Three-dimensional Periodic Structures Research Articles

Preparation and Adsorption Photocatalytic Properties of PVA/TiO2 Colloidal Photonic Crystal Films.

Polyvinyl alcohol (PVA)/TiO2/colloidal photonic crystal (CPC) films with photocatalytic properties are presented, where TiO2 nanoparticles were introduced into the PVA gel network. Such PVA/TiO2/CPC films possess three-dimensional periodic structures that are supported with a PVA/TiO2 composite gel. The unique structural color of CPCs can indicate the process of material preparation, adsorption, and desorption. The shift of diffraction peaks of CPCs can be more accurately determined using fiber-optic spectroscopy. The effect of the PVA/TiO2/CPC catalyst films showed better properties as the degradation of methylene blue (MB) by the PVA/TiO2/CPC film catalyst in 4 h was 77~90%, while the degradation of MB by the PVA/TiO2 film was 33% in 4 h, indicating that the photonic crystal structure was 2.3~2.7 times more effective than that of the bulk structure.

Chemical bonding in Uranium-based materials: A local vibrational mode case study of Cs UO Cl and UCl crystals.

The Local Vibrational Mode Analysis, initially applied to diverse molecular systems, was extended to periodic systems in 2019. This work introduces an enhanced version of the LModeA software, specifically designed for the comprehensive analysis of two and three-dimensional periodic structures. Notably, a novel interface with the Crystal package was established, enabling a seamless transition from molecules to periodic systems using a unified methodology. Two distinct sets of uranium-based systems were investigated: (i) the evolution of the Uranyl ion (UO ) traced from its molecular configurations to the solid state, exemplified by Cs UO Cl and (ii) Uranium tetrachloride (UCl ) in both its molecular and crystalline forms. The primary focus was on exploring the impact of crystal packing on key properties, including IR and Raman spectra, structural parameters, and an in-depth assessment of bond strength utilizing local mode perspectives. This work not only demonstrates the adaptability and versatility of LModeA for periodic systems but also highlights its potential for gaining insights into complex materials and aiding in the design of new materials through fine-tuning.

Improving mass transfer in anion exchange membrane water electrolysis by ordered gas diffusion layer

For tight assembly electrochemical gas evolution devices, such as anion exchange membrane water electrolysis (AEMWE), bubbles blocking gas diffusion layer (GDL) channels is one of the key reasons for cell performance degradation under high current densities. To enhance mass transport in GDLs at high current densities, herein we report a 3D printed Ni GDL (GDL3D print) with straight-through pores and three-dimensional periodic structures. Due to its periodic structures and high hydrophilicity, GDL3D print is more conducive to the rapid escape of bubbles and timely replenishment of water, showing higher mass transfer efficiency and lower ohmic resistance. Therefore, compared with the commercial nickel foam (NF), GDL3D print exhibits better cell performance not only in 1 mol/L KOH solutions but also in pure-water-fed AEMWE, and the cell voltage of AEMWE using GDL3D print as the anode GDL is only 1.8 V at 1 A cm−2. This work provides a useful guidance for GDL design for tight assembly electrochemical gas evolution devices.

Preparation and Magnetic Properties of Fe-Co–Ni Magnetic Nanowire Arrays with Three-Dimensional Periodic Structures

Preparation and Magnetic Properties of Fe-Co–Ni Magnetic Nanowire Arrays with Three-Dimensional Periodic Structures

Mode converter using bent and twisted coupled-multicore fibers for group delay spread reduction

A mode converter using bent and twisted coupled-multicore fiber for the reduction of the group delay spread is proposed. The bent and twisted fiber, which is one of the periodic structures, can work as a long-period grating mode converter by properly setting the twist rate. To investigate the mode conversion characteristics, a simple and effective eigenmode analysis for three-dimensional periodic structures is proposed. We found that to convert the specified modes, the core layout is also important as well as the twist rate. For example, the mode conversion behaviors of 4CFs with square lattice and triangular lattice layouts are greatly different although each 4CF enables the specified mode conversion. It is revealed that, by switching the higher and lower order modes, the group delay can be equalized, resulting in the suppression of the group delay spread. It leads to reducing the complexity of the multiple-input multiple-output receiver in the mode division multiplexing system.

