Chiral symmetry breaking in bent-core liquid crystals

Two-fluid model for a fluid with tetrahedral-octupolar order

We investigate the macroscopic dynamics of a two-fluid system with tetrahedral order. As all normal-fluid two-fluid systems one has-compared to a simple fluid-the velocity difference between the two subsystems and the concentration of one component as additional macroscopic variables. Depending on the type of system, the concentration can either be a conserved quantity or relax on a long, but finite timescale. Due to the existence of the tetrahedral order such a system breaks parity symmetry. Here we discuss physical systems without preferred direction in real space, meaning that our description applies to optically isotropic materials. We find a number of reversible as well as dissipative dynamic cross-coupling terms due to the additional octupolar order, when compared to a fluid mixture. As the most interesting cross-coupling term from an experimental point of view, we identify a dissipative cross-coupling between the relative velocity and the usual velocity gradients. Applying a shear flow in a plane, this dissipative cross-coupling leads to a velocity difference perpendicular to the shear plane. As a result one can obtain a spatially homogeneous oscillation of the relative velocity. In addition, this induced relative velocity can couple as a function of time and space to the concentration, which gives rise to an overdamped propagating soundlike mode, where the overdamping arises from the fact that velocity difference is a macroscopic variable and not strictly conserved. We also show that electric field gradients are connected with an analogous reversible cross-coupling and can lead in a planar shear geometry to an overdamped propagating mode as well.

General liquid-crystal theory for anisotropically shaped molecules: Symmetry, orientational order parameters, and system free energy

A general theory of liquid crystals is presented, starting from the group-theory symmetry analysis of the constituting molecules. A particular attention is paid to the type of elastic free-energies and their relationships with the molecular symmetries. The orientational order-parameter tensors are identified for each molecular symmetry, in a consideration of consistently keeping the leading, characteristic elastic free energies in a model. The order parameters are expressed in terms of symmetric traceless tensors, some of high orders, for all major molecular symmetries, including seven groups of axial symmetries and seven groups of polyhedral symmetries. For spatially inhomogeneous liquid crystals, the couplings of these tensors in the elastic energies are derived by expanding the interaction energies between these molecules. The aim is to provide a general view of the molecular symmetries of individual molecules, orientational order parameters characterizing the orientational distribution functions, and the elastic free energies, all under one single group-theory approach.

Chirality of Liquid Crystals Formed from Achiral Molecules Revealed by Resonant X-Ray Scattering

Intensive research on chiral liquid crystals (LCs) has been fueled by their actively tunable physicochemical properties and structural complexity, comparable to those of sophisticated natural materials. Herein, recent progress in the discovery of new classes of chiral LCs, enabled by a combination of nano- and macroscale investigations is reviewed. First, an overview is provided of liquid crystalline phases, made of chiral and achiral low-weight molecules, that exhibit chiral structure and/or chiral morphology. Then, recent progress in the discovery of new classes of chiral LCs, particularly enabled by the application of resonant X-ray scattering is described. It is shown that the method is sensitive to modulations of molecular orientation and therefore provides information hardly accessible by means of other techniques, such as the sense of helical structures or chirality transfer across length scales. Finally, a perspective is presented on the future scope, opportunities, and challenges in the field of chiral LCs, in particular related to nanocomposites.

Mean-field model of boomerang nematic liquid crystals with diminished coupling of molecular uniaxial and biaxial susceptibilities

The mean-field theory approach has been applied to the boomerang type particles from P. I. C. Teixeira, A. Masters, and B. Mulder [Mol. Cryst. Liq. Cryst. 323, 167 (1998)MCLCE91058-725X10.1080/10587259808048440] but with diminished strength of the interaction coefficient responsible for the coupling between molecular uniaxial and biaxial susceptibilities. For the rodlike particles, when the apex boomerang angle is larger than 107.35^{∘}, the stable uniaxial rodlike phase occurs. For smaller angles, beyond the point where the transition is of the second order (the Landau point) and for diminished parameter of molecular biaxial-uniaxial coupling, a biaxial phase is observed with the transition undergoing directly from the isotropic phase. According to the order parameters the character of this transition is of the first order. Such behavior is in accordance with the Sonnet-Durand-Virga model of the biaxial phases. The change in the type of the phase transition order is also illustrated by the changes in the equations of state and the changes in second and third derivatives of the free energy. The possibilities to tailor interaction coefficients of real molecules to obtain such a phase transition scenario are discussed.

