Macroscopic Isotropy Research Articles

General Modification Strategy on Amorphous Materials to Boost Catalytic Performance

AbstractAmorphous materials with a high number of unsaturated coordinated dangling bonds exhibits macroscopic homogeneity and isotropy, making it easily modifiable to improve the catalytic properties. At present, several feasible modification strategies for amorphous materials have been proposed and applied to multiple catalytic fields. This review aims to provide a comprehensive overview of recent research advancements in the modification of amorphous materials for catalysis. First, the general strategies for modifying amorphous materials are summarized. Subsequently, the potential applications of modified amorphous materials in electrocatalysis and photocatalysis are highlighted. Additionally, the positive effects of various modification tools on the catalytic properties of amorphous materials are elucidated. Finally, a summary of the challenges and offer a critical perspective on the further development of modified amorphous materials are presented. The primary goal of this review is to offer a systematic understanding of how to enhance catalytic performance and to stimulate further research on amorphous catalysts in the future.

Lattice sums for double periodic polyanalytic functions

In 1892, Lord Rayleigh estimated the effective conductivity of rectangular arrays of disks and proved, employing the Eisenstein summation, that the lattice sum S_2 is equal to pi for the square array. Further, it became clear that such equality can be treated as a necessary condition of the macroscopic isotropy of composites governed by the Laplace equation. This yielded the description of two-dimensional conducting composites by the classic elliptic functions, including the conditionally convergent Eisenstein series. In 1935, Natanzon used a polyharmonic function to solve the plane elasticity problem. This paper is devoted to the extension of the classic lattice sums to the lattice sums for double periodic (pseudoperiodic) polyanalytic functions. The exact relations and computationally effective formulae between the polyanalytic and classic lattice sums are established. Polynomial representations of the lattice sums are obtained. They are a source of new exact formulae for the lattice sums.

Nanostructured Lipid Carriers for Enhanced Transscleral Delivery of Dexamethasone Acetate: Development, Ex Vivo Characterization and Multiphoton Microscopy Studies

Corticosteroids, although highly effective for the treatment of both anterior and posterior ocular segment inflammation, still nowadays struggle for effective drug delivery due to their poor solubilization capabilities in water. This research work aims to develop nanostructured lipid carriers (NLC) intended for periocular administration of dexamethasone acetate to the posterior segment of the eye. Pre-formulation studies were initially performed to find solid and liquid lipid mixtures for dexamethasone acetate solubilization. Pseudoternary diagrams at 65 °C were constructed to select the best surfactant based on the macroscopic transparency and microscopic isotropy of the systems. The resulting NLC, obtained following an organic solvent-free methodology, was composed of triacetin, Imwitor® 491 (glycerol monostearate >90%) and tyloxapol with Z-average = 106.9 ± 1.2 nm, PDI = 0.104 ± 0.019 and zeta potential = -6.51 ± 0.575 mV. Ex vivo porcine sclera and choroid permeation studies revealed a considerable metabolism in the sclera of dexamethasone acetate into free dexamethasone, which demonstrated higher permeation capabilities across both tissues. In addition, the NLC behavior once applied onto the sclera was further studied by means of multiphoton microscopy by loading the NLC with the fluorescent probe Nile red.

Research Progress on Blue-Phase Liquid Crystals for Pattern Replication Applications.

Blue-Phase Liquid Crystals (BPLCs) are considered to be excellent 3D photonic crystals and have attracted a great deal of attention due to their great potential for advanced applications in a wide range of fields including self-assembling tunable photonic crystals and fast-response displays. BPLCs exhibit promise in patterned applications due to their sub-millisecond response time, three-dimensional cubic structure, macroscopic optical isotropy and high contrast ratio. The diversity of patterned applications developed based on BPLCs has attracted much attention. This paper focuses on the latest advances in blue-phase (BP) materials, including applications in patterned microscopy, electric field driving, handwriting driving, optical writing and inkjet printing. The paper concludes with future challenges and opportunities for BP materials, providing important insights into the subsequent development of BP.

