Rectangular Unit Cell Research Articles

Multiple high-Q resonances from mirror-coupled dielectric arrays

This paper reports how high-Q resonances can be created at multiple designated wavelengths in a low-index-contrast dielectric nanoparticle array coupled with a metal mirror. A rectangular array of TiO2 nanoparticles over a silver film (separated by a SiO2 spacer layer) can support collective resonances of magnetic and electric dipoles with their wavelengths determined mainly by the lattice spacings of the rectangular lattice. These resonances can be modulated by the spacer layer thickness to form accidental bound states in the continuum. Furthermore, resonances related to the periodicity along the diagonal of the rectangular unit cell can be produced by perturbing the lattice through modifying the dimensions of adjacent nanoparticles in the unit cell. Our result expands the potential of lattice resonances in low-index-contrast dielectric lattices, making them promising for applications in compact multi-wavelength and unidirectional light-emitting devices.

Analytical prediction of the formation factor for anisotropic mono-sized unconsolidated porous media

The rectangular Representative Unit Cell (RUC) models for mono-sized isotropic unconsolidated porous media have been extended to anisotropic media. Volume averaging was applied to Ohm's law in order to propose analytical expressions for the formation factor for electrical conduction in terms of the pore-scale linear dimensions. The formation factor, crucial for understanding electrical conduction in porous media, has significant applications in subsurface geophysics, petroleum reservoir characterization, and the durability assessment of construction materials. These analytical models provide valuable insights for optimizing the electrical properties of porous structures in various engineering fields, for example in mapping groundwater resources, differentiating oil-bearing zones in reservoirs, and predicting ion migration in concrete. Aspect ratios of the cell and solid dimensions have been introduced, and the formation factor expressed in terms thereof for five different arrays, i.e. a regular, a non-overlapping streamwisely fully staggered, an overlapping streamwisely fully staggered, a non-overlapping transversally fully staggered, and an overlapping transversally fully staggered array. The Laplace equation has furthermore been solved numerically for two-dimensional versions of the different arrays and the formation factor computed for several values of the aspect ratios. The proposed analytical models have been validated against the generated numerical data and compared to experimental and numerical data obtained from the literature. The proposed models have also been adapted to include a percolation threshold porosity in order to improve the model predictions for very low porosity media.

Assembly Structure Formation in Bulk and Ultrathin Films of Poly(substituted methylene) Having an Azobenzene Side Chain.

The density of the side chain introduced to a polymer main chain greatly influences the properties and functions of the polymer. This work first reports on the packing structure and properties at an interface of a poly(substituted methylene) where an azobenzene side chain is introduced at every carbon atom in the main chain (C1PAz). The structure and properties are compared with those of a conventional vinyl polymer [poly(methacrylate)] possessing an identical side-chain structure (C2PAz). The packing structure in the bulk state analyzed by X-ray measurements revealed that C1PAz adopts a highly ordered rectangular unit cell structure, whereas C2PAz shows a less ordered lamellar one. Langmuir film balance experiments indicated that both polymers with the trans-azobenzene give essentially the identical 2D side-chain occupying area on water, which agrees well with the smectic B (hexatic packing) model based on the X-ray data. Upon transfer onto a solid substrate, only C1PAz shows a conformational transformation to a spread bilayer-type layer, most probably due to conformational frustration stemming from the crowding of the side chains. This study proposes new insights into the effects of side-chain density on the self-assembly and photoreaction of azobenzene-containing polymers, which are expected to expand the possibilities of polymer design for various applications.

Numerical investigation of the mechanical properties of lattice structures inspired from polycrystalline materials

In this work, polycrystalline-like lattice structures that are inspired by the geometry of polycrystalline materials are designed. They are generated by filling periodic lattice structures into a Voronoi diagram. Then, finite element analyses of two periodic and eight polycrystalline-like lattice structures are performed to compare their mechanical properties. The numerical results show that polycrystalline-like lattice structures consisting of anisotropic rectangular X-type periodic unit cells are isotropic at the macroscale. Moreover, they have a higher specific stiffness and specific strength than periodic lattice structures under compression. Then, the energy absorption capability is investigated. Five energy absorption indicators (energy absorption, energy absorption per unit volume, specific energy absorption per unit mass, crush stress efficiency, and plateau stress) reveal that polycrystalline-like lattice structures are better energy absorption structures. Furthermore, the defect sensitivity of missing struts is discussed. The findings of this work offer a new route for designing novel lattice structures.

