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.

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.

Publisher's Note:

This corrects the article DOI: 10.1103/PhysRevE.96.062702.

Molecular field theory for biaxial nematics formed from liquid crystal dimers and inhibited by the twist-bend nematic.

Liquid crystal dimers with odd spacers are good candidates as materials for biaxial nematic phases (NB). The dimers are flexible molecules sustaining biaxial conformations, and couplings between the conformational and orientational distributions could be expected to stabilise NB. We apply a molecular field theory for flexible molecules developed elsewhere to study a simple system made up of dimers composed of two cylindrically symmetric mesogenic groups. Our model allows for two idealised conformations: one linear and one bent at a tetrahedral angle. For a restricted set of chain lengths, the model predicts a first-order reentrant phase transition from the NB phase into a low temperature uniaxial nematic phase (NU). However the formation of the biaxial nematic could be blocked by the appearance of a twist-bent nematic.

Correction: Miscibility studies of two twist-bend nematic liquid crystal dimers with different average molecular curvatures. A comparison between experimental data and predictions of a Landau mean-field theory for the NTB-N phase transition.

Correction for 'Miscibility studies of two twist-bend nematic liquid crystal dimers with different average molecular curvatures. A comparison between experimental data and predictions of a Landau mean-field theory for the NTB-N phase transition' by D. O. López et al., Phys. Chem. Chem. Phys., 2016, 18, 4394-4404.

Miscibility studies of two twist-bend nematic liquid crystal dimers with different average molecular curvatures. A comparison between experimental data and predictions of a Landau mean-field theory for the NTB-N phase transition.

We report a calorimetric study of a series of mixtures of two twist-bend liquid crystal dimers, the 1'',7''-bis(4-cyanobiphenyl)-4'-yl heptane (CB7CB) and 1''-(2',4-difluorobiphenyl-4'-yloxy)-9''-(4-cyanobiphenyl-4'-yloxy) nonane (FFO9OCB), the molecules of which have different effective molecular curvatures. High-resolution heat capacity measurements in the vicinity of the NTB-N phase transition for a selected number of binary mixtures clearly indicate a first order NTB-N phase transition for all the investigated mixtures, the strength of which decreases when the nematic range increases. Published theories predict a second order NTB-N phase transition, but we have developed a self-consistent mean field Landau model using two key order parameters: a symmetric and traceless tensor for the orientational order and a short-range vector field which is orthogonal to the helix axis and rotates around of the heliconical structure with an extremely short periodicity. The theory, in its simplified form, depends on two effective elastic constants and explains satisfactorily our heat capacity measurements and also predicts a first-order NTB-N phase transition. In addition, as a complementary source of experimental measurements, the splay (K1) and bend (K3) elastic constants in the conventional nematic phase for the pure compounds and some selected mixtures have been determined.

Dielectric, calorimetric and mesophase properties of 1''-(2',4-difluorobiphenyl-4'-yloxy)-9''-(4-cyanobiphenyl-4'-yloxy) nonane: an odd liquid crystal dimer with a monotropic mesophase having the characteristics of a twist-bend nematic phase.