Meta-Kagome lattice structures for broadband vibration isolation

One-dimensional (1D) phononic crystal (PC) beams have been extensively studied due to their bandgap properties, but the idea of using this functional beam components to form three-dimensional (3D) periodic structures has rarely been mentioned. In this paper, the PC beam element is used to replace the ordinary member of the conventional Kagome lattice structures, thus, a meta-Kagome lattice (MKL) structure is innovatively constructed with broadband vibration isolation performance. The dispersion analysis is performed to reveal the mechanism of bandgap formation and the reason of getting broad bandgaps. Three kinds of MKL structures, namely, with triangular, rectangular and hexagonal pyramids are designed. The vibration transmission properties of the MKL columns with or without interfaces are studied to illustrate the isolation effect. Moreover, the vibration isolation performance of the sandwich structures composed of MKL cores is also studied, and the influence of the skin characteristics on the properties is discussed. Vibration transmission tests were conducted to verify the results. This work provides a new method to develop 3D multi-functional lattice structures, especially for load-bearing and vibration reduction.

Design of metasurfaces in 3D for omnidirectional band gaps: The scalar wave case

We discuss a comprehensive process for designing the material properties of three-dimensional periodic structures that are tasked to exhibit user-defined omnidirectional band gaps. To this end, we build upon the framework first posited in Goh and Kallivokas (2019) for two-dimensional metamaterials, and aim at engineering the dispersive properties of a metamaterial’s 3D unit cell using an inverse medium approach. The inversion is driven by forcing the vanishing of trial group velocities at the target band gap frequencies, subject to the satisfaction of the Floquet–Bloch eigenvalue problem defined over the unit cell’s IBZ. Omnidirectionality is controlled by enforcing the vanishing of the group velocities along the IBZ’s high-symmetry lines. Using an adjoint method, the unit cell’s properties are iteratively updated until the design goal is attained. Numerical examples for acoustic metamaterials and metasurfaces demonstrate the methodology.

Wideband Simulations of Periodic Structures by the Hybrid Spectral FDTD/TD-VFz Method

The spectral finite-difference time-domain method is combined with the discrete-time time-domain vector fitting (TD-VFz) algorithm to analyze three-dimensional (3-D) periodic structures excited by oblique incident plane waves over a wide frequency band. The time signal reconstruction with TD-VFz produces an untruncated response over an infinite time window allowing an accurate spectral result, especially near the cutoff frequency separating the spectrum propagating wave region of the evanescent wave region.

Robust optimization of attenuation bands of three-dimensional periodic frame structures

Robust optimization of attenuation bands of three-dimensional periodic frame structures

Enhanced Measurement Accuracy for Nanostructures Using Hybrid Metrology

Light-matter interplay is widely used for analyzing the topology of surfaces on small scales for use in areas such as nanotechnology, nanoelectronics, photonics, and advanced materials. Conventional optical microscope imaging methods are limited in resolution to a value comparable to the wavelength, the so-called Abbe limit, and cannot be used to measure nano-sized structures. Scatterometry and Mueller ellipsometry are spectroscopic optical methods that can measure structures smaller than the wavelength. However, the relative uncertainties of the structure dimensions measured with scatterometry increase with decreasing structure size, and the industry is therefore replacing simple intensity based scatterometry with Mueller ellipsometry for the most demanding measurements. The accuracy of Mueller ellipsometry and scatterometry are closely related to the ability of the employed regression and regularization algorithms to extract the structural dimension. In this work, we demonstrate how the measurement accuracy on three-dimensional periodic structures may be increased by measuring the same periodic structure with multiple techniques and applying a χ2-regression method that finds the best solution based on the input from all the instruments. We furthermore report on a new and improved calibration method for Mueller ellipsometry and demonstrate how the Mueller matrix may be used to find the geometrical anisotropy of the structure.