Investigation and Tailoring of Rotating Squares' and Rectangles' Auxetic Structure Behavior through Computational Simulations of 6082T6 Aluminum Alloy Structures.

Auxetic structures, renowned for their unique lateral expansion under longitudinal strain, have attracted significant research interest due to their extraordinary mechanical characteristics, such as enhanced toughness and shear resistance. This study provides a systematic exploration of these structures, constructed from rigid rotating square or rectangular unit cells. Incremental alterations were applied to key geometrical parameters, including the angle (θ) between connected units, the side length (a), the side width (b) of the rotating rigid unit, and the overlap distance (t). This resulted in a broad tunable range of negative Poisson's ratio values from -0.43 to -1.78. Through comprehensive three-dimensional finite-element analyses, the intricate relationships between the geometric variables and the resulting bulk Poisson's ratio of the modeled auxetic structure were elucidated. This analysis affirmed the auxetic behavior of all investigated samples, characterized by lateral expansion under tensile force. The study also revealed potential stress concentration points at interconnections between rotating units, which could impact the material's performance under high load conditions. A detailed investigation of various geometrical parameters yielded fifty unique samples, enabling in-depth observation of the impacts of geometric modifications on the overall behavior of the structures. Notably, an increase in the side width significantly enhanced the Poisson's ratio, while an increase in the overlap distance notably reduced it. The greatest observable change in the Poisson's ratio was a remarkable 202.8%, emphasizing the profound influence of geometric parameter manipulation. A cascaded forward propagation-backpropagation neural network model was deployed to determine the Poisson's ratio for auxetic structures, based on the geometric parameters and material properties of the structure. The model's architecture consisted of five layers with varying numbers of neurons. The model's validity was affirmed by comparing its predictions with FEA simulations, with the maximum error observed in the predicted Poisson's ratio being 8.62%.

Reexamine the emergence and stability of the square cylinder phase in block copolymers.

Recently, a few AB-type multiblock copolymers have been successfully designed to form stable square cylinder phase based on self-consistent field theory (SCFT) calculations. The previous works only identify the stability region of the square phase but not analyzing its stability, which is closely related to the free-energy landscape. In this work, we have reexamined the stability of the square phase in $\mathrm{B_1 A_1 B_2 A_2 B_3}$ linear pentablock and $\mathrm{(B_1AB_2)_5}$ star triblock copolymers by drawing the free-energy landscape with respect to the two dimensions of a rectangular unit cell. Our results demonstrate that the square phase continuously transfers to the rectangular phase as the degree of packing frustration is gradually released. Moreover, the prolate contour lines of the free-energy landscape indicate the weak stability of the square phase in the $\mathrm{B_1 A_1 B_2 A_2 B_3}$ copolymer. In contrast, the stability of the square phase is notably improved in the $\mathrm{(B_1AB_2)_5}$ copolymer due to its enhanced concentration of bridging configurations. Our work sheds light on the understanding of the stability of the square cylinder phase in block copolymers. Accordingly, we propose some possible strategies for further designing new AB-type block copolymer systems to obtain more stable square phase.

