Twist-bend Nematic Research Articles

Light scattering study of the "pseudo-layer" compression elastic constant in a twist-bend nematic liquid crystal.

The nematic twist-bend (TB) phase, exhibited by certain achiral thermotropic liquid crystalline (LC) dimers, features a nanometer-scale, heliconical rotation of the average molecular long axis (director) with equally probable left- and right-handed domains. On meso to macroscopic scales, the TB phase may be considered as a stack of equivalent slabs or "pseudo-layers", each one helical pitch in thickness. The long wavelength fluctuation modes should then be analogous to those of a smectic-A phase, and in particular the hydrodynamic mode combining "layer" compression and bending ought to be characterized by an effective layer compression elastic constant Beff and average director splay constant K. The magnitude of K is expected to be similar to the splay constant of an ordinary nematic LC, but due to the absence of a true mass density wave, Beff could differ substantially from the typical value of ∼106 Pa in a conventional smectic-A. Here we report the results of a dynamic light scattering study, which confirms the "pseudo-layer" structure of the TB phase with Beff in the range 103-104 Pa. We show additionally that the temperature dependence of Beff at the TB to nematic transition is accurately described by a coarse-grained free energy density, which is based on a Landau-deGennes expansion in terms of a heli-polar order parameter that characterizes the TB state and is linearly coupled to bend distortion of the director.

Local distortion energy and coarse-grained elasticity of the twist-bend nematic phase.

The recently discovered twist-bend nematic phase of achiral bent-shaped molecules, NTB, has a doubly degenerate ground-state with a periodically modulated heliconical structure and unusual distortion elasticity, the theoretical description of which is still debated. We show that the NTB phase has the same macroscopic symmetry as another periodic mesophase, the chiral smectic-A, SmA*. Based on this NTB/SmA* analogy, we develop a coarse-grained elastic model for the NTB phase. Adopting one of the existing microscopic NTB elastic models, we calculate the coarse-grained elastic constants, coherence and penetration lengths in terms of a few Frank-like nematic elastic coefficients that can be measured in macroscopic experiments. The same coarse-grained approach, applied to different local elastic models, may provide an efficient experimental test of their validity. We show that the anisotropy of the NTB coarse-grained elasticity is opposite to that of the SmA*, leading probably to different configurations of some of the defects of the "layered" NTB structure. Moreover, we argue that the intrinsic chiral frustration of the NTB phase may be resolved by penetration of the twist field into the bulk through a network of screw dislocations of the NTB pseudo-layers, resulting in a twist-bend analogue of the twist grain boundary phase TGBA.

Elastic continuum theory: towards understanding of the twist-bend nematic phases.

The twist-bend nematic phase, N_{TB}, may be viewed as a heliconical molecular arrangement in which the director n precesses uniformly about an extra director field, t. It corresponds to a nematic ground state exhibiting nanoscale periodic modulation. To demonstrate the stability of this phase from the elastic point of view, a natural extension of the Frank elastic energy density is proposed. The elastic energy density is built in terms of the elements of symmetry of the new phase in which intervene the components of these director fields together with the usual Cartesian tensors. It is shown that the ground state corresponds to a deformed state for which K_{22}>K_{33}. In the framework of the model, the phase transition between the usual and the twist-bend nematic phase is of second order with a finite wave vector. The model does not require a negative K_{33} in agreement with recent experimental data that yield K_{33}>0. A threshold is predicted for the molecular twist power below which no transition to a twist-bend nematic may occur.

Apolar bimesogens and the incidence of the twist-bend nematic phase.

The nematic twist-bend phase (NTB) was, until recently, only observed for polar mesogenic dimers, trimers or bent-core compounds. In this article, we report a comprehensive study on novel apolar materials that also exhibit NTB phases. The NTB phase was observed for materials containing phenyl, cyclohexyl or bicyclooctyl rings in their rigid-core units. However, for materials with long (>C7) terminal chains or mesogenic core units comprising three ring units, the NTB phase was not observed and instead the materials exhibited smectic phases. One compound was found to exhibit a transition from the NTB phase to an anticlinic smectic C phase; this is the first example of this polymorphism. Incorporation of lateral substitution with respect to the central core unit led to reductions in transition temperatures; however, the NTB phase was still found to occur. Conversely, utilising branched terminal groups rendered the materials non-mesogenic. Overall, it appears that it is the gross molecular topology that drives the incidence of the NTB phase rather than simple dipolar considerations. Furthermore, dimers lacking any polar groups, which were prepared to test this hypothesis, were found to be non mesogenic, indicating that at the extremes of polarity these effects can dominate over topology.

