Hexagonal Packing Research Articles

Crystallographic Analysis of TiO2 Polymorphism (Brookite, Anatase, Rutile)

Crystallographic analysis of three TiO2 structures shows that all of them have a rhombohedral anion sublattice close to their cubic closest packing. In brookite it competes with the hexagonal packing, and the packing of TiO6 octahedra is less regular. High symmetry of anatase and rutile is initiated by the local (cubic) symmetry of TiO6 octahedra. Cations occupy most symmetrical special positions and provide a coherent assembly of these “building units” by spreading the local symmetry over the entire structure.

Thin carbon hollow fiber membrane with Knudsen diffusion for hydrogen/alkane separation: Effects of hollow fiber module design and gas flow mode

Recovery of heavier hydrocarbons, C2~C4 olefins and paraffins, from gas streams is of great importance economically. In this study, asymmetric carbon hollow fiber membranes (CHFMs) were prepared by a one-step vacuum-assisted dip coating and pyrolysis, and investigated for H2/CO2, H2/C2H6, and H2/C3H8 separations. To increase the mechanical strength of the CHFMs, a porous alumina hollow fiber with ID/OD = 2 mm/4 mm was used as the supporting material. A solution of polyetherimide in N-methyl-2-pyrrolidone was used as the casting solution. The effects of (1) membrane preparation parameters, (2) fiber packing densities, (3) fiber packing arrangement, and (4) gas flow configuration (inside-out or outside-in) on the gas-separation performance were also investigated. The results showed that decreasing the concentration of the casting dope and the number of coating cycles was found to be the most effective approach to increase the H2 permeance, while maintaining the H2/CO2 selectivity. Further, as the fiber packing density was increased from 5.54% to 38.78% for the hexagonal packing configuration, the H2 permeance increased from 362.04 GPU to 711.61 GPU, without any decrease in the gas selectivity. The as-prepared CHFM exhibited the maximum gas permeance of 711.61 GPU for H2 and the following gas selectivity: 2.79, 4.65, and 5.34 towards H2/CO2, H2/C2H6, and H2/C3H8, respectively. The successful preparation and modularization of the CHFM is advantageous and industrially relevant for several gas-separation applications, such as H2 energy production from CO2, C2H6, and C3H8, and olefins/paraffins recovery.

Aggregation State of Residual α-Helices and Their Influence on Physical Properties of S. c. ricini Native Fiber.

Formation of the α-helical conformation in the poly-l-alanine (PA) sequence regions, subsequent structural transition to β-sheet during natural spinning, and presence of residual α-helices in Samia cynthia ricini (S. c. ricini) native silk fiber have been experimentally proven. However, the aggregation state of the residual α-helices, and their influence on the mechanical deformation behavior in native fiber remain unclear. Here we show that the α-helices form an ordered aggregation state with a hexagonal packing in the aqueous solution, some of which remain during natural spinning. X-ray scattering and differential scanning calorimetry (DSC) analyses revealed occurrence of a structural transition of the residual α-helices to the β-sheet structure, accompanied by disappearance of the plateau region in the force-strain curve, due to heat-treatment at ~220 °C. On the basis of X-ray scattering before and after tensile stretching of S. c. ricini native silk, a direct connection between the plateau region and the α-helix to β-sheet structural transition was confirmed. Our findings demonstrate the importance of the PA sequence regions in fiber structure formation and their influence on the tensile deformation behavior of S. c. ricini silk, features believed to be essentially similar in other saturniid silks. We strongly believe the residual ordered α-helices to be strategically and systematically designed by S. c. ricini silkworms to impart flexibility in native silk fiber. We anticipate that these knowledge forms a basis for fruitful strategies in the design and development of amino acid sequences for artificial silks with desired mechanical properties.

