One-dimensional Rods Research Articles

One-dimensional KNN micro rods doping to facilitate the energy conversion performance of a KNN MRs/P(VDF-TrFE) composite

Piezoelectric self-powered electronic devices can convert ambient mechanical vibrations into electrical energy in an environmentally friendly manner, significantly alleviating the scarcity of non-renewable sources. This work prepares an one-dimensional potassium sodium niobate micro rods (1D KNN MRs) using the molten salt - topological chemical reaction method, showing the significant advantages over 0-dimension (0D) nanoparticles due to its anisotropy. Simultaneously, KNN MRs are introduced into poly (vinylidene fluoride-trifluoroethylene) to form a KNN MRs/P(VDF-TrFE) piezoelectric composite, effectively facilitating the piezoelectric β-phase in P(VDF-TrFE) film, and contributing to a high remnant polarization (Pr ∼12.3 μC/cm2) at 125 MV/m and a high piezoelectric constant (d33 = −28 pC/N). Interestingly, a piezoelectric sensor assembled by KNN MRs/P(VDF-TrFE) composite shows a considerable piezoelectric output of 17.6 V at a scene of 2.5 MPa stress, offering a novel route for designing the optimum ceramic/polymer combinations suitable for mechanical energy conversion and energy harvesting.

Revised Enskog equation for hard rods

We point out that Percus’s collision integral for one-dimensional hard rods (Percus 1969 Phys. Fluids 12 1560–3) does not preserve the thermal equilibrium state in an external trapping potential. We derive a revised Enskog equation for hard rods and show that it preserves this thermal state exactly. In contrast to recent proposed kinetic equations for dynamics in integrability-breaking traps, both our kinetic equation and its thermal states are explicitly nonlocal in space. Our equation differs from earlier proposals at third order in spatial derivatives and we attribute this discrepancy to the choice of collision integral underlying our approach.

Peridynamic study of fatigue failure of engineered cementitious composites

Fatigue crack propagation is crucial in studying fatigue in engineered cementitious composites (ECC). This paper established a peridynamics (PD)-based fatigue crack propagation model for ECC, incorporating the “cycle broken bonds number” to enhance calculation efficiency. First, the PD fatigue crack propagation model was constructed, and the validity of the model was verified by simulating the fatigue crack propagation path of an inclined edge crack in the plate. Secondly, an improved PMB model considering the strain softening stage was used to model the ECC cement matrix, and the fibers were modeled as one-dimensional cyclic dynamic rods to establish a PD fully discrete model of ECC. At the same time, an interface exponential friction attenuation model was introduced. Then, the effectiveness and validness of the fully discrete model were verified by simulating single fiber pull-out tests and uniaxial tensile tests of ECC specimens. Finally, the fatigue crack propagation forms of ECC beams with mid span Type I cracks under three-point bending fatigue loads were studied, and the effects of fiber volume fraction, stress level, and fiber length on the crack propagation forms and structural deflection of ECC beams under four-point bending fatigue loads were investigated.

The Role of Frequency and Impedance Contrasts in Bandgap Closing and Formation Patterns of Axially-Vibrating Phononic Crystals

Abstract Bandgaps, or frequency ranges of forbidden wave propagation, are a hallmark of phononic crystals (PnCs). Unlike their lattice counterparts, PnCs taking the form of continuous structures exhibit an infinite number of bandgaps of varying location, bandwidth, and distribution along the frequency spectrum. While these bandgaps are commonly predicted from benchmark tools such as the Bloch-wave theory, the conditions that dictate the patterns associated with bandgap symmetry, attenuation, or even closing in multi-bandgap PnCs remain an enigma. In this work, we establish these patterns in one-dimensional rods undergoing longitudinal motion via a canonical transfer-matrix-based approach. In doing so, we connect the conditions governing bandgap formation and closing to their physical origins in the context of the Bragg condition (for infinite media) and natural resonances (for finite counterparts). The developed framework uniquely characterizes individual bandgaps within a larger dispersion spectrum regardless of their parity (i.e., odd versus even bandgaps) or location (low versus high-frequency), by exploiting dimensionless constants of the PnC unit cell which quantify the different contrasts between its constitutive layers. These developments are detailed for a bi-layered PnC and then generalized for a PnC of any number of layers by increasing the model complexity. We envision this mathematical development to be a future standard for the realization of hierarchically structured PnCs with prescribed and finely tailored bandgap profiles.

