Hexagonal Packing Research Articles

Multiple Linear Regression Modeling of Nanosphere Self-Assembly via Spin Coating.

Nanosphere lithography employs single- or multilayer self-assembled nanospheres as a template for bottom-up nanoscale patterning. The ability to produce self-assembled nanospheres with minimal packing defects over large areas is critical to advancing applications of nanosphere lithography. Spin coating is a simple-to-execute, high-throughput method of nanosphere self-assembly. The wide range of possible process parameters for nanosphere spin coating, however-and the sensitivity of nanosphere self-assembly to these parameters-can lead to highly variable outcomes in nanosphere configuration by this method. Finding the optimum process parameters for nanosphere spin coating remains challenging. This work adopts a design-of-experiments approach to investigate the effects of seven factors-nanosphere wt%, methanol/water ratio, solution volume, wetting time, spin time, maximum revolutions per minute, and ramp rate-on two response variables-percentage hexagonal close packing and macroscale coverage of nanospheres. Single-response and multiple-response linear regression models identify main and two-way interaction effects of statistical significance to the outcomes of both response variables and enable prediction of optimized settings. The results indicate a tradeoff between the high ramp rates required for large macroscale coverage and the need to minimize high shear forces and evaporation rates to ensure that nanospheres properly self-assemble into hexagonally packed arrays.

Ammonium Metatungstate, (NH4)6[H2W12O40]: Crystallization and Thermal Behavior of Various Hydrous Species

Various hydrous ammonium metatungstate phases (NH4)6[H2W12O40]·XH2O (AMT-X) have been obtained in the form of single crystals, using supersaturated solutions, antisolvent crystallization, and partial dehydration as strategies for crystal growth. On the basis of laboratory X-ray diffraction data, the crystal structures of the hydrous phases with X = 22, 12.5, 9.5, 8.5, 6, 4, and 2 as well of the cocrystals with X = 12-ethanol and X = 4-2acetone have been determined for the first time. AMT-22 forms the solid solution series (NH4)6–xKx[H2W12O40]·22H2O with the potassium salt (PMT-22) without a miscibility gap. Its tetragonal crystal structure shows a distorted cubic close-packed arrangement of the spherical α-Keggin-type [H2W12O40]6– anions with disordered ammonium N and water O atoms in the voids. The crystal structures of the other, less-hydrated AMT phases can be derived from distorted hexagonal rod packings of the α-Keggin anions, likewise with the cations and crystal water molecules in the voids. The thermal behavior of AMT-22 crystals reveals a quick dehydration, with AMT-9.5 as an intermediate and AMT-4 as a stable hydrate phase under ambient conditions. Upon further heating, the material decomposes with stepwise formation of AMT-2, AMT-1, AMT-0, and an amorphous phase, before orthorhombic WO3 forms above 400 °C. One of the commercially available AMT phases, “(NH4)6[H2W12O40]·XH2O” (with X = unspecified) has a water content of X = 4 but crystallizes in a structure other than AMT-4. Consequently, the 4-hydrate shows polymorphic behavior.

Re-entrant transition as a bridge of broken ergodicity in confined monolayers of hexagonal prisms and cylinders

The entropy-driven monolayer assembly of hexagonal prisms and cylinders was studied under hard slit confinement. At the conditions investigated, the particles have two distinct and dynamically disconnected rotational states: unflipped and flipped, depending on whether their circular/hexagonal face is parallel or perpendicular to the wall plane. Importantly, these two rotational states cast distinct projection areas over the wall plane that favor either hexagonal or tetragonal packing. Monte Carlo simulations revealed a re-entrant melting transition where an intervening disordered Flipped-Unflipped (FUN) phase is sandwiched between a fourfold tetratic phase at high concentrations and a sixfold triangular solid at intermediate concentrations. The FUN phase contains a mixture of flipped and unflipped particles and is translationally and orientationally disordered. Complementary experiments were conducted with photolithographically fabricated cylindrical microparticles confined in a wedge cell. Both simulations and experiments show the formation of phases with comparable fraction of flipped particles and structure, i.e., the FUN phase, triangular solid, and tetratic phase, indicating that both approaches sample analogous basins of particle-orientation phase-space. The phase behavior of hexagonal prisms in a soft-repulsive wall model was also investigated to exemplify how tunable particle–wall interactions can provide an experimentally viable strategy to dynamically bridge the flipped and unflipped states.