This paper reports a novel liquid crystal phase having the characteristics of a twist-bend nematic phase formed by a non-symmetric ether-linked liquid crystal dimer. The dimer 1''-(2',4-difluorobiphenyl-4'-yloxy)-9''-(4-cyanobiphenyl-4'-yloxy) nonane (FFO9OCB) exhibits two liquid-crystalline phases on cooling at a sufficiently high rate from the isotropic phase. The high temperature mesophase has been reported in the literature as nematic and confirmed in this study. The other mesophase is metastable and can be supercooled giving rise to a glassy state. Its identification and characterization are based on optical textures, broadband dielectric spectroscopy, calorimetry, measurements of both splay and bend elastic constants in the nematic phase and miscibility studies. It is concluded that the low temperature mesophase exhibits the characteristics of a twist-bend nematic phase. Dielectric measurements enable us to obtain the static permittivity and information about the molecular dynamics in the isotropic phase, in the nematic mesophase and across the isotropic-to-nematic phase transition. Two orientations, parallel and perpendicular to the director, have been investigated. In the high temperature nematic mesophase, the dielectric anisotropy is found to be positive. Measurements of the parallel component of the dielectric permittivity are well-explained by the molecular theory of dielectric relaxation in nematic dimers (M. Stocchero, A. Ferrarini, G. J. Moro, D. A. Dunmur and G. R. Luckhurst, J. Chem. Phys., 2004, 121, 8079). The dimer is modelled as a mixture of cis and trans conformers and the model allows an estimate of their relative populations at each temperature. The nematic-to-isotropic phase transition has been exhaustively studied from the accurate evolution of the heat capacity and the static dielectric permittivity data. It has been concluded that the transition is first order in nature, but close to tricritical. The nature of the nematic-to-the novel liquid crystal phase transition is difficult to analyze to the same extent because of insufficient precision. Only observations at cooling rates of 10 K min(-1) or higher were possible because on heating from the glassy state, the twist-bend nematic mesophase crystallizes at temperatures far below the nematic-nematic phase transition.

Molecular field theory for biaxial smectic A liquid crystals.

Thermotropic biaxial nematic phases seem to be rare, but biaxial smectic A phases less so. Here we use molecular field theory to study a simple two-parameter model, with one parameter promoting a biaxial phase and the second promoting smecticity. The theory combines the biaxial Maier-Saupe and McMillan models. We use alternatively the Sonnet-Virga-Durand (SVD) and geometric mean approximations (GMA) to characterize molecular biaxiality by a single parameter. For non-zero smecticity and biaxiality, the model always predicts a ground state biaxial smectic A phase. For a low degree of smectic order, the phase diagram is very rich, predicting uniaxial and biaxial nematic and smectic phases, with the addition of a variety of tricritical and tetracritical points. For higher degrees of smecticity, the region of stability of the biaxial nematic phase is restricted and eventually disappears, yielding to the biaxial smectic phase. Phase diagrams from the two alternative approximations for molecular biaxiality are similar, except inasmuch that SVD allows for a first-order isotropic-biaxial nematic transition, whereas GMA predicts a Landau point separating isotropic and biaxial nematic phases. We speculate that the rarity of thermotropic biaxial nematic phases is partly a consequence of the presence of stabler analogous smectic phases.

Chemically induced twist-bend nematic liquid crystals, liquid crystal dimers, and negative elastic constants.

Here we report the chemical induction of the twist-bend nematic phase in a nematic mixture of ether-linked liquid crystal dimers by the addition of a dimer with methylene links; all dimers have an odd number of groups in the spacer connecting the two mesogenic groups. The twist-bend phase has been identified from its optical texture and x-ray scattering pattern as well as NMR spectroscopy, which demonstrates the phase chirality. Theory predicts that the key macroscopic property required for the stability of this chiral phase formed from achiral molecules is for the bend elastic constant to tend to be negative; in addition the twist elastic constant should be smaller than half the splay elastic constant. To test these important aspects of the prediction we have measured the bend and splay elastic constants in the nematic phase preceding the twist-bend nematic using the classic Frederiks methodology and all three elastic constants employing the dynamic light scattering approach. Our results show that, unlike the splay, the bend elastic constant is small and decreases significantly as the transition to the induced twist-bend nematic phase is approached, but then exhibits unexpected behavior prior to the phase transition.

Flexoelectrically driven electroclinic effect in the twist-bend nematic phase of achiral molecules with bent shapes.

