Array Of Spheres Research Articles

Nano-antenna synthesis for an arbitrary far-field radiation pattern and polarization based on vector spherical wave functions expansion.

A systematic method is proposed to synthesize a nano-antenna based on theoretical principles. This nano-antenna, which is composed of a set of small dielectric spheres, is designed to have a desired far-field radiation pattern and polarization. The basis of the proposed method is expanding all electromagnetic waves into the series of vector spherical wave functions. First, the forward problem of calculation of scattering from single and multiple spheres is studied. For cases with more than one sphere, a multiple scattering method is implemented to calculate total scattering. Near-field and far-field waves, absorption, extinction, and differential scattering cross sections are calculated for a single sphere with different sizes and permittivities. Moreover, far-field waves for linear arrays of small spheres are analyzed. All results are validated using an electromagnetic simulation software. Next, the problem of inverse scattering begins by considering a three-dimensional arbitrary pattern and polarization. The aim is to find a set of spheres that generates this pattern. Particle swarm optimization and non-iterative spectral-domain forward scattering methods are combined as a novel method to find the optimal positions of the spheres.

Optical method for measuring the volume fraction of granular media: Application to faced-centered cubic lattices of monodisperse spheres.

In order to understand the dynamics of granular flows, one must have knowledge about the solid volume fraction. However, its reliable experimental estimation is still a challenging task. Here, we present the application of a stochastic-optical method (SOM) [L. Sarno et al., Granul. Matter 18, 80 (2016)10.1007/s10035-016-0676-3] to an array of spheres arranged according to faced-centered cubic lattices, where spheres' locations are known a priori. The purpose of this study is to test the robustness of the image binarization algorithm, introduced in the SOM for the indirect estimation of the near-wall volume fraction through an optically measurable quantity, defined as two-dimensional volume fraction. A comprehensive range of volume fractions and illumination conditions are numerically and experimentally investigated. The proposed binarization algorithm is found to yield reasonably accurate estimations of the two-dimensional volume fraction with a root-mean-square error smaller than 0.03 for all investigated illumination conditions. A slightly worse performance is observed for samples with relatively low volume fractions (<0.3), where the binarization algorithm occasionally cannot identify the surface elements in the second and third layers of the regular lattice.

Initial Stage Sintering of Polycrystalline Spheres: A Model and Experiments

Conventional models for initial stage sintering consider sintering to occur between two single crystal spheres, although most powder particles are polycrystalline in reality. The conventional Coble model is modified to take into account multiple grain boundaries intersecting a neck in sintering between polycrystalline particles. The exponents N and M in the rate equation (x/R)^N α (t/ R^M), for polycrystals were found to be 4 and 2, respectively, in contrast to 6 and 4 in single crystals; here x, R and t are the neck radius, particle radius and time, respectively. In addition there is a 1/d^2 dependence, where d is the grain size. Analysis reveals that initial stage sintering will be enhanced in polycrystalline particles when the neck is large and there are a large number of grains within a particle. Accompanying experiments on close packed irregular 2D arrays of polycrystalline zirconia spheres showed that the neck growth rate was higher for the particles containing a large number of grains, compared to those with only a few grains.

Bilayer Heterostructure Photonic Crystal Composed of Hollow Silica and Silica Sphere Arrays for Information Encryption.

Utilizing photonic crystals to fabricate information encryption materials has attracted widespread interest due to their tunable optical properties and responsiveness to external stimuli. In most of the previously reported systems, the information is hidden at a specific angle and the angle-dependent invisibility is a limitation. Meanwhile, poor structural stability is still a key issue that needs to be solved for potential applications. In this paper, a bilayer heterostructure photonic crystal containing ordered hollow silica inverse opal arrays, amorphous silica opal arrays, and poly(vinyl alcohol) (adhesive) is successfully constructed. It makes the information highly invisible at any angle and also achieves information encryption. With this strategy, the information can be hidden by the noniridescent structural color derived from the strong scattering effect of light from the top layer of amorphous silica sphere arrays. After wiping with ethanol or a refractive-index-matching solvent, the scattering effect vanishes and the amorphous silica sphere arrays become transparent. The reflected light of the bottom layer caused by the increasing refractive index contrast between the inside and outside of the hollow silica spheres could rapidly reveal the hidden information. The bilayer photonic crystal exhibits robust structural stability, and the hiding/revealing process is completely reversible, which shows great potential applications in steganography and information encryption.