Isotropic porous graphite foam/epoxy composites with outstanding heat dissipation and excellent electromagnetic interference shielding performances

In the field of radio frequency chips package, design of isotropic material was a significant challenge to efficiently resolve undesirable electromagnetic radiation and excessive heat accumulation in confined tiny spaces. Here, a brand-new material design concept was proposed and successfully verified through controllable graphitization degree of carbon materials and curvature of twisted graphite sheets during heating and foaming process of asphalt. Concretely, aromatic compounds of the asphalt condensed to form sheet-like macromolecules, which were twisted and oriented along the pore walls. Eventually, these macromolecules were highly graphitized, which expectedly realized the consummate integration of local orientation and macroscopic isotropy. Particularly, a special interlocking epoxy was introduced to prepare epoxy/graphite foam composites (EP-GFs). The EP-GFs (average pore size 0.09 mm) demonstrated an isotropic thermal conductivity up to 118.5 ± 5.8 W·m−1·K−1. Astoundingly, EP-GFs (average pore size 0.244 mm) showed an isotropic electromagnetic interference shielding efficiency (EMI SE), reaching up to 113 dB in 8–12 GHz. Therefore, the EP-GFs completely integrated outstanding thermal conductivity, excellent EMI SE and isotropy macroscopically. Interestingly, the EP-GFs can be cured by Joule heat of low-voltage direct current, and the primary heating region was the contact interface between copper sheets instead of the whole bonded product. This work offered a facile feasible strategy for fabricating isotropic materials to address heat dissipation and electromagnetic pollution of advanced electronic devices in an economical and environmentally friendly manner.

Mechanically-grown morphogenesis of Voronoi-type materials: Computer design, 3D-printing and experiments

The present work introduces a novel and versatile computer-design and experimental strategy to obtain random Voronoi-type geometries, called M-Voronoi (from mechanically grown), with smooth void shapes and variable intervoid ligament sizes that can reach very low relative densities. This is achieved via a numerical, large strain, nonlinear elastic, void growth mechanical process. Originally small circular voids embedded in a cell of arbitrary shape (triangle, circle, rectangle, trapezoid) grow when subjected to displacement (Dirichlet) boundary conditions. The deformed voids evolve into smooth Voronoi-type geometrical shapes leading to macroscopic isotropy or anisotropy depending on the prescribed boundary conditions. The void growth process is a direct consequence of mass conservation and the incompressibility of the surrounding nonlinear elastic matrix phase and the final achieved relative density may be analytically estimated in terms of the determinant of the applied deformation gradient. In order to study the mechanical properties of the M-Voronoi materials, we focus on two-dimensional porous polymer square representative isotropic and anisotropic geometries in terms of void size and realization, which are 3D-printed and experimentally tested under uniaxial compression. For comparison, we also test random polydisperse porous materials with circular voids, standard eroded Voronoi geometries and hexagonal honeycombs. The first two are also isotropic while the latter are only isotropic in the linear elastic regime. We show that the randomness of the M-Voronoi geometry and their non-uniform intervoid ligament size leads to enhanced mechanical properties at large compressive strains with no apparent peak-stress and strong hardening well before densification. By comparing them with the hexagonal geometries, which tend to exhibit a peak-stress and a plateau-type response, we show that the hardening response of the M-Voronoi is mainly due to their geometrical characteristics and less due to the polymer hardening response. Anisotropic M-Voronoi are also produced and tested indicating that anisotropy only enhances the initial stiffness along the longitudinal direction but instead leads to lower buckling loads and hardening rates than the corresponding isotropic M-Voronoi in the nonlinear regime.

Crack initiation and growth in additively printed ABS: Effect of print architecture studied using DIC

Acrylonitrile Butadiene Styrene or ABS is a popular and inexpensive isotropic, amorphous thermoplastic widely used for Additive Manufacturing (AM) of engineering parts. An AM process called Fused Filament Fabrication (FFF) involving layer-by-layer deposition of melted thermoplastic wire through a heated nozzle along predetermined paths is common for printing thermoplastics such as ABS. Individual layers printed during AM can be configured differently and could introduce anisotropy into the part due to weaker planes between individual beads even when the feedstock is isotropic. This research examines the tensile and fracture behaviors of three in-plane print architectures, namely [0°/90°]n, [45°/-45°]n and [0°/45°/90°/-45°]n orientations. The full-field measurement of local in-plane displacements are performed optically using Digital Image Correlation (DIC) method up to crack initiation and during crack growth in quasi-statically loaded 3-point bend edge-notched specimens. A simple method of analyzing DIC data by transferring it to a corresponding finite element model for computing the J-integral and then partitioning it into individual stress intensity factors is developed. Even though the printed architectures show macroscopic elastic isotropy, significant differences in the failure strain, crack initiation and growth parameters, and failure modes among the three architectures are observed. These differences are explained using tests performed on comparable unidirectional prints. The results suggest that [0°/45°/90°/-45°]n are preferable to the other two more common configurations for a relatively graceful failure behavior and higher resistance to crack growth, suggesting that better fracture performance could be achieved by manipulating print architecture.

