Tetrahedral Particles Research Articles

DEM simulation on random packings of binary tetrahedron-sphere mixtures

The random packings of binary tetrahedron-sphere mixtures were numerically reproduced by DEM simulations. The influences of particle shape (characterized by eccentricity ζ and height ratio η), particle size, and composition on the packing density of binary tetrahedron-sphere mixtures were systematically investigated. The properties of equivalent packing diameter are identified by both macroscopic and microscopic parameters. The results show that the equivalent packing diameter of tetrahedra is independent of the particle shape (ζ and η) deviation. The minimal specific volume variations ΔV are negative for each case with the size ratio ranging from 0.5 to 1 caused by the shape particularity of tetrahedra. The overall mean coordination number (CN) obtained at r = 1 (here, r = ds/dte, ds and dte are respectively sphere diameter and equivalent volume sphere diameter of tetrahedral particles) is almost identical and does not change with the variation of composition. The mean stress analysis shows that the equivalent packing diameter is not only universal for the microstructure parameters, but also for the mechanical properties of tetrahedron-sphere binary packings.

Packing of different shaped tetrahedral particles: DEM simulation and experimental study

Packings of different mono-sized tetrahedral particles under 3D vibrations were studied by physical experiments and DEM simulations. The effects of vibration conditions and particle shape on the packing densification were comprehensively investigated and optimized. Corresponding characteristic microscopic properties such as coordination number (CN), particle contact type, radial distribution function (RDF), and particle orientations were numerically characterized and analyzed. The results show that the DEM model can be well validated by physical experiments. Microscopic analysis indicates that the minimum mean CN appears for tetrahedral particles with regular shape. The RDF shows that as the shape deviates from regular tetrahedral particles, the frequency of face-face, vertex-face and edge-edge contacts all decreases while that of edge-face contact increases. The cluster evolutions demonstrate that the reduction or disappearance of two important local clusters (dimer and wagon wheel structures) is one of the main reasons for the decrease of packing density of irregular tetrahedral particles.

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.

Assembly of clathrates from tetrahedral patchy colloids with narrow patches.

Here, we revisit the assembly of colloidal tetrahedral patchy particles. Previous studies have shown that the crystallization of diamond from the fluid phase depends more critically on patch width than on the interaction range: particles with patches narrower than 40° crystallize readily and those with wide patches form disordered glass states. We find that the crystalline structure formed from the fluid also depends on the patch width. Whereas particles with intermediate patches assemble into diamond (random stacking of cubic and hexagonal diamond layers), particles with narrow patches (with width ≈20° or less) crystallize frequently into clathrates. Free energy calculations show that clathrates are never (in the pressure-temperature plane) thermodynamically more stable than diamond. The assembly of clathrate structures is thus attributed to kinetic factors that originate from the thermodynamic stabilization of pentagonal rings with respect to hexagonal ones as patches become more directional. These pentagonal rings present in the fluid phase assemble into sII clathrate or into large clusters containing 100 particles and exhibiting icosahedral symmetry. These clusters then grow by interpenetration. Still, the organization of these clusters into extended ordered structures was never observed in the simulations.

Lattice Boltzmann simulation of fluid flow through random packing beds of Platonic particles: Effect of particle characteristics

The influence of particle characteristics, such as shape, size, and volume fraction, on the permeability of porous media was investigated by combining the randomly packed beds of Platonic particles with the lattice Boltzmann method. Quantitative solutions of the permeability as a function of these characteristic parameters in mono-sized particle packing structures were obtained. The D3Q19 model is presented here, which was tested by three simple benchmark tests. A series of packed beds of Platonic particles as well as spherical particles were generated in a random manner. Numerical studies on factors influencing the permeability of materials were carried out to comprehensively study their impacts. The results revealed that the permeability significantly increased with increasing equivalent diameter of the particles (or decreasing volume fraction). At a fixed size and volume fraction of particles, the permeability of the Platonic particle packing structures was also influenced by particle morphology: permeability significantly reduced as the particle sphericity decreased. The permeability of tetrahedral particle packing structures dropped by more than 40% compared with that of corresponding spherical particle systems.