Micropolar Elasticity in Physically-Based Animation

We explore micropolar materials for the simulation of volumetric deformable solids. In graphics, micropolar models have only been used in the form of one-dimensional Cosserat rods, where a rotating frame is attached to each material point on the one-dimensional centerline. By carrying this idea over to volumetric solids, every material point is associated with a microrotation, an independent degree of freedom that can be coupled to the displacement through a material's strain energy density. The additional degrees of freedom give us more control over bending and torsion modes of a material. We propose a new orthotropic micropolar curvature energy that allows us to make materials stiff to bending in specific directions. For the simulation of dynamic micropolar deformables we propose a novel incremental potential formulation with a consistent FEM discretization that is well suited for the use in physically-based animation. This allows us to easily couple micropolar deformables with dynamic collisions through a contact model inspired from the Incremental Potential Contact (IPC) approach. For the spatial discretization with FEM we discuss the challenges related to the rotational degrees of freedom and propose a scheme based on the interpolation of angular velocities followed by quaternion time integration at the quadrature points. In our evaluation we validate the consistency and accuracy of our discretization approach and demonstrate several compelling use cases for micropolar materials. This includes explicit control over bending and torsion stiffness, deformation through prescription of a volumetric curvature field and robust interaction of micropolar deformables with dynamic collisions.

Flexural vibration bandgaps in one-dimensional periodic rods with tri-wing rhombus ligament resonators

Structural stiffness of phononic crystals (PnCs) can affect their bandgap properties. It thus needs to consider stiffness in the design of the unit cell of a PnC. In this paper, a local resonant (LR) rod composed of tri-wing rhombus ligament (TRL) resonators arranged periodically within a common hollow rod is proposed to create a low-frequency flexural vibration bandgap. The dispersion relations, mode of resonances and vibration transfer function are studied using a finite element method. Low-frequency forbidden bands can be effectively shifted by changing the resonator geometries. In addition, both numerical simulations and sample test are conducted to verify the low-frequency bandgap. The results show that the hollow rod with TRL resonators can create a low-frequency flexural vibration bandgap as well as have high support structure stiffness.

Transient analysis of monopiles embedded in layered saturated soils under vertical excitations

This paper investigates the transient dynamic response of vertical loaded monopiles embedded in layered saturated soils. Firstly, the piles are modeled as the one-dimensional rods, which are solved by the finite element method (FEM). Then the analytical layer-element solutions of layered saturated soils are used as the kernel functions of the boundary element method (BEM), and the boundary integral equation of the soils are further acquired. By introducing the pile-soil interface conditions, the transient response of the pile-soil system is obtained with the aid of the FEM-BEM coupled method. The proposed method is verified by comparing the results with those in existing literature and ABAQUS. Finally, parametric studies are conducted to determine the effects of the length-diameter ratio, pile-soil modulus ratio, stratification and permeability.

Nanosheets/nanoparticles-composed hierarchical manganese oxides enabled by molybdenum nitride rods for boosted oxygen reduction reaction electrocatalysis

Catalyst microgeometry plays a more important role than activity in determining output performance of metal-air batteries. However, this is often overlooked. Herein, hierarchical manganese oxides anchored by one-dimensional molybdenum nitride rods (Mn/Mo2N) were constructed for efficient oxygen reduction reaction (ORR) electrocatalysis. The composition-optimized 10%Mn/Mo2N possessed a higher catalytic capability than commercial Pt/C catalyst in a homemade zinc-air battery (ZAB), even though the former exhibited a lower have-wave potential than the latter in rotating disk electrode (RDE) measurements. Moreover, the ZAB driven by 10%Mn/Mo2N possessed a larger discharging specific capacity than the one driven by Pt/C. This improved discharging performance was attributed to the high dimension of hierarchical features of Mn oxides anchored on Mo2N, which benefited the stabilization of active sites and accelerated mass transmission originating from the one-dimensional Mo2N rods. This inference was further confirmed by the high peak power densities of ZABs driven by high-dimensional 2%Mn/Mo2C-Mo2N, 5%Co/Mo2C-Mo2N, which exhibited relatively low catalytic activities in RDE measurements. For ORR electrocatalysts, the relationship between ORR activity and the corresponding ZAB power was built on the first attempt. This work highlighted the significance of hierarchical microgeometry, rather than the intrinsic activity, on boosting the electrocatalytic kinetics of a catalyst for efficiently practical electrochemical energy conversion.

