Biaxiality-driven twist-bend to splay-bend nematic phase transition induced by an electric field.

Although the existence of the twist-bend (NTB) and splay-bend (NSB) nematic phases was predicted long ago, only the former has as yet been observed experimentally, whereas the latter remains elusive. This is especially disappointing because the NSB nematic is promising for applications in electro-optic devices. By applying an electric field to a planar cell filled with the compound CB7CB, we have found an NTB-NSB phase transition using birefringence measurements. This field-induced transition to the biaxial NSB occurred, although the field was applied along the symmetry axis of the macroscopically uniaxial NTB Therefore, this transition is a counterintuitive example of breaking of the macroscopic uniaxial symmetry. We show by theoretical modeling that the transition cannot be explained without considering explicitly the biaxiality of both phases at the microscopic scale. This strongly suggests that molecular biaxiality should be a key factor favoring the stability of the NSB phase.

Understanding the twist-bend nematic phase: the characterisation of 1-(4-cyanobiphenyl-4'-yloxy)-6-(4-cyanobiphenyl-4'-yl)hexane (CB6OCB) and comparison with CB7CB.

The synthesis and characterisation of the nonsymmetric liquid crystal dimer, 1-(4-cyanobiphenyl-4'-yloxy)-6-(4-cyanobiphenyl-4'-yl)hexane (CB6OCB) is reported. An enantiotropic nematic (N)-twist-bend nematic (NTB) phase transition is observed at 109 °C and a nematic-isotropic phase transition at 153 °C. The NTB phase assignment has been confirmed using polarised light microscopy, freeze fracture transmission electron microscopy (FFTEM), (2)H-NMR spectroscopy, and X-ray diffraction. The effective molecular length in both the NTB and N phases indicates a locally intercalated arrangement of the molecules, and the helicoidal pitch length in the NTB phase is estimated to be 8.9 nm. The surface anchoring properties of CB6OCB on a number of aligning layers is reported. A Landau model is applied to describe high-resolution heat capacity measurements in the vicinity of the NTB-N phase transition. Both the theory and heat capacity measurements agree with a very weak first-order phase transition. A complementary extended molecular field theory was found to be in suggestive accord with the (2)H-NMR studies of CB6OCB-d2, and those already known for CB7CB-d4. These include the reduced transition temperature, TNTBN/TNI, the order parameter of the mesogenic arms in the N phase close to the NTB-N transition, and the order parameter with respect to the helix axis which is related to the conical angle for the NTB phase.

Molecular dynamics of a binary mixture of twist-bend nematic liquid crystal dimers studied by dielectric spectroscopy.

We report a comprehensive dielectric characterization of a liquid crystalline binary mixture composed of the symmetric mesogenic dimer CB7CB and the nonsymmetric mesogenic dimer FFO9OCB. In addition to the high-temperature nematic phase, such a binary mixture shows a twist-bend nematic phase at room temperature which readily vitrifies on slow cooling. Changes in the conformational distribution of the dimers are reflected in the dielectric permittivity and successfully analyzed by means of an appropriate theoretical model. It is shown that the dielectric spectra of the mixture reflect the different molecular dipole properties of the components, resembling in the present case the characteristic dielectric spectra of nonsymmetric dimers. Comparison of the nematic and twist-bend nematic phases reveals that molecular dynamics are similar despite the difference in the molecular environment.

Deuterium NMR investigations of field-induced director alignment in nematic liquid crystals.

There have been many investigations of the alignment of nematic liquid crystals by either a magnetic and/or an electric field. The basic features of the important hydrodynamic processes for low molar mass nematics have been characterized for the systems in their equilibrium and non-equilibrium states. These have been created using electric and magnetic fields to align the director and deuterium nuclear magnetic resonance ((2)H NMR) spectroscopy has been used to explore this alignment. Theoretical models based on continuum theory have been developed to complement the experiments and found to describe successfully the static and the dynamic phenomena observed. Such macroscopic behaviour has been investigated with (2)H NMR spectroscopy, in which an electric field in addition to the magnetic field of the spectrometer is used to rotate the director and produce a non-equilibrium state. This powerful technique has proved to be especially valuable for the investigation of nematic liquid crystals. Since the quadrupolar splitting for deuterons observed in the liquid crystal phase is determined by the angle between the director and the magnetic field, time-resolved and time-averaged (2)H NMR spectroscopies can be employed to investigate the dynamic director alignment process in a thin nematic film following the application or removal of an electric field. In this article, we describe some seminal studies to illustrate the field-induced static and dynamic director alignment for low molar mass nematics.

