Chiral Pattern Research Articles

Tailoring long-range superlattice chirality in molecular self-assemblies via weak fluorine-mediated interactions.

Controllable fabrication of enantiospecific molecular superlattices is a matter of imminent scientific and technological interest. Herein, we demonstrate that long-range superlattice chirality in molecular self-assemblies can be tailored by tuning the interplay of weak intermolecular non-covalent interactions between hexaphenylbenzene-based enantiomers. By means of high-resolution scanning tunneling microscopy measurements, we demonstrate that the functionalization of a hexaphenylbenzene-based molecule with fluorine (F) atoms leads to the formation of molecular self-assemblies with distinct long-range chiral recognition patterns. We employed density functional theory calculations to quantify F-mediated lone pair F⋯π, C-H⋯F, and F⋯F interactions attributed to the distinct enantiospecific molecular self-organizations. Our findings underpin a viable route to fabricate long-range chiral recognition patterns in supramolecular assemblies by engineering the weak non-covalent intermolecular interactions.

Metastable order protected by destructive many-body interference

The phenomenon of metastability can shape dynamical processes on all temporal and spatial scales. Here, we induce metastable dynamics by pumping ultracold bosonic atoms from the lowest band of an optical lattice to an excitation band, via a sudden quench of the unit cell. The subsequent relaxation process to the lowest band displays a sequence of stages, which include a metastable stage, during which the atom loss from the excitation band is strongly suppressed. Using classical-field simulations and analytical arguments, we provide an explanation for this experimental observation, in which we show that the transient condensed state of the atoms in the excitation band is a dark state with regard to collisional decay and tunneling to a low-energy orbital. Therefore the metastable state is stabilized by destructive interference due to the chiral phase pattern of the condensed state. Our experimental and theoretical study provides a detailed understanding of the different stages of a paradigmatic example of many-body relaxation dynamics.

Chiral and non-centrosymmetric effects on the nonlinear wave propagation characteristics of architectured cellular materials

ABSTRACT In the current work, we study the role of chirality and non-centrosymmetry on the nonlinear wave propagation characteristics of periodic architectured media. The considered nonlinearities arise from the higher-order inner element kinematics of the periodic media and are therefore directly related to its structural pattern. Regarding centrosymmetric designs, the frequency corrections obtained -in the context of the Lindstedt-Poincare method- suggest that chiral architectures are more sensitive to inner kinematic nonlinearities than well-known, achiral lattice designs. In particular, for hexachiral lattice designs, non-negligible frequency corrections are obtained, not only for the primal eigenmode, but also for higher-order modes, extensively modifying the linear band diagram structure. To the contrary, for achiral, triangular and square lattice designs, inner kinematic nonlinearities mainly influence the primal, lowest eigenmode, with the higher-order modes to remain practically unaffected. Non-centrosymmetric inner designs modify the linear and nonlinear wave propagation material attributes both for chiral and achiral lattice patterns. However, the frequency ranges affected are strongly lattice dependent, with hexachiral and triangular lattices to be primarily influenced in their high frequency range, contrary to square lattices, which are mainly affected in their low frequency region.

Interpretation of chiral symmetry breaking and octupole correlations in Cs124 by the reflection-asymmetric triaxial particle rotor model

The positive-parity doublet bands with configuration $\ensuremath{\pi}{h}_{11/2}\ensuremath{\bigotimes}\ensuremath{\nu}{h}_{11/2}$ and negative-parity bands with $\ensuremath{\pi}{h}_{11/2}\ensuremath{\bigotimes}\ensuremath{\nu}({g}_{7/2}{d}_{5/2})$ observed in $^{124}\mathrm{Cs}$, and the possibility of multiple chiral doublets ($\mathrm{M}\ensuremath{\chi}\mathrm{D}$) with octupole correlations are investigated using the reflection-asymmetric triaxial particle rotor model. The calculated excitation energies, energy staggering parameters, and the electromagnetic transitional probabilities are in good agreement with the data available and satisfy the expected features of chiral doublet bands. The angular momentum geometry and its evolution with spin are studied with the angular momentum components and the azimuthal plot. In comparison with a typical chiral vibration pattern for the positive-parity doublet bands, a transient static chirality around $I=12\ensuremath{\hbar}$ is shown for the calculated negative-parity doublet bands.