We extend the twist-bend nematic (N(TB)) model to describe the electro-optics of this novel phase. We predict an electroclinic effect (ECE) subject to a dc electric field E applied perpendicular to the helix axis or wave vector q, with rotation of the N(TB) optic axis around E. This linear effect, with its flexoelectric origin, is a close analog to the electro-optic effects observed for chiral liquid crystals. However, in nematics composed of achiral molecules having a bent shape, it is the electro-optic signature of the N(TB) phase. We test our model experimentally in the low-temperature nematic phase of the odd liquid crystal dimer, CB7CB, with its molecules having, on average, a bent shape. The ECE measurements confirm the previously proposed twist-bend nematic structure of this phase, with its broken chiral symmetry, extremely short (<10 nm) doubly degenerate pitch and ultrafast, submicrosecond response times.

Biaxiality-induced magnetic field effects in bent-core nematics: molecular-field and Landau theory.

Nematic liquid crystals composed of bent-core molecules exhibit unusual properties, including an enhanced Cotton-Mouton effect and an increasing isotropic (paranematic)-nematic phase transition temperature as a function of magnetic field. These systems are thought to be good candidate biaxial liquid crystals. Prompted by these experiments, we investigate theoretically the effect of molecular biaxiality on magnetic-field-induced phenomena for nematic liquid crystals, using both molecular field and Landau theory. The geometric mean approximation is used in order to specify the degree of molecular biaxiality using a single parameter. We reproduce experimental field-induced phenomena and predict also an experimentally accessible magnetic critical point. The Cotton-Mouton effect and temperature dependence of the paranematic-nematic phase transition are more pronounced with increased molecular biaxiality. We compare our theoretical approaches and make contact with recent relevant experimental results on bent-core molecular systems.

Properties of the static NMR response of a confined thin nematic film of 5CB-d2 under crossed electric and magnetic fields: theory and experiments.

This work describes an investigation of the static (or quasistatic) nuclear magnetic resonance (NMR) response in a nematic liquid crystal confined between two planar conducting plates and subject to a magnetic field and an electric field produced by a difference of voltage applied on the plates. Deuterium NMR spectroscopy of 4-pentyl-d(2)-4'-cyanobiphenyl (5CB-d(2)) under these conditions has revealed a voltage dependent inhomogeneous director distribution for a particular narrow range of voltages and for a fixed magnetic field (that of the spectrometer). In the ideal setup the two plates are assumed to be rigorously parallel, so that a difference of voltage applied on the plates leads to a constant electric field normal to them. When the magnetic field is parallel to the plates (orthogonal geometry) there exists a threshold value of the electric field for which the effect of both fields exactly compensate; moreover, for stronger electric field the director aligns with the electric field while for weaker electric field the director aligns with the magnetic field. If there is a lack of parallelism between the two plates, the electric field becomes inhomogeneous so that it may be larger than the threshold value in some region of the sample and smaller in the remaining part of the sample. In that case the director will adopt essentially two orientations within the sample, namely, parallel or perpendicular to the magnetic field, and the position of the frontier between the two domains depends on the voltage. This feature is clearly shown by deuterium NMR spectra that exhibit a transfer of intensity between two quadrupolar doublets with increase in the applied voltage. The coexistence of two director populations occurs for a range of voltages that depends on the degree of nonparallelism; accordingly, an estimation of this range by NMR yields an experimental estimation of the lack of parallelism. A tiny tilt of the magnetic field (nonorthogonal geometry) entrains a notably different behavior since a single doublet with voltage dependent splitting is observed in this case. In a first stage (simple model) of this work, the main features observed for the orthogonal and nonorthogonal geometries are interpreted within the framework of Leslie-Ericksen theory by employing the concept of a single effective field replacing the two real fields. However, the spectra reveal an additional director distribution, especially for the orthogonal geometry, that cannot be interpreted by this simple approach. In a second stage (advanced model), these less clear features have been investigated by numerical simulations of a two-dimensional model which includes the effects of inversion walls and of the high relative dielectric anisotropy of 5CB.

Disentangling molecular motions involved in the glass transition of a twist-bend nematic liquid crystal through dielectric studies.