Plasmonic ordered pore array Ag film coated glass: transparent and solar heat reflective material

In this paper, we fabricate ordered pore array (OPA) Ag film coated glass with the aid of polystyrene sphere (PS) array templates. This kind of OPA Ag coated glass has optical advantages of visible transparency, blue and near-infrared resistance. The average visible transmittance is 68%, including a transmission peak of 78% located at 570 nm, and low average transmittance of 48% in the blue light region that is not damaging to the eyes. The near-infrared light blocking rate is 67%, among which 40% light is reflected directly, indicating the reflection domination.

An efficient 3D ordered mesoporous Cu sphere array electrocatalyst for carbon dioxide electrochemical reduction

The electrochemical reduction of CO2 is a promising solution for sustainable energy research and carbon emissions. However, this solution has been challenged by the lack of active and selective catalysts. Here, we report a two-step synthesis of 3D ordered mesoporous Cu sphere arrays, which is fabricated by a dual template method using a poly methyl methacrylate (PMMA) inverse opal and the nonionic surfactant Brij 58 to template the mesostructure within the regular voids of a colloidal crystal. Therefore, the well-ordered 3D interconnected bi-continuous mesopores structure has advantages of abundant exposed catalytically active sites, efficient mass transport, and high electrical conductivity, which result in excellent electrocatalytic CO2RR performance. The prepared 3D ordered mesoporous Cu sphere array (3D-OMCuSA) exhibits a low onset potential of -0.4 V at a 1 mA cm−2 electrode current density, a low Tafel slope of 109.6 mV per decade and a long-term durability in 0.1 M potassium bicarbonate. These distinct features of 3D-OMCuSA render it a promising method for the further development of advanced electrocatalytic materials for CO2 reduction.

Lagrangian investigation of pseudo-turbulence in multiphase flow using superposable wakes

A method is introduced for approximating the fully resolved flow through a monodisperse array of spheres using only the locations of the spheres and the volume-averaged Reynolds number. A pseudoturbulence stress model is proposed for use in a Lagrangian framework.

Architecture design and applications of nanopatterned arrays based on colloidal lithography

Nanopatterned arrays have potential applications in diverse devices, including high-density memory, wettability control, electronic chips, biochips, plasmonics (such as plasmon sensors, plasmon-enhanced molecular spectroscopy, and plasmon-mediated chemical reactions), and so on. In this tutorial, we first introduce colloidal lithography (CL) technique as an important method to prepare nanopatterned arrays. Based on the formation of a mask by self-assembly of polystyrene (PS) colloid spheres, the nanopatterned arrays can be achieved by following a series of various deposition, etching, transfer, and their combination steps. According to the structural differences of the acquired surface patterns, diverse nanopatterned arrays are fabricated by controlling the fabrication routes. Technical issues are discussed in detail, such as preparation and modification of the large-area and ordered PS colloid sphere arrays and design and hybridization of nanostructured arrays of films with various shapes. In the meantime, the potential applications of these nanopatterned array films are reviewed and summarized. Hopefully, the present tutorial will inspire more ingenious designs of nanopatterned arrays and developments of using CL technique in potential applications.

Controlling three-dimensional optical fields via inverse Mie scattering.