Controllable propagation and transformation of chiral intensity field at focus.

As an intrinsic feature of the optical field, chirality could induce many novel phenomena due to the interaction between chiral light and matter. Thus, the generation of optical fields possessing 2D or 3D chiral intensity patterns, called chiral intensity fields, has been widely studied. However, the control of chiral intensity field along the optical axis is still a challenge. Here, we propose a method to manipulate the axial propagation property of a focused chiral intensity field. Two modulation effects are realized: extended chiral intensity field with a focal depth >2λ at 90% mode correlation and tunable transformation of chirality during the axial propagation. This method is simple, stable, and easy to perform and therefore offers broad applications especially in optical tweezers and metamaterial fabrication.

Pattern Formation and Defect Ordering in Active Chiral Nematics.

Many biological systems display intriguing chiral patterns and dynamics. Here, we present an active nematic theory accounting for individual spin to explore the collective handedness in chiral rod-shaped aggregations. We show that coordinated individual spin and motility can engender a vortex-array pattern with chirality and drive ordering of topological defects. During this chiral process, the stationary trefoil-like defects self-organize into a periodic, hexagon-dominated polygonal network, which segregates persistently rotating cometlike defects in pairs within each polygon, leading to a translation symmetry at the global scale while a broken reflection symmetry at the local scale. Such defect ordering agrees exactly with the Voronoi tiling of two-dimensional space and the emergence of the hexagonal symmetry is deciphered in analogy with topological charge neutralization. We calculate energy barriers to the topological transition of the defect ordering and explain the existing metastable states with nonhexagonal polygons. Our findings shed light on the chiral morphodynamics in life processes and also suggest a potential route towards tuning self-organization in active materials.

Biomimetic design of iridescent insect cuticles with tailored, self-organized cholesteric patterns

Replicating biological patterns is promising for designing materials with multifaceted properties. Twisted cholesteric liquid crystal patterns are found in the iridescent tessellated cuticles of many insects and a few fruits. Their accurate replication is extremely difficult since discontinuous patterns and colors must coexist in a single layer without discontinuity of the structures. Here, a solution is demonstrated by addressing striped insect cuticles with a complex twisted organization. Geometric constraints are met by controlling the thermal diffusion in a cholesteric oligomer bilayer subjected to local changes in the molecular anchoring conditions. A multicriterion comparison reveals a very high level of biomimicry. Proof-of-concept prototypes of anti-counterfeiting tags are presented. The present design involves an economy of resources and a high versatility of chiral patterns unreached by the current manufacturing techniques such as metallic layer vacuum deposition, template embossing and various forms of lithography which are limited and often prohibitively expensive.

Multiparameter Controllable Chiral Optical Patterns

We demonstrate a method to generate multiparameter controllable chiral optical patterns. In the method, we introduce a phase calculation method of the rotation matrix and the transformation matrix. The controllable characteristics of the chiral optical patterns, which are generated by an annular subzone vortex phase plate, are demonstrated. The direction and spatial distribution of the eccentricity of the generated optical patterns can be freely regulated. The restriction on the direction of a chiral optical pattern by the single phase gradient (\ifmmode\pm\else\textpm\fi{}\ensuremath{\Delta}l) of an annular subzone vortex is solved. A chiral optical pattern is modulated by using the light-field superposition and phase shift, which is experimentally achieved by a spatial light modulator. The numerical and experimental results indicate that the controllable degrees of freedom are as many as five, namely, shape, size, direction, eccentricity, and number of arrays. Furthermore, we analyze the spatial propagation of the controllable chiral optical patterns in turbulence. The generation of chiral optical patterns has great potential application in optical tweezers, optical micromechanics, chiral microstructure fabrication, rotating microscopic illumination, and so on.

Handedness-dependent quasiparticle interference in the two enantiomers of the topological chiral semimetal PdGa

It has recently been proposed that combining chirality with topological band theory results in a totally new class of fermions. Understanding how these unconventional quasiparticles propagate and interact remains largely unexplored so far. Here, we use scanning tunneling microscopy to visualize the electronic properties of the prototypical chiral topological semimetal PdGa. We reveal chiral quantum interference patterns of opposite spiraling directions for the two PdGa enantiomers, a direct manifestation of the change of sign of their Chern number. Additionally, we demonstrate that PdGa remains topologically non-trivial over a large energy range, experimentally detecting Fermi arcs in an energy window of more than 1.6 eV that is symmetrically centered around the Fermi level. These results are a consequence of the deep connection between chirality in real and reciprocal space in this class of materials, and, thereby, establish PdGa as an ideal topological chiral semimetal.

