Twist Grain Boundary Research Articles

Pattern formation at the traveling liquid-crystal twist grain boundary-smectic a interface

Pattern formation at phase boundaries moving in a temperature gradient is one of the major areas of nonequilibrium physics attracting considerable attention. While most of the early work concentrated on the moving solid-liquid interface, now the focus has changed to phase transitions characterized by broken continuous symmetry. Most recently we investigated consequences to interfacial patterns of a chirality-induced equilibrium length. Here we study patterns at another chiral interface where one of the phases has a chirality-induced defect lattice, the twist grain boundary (TGB) phase. The TGB state is analogous to the vortex lattice in Type-II superconductors predicted by the Gennes’ analogy between the nematic (N)-smectic A (A) transition and the normal-superconducting transition. In this analogy, a cholesteric A transition is analogous to the normal-superconducting transition in an external magnetic field and a theory has been developed for its analogous vortex lattice, the TGB phase, when this transition is Type II. We study patterns formed at the traveling TGB-A phase boundary. Different patterns are observed depending on whether TGB grows into A or A into TGB. Indeed, this maybe the first time a steady-state pattern is observed in directional melting (i.e. TGB growing into A). As these patterns have a broad band of wavelengths, they are difficult to characterize physically. Thus, we introduced a novel analysis (most simply but not rigorously described as) measuring the fractal dimension of the patterns at these traveling interfaces. Two lengths emerged from this analysis: a longer one set by sample thickness and a shorter one set by the smallest TGB unit that can grow into an oriented smectic A phase. We invoke our old dynamic arguments to account for why TGB cannot propagate at a second-order TGB-cholesteric phase transition so it is eventually squeezed out leaving behind a direct cholesteric-A transition.

Columnar and smectic ordering in a TGBA phase

Optical textures characteristic of cholesteric and columnar structures were simul- taneously detected for the first time in the same mesophase of a liquid crystal. However, X-ray diffraction measurements show that the mesophase under consideration is smectic A in nature. We show here that the compound presents, indeed, a twist grain boundary (TGB) phase within a large temperature range, and we propose an explanation of the supramolecular organization in this phase.

Mesophasic helical structures with high twisting power in optically active 3-methyladipic acid bis esters

A homologous series of novel twin molecules, (R)-3-methyladipic acid bis[4-(5-alkyl-2-pyrimidinyl)phenyl] ester, has been prepared and the physical properties investigated, where the chirality was generated in the system by introducing the chiral centre in the central region of the molecular structure. Heptyl and octyl members of the series show a monotropic cholesteric phase. The chirality-dependent properties of the series of the twin materials were compared with those of analogous ‘monomeric’ materials carrying a chiral centre in the peripheral aliphatic chain. Pitch measurements revealed that the twin materials induce a strong helical structure in both cholesteric and chiral smectic C phases. Furthermore, a chiral twin molecule possessing only one phenyl ring at each core part, i.e.(R)-3-methyladipic acid bis(4-octyloxyphenyl) ester, was prepared. The S*c pitch of this compound was found to be longer than that for the former series of twin materials. These results allow us to propose a possible model for producing the strong helical structure in the S*c phases where the chirality had been induced by the twin molecules. In addition, the strong desire for the twin materials to form a helical ordering in smectic phases was also found to induce an unusual smectic phase, in contact studies with an achiral liquid-crystalline material, where a texture similar to that reported for the twist grain boundary (TGB) phases was observed.

Twisted line liquids

We propose a model of directed lines where the average direction has the nature of a cholesteric liquid crystal. This model, for instance, would describe the liquid of screw dislocations in the twist-grain-boundary (TGB) phase of liquid crystals. We show that the presence of lines does not alter the long wavelength elasticity of a cholesteric and, therefore, does not stabilize Landau-Peierls instability of the cholesteric phase. We discuss other possible mechanisms for stabilizing the twist-grain-boundary phase.

Optical activity and light scattering in the isotropic and smectic A* phases of a highly chiral smectic liquid crystal

Abstract The results of optical activity measurements on the smectic A* phase of 1-methylheptyl 4′-[(4-n-tetradecyloxyphenyl)proprioloyloxy]biphenyl-4-carboxylate (14P1M7) and the chiral nematic phase of a chiral–racemic mixture of S-4-(2-methylbutyl)phenyl 4-decyloxybenzoate (CE6) are shown to be extremely similar. This is in full agreement with the proposed model of the A* phase as a twistgrain-boundary (TGB) phase. In addition, new light scattering measurements using circularly polarized light in a back-scattering geometry yield information on the fluctuations in the isotropic phase. Unlike in chiral nematics where only one structural mode is affected, the data show a strong deviation from the normal temperature dependence near the isotropic–smectic A* transition for two structural modes. Possible reasons for this behaviour in highly chiral smectic liquid crystals are discussed.