Stabilising the tetrahedral defect configuration in nematic shells

ABSTRACTMonte Carlo simulations are used to investigate the director configurations and the arrangements of the disclination lines that form in nematic shells surrounding interior spherical and polyhedral particles. For nematic shells formed around an interior spherical particle, a tetrahedral arrangement of the disclination lines is observed but this arrangement is lost if the interior sphere is shifted from the centre. The simulations indicate that a narrower angular distribution is observed for interior tetrahedral particles and, for non-centrosymmetric shells, the distribution is significantly less broadened compared to similar spherical inclusions. Other shape polyhedral particles are shown to give disclination geometries of different symmetries.

Emulsion Droplets Stabilized by Close-Packed Janus Regular Polygonal Particles.

In Pickering-Ramsden emulsions, the packing structure of the colloidal particles at the liquid-liquid (or liquid-gas) interface significantly affects the structure and behavior of the emulsion. Here, using a series of platelike particles with regular polygonal shapes and Janus amphiphilicity, we created emulsion droplets stabilized by close-packed polygonal particles at the interface. The systematic variation of the particle morphology shows that the geometrical features of the regular polygons in (curved) planar packing dominate over the self-assembled structures. The structures are tessellations of triangular, square, and hexagonal particles at the surface for large droplets and regular tetrahedral, cubic, and dodecahedral particle shells of triangular, square, and pentagonal particles for small droplets, respectively. This work creates the possibility of geometrically designing the structure and functionality of emulsions.

Micromechanical analysis on the compaction of tetrahedral particles

Understanding the roles of particle properties in powder compaction is important to many industrial products, such as tablets in pharmaceutics, briquettes in iron ore handling and green compacts in powder metallurgy. However, the role of particle shape in bulk compression and how it is related to the properties of the final compact are not well understood. In this study, we investigated the structural evolution, force distribution and compact strength of tetrahedral particles using discrete element method, with a focus on the effect of particle interlocking due to non-spherical particle shape. Tetrahedral particles were constructed using clumped sphere approach, which allows multiple contacts being set up between two contacted particles. Die compaction followed by unconfined compression were conducted on the assemblies of both spherical and tetrahedral particles. The results showed that the tetrahedral particle shape reduces the degree of particle rearrangement at the early stage of bulk compression but enhances the resistance to bulk deformation at the later stage due to enhanced shear resistance at interparticle contacts. The compact of tetrahedral particles presents a higher compressive strength due to increased number of interparticle bonding. Compared to the spherical particles, the macroscopic failure mode tends to be more ductile for the tetrahedral particles. The tetrahedral particle shape has no effect on the dominant bond failure mode but leads to a wider shear banding, more dispersed bond breakage and a slower bond breakage process. This work highlights the role of particle shape in densification mechanism and mechanical response of the formed powder compact.

How to simulate patchy particles⋆.

Patchy particles is the name given to a large class of systems of mesoscopic particles characterized by a repulsive core and a discrete number of short-range and highly directional interaction sites. Numerical simulations have contributed significantly to our understanding of the behaviour of patchy particles, but, although simple in principle, advanced simulation techniques are often required to sample the low temperatures and long time-scales associated with their self-assembly behaviour. In this work we review the most popular simulation techniques that have been used to study patchy particles, with a special focus on Monte Carlo methods. We cover many of the tools required to simulate patchy systems, from interaction potentials to biased moves, cluster moves, and free-energy methods. The review is complemented by an educationally oriented Monte Carlo computer code that implements all the techniques described in the text to simulate a well-known tetrahedral patchy particle model.