Crystal Chemical Study of Two Scandium(III) Complexes with Pivaloyltrifluoroacetone

A scandium(III) tris-(pivaloyltrifluoroacetonate) complex [Sc(ptac)3] is synthesized, purified, and characterized by the elemental analysis, IR spectroscopy, and the TG/DTA technique. The complex is a highly volatile and low-melting compound that is stable in air and to heat. Slow evaporation of the mother ethanol liquor at room temperature leads to the growth of single crystals of a mixed-ligand complex with an alcohol molecule: [Sc(EtOH)(ptac)3]. By single crystal X-ray diffraction at a temperature of 150(2) K the [Sc(ptac)3] and [Sc(EtOH)(ptac)3] structures are solved. The crystallographic data are: for C24H30F9O6Sc space group P-1, a = 9.1565(2) A, b = 9.6854(3) A, c = 17.3271(4) A, β = 79.927(1)°, V = 1465.79(7) A3, Z = 2, dcalc = 1.428 g/cm3, R = 0.041; for C26F9O7Sc space group P-1, a = 9.9376(3) A, b = 13.0243(4) A, c = 13.2743(4) A, β = 111.932°, V = 1575.85(8) A3, Z = 2, dcalc = 1.426 g/cm3, R = 0.048. Both structures are composed of neutral molecules; the metal atom coordinates six oxygen atoms of three ligands of β-diketone ([Sc(ptac)3]) and additionally an oxygen atom of the ethanol molecule ([Sc(EtOH)(ptac)3]). Tert-butyl and trifluoromethyl substituents in both complexes are oriented so that they create a facial isomer. The Sc-O distances are within 2.07–2.11 A in [Sc(ptac)3], and in [Sc(EtOH)(ptac)3] they are within 2.10–2.24 A. In the crystals of both compounds, the molecules are linked by only van der Waals interactions, forming a pseudo-layered structure with a hexagonal arrangement inside the layer. Six shortest Sc⋯Sc distances in [Sc(ptac)3] are within 8.34–10.42 A. In [Sc(EtOH)(ptac)3], a distorted hexagonal packing has an average parameter of ~9.5 A.

The Elastic Properties of Unidirectional Bamboo Fibre Reinforced Epoxy Composites

Natural fibres such as kenaf, jute, bamboo, flax and wood have been the subject of intensive researches in the area of fibre reinforced composite due to their environmental advantages of being renewable, biodegradable and sustainable. Bamboo fibre can be a good choice of natural fibre reinforcement for structural applications due to its excellent strength to weight ratio that is comparable to that of mild steel. In this study, mechanical properties of both continuous and short bamboo fibre reinforced composites are predicted using micromechanical approaches. The finite element method was used where three-dimensional micromechanical representative volume element with square and hexagonal packing geometry was implemented. The results were then compared with the findings from analytical approach that includes the rule of mixture and the Halpin-Tsai model. It was found that for all properties, the FEM and analytical methods give comparable trends of property on volume fraction plots. Furthermore, the longitudinal modulus given by all models are in excellent agreement as it increases linearly with the increase in bamboo fibre volume fraction.

Polyelectrolyte Microgels at a Liquid-Liquid Interface: Swelling and Long-Range Ordering.

In this work, we studied the behavior of charged microgels at a liquid-liquid interface by means of dissipative particle dynamics simulations with explicit electrostatic interactions; the liquids represent polar and nonpolar solvents like water and oil. The effect of the fraction of charged groups and both solvents qualities on the microgel size, shape, degree of immersion into different liquids, and 2D ordering of the microgels at the interface is studied. For the case of both athermal solvents, we demonstrated that increasing the fraction of charged units results in significant swelling of the microgel inside the polar liquid and a dramatic drop in the number of adsorbed monomer units. For the case of a bad nonpolar solvent for the polyelectrolyte microgels, they easily get detached from the surface into the polar solvent. When the opposite case of a bad polar solvent is considered (like high temperatures for thermosensitive PNIPAM- or PVCL-based microgels), the microgels demonstrate a decrease of the swelling perpendicular to the interface at low χ-values, and they start to swell into the nonpolar liquid at high χ-values. Two approaches for accounting for different dielectric permittivity of the liquids were considered: implicit and explicit ones; we obtained that the results of the two approaches were always in qualitative agreement. However, the explicit model is necessary to correctly reproduce the physics of the phenomena in certain regimes, in particular, when the charged molecules move through the interface of two liquids. Finally, the microgels ordering was studied at the liquid-liquid interface. We found that even at rather low fraction of charged monomer units the microgels exhibit an almost ideal hexagonal packing even though the average distance between the microgels centers is significantly larger than the microgel diameter, while uncharged microgels positions were completely random. This implies that the interfacial ordering can be controlled by using pH-sensitive monomer units in the microgel structure.