Emerging contact force heterogeneity in ordered soft granular media

Under external perturbations, inter-particle forces in disordered granular media are well known to form a heterogeneous distribution with filamentary patterns. Better understanding these forces and the distribution is important for predicting the collective behavior of granular media, the media second only to water as the most manipulated material in global industry. However, studies in this regard so far have been largely confined to granular media exhibiting only geometric heterogeneity, leaving the dimension of mechanical heterogeneity a rather uncharted area. Here, through a FEM contact mechanics model, we show that a heterogeneous inter-particle force distribution can also emerge from the dimension of mechanical heterogeneity alone. Specifically, we numerically study inter-particle forces in packing of mechanically heterogeneous disks arranged over either a square or a hexagonal lattice and under quasi-static isotropic compression. Our results show that, at the system scale, a hexagonal packing exhibit a more heterogeneous inter-particle force distribution than a square packing does; At the particle scale, for both packing lattices, preliminary analysis shows the consistent coexistence of outliers (i.e., softer disks sustaining larger forces while stiffer disks sustaining smaller forces) in comparison to their homogeneous counterparts, which implies the existence of nonlocal effect. Further analysis on the portion of outliers and on spatial contact force correlations suggest that the hexagonal packing shows more pronounced nonlocal effect over the square packing under small mechanical heterogeneity. However, such trend is reversed when assemblies becomes more mechanically heterogeneous. Lastly, we confirm that, in the absence of particle reorganization events, contact friction merely plays the role of packing stabilization while its variation has little effect on inter-particle forces and their distribution.

\u03a0-GISANS: probing lateral structures with a fan shaped beam

We have performed grazing incidence neutron small angle scattering using a fan shaped incident beam focused along one dimension. This allows significantly reduced counting times for measurements of lateral correlations parallel to an interface or in a thin film where limited depth resolution is required. We resolve the structure factor of iron inclusions in aluminium oxide and show that the ordering of silica particles deposited on a silicon substrate depends on their size. We report hexagonal packing for 50 nm but not for 200 nm silica spheres deposited by a modified Langmuir-Schaefer method on a silicon substrate. For the 200 nm particles we extract the particles shape from the form factor. Moreover, we report dense packing of the particles spread on a free water surface. We name this method π-GISANS to highlight that it differs from GISANS as it gives lateral information while averaging the in-depth structure.

A Reinterpretation of Evidence for the Endothelial Glycocalyx Filtration Structure.

The endothelial glycocalyx (eGlx) is thought to be the primary macromolecular filter for fluid flux out of the vasculature. This filter maintains the higher protein concentration within the vessel lumen relative to the tissue. Whilst the arguments for the eGlx being the size filter are convincing the structural evidence has been limited to specialized stains of perfusion fixed tissue, which are further processed for resin embedding for transmission electron microscopy. The staining and processing of the delicate pore structure has left many researchers struggling to interpret the observed surface coat. Previous work has alluded to a 19.5 nm spacing between fibers; however, whilst repeatable it does not give an eGlx pore size consistent with known glycosaminoglycan (GAG) molecular structure due to the required fiber thickness of >10 nm. Here a new interpretation is proposed based on the likelihood that the electron micrographs of are often of collapsed eGlx. The 19.5 nm spacing measured may therefore be the core protein of the proteoglycans (PGs) with the GAGs wrapped up around them rather than in an expanded in vivo state. The concept is explored to determine that this is indeed consistent with experimental measurements of permeability if the syndecans are predominately dimerized. Further an alteration of core protein lattice from hexagonal packing to square packing dramatically changes the permeability which could be facilitated via known mechanisms such as transient actin binding.

