and we provide simple scaling expressions that could help engineer the elastic properties of composite nematic liquid crystals.

Can elastic constants and surface alignment be obtained from polarized microscopy images of nematic droplets? A Monte Carlo study

We present a Monte Carlo study of the effects of elastic anisotropy on the textures of nematic droplets with different boundary conditions. Simulated polarized optical microscopy (POM) images are analysed for uniaxial nematics with radial, bipolar and toroidal boundaries and for numerous combinations of the splay, twist and bend elastic constant values. An atlas of simulated textures is presented as an aid to understanding new experimental results.