Controlling the propagation of optical fields in three dimensions using arrays of discrete dielectric scatterers is an active area of research. These arrays can create optical elements with functionalities unrealizable in conventional optics. Here, we present an inverse design method based on the inverse Mie scattering problem for producing three-dimensional optical field patterns. Using this method, we demonstrate a device that focuses 1.55-μm light into a depth-variant discrete helical pattern. The reported device is fabricated using two-photon lithography and has a footprint of 144 μm by 144 μm, the largest of any inverse-designed photonic structure to date. This inverse design method constitutes an important step toward designer free-space optics, where unique optical elements are produced for user-specified functionalities.

Direct numerical simulation of mass transfer in bidisperse arrays of spheres

AbstractIn this study, an efficient ghost cell‐based immersed boundary method is used to perform direct numerical simulations of mass‐transfer processes in bidisperse arrays. Stationary spherical particles, with a size ratio of 1.5, are homogeneously distributed in a periodic domain in the spanwise directions. Simulations are performed over a range of solids volume fractions, volume fraction ratios of small‐to‐large particles, and Reynolds numbers. Through our studies, we find that large particles have a negative influence on the overall mass‐transfer performance; however, the performance of individual particle species is independent on the relative volume fraction ratios. We propose two correlations: (a) a refitted Gunn correlation for a better description of the interfacial transfer performance based on individual particle species; (b) a fractional calculation for a simple estimation of the overall performance in bidisperse systems using characteristics of individual particle species. We also investigate how well the overall mass‐transfer coefficient can be predicted by defining an appropriate equivalent diameter.

Three dimensional discrete element simulation of cylindrical cavity expansion from zero initial radius in sand

This study seeks to assess the influence of choice of initial cavity radius on the soil response during cavity expansion in sandy soil adopting three-dimensional discrete element simulations and obtaining the size of the influence zone when the expansion starts from zero initial radius. Sandy soil is modelled adopting rolling resistance contact model to capture the effects of particle interlocking, and the microscopic parameters are calibrated utilising linear model deformability method for both loose and dense sands against experimental results. Four cylindrical cavity expansions that commenced from different initial radii are simulated in dense and loose sand specimens. The large-scale three-dimensional model is proposed with more than 500,000 particles, enabling precise volumetric dilation and contraction predictions using strain rate tensors. During the cavity expansion process, cavity pressure is constantly recorded by appropriate subroutines, while the stress-strain and void ratio variations are continuously monitored using an array of prediction spheres situated close to the internal cavities.The results confirm that the initial cavity radius chosen has conspicuous effects on the cavity pressure, the stress path, the volumetric strain and the deviatoric stress, especially at the initial stage of expansion; however, these effects become less pronounced and are ultimately minor as the cavity reaches full expansion. The results confirmed that given the same expansion volume, the pressure required to create a cavity is significantly larger than expanding an existing cavity in the same soil medium, whereas the pressure needed to maintain an already expanded cavity is not sensitive to the choice of initial cavity radius. The results obtained were further validated adopting the variations of stress path, deviatoric stress and volumetric strain in the vicinity of the cavity wall. The findings from this study may provide practicing engineers with confidence in determining the appropriate size of the pilot hole in driven pile installation and horizontal directional drilling for trenchless piping in sandy soil. In addition, the lateral soil displacement induced by cavity expansion is also examined in this study. It is concluded that the radial displacement due to cavity expansion in loose sand can reach 25af (af representing the final cavity radius), while a larger influence zone must be considered by practicing engineers when dealing with dense sand.

Large-scale fabrication of 3D hierarchical MoSe2 hollow sphere arrays with like-Pacific Plate architecture for high-performance hydrogen evolution reaction