Edge-Active Enriched MoS2 Porous Nanosheets as Efficient Pt-Free Catalysts toward the Triiodide Reduction Reaction

Developing high-efficiency counter electrode (CE) catalysts for the triiodide (I3–) reduction reaction (IRR) is of great significance for the development of cost-effective dye-sensitized solar cells (DSSCs). From the perspective of further enhancing the catalytic activity of CE catalysts by exposing more active sites, edge-active enriched MoS2 porous nanosheets are elaborately constructed using the as-prepared one-dimensional MoO3 rods and poly(vinylpyrrolidone) (PVP) as a template-directing agent and surfactant based on the dissolution–recrystallization strategy (MoS2-P), respectively, while the MoS2 quasi-particles (MoS2-C) and irregular MoS2 aggregations are also synthesized using cetyltrimethyl ammonium bromide (CTAB) as a surfactant and commercial MoO3 powder as a molybdenum source under similar reaction processes. Benefiting from the high specific surface area, exposure of edge active sites, and effective ion diffusion-favored structure, MoS2-P delivers good photovoltaic performance (PCE = 8.16%, Voc = 0.782 V, Jsc = 16.77 mA/cm2, FF = 0.62) when used as a CE catalyst for DSSCs, superior to that of MoS2-C (PCE = 6.87%, Voc = 0.741 V, Jsc = 15.91 mA/cm2, FF = 0.58), which is comparable with that of the Pt-based device (PCE = 8.33%, Voc = 0.775 V, Jsc = 16.85 mA/cm2, FF = 0.64). A series of electrochemical results further reveal that the obtained MoS2-P has good catalytic activity for the IRR and electrochemical stability in iodine-based electrolytes. Hence, our work may provide a promising catalyst for the energy conversion field.

Взаимная гравитационная энергия сфероидальных тел

The problem of mutual gravitational energy Wmut for a system of two homogeneous prolated spheroids whose symmetry axes are on the same line is set and solved. The method of equigravitating elements is applied, where the external potentials of three-dimensional spheroids are represented by the potentials of one-dimensional inhomogeneous focal rods. The solution of the problem is reduced to the integration of the potential of one rod over the segment of the second rod. As a result, the expression Wmut for two prolated spheroids can be obtained in a finite analytic form through elementary functions. The force of attraction between the spheroids is found. The function Wmut is also represented by a series of degrees of eccentricity of the spheroids. Possible applications of the obtained results are discussed.

Elastic wave dispersion equation considering material and geometric nonlinearities

In this letter, we describe the propagation of longitudinal waves in one-dimensional nonlinear elastic thin rods with material nonlinearity and geometric nonlinearity. Mathematical analysis is used to derive the analytical dispersion relationship of longitudinal waves; subsequently, the numerical Fourier spectrum method is used to solve the nonlinear wave equation directly and the results are used to verify the correctness of the derived nonlinear dispersion relation.

Epitaxial intergrowths and local oxide relaxations in natural bixbyite Fe2-x Mn x O3.

The scattering pattern of a crystal obeys the symmetry of the crystal structure through the corresponding Laue group. This is usually also true for the diffuse scattering, containing information about disorder, but here a case is reported where the diffuse scattering is of lower symmetry than the parent crystal structure. The mineral bixbyite has been studied by X-ray and neutron scattering techniques since 1928 with some of the most recent studies characterizing the low-temperature transition to a magnetically disordered spin-glass state. However, bixbyite also exhibits structural disorder, and here single-crystal X-ray and neutron scattering is used to characterize the different modes of disorder present. One-dimensional rods of diffuse scattering are observed in the cubic mineral bixbyite, which break the expected symmetry of the scattering pattern. It is shown that this scattering arises from epitaxial intergrowths of the related mineral, braunite. The presence of this disorder mode is found to be directly observable as well-defined residuals in the average structure refined against the Bragg diffraction. An additional three-dimensional diffuse scattering component is observed in neutron scattering data, which is shown to originate from the substitutional disorder on the Fe/Mn sites. This occupational disorder gives rise to local relaxations of the oxide sublattice, and the pattern of oxide displacements can be rationalized based on crystal-field theory. The combined use of neutron and X-ray single-crystal scattering techniques highlights their great complementarity. In particular, the large sample requirements for neutron scattering experiments prove to be an obstacle in solving the intergrowth disorder due to several growth orientations, whereas for X-ray scattering the one-dimensional nature of the intergrowth disorder renders solving this a more tractable task. On the other hand, the oxide relaxations cannot be resolved using X-rays due to the low Mn/Fe contrast. By combining the two approaches both types of disorder have been characterized.