Multi-Step Crystallization of Self-Organized Spiral Eutectics.

A method for the solidification of metallic alloys involving spiral self-organization is presented as a new strategy for producing large-area chiral patterns with emergent structural and optical properties, with attention to the underlying mechanism and dynamics. This study reports the discovery of a new growth mode for metastable, two-phase spiral patterns from a liquid metal. Crystallization proceeds via a non-classical, two-step pathway consisting of the initial formation of a polytetrahedral seed crystal, followed by ordering of two solid phases that nucleate heterogeneously on the seed and grow in a strongly coupled fashion. Crystallographic defects within the seed provide a template for spiral self-organization. These observations demonstrate the ubiquity of defect-mediated growth in multi-phase materials and establish a pathway toward bottom-up synthesis of chiral materials with an inter-phase spacing comparable to the wavelength of infrared light. Given that liquids often possess polytetrahedral short-range order, our results are applicable to many systems undergoing multi-step crystallization.

Generation of optical chirality patterns with plane waves, evanescent waves and surface plasmon waves.

We systematically investigate the generation of optical chirality patterns by applying the superposition of two waves in three scenarios, namely free-space plane waves, evanescent waves of totally reflected light at dielectric interface and propagating surface plasmon waves on a metallic surface. In each scenario, the general analytical solution of the optical chirality pattern is derived for different polarization states and propagating directions of the two waves. The analytical solutions are verified by numerical simulations. Spatially structured optical chirality patterns can be generated in all scenarios if the incident polarization states and propagation directions are correctly chosen. Optical chirality enhancement can be obtained from the constructive interference of free-space circularly polarized light or enhanced evanescent waves of totally reflected light. Surface plasmon waves do not provide enhanced optical chirality unless the near-field intensity enhancement is sufficiently high. The structured optical chirality patterns may find applications in chirality sorting, chiral imaging and circular dichroism spectroscopy.

Membrane active Janus-oligomers of β3-peptides.

Self-assembling peptides offer a versatile set of tools for bottom-up construction of supramolecular biomaterials. Among these compounds, non-natural peptidic foldamers experience increased focus due to their structural variability and lower sensitivity to enzymatic degradation. However, very little is known about their membrane properties and complex oligomeric assemblies - key areas for biomedical and technological applications. Here we designed short, acyclic β3-peptide sequences with alternating amino acid stereoisomers to obtain non-helical molecules having hydrophilic charged residues on one side, and hydrophobic residues on the other side, with the N-terminus preventing formation of infinite fibrils. Our results indicate that these β-peptides form small oligomers both in water and in lipid bilayers and are stabilized by intermolecular hydrogen bonds. In the presence of model membranes, they either prefer the headgroup regions or they insert between the lipid chains. Molecular dynamics (MD) simulations suggest the formation of two-layered bundles with their side chains facing opposite directions when compared in water and in model membranes. Analysis of the MD calculations showed hydrogen bonds inside each layer, however, not between the layers, indicating a dynamic assembly. Moreover, the aqueous form of these oligomers can host fluorescent probes as well as a hydrophobic molecule similarly to e.g. lipid transfer proteins. For the tested, peptides the mixed chirality pattern resulted in similar assemblies despite sequential differences. Based on this, it is hoped that the presented molecular framework will inspire similar oligomers with diverse functionality.

Accurate chiral pattern recognition for amines from just a single chemosensor

The current work proposes a novel method for accurate pattern recognition of (mono- and di-) amines and determination of enantiomeric excess (ee) using molecular self-assembly.

Dynamic Spirals of Nanoparticles in Light-Responsive Polygonal Fields.