Cholesterics of colloidal helices: Predicting the macroscopic pitch from the particle shape and thermodynamic state

Building a general theoretical framework to describe the microscopic origin of macroscopic chirality in (colloidal) liquid crystals is a long-standing challenge. Here, we combine classical density functional theory with Monte Carlo calculations of virial-type coefficients to obtain the equilibrium cholesteric pitch as a function of thermodynamic state and microscopic details. Applying the theory to hard helices, we observe both right- and left-handed cholesteric phases that depend on a subtle combination of particle geometry and system density. In particular, we find that entropy alone can even lead to a (double) inversion in the cholesteric sense of twist upon changing the packing fraction. We show how the competition between single-particle properties (shape) and thermodynamics (local alignment) dictates the macroscopic chiral behavior. Moreover, by expanding our free-energy functional, we are able to assess, quantitatively, Straley's theory of weak chirality, which is used in several earlier studies. Furthermore, by extending our theory to different lyotropic and thermotropic liquid-crystal models, we analyze the effect of an additional soft interaction on the chiral behavior of the helices. Finally, we provide some guidelines for the description of more complex chiral phases, like twist-bend nematics. Our results provide new insights into the role of entropy in the microscopic origin of this state of matter.

The relationship between molecular structure and the incidence of the NTB phase

In this work, we present the first part of a study into the relationship between molecular structure and the occurrence of the ‘twist-bend nematic phase’ (NTB). Given the large amount of chemical space that might reasonably be expected to give rise to the NTB phase, this paper is only concerned with methylene-linked bimesogens bearing polar terminal groups based on the initial work of George Gray on cyanobiphenyls. As with other studies, we find that the NTB phase is observed only for materials that contain an odd number of methylene units in the spacer chain. It also appears that, in a given series of materials, there is a weak negative correlation between the dipole moment of the individual mesogenic units and the thermal stability of the NTB phase. Furthermore, we find that increasing the length–breadth ratio of the individual mesogenic units also provides a significant increase in the thermal stability of the NTB phase. The electrooptic behaviour of two materials, one with a terminal nitrile unit and one with an isothiocyanate group, was investigated. The NTB phase of the NCS-terminated material can be switched with a large applied voltage (20 V μm−1); however, the analogous nitrile-terminated material showed no electrooptic response under these conditions. Either the threshold voltage to switching is simply lower for isothiocyanate materials than nitriles or that there is more than one phase currently identified as the twist-bend nematic.

Double-well elastic theory for twist-bend nematic phases.

The ground state of twist-bend nematic liquid crystals is a heliconical molecular arrangement in which the nematic director precesses uniformly about an axis, making a fixed angle with it. Both precession senses are allowed in the ground state of these phases. When one of the two helicities is prescribed, a single helical nematic phase emerges. A quadratic elastic theory is proposed here for each of these phases which features the same elastic constants as the classical theory of the nematic phase, requiring all of them to be positive. To describe the helix axis, it introduces an extra director field which becomes redundant for ordinary nematics. Putting together helical nematics with opposite helicities, we reconstruct a twist-bend nematic, for which the quadratic elastic energies of the two helical variants are combined in a nonconvex energy. States with minimal energy and opposite helicities may come in contact along an interface belonging to a special family of developable surfaces, including a peculiar cone, which can be constructed through a general method.

Twist-bend heliconical chiral nematic liquid crystal phase of an achiral rigid bent-core mesogen.

The chiral, heliconical (twist-bend) nematic ground state is reported in an achiral, rigid, bent-core mesogen (UD68). Similar to the nematic twist-bend (N(TB)) phase observed in bent molecular dimers, the N(TB) phase of UD68 forms macroscopic, smecticlike focal-conic textures and exhibits nanoscale, periodic modulation with no associated modulation of the electron density, i.e., without a detectable lamellar x-ray reflection peak. The N(TB) helical pitch is p(TB) ∼ 14 nm. When an electric field is applied normal to the helix axis, a weak electroclinic effect is observed, revealing 50-μm-scale left- and right-handed domains in a chiral conglomerate.

Nematic twist-bend phase with nanoscale modulation of molecular orientation

A state of matter in which molecules show a long-range orientational order and no positional order is called a nematic liquid crystal. The best known and most widely used (for example, in modern displays) is the uniaxial nematic, with the rod-like molecules aligned along a single axis, called the director. When the molecules are chiral, the director twists in space, drawing a right-angle helicoid and remaining perpendicular to the helix axis; the structure is called a chiral nematic. Here using transmission electron and optical microscopy, we experimentally demonstrate a new nematic order, formed by achiral molecules, in which the director follows an oblique helicoid, maintaining a constant oblique angle with the helix axis and experiencing twist and bend. The oblique helicoids have a nanoscale pitch. The new twist-bend nematic represents a structural link between the uniaxial nematic (no tilt) and a chiral nematic (helicoids with right-angle tilt).

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.

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.

Correction to “The Chirality of a Twist–Bend Nematic Phase Identified by NMR Spectroscopy”

A correction to the article in J. Phys. Chem. B 2012, 116, 7940?7951. DOI: 10.1021/jp302705n

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.