Nematic twist-bend phase under external constraints

ABSTRACT

The recently discovered twist-bend nematic phase, N_TB, has short-pitched heliconical structure with doubly degenerate handedness. In contrast to the classic nematic, in the N_TB phase the director is spontaneously distorted, resulting in unusual elastic properties. The response of the N_TB phase to external stimuli, like chiral doping or applied fields might provide further information about its structure and can find utilisation in practical applications. Here, the N_TB behaviour is theoretically investigated under chiral doping and strong electric fields. We show that the chiral doping removes the N_TB degeneration and modifies the conical tilt angle, leaving the pitch unchanged. Thus, the N_TB helical twisting power is very high and strongly non-linear. Under electric field, we consider separately the ferroelectric, flexoelectric and dielectric couplings. We show that the experiments reported so far disagree with the ferroelectric behaviour, indicating that the N_TB phase is not spontaneously polarised. On the contrary, the observed polar effects fit well with the flexoelectric coupling, confirming the degenerated heliconical structure of the phase. Under very strong fields, we predict a second-order twist-bend nematic – nematic phase transition due to the dielectric torque on the director.     

Nanostructure and dielectric properties of a twist-bend nematic liquid crystal mixture

We present freeze-fracture transmission electron microscopy (FF-TEM), dielectric spectroscopy and electro-optic measurements on a dimeric liquid crystal mixture, which previously was proposed to form the twist-bend nematic (N_tb) phase. Our FF-TEM studies provide a direct image of a 10.5 nm periodic structure, consistent with the expected nanoscale, heliconical twist-bend modulation of the molecular orientation. Dielectric measurements in the 100 Hz to 10 MHz range reveal three nearly Debye-type dispersion processes in the nematic and the twist-bend phase. Low frequency 8 V/µm electric fields applied on planar cells cause the optical-scale stripe texture (another characteristic feature of the N_tb phase) to disappear. Higher (>16 V/µm) fields gradually realign the heliconical axis along the electric field; it relaxes back after the field removal.     

Smectic-like bâtonnets in nematic/twist-bend nematic biphasic samples

ABSTRACT

We have studied a mixture of the twist-bend nemogenic dimer CB7CB with rod-like nematic molecules, which exhibits nematic (N) and twist-bend nematic (N_TB) phases and a very large biphasic coexistence range. At the N-N_TB transition, we observe the nucleation of highly anisometric N_TB droplets which are very similar to the classic smectic A (SmA) bâtonnets. These observations confirm the recently proposed close analogy between the N_TB and SmA phases, on the basis of their identical macroscopic symmetry. As for their smectic analogues, the N_TB bâtonnets are fluid in two dimensions; they easily merge when brought into contact and they are solid-like in that they did not flow along their optic axis. The observed fluidity and low viscosity show that the N_TB phase is indeed a nematic phase, i.e. an anisotropic fluid, rather than a soft crystal or glassy state. Unlike their smectic analogues, the N_TB bâtonnets have almost perfect symmetry of revolution and the axis of the N_TB helix is uniformly aligned parallel to the long axis of the bâtonnet. The large aspect ratio of the bâtonnets, typically ≈ 10–30, indicates a very strong anisotropy of the N-N_TB interfacial energy, W₂/W₀ ≈ 200–2000, and suggests that the anchoring energy differs from the usual Rapini–Papoular form.     

Twist-bend nematic phase in cyanobiphenyls and difluoroterphenyls bimesogens

ABSTRACT

The paper reviews assignment of the low-temperature nematic phase observed in simple bimesogenic or dimeric systems based on cyanobiphenyls and difluoroterphenyls to the twist-bend nematic phase, N_TB, using a range of experimental techniques. These include DSC, X-rays, Polarising Microscopy, electro-optics, birefringence and measurements of the electroclinic effect arising from flexoelectricity. An emphasis is laid on the observations of the chiral domains of opposite handedness at zero field in an otherwise achiral liquid crystalline system in this phase. These observations are a direct consequence of the structure of the twist-bend phase predicted by Ivan Dozov for achiral bent core molecules. The paper reviews the electro-optic phenomena and the observed electroclinic effect and how these observations assign it as the N_TB phase. Results of the nanoscale helical pitch measurements using freeze-fracture microscopy are reviewed and discussed briefly. Results of the measurements of elastic constants especially close to the N–N_TB transition are also reviewed.     