Influence of local cubic anisotropy on the transition towards an equipartition regime in a 3D texture-less random elastic medium

At long lapse times in randomly fluctuating media with macroscopic isotropy (texture-less media), the energy of elastic waves is equipartitioned between compressional (P) and shear (S) waves. This property is independent of the local isotropy or anisotropy of the heterogeneous constitutive tensor and of the type of source. However the local symmetry of the constitutive tensor does influence the rate of convergence to equipartition and this paper discusses the precise influence of local anisotropy on the time required to reach equipartition. More particularly, a randomly-fluctuating medium is considered, whose behavior is statistically isotropic, and locally cubic. After calculating all the differential and total scattering cross-sections in that case, an analytical formula is derived for the rate of convergence to the equipartition regime, function of the second-order statistics of the mechanical parameter fields (bulk and shear moduli and anisotropy parameter). The local anisotropy is shown to influence strongly that transition rate, with a faster transition when the fluctuations of the anisotropy parameter are positively correlated to those of the shear modulus. A numerical model is constructed to illustrate numerically these results. Since the asymptotic regime of equipartition cannot be simulated directly because it would require too large a computational domain, boundaries are introduced and mechanical properties are chosen so as to minimize their influence on equipartition.

Designing isotropic composites reinforced by aligned transversely isotropic particles of spheroidal shape

The aim of this paper is to study the design of isotropic composites reinforced by aligned spheroidal particles made of a transversely isotropic material. The problem is investigated analytically using the framework of mean-field homogenization. Conditions of macroscopic isotropy of particle-reinforced composites are derived for the dilute and Mori–Tanaka's schemes. This leads to a system of three nonlinear equations linking seven material constants and two geometrical constants. A design tool is finally proposed, which permits to determine admissible particles achieving macroscopic isotropy for a given isotropic matrix behavior and a given particle aspect ratio. Correlations between transverse and longitudinal moduli of admissible particles are studied for various particle shapes. Finally, the design of particles is investigated for aluminum and steel matrix composites.

The General Mathematical Theory of Plasticity and the Il’yushin Postulates of Macroscopic Definability and Isotropy

The physical laws characterizing the relation between stresses and strains are considered and analyzed in the general modern theory of elastoplastic deformations and in its postulates of macroscopic definability and isotropy for initially isotropic continuous media. The fundamentals of this theory in continuum mechanics were developed by A.A. Il’yushin in the mid-twentieth century. His theory of small elastoplastic deformations under simple loading became a generalization of Hencky’s deformation theory of flow, whereas his theory of elastoplastic processes which are close to simple loading became a generalization of the Saint-Venant–Mises flow theory to the case of hardening media. In these theories, the concepts of simple arid complex loading processes arid the concept of directing form change tensors are introduced; the Bridgman law of volume elastic change and the universal Roche–Eichinger laws of a single hardening curve under simple loading are adopted; and the Odquist hardening for plastic deformations is generalized to the case of elastoplastic hardening media for the processes of almost simple loading without consideration of a specific history of deformations for the trajectories with small arid mean curvatures. In this paper we discuss the possibility of using the isotropy postulate to estimate the effect of forming parameters in the stress-strain state appeared due to the strain-induced anisotropy during the change of the internal structures of materials. We also discuss the possibility of representing the second-rank symmetric stress and strain tensors in the form of vectors in the linear coordinate six-dimensional Euclidean space. An identity principle is proposed for tensors and vectors.