Discrete modelling of the compaction of non-spherical particles using a multi-sphere approach

A numerical model based on the discrete element method (DEM) was developed to study the compaction behaviour of non-spherical particles. Spheroidal and tetrahedral particles of different aspect ratios were approximated by a multi-sphere approach in which overlapping spheres were glued together to represent the particle shapes. For the compactions of spheroidal particles, the effect of aspect ratio on the compaction was mainly due to the difference in the initial packing. The compact compressive strength also increased with the aspect ratio. For the tetrahedral particles, the non-convexity shape index was proposed to represent the degree of inter-particle locking. With increasing non-convexity and thus inter-particle locking, larger consolidation pressure was required to achieve the same density. The failure region upon the unconfined pressure also moved from the bottom to the top with increasing non-convexity as force transfer was more difficult in the compacts. The simulations also indicated that the bulk failure of the compacts was dominated by the shear-induced bond breakage. The findings facilitate a better understanding of the relation of particle shape to the compaction behaviour and compact strength.

Numerical simulation of tetrahedral particle mixing and motion in rotating drums

A regular tetrahedron is the simplest three-dimensional structure and has the largest non-sphericity. Mixing of tetrahedral particles in a thin drum mixer was studied by the soft-sphere-imbedded pseudo-hard particle model and compared with that of spherical particles. The two particle types were simulated with different rotation speeds and drum filling levels. The Lacey mixing index and Shannon information entropy were used to explore the effects of sphericity on the mixing and motion of particles. Moreover, the probability density functions and mean values and variances of motion velocities, including translational and rotational, were computed to quantify the differences between the motion features of tetrahedra and spheres. We found that the flow regime depended on the particle shape in addition to the rotation speed and filling level of the drum. The mixing of tetrahedral particles was better than that of spherical particles in the rolling and cascading regimes at a high filling level, whereas it may be poorer when the filling level was low. The Shannon information entropy is better than the Lacey mixing index to evaluate mixing because it can reflect the real change of flow regime from the cataracting to the centrifugal regime, whereas the mixing index cannot.

Structural, optical and ellipsometric characteristics of PVD synthesized SnO2 thin films on Pt coated silicon wafers

Tin oxide thin films were prepared on Pt coated-Si wafers by physical vapor deposition technique. The development of rutile structure of SnO2 was revealed by XRD measurements after annealing the thin films at 750°C for two hours. The formation of tetrahedral shape particles at different size distributed randomly on the Pt coated Si wafer was confirmed by SEM images. The refractive index, extinction coefficient, thickness, and roughness of the thin films were evaluated using ellipsometric measurements. The energy bandgap of the SnO2 thin films was calculated from the spectrophotometric measurement and is found to be 3.6±0.02eV before and 3.8±0.02eV after annealing, respectively.

DEM dynamic simulation of tetrahedral particle packing under 3D mechanical vibration

The transition from random loose packing (RLP) to random close packing (RCP) of mono-sized regular tetrahedral particles under 3D mechanical vibration was modeled by using discrete element method. The effects of vibration conditions and container size on the packing densification were systematically studied, and the macro and micro properties such as packing density, coordination number (CN), particle contact type, radial distribution function (RDF), particle orientation correlation, and forces between particles were characterized and analyzed. The randomness of the obtained dense packings and corresponding densification mechanisms were also investigated. The results show that RCP of the tetrahedral particles can be realized by properly controlling the vibration conditions. And the obtained maximum random packing density can reach about 0.7402 by extrapolating the packing densities in different sized containers. The average CN for RLP and RCP are 7 and 6.3, and the CN distribution for RCP is higher and narrower than that for RLP. From RLP to RCP, the frequency of face to face (F-F) contact between two particles increases, while that of vertex to face (V-F) contact and edge to face (E-F) contact decreases, and edge to edge (E-E) contact does not change much. RDF characterization shows four obvious peaks on the curves of RLP and RCP, where the height of the first peak (F-F contact) increases while that of other peaks decreases from RLP to RCP. The densification mechanism can be ascribed to the formation of wagon wheel local dense structures through rearrangement by ‘pushing filling’ and ‘jumping filling’.