Influence of tetrahedral order on ferromagnetic gel phases

We investigate the macroscopic dynamics of gels with tetrahedral/octupolar symmetry, which possess in addition a spontaneous permanent magnetization. We derive the corresponding static and dynamic macroscopic equations for a phase, where the magnetization is parallel to one of the improper fourfold tetrahedral symmetry axes. Apart from elastic strains, we take into account relative rotations between the magnetization and the elastic network. The influence of tetrahedral order on these degrees of freedom is investigated and some experiments are proposed that are specific for such a material and allow to indirectly detect tetrahedral order. We also consider the case of a transient network and predict that stationary elastic shear stresses arise when a temperature gradient is applied.

Nematic twist-bend phase in an external field

The response of the nematic twist-bend ([Formula: see text]) phase to an applied field can provide important insight into the structure of this liquid and may bring us closer to understanding mechanisms generating mirror symmetry breaking in a fluid of achiral molecules. Here we investigate theoretically how an external uniform field can affect structural properties and the stability of [Formula: see text] Assuming that the driving force responsible for the formation of this phase is packing entropy, we show, within Landau-de Gennes theory, that [Formula: see text] can undergo a rich sequence of structural changes with the field. For the systems with positive anisotropy of permittivity, we first observe a decrease of the tilt angle of [Formula: see text] until it transforms through a field-induced phase transition to the ordinary prolate uniaxial nematic phase (N). Then, at very high fields, this nematic phase develops polarization perpendicular to the field ([Formula: see text]). For systems with negative anisotropy of permittivity, the results reveal new modulated structures. Even an infinitesimally small field transforms [Formula: see text] to its elliptical counterpart ([Formula: see text]), where the circular base of the cone of the main director becomes elliptic. With stronger fields, the ellipse degenerates to a line, giving rise to a nonchiral periodic structure, the nematic splay-bend ([Formula: see text]), where the two nematic directors are restricted to a plane. The three structures-[Formula: see text], [Formula: see text], and [Formula: see text]-with a modulated polar order are globally nonpolar. But further increase of the field induces phase transitions into globally polar structures with nonvanishing polarization along the field's direction. We found two such structures, one of which is a polar and chiral modification of [Formula: see text], where splay and bend deformations are accompanied by weak twist deformations ([Formula: see text]). Further increase of the field unwinds this structure into a polar nematic ([Formula: see text]) of polarization parallel to the field.

Generic first-order phase transitions between isotropic and orientational phases with polyhedral symmetries

Polyhedral nematics are examples of exotic orientational phases that possess a complex internal symmetry, representing highly nontrivial ways of rotational symmetry breaking, and are subject to current experimental pursuits in colloidal and molecular systems. The classification of these phases has been known for a long time; however, their transitions to the disordered isotropic liquid phase remain largely unexplored, except for a few symmetries. In this work, we utilize a recently introduced non-Abelian gauge theory to explore the nature of the underlying nematic-isotropic transition for all three-dimensional polyhedral nematics. The gauge theory can readily be applied to nematic phases with an arbitrary point-group symmetry, including those where traditional Landau methods and the associated lattice models may become too involved to implement owing to a prohibitive order-parameter tensor of high rank or (the absence of) mirror symmetries. By means of exhaustive Monte Carlo simulations, we find that the nematic-isotropic transition is generically first-order for all polyhedral symmetries. Moreover, we show that this universal result is fully consistent with our expectation from a renormalization group approach, as well as with other lattice models for symmetries already studied in the literature. We argue that extreme fine tuning is required to promote those transitions to second-order ones. We also comment on the nature of phase transitions breaking the O(3) symmetry in general cases.