All-dielectric carpet cloaks with three-dimensional anisotropy control

Abstract In this article, we propose all-dielectric carpet cloaks composed of jungle gym shaped dielectric unit cells and present a design strategy for three-dimensional (3-D) anisotropy control based on the transformation optics. The carpet cloaks are 3-D printable and operate with polarization independent incident waves in arbitrary incident angles due to the 3-D anisotropy control. Realizable anisotropic permittivities of cubic and rectangular unit cells are numerically studied based on the relative permittivity and loss tangent of ɛ r = 2.9 and tan δ = 0.02 of ultra-violet curing resin measured at the microwave frequency. It is shown that the unit cell has little frequency dependence even with the anisotropy in the low frequency range where the effective medium approximation is valid. A carpet cloak is designed based on the design method with a quasi-conformal coordinate transformation and implemented with the unit cells taking into account its realizable anisotropy. Polarization independent 3-D cloaking operations of the designed cloak are confirmed numerically. The designed cloak is fabricated by stereolithography 3-D printing technology and its cloaking performances are evaluated experimentally at 10 GHz. It is shown that non-specular reflections are well suppressed by the carpet cloak for both TE and TM incident waves with different incident angles of 30, 45, and 60°. Frequency independent cloaking operations are also shown experimentally in the X-band. The measured near-field distributions and bistatic radar cross sections are in good agreement with simulated predictions and the validity of the design method is confirmed.

How water desorbs from calcite.

Calcite is the most abundant carbonate mineral in Earth's crust. Upon cleavage, the (10.4) plane with a rectangular unit cell is exposed. Interestingly, several experiments suggest a (2 × 1) surface reconstruction. However, clear experimental evidence and a theoretical confirmation were long missing. Recently, convincing indication for a (2 × 1) reconstruction has been given by atomic force microscopies taken at 5 K. Here, we show temperature-programmed desorption (TPD) experiments of water and ethanol desorbing from calcite (10.4) around room temperature. The TPD curves fit excellently to a kinetic model considering two different adsorption sites, as expected in case of a (2 × 1) reconstruction. This finding applies to the desorption of water and ethanol, illustrating that the effect is characteristic for the calcite cleavage plane. Our results thus show that the (2 × 1) reconstruction not only exists at room temperature but has significant impact on the interfacial properties of calcite.

Elasticity-based locally-exact homogenization theory for three-phase composites considering the morphological effect of carbon fibers

Elasticity-based locally-exact homogenization theory (LEHT) is further extended in this paper to investigate the mechanical behaviors of three-phase composites with orthotropic interlayer as well as circumferentially orthotropic (CO) and radially orthotropic (RO) carbon fibers that are determined by their morphological basal plane. Taking advantage of the Fourier series representations for displacements of each phase, in-plane and out-of-plane exact solutions are obtained for orthotropic media through rigorous mathematical derivations and the internal eigenvalue functions are directly solved within rectangular and hexagonal representative unit cells (RUCs) subjected to axial normal, transverse loading and axial shear loading, respectively. The balanced variational principle is applied to enforce periodical boundary conditions which ensures rapid convergence of displacement fields. The solutions of LEHT are verified with far-field Eshelby problems with good agreement and the morphological effects of fiber are investigated by comparing CO/RO properties and equivalent transversely isotropic (TI) parameters obtained from replacement scheme. Homogenized elastic moduli of RUCs with orthotropic interlayer are predicted through homogenization constitutive relations and compared to special extension of the composite cylinders approach and numerical results based on the asymptotic expansion homogenization method to demonstrate excellent correlation. Finally, the effects of orthotropic interlayer have been demonstrated and local stress distributions are obtained from a “top-to-down” procedure, illustrating constituents’ interactions from microscope perspective and identifying the possible crack initiations/propagations within microstructures.

Control of the piezoelectric and flexoelectric homogenized properties of architected materials by tuning their inner topology

The present contribution aims to study the effect the inner topology of periodic architected materials on their effective piezoelectric and flexoelectric properties. An analysis is performed to study the sensitivity of the effective flexoelectric moduli to the geometrical variables of the considered unit cells of periodic lattice materials. More specifically, hexagonal, re-entrant auxetic, and rectangular unit cells are investigated in terms of their relative piezoelectric and flexoelectric response. The base material obeys a piezoelectric behavior, and the homogenized electromechanical properties are evaluated using the extended Hill–Mandel macrohomogeneity condition articulated with variational principles in the context of periodic multiphysical homogenization. The developed modeling framework of coupled electromechanical phenomena accounts for the higher gradient effects modeled by flexoelectricity that are induced by the strong gradient of properties that exist at the microlevel of the lattice unit cell. Regular hexagonal, re-entrant hexagonal and rectangular lattice unit cells are mutually compared in terms of their flexoelectric properties. The regular hexagonal UC shows the highest piezoelectric moduli, whereas the flexoelectric moduli are found to be maximum for the re-entrant UC. The coupling between mechanical and electrical fields is attested by the non-uniform distribution of the electric potential within the three studied architected materials subjected to a uniform strain.

