Correlations in the isotropic phases of chiral liquid crystals: the role of helicity modes

Controlling Mirror Symmetry Breaking and Network Formation in Liquid Crystalline Cubic, Isotropic Liquid and Crystalline Phases of Benzil-Based Polycatenars

Spontaneous development of chirality in systems composed of achiral molecules is important for new routes to asymmetric synthesis, chiral superstructures and materials, as well as for the understanding of the mechanisms of emergence of prebiotic chirality. Herein, it is shown that the 4,4'-diphenylbenzil unit is a universal transiently chiral bent building block for the design of multi-chained (polycatenar) rod-like molecules capable of forming a wide variety of helically twisted network structures in the liquid, the liquid crystalline (LC) and the crystalline state. Single polar substituents at the apex of tricatenar molecules support the formation of the achiral (racemic) cubic double network phase with Ia 3 ‾ d symmetry and relatively small twist along the networks. The combination of an alkyl chain with fluorine substitution leads to the homogeneously chiral triple network phase with I23 space group, and in addition, provides a mirror symmetry broken liquid. Replacing F by Cl or Br further increases the twist, leading to a short pitch double gyroid Ia 3 ‾ d phase, which is achiral again. The effects of the structural variations on the network structures, either leading to achiral phases or chiral conglomerates are analyzed.

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.

Columnar fluctuations as a source of non-Fermi-liquid behavior in weak metallic magnets

It is shown that columnar fluctuations, in conjunction with weak quenched disorder, lead to a T{3/2} temperature dependence of the electrical resistivity. This is proposed as an explanation of the observed non-Fermi-liquid behavior in the helimagnet MnSi, with one possible realization of the columnar fluctuations provided by Skyrmion lines that have independently been proposed to be present in this material.

Frustration in smectic layers of polar Gay-Berne systems

The main focus of the present paper is studying dipolar frustration within smectic- A(d) layers as induced by dipole-dipole interactions. Our reference point is the Gay-Berne system with kappa=4, kappa'=5, mu=2 and nu=1, which in the phase diagram shows a stable "island" of smectic- A phase with a short-range hexagonal order within each layer [Phys. Rev. E 57, 6685 (1998)]. We carry out isothermal-isobaric Monte Carlo simulations for a dipolar version of this model, where the Gay-Berne interaction is supplemented by interaction between longitudinal dipole moments. For a fixed off-center position of the dipoles we increase value of the dipole moment and follow evolution of the liquid-crystalline part of the phase diagram focusing on changes of the nematic-smectic- A phase boundaries and on structural response of the smectic- A layers. For weak dipoles only the classical smectic- A phase is stabilized, which then transforms into smectic- A(d) with layers being formed by two ferroelectrically polarized sublayers of opposite polarization. Average positions of dipoles that contribute to the polarization of a sublayer are located in a common plane, referred to as a dipolar plane. For not too strong dipole-dipole interactions increasing magnitude of the dipole moment causes stabilization of nematic at the expense of smectic- A(d). Under the same conditions the layer spacing increases and the distance between the dipolar planes within layers decreases. Each smectic sublayer is characterized by a short-range hexagonal order of the molecular centers of mass. With the dipole moment exceeding the threshold value, the polarization planes that built up the layers start to merge, which sets in the dipolar frustration. This, in turn, forces the system to develop a competition between frustrated hexagonal- and frustration-free tetragonal local order within each layer. When the local hexagonal order is transformed into the tetragonal one the stability range of smectic-A(d) increases with increasing dipole moment at the expense of the nematic phase. Similar competition is observed in crystalline phases. For small dipole moment only crystalline structures with long-range hexagonal order appear stable. They evolve with dipolar strength into monoclinic and tetragonal lattices.

Blue quantum fog: chiral condensation in quantum helimagnets

It is shown that a condensation transition involving a chiral order parameter can occur in itinerant helimagnets, in analogy to the transition between the isotropic phase and the phase known as blue fog or blue phase III in cholesteric liquid crystals. It is proposed that such a transition is the explanation for recent neutron scattering results in MnSi. Predictions are made that will allow for experimental tests of this proposal.

Minimal coupling model of the biaxial nematic phase

A minimal coupling model exhibiting isotropic, uniaxial, and biaxial nematic phases is analyzed in detail and its relation to existing models known in the literature is clarified. Its intrinsic symmetry properties are exploited to restrict the relevant ranges of coupling constants. Further on, properties of the model are thoroughly investigated by means of bifurcation theory as proposed by Kayser and Raveché [Phys. Rev. A 17, 2067 (1978)] and Mulder [Phys. Rev. A 39, 360 (1989)]. As a first step toward this goal, the bifurcation theory is applied to a general formulation of density functional theory in terms of direct correlation functions. On a general formal level, the theory is then analyzed to show that the bifurcation points from the reference, high-symmetry equilibrium phase to a low-symmetry structure depend only on the properties of the one-particle distribution function and the direct pair correlation function of the reference phase. The character of the bifurcation (whether spinodal, critical, tricritical, isolated Landau point, etc.) depends, in addition, on a few higher-order direct correlation functions. Explicit analytical results are derived for the case when only the leading L=2 terms of the potential (mean-field analysis) or of the direct pair correlation function expansion in the symmetry-adapted basis are retained. Formulas are compared with the numerical calculations for the mean-field, momentum L=2 potential model, in which case they are exact. In particular, bifurcations from the isotropic and uniaxial nematic to the biaxial nematic phases are discussed. The possibility of the recently reported nematic uniaxial-nematic biaxial tricritical point [A. M. Sonnet, E. G. Virga, and G. E. Durand, Phys. Rev. E 67, 061701 (2003)] is analyzed as well.

Fluctuations of the tensor order-parameter modes in a cholesteric liquid crystal

We use a Landau-de Gennes free energy to calculate the fluctuations of the five independent modes of the tensor order parameter for a cholesteric liquid crystal. Our results include, as a limiting case, the two classical director modes, known as the twist mode and the "umbrella" mode. We find, however, in contrast to the classical director model, that there can be substantial temperature dependence to the umbrella mode, as well as three additional modes near the transition to the isotropic phase. We comment on a recent experiment that suggests that two of these additional modes may have already been detected.

Self-consistent model of blue phase III to isotropic phase transition

In previous publications [Phys. Rev. Lett. 81, 1457 (1998)]; Phys. Rev. E 61, 2759 (2000)]], a simplified model with the scalar order parameter and without the cubic term in the Hamiltonian has been used to account for the phase transition between the two isotropic chiral liquids. The present approach is a step towards full analysis of this transition using de Gennes tensor order parameter and the higher-order self-consistent approach. The importance of the cubic term for a proper description of this phase transition is indicated.