Chiral V‐shaped Pyrenes: Hexagonal Packing, Superhelix, and Amplified Chiroptical Performance

AbstractHere, we designed symmetric and dissymmetric chiral V‐shaped pyrenes by linking achiral pyrenes to trans‐1,2‐cyclohexane diamine scaffolds with varied spacers to investigate their circular dichroism (CD) and circularly polarized excimer emission (CPEE). In molecular solution, the symmetric V‐shaped molecules (P1, P2, P3) displayed spacer‐dependent CD and CPEE originating from the intramolecular excimers while the dissymmetric V‐shaped B was silent in CD and CPEE. Upon self‐assembly, the chiral V‐shaped conformation guided a helical hexagonal packing. Notably, P1 self‐assembled into delicate superhelices with optimum chiroptical activities and the largest gCD for pyrene derivatives to date. The dissymmetric B formed two distinct hexagonal aggregates as twists and rectangular nanotubes with greatly amplified CPEE. This work demonstrates unprecedented hexagonal superhelices from chiral V‐shaped scaffolds and provides a deep insight into the relationship between molecular conformation, supramolecular architectures, and their chiroptical performance.

Chiral V-shaped Pyrenes: Hexagonal Packing, Superhelix, and Amplified Chiroptical Performance.

Here, we designed symmetric and dissymmetric chiral V-shaped pyrenes by linking achiral pyrenes to trans-1,2-cyclohexane diamine scaffolds with varied spacers to investigate their circular dichroism (CD) and circularly polarized excimer emission (CPEE). In molecular solution, the symmetric V-shaped molecules (P1, P2, P3) displayed spacer-dependent CD and CPEE originating from the intramolecular excimers while the dissymmetric V-shaped B was silent in CD and CPEE. Upon self-assembly, the chiral V-shaped conformation guided a helical hexagonal packing. Notably, P1 self-assembled into delicate superhelices with optimum chiroptical activities and the largest gCD for pyrene derivatives to date. The dissymmetric B formed two distinct hexagonal aggregates as twists and rectangular nanotubes with greatly amplified CPEE. This work demonstrates unprecedented hexagonal superhelices from chiral V-shaped scaffolds and provides a deep insight into the relationship between molecular conformation, supramolecular architectures, and their chiroptical performance.

Synthesis and surface properties of amphiphilic copolymer consisting of hydrophobic perfluorocarbon and hydrophilic zwitterionic blocks

Amphiphilic copolymers are receiving increasing attention due to their special features in solubility and self-assembling. Random and block copolymers containing superhydrophobic 2-perfluorooctylethyl acrylate (FA-C8) and superhydrophilic 3-[dimethyl (2′-methacryloyloxyethyl) ammonio] propanesulfonate (MAPS) segments were designed and synthesized in this work, namely PFA-C8-b-PMAPS and P(FA-C8-ran-MAPS). Synthesized polymers were characterized by 1H nuclear magnetic resonance and differential scanning calorimetry (DSC) measurements, proving the achievement of copolymers without residual PFA-C8. The molecular aggregation structure of FA-C8 in PFA-C8-b-PMAPS and P(FA-C8-ran-MAPS) was revealed by DSC and wide-angle X-ray diffraction measurements. On one hand, the PFA-C8 segments in P(FA-C8-b-MAPS) formed hexagonal packing with lamellar structures. On the other hand, although the lamellar structure is not observed in P(FA-C8-ran-MAPS) samples, the hexagonal packing of FA-C8 exhibited higher thermal stability than that of those in the PFA-C8 sample. Moreover, the polymeric film of P(FA-C8-ran-MAPS) exhibited strong oleophobicity under both air and water conditions.

Ion-dependent DNA configuration in bacteriophage capsids

Bacteriophages densely pack their long double-stranded DNA genome inside a protein capsid. The conformation of the viral genome inside the capsid is consistent with a hexagonal liquid crystalline structure. Experiments have confirmed that the details of the hexagonal packing depend on the electrochemistry of the capsid and its environment. In this work, we propose a biophysical model that quantifies the relationship between DNA configurations inside bacteriophage capsids and the types and concentrations of ions present in a biological system. We introduce an expression for the free energy that combines the electrostatic energy with contributions from bending of individual segments of DNA and Lennard-Jones-type interactions between these segments. The equilibrium points of this energy solve a partial differential equation that defines the distributions of DNA and the ions inside the capsid. We develop a computational approach that allows us to simulate much larger systems than what is possible using the existing molecular-level methods. In particular, we are able to estimate bending and repulsion between the DNA segments as well as the full electrochemistry of the solution, both inside and outside of the capsid. The numerical results show good agreement with existing experiments and with molecular dynamics simulations for small capsids.