A rosette approach for the determination of the compliance matrix

The computation of the Young's moduli and Poisson's ratio using finite element analysis is comparatively straight forward in the case of systems with non-orthogonal lattice vectors. However, the corresponding calculation of the shear coupling coefficients and the shear modulus is more demanding and less readily attainable. Yet these are needed in order to determine the compliance matrix, which is essential in order to obtain a complete description of the mechanical properties of a structure in any direction. Based on these considerations, this work aims at providing a general methodology for the computation of the complete compliance matrix for systems with non-orthogonal lattice vectors from measurements of the Young's modulus and Poisson's ratio obtained using a suitable rosette of unit cells. The theoretical framework will be outlined and then applied on an accordion-like honeycomb that does not possess a rectangular unit cell and has potential applications in cellular scaffolding, particularly of heart muscle tissue. For the computation, the values of the Young's moduli and Poisson's ratio from three differently-orientated non-rectangular unit cells were obtained using finite element simulations allowing the determination of the complete compliance matrix. The results were validated by comparison with numerical simulations carried out on another unit cell having a different orientation from the other three.

Sandwich structure with negative Poisson’s ratio of periodic rectangular tube: Mechanical properties and energy absorption

Due to its unique deformation form, Negative Poisson’s ratio sandwich structure has excellent energy absorption, but the low load capacity limits its engineering applications. In this paper, we design a new negative Poisson’s ratio rectangular tube periodic sandwich structure. There are many beams in this structure which appear plastic hinges when compressed. After further compression, the rectangular tube wall buckles and the core shrinks inward, which realizes that the structure exhibits high-performance energy absorption ability and excellent mechanical properties. Three-dimensional finite element model of sandwich structure with negative Poisson’s ratio of periodic rectangular tube quasi-static compression test and low-velocity impact were investigated by the use of ABAQUS/Explicit software. The accuracy of the simulation method was verified by the comparison of test and simulation results. Based on the validated numerical models were further investigated to comprehensively understand the influence of rectangular tube unit cell wall thickness ( t) and cell height ( h) on the load capacity and energy absorption capacity of the specimen. The energy absorption capacity and mechanical properties of the proposed negative Poisson’s ratio sandwich structure could be enhanced by optimizing the design of rectangular tube unit cell wall thickness ( t) and rectangular tube unit cell height ( h). The present findings offer insights into the application of negative Poisson’s ratio sandwich structure impact energy-absorbing structures in aerospace, automotive and other fields.

Equivalent circuit analysis of a mode-converting metacell in a coaxial transmission line at microwave frequencies

To provide for an ever-increasing need for camouflage, experts in stealth have been envisioning for a few years to use metasurfaces and their unconventional electromagnetic properties to serve as efficient cloaking devices. To prepare for the use of surface-mounted electronic components, useful for frequency-selecting purposes, we take interest in an equivalent circuit analysis of metasurfaces. Indeed, metasurfaces using electronic components invite one to combine the passive behavior of the host structure with that of the lumped elements. The equivalent circuit analysis of the hosting surface deprived of electronic components has so far been dedicated to the case of metasurfaces constituted by rectangular or square unit cells. This work, therefore, aims at extending the former study on Cartesian unit cells to the coaxial geometry of interest. The validity of such a method is then assessed by comparison with the numerical simulation results obtained using a finite-element method.