The NTB phase in an achiral asymmetrical bent-core liquid crystal terminated with symmetric alkyl chains

ABSTRACT

The characteristics of the twist-bend nematic (N_TB) phase of an achiral asymmetrical rigid bent-core liquid crystal (LC), the ends of which are terminated by symmetric alkyl chains, are reported. The nematic–nematic phase transition and its properties are studied by differential scanning calorimetry (DSC), polarising microscopy and the electro-optic techniques. Large domains of opposite handedness are observed in the absence of the external field in the N_TB phase. Another set of periodic striped pattern consisting of domains with sharp boundaries is formed when a high-frequency electric field with a magnitude above its threshold is applied across a planarly aligned cell. The neighbouring domains are of opposite chirality. The temperature dependence of the heliconical angle θ₀ is determined from the birefringence measurements using Haller’s extrapolation technique. This material shows lower values of the heliconical angle (~9.3° at a temperature of 155°C within the N_TB phase) when compared with the previously reported dimer-based twist-bend nematic LCs (31°±3°).     

The influence of chirality on the difference in flexoelectric coefficients investigated in uniform lying helix,Grandjean and twisted nematic structures

Measurements of the difference in flexoelectric coefficients (e ₁ – e ₃), using the sign convention as originally defined by Meyer, are reported from three experiments employing the flexoelectro-optic effect in different geometries. The uniform lying helix (ULH) structure is used to measure the tilt angle of the liquid crystal director with respect to the helix axis for an applied electric field, in order to infer a value for (e ₁ – e ₃). Alternatively, measurements of the flexoelectric difference can be made by considering the transmission through a device with an in-plane electric field aligned in either the Grandjean structure for highly chiral materials, or a twisted nematic (TN) structure for largely achiral materials. The results from the Grandjean and ULH structures show the equivalence of the measurement techniques with helix axis either perpendicular or parallel to the substrates. Further comparison of these results with the measurement from the achiral TN device shows that the difference in flexoelectric coefficients displays no dependence on chirality, demonstrating that flexoelectricity is purely associated with splay and bend director deformations, as expected from symmetry considerations.     

Optical measurement of flexoelectric polarisation change in liquid crystals doped with bent-core molecules using hybrid-aligned structure

We proposed an optical measurement method for determination of flexoelectric polarisation change in liquid crystals (LCs), which can be induced in highly distorted LC geometries. A hybrid-aligned nematic LC (NLC) mode was introduced to evaluate the direction and magnitude of the flexoelectric polarisation. We measured the DC offset amounts for equivalent brightness levels between forward and reverse bias vertical electric fields to estimate the sign and magnitude of e_s?e_b of flexoelectric coefficients. Additionally, the optical incident angle (α_max) for the maximum effective birefringence was investigated to predict the depth distribution of the LC director affecting the magnitude of the flexoelectric polarisation. The relationship between the variations of the DC offset and α_max by the flexoelectric polarisation changes was examined using the NLC mixtures doped with three selected bent-core LCs.     

The oblique chiral nematic phase in calamitic bimesogens

ABSTRACT

The discovery of the oblique chiral (or, the twist-bend, N_TB) nematic phase predicted for bent-core mesogens has engendered much interest due to its unique structure and physical properties, and the possibility of use in the next generation of fast electro-optic technology. Bimesogenic calamitic as well as bent-core mesogens are found to form the N_TB phase. Here, we report direct measurements of the temperature dependence of the conical tilt and the evidence of volcano-like orientational distribution of molecules in the N_TB phase. Optical and x-ray scattering investigations of two single-component calamitic bimesogens and their mixtures show that, while the Maier–Saupe orientational distribution function (ODF) is valid for the higher temperature nematic phase, a generalised expansion in terms of even Legendre functions is needed for the N_TB phase. Temperature dependence of the ODFs and the order parameters 〈P₂(cosβ)〉, 〈P₄(cosβ)〉, and 〈P₆(cosβ)〉 has been measured in both phases. The parameters 〈P₂(cosβ)〉 and 〈P₄(cosβ)〉 increase/decrease in the N/N_TB phase with decreasing temperature, while 〈P₆(cosβ)〉 remains vanishingly small for all samples. The value of 〈P₄(cosβ)〉 becomes negative in the N_TB phase confirming a conical distribution of molecules as they follow a helical trajectory keeping the local director tilted at an angle α wrt the macroscopic director. The heliconical tilt calculated from ODFs, exhibits a power law behaviour with temperature, vanishing at the transition to the N phase.     

Formation of periodic zigzag patterns in the twist-bend nematic liquid crystal phase by surface treatment

ABSTRACT

Zigzag patterns were successfully generated in the twist-bend nematic (N_TB) phase of 1-(4-cyanobiphenyl-4′-yl)-6-(4-cyanobiphenyl-4′-yloxy)hexane (CB6OCB) via simple surface treatment. A detailed microscopy study using polarised optical microscopy and fluorescence confocal polarising microscopy was performed to observe the director arrangement in the zigzags, where distinctive periodic patterns were found to be aligned perpendicular to the rubbing direction. These patterns originate from the structural instability and generation of splay deformation with focal conic domain-like structures that are typically found in smectic phases, revealing that the N_TB phase has physical properties similar to those of the smectic phase. Observation of these unusual zigzag patterns in the N_TB phase opens an avenue for use of this phase in potential applications such as optical modulators and gratings.     