Nanoparticles tend to aggregate once integrated into soft matter and consequently, self-assembling nanoparticles into large-scale, regular, well-defined, and ultimately chiral patterns remains an ongoing challenge toward the design and realization of organized superstructures of nanoparticles. The patterns of nanoparticles that are reported in liquid crystals so far are all static, and this lack of responsiveness extends to assemblies of nanoparticles formed in topological singularities and other localized structures of anisotropic matter. Here, it is shown that gold nanoparticles form spiral superstructures in polygonal fields of cholesteric liquid crystals. Moreover, when the cholesteric liquid crystals incorporate molecular photoswitches in their composition, the pitch of the nanoparticulate spirals follows the light-induced reorganization of the cholesteric liquid crystals. These experimental findings indicate that chiral liquid crystals can be used as chiral and dynamic templates for soft photonic nanomaterials. Controlling the geometry of these spirals of nanoparticles will ultimately allow modulating the plasmonic signature of hybrid and chiral systems.

Concept of chiral image storage and selection based on liquid crystals by circular polarization.

We demonstrate a liquid crystal (LC)-based optical device with the polarization switching capability, which can store two different chiral images to be selected according to the polarization state of the viewing polarizer. The chiral dual-image device consists of chiral surface patterns for image storage and the LC layer as a tunable phase retarder. Each chiral surface pattern behaves as a helical photonic crystal that reflects circularly polarized light at a specific wavelength. Depending on the applied voltage across the LC layer, either a right-handed or a left-handed circular polarization image appears, and thus one of the two stored images can be selectively read by the polarization state. Our concept of the LC-based chiral image storage and selection provides simplicity in fabrication, flexibility in design, and high optical efficiency. It will be directly applicable for reflective-type 3D displays, color filters, and anti-counterfeiting devices.

Helicoidal Patterning of Nanorods with Polymer Ligands.

Chiral packing of ligands on the surface of nanoparticles (NPs) is of fundamental and practical importance, as it determines how NPs interact with each other and with the molecular world. Herein, for gold nanorods (NRs) capped with end-grafted nonchiral polymer ligands, we show a new mechanism of chiral surface patterning. Under poor solvency conditions, a smooth polymer layer segregates into helicoidally organized surface-pinned micelles (patches). The helicoidal morphology is dictated by the polymer grafting density and the ratio of the polymer ligand length to nanorod radius. Outside this specific parameter space, a range of polymer surface structures was observed, including random, shish-kebab, and hybrid patches, as well as a smooth polymer layer. We characterize polymer surface morphology by theoretical and experimental state diagrams. The helicoidally organized polymer patches on the NR surface can be used as a template for the helicoidal organization of other NPs, masked synthesis on the NR surface, as well as the exploration of new NP self-assembly modes.

Helicoidal Patterning of Nanorods with Polymer Ligands

AbstractChiral packing of ligands on the surface of nanoparticles (NPs) is of fundamental and practical importance, as it determines how NPs interact with each other and with the molecular world. Herein, for gold nanorods (NRs) capped with end‐grafted nonchiral polymer ligands, we show a new mechanism of chiral surface patterning. Under poor solvency conditions, a smooth polymer layer segregates into helicoidally organized surface‐pinned micelles (patches). The helicoidal morphology is dictated by the polymer grafting density and the ratio of the polymer ligand length to nanorod radius. Outside this specific parameter space, a range of polymer surface structures was observed, including random, shish‐kebab, and hybrid patches, as well as a smooth polymer layer. We characterize polymer surface morphology by theoretical and experimental state diagrams. The helicoidally organized polymer patches on the NR surface can be used as a template for the helicoidal organization of other NPs, masked synthesis on the NR surface, as well as the exploration of new NP self‐assembly modes.

Chiral-Icosahedral ( I) Symmetry in Ubiquitous Metallic Cluster Compounds (145A,60X): Structure and Bonding Principles.