Assembly and Dynamic Analysis of Square Colloidal Crystals via Templated Capillary Assembly.

Capillary assembly has the ability to engineer centimeter-sized regions of discrete colloidal superstructures and microarrays. However, its use as a tool for directing crystallization of colloids into surface-bound nonclose-packed arrays is limited. Furthermore, the use of quantitative particle tracking tools to investigate evaporative assembly dynamics is rarely employed. In this contribution, we use templated capillary assembly to fabricate square-packed lattices of spherical, organosilica colloids using designed patterned boundaries. Particle tracking algorithms reveal that the assembly of square-packed regions is controlled by the interplay between confinement-driven nuclei formation and osmotic pressure-driven restructuring. We find that the incorporation of a square template increases the yield of particles bearing four nearest neighbors (Zn = 4) from 4 to 39%, obtained using a heavier and more viscous solvent. Maximal square-packed domains occur at specific initial particle concentrations (1.75-2.25 wt % or φ = 0.013-0.017), indicating that rearrangements are a function of osmotic force. We use particle tracking methods to dynamically monitor conversions between square and hexagonal packing, revealing a cyclical transition between 4 and 6 coordinated particles throughout meniscus recession. Our method is highly scalable and inexpensive and can be adapted for use with different particle sizes and compositions, as well as for targeted open-packed geometries. Our findings will inform the large area, defect-free assembly of nonclose-packed lattices of unexplored varieties that are necessary for the continued expansion of colloid-based materials with vast applications in optical electronics.

Hexagonal and Ring Packing Method for Solving Circle Packing Problem using Modified Heuristics

A heuristic technique is a perspective used for problem solving, which employs a problem specific domain knowledge which might not be optimal, but sufficient for the immediate goals. The most common heuristic is trial and error, employed everywhere and anywhere. One such application is Circle Packing Problem (CPP), which is difficult to solve as it is a NP problem which is of high theoretical and practical value. In this paper we consider uniform packing of unit circles (diameter 2) in an enclosing circle. To make this study possible a class of heuristic global optimization algorithm, the Energy Paving Algorithm and a generated Monte Carlo method were studied. The heuristics applied in this study are – ring and hexagonal. The computational effectiveness of our study has been validated against these sets of algorithms. One of the applied heuristics, Hexagon packing, being a ‘natural’ geometry showed better packing efficiency than existing literature. Our second heuristic shows, higher efficiency in terms of CPU run time but underutilized available outer area. In this study, the circles are packed in 2D which is a simplified version of the various problems existing in nature as container loading, sensor network layout which has been studied by mathematicians, computer scientists and operation researchers.

Autonomous Formation and Annealing of Colloidal Crystals Induced by Light‐Powered Oscillations of Active Particles

AbstractSelf‐organization through communication is observed in many systems throughout nature, often resulting in a collective response to a change in the environment. Herein, we demonstrate a synthetic system that exhibits chemical communication between small active and larger inactive particles which drives the reversible assembly of the latter into colloidal crystals. Specifically, we report the autonomous hexagonal packing of inert silica particles due to the oscillatory behavior of neighboring silver phosphate micromotors under UV light in the presence of hydrogen peroxide. The colloidal crystals are formed under UV illumination and relax into a disordered state when the light is turned off. Furthermore, oscillatory waves generated by the active particles cause “autonomous annealing”, or elimination of defects between crystal boundaries of the silica colloidal crystals.