Effect of ausforming on the anisotropy of low temperature bainitic transformation

Ausforming is the process by which austenite is plastically deformed prior to bainitic or martensitic transformation. The advantages of such a process on the kinetics of the bainitic transformations have already been reported, but little is found about the effect on the morphology and crystallography of the final microstructure, and in most cases the studies deal with high C steels. Since ausforming has been suggested to be an alternative to transfer the concept of nanostructured bainite to medium carbon contents, the necessity to study the effect of prior plastic deformation on the subsequent bainitic transformation in those steels arises. By means of techniques such as high-resolution dilatometry, scanning electron microscopy, electron backscatter diffraction and X-Ray diffraction, it has been proven that, in a medium carbon steel (0.4 wt%), the macroscopic isotropy that characterizes the bainitic transformation can be altered, under certain conditions, by plastically deforming austenite prior to transformation. The alteration is such that, at low temperatures, the interpretation of the dilatometric response or the plate thickness measurements can be hindered. In addition, the final microstructure is also affected, presenting highly ordered bainitic ferrite plates, most of them correspondent to specific crystallographic variants.

Consideration of arbitrary inclusion shapes in the framework of isotropic continuum micromechanics: The replacement Eshelby tensor approach

The effective behavior of matrix-inclusion materials is governed by the properties and volume fractions of involved material phases as well as by the morphology of the inclusion domain. Eshelby’s solutions on the ellipsoidal inclusion problem (Eshelby, 1957) paved the way to the development of a vast number of continuum micromechanics based homogenization schemes for evaluation of effective properties. This paper proposes an approach for utilizing these homogenization schemes also for non-ellipsoidal inclusions with particular focus on macroscopic isotropy. The key concept is to replace the originally-used Eshelby tensor by an analogous representation capturing the effect of non-spherical inclusions on strain fluctuation within the material domain. The so-called replacement Eshelby tensor is obtained by numerical evaluation of two adjustment factors being functions of the inclusion morphology and the stiffness contrast between the matrix and inclusion phase. These factors are evaluated and discussed for selected inclusion morphologies. Finally, the replacement Eshelby tensor approach is implemented in a homogenization procedure for effective elastic properties (cascade continuum micromechanics model (Timothy and Meschke, 2016)) as well as in a scheme for determining effective yield surfaces in case of plastic material behavior (Traxl and Lackner, 2015).

Vibration of a mistuned three-bladed rotor under regular and chaotic excitations

This study considers forced vibrations of a rotating structure consisting of a rigid hub and three flexible beams. The blades are nominally made of a multilayered laminate with a specific stacking sequence resulting in full isotropic macroscopic material behaviour. However, in the performed analysis it is assumed that the rotor has been mistuned because of manufacturing tolerances of the composite material. These inaccuracies are represented by deviations of reinforcing fibres orientations from their nominal values. The considered tolerances break the intended macroscopic material isotropy and make the laminate to exhibit the fully orthotropic behaviour. Based on previous authors research, the system of four mutually coupled dimensionless ordinary differential governing equations is adopted. Forced responses of the system under regular and chaotic excitations are investigated.

An anisotropic full Brillouin zone model for the three dimensional phonon Boltzmann transport equation

A model and associated numerical method are presented for simulation of heat transport at the microscale via the solution of the three dimensional phonon Boltzmann Transport Equation (BTE). In small domains, the full Brillouin Zone has a finite number of vibrational modes, as determined by Born von-Karman boundary conditions. As a result of this discreteness, the present method allows for general crystal anisotropy and finite dimensional effects that naturally permit anisotropic thermal transport and energy flow. The method is shown and verified using analytical solutions for isotropic flows. Then numerical experiments are performed to calculate temperature and energy in a fin field effect transistor made of a cubic crystalline material. The anisotropic thermal conductivity and the consequences on thermal fields are calculated. The differences between an isotropic solution and the anisotropic model are shown to be significant with differences in the temperatures approximately 10%. At larger scales, where scattering effects dominate, differences in the solutions become smaller and macroscopic isotropy is recovered due to the cubic symmetry of the material.

