Theory of a critical point in the blue-phase-III-isotropic phase diagram

Unraveling the Mystery of the Blue Fog: Structure, Properties, and Applications of Amorphous Blue Phase III

The amorphous blue phase III of cholesteric liquid crystals, also known as the "blue fog," are among the rising stars in materials science that can potentially be used to develop next-generation displays with the ability to compete toe-to-toe with disruptive technologies like organic light-emitting diodes. The structure and properties of the practically unobservable blue phase III have eluded scientists for more than a century since it was discovered. This progress report reviews the developments in this field from both fundamental and applied research perspectives. The first part of this progress report gives an overview of the 130-years-long scientific tour-de-force that very recently resulted in the revelation of the mysterious structure of blue phase III. The second part reviews progress made in the past decade in developing electrooptical, optical, and photonic devices based on blue phase III. The strong and weak aspects of the development of these devices are underlined and criticized, respectively. The third- and-final part proposes ideas for further improvement in blue phase III technology to make it feasible for commercialization and widespread use.

Electro-optical Memory of a Nanoengineered Amorphous Blue-Phase-III Polymer Scaffold

An electro-optical (EO) memory device is presented, which is based on a 3D nanostructured polymer scaffold of the amorphous blue phase III (BPIII) of cholesteric liquid crystals (LCs), which can impart optical isotropy, optical activity, and sub-millisecond EO response of BPIII to conventional nematic LCs. This functional scaffold also enables the first experimental observation of the long debated structure of BPIII.

Blue phase liquid crystal: strategies for phase stabilization and device development

The blue phase liquid crystal (BPLC) is a highly ordered liquid crystal (LC) phase found very close to the LC-isotropic transition. The BPLC has demonstrated potential in next-generation display and photonic technology due to its exceptional properties such as sub-millisecond response time and wide viewing angle. However, BPLC is stable in a very small temperature range (0.5-1 °C) and its driving voltage is very high (∼100 V). To overcome these challenges recent research has focused on solutions which incorporate polymers or nanoparticles into the blue phase to widen the temperature range from around few °C to potentially more than 60 °C. In order to reduce the driving voltage, strategies have been attempted by modifying the device structure by introducing protrusion or corrugated electrodes and vertical field switching mechanism has been proposed. In this paper the effectiveness of the proposed solution will be discussed, in order to assess the potential of BPLC in display technology and beyond.

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.

Observation of a possible tetrahedratic phase in a bent-core liquid crystal

An experimental study of the heat capacity, mass density, magnetic-field-induced optical birefringence, linewidth and intensity of scattered light, and the viscosities associated with nematic order parameter fluctuations and fluid flow has been performed on an achiral bent-core liquid crystal above its clearing point temperature. The measurements reveal a transition between two optically isotropic phases that is consistent with recent theoretical predictions of a "tetrahedratic" form of orientational order.

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.

Frank-Kasper, quasicrystalline and related phases in liquid crystals

The review covers 3-dimensional and some 2-dimensional self-assembly patterns of supramolecular liquid crystals possessing either quasi-periodic or closely related truly periodic order. Compounds showing such structures are amphiphilic, and most often wedge-shaped, with dendrons being the most common examples. The topology is described in terms of 3D and 2D tiling of a variety of polyhedra or polygons, respectively. Analogy is made with structures of metallic alloys and soap froth. The recently discovered dodecagonal liquid quasicrystal is compared with the different tetrahedrally close packed Frank-Kasper phases in thermotropic and lyotropic liquid crystals. Parallels are also drawn with honeycomb columnar phases with related plane tilings, including that of distorted pentagons. The potential for the creation of nearly isotropic photonic bandgap materials is mentioned.

Correlation length and chirality of the fluctuations in the isotropic phase of nematic and cholesteric liquid crystals

Light-scattering measurements of the correlation length in the isotropic phase of a nematic liquid crystal reveal a temperature dependence following Landau-de Gennes theory for the isotropic phase with a bare correlation length smaller than has been measured in other liquid crystals. Similar measurements in a cholesteric liquid crystal demonstrate that the correlation length in the isotropic phase is larger than typically found in nematics and that the chirality of the fluctuations in the isotropic phase is slightly higher than the chirality of the cholesteric phase. Landau-de Gennes theory of the cholesteric phase describes the chirality in the cholesteric phase well but predicts that the chirality in the isotropic phase is temperature independent, which is not consistent with the data. There is a discontinuity in the chirality at the cholesteric-isotropic transition of about 15%, which is less than the predictions of Landau-de Gennes theory but more than the typical specific volume discontinuity at transitions to the isotropic phase. Except for a mismatch in the discontinuities at the transition, the chirality data resemble the temperature behavior of variables just below a critical point, in spite of the fact that this system is far from a critical point.