On the influence of a network on optically isotropic fluid phases with tetrahedral/octupolar order

We investigate the influence of transient or permanent elasticity on liquid phases with octupolar (tetrahedral) order, a question that has never been addressed before. The focus will be on optically isotropic liquid phases with tetrahedral order including the T _d phase and the chiral T phase introduced by Fel. It turns out that the presence of both, a network as well as tetrahedral order can lead to the formation of chiral domains of both hands in an optically isotropic fluid due to a completely novel mechanism, thus providing a possible macroscopic explanation for recent experimental observations. We study in detail how elasticity influences the macroscopic dynamics of both, the T _d and the T phase. The simultaneous presence of a transient network as well as of octupolar order is shown to lead to completely new cross-coupling phenomena for optically isotropic systems including transient dissipative elastic strains due to temperature gradients.

Computer simulation study of a mesogenic lattice model based on long-range dispersion interactions

In contrast to thermotropic biaxial nematic phases, for which some long sought for experimental realizations have been obtained, no experimental realizations are yet known for their tetrahedratic and cubatic counterparts, involving orientational orders of ranks 3 and 4, respectively, also studied theoretically over the last few decades. In previous studies, cubatic order has been found for hard-core or continuous models consisting of particles possessing cubic or nearly cubic tetragonal or orthorhombic symmetries; in a few cases, hard-core models involving uniaxial (D_{∞h}-symmetric) particles have been claimed to produce cubatic order as well. Here we address by Monte Carlo simulation a lattice model consisting of uniaxial particles coupled by long-range dispersion interactions of the London-De Boer-Heller type; the model was found to produce no second-rank nematic but only fourth-rank cubatic order, in contrast to the nematic behavior long known for its counterpart with interactions truncated at nearest-neighbor separation.

Twist-bend nematic phases of bent-shaped biaxial molecules

How can a change in molecular structure affect the relative stability and structural properties of the twist-bend nematic phase (NTB)? Here we extend the mean-field model(1) (C. Greco, G. R. Luckhurst and A. Ferrarini, Soft Matter, 2014, 10, 9318) for bent-shaped achiral molecules, to study the influence of arm molecular biaxiality and the value of the molecule's bend angle on the relative stability of NTB. In particular we show that by controlling the biaxiality of the molecule's arms, up to four ordered phases can become stable. They involve local uniaxial and biaxial variants of NTB, together with uniaxial and biaxial nematic phases. However, a V-shaped molecule shows a stronger ability to form stable NTB than a biaxial nematic phase, where the latter phase appears in the phase diagram only for bend angles greater than 140° and for large biaxiality of the two arms.

Modulated nematic structures induced by chirality and steric polarization

What kind of one-dimensional modulated nematic structures (ODMNS) can form nonchiral and chiral bent-core and dimeric materials? Here, using the Landau-de Gennes theory of nematics, extended to account for molecular steric polarization, we study a possibility of formation of ODMNS, both in nonchiral and intrinsically chiral liquid crystalline materials. Besides nematic and cholesteric phases, we find four bulk ODMNS for nonchiral materials, two of which, to the best of our knowledge, have not been reported so far. These two structures are longitudinal (N_{LP}) and transverse (N_{TP}) periodic waves where the polarization field being periodic in one dimension stays parallel and perpendicular, respectively, to the wave vector. The other two phases are the twist-bend nematic phase (N_{TB}) and the splay-bend nematic phase (N_{SB}), but their fine structure appears more complex than that considered so far. The presence of molecular chirality converts nonchiral N_{TP} and N_{SB} into new N_{TB} phases. Surprisingly, the nonchiral N_{LP} phase can stay stable even in the presence of intrinsic chirality.