Structured Alumina Substrates for Environmental Catalysis Produced by Stereolithography

Modern catalysts for internal combustion engine applications are traditionally constituted by honeycomb substrates on which a coating of the catalytically active phase is applied. Due to the laminar flow of the gases passing through their straight channels, these structures present low heat and mass transfer, thus leading to relatively large catalyst sizes to compensate for the low catalytic activity per unit of volume. Better conversion efficiency can be achieved if three-dimensional periodic structures are employed, because of the resulting gases’ tortuous paths. Furthermore, the increased catalytic activity implies a reduction in the overall catalyst volume, which can translate to a decreased usage of precious metals as active phase. By exploiting the ceramic Stereolithography technique (i.e., SLA) it is nowadays possible to accurately 3D print complex alumina-based lattices to be used as ceramic substrates for catalysis. In this work, closed-walls lattices consisting of a rotated cubic cell of 2 mm dimensions were designed, 3D printed via SLA and finally washcoated with V2O5-WO3-TiO2. The samples were tested for the selective catalytic reduction of NO by NH3 in a heated quartz glass reactor and the performance of the innovative 3D-printed substrate was compared with the catalytic efficiency of the conventional cordierite honeycombs.

Topology optimization of 3D photonic crystals with complete bandgaps.

The design of photonic crystals with complete bandgaps has recently received considerable research focus for numerous reasons. This work leverages well-known nonlinear programming techniques to alleviate the non-smoothness caused by degenerate eigenvalues such that topology optimization problems can be solved with the open-source IPOPT software. A fully-vectorial plane wave expansion technique is used with an iterative eigensolver to efficiently predict dispersion properties of candidate structures. Nonlinear programming is employed to solve the inverse problem of designing three-dimensional periodic structures that exhibit complete two-dimensional (2D) and three-dimensional (3D) photonic bandgaps. Mesh refinement is performed to alleviate the large computational burden of designing and analyzing photonic crystals, and a periodic density filter is implemented to impose a minimum feature size for manufacturability considerations.

Methods for tuning plasmonic and photonic optical resonances in high surface area porous electrodes

Surface plasmons have found a wide range of applications in plasmonic and nanophotonic devices. The combination of plasmonics with three-dimensional photonic crystals has enormous potential for the efficient localization of light in high surface area photoelectrodes. However, the metals traditionally used for plasmonics are difficult to form into three-dimensional periodic structures and have limited optical penetration depth at operational frequencies, which limits their use in nanofabricated photonic crystal devices. The recent decade has seen an expansion of the plasmonic material portfolio into conducting ceramics, driven by their potential for improved stability, and their conformal growth via atomic layer deposition has been established. In this work, we have created three-dimensional photonic crystals with an ultrathin plasmonic titanium nitride coating that preserves photonic activity. Plasmonic titanium nitride enhances optical fields within the photonic electrode while maintaining sufficient light penetration. Additionally, we show that post-growth annealing can tune the plasmonic resonance of titanium nitride to overlap with the photonic resonance, potentially enabling coupled-phenomena applications for these three-dimensional nanophotonic systems. Through characterization of the tuning knobs of bead size, deposition temperature and cycle count, and annealing conditions, we can create an electrically- and plasmonically-active photonic crystal as-desired for a particular application of choice.

Fluid interfacial energy drives the emergence of three-dimensional periodic structures in micropillar scaffolds

Structures that are periodic on a microscale in three dimensions are abundant in nature, for example, in the cellular arrays that make up living tissue. Such structures can also be engineered, appearing in smart materials1–4, photonic crystals5, chemical reactors6, and medical7 and biomimetic8 technologies. Here we report that fluid–fluid interfacial energy drives three-dimensional (3D) structure emergence in a micropillar scaffold. This finding offers a rapid and scalable way of transforming a simple pillar scaffold into an intricate 3D structure that is periodic on a microscale, comprising a solid microscaffold, a dispersed fluid and a continuous fluid. Structures generated with this technique exhibit a set of unique features, including a stationary internal liquid–liquid interface. Using this approach, we create structures with an internal liquid surface in a regime of interest for liquid–liquid catalysis. We also synthesize soft composites in solid, liquid and gas combinations that have previously not been shown, including actuator materials with temperature-tunable microscale pores. We further demonstrate the potential of this method for constructing 3D materials that mimic tissue with an unprecedented level of control, and for microencapsulating human cells at densities that address an unresolved challenge in cell therapy. The revelation that fluid–fluid interfacial energy can drive structure formation in micropillar scaffolds offers a scalable way of synthesizing soft composites, which may have applications in building materials that mimic biological tissue.