Расчет температурного поля многослойных несущих конструкций численными методами

Modern approaches to the electronic means design include modeling of thermophysical processes occurring in the apparatus being developed. At the same time, a common task in thermophysical modeling is the problem of determining the temperature field of the supporting structure of an electronic device (board, substrate). Knowledge of the quantitative indicators of the supporting structure temperature field directly affects the prediction of the entire electronic device reliability. The load-bearing structures of electronic devices are increasingly made in the form of multilayer structures where conductive, insulating and semiconductor layers can be present. These features impose new requirements on the development of mathematical models, algorithms, application software packages for calculating the temperature fields of the supporting structures of electronic means. The article considers the process of modeling the temperature field for the supporting structures of electronic means using common software systems MathCAD and SolidWorks. The whole variety of supporting structures of electronic means is divided into three categories: conditionally one-dimensional, conditionally two-dimensional and three-dimensional. It is shown that the temperature fields of conditionally one-dimensional (rods) and conditionally two-dimensional (single-layer boards and substrates) structures should be calculated by the finite difference method in the MathCAD software package. Temperature fields of three-dimensional load-bearing structures, including complex geometric configurations, should be calculated using the finite element method in the SolidWorks software package. The developed algorithms for calculating temperature fields are verified by solving a test problem. Comparative analysis has shown that the discrepancy between the calculation results relative to the test problem does not exceed 0.8%. The developed algorithms for calculating the temperature field can be practically useful in the engineering activities of the developer of electronic equipment.

Numerical Exploration on Snap Buckling of a Pre-Stressed Hemispherical Gridshell

AbstractMotivated by the observations of snap-through phenomena in pre-stressed strips and curved shells, we numerically investigate the snapping of a pre-buckled hemispherical gridshell under apex load indentation. Our experimentally validated numerical framework on elastic gridshell simulation combines two components: (i) discrete elastic rods method, for the geometrically nonlinear description of one-dimensional rods, and (ii) a naive penalty-based energy functional, to perform the non-deviation condition between two rods at joint. An initially planar grid of slender rods can be actuated into a three-dimensional hemispherical shape by loading its extremities through a prescribed path, known as buckling-induced assembly; next, this pre-buckled structure can suddenly change its bending direction at some threshold points when compressing its apex to the other side. We find that the hemispherical gridshell can undergo snap-through buckling through two different paths based on two different apex loading conditions. The structural rigidity increases as the number of rods in the gridshell structure becomes denser, which emphasizes the mechanically nonlocal property in hollow grids, in contrast to the local response of continuum shells. The findings may bridge the gap among rods, grids, knits, and shells, for a fundamental understanding of a group of thin elastic structures, and inspire the design of novel micro-electro-mechanical systems and functional metamaterials.

1D Zn2GeO4 rods supported on Ni foam for high performance non-enzymatic hydrogen peroxide sensor

One-dimensional (1D) Zn2GeO4 rods were in-situ grown on Ni foam (NF) using a ethylenediamine (En)/water mixed solvent by a hydrothermal route in one single step. Such rhombohedral phase Zn2GeO4 rods are 1–2 μm in diameter and a few micrometers in length. Ethylenediamine is found to play a critical role in coordinating with starting zinc and germanium ions and acting as template. The Zn2GeO4/NF was developed as a new none-enzymatic hydrogen peroxide (H2O2) sensor. In electrochemical studies, the Zn2GeO4/NF electrode exhibits high sensitivity (3974 μM mM−1 cm−2), wide linear detection range (1–4000 μM), fast response (<9 s), low detection limit (1 μM), excellent selectivity and stability towards H2O2. Several factors such as intrinsic nature of Zn2GeO4, the unique microstructure and the seamless contact with NF are believed to attributed to the excellent electrochemical sensing performances.