Influence of molecular architecture, hydrogen bonding, chemical moieties and flexible chain for smectic polymorphism in (4)EoBD(3)AmBA:nOBAs

A novel series of calamitic, complementary hydrogen-bonded (HB), meta-extended Schiff base core containing liquid crystalline (LC) complexes with ethoxy chain at one end and varied flexible chain at other end, viz., (4)EoBD(3)AmBA:nOBAs for n = 3–12 is reported. 1H, 13C NMR and FTIR spectroscopy confirm complex formation. LC phases, phase transition temperatures (T C) and enthalpy are characterized by polarizing optical microscopy and differential scanning calorimetry(DSC). SmA, SmC, SmBcryst,SmF, SmI, SmE, SmG and SmH phases are exhibited. Clearing and melting temperatures exhibit odd–even effect. Schiff base bridged by oxygen atom promoted of smectic phase occurrence. Complementary HB-induced and -enhanced tilted smectic phase range. Large LC phase variants, i.e., tetra, penta and hexa are observed. Hexa LC phase variant for n = 6 and 12. Unlike in p-n-alkoxy benzoic acids (nOBAs), Nematic phase is quenched. Quasi two-dimensional LC SmF and SmI phases identified. Lower (for n = 3,5), intermediate (for n = 6,7) and higher (n = 9) homologues exhibit 3D SmBcryst phase. Monotropic LC phase occurrence is also noticed. Apart from other LC phase transitions, SmA–SmC transition is mostly found to be second order or very weakly first order nature. Phase diagram by DSC infers existence of multi-critical points in the vicinity of SmF and SmI phase structures with psuedo hexagonal packing. Influence of meta-extended core, complementary HB and flexibility component are discussed for LC phase abundance. Role of orientational disorder induced by flexible component discussed. In comparison with LC phase occurrence in (4)MeoBD(3)AmBA:nOBAs, shielded inductomeric effect is argued for large thermal range of tilted smectic phases. Integrated and differential heat energies are estimated in successive heating and cooling scans to investigate optimized realization of LC phases. Results are discussed in the wake of contemporary reports in other LCs.

Magnesium intermetallics: synthesis and structure of Eu2Pt2Mg and Sr2Pt2Mg

AbstractThe intermetallic phases Sr2Pt2Mg and Eu2Pt2Mg were obtained by reaction of the elements in sealed tantalum tubes at high temperature. Sr2Pt2Mg crystallizes with the monoclinic Ca2Ir2Si type (C2/c,a = 1020.7(7),b = 597.7(4),c = 827.0(4) pm,β = 103.37(5)°), while Eu2Pt2Mg adopts the orthorhombic W2CoB2-type structure (Immm,a = 440.31(5),b = 582.20(6),c = 914.11(9) pm,wR = 0.0359, 277F2values, 14 variables). The magnesium atoms in both structures are coordinated by four Pt2dumb-bells with a rectangular planar coordination in Eu2Pt2Mg (268 pm Pt–Mg) and a distorted tetrahedral one in Sr2Pt2Mg (273–275 pm Pt–Mg). The Pt–Pt distances are 277 pm in the europium and 269 pm in the strontium compound. The polyanionic [Pt2Mg] units are planar in Eu2Pt2Mg and separated by the europium atoms. The Sr2Pt2Mg structure shows the motif of hexagonal rod packing for the [Pt2Mg] rows that are embedded in a strontium matrix. Chemical bonding and the influence of the valence electron count on the formation of the structure types are discussed.

