Functional π-Gelators and Their Applications

An overview on the recent developments in the field of liquid crystalline bent-core molecules (so-called banana liquid crystals) is given. After some basic issues, dealing with general aspects of the systematisation of the mesophases, development of polar order and chirality in this class of LC systems and explaining some general structure–property relationships, we focus on fascinating new developments in this field, such as modulated, undulated and columnar phases, so-called B7 phases, phase biaxiality, ferroelectric and antiferroelectric polar order in smectic and columnar phases, amplification and switching of chirality and the spontaneous formation of superstructural and supramolecular chirality.

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Bent-core liquid crystals: polar order, superstructural chirality and spontaneous desymmetrisation in soft matter systems

Modal decomposition of light has been known for a long time, applied mostly to pattern recognition. With the commercialization of liquid-crystal devices, digital holography as an enabling tool has become accessible to all, and with it all-digital tools for the decomposition of light have finally come of age. We review recent advances in unravelling the properties of light, from the modal structure of laser beams to decoding the information stored in orbital angular momentum (OAM)-carrying fields. We show application of these tools to fiber lasers, solid-state lasers, and structured light created in the laboratory by holographic laser beam shaping. We show by experimental implementation how digital holograms may be used to infer the intensity, phase, wavefront, Poynting vector, polarization, and OAM density of some unknown optical field. In particular, we outline how virtually all the previous ISO-standard beam diagnostic techniques may be readily replaced with all-digital equivalents, thus paving the way for unravelling of light in real time. Such tools are highly relevant to the in situ analysis of laser systems, to mode division multiplexing as an emerging tool in optical communication, and for quantum information processing with entangled photons.

Creation and detection of optical modes with spatial light modulators

Since the discovery of the liquid-crystalline state of matter 125 years ago, this field has developed into a scientific area with many facets. This Review presents recent developments in the molecular design and self-assembly of liquid crystals. The focus is on new exciting soft-matter structures distinct from the usually observed nematic, smectic, and columnar phases. These new structures have enhanced complexity, including multicompartment and cellular structures, periodic and quasiperiodic arrays of spheres, and new emergent properties, such as ferroelctricity and spontaneous achiral symmetry-breaking. Comparisons are made with developments in related fields, such as self-assembled monolayers, multiblock copolymers, and nanoparticle arrays. Measures of structural complexity used herein are the size of the lattice, the number of distinct compartments, the dimensionality, and the logic depth of the resulting supramolecular structures.

Development of structural complexity by liquid-crystal self-assembly.

We report experimental results that show a large and symmetric population of D and L crystals moving
into complete chiral purity, with one of the enantiomers completely disappearing. The results indicate (i) a
new symmetry breaking process incompatible with the hypothesis of an initial single chiral phase or
‘‘mother crystal,’’ (ii) that total symmetry breaking and complete chiral purity can be achieved from a
system that initially includes both enantiomers, and (iii) that this is achieved through a nonlinear
autocatalytic-recycling process.

Chiral Symmetry Breaking during Crystallization: Complete Chiral Purity induced by Nonlinear Autocatalysis and Recycling

New chiral dimers consisting of a rod-like and cholesterol mesogenic units are reported to form a chiral twist-bend nematic phase (NTB*) with heliconical structure. The compressibility of the NTB phase made of bent dimers was found to be as large as in smectic phases, which is consistent with the nanoperiodic structure of the NTB phase. The atomic force microscopy observations in chiral bent dimers revealed a periodicity of about 50 nm, which is significantly larger than the one reported previously for non-chiral compounds (ca. 10 nm).

A Twist‐Bend Nematic (NTB) Phase of Chiral Materials

Complex materials often exhibit a hierarchical structure with an intriguing mechanism responsible for the 'propagation' of order from the molecular to the nano- or micro-scale level. In particular, the chirality of biological molecules such as nucleic acids and amino acids is responsible for the helical structure of DNA and proteins, which in turn leads to the lack of mirror symmetry of macro-bio-objects. To fully understand mechanisms of cross-level order transfer there is an intensive search for simpler artificial structures exhibiting hierarchical arrangement. Here we present complex systems built of achiral molecules that show four levels of structural chirality: layer chirality, helicity of a basic repeating unit, mesoscopic helix and helical filaments. The structures are identified by a combination of hard and soft x-ray diffraction measurements, optical studies and theoretical modelling. Similarly to many biological systems, the studied materials exhibit a coupling between chirality at different levels.

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Multi-level chirality in liquid crystals formed by achiral molecules.

In recent years there are several reports showing that bent-core mesogenic molecules are able to form biaxial nematic phase in which molecular rotation around the long molecular axis is strongly hindered. The x-ray pattern with azimuthally split signals at low angle region of diffraction is usually given as evidence for the biaxial nematic phase. We show experimentally and theoretically that such x-ray pattern is due to the local smectic-$C$ fluctuations (``cybotactic'' groups) in the uniaxial nematic phase.

Structure studies of the nematic phase formed by bent-core molecules.

Periodic structures of phases with orientational order of molecules but homogenous electron density distribution: a short pitch cholesteric phase, blue phase and twist-bend nematic phase, were probed by resonant soft X-ray scattering (RSoXS) at the carbon K-edge. The theoretical model shows that in the case of a simple heliconical nematic structure, two resonant signals corresponding to the full and half pitch band should be present, while only the full pitch band is observed experimentally. This suggests that the twist-bend nematic phase has a complex structure with a double-helix built of two interlocked, shifted helices. We confirm that the helical pitch in the twist-bend nematic phase is in a 10 nm range for both the chiral and achiral materials. We also show that the symmetry of the blue phase can be unambiguously determined through a resonant enhancement of the X-ray diffraction signals, by including polarization effects, which are found to be an important indicator in phase structure determination.

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Structure of nanoscale-pitch helical phases: blue phase and twist-bend nematic phase resolved by resonant soft X-ray scattering.

The behaviour of polar, broken-layer-type columnar aliases made of bent molecules (B 1Rev and B 1RevTilted ) was studied under an applied electric field. There are two competing mechanisms of ferroelectric switching in the polar B 1RevTilted columnar phase: collective rotation around the long molecular axis and collective rotation around the tilt cone. The proposed model shows that the main factor discriminating the type of switching is the width of the column cross-section.

Nataša Vaupotič

Papers

A Twist‐Bend Nematic (NTB) Phase of Chiral Materials

Multi-level chirality in liquid crystals formed by achiral molecules.

Structure studies of the nematic phase formed by bent-core molecules.

Structure of nanoscale-pitch helical phases: blue phase and twist-bend nematic phase resolved by resonant soft X-ray scattering.

Switching mechanism in polar columnar mesophases made of bent-core molecules.