Discrete element simulation of surface mechanical attrition treatment with rough-surface sonotrode

Surface mechanical attrition treatment (SMAT) is a specialized cold working method that is used to induce compressive residual stresses and refine crystalline grains at the surface of metal components. This technique is increasingly employed in different industries, and the control and optimization of the method require fundamental understanding and accurate process modelling, in particularly detailed information regarding the shot-target interaction. This paper presents a Discrete Element Method (DEM) study of the shot dynamics with rough sonotrodes. These rough surfaces are created by grouping in a hexagonal packing of identical spheres. Different roughness values are obtained by varying the sphere diameter and spacing. The coefficient of restitution (CoR) between shot and target used in our DEM simulations was obtained from Finite Element Method (FEM) simulations of multiple shot-target impacts. The DEM results are analyzed after the SMAT process has reached the steady state. The relationships between surface roughness and the resulting impact angle and velocity distributions are investigated. Furthermore, based on a parametric study, we conducted correlation analyses between processing parameters and shot dynamics, and identified key conditions, using the mechanistic models. The proposed numerical method and findings of this study could be used to tailor the SMAT processes.

Design of Asymptotically Optimal Improper Constellations With Hexagonal Packing

This paper addresses the problem of designing asymptotically optimal improper constellations with a given circularity coefficient (correlation coefficient between the constellation and its complex conjugate). The designed constellations are optimal in the sense that, at high signal-to-noise-ratio (SNR) and for a large number of symbols, yield the lowest probability of error under an average power constraint for additive white Gaussian noise channels. As the number of symbols grows, the optimal constellation is the intersection of the hexagonal lattice with an ellipse whose eccentricity determines the circularity coefficient. Based on this asymptotic result, we propose an algorithm to design finite improper constellations. The proposed constellations provide significant SNR gains with respect to previous improper designs, which were generated through a widely linear transformation of a standard $M$ -ary quadrature amplitude modulation constellation. As an application example, we study the use of these improper constellations by a secondary user in an underlay cognitive radio network.

Breaking Parallel Orientation of Rods via a Dendritic Architecture toward Diverse Supramolecular Structures

AbstractSelf‐assembled nanostructures of rod‐like molecules are commonly limited to nematic or layered smectic structures dominated by the parallel arrangement of the rod‐like components. Distinct self‐assembly behavior of four categories of dendritic rods constructed by placing a tri(hydroxy) group at the apex of dendritic oligo‐fluorenes is observed. Designed hydrogen bonding and dendritic architecture break the parallel arrangement of the rods, resulting in molecules with specific (fan‐like or cone‐like) shapes. While the fan‐shaped molecules tend to form hexagonal packing cylindrical phases, the cone‐shaped molecules could form spherical motifs to pack into various ordered structures, including the Frank–Kasper A15 phase and dodecagonal quasicrystal. This study provides a model system to engineer diverse supramolecular structures by rod‐like molecules and sheds new light into the mechanisms of the formation of unconventional spherical packing structures in soft matter.

Breaking Parallel Orientation of Rods via a Dendritic Architecture toward Diverse Supramolecular Structures.

Self-assembled nanostructures of rod-like molecules are commonly limited to nematic or layered smectic structures dominated by the parallel arrangement of the rod-like components. Distinct self-assembly behavior of four categories of dendritic rods constructed by placing a tri(hydroxy) group at the apex of dendritic oligo-fluorenes is observed. Designed hydrogen bonding and dendritic architecture break the parallel arrangement of the rods, resulting in molecules with specific (fan-like or cone-like) shapes. While the fan-shaped molecules tend to form hexagonal packing cylindrical phases, the cone-shaped molecules could form spherical motifs to pack into various ordered structures, including the Frank-Kasper A15 phase and dodecagonal quasicrystal. This study provides a model system to engineer diverse supramolecular structures by rod-like molecules and sheds new light into the mechanisms of the formation of unconventional spherical packing structures in soft matter.