Analytical relationships for yield stress of five mechanical meta-biomaterials

In this article, five fundamental unit cells namely BCC, hexagonal packing, rhombicuboctahedron, diamond, and truncated octahedron, for which there was a lack of accurate analytical yield stress relationship in the literature, were studied analytically and numerically using the Timoshenko and Euler–Bernoulli beam theories. Two different approaches based on force or displacement methods were considered. The results of the analytical models were validated against finite element models results as well as experimental data from literature. The results demonstrated that the newly developed analytical relationships based on Timoshenko beam theory give more accurate results as compared to Euler–Bernoulli beam theory, especially in higher values of relative densities.

Nanostructured Molecular Imprinted Polymers for Chemosensing of Hormone Proteins

Immunoassays and high-performance liquid chromatography combined with mass spectrometry are common methods to selectively determine protein biomarkers in biological samples. The excellent accuracy of these determinations is at the expense of a high cost, including the cost of specific antibodies supply or instrumentation and experienced operation. Several biosensors were devised and fabricated for fast and selective quantification of the protein biomarkers. The most interesting protein biomarkers belong to the glycoprotein family. Unfortunately, it seems challenging to generate antibodies for this family because of low immunogenicity. Thus, an alternative research field is developing which claims to synthesize more stable artificial antibody-like receptors for the replacement of natural antibodies.Here, a semi-covalent procedure is proposed to elaborate surface imprinted polymers for selective recognition of gonadotropin hormones.1,2 Briefly, this strategy consists of a combination of three methods, namely, (i) lithography, (ii) surface imprinting, and (iii) semi-covalent imprinting. Hard template silica beads were used as a mold to prepare a highly organized opal structure. On top of this, template proteins were immobilized. Later, the protein was derivatized with functional monomers. These functionalized template molecules were electrochemically cross-linked with an excess of cross-linking monomer. Removal of the silica mold creates a nanostructure containing molecular cavities on the surface. Such nanostructures are advantageous for non-restrictive diffusion of bulky proteins toward the respective molecular cavities.We confirmed regular and hexagonal packing of silica beads, resulting in inverse opal surface imprinted molecular films, by Scanning Electron Microscope (SEM). The recognition of proteins by the nanostructured molecular imprinted polymer films was transduced with the help of capacitive impedimetry. The suitability of the synthetic receptor was further confirmed by measuring proteins in real blood serum samples.

Axially oriented guest induced crystallization in syndiotactic polystyrene unstretched fibers

Guest-induced crystallization of amorphous s-PS fibers, although prepared with slow take-up speeds (e.g., 80 m/min) and in the absence of mechanical stretching, unexpectedly leads to high degrees of axial orientation (0.7 < fc < 0.8) of co-crystalline phases. Similar high degrees of axial orientation can be maintained after suitable guest removal procedures, leading to nanoporous-crystalline (NC) phases. High degrees of orientation are even maintained after high temperature (e.g., 200 °C) treatments leading to dense crystalline α phases, although this phase transition implies change of polymer conformation from helical to zig-zag planar. Hence, guest induced crystallization of amorphous s-PS fibers not only leads to NC forms (suitable for removal of organic pollutants from the environment) or to co-crystalline forms with active guests (e.g., suitable for antimicrobial release) but also lead, without stretching, to axial orientation. For the disordered NC form, fiber patterns are for the first time reported, showing only four diffraction peaks, which suggest the occurrence of a hexagonal packing of chain axes of s(2/1)2 polymer helices. The NC nature of this disordered crystalline form is clearly confirmed by tests of perchloroethylene uptake, from dilute aqueous solutions (500 ppb).

Development of a compressive failure model for carbon fiber composites and associated uncertainties

An approach to increase the value of carbon fiber for wind turbines blades, and other compressive strength driven designs, is to identify pathways to increase its cost-specific compressive strength. A finite element model has been developed to evaluate the predictiveness of current finite element methods and to lay groundwork for future studies that focus on improving the cost-specific compressive strength. Parametric studies are conducted to understand which uncertainties in the model inputs have the greatest impact on compressive strength predictions. A statistical approach is also presented that enables the micromechanical model, which is deterministic, to efficiently account for statistical variability in the fiber misalignment present in composite materials; especially if the results from the hexagonal and square pack models are averaged. The model was found to agree well with experimental results for a Zoltek PX-35 pultrusion. The sensitivity studies suggest that the fiber packing and the interface shear strength have the greatest impact on compressive strength prediction for the fiber reinforced polymer studied here. Based on the performance of the modeling approach presented in this work, it is deemed sufficient for future work which will seek to identify carbon fiber composites with improved cost-specific compressive strength.

