Chiral Topology Research Articles

Chiral topologies for composite morphing structures – Part I: Development of a chiral rib for deformable airfoils

The paper moves from a technological process developed in previous works to produce chiral honeycombs made of thin composite laminates. Such approach is applied in this work to manufacture the morphing ribs for a variable camber wing‐box. The specifications for such components are obtained by developing a finite element model of a demonstrator, which is designed taking into account aeroelastic performances, structural, and technological issues. In the first part of the paper, the design of such a demonstrator is presented and the role of composite chiral ribs with auxetic behavior is outlined. Production, testing, and numerical studies of manufacturing trials are performed to assess the technological process applied to small‐sized chiral units made of different materials, to investigate their mechanical properties, and to validate a numerical approach for design and analysis. A complete chiral composite rib is then produced and tests are carried out to verify the overall structural response and to validate the numerical approach.

Chiral topologies for composite morphing structures – Part II: Novel configurations and technological processes

The article presents the advancements in the technological processes developed to produce chiral honeycombs made of thin composite laminates. An original technological process, which was applied to produce chiral components for aerospace morphing structures, is critically analysed and a new approach is proposed. The objective of such approach is the production of thin‐walled chiral composite structures with enhanced strength properties by using a more feasible technology. According to the new methodology, chiral honeycombs with polygonal nodes are obtained by assembling thin‐walled prismatic composite tubes. Numerical models are developed to investigate the behaviour of such topologies. A comparison with the performances of chiral honeycombs with cylindrical nodes is presented, showing that the new configuration can provide negative Poisson's ratios that tend to the theoretical limit of −1 as the stiffness of the polygonal nodes is increased. Thereafter, a method to fill partially the nodes is proposed and numerically assessed, to enhance at the same time the auxetic behaviour and the mechanical properties of the chiral honeycomb. Finally a complete manufacturing process is developed. Hexa‐chiral structural units are manufactured and subsequently tested to assess the auxetic response. Results are in acceptable agreement with numerical predictions and indicate that the novel technological route provides a significant contribution for the application of composite chiral honeycomb to morphing structures.

Homochiral Metal–Organic Framework with Intrinsic Chiral Topology and Helical Channels

Presented here is an unusual microporous metal–organic framework (FIR-30) integrating helical channels, intrinsical chirality, and permanent porosity. The structure of FIR-30 containing three types of cages has two interpenetrating helical channel systems with opposite handedness, which can be considered a surface with the same topology as gyroid, and the generation of chirality is related with the intrinsically chiral topology of FIR-30. The results provide new insight toward the construction of chiral MOFs with helical channels.

Quantum resistor-capacitor circuit with Majorana fermion modes in a chiral topological superconductor.

We investigate the mesoscopic resistor-capacitor circuit consisting of a quantum dot coupled to spatially separated Majorana fermion modes in a chiral topological superconductor. We find substantially enhanced relaxation resistance due to the nature of Majorana fermions, which are their own antiparticles and are composed of particle and hole excitations in the same abundance. Further, if only a single Majorana mode is involved, the zero-frequency relaxation resistance is completely suppressed due to a destructive interference. As a result, the Majorana mode opens an exotic dissipative channel on a superconductor which is typically regarded as dissipationless due to its finite superconducting gap.

On chiral symmetry breaking, topology and confinement

We start with the relation between the chiral symmetry breaking and gauge field topology. New lattice result further enhance the notion of Zero Mode Zone, a very narrow strip of states with quasizero Dirac eigenvalues. Then we move to the issue of "origin of mass" and Brown-RHo scaling: a number of empirical facts contradicts to the idea that masses of quarks and such hadrons as $\rho,N$ decrease near $T_c$. We argue that while at $T=0$ the main contribution to the effective quark mass is chirally odd $m_{\snchi}$, near $T_c$ it rotates to chirally-even component $m_\chi$, because "infinite clusters" of topological solitons gets split into finite ones. Recent progress in understanding of topology require introduction of nonzero holonomy $<A_0>\neq 0$, which splits instantons into $N_c$ (anti)selfdual "instanton-dyons". Qualitative progress, as well as first numerical studios of the dyon ensemble are reported. New connections between chiral symmetry breaking and confinement are recently understood, since instanton-dyons generates holonomy potential with a minimum at confining value, if the ensemble is dense enough.