Optimizing of electrocatalytic hydrogen evolution reaction (HER) activity is still a gigantic challenge for improving catalysts in renewable energy field. In this research, large-scale neoteric three-dimensional (3D) hierarchical MoSe2 hollow sphere arrays with like-Pacific Plate architecture were triumphantly prepared via a facile and reliable approach. The like-Pacific Plate architecture consists of many 3D MoSe2 arrays plates with the dimensions of 10–35 μm, which is assembled by plentiful closely connecting hierarchical MoSe2 hollow spheres with the outer diameter, hierarchically secondary unit size and shell thickness of 450 nm, 25 nm and 10 nm, respectively. The products exhibited remarkable HER performance with small Tafel slope (58.5 mV dec−1), low overpotential (169.8 mV) at 10 mA cm−2, high conductivity and durable stability, which are attribute to the mechanisms (1) 3D hollow framework furnishes large specific surface area, (2) hierarchical structure generates more active sites, (3) like-Pacific Plate architecture facilitates the touch of electrolyte and catalyst, and (4) closely packed arrays expedite the migration of electron. The current work indicates that unique 3D hierarchical hollow sphere arrays with like-Pacific Plate architecture will be a potential candidate for effective electrocatalytic water splitting catalyst material with energy source application.

Bound states in the continuum and Fano resonances in the Dirac cone spectrum

We consider light scattering by two dimensional arrays of high-index dielectric spheres arranged into the triangular lattice. It is demonstrated that in the case a triple degeneracy of resonant leaky modes in the Gamma-point the scattering spectra exhibit a complicated picture of Fano resonances with extremely narrow line-width. The Fan features are explained through coupled mode theory for a Dirac cone spectrum as a signature of optical bound states in the continuum (BIC). It is found that the standing wave in-Gamma BIC induces a ring of off-Gamma BICs due to different scaling laws for real and imaginary parts of the resonant eigenfrequencies in the Dirac cone spectrum. A quantitative theory of the spectra is proposed.

Periodic Metallo-Dielectric Structures: Electromagnetic Absorption and its Related Developed Temperatures.

Multi-layer, metallo-dielectric structures (screens) have long been employed as electromagnetic band filters, either in transmission or in reflection modes. Here we study the radiation energy not transmitted or reflected by these structures (trapped radiation, which is denoted—absorption). The trapped radiation leads to hot surfaces. In these bi-layer screens, the top (front) screen is made of metallic hole-array and the bottom (back) screen is made of metallic disk-array. The gap between them is filled with an array of dielectric spheres. The spheres are embedded in a dielectric host material, which is made of either a heat-insulating (air, polyimide) or heat-conducting (MgO) layer. Electromagnetic intensity trapping of 97% is obtained when a 0.15 micron gap is filled with MgO and Si spheres, which are treated as pure dielectrics (namely, with no added absorption loss). Envisioned applications are anti-fogging surfaces, electromagnetic shields, and energy harvesting structures.

Synthesis of Fullerene-Fluorene Dyads through the Platinum-Catalyzed Reactions of [60]Fullerene with 9-Ethynyl-9H-fluoren-9-yl Carboxylates.

The single-step regio- and stereoselective platinum-catalyzed reactions of [60]fullerene with a series of 9-ethynyl-9H-fluoren-9-yl carboxylates afforded fullerene-fluorene dyads in their [2 + 2] cycloaddition forms. The presented reactions represent the first examples of the use of easily accessible fluorenyl carboxylates as fluorenylideneallene precursors. In addition, the single-crystal X-ray structure of one of the dyads reveals a distorted cyclobutane ring. Furthermore, the dyad forms a layered structure with close-packed arrays of C60 spheres in its crystals.

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.

Fabrication, Characterization, and Application of Large-Scale Uniformly Hybrid Nanoparticle-Enhanced Raman Spectroscopy Substrates.