The Relationship between Solid Content and Particle Size Ratio of Waterborne Polyurethane

A series of high solid content carboxylic acid/sulfonic acid waterborne polyurethanes was prepared by the emulsion dispersion method. The particle size and solid content were measured. By changing the particle size of the large particles to achieve different particle size ratios, high solid content waterborne polyurethanes were obtained at specific particle size ratios. When the particle size ratio was >7, 4–5 or 2–3, the aqueous polyurethane could reach a higher solid content (more than 56%). This indicated that solid content is related to particle size distribution in high solid content waterborne polyurethane. Moreover, the corresponding three-dimensional stacked models (simple cubic accumulation, face-centered cubic accumulation, cubic close packing and hexagonal closest packing) were established.

Finite element analysis of mechanical response of cellulosic fiber-reinforced composites

An investigation is carried out on natural cellulosic fibers which have gained interest in the composite field due to their superior specific properties as well as their eco-friendly environment character and biodegradability. A multi-scale finite element (FE) model of natural fiber composite materials is developed. The study is performed for multiple fibers in hexagonal packings with 10, 20, and 30% of fiber mass fractions. The mechanical behavior of the composite, processed by means of hand lay-up method and examined thanks to scanning electron microscopy (SEM), is simulated at macro-scale as well as mesoscopic scale. In particular, the response to tensile and three-point bending test is studied. Linear material properties are obtained by using pure strain assumptions in the implicit analysis of the composite, while the non-linear behavior and viscoelastic parameters require the explicit dynamic analysis. Simulation is performed thanks to ABAQUS finite element software. Comparison of experimental and FEM tensile and three-point bending strength shows very good agreement. From the results, it has been found that the prepared natural fiber composite materials can be used for structural engineering applications.

Parallel Volume Integral Equation Method for Two-Dimensional Elastodynamic Analysis

The parallel volume integral equation method (PVIEM) is applied for the analysis of two-dimensional elastic wave scattering problems in an unbounded isotropic solid containing various types of multiple multilayered anisotropic inclusions. It should be noted that the volume integral equation method (VIEM) does not require the use of the Green’s function for the anisotropic inclusion — only the Green’s function for the unbounded isotropic matrix is needed. A detailed analysis of the SH wave scattering problem is presented for various types of multiple multilayered orthotropic inclusions. Numerical results are presented for the elastic fields at the interfaces for square and hexagonal packing arrays of various types of multilayered orthotropic inclusions in a broad frequency range of practical interest. Standard parallel programming was used to speed up computation in the VIEM. The PVIEM enables us to investigate the effects of single/multiple scattering, fiber packing type, fiber volume fraction, single/multiple layer(s), multilayer’s shapes and geometry, isotropy/anisotropy, and softness/hardness of various types of multiple multilayered anisotropic inclusions on displacements and stresses at the interfaces of the inclusions and far-field scattering patterns. Also, powerful capabilities of the PVIEM for the analysis of general two-dimensional multiple scattering problems are investigated.

Interplay of weak noncovalent interactions in two conjugated positional isomers: A combined X-ray, optical properties and theoretical investigation

Two conjugated positional isomers {(2Z,2′Z)-3,3'-(1,4-phenylene)bis (2-(pyridin-2-yl)acrylonitrile), I and (2Z,2′Z)-2,2'-(1,4-phenylene)bis (3-(pyridin-2-yl)acrylonitrile), II} in which –CN group is attached to either first or second carbon atom of the CC unit, have been synthesized. One of the isomers I crystallized as a hydrated form. Single crystal X-ray analysis has been performed and a detailed quantitative analysis on the weak noncovalent interactions was presented. The results suggest that these three molecules showed different crystal packing. The positioning of the –CN group at different carbon atom of the CC unit in the isomers and the presence of a water molecule in the crystal lattice alters the distribution of electrostatic potentials. Lattice energy calculation revealed that a water molecule destabilizes the isomer I by 20.5 kcal mol−1 and the isomer II was found to be more stable. The energy frameworks displayed hexagonal packing for isomers I and II, but the variation in the magnitude of electrostatic and dispersion energies and the arrangement of molecules in the crystalline state. The Hirshfeld surface and QTAIM approaches were used to study the nature and the extent of different intermolecular interactions observed in these structures. The results indicated that intermolecular C–H⋯N interactions play a significant role in the stabilization and H–H bonding was also substantially contributing to the stabilization. UV–Vis spectral data were reported for I and II in solution and solid phases and showed similar optical properties.