Broadband dielectric spectroscopy spanning frequencies from 10(-2) to 1.9 × 10(9) Hz has been used to study the molecular orientational dynamics of the glass-forming liquid crystal 1",7"-bis (4-cyanobiphenyl-4'-yl)heptane (CB7CB) over a wide temperature range of the twist-bend nematic phase. In such a mesophase two different relaxation processes have been observed, as expected theoretically, to contribute to the imaginary part of the complex dielectric permittivity. For measurements on aligned samples, the processes contribute to the dielectric response to different extents depending on the orientation of the alignment axis (parallel or perpendicular) with respect to the probing electric field direction. The low-frequency relaxation mode (denoted by µ(1)) is attributed to a flip-flop motion of the dipolar groups parallel to the director. The high-frequency relaxation mode (denoted by µ(2)) is associated with precessional motions of the dipolar groups about the director. The µ(1)-and µ(2)-modes are predominant in the parallel and perpendicular alignments, respectively. Relaxation times for both modes in the different alignments have been obtained over a wide temperature range down to near the glass transition temperature. Different analytic functions used to characterize the temperature dependence of the relaxation times of the two modes are considered. Among them, the critical-like description via the dynamic scaling model seems to give not only quite good numerical fittings, but also provides a consistent physical picture of the orientational dynamics on approaching the glass transition.

Phase behavior and properties of the liquid-crystal dimer 1'',7''-bis(4-cyanobiphenyl-4'-yl) heptane: a twist-bend nematic liquid crystal.

The liquid-crystal dimer 1'',7''-bis(4-cyanobiphenyl-4'-yl)heptane (CB7CB) exhibits two liquid-crystalline mesophases on cooling from the isotropic phase. The high-temperature phase is nematic; the identification and characterization of the other liquid-crystal phase is reported in this paper. It is concluded that the low-temperature mesophase of CB7CB is a new type of uniaxial nematic phase having a nonuniform director distribution composed of twist-bend deformations. The techniques of small-angle x-ray scattering, modulated differential scanning calorimetry, and dielectric spectroscopy have been applied to establish the nature of the nematic-nematic phase transition and the structural features of the twist-bend nematic phase. In addition, magnetic resonance studies (electron-spin resonance and (2)H nuclear magnetic resonance) have been used to investigate the orientational order and director distribution in the liquid-crystalline phases of CB7CB. The synthesis of a specifically deuterated sample of CB7CB is reported, and measurements showed a bifurcation of the quadrupolar splitting on entering the low-temperature mesophase from the high-temperature nematic phase. This splitting could be interpreted in terms of the chirality of the twist-bend structure of the director. Calculations using an atomistic model and the surface interaction potential with Monte Carlo sampling have been carried out to determine the conformational distribution and predict dielectric and elastic properties in the nematic phase. The former are in agreement with experimental measurements, while the latter are consistent with the formation of a twist-bend nematic phase.

Field-induced alignment of the nematic director: studies of nuclear magnetic resonance spectral oscillations in the limit of fast director rotation.

Time-resolved NMR spectroscopy is a powerful method to investigate field-induced rotation of the director in a nematic liquid crystal. The method requires that the director does not rotate significantly during the acquisition of the free induction decay and hence the NMR spectrum. We have extended the method to systems where this is not the case and the observed NMR spectra are now found to contain novel oscillatory features. To understand these oscillations, we have developed a model combining both director and spin dynamics. In addition to increasing the information content of the time-resolved NMR spectra, it also proves possible to determine the field-induced relaxation time from a single spectrum.

Director alignment by crossed electric and magnetic fields: a deuterium NMR study.