High resolution study of the structure of the Σ=5 [001] twist grain boundary in NiO

The existence of grain boundaries (GBs) in many advanced ceramics can significantly alter their performance, rendering the study of GB structure an essential part of understanding ceramic properties on a fundamental level. Furthermore, the debate regarding the stability of [001] twist GBs in rocksalt-structured oxides provides the impetus for comparing experimental observations of the Σ=5 [001] twist GB structure in NiO with the stable GB structure calculated by Tasker and Duffy (Fig. 1). The Tasker and Duffy structure was obtained by introducing a Schottky defect in each of the GB unit cells, resulting in a 20% decrease in atomic density at the GB. High resolution TEM (HRTEM) employing Fresnel fringe and lattice imaging techniques (Fig. 2) supplemented with image simulations of six possible configurations for the NiO Σ=5 [001] twist GB structure using the TEMPAS program (Fig. 3) were the primary experimental methods used in an attempt to detect this reduced atomic density in NiO Σ=5 [001] twist GBs manufactured by a modified Schober-Balluffi method. Since the Fresnel fringe technique consists of a change in Fresnel fringe contrast with defocus due to a change in mean inner potential at the GB, it becomes necessary to consider the contribution of the various causes of a change in mean inner potential to the resulting contrast. These causes include: (i) a change in atomic density or a change in atomic structure at the GB, (ii) the existence of a space charge at the GB, (iii) the existence of a thin amorphous film at the GB, (iv) the presence of impurities at the GB or a change in composition across the GB, and (v) GB grooving. The contribution of a GB space charge to the change in mean inner potential at the GB is assumed to be small, given that the space charge associated with with a GB in an ionic crystal is on the order of a few tenths of a volt, whereas the mean inner potential at the GB is on the order of 15 - 20 V. An attempt to address the impurity and grooving issues was made by performing EDS and EELS across the GB in an ultra-high vacuum, high resolution STEM.

Freeze-fracture TEM of the helical smectic A* phase

A new liquid crystal (called the smectic-A* phase) that combines cholesteric twist and smectic layering was a surprise as smectic phases preclude twist distortions. However, the twist grain boundary (TGB) model of Renn and Lubensky predicted a defect-mediated smectic phase that incorporates cholesteric twist by a lattice of screw dislocations. The TGB model for the liquid crystal analog of the Abrikosov phase of superconductors consists of regularly spaced grain boundaries of screw dislocations, parallel to each other within the grain boundary, but rotated by a fixed angle with respect to adjacent grain boundaries. The dislocations divide the layers into blocks which rotate by a discrete amount, Δθ, given by the ratio of the layer spacing, d, to the distance between grain boundaries, lb; Δθ ≈ d/lb (Fig. 1).

Multicritical behavior of Abrikosov vortex lattices near the cholesteric–smectic-A–smectic-C*point

The mean-field phase diagram of the cholesteric--smectic-A--smectic-${\mathrm{C}}^{\mathrm{*}}$ (${\mathit{N}}^{\mathrm{*}--}$Sm-A--Sm-${\mathit{C}}^{\mathrm{*}}$) point is derived within the framework of the chiral Chen-Lubensky model. We show that on the Sm-${\mathit{C}}^{\mathrm{*}}$ side of the phase diagram, one or two additional twist-grain-boundary (TGB) (or chiral-smectic) phases will occur. These additional chiral-smectic phases, the ${\mathrm{TGB}}_{\mathit{C}}$ and ${\mathrm{TGB}}_{\mathit{C}}^{\mathrm{*}}$ phases, are highly dislocated versions of smectic-C and smectic-${\mathit{C}}^{\mathrm{*}}$ phases, respectively. According to the de Gennes superconductor analogy, the grain-boundary phase which occurred on the smectic-A side of the phase diagram (known as the ${\mathrm{TGB}}_{\mathit{A}}$ or chiral Sm-${\mathit{A}}^{\mathrm{*}}$ phase) is the analog of the Abrikosov vortex lattice in type-II superconductors. However, the ${\mathrm{TGB}}_{\mathit{C}}$ and ${\mathrm{TGB}}_{\mathit{C}}^{\mathrm{*}}$ phases would correspond to Abrikosov vortex lattices in a hypothetical superconductor where the Ginzburg parameter \ensuremath{\kappa} is negative and the photon has Bose condensed. These additional phases are predicted to occur near the recently observed ${\mathit{N}}^{\mathrm{*}--}$Sm-${\mathit{A}}^{\mathrm{*}--}$Sm-${\mathit{C}}^{\mathrm{*}}$ multicritical point. We discuss the ${\mathit{N}}^{\mathrm{*}\mathrm{\ensuremath{-}}}$${\mathrm{TGB}}_{\mathit{C}}$, ${\mathrm{TGB}}_{\mathit{A}\mathrm{\ensuremath{-}}}$${\mathrm{TGB}}_{\mathit{C}}$, and ${\mathrm{TGB}}_{\mathit{A}\mathrm{\ensuremath{-}}}$${\mathrm{TGB}}_{\mathit{C}}^{\mathrm{*}}$ phase transitions. Because of the twist, the XY-like Sm-A--Sm-C is (usually) replaced by the Ising-like ${\mathrm{TGB}}_{\mathit{A}\mathrm{\ensuremath{-}}}$${\mathrm{TGB}}_{\mathit{C}}$. However, if the Sm-${\mathit{C}}^{\mathrm{*}}$ helicoidal pitch length is somewhat smaller than the cholesteric pitch length, then the ${\mathrm{TGB}}_{\mathit{A}\mathrm{\ensuremath{-}}}$${\mathrm{TGB}}_{\mathit{C}}$ transition would be replaced by the ${\mathrm{TGB}}_{\mathit{A}\mathrm{\ensuremath{-}}}$${\mathrm{TGB}}_{\mathit{C}}^{\mathrm{*}}$ transition.