Band gap optimization of one-dimension elastic waveguides using spatial Fourier plane wave expansion coefficients

Periodic elastic waveguides, such as rods, beams, and shafts, exhibit frequency bands where wave reflections at impedance discontinuities cause strong wave attenuation by Bragg scattering. Such frequency bands are known as stop bands or band gaps. This work presents a shape optimization technique for one-dimensional periodic structures. The proposed approach, which aims to maximize the width of the first band gap, uses as tuning parameters the spatial Fourier coefficients that describe the shape of the cell cross-section variation along its length. Since the optimization problem is formulated in terms of Fourier coefficients, it can be directly applied to the Plane Wave Expansion (PWE) method, commonly used to obtain the dispersion diagrams, which indicate the presence of band gaps. The proposed technique is used to optimize the shape of a straight bar with both solid and hollow circular cross-sections. First, the optimization is performed using the elementary rod, the Euler-Bernoulli and Timoshenko beam, and the shaft theoretical models in an independent way. Then, the optimization is conducted to obtain a complete band gap in the dispersion diagrams, which includes the three wave types, i.e., longitudinal, bending, and torsional. All numerical results provided feasible shapes that generate wide stop bands in the dispersion diagrams. The proposed technique can be extended to two- and three-dimensional periodic frame structures, and can also be adapted for different classes of cost functions.

Imaging of bi-anisotropic periodic structures from electromagnetic near-field data

Abstract This paper is concerned with the inverse scattering problem for the three-dimensional Maxwell equations in bi-anisotropic periodic structures. The inverse scattering problem aims to determine the shape of bi-anisotropic periodic scatterers from electromagnetic near-field data at a fixed frequency. The factorization method is studied as an analytical and numerical tool for solving the inverse problem. We provide a rigorous justification of the factorization method which results in the unique determination and a fast imaging algorithm for the periodic scatterer. Numerical examples for imaging three-dimensional periodic structures are presented to examine the efficiency of the method.

Macroscopic models for filtration and heterogeneous reactions in porous media

Derivation of macroscopic models for advection-diffusion processes in the presence of dominant heterogeneous (e.g., surface) reactions using homogenisation theory or volume averaging is often deemed unfeasible (Valdés-Parada et al., 2011; Battiato and Tartakovsky, 2011a) due to the strong coupling between scales that characterise such systems. In this work, we show how the upscaling can be carried out by applying and extending the methods presented in Allaire and Raphael (2007), Mauri (1991). The approach relies on the decomposition of the microscale concentration into a reactive component, given by the eigenfunction of the advection-diffusion operator, the associated eigenvalue which represents the macroscopic effective reaction rate, and a non-reactive component. The latter can be then upscaled with a two-scale asymptotic expansion and the final macroscopic equation is obtained for the leading order. The same method can also be used to overcome another classical assumption, namely of non solenoidal velocity fields, such as the case of deposition of charged colloidal particles driven by electrostatic potential forces. The whole upscaling procedure, which consists in solving three cell problems, is implemented for arbitrarily complex two- and three-dimensional periodic structures using the open-source finite volume library OpenFOAM®. We provide details on the implementation and test the methodology for two-dimensional periodic arrays of spheres, and we compare the results against fully resolved numerical simulations, demonstrating the accuracy and generality of the upscaling approach. The effective velocity, dispersion and reaction coefficients are obtained for a wide range of Péclet and surface Damköhler numbers, and for Coulomb-like forces to the grains. Noticeably, all the effective transport parameters are significantly different from the non-reactive (conserved scalar) case, as the heterogeneity introduced by the reaction strongly affects the micro-scale profiles.