Isotropy prohibits the loss of strong ellipticity through homogenization in linear elasticity

Since the seminal contribution of Geymonat, Müller, and Triantafyllidis, it is known that strong ellipticity is not necessarily conserved by homogenization in linear elasticity. This phenomenon is typically related to microscopic buckling of the composite material. The present contribution concerns the interplay between isotropy and strong ellipticity in the framework of periodic homogenization in linear elasticity. Mixtures of two isotropic phases may indeed lead to loss of strong ellipticity when arranged in a laminate manner. We show that if a matrix/inclusion type mixture of isotropic phases produces macroscopic isotropy, then strong ellipticity cannot be lost.

Effective mass density based topology optimization of locally resonant acoustic metamaterials for bandgap maximization

Because effective material properties are essential concepts in the analyses of wave phenomena in metamaterials, they may also be utilized in the optimal design of metamaterials. In this work, we propose a topology optimization method directly using the Effective Mass Density (EMD) concept to maximize the first bandgaps of two-dimensional solid Locally Resonant Acoustic Metamaterials (LRAMs). When the first bandgap is characterized by the negative EMD, the bandgap maximization can be formulated efficiently as a topology optimization problem to broaden the frequency zone of the negative EMD values. In this work, EMD is calculated by considering the macroscopic isotropy of LRAMs in the long wavelength limit. To facilitate the analytical sensitivity analysis, we propose an elaborate calculation scheme of EMD. A sensitivity averaging technique is also suggested to guarantee the macroscopically isotropic behavior of the LRAMs. In the present study, the coating layer interfacing the core and the matrix of a ternary LRAM is chosen as the design region because it significantly influences the bandgap. By considering several numerical examples, the validity of this method is verified, and the effects of the mass constraint ratios on the optimized results are also investigated.

Simulation and verification of macroscopic isotropy of hollow alginate-based microfibers

A simulation of tensile strength of various alginate-based hollow microfibers using FEA analysis has been conducted with the hypothesis of macroscopic isotropy and linear elastic-plastic behavior. Results of student t-tests indicated that there was no significant difference between the experimental and simulated tensile strengths (p = 0.37, α = 0.05), while there was a significant reduction in elasticity as a result of chitosan coating (p = 0.024, α = 0.05). The hypothesis of macroscopic isotropy was verified by highly correlated (R2 ≥ 0.92) theoretical and experimental elongation at break measurements, findings that could be extended to the failure analysis of alginate microfibers used in regenerative medicine.

Functionalization of molecular glasses: effect on the glass transition temperature

Molecular glasses constitute an appealing class of materials combining the advantages associated with small molecules with the potential to form glassy phases. However, the current design of functional molecular glasses is highly dependent on a trial and error approach. By achieving a better understanding of the microscopic behaviors that govern the propensity of a system to generate a glassy state, the glassy behavior of new molecules can be identified before their synthesis. Full-atomistic simulation is genuinely invaluable for achieving this goal. A series of functionalized triazine-based molecular glasses previously synthesized and characterized were thus used as models to carry out simulations. To estimate the link between microscopic calculations and macroscopic properties, mechanical equilibrium and isotropy have first to be achieved. The reproducibility of the simulation results and their linear correlations with experimental data are two essential criteria for corroborating the validity of our method. Mobility of the core and the functional “headgroups” can then be interpreted, rationalizing the effect of molecular structure on the formation of glasses, and on the important differences in Tg observed for this series of compounds.

蓝相液晶光电特性研究

Blue phase liquid crystals(BPLCs) show fast response time and macroscopic optical isotropy due to their double twist cylinder structure.With polymer stabilization,the thermal stability of BPLCs can be improved dramatically.However,it induces some problems to the electro-optic properties of BPLCs material such as high driving voltage,hysteresis and so on.In this paper,different concentrations of chiral dopant,polymer network of the BPLC,and temperature effect are investigated to improve the electro-optic properties of BPLCs and analyze the mechanism that affect the electro-optic properties of the BPLCs device.

On the macroscopic elastic moduli of inhomogeneous materials and random orthorhombic polycrystals

Real-world randomly inhomogeneous materials generally do not have unique macroscopic (effective) elastic moduli, but those scattered over some uncertainty intervals. Macroscopic isotropy and homogeneity hypotheses for the materials should be weakened to take into account this fact. We derive the explicit expressions of the best available upper and lower estimates on the uncertainty ranges for the moduli of practical random orthorhombic polycrystals (the shape and crystalline orientations of their grains are uncorrelated), with illustrating numerical results.