Projected Entangled-Pair States Can Describe Chiral Topological States

We show that projected entangled-pair states (PEPS) in two spatial dimensions can describe chiral topological states by explicitly constructing a family of such states with a nontrivial Chern number. They are ground states of two different kinds of free-fermion Hamiltonians: (i)local and gapless; (ii)gapped, but with hopping amplitudes that decay according to a power law. We derive general conditions on topological free-fermionic projected entangled-pair states that show that they cannot correspond to exact ground states of gapped, local parent Hamiltonians and provide numerical evidence demonstrating that they can nevertheless approximate well the physical properties of topological insulators with local Hamiltonians at arbitrary temperatures.

Internally resonating lattices for bandgap generation and low-frequency vibration control

The paper reports on a structural concept for high stiffness and high damping performance. A stiff external frame and an internal resonating lattice are combined in a beam-like assembly which is characterized by high frequency bandgaps and tuned vibration attenuation at low frequencies. The resonating lattice consists of an elastomeric material arranged according to a chiral topology which is designed to resonate at selected frequencies. The concept achieves high damping performance by combining the frequency-selective properties of internally resonating structures, with the energy dissipation characteristics of their constituent material. The flexible ligaments, the circular nodes and the non-central interactions of the chiral topology lead to dynamic deformation patterns which are beneficial to energy dissipation. Furthermore, tuning and grading of the elements of the lattice allows for tailoring of the resonating properties so that vibration attenuation is obtained over desired frequency ranges. Numerical and experimental results demonstrate the tuning flexibility of this concept and suggest its potential application for load-carrying structural members parts of vibration and shock prone systems.

A 3-D open-framework material with intrinsic chiral topology used as a stationary phase in gas chromatography

Compared with liquid chromatography and capillary electrophoresis, the diversity of gas chromatography chiral stationary phases is rather limited. Here, we report the fabrication of Co(D-Cam)1/2(bdc)1/2(tmdpy) (D-Cam = D-camphoric acid; bdc = 1,4-benzenedicarboxylate; tmdpy = 4,4'-trimethylenedipyridine)-coated open tubular columns for high-resolution gas chromatographic separation of compounds. The Co(D-Cam)1/2(bdc)1/2(tmdpy) compound possesses a 3-D framework containing enantiopure building blocks embedded in intrinsically chiral topological nets. In this study, two fused-silica open tubular columns with different inner diameters and lengths, including column A (30 m × 530 μm i.d.) and column B (2 m × 75 μm i.d.), were prepared by a dynamic coating method using Co-(D-Cam)1/2(bdc)1/2(tmdpy) as the stationary phase. The chromatographic properties of the two columns were investigated using n-dodecane as the test compound at 120 °C. The number of theoretical plates (plates/m) of the two metal-organic framework columns was 1,450 and 3,100, respectively. The separation properties were evaluated using racemates, isomers, alkanes, alcohols, and Grob's test mixture. The limit of detection and limit of quantification were found to be 0.125 and 0.417 ng for citronellal enantiomers, respectively. Repeatability (n = 6) showed lower than 0.25 % relative standard deviation (RSD) for retention times and lower than 2.2 % RSD for corrected peak areas. The experimental results showed that the stationary phase has excellent selectivity and also possesses good recognition ability toward these organic compounds, especially chiral compounds.

Design of a Morphing Airfoil with Composite Chiral Structure

The paper presents a design study for a morphing structural concept, which could be used to obtain a passively actuated high-lift wing configuration. A composite chiral honeycomb core is used to allow large variations of camber at limited strain levels in the structure of the aerodynamic surface. The design hypothesis is first assessed bymeans of structural analyses, which are performed applying two-dimensional and three-dimensional finite elements schemes. The results confirm the morphing capabilities in the chordwise direction of the structure, which still retains noteworthy axial and torsional stiffness properties. The aeroelastic performances of the morphing airfoil are then optimized, taking into account aeroelastic stability as well as strength constraints. The optimal parameters of chiral network and the required stiffness properties of the covering skin are identified. Overall, the work confirms the promising performances of morphing structures based on chiral topologies and assesses a numerical approach for the design of morphing aerodynamic structures.