Surface-enhanced Raman spectroscopy (SERS) substrates with high sensitivity and reproducibility are highly desirable for high precision and even molecular-level detection applications. Here, large-scale uniformly hybrid nanoparticle-enhanced Raman spectroscopy (NERS) substrates with high reproducibility and controllability were developed. Using oxygen plasma treatment, large-area and uniformly rough polystyrene sphere (URPS) arrays in conjunction with 20 nm Au films (AuURPS) were fabricated for SERS substrates. Au nanoparticles and clusters covered the surface of the URPS arrays, and this increased the Raman signal. In the detection of malachite green (MG), the fabricated NERS substrates have high reproducibility and sensitivity. The enhancement factor (EF) of Au nanoparticles and clusters was simulated by finite-difference time-domain (FDTD) simulations and the EF was more than 104. The measured EF of our developed substrate was more than 108 with a relative standard deviation as low as 6.64%–13.84% over 15 points on the substrate. The minimum limit for the MG molecules reached 50 ng/mL. Moreover, the Raman signal had a good linear relationship with the logarithmic concentration of MG, as it ranged from 50 ng/mL to 5 μg/mL. The NERS substrates proposed in this work may serve as a promising detection scheme in chemical and biological fields.

Numerically investigating a wide-angle polarization-independent ultra-broadband solar selective absorber for high-efficiency solar thermal energy conversion

In this paper, an efficient solar selective absorber based on a tungsten sphere array and a tungsten grating is proposed and demonstrated numerically. The proposed structure has a spectral range of 300–1777 nm, with an absorption higher than 95% and an infrared thermal emittance as low as 0.03% at wavelengths greater than 6.15 μm. As a result, the solar thermal conversion efficiency of the optimized solar absorber can obtain 92.23% at an operating temperature of 373.15 K. In addition, the proposed absorber is polarization-independent and can maintain a high solar absorption in a wide range of incident angles from 0° to 50° for both transverse electric and transverse magnetic waves. A detailed analysis by 3D full-wave simulations indicates the broadband absorption mechanism can be attributed to the coupling effect of multi-plasmon resonance modes. The optimized absorber shows great potential for solar thermal applications that require wide-angle polarization-independent ultra-broadband absorption and low infrared thermal emittance.

Ability of a pore network model to predict fluid flow and drag in saturated granular materials

The local flow field and seepage induced drag obtained from Pore Network Models (PNM) is compared to Immersed Boundary Method (IBM) simulations, for a range of linear graded and bimodal samples. PNM were generated using a weighted Delaunay Tessellation (DT), along with the Modified Delaunay Tessellation (MDT) which considers the merging of tetrahedral Delaunay cells. Two local conductivity models are compared in simulating fluid flow in the PNM. The local pressure field was very accurately captured, while the local flux (flow rate) exhibited more scatter and sensitivity to the choice of the local conductance model. PNM based on the MDT clearly provided a better correlation with the IBM. There was close similarity in the network shortest paths, indicating that the PNM captures dominant flow channels. Comparison of streamline profiles demonstrated that local pressure drops coincided with the pore constrictions. A rigorous validation was undertaken for the drag force calculated from the PNM by comparing with analytical solutions for ordered array of spheres. This method was subsequently applied to all samples, and the calculated force was compared with the IBM data. Linear graded samples were able to calculate the force with reasonable accuracy, while the bimodal samples exhibited slightly more scatter.

Numerical calculation of permeability of periodic porous materials: Application to periodic arrays of spheres and 3D scaffold microstructures

SummaryIn this paper, an efficient numerical method is proposed to calculate the anisotropic permeability in porous materials characterized by a periodic microstructure. This method is based on pore‐scale fluid dynamic simulations using a static volume of fluid method. Unlike standard solution procedures for this type of problem, we here solve an average constitutive equation over both fluid and solid domain by use of a subgrid model to accurately capture momentum transfer from the fluid to solid interface regions. Using numerical simulations on periodic arrays of spheres, we first demonstrate that, by using the subgrid interface model, more accurate results can be produced, for the velocity and pressure fields, than via more conventional approaches. We then apply numerical upscaling over the unit cell to calculate the full anisotropic permeability from the pore‐scale numerical results. The obtained permeability values for a variety of periodic arrays of spheres in different arrangements and packing orders are in good agreement with semianalytical results reported in literature. This validation allows for the permeability assessment of more complex structures such as isotropic gyroid structures, or anisotropic cases, here modeled in their simplest form, the ellipsoidal inclusion.