Macroscopic order in a nematic liquid crystal: Perturbation by spontaneous director fluctuations.

The dynamic alignment of the nematic director by near-orthogonal electric and magnetic fields has been investigated. The intermediate states during the relaxation process were found, with the aid of time-resolved deuterium NMR spectroscopy, to be markedly nonuniform. The macroscopic order was perturbed, although the initial and final states of the director appear to be essentially uniform. However, the initial state does have a profound influence on the uniformity of the director in the intermediate states. We have developed a fundamental model based on the effect of spontaneous director fluctuations to explain these unusual NMR observations.

Twist, tilt, and orientational order at the nematic to twist-bend nematic phase transition of 1″,9″-bis(4-cyanobiphenyl-4'-yl) nonane: A dielectric, (2)H NMR, and calorimetric study.

The nature of the nematic-nematic phase transition in the liquid crystal dimer 1″,9″-bis(4-cyanobiphenyl-4'-yl) nonane (CB9CB) has been investigated using techniques of calorimetry, dynamic dielectric response measurements, and (2)H NMR spectroscopy. The experimental results for CB9CB show that, like the shorter homologue CB7CB, the studied material exhibits a normal nematic phase, which on cooling undergoes a transition to the twist-bend nematic phase (N(TB)), a uniaxial nematic phase, promoted by the average bent molecular shape, in which the director tilts and precesses describing a conical helix. Modulated differential scanning calorimetry has been used to analyze the nature of the N(TB)-N phase transition, which is found to be weakly first order, but close to tricritical. Additionally broadband dielectric spectroscopy and (2)H magnetic resonance studies have revealed information on the structural characteristics of the recently discovered twist-bend nematic phase. Analysis of the dynamic dielectric response in both nematic phases has provided an estimate of the conical angle of the heliconical structure for the N(TB) phase. Capacitance measurements of the electric-field realignment of the director in initially planar aligned cells have yielded values for the splay and bend elastic constants in the high temperature nematic phase. The bend elastic constant is small and decreases with decreasing temperature as the twist-bend phase is approached. This behavior is expected theoretically and has been observed in materials that form the twist-bend nematic phase. (2)H NMR measurements characterize the chiral helical twist identified in the twist-bend nematic phase and also allow the determination of the temperature dependence of the conical angle and the orientational order parameter with respect to the director.

Molecular geometry, twist-bend nematic phase and unconventional elasticity: a generalised Maier-Saupe theory.

It has been found that bent-shaped achiral molecules can form a liquid crystal phase, called the Twist-Bend Nematic (NTB), which is locally polar and spontaneously twisted having a tilted director, with a conglomerate of degenerate chiral domains with opposite handedness and pitch of a few molecular lengths. Here, using a major extension of the Maier-Saupe molecular field theory, we can describe the transition from the nematic (N) to the NTB phase. We provide a consistent picture of the structural and elastic properties in the two phases, as a function of the molecular bend angle, and show that on approaching the transition there is a gradual softening of the bend mode in the N phase. This points to the crucial role of the molecular shape for the formation of modulated nematic phases and their behaviour.

Enantiotopic discrimination and director organization in the twist-bend nematic phase.

Extending a molecular field model for the orientational order in the nematic phase, we calculate the (2)H-NMR splittings for the achiral solute 8CB-d2 in the twist-bend nematic phase formed by the achiral liquid crystal dimer CB7CB. We give an explanation for the enantiotopic discrimination observed in the spectra and comparison with experimental data allows us to provide quantitative estimates of the order parameters (pitch and conical angle) that characterize the director modulation of the twist-bend nematic phase.