Cd3 and Cd4 clusters in the rare earth (RE) metal-rich phases RE10OsCd3 and RE4OsCd

The rare earth-rich intermetallic compounds RE4OsCd (Gd4RhIn type, RE = La–Nd, Sm, Gd) and RE10OsCd3 (Er10FeCd3 type, RE = Y, Sm, Gd–Tm, Lu) were synthesized by induction melting of the pure elements in sealed niobium ampoules and characterized through their X-ray powder patterns. The structures of Ce4OsCd, Nd4Os0.83Cd1.17, Sm9.87OsCd3.13, and Tm9.89OsCd3.11 were refined from X-ray single crystal diffractometer data. These intermetallics are the first ternary osmium–cadmium compounds. The striking structural feature is an adamantane-like network of osmium-centered trigonal prisms in the RE4OsCd phases with Cd4 tetrahedra (308 pm Cd–Cd in Ce4OsCd) in the cavities. The RE10OsCd3 phases exhibit triangular Cd3 clusters (328 pm Cd–Cd in Sm9.87OsCd3.13) which, together with rare earth atoms, form chains of corner- and face-sharing Cd3RE tetrahedra. Further motifs are Os@RE6 trigonal prisms (TP) that are condensed to empty RE6 octahedra (O), building infinite…TP–O–O… rows in c direction. The two types of rows show the motif of a hexagonal rod packing.

A multiscale analysis of DNA phase separation: from atomistic to mesoscale level.

DNA condensation and phase separation is of utmost importance for DNA packing in vivo with important applications in medicine, biotechnology and polymer physics. The presence of hexagonally ordered DNA is observed in virus capsids, sperm heads and in dinoflagellates. Rigorous modelling of this process in all-atom MD simulations is presently difficult to achieve due to size and time scale limitations. We used a hierarchical approach for systematic multiscale coarse-grained (CG) simulations of DNA phase separation induced by the three-valent cobalt(III)-hexammine (CoHex3+). Solvent-mediated effective potentials for a CG model of DNA were extracted from all-atom MD simulations. Simulations of several hundred 100-bp-long CG DNA oligonucleotides in the presence of explicit CoHex3+ ions demonstrated aggregation to a liquid crystalline hexagonally ordered phase. Following further coarse-graining and extraction of effective potentials, we conducted modelling at mesoscale level. In agreement with electron microscopy observations, simulations of an 10.2-kb-long DNA molecule showed phase separation to either a toroid or a fibre with distinct hexagonal DNA packing. The mechanism of toroid formation is analysed in detail. The approach used here is based only on the underlying all-atom force field and uses no adjustable parameters and may be generalised to modelling chromatin up to chromosome size.

Nanopatterns with a Square Symmetry from an Orthogonal Lamellar Assembly of Block Copolymers.

A nanosquare array is an indispensable element for the integrated circuit design of electronic devices. Block copolymer (BCP) lithography, a promising bottom-up approach for sub-10 nm patterning, has revealed a generic difficulty in the production of square symmetry because of the thermodynamically favored hexagonal packing of self-assembled sphere or cylinder arrays in thin-film geometry. Here, we demonstrate a simple route to square arrays via the orthogonal self-assembly of two lamellar layers on topographically patterned substrates. While bottom lamellar layers within a topographic trench are aligned parallel to the sidewalls, top layers above the trench are perpendicularly oriented to relieve the interfacial energy between grain boundaries. The size and period of the square symmetry are readily controllable with the molecular weight of BCPs. Moreover, such an orthogonal self-assembly can be applied to the formation of complex nanopatterns for advanced applications, including metal nanodot square arrays.