Effects of cholesterol on the structure and collapse of DPPC monolayers

Cholesterol induces faster collapse by compressed films of pulmonary surfactant. Because collapse prevents films from reaching the high surface pressures achieved in the alveolus, most therapeutic surfactants remove or omit cholesterol. The studies here determined the structural changes by which cholesterol causes faster collapse by films of dipalmitoyl phosphatidylcholine, used as a simple model for the functional alveolar film. Measurements of isobaric collapse, with surface pressure held constant at 52 mN/m, showed that cholesterol had little effect until the mol fraction of cholesterol, Xchol, exceeded 0.20. Structural measurements of grazing incidence X-ray diffraction at ambient laboratory temperatures and a surface pressure of 44 mN/m, just below the onset of collapse, showed that the major structural change in an ordered phase occurred at lower Xchol. A centered rectangular unit cell with tilted chains converted to an untilted hexagonal structure over the range of Xchol = 0.0–0.1. For Xchol = 0.1–0.4, the ordered structure was nearly invariant; the hexagonal unit cell persisted, and the spacing of the chains was essentially unchanged. That invariance strongly suggests that above Xchol = 0.1, cholesterol partitions into a disordered phase, which coexists with the ordered domains. The phase rule requires that for a binary film with coexisting phases, the stoichiometries of the ordered and disordered regions must remain constant. Added cholesterol must increase the area of the disordered phase at the expense of the ordered regions. X-ray scattering from dipalmitoyl phosphatidylcholine/cholesterol fit with that prediction. The data also show a progressive decrease in the size of crystalline domains. Our results suggest that cholesterol promotes adsorption not by altering the unit cell of the ordered phase but by decreasing both its total area and the size of individual crystallites.

Slot coupled dual band high gain circularly polarized metasurface antenna

This article presents a slot coupled dual-band metasurface (MTS) based antenna with high gain and circular polarization characteristics. The MTS consists of two different unit cells, which give rise to two operating bands. The metasurface is excited by the slot aperture fed by a 50 Ω microstrip feed-line. The circular polarization is achieved by the diagonally oriented rectangular patch-based unit cells on top of the square substrate. Two orthogonal modes of MTS are required to produce circularly polarized waves, and these modes are excited by the slot aperture. The proposed MTS-inspired antenna is fabricated and experimentally validated. The experimentally verified impedance bandwidth of 33.71% in the lower frequency band and 5.35% in the upper-frequency band is achieved. The measured 3 dB (AR <3 dB)axial ratio bandwidth of 6.22% and 0.98% with a peak gain of 8.89 and 6.32 dBic is achieved with respect to 4.8 and 6.4 GHz resonant frequencies.

Design and Analysis of Metamaterial-Based SWB-MIMO Antenna

The design and analysis of a four-port multi-input multi-output (MIMO) super wideband antenna (SWB) with a metamaterial superstrate are proposed. Initially, a single antenna is constructed with a hexagonal radiator loaded with dodecagon slots along with a slotted partial ground. An impedance bandwidth of 4.1–14.7 GHz is achieved by using symmetric coplanar waveguide feeding technique and three iterations of dodecagon slot-loaded radiating element. The design is extended to a 2 × 2 MIMO antenna with dimensions 50 × 50 × 1.6 mm3. The four symmetrical SWB antennas are placed orthogonally to each other at four corners of a square-shaped FR4 substrate. A metamaterial superstrate is used above the four-port antenna to increase the antenna’s performance characteristics. A 7 × 7 array of rectangular metamaterial unit cells acts as a building block for the metamaterial superstrate to improve impedance matching, enhance isolation between the elements, and boost the antenna’s gain. The metamaterial unit cells are made up of three rectangular rings that are put on top of a 1.6 mm thick FR4 substrate. With a mutual coupling of (>15 dB), the antenna achieved S11 < −10 dB for an impedance bandwidth of 11 GHz. The gain enhancement of up to 1.73 dB is obtained in C and X bands using metamaterial superstrate. The antenna characteristics mainly peak gain, return loss, bandwidth, and isolation are examined. The simulated results affirm a decent deal with experimental results.