The twist-bend nematic phase: translational self-diffusion and biaxiality studied by 1H nuclear magnetic resonance diffusometry

ABSTRACT

Recently, there has been a surge of interest in mesogens exhibiting the twist-bend nematic (N_TB) phase that is shown to be chiral even though formed by effectively achiral molecules. Although it now seems to be clear that the N_TB phase in the bulk is formed by degenerate domains having opposite handedness, the presence of a supramolecular heliconical structure proposed in the Dozov model has been contradicted by the Hoffmann et al. model in which the heliconical arrangement is replaced by a polar nematic phase. The evidence in support of this is that the quadrupolar splitting tensor measured in various experiments is uniaxial and not biaxial as expected for the twist-bend nematic structure. In this debate, among other evidence, the molecular translational diffusion, and its magnitude with respect to that in the nematic phase above the N_TB phase, has also been invoked to eliminate or to confirm one model or the other. We attempt to resolve this issue by reporting the first measurements of the translational self-diffusion coefficients in the nematic and twist-bend nematic phases formed 1″,7″-bis-4-(4′-cyanobiphenyl-4′-yl) heptane (CB7CB). Such measurements certainly appear to resolve the differences between the two models in favour of that for the classic twist-bend nematic phase.     

Nematic and smectic liquid single crystal elastomers: Influence of external stress parallel and perpendicular to the director

The influence of uniaxial mechanical stress applied parallel or perpendicular to the director axis (optical axis) of nematic and smectic-A elastomers having a permanent macroscopically ordered monodomain structure is investigated. Due to the different phase structures applying an external mechanical stress leads to completely different responses with respect to the young moduli and reorientation processes of the director. Nematic elastomers exhibit a weak anisotropy of the moduli parallel (μ₁₁ and perpendicular (μ) to the optical axis with μ₁₁ / μ = 1.5. The moduli are mainly determined by the rubber elasticity of the poly(siloxane) network. Applying the mechanical stress perpendicular to the initial director axis causes a rotation of the director axis that is connected with a periodic pattern formation and a ‘soft elastic’ response. For smectic-A elastomers μ₁₁/μ is in the order of 10². While μ reflects a rubber elastic response similar to that of the nematic system, μ₁₁ indicates an enthalpy-elastic behaviour of the one-dimensional long range order of the smectic layers. In this direction reorientation of the phase structure with a deformation of the smectic layers occurs above a threshold elongation. In contrast to the nematic networks, a deformation perpendicular to the optical axis causes no director reorientation, displaying the liquid-like properties within the smectic layers.     

Sulfur-linked cyanobiphenyl-based liquid crystal dimers and the twist-bend nematic phase

ABSTRACT

The synthesis and characterisation of two series of cyanobiphenyl-based liquid crystal dimers containing sulfur links between the spacer and mesogenic units, the 4?-[1,ω-alkanediylbis(thio)]bis-[1,1?-biphenyl]-4-carbonitriles (CBSnSCB), and 4?-({ω-[(4?-cyano[1,1?-biphenyl]-4-yl)oxy]alkyl}thio)[1,1?-biphenyl]-4-carbonitriles (CBSnOCB) are described. The odd members of both series show twist-bend nematic and nematic phases, whereas the even members exhibit only the nematic phase. An analogous cyanoterphenyl-based dimer, 3⁴-{6-[(4?-cyano[1,1?-biphenyl]-4-yl)thio]-hexyl}[1¹,2¹:2⁴,3¹-terphenyl]-1⁴-carbonitrile (CT6SCB), is also reported and shows enantiotropic N_TB and N phases. The transitional properties of these dimers are discussed in terms of molecular curvature, flexibility and biaxiality. The same molecular factors also influence the birefringence of nematic phases. Resonant X-ray scattering studies of the twist-bend nematic phase at both the carbon and sulfur absorption edges were performed, which allowed for the determination of critical behaviour of the helical pitch at the transition to the nematic phase, the behaviour was found to be independent of molecular structure. It was also observed that despite the different molecular bending angle and flexibility, in all compounds the helical pitch length far from the N-N_TB transition corresponds to 4 longitudinal molecular distances.     

Utilising Saturated Hydrocarbon Isosteres of para Benzene in the Design of Twist-Bend Nematic Liquid Crystals

The nematic twist-bend (N_TB) liquid crystal phase possesses a local helical structure with a pitch length of a few nanometres and is the first example of spontaneous symmetry breaking in a fluid system. All known examples of the N_TB phase occur in materials whose constituent mesogenic units are aromatic hydrocarbons. It is not clear if this is due to synthetic convenience or a bona fide structural requirement for a material to exhibit this phase of matter. In this work we demonstrate that materials consisting largely of saturated hydrocarbons can also give rise to this mesophase.     