A comparison of the conformational distributions of the achiral symmetric liquid crystal dimer CB7CB in the achiral nematic and chiral twist-bend nematic phases.

The sets of residual dipolar couplings between carbon and hydrogen nuclei obtained from the proton-encoded (13)C 2D NMR experiment are used to investigate the conformational changes which occur when the achiral symmetric liquid crystal dimer CB7CB changes from the achiral nematic to the chiral twist-bend nematic phase. It is found that these changes are a consequence of the chirality of the twist-bend nematic phase, rather than being the driving force for the stability of this phase.

Chiral solutes can seed the formation of enantiomorphic domains in a twist-bend nematic liquid crystal.

The twist-bend nematic, an enantiomorphic liquid-crystalline phase, exhibited by the structurally symmetric liquid-crystal dimer CB7CB is induced to form a single domain of uniform handedness, in the bulk, by the addition of the dopant chiral solute (S)-1-phenylethanol. Addition of a nonracemic (or scalemic) mixture of both R and S enantiomers of this solute produced equal volumes of P and M chiral domains for the twist-bend nematic phase. This seeding of the domains in an enantiomorphic nematic conglomerate is revealed using deuterium NMR spectroscopy.

The chirality of a twist-bend nematic phase identified by NMR spectroscopy.

One of the defining characteristics of the twist-bend nematic phase, formed by the methylene-linked liquid crystal dimer 1″,7″-bis(4-cyanobiphenyl-4'-yl) heptane (CB7CB), is its chirality. This new nematic phase, predicted by Dozov, is of particular interest because although the constituent molecules are achiral the phase itself is chiral. Here, we describe the use of NMR spectroscopy to determine experimentally whether in reality the phase is chiral or not. The basis of this novel procedure is that the equivalence of the protons or deuterons in a prochiral methylene group in a nematic phase with D∞h symmetry is lost in a chiral phase because its symmetry is reduced to D∞ on removal of the mirror plane. Recording proton-enhanced local field (PELF) NMR experiments shows that in the standard nematic phase all of the methylene groups in the heptane spacer have equivalent pairs of C-H groups but this equivalence is lost for the six prochiral methylene groups with their enantiotopic protons on passing to the twist-bend nematic. Strikingly, this equivalence is not lost for the central methylene group where the two protons are homotopic. We also show how the phase chirality can be demonstrated with probe molecules which contain deuteriated prochiral methylene groups, using 4-octyl-4'-cyanobiphenyl-d2, perdeuteroacenaphthene-d10, and acenaphthene-d4 as examples. For the standard nematic phase deuterium, NMR shows that the deuterons in these methylene groups are equivalent but, as expected, in the twist-bend nematic phase this equivalence is lost. The deuterium NMR spectra of these probe molecules dissolved in CB7CB have been recorded from the isotropic phase, through the nematic and deep into the supercooled twist-bend nematic.

Molecular-field-theory approach to the Landau theory of liquid crystals: uniaxial and biaxial nematics.

Nematic liquid crystal phase diagrams in temperature-biaxiality space are usually complex. We construct a Landau theory based on the analogous molecular-field theory for orthorhombic biaxial nematic fluids. A formal procedure yields coefficients (some of which, unusually, can be tensorial) in this Landau expansion, correctly predicts the complete set of invariants formed from the ordering tensors, and avoids ad hoc parametrization of the molecular biaxiality. By regularizing the Landau expansion to avoid unwanted order parameter divergences at low temperatures, we predict phase behavior over the whole range of biaxiality. The resulting phase diagrams have the same topology as those of molecular-field theory.

Molecular field theory for biaxial nematic liquid crystals composed of molecules with C(2h) point group symmetry.

The biaxial nematic phase is generally taken, either explicitly or implicitly, to have D(2h) point group symmetry. However, it is possible for the biaxial phase to have a lower symmetry depending on that of its constituent molecules. Here we develop a molecular field theory for a nematogen composed of C(2h) molecules in terms of the nine independent second rank orientational order parameters defining the C(2h) biaxial nematic. In addition, there is a rank one order parameter constructed from two pseudovectors which is only nonzero in the C(2h) phase. The theory is simplified by removing all but the three dominant order parameters. The predicted phase behavior is found to be rich with three possible biaxial nematic phases and with the transitions involving a biaxial nematic phase exhibiting tricritical points.