Electrochemical Impedance Characterization of Blood Cell Suspensions. Part 1: Basic Theory and Application to Two-Phase Systems

Electrochemical impedance spectra of composite materials contain information on the topological arrangement, volume fraction, and shape of particles, as well as the dielectric properties of the matrix and particles. The objective of this study is to investigate how these parameters affect the dielectric spectrum and what reliable information can be extracted from experimental data. The main attention was focused on systems with dielectric behavior similar to that of human blood. Mostly plasma and erythrocytes determine the dielectric properties of whole blood. Erythrocytes suspended in plasma can be considered as three-phase systems with single-shelled particles. A theoretical approach based on the effective medium theory is developed for calculating the effective permittivity and conductivity of three-phase composites at a wide frequency range (from 0 to 1 GHz). A finite-difference method is applied to model three-dimensional periodic structures. A special case of two-phase materials is used to demonstrate the influence of the shape and arrangement of particles on dielectric properties. Theoretical and numerical approaches are applied to two-phase composites with spherical, spheroidal and biconcave particles and are compared with each other and with published data. It is shown that two-phase composites exhibit only β-dispersion. In contrast to the quasi-static limit, the wide-bandwidth impedance spectroscopy makes it possible to distinguish between disordered and regular arrangements of spheroidal and biconcave particles. The results can be used to analyze the dielectric properties of blood, which is very promising for various medical applications. This study of two-phase composites can be further extended to three-phase composites.

Flux pinning mechanisms and a vortex phase diagram of tin-based inverse opals

Three-dimensional periodic tin structures were synthesized by filling pores in silicon opals with a sphere diameter of 194 nm (Sn190) and 310 nm (Sn300). The samples were examined by the ultra-small-angle x-ray diffraction method, energy dispersive x-ray microanalysis and scanning electron microscopy. It was found that the inverse opal structure consists of tin nanoparticles inscribed in octahedral and tetrahedral pores with diameters of 128 nm and 70 nm for the sample Sn300, and 80 nm and 42 nm for the sample Sn190. The study of the magnetic properties of the samples by SQUID magnetometry showed that magnetization reversal curves exhibit hysteretic behavior. The mechanisms of magnetic flux pinning in the samples depend on the size of the tin nanoparticles. Tin nanoparticles in Sn300 behave like a classical type-I superconductor. The hysteretic behavior of the magnetization reversal curves at low magnetic fields is due to the formation of a network of superconducting contours in Sn300. These superconducting contours effectively trap the magnetic flux. The octahedral tin nanoparticles in Sn190 remain type-I superconductors, but smaller tetrahedral particles behave like type-II superconductors. Type-I and II superconducting particles in Sn190 lead to the coexistence of different mechanisms of flux pinning. These are flux trapping by superconducting contours at low magnetic fields and flux pinning by tetrahedral particles due to the surface barrier at high magnetic fields.

Three-dimensional periodic structures of gold nanoclusters in the interstices of sub-100 nm polymer particles toward surface-enhanced Raman scattering

Regularly ordered polymer nanoparticle (PNP) assemblies incorporating gold nanoparticle (Au NP) clusters into the PNP interstices were fabricated by a simultaneous deposition of PNPs and Au NPs on a glass substrate. Monodisperse PNPs with an average size of 66 nm were employed as a template in the co-assembly to create the sub-100 nm periodic Au nanostructures on the substrate. First, mono-layering of PNP array with incorporation of 14 nm Au NPs was performed by a drop-casting to examine the number ratio of Au NPs to PNPs for multi-layering. Absorption spectra of the mono-layered co-assemblies of PNPs and Au NPs were employed to characterize the clustered state of Au NPs in the interstices of mono-layered PNPs. The number ratio suitable for homogeneous incorporation of Au NPs clustered in the interstice was found to be ranged from 6 to 8 in the characterization. Then, multi-layered co-assemblies of PNPs and clustered Au NPs were fabricated by a vertical deposition method with the Au NP number ratio of 8 to PNPs. Lifting rate of the substrate on which the PNPs were deposited was varied in the vertical deposition method to tune the film thickness of NP co-assembly. A decrease in the lifting rate to 1 μm/s could thicken the film to 0.71 μm corresponding to 13 layers of PNPs, resulting in the fabrication of periodic structures of Au NP clusters with a high packing density. Signal-to-noise ratio in the Raman measurement using p-mercaptobenzoic acid as a target molecule was successfully enhanced by multi-layering of the co-assembly, indicating that Au NP clusters were homogeneously incorporated into the interstices of PNPs in the co-assemblies.