The Chiral Twist-Bend Nematic Phase (N*TB)

The twist-bend nematic, N_TB, phase has been observed for chiral materials in which chirality is introduced through a branched 2-methylbutyl terminal tail. The chiral twist-bend nematic phase, N*_TB, is completely miscible with the N_TB phase of the standard achiral material, CB6OCB. The N*_TB phase exhibits optical textures with lower birefringence than those observed for the achiral N_TB phase, suggesting an additional mechanism of averaging molecular orientations. The N*−N*_TB transition temperatures for the chiral materials are higher than the N_TB−N transition temperatures seen for the corresponding racemic materials. This suggests the double degeneracy of helical twist sense in the phase is removed by the intrinsic molecular chirality. A square lattice pattern is observed in the N* phase over a temperature range of several degrees above the N*_TB–N phase transition, which may be attributed to a non-monotonic dependence of the bend elastic constant.     

Some N.M.R. experiments using lyotropic nematic liquid crystals

Abstract

A series of lyotropic nematic liquid crystals based on aniso-dimensional micelles can be subdivided according to micelle shape and diamagnetic susceptibility anisotropy. The proton magnetic resonance spectra of benzene dissolved in dilute solution in several of these phases have been analysed. The signs of the partially averaged dipole–dipole coupling give information about the relative alignment of the six-fold symmetry axis of benzene, the director and the magnetic field. The system caesium perfluorooctanoate/water is unusual in two respects. The system forms a nematic phase with only a binary mixture and the disk micelles align in a perpendicular plane to the magnetic field. As a result the binary system has been studied previously in some detail (see N. Boden, S. A. Come and K. W. Jolley, 1987, J. phys. Chem. 91, 4092). New measurements on the interesting phase diagram have been accomplished using caesium-133 and deuterium magnetic resonance measurements at various temperatures. Some dilatometric measurements have been made to complement the N.M.R. studies.     

Pentaerythritol Derived Tetrapode Exhibiting a Nematic-Like Mesophase at Ambient Temperatures

The nematic liquid-crystalline phase exhibits average orientational order, with no positional organisation. So-called modulated nematic phases exhibit this same orientational order with an additional spatially periodic modulation of the nematic director, the most common of which is the twist-bend nematic phase. We report a pentaerythritol derived tetrapode which exhibits a nematic-like mesophase at ambient temperature, and we denote this new mesophase ‘N_X’ to indicate a nematic phase of unknown structure. X-ray scattering experiments refute the possibility of positional order, yet optical textures are consistent with a periodic structure. We suggest that the mesophase exhibited by this material is a new type of nematic-like mesophase with some form of modulated structure. We find the N_X phase to exhibit an electrooptic response consistent with a nematic-like phase.     

Confinement and orientational study at liquid crystal phase transitions

Abstract

We have studied the heat capacity of the thermotropic liquid crystal, octylcyanobiphenyl (8CB), confined to the nearly cylindrical, 0·2 μm diameter pores of Anopore membranes. Orientation of the nematic director within the pores can be controlled with surface treatment. It is known from NMR measurements that the nematic director is aligned parallel to the pore axis in the untreated membrane. A perpendicular alignment is obtained when the pore surface is treated with lecithin. The second order smectic A to nematic (S_A–N) and the weakly first order nematic to isotropic (N–I) phase transitions of 8CB were studied in these pores, for both director orientations, using an AC calorimetry technique. Effects on heat capacity amplitudes, transition temperature shifts, rounding and broadening of these phase transitions will be presented and contrasted with bulk measurements.     

Effect of the linking unit on the twist-bend nematic phase in liquid crystal dimers: a comparative study of two homologous series of methylene- and ether-linked dimers

ABSTRACT

Two series of bimesogens with phenyl benzoate mesogenic units were prepared: one series having a heptamethylene spacer and the other a pentamethylene spacer with two ether-linking groups. These materials were prepared to provide experimental backing to the widely held hypothesis that methylene-linked bimesogens are more likely to exhibit the twist-bend nematic mesophase than their ether-linked counterparts. Several of the methylene-linked materials exhibited nematic and N_TB mesophases, whereas the analogous ether-linked materials gave only nematic phases albeit with significantly higher clearing points. Virtual N–N_TB transition temperatures for both methylene- and ether-linked bimesogens were extrapolated by constructing binary phase diagrams with the well-studied twist-bend material CB9CB. Contrary to our expectations these virtual transition temperatures were in most cases higher for the ether-linked bimesogens than in the analogous methylene compounds, this runs counter to reported theories and hypotheses that the incorporation of ether-linking groups should serve to destabilise the N_TB phase.