The static director distribution in thin nematic liquid crystal cells, subject to both electric and magnetic fields, has been investigated using a combination of deuterium nuclear magnetic resonance (NMR) spectroscopy and continuum theory in terms of the director distribution function, which gives the probability density for finding the director at a given orientation. A series of deuterium NMR spectra for the nematic liquid crystal, 4-pentyl-d(2)-4'-cyanobiphenyl deuteriated in the α position of the pentyl chain were acquired as a function of the applied electric field. This powerful experimental technique allowed us to observe uniform and nonuniform director alignment depending on the angle between the two fields and their relative strength. On the basis of the detailed experimental results, we have explored the factors that influence the nature of both the uniform and the nonuniform director distributions. We have discussed the questions that are raised by our attempt to understand the static director distribution as a function of the angle between the two fields. We have discovered that the alignment of the director at the surface of the Teflon spacers is essential in addition to the random variation in the cell thickness in order to account for the static director distribution determined from the NMR spectra.

Simple model for biaxial smectic-A liquid-crystal phases.

We have generalized the McMillan theory of liquid crystalline smectic order in uniaxial particle fluids to biaxial particles. Upon varying the control parameter, a uniaxial nematic phase may: (i) order biaxially first, then smectically; (ii) order smectically first, then biaxially; and (iii) simultaneously order biaxially and smectically. We investigate, in the limit of complete orientational order of the molecular major axes, which of these scenarios are realized for a simple model of particles with the symmetry of rectangular parallelepipeds. We also present a generic variational derivation of the theory based on the identification of the dominant order parameters for the most ordered phase.

Molecular theory of dielectric relaxation in nematic dimers.

This paper reports a theory for the dielectric relaxation of dimeric mesogenic molecules in a nematic liquid crystal phase. Liquid crystal dimers consist of two mesogenic groups linked by a flexible chain. Recent experimental studies [D. A. Dunmur, G. R. Luckhurst, M. R. de la Fuente, S. Diez, and M. A. Perez Jubindo, J. Chem. Phys. 115, 8681 (2001)] of the dielectric properties of polar liquid crystal dimers have found unexpected results for both the static (low frequency) and variable frequency dielectric response of these materials. The theory developed in this paper provides a quantitative model with which to understand the observed experimental results. The mean-square dipole moments of alpha,omega-bis[(4-cyanobiphenyl-4'-yl]alkanes in a nematic phase have been calculated using both the rotational isomeric state model and a full torsional potential for the carbon-carbon bonds of the flexible chain. The orienting effect of the nematic phase is taken into account by a parametrized potential of mean torque acting on the mesogenic groups and the segments in the flexible chain. Results of calculations using the full torsional potential are in excellent agreement with experimental results for comparable systems. The probability density p(eq)(beta(A),beta(B)) for the orientation of the mesogenic groups (A,B) along the nematic director is also calculated. The resultant potential of mean torque is a surface characterized by four deep energy wells or sites equivalent to alignment of the terminal groups A and B approximately parallel and antiparallel to the director; of course, the reversal of the director leads to equivalent sites. This potential energy surface provides the basis for a kinetic model of dielectric relaxation in nematic dimers. Solution of the Fokker-Planck equation corresponding to this four-site model gives the time dependence of the site populations, and hence the time-correlation functions for the total dipole moment along the director. In this model the end-over-end rotation of the molecule, corresponding to simultaneous reversal of both mesogenic groups, is excluded because the activation energy is too large. Results are presented for a number of cases, in which a dipole is located on one or both of the mesogenic groups, and additionally where the groups differ in size. For the latter, under particular conditions, the correlation function exhibits a biexponential decay, which corresponds to two low frequency absorptions in the dielectric spectrum. This is exactly what has been observed for nonsymmetric nematic dimers having different groups terminating a flexible chain. Experimental results over a range of temperature for the nonsymmetric dimer alpha-[(4-cyanobiphenyl)-4'-yloxy]-omega-(4-decylanilinebenzylidene-4'-oxy)nonane can be fitted precisely to the theory, which provides new insight into the orientational and conformational dynamics of molecules in ordered liquid crystalline phases.