Dominant biaxial quadrupolar contribution to the nematic potential of mean torque.

Within the general quadrupolar model for biaxial nematic liquid crystals, whose potential of mean torque extends that in the Maier-Saupe theory with two extra interaction terms, we propose a quantitative criterion to identify the dominant biaxial interaction. We show that the ratio of the biaxial-to-uniaxial and uniaxial-to-isotropic transition temperatures is almost independent of one interaction parameter, thus indicating the other as dominant. We also show that there is a significant mismatch between the principal orientational order parameters predicted by the theory and those measured for the biaxial phase of a tetrapode.

Biaxial nematic phases and V-shaped molecules: a Monte Carlo simulation study.

Inspired by recent claims that compounds composed of V-shaped molecules can exhibit the elusive biaxial nematic phase, we have developed a generic simulation model for such systems. This contains the features of the molecule that are essential to its liquid crystal behavior, namely the anisotropies of the two arms and the angle between them. The behavior of the model has been investigated using Monte Carlo simulations for a wide range of these structural parameters. This allows us to establish the relationship between the V-shaped molecule and its ability to form a biaxial nematic phase. Of particular importance are the criteria of geometry and the relative anisotropy necessary for the system to exhibit a Landau point, at which the biaxial nematic is formed directly from the isotropic phase. The simulations have also been used to determine the orientational order parameters for a selection of molecular axes. These are especially important because they reveal the phase symmetry and are connected to the experimental determination of this. The simulation results show that, whereas some positions are extremely sensitive to the phase biaxiality, others are totally blind to this.

Biaxial nematics: computer simulation studies of a generic rod-disc dimer model.

One possible route to the elusive biaxial nematic phase is through rod-disc dimers in which the rod and disc mesogenic units are linked via a flexible spacer. We have developed a continuous generic model of such rod-disc dimers in which neighbouring like groups tend to align parallel to each other while unlike groups tend to be orthogonal. A torsional potential controls the relative orientations of the groups within a single dimer; depending on the strength of the torsional potential, the groups may be orthogonal or parallel in the conformational ground state. Monte Carlo simulations show that a rigid rod-disc dimer is most likely to form a biaxial nematic phase if the anisotropies of the two groups are the same. Introduction of flexibility is found to have little effect on the qualitative behaviour of the dimer as the relative anisotropy of the two mesogenic groups is changed. However, when the torsional potential strongly favours the alignment of the rod and disc within a single molecule with their symmetry axes parallel there is a dramatic change. The system then exhibits a strong hysteresis in the molecular shape and biaxiality and the biaxial nematic-isotropic transition becomes strongly first order, in marked contrast to the second-order character usually found for this transition. This first-order transition is observed to occur for a range of relative anisotropies of the two groups rather than at a single point.

Studies of translational diffusion in the smectic A phase of a Gay-Berne mesogen using molecular dynamics computer simulation.

Molecular dynamics computer simulations are used to determine the self-diffusion coefficients for a Gay-Berne model mesogen GB (4.4,20,1,1) in the isotropic, nematic and smectic A phases along two isobars. The values of the parallel and perpendicular diffusion coefficients, D(parallel) and D(perpendicular), are calculated and compared in the different phases. For the phase sequence isotropic-smectic A, D(perpendicular)*> or =D(parallel)* over the whole smectic A range with the ratio D(parallel)*/D(perpendicular)* decreasing with decreasing temperature. At a higher pressure, a nematic phase is observed between these two phases and we find that D(parallel)*>D(perpendicular)* throughout the nematic region and the inequality D(parallel)*>D(perpendicular)* remains on entering the smectic A phase. However, the ratio D(parallel)*/D(perpendicular)* decreases with decreasing temperature within the smectic A range and eventually this ratio inverts such that D(perpendicular)*>D(parallel)* at low temperatures. The temperature dependence of the parallel diffusion coefficient in the smectic A phase for this model mesogen is compared to that predicted by a theoretical model for diffusion subject to a cosine potential.