Broadband Circularly Polarized Microstrip Patch Antenna With Diamond-Shaped Artificial Ground Structure

This paper presents a broadband circularly polarized patch antenna with an artificial ground structure (AGS), which has rotated rectangular unit cells with respect to the sides of the rectangular ground plane, as a polarizer. A two-element ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2\times 1$ </tex-math></inline-formula> ) array configuration of the antenna is also presented. The rectangular unit cells are rotated by 45° with respect to the sides of a square dielectric substrate, named a diamond-shaped AGS (DAGS). The overall dimensions of the AGS are smaller than those of the ground plane. The rotated unit cells and the smaller AGS patch dimensions effectively suppress surface wave resonance on the AGS. The proposed antenna achieves a wide 3-dB axial ratio bandwidth in the boresight direction. The proposed design has a flatter gain curve in the operating frequency band compared to that for conventional designs. It is found that the array configuration outperforms the single-element structure.

CSRR-Loaded Compact Quad Port MIMO Diversity Antenna for UWB Applications

In this article, a miniature MIMO antenna with four ports along with a complementary split ring resonator embedded in the ground plane, is presented. The proposed antenna consists of four identical radiating elements each of which has two isosceles triangles and one rectangular slot cut from the basic rectangular patch and placed on the same plane. The isolation of the proposed antenna has been improved by taking 4 L-shaped strips and two rectangular CSRR unit cells on the ground plane between antenna elements. The antenna characteristics, such as return loss (<−10 dB), isolation parameter (>18 dB), peak gain values vary from 0.5to 3.6 dB, the maximum efficiency of 84%, were measured. Further diversity of the MIMO antenna has been measured with reference to ECC<0.02, DG>9.95, TARC< −15 dB, MEG at each port less than 3 dB along with CCL<0.35 bits/s/Hz. The measured impedance bandwidth achieved from 2.8 to 18 GHz encompasses the whole ultra wideband range. The prototype antenna is quite suitable for today’s wireless communication devices.

Two-Dimensional Composite Acoustic Metamaterials of Rectangular Unit Cell from Pentamode to Band Gap

Pentamode metamaterials have been receiving an increasing amount of interest due to their water-like properties. In this paper, a two-dimensional composite pentamode metamaterial of rectangular unit cell is proposed. The unit cells can be classified into two groups, one with uniform arms and the other with non-uniform arms. Phononic band structures of the unit cells were calculated to derive their properties. The unit cells can be pentamode metamaterials that permit acoustic wave travelling or have a total band gap that impedes acoustic wave propagation by varying the structures. The influences of geometric parameters and materials of the composed elements on the effective velocities and anisotropy were analyzed. The metamaterials can be used for acoustic wave control under water. Simulations of materials with different unit cells were conducted to verify the calculated properties of the unit cells. The research provides theoretical support for applications of the pentamode metamaterials.

Antiphase Domain Boundary Formation in 2D Ba–Ti–O on Pd(111): An Alternative to Phase Separation

2D oxide quasicrystals (OQCs) are unique structures arising from atoms positioned at the vertices of a dodecagonal triangle–square–rhombus tiling. The prototypical example for OQCs is derived from BaTiO3 on Pt(111). Herein, scanning tunneling microscopy (STM) and low‐energy electron diffraction (LEED) investigations of 2D oxide layers derived from BaTiO3 on Pd(111) are reported. Upon ultrahigh vacuum (UHV) annealing, different long‐range ordered structures are observed with a base of four vertex atoms forming two edge‐sharing equilateral triangles. By a periodic repetition of this base in either quadratic or rectangular unit cells, a triangle–square tiling (known as σ‐phase approximant or 32.4.3.4 Archimedean tiling) or a triangle–rhombus tiling is formed. Both structures vary strongly in their vertex density. In addition, the formation of antiphase domain boundaries in the σ phase is observed resulting in a well‐ordered incorporation of rhombuses in the triangle–square tiling. A systematic variation of the frequency of these domain boundaries is identified as a mechanism for an incremental increase in the global vertex density, mediating between pure triangle–square and triangle–square–rhombus tilings.