From comb-like polyelectrolytes to polyelectrolyte-surfactant complexes: Effect of the length of the aliphatic tail of the counterions on self-organization in solid state

Cationic comb-like polyelectrolyte poly(11-acryloyloxyundecyltrimethylammonium) with acidic residues of acetic, butanoic, hexanoic, octanoic, decanoic, dodecanoic acids as counterions were synthesized. Those polyelectrolyte series on increasing of counterion tail length demonstrate the smooth transition from typical comb-like polyelectrolytes to polyelectrolyte-surfactant complexes. All complexes are water soluble, and dissociate in aqueous NaCl. Increasing of counterion hydrophobicity results transformation from hexagonal packing (acetic and butanoic counterions) to amorphous phase (hexanoic counterions) and then to lamellar packing (octanoic, decanoic and dodecanoic counterions) of solid complexes. The formed structures are stable up to 150 °C and decompose with destruction of chemical structure.

Hemimicelle formation of semi-fluorocarbon chains at air–water interface: coarse-grained molecular dynamics study with an extension of the SPICA force field

The hemimicelle formation of long-chain semi-fluorocarbon diblocks at the air – water interface is studied using coarse-grained molecular dynamics simulations with a SPICA force field. From a series of simulations with varying the number of chains, the critical saturated size of a single micelle was predicted; its structural metrics such as the hexagonal chain packing order, density distribution, shape, mean diameter, and the orientation of the fluorinated (F-blocks) and hydrogenated segments (H-blocks) at the interface were found to be consistent with the previous experimental and atomistic simulation results. The diblock assemblies larger than the saturated size spontaneously split into multiple micelles separated by a metastable parallel phase (P-phase). This P-phase could be the reason for the non-coalescence and elastic behaviour of the hemimicelle assemblies. From the simulation with a low molecular arrangement area, the mechanism of the micelle formation of saturated sizes is illustrated. The results reveal that the mutual-phobicity and interfacial tension difference of F- and H-blocks with the water are sufficient to drive the self-assembly and can provide a significant thermodynamic stability to the micelles, where the increasing packing strain between the layer curvature and the planarizing water surface tension can determine the size of the saturated hemimicelles.

Wheel structured Zeonex-based photonic crystal fiber sensor in THz regime for sensing milk.

In this paper, a wheel structured Zeonex-based hexagonal packing photonic crystal fiber (PCF) sensor has been proposed for sensing camel milk with a refractive index of 1.3423 and cow milk with a refractive index of 1.3459. This sensor has been investigated for porosities of 85%, 90%, and 98% within a terahertz (THz) region ranging from 0.2 to 2.0 THz. At an operating frequency of 2 THz, this sensor has shown a maximum sensitivity of 81.16% and 81.32% for camel and cow milk, respectively. EML of 0.033013 cm−1 and 0.03284 cm−1 has been found for camel and cow milk, respectively, at the same operating conditions with negligible confinement losses of 8.675 times 10–18 cm−1 1.435 times 10–18 cm−1. Several other parameters, such as the effective area, flattened dispersion, and numerical aperture, have also been obtained during the investigation. Since considerable attention has not been given yet in detecting various types of dairy products using PCF terahertz sensors, this design will pave a whole new path in further implementing THz sensing in the dairy industry.

Numerical micromechanics model of carbon fiber-reinforced composite using various periodical fiber arrangement

A numerical model of unidirectional carbon fiber-reinforced polymer composite material at the micro-level has been introduced to complement the experiment and analytical model in estimating the elastic properties of composite material. Idealization was performed in the model by using a periodically distributed fiber following square and hexagonal packing arrangement. The determination of the unit cell configuration was made by considering the periodic boundary condition associated with the selected configuration. The idealization using periodic fiber arrangement was proved to adequately estimate the elastic properties of composite material. The hexagonal model was proved to solve the drawbacks of the square model in estimating the shear properties with error reduction up to 50 % in comparison to the square model.