Lehmann effects and rotatoelectricity in liquid crystalline systems made of achiral molecules

We discuss Lehmann effects and rotato-electricity for liquid crystalline phases made of achiral molecules. We point out that for static and dynamic Lehmann effects to exist, it is not necessary to have chiral molecules provided the overall structure has macroscopic chirality. This question is of direct relevance for liquid crystalline phases formed by bent-core molecules provided they have a sufficiently low symmetry. This includes systems which break parity symmetry and have overall C(2) or C(1) symmetry. We point out that for liquid crystalline gels and elastomers one should be able to observe rotato-electricity for systems with macroscopic chirality. Rotatoelectricity is associated with the relative rotations between two subsystems, namely, between the network and the director, in an external electric field. Candidates include gels and even monolayers prepared from bent-core molecules with sufficiently low symmetry.

Tetrahedratic mesophases, chiral order, and helical domains induced by quadrupolar and octupolar interactions

We present an exhaustive account of phases and phase transitions that can be stabilized in the recently introduced generalized Lebwohl-Lasher model with quadrupolar and octupolar microscopic interactions [L. Longa, G. Pająk, and T. Wydro, Phys. Rev. E 79, 040701(R) (2009)]. A complete mean-field analysis of the model, along with Monte Carlo simulations allows us to identify four distinct classes of the phase diagrams with a number of multicritical points where, in addition to the standard uniaxial and biaxial nematic phases, the other nematic like phases are stabilized. These involve, among the others, tetrahedratic (T), nematic tetrahedratic (N(T)), and chiral nematic tetrahedratic (N(T)(*)) phases of global T(d), D(2d), and D(2) symmetry, respectively. Molecular order parameters and correlation functions in these phases are determined. We conclude with generalizations of the model that give a simple molecular interpretation of macroscopic regions with opposite optical activity (ambidextrous chirality), observed, e.g., in bent-core systems. An estimate of the helical pitch in the N(T)(*) phase is also given.

Symmetry breaking in confined fluids

The recent progress in the theoretical investigation of the symmetry breaking (the existence of a stable state of a system, in which the symmetry is lower than the symmetry of the system itself) for classical and quantum fluids is reviewed. The emphasis is on the conditions which cause symmetry breaking in the density distribution for one component fluids and binary mixtures confined in a closed nanoslit between identical solid walls. The existing studies have revealed that two kinds of symmetry breaking can occur in such systems. First, a one-dimensional symmetry breaking occurs only in the direction normal to the walls as a fluid density profile asymmetric with respect of the middle of the slit and uniform in any direction parallel to the walls. Second, a two-dimensional symmetry breaking occurs in the fluid density distribution which is nonuniform in one of the directions parallel to the walls and asymmetrical in the direction normal to the walls. It manifests through liquid bumps and bridges in the fluid density distribution. For one component fluids, conditions of existence of symmetry breaking are provided in terms of the average fluid density, strength of fluid-solid interactions, distance at which the solid wall generates a hard core repulsion, and temperature. In the case of binary mixtures, the occurrence of symmetry breaking also depends on the composition of the confined mixtures.

Mesogenic lattice models with partly antinematic interactions producing uniaxial nematic phases

The present paper considers nematogenic lattice models, involving particles of D_{2h} symmetry, whose centers of mass are associated with a three-dimensional simple cubic lattice; the pair potential is isotropic in orientation space and restricted to nearest neighbors. Let two orthonormal triads define orientations of a pair of interacting particles; the simplest potential models proposed in the literature can be reduced to a linear combination involving the squares of the scalar products between corresponding unit vectors only and depending on three parameters. By now, various sets of potential parameters have been proposed and studied in the literature, some of which capable of producing biaxial orientational order at sufficiently low temperature. On the other hand, in experimental terms, mesogenic biaxial molecules mostly produce uniaxial mesophases; thus we address here two very simple cases, involving a nematic (calamitic) term as well as one (model P0M) or two (model PPM) antinematic ones, whose coefficients are set equal in magnitude; when only one antinematic coefficient is used, the third one is set to zero. The calamitic term favors the alignment of two corresponding molecular axes, whereas antinematic terms or geometric constraints tend to keep two other pairs of axes mutually orthogonal. The models were investigated by molecular-field treatments and Monte Carlo simulation and found to predict a first- or second-order transitions between uniaxial nematic and isotropic phases; the molecular-field treatments yielded results in reasonable agreement with simulation.