Numerical Method for Direct Solution to Form-Finding Problem in Convex Gridshell

AbstractElastic gridshell is a class of net-like structure formed by an ensemble of elastically deforming rods coupled through joints, such that the structure can cover large areas with low self-weight and allow for a variety of aesthetic configurations. Gridshells, also known as X-shells or Cosserat Nets, are a planar grid of elastic rods in its undeformed configuration. The end points of the rods are constrained and positioned on a closed curve—the final boundary—to actuate the structure into a 3D shape. Here, we report a discrete differential geometry-based numerical framework to study the geometrically nonlinear deformation of gridshell structures, accounting for non-trivial bending-twisting coupling at the joints. The form-finding problem of obtaining the undeformed planar configuration given the target convex 3D topology is then investigated. For the forward (2D to 3D) physically based simulation, we decompose the gridshell structure into multiple one-dimensional elastic rods and simulate their deformation by the well-established discrete elastic rods (DER) algorithm. A simple penalty energy between rods and linkages is used to simulate the coupling between two rods at the joints. For the inverse problem associated with form-finding (3D to 2D), we introduce a contact-based algorithm between the elastic gridshell and a rigid 3D surface, where the rigid surface describes the target shape of the gridshell upon actuation. This technique removes the need of several forward simulations associated with conventional optimization algorithms and provides a direct solution to the inverse problem. Several examples—hemispherical cap, paraboloid, and hemi-ellipsoid—are used to show the effectiveness of the inverse design process.

Synthesis and applications of anisotropic nanoparticles with precisely defined dimensions.

Shape and size play powerful roles in determining the properties of a material; controlling these aspects with precision is therefore an important, fundamental goal of the chemical sciences. In particular, the introduction of shape anisotropy at the nanoscale has emerged as a potent way to access new properties and functionality, enabling the exploration of complex nanomaterials across a range of applications. Recent advances in DNA and protein nanotechnology, inorganic crystallization techniques, and precision polymer self-assembly are now enabling unprecedented control over the synthesis of anisotropic nanoparticles with a variety of shapes, encompassing one-dimensional rods, dumbbells and wires, two-dimensional and three-dimensional platelets, rings, polyhedra, stars, and more. This has, in turn, enabled much progress to be made in our understanding of how anisotropy and particle dimensions can be tuned to produce materials with unique and optimized properties. In this Review, we bring these recent developments together to critically appraise the different methods for the bottom-up synthesis of anisotropic nanoparticles enabling exquisite control over morphology and dimensions. We highlight the unique properties of these materials in arenas as diverse as electron transport and biological processing, illustrating how they can be leveraged to produce devices and materials with otherwise inaccessible functionality. By making size and shape our focus, we aim to identify potential synergies between different disciplines and produce a road map for future research in this crucial area.

Design of higher valency in covalent organic frameworks.

The valency (connectivity) of building units in covalent organic frameworks (COFs) has been primarily 3 and 4, corresponding to triangles and squares or tetrahedrons, respectively. We report a strategy for making COFs with valency 8 (cubes) and "infinity" (rods). The linker 1,4-boronophenylphosphonic acid-designed to have boron and phosphorus as an isoelectronic combination of carbon-group elements-was condensed into a porous, polycubane structure (BP-COF-1) formulated as (-B4P4O12-)(-C6H4-)4 It was characterized by x-ray powder diffraction techniques, which revealed cubes linked with phenyls. The isoreticular forms (BP-COF-2 to 5) were similarly prepared and characterized. Large single crystals of a constitutionally isomeric COF (BP-COF-6), composed of rod units, were also synthesized using the same strategy, thus propelling COF chemistry into a new valency regime.

Higher-valency ligands for COFs

Framework Materials Metal-organic frameworks (MOFs) have exhibited more extensive connectivity (valency) and topological diversity than covalent organic frameworks (COFs), mainly because MOF linkers can connect from 3 to 24 discrete units or even infinity for one-dimensional rods. For COFs, linkers generally have a valency of 3 or 4 that reflect the valency of organic carbon. Gropp et al. created cubane-like linkers from 1,4-boronophenylphosphonic acid that could condense to make COFs with a valency of 8 or, by adding acid, could form large, single crystals with an infinite-rod topology. Science , this issue p. [eabd6406][1] [1]: /lookup/doi/10.1126/science.abd6406

Electrochemical Reduction of SiO2 Granules to One-Dimensional Si Rods Using Ag-Si Eutectic Alloy

Electrochemical Reduction of SiO2 Granules to One-Dimensional Si Rods Using Ag-Si Eutectic Alloy