There exists a special kind of perfection-in symmetry, simplicity, and stability-attainable for structures generated from precisely 60 ligands (all of a single type) that protect 145 metal-atom sites. The symmetry in question is icosahedral ( Ih), generally, and chiral icosahedral ( I) in particular. A 60-fold equivalence of the ligands is the smallest number to allow this kind of perfection. Known cluster compounds that approximate this structural ideal include palladium-carbonyls, Ih-Pd145(CO)60; gold-thiolates, I-Au144(SR)60; and gold-alkynyls, I-Au144(C2R)60. Many other variants are suspected. The Pd145 compound established the basic achiral structure-type. However, the Au144-thiolate archetype is prominent, historically in its abundance and ease of preparation and handling, in its proliferation in many laboratories and application areas, and ultimately in the intrinsic chirality of its geometrical structure and organization of its bonding network or connectivity. As discovered by mass spectrometry (the "30-k anomaly") in 1995, it appeared as a broad single peak, as solitary and symmetrical as Mount Fuji, centered near 30 kDa (∼150 Au atoms), provoking these thoughts: Surely this phenomenon requires a unique explanation. It appears to be the Buckminsterfullerene (carbon-60) of gold-cluster chemistry. Herein we provide an elementary account of the unexpected discovery, in which the Pd145-structure played a critical role, that led to the identification and prediction, in 2008, of a fascinating new molecular structure-type, evidently the first one of chiral icosahedral symmetry. Rigorous confirmation of this prediction occurred in early spring 2018, when two single-crystal X-ray crystallography reports were submitted, each one distinguishing both enantiomeric structures and noting profound chirality for the surface (ligand) layer. The emphasis here is on the structure and bonding principles and how these have been elucidated. Our aim has been to present this story in simplest terms, consistent with the radical simplicity of the structure itself. Because it combines intrinsic profound chirality, at several levels, with the highest possible symmetry-type (icosahedral), the structure may attract broader interest also from educators, especially if studied in tandem with the analysis of hollow (shell) metallic systems that exhibit the same chirality and symmetry. Because the shortest (stiffest) bonds follow the chiral 3-way weave pattern of the traditional South-Asian reed football, this cultural artifact may be used to introduce chiral-icosahedral symmetry in a pleasant and memorable way. One may also appreciate easily the bonding and excitations in I-symmetry metallic nanostructures via the golden fullerenes, that is, the proposed hollow Au60,72 spheres. Beyond any aesthetic or pedagogical value, we aim that our Account may provide a firm foundation upon which others may address open questions and the opportunities they present. This Account can scarcely hint at the prospects for further fundamental understanding of these compounds, as well as a widening sphere of applications (chemical, electronic, imaging). The compounds remain crucial to a wider field presently under intense development.

Equivalent beam model of SWNT and DWNT with imperfections

The influence of the carbon nanotube’s characteristics on the mechanical properties of nanocomposites has been, and still is the subject of a large number of scientific papers. The numerical method approach for modelling the carbon nanotubes and nanocomposite materials is proven and effective, but nevertheless has some disadvantages. Also, different defects within carbon nanotubes structure, like vacancies, as well as the waviness of the nanotubes, considerably influence the mechanical properties of the nanotubes and thus deteriorate the final mechanical properties of the nanocomposites. The paper at hand presents and examines the equivalent beam finite element model of single and double walled carbon nanotubes of different patterns, based on the data obtained by structural mechanics FEM model from authors’ previous works. Several examples of armchair and zig-zag pattern for single walled carbon nanotube and armchair, zig – zag and two chiral patterns for double walled carbon nanotubes, with different vacancies and waviness ratio, are prepared and examined.

Magnetic Helicity Condensation and the Solar Cycle

Abstract Solar filaments exhibit a global chirality pattern where dextral/sinistral filaments, corresponding to negative/positive magnetic helicity, are dominant in the northern/southern hemisphere. This pattern is opposite to the sign of magnetic helicity injected by differential rotation along east–west oriented polarity inversion lines, posing a major conundrum for solar physics. A resolution of this problem is offered by the magnetic helicity-condensation model of Antiochos. To investigate the global consequences of helicity condensation for the hemispheric chirality pattern, we apply a temporally and spatially averaged statistical approximation of helicity condensation. Realistic magnetic field configurations in both the rising and declining phases of the solar cycle are simulated. For the helicity-condensation process, we assume convective cells consisting of positive/negative vorticities in the northern/southern hemisphere that inject negative/positive helicity. The magnitude of the vorticity is varied as a free parameter, corresponding to different rates of helicity injection. To reproduce the observed percentages of dominant and minority filament chiralities, we find that a vorticity of magnitude 2.5 × 10−6 s−1 is required. This rate, however, is insufficient to produce the observed unimodal profile of chirality with latitude. To achieve this, a vorticity of at least 5 × 10−6 s−1 is needed. Our results place a lower limit on the small-scale helicity injection required to dominate differential rotation and reproduce the observed hemispheric pattern. Future studies should aim to establish whether the helicity injection rate due to convective flows and/or flux emergence across all latitudes of the Sun is consistent with our results.