TEM study on freeze-fracture structure of smectic A* phase

Liquid crystals (LCs) with chiral molecules show helical structure. The most well known LC phase having helical structure is cholesteric, in which average direction of molecular axes rotates around a helical axis, as shown in Fig. 1. Two kinds of helical structures were found in smectic phases. The smectic A* phase contains the helical axis parallel to the smectic layers, and in the smectic C* phase, it is perpendicular. The Smectic A* phase was recently discovered in 1-methylheptyl 4'-[[(tetradecyloxyphenyl)propionyl]oxy]biphenyl-4-carboxylate, (+14P1M7). +14P1M7 changes its phase from isotropic melt to A* phase at 93°C and C* phase at 89.5°C, while a racemic mixture shows the untwisted A and C phase. The structure of smectic A* phase was predicted by Renn and Lubensky by hypothesizing a Twist grain boundary (TGB) phase in analogy with the Abrikosov phase in superconductors.

Twist-grain-boundary phases near the nematic-smectic-A-smectic-C point in liquid crystals.

We generalize the Chen-Lubensky model for the point where the nematic, smectic-A, and smectic-C liquid-crystalline phases meet (the NAC point) to include the effects of molecular chirality. We calculate the phase diagram for this model when the possibility of a twist-grain-boundary (TGB) phase is included and when it is not. In the latter case, we find that the NAC multicritical point becomes a critical end point where first-order cholesteric to smectic-A and cholesteric to chiral-smectic-C phase boundaries meet a second-order smectic-A to chiral-smectic-C phase boundary. In the former case, we find that the TGB phase always intervenes between the cholesteric and smectic-A phases near the NAC multicritical point of the nonchiral system. The connection between these results and the recent observations of a chiral smectic phase near the NAC point by Goodby and co-workers [Nature 337, 449 (1988); J. Am. Chem. Soc. 111, 8119 (1989)] is discussed briefly.

Abrikosov dislocation lattice in a model of the cholesteric–to–smectic-Atransition

The nematic--to--smectic-A transition in liquid crystals is analogous to the normal to superconducting transition in metals with the Frank director n in liquid crystals playing the role of the vector potential A in metals. The liquid-crystal analog of an external magnetic field is a field, arising, for example, from molecular chirality, leading to a nonzero \ensuremath{\nabla}\ifmmode\times\else\texttimes\fi{}n in the equilibrium nematic phase. The cholesteric (twisted nematic) phase is the analog of a normal metal in an external magnetic field. In type-II superconductors in an external magnetic field, the Abrikosov flux lattice phase with partial flux penetration intervenes between the low-temperature Meissner phase and the high-temperature normal-metal phase. In this paper we study the analog in liquid crystals containing chiral molecules of the Abrikosov phase in superconductors. Using a covariant form of the de Gennes free energy, we find that in mean-field theory a state, which we call the twist-grain-boundary (TGB) state, with regularly spaced grain boundaries consisting of parallel screw dislocations, intervenes between the smectic and cholesteric phases. We calculate the liquid-crystal analogs of the upper and lower critical fields ${H}_{c2}$ and ${H}_{c1}$. The properties of the TGB phase depend on the angle 2\ensuremath{\pi}\ensuremath{\alpha} between axes of dislocations in adjacent grain boundaries. \ensuremath{\alpha} can be rational or irrational. When \ensuremath{\alpha}=p/q for mutually prime integers p and q, the TGB state has a q-fold screw axis and quasicrystalline symmetry for crystallographically forbidden q. Our calculations ignore exponentially small terms favoring lock in at rational \ensuremath{\alpha}. We calculate the x-ray scattering intensities in the cholesteric phase near the TGB phase boundary and in the TGB phase for rational and irrational \ensuremath{\alpha}. We also discuss experimental difficulties in observing the TGB state and the possible effects fluctuations not included in mean-field theory might have on its existence.

GRAIN BOUNDARY STRUCTURE IN NiO

Transmission electron microscopy is used to study the structure of grain boundaries (GBs) in NiO. tilt GBs in NiO are generally found to be faceted. Structural periodicities within facets have been observed at low and high misorientation. An effective reduced atomic density at the GB within a region of 0.5 to 0.8 nm in width is suggested by the defocus contrast behavior of high-angle tilt and twist GBs.