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.

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

The phenomenological theory of chiral liquid crystals is further developed by generalizing the model of self-consistent correlations [J. Englert, L. Longa, H. Stark, and H.-R. Trebin, Phys. Rev. Lett. 81, 1457 (1998)]. In the present approach, not only a leading helicity mode of the tensor order parameter is retained but also the remaining four modes. By considering a full fluctuating spectrum of the order parameter, the role of correlations between helicity modes in the isotropic phases is studied. Additionally, an exact form of the two-point correlation function in real space is derived and its properties are thoroughly discussed. It is shown that for chiral isotropic liquids purely chiral modes could be identified that do not exist for an ordinary liquid. Detailed results of the numerical calculations are compared with those obtained from the earlier model and these show regions where the coupling between the modes becomes important, in agreement with the available experimental data. Though the analysis up to first-order cumulant expansion does not predict a direct phase transition between the blue phase III and the isotropic phase, it is fairly easy to identify two differently correlated regions in a temperature-chirality plane. Various structural quantities, such as optical activity and specific heat, also reveal a behavior characteristic of two isotropic phases with different correlation lengths.

Effective index of refraction, optical rotation, and circular dichroism in isotropic chiral liquid crystals

This paper concerns optical properties of the isotropic phase above the isotropic-cholesteric transition and of the blue phase BP III. We introduce an effective index, which describes spatial dispersion effects such as optical rotation, circular dichroism, and the modification of the average index due to the fluctuations. We derive the wavelength dependence of these spatial dispersion effects quite generally without relying on an expansion in powers of the chirality and without assuming that the pitch of the cholesteric P is much shorter than the wavelength of the light lambda, an approximation that has been made in previous studies of this problem. The theoretical predictions are supported by comparing them with experimental spectra of the optical activity in the BP III phase.

Phase behavior and blue-phase-III-isotropic critical point in (R)-(S) mixtures of a chiral liquid crystal with a direct twist-grain-boundary to blue-phase transition

We have investigated mixtures of the (R) and (S) enantiomers of a chiral liquid crystal, (R)- or (S)-1-methylheptyl 3'-fluoro-4'-(3-fluoro-4-octadecyloxybenzoyloxy)tolane-4-carboxylate using high-resolution adiabatic scanning calorimetry. The pure (R) compound has a direct transition from the twist-grain-boundary to the blue phase without an intermediary chiral nematic phase. For the blue phases a different kind of phase behavior as a function of enantiomeric excess is observed, most probably related to the presence of a twist-grain-boundary-A instead of a chiral nematic phase below the blue phases. The general form of this phase diagram is compared with traditional blue-phase behavior. Furthermore a blue-phase-III-isotropic phase critical point, analoguous to that of a liquid-gas system, is observed, consistent with experimental and theoretical work recently published in this field. Finally, the effect of changing enantiomeric excess on the latent heats of the different first order phase transitions is measured and discussed.

Theory of chiral modulations and fluctuations in smectic-A liquid crystals under an electric field

Chiral liquid crystals often exhibit periodic modulations in the molecular director; in particular, thin films of the smectic-C* phase show a chiral striped texture. Here, we investigate whether similar chiral modulations can occur in the induced molecular tilt of the smectic-A phase under an applied electric field. Using both continuum elastic theory and lattice simulations, we find that the state of uniform induced tilt can become unstable when the system approaches the smectic-A-smectic-C* transition or when a high electric field is applied. Beyond that instability point, the system develops chiral stripes in the tilt, which induce corresponding ripples in the smectic layers. The modulation persists up to an upper critical electric field and then disappears. Furthermore, even in the uniform state, the system shows chiral fluctuations, including both incipient chiral stripes and localized chiral vortices. We compare these predictions with observed chiral modulations and fluctuations in smectic-A liquid crystals.