Synthesis, structure and properties of microporous metal–organic frameworks constructed from Ni(II)/Cd(II), Tpt and H4bpta

Abstract Two new three-dimensional (3D) porous metal-organic frameworks, [Ni(tpt)2/3(bpta)1/4(H2O)2(OH)]⋅solve (1) and [Cd(tpt)(H2bpta)]⋅solve (2) (tpt = 2,4,6-tris(4-pyridyl)-1,3,5-triazine, H4bpta = (1,1'-biphenyl)-2,2',6,6'-tetracarboxylic acid) have been prepared, and characterized by single-crystal X-ray diffraction, IR spectra, PXRD, and TG analysis. The results show that complex 1 has a 3D bor network structure with 56.9% solvent-accessible volume, and 2 reveals a novol 3,5-coordinated chiral topology with vertex symbol (4.72)(43.62.74.8) and 52.5% accessible void in the structure. Moreover, gas adsorption properties of desolvated 1 and 2 were investigated.

Ridge-Tile-like Chiral Topology: Synthesis, Resolution, and Complete Chiroptical Characterization of Enantiomers of Edge-Sharing Binuclear Square Planar Complexes of Ni(II) Bearing Achiral Ligands

Binuclear square planar Ni(II) complexes are described, formed by two tridentate ligands with two imine-nitrogens coordinating two nickel atoms. Such complexes are synthetically readily available with great structural variety and present new types of ridge-tile-like chiral compounds that are reasonably stable in the appropriate "bent" conformation. Enantiomerically pure samples of these compounds have been obtained for the first time using HPLC with a chiral stationary phase. Absolute configurations and chiroptical properties are fully characterized by ECD, VCD, ORD spectroscopy, and theoretical calculations. These new compounds with ridge-tile-like chiral topology are configurationally reasonably stable [DeltaG(double dagger) = 121.4 kJ mol(-1), t(1/2) = 14.9 h (78 degrees C, ethanol)], and therefore their chemistry, physical properties, and applications can be systematically studied.

Assembly of Two Metal−Organic Frameworks with Intrinsic Chiral Topology from Achiral Materials

The assembly of Cu(CH3COO)2·H2O and pyridine-4,5-imidazoledicarboxylic acid (H3PyImDC) under solvothermal conditions in the presence of different organic templates yielded two three-dimensional chiral frameworks, |(C3H10N2)(C3H7NO)0.5(H2O)2|[CuIIC10H5O4N3] (1) and |(C4H9NO)0.5(H2O)8|[CuII2CuI(C10H5O4N3)2(C10H6O4N3)] (2). Both of the compounds crystallized in the cubic, P4332 space group and possessed open helical channels in the frameworks. To the best of our knowledge, compounds 1 and 2 present the first synthesized MOFs with a bmn and lcy-a net. Further characterization of the two compounds has been performed, including X-ray powder diffraction, inductively coupled plasma analysis, CHN, IR spectra, fluorescence spectra, X-ray photoelectron spectroscopy spectrum and thermogravimetric-differential thermal analysis.

Composite chiral structures for morphing airfoils: Numerical analyses and development of a manufacturing process

This paper investigates complex composite cellular structures featuring a chiral topology with the ability to undergo large overall displacements with limited straining of its components. Numerical analyses are performed to exploit such properties in the design of a morphing airfoil. The advantages associated with the use of composites are investigated by comparing the numerical results with those obtained with a metallic structure. A manufacturing process is then developed to assemble the considered structural configurations using composite materials. The novel process developed is described as applied to the manufacturing of macro chiral components that are tested to evaluate their ability to undergo large deformations. Finally, detailed numerical models of the manufactured structures are presented as a possible approach to evaluate the strength of the proposed configuration.

New (3,4)-connected intrinsically chiral topology observed in a homochiral coordination polymer from achiral precursors

An unpredicted (3,4)-connected topology with intrinsic chirality presented in a homochiral coordination polymer [Cu2(L)CN]n (1; L = 5-(4-pyridyl)tetrazole) was first shown here, which reveals a new possibility for the construction of lowly-connected chiral framework materials with potential applications.

Integrated Molecular Chirality, Absolute Helicity, and Intrinsic Chiral Topology in Three-Dimensional Open-Framework Materials

While chiral materials are common, few are known that integrate molecular chirality, absolute helicity, and 3-D intrinsically chiral topological nets in one material. Such multihomochiral features may lead to enhanced chiral recognition processes that are important for enantioselective catalysis or separation. Reported here are a series of 3-D open-framework materials with unusual integration of various homochiral and homohelical features, even in the bulk sample.

Multiple functions of ionic liquids in the synthesis of three-dimensional low-connectivity homochiral and achiral frameworks.

Multiple functions of ionic liquids in the synthesis of three-dimensional low-connectivity homochiral and achiral frameworks.

Numerical and experimental analysis of the static compliance of chiral truss-core airfoils

This paper presents an innovative wing profile featuring an internal truss-like structure of chiral topology. The chiral design is selected because of its unique deformation characteristics, which produce a theoretical, in-plane Poisson's ratio of -1. Such a Poisson's ratio yields a very high shear modulus, which in principle does not require the wing profile to be defined by a closed section or stressed-skin configuration. In addition, the peculiar deformation mechanism of the chiral configuration allows large decambering deflections to occur, with all the members of assembly behaving within the linear range of the material. Hence the proposed design combines large chordwise compliance and large in-plane shear stiffness. Such conflicting mechanical properties can be achieved through the proper selection of a limited number of geometric parameters defining the core configuration. The objective of the paper is to investigate the compliance characteristics of the airfoil. Two-dimensional profiles, designed according to results from previous investigations, are manufactured and tested to assess compliance and evaluate decambering deflection limits. The experimental analysis is guided by numerical models that account for deviations from the ideal configuration due to manufacturing limitations. Numerical and experimental results demonstrate the influence of core geometry on the compliance and confirm the ability of chiral-core airfoils to sustain large deflections while not exceeding yield strain limits.

Smart shape memory alloy chiral honeycomb

An auxetic (or negative Poisson's ratio) material expands in all directions when pulled in only one, behaving in an opposite way compared with “classical” materials. A structure not super-imposable with its mirror image is defined as chiral. A chiral structural honeycomb (noncentresymmetric) features auxeticity, i.e., a negative Poisson's ratio behaviour in the plane. Although chirality is common in nature and organic chemistry, it is an unusual characteristic in structural materials and components. We have manufactured truss assemblies based on cells of chiral honeycomb topology using shape memory alloy (SMA) ribbons as core material. The main objective of this work is to obtain a new functional structure combining the chiral honeycomb topology and shape memory alloys as a new concept of smart cellular solid. The chiral SMA honeycomb can be used in new types of deployable antenna reflectors, allowing the compression of the structure in a small volume of space for subsequent deployment. The new honeycomb concept could also be used in packaging applications to store strain energy during an impact loading and as a core for a sandwich structure for damping or for crashworthiness.

Asymmetric Karplus curves for the protein side-chain 3 J couplings

The standard Karplus equation for calculating 3J coupling constants from any given dihedral angle requires three empirical coefficients be determined that relate to the magnitudes of three modes of the angle dependency of 3J. Considering cosine modes only (bimodal, unimodal and baseline component), Karplus curves are generally symmetric with respect to the sign of the angle argument. Typically, their primary and secondary maxima differ in amplitude, whereas the two minima are of equal depth. However, chiral molecular topologies, such as those surrounding the main-chain and side-chain torsions in amino-acid residues, preclude, as regards substituent positioning, exact mirror-image conformations from being formed--for any given torsion-angle value. It is therefore unlikely that 3J couplings assume identical values for the corresponding positive and negative dihedral angles. This suggests that a better empirical fit of the torsion-angle dependency of 3J could be obtained when removing the constraint of symmetrically identical coupling constants. A sine term added to the Karplus equation allows independent modelling of both curve minima typically located near dihedral-angle values of +90 degrees and -90 degrees. Revisiting an extensive 3J coupling dataset previously recorded to determine the side-chain torsions chi1 in the protein flavodoxin, the asymmetric Karplus model accomplishes a more accurate fit to the experimental data. Asymmetries revealed in the angle dependencies exceed the experimental precision in determining 3J. Accounting for these effects helps improve molecular models.

Dynamic Response of Chiral Truss-core Assemblies

ABSTRACT: Periodic cellular configurations with negative Poisson's ratio have attracted the attention of several researchers because of their superior dynamic characteristics. Among the geometries with a negative Poisson's ratio, the chiral topology features localized deformed configurations when excited at one of its natural frequencies. This is of particular importance as resonance can be exploited to minimize the power required for the appearance of localized deformations, thus giving practicality to the concept. The particular nature of these deformed configurations and the authority provided by the chiral geometry suggest the application of the proposed structural configuration for the design of innovative lifting devices, such as helicopter rotor blades or airplane wings. The dynamic characteristics of chiral structures are here investigated through a numerical model and experimental investigations. The numerical formulation uses dynamic shape functions to accurately describe the behavior of the considered structural assembly over a wide frequency range. The model is used to predict frequency response functions, and to investigate the occurrence of localized deformations. Experimental tests are also performed to demonstrate the accuracy of the model and to illustrate the peculiarities of the behavior of the considered chiral structures.