Dispersion behavior of 3D-printed columns with homogeneous microstructures comprising differing element shapes

We used additive manufacturing (3D printing) to create ordered porous beds from a range of geometric shapes, including truncated icosahedra (approximating spheres), tetrahedral, octahedral, triangular bipyramid, and stellar octangular particles. We show that the printed porous media were highly reproducible and had excellent fidelity in physically reproducing computer-aided design models, with differences between designed and experimentally measured particle locations within ±0.5%, and within 1.3% in terms of bed porosity. Experimental residence time distributions were measured and the reduced plate height, h, was determined under different reduced velocities (Peclet number, Pe=4–400). The results (using equivalent particle diameter to non-dimensionalize) show that, for the simple cubic (SC) arrangement, tetrahedral particles had a lower plate height (hmin=1.56) than all other particle shapes tested, including spherical particles. We also, for the first time, experimentally validated computational predictions of the performance of SC, body centered cubic (BCC) and face centered cubic (FCC) arrangements of spheres, confirming that FCC is indeed superior (hmin=1.12) to SC (hmin=1.62). We conclude that the capability offered by additive manufacturing in controlling not only packing configuration but also shape, position and orientation of the geometric elements within the porous bed may, in the future, play a fundamental role in the design of highly efficient 3D-printed columns.

Growth morphology and special diffraction characteristics of multifaceted gold nanoparticles

This paper deals with morphology of synthesized nano gold particles through seed based growth. Various types of morphologies have been observed. They primarily relate to decahedral and truncated tetrahedral shapes. Their relative abundance is dependent on temporal evolution of nanoparticles. These shapes are understood to have evolved from a seed having symmetry that is a supergroup of the point groups possessed by these nanoparticles. The usual pentagonal twinned morphologies observed under High Resolution Transmission Electron Microscopy have displayed two distinct types of interfaces. They have been attributed to cubic and icosahedral three-fold orientations. Such a discussion is lacking in literature. The five triangular faces of decahedral particles are essentially rotational twins resulting out of a common five-fold axis. Two special diffraction features for truncated tetrahedral particles have been observed. They refer to (i) triangular streaks around Braggs spots conforming to three fold symmetry of these particles and (ii) by observation of forbidden reflections of the type 1/3{422} and 2/3{422} along 〈422〉 directions. Latter has been understood in terms of intrinsic fault whereas former arises owing to shape transform of nanoparticles. The presence of faults has helped rationalize decrease of lattice parameter vis-à-vis that of standard FCC gold. The variation of intensities of these forbidden reflections seems to be arising out of density of such intrinsic faults in nano gold particles in addition to dynamical effects.

Direct numerical simulation of gas-solid-liquid flows with capillary effects: An application to liquid bridge forces between spherical particles.

In this study, a numerical method is developed to perform the direct numerical simulation (DNS) of gas-solid-liquid flows involving capillary effects. The volume-of-fluid method employed to track the free surface and the immersed boundary method is adopted for the fluid-particle coupling in three-phase flows. This numerical method is able to fully resolve the hydrodynamic force and capillary force as well as the particle motions arising from complicated gas-solid-liquid interactions. We present its application to liquid bridges among spherical particles in this paper. By using the DNS method, we obtain the static bridge force as a function of the liquid volume, contact angle, and separation distance. The results from the DNS are compared with theoretical equations and other solutions to examine its validity and suitability for modeling capillary bridges. Particularly, the nontrivial liquid bridges formed in triangular and tetrahedral particle clusters are calculated and some preliminary results are reported. We also perform dynamic simulations of liquid bridge ruptures subject to axial stretching and particle motions driven by liquid bridge action, for which accurate predictions are obtained with respect to the critical rupture distance and the equilibrium particle position, respectively. As shown through the simulations, the strength of the present method is the ability to predict the liquid bridge problem under general conditions, from which models of liquid bridge actions may be constructed without limitations. Therefore, it is believed that this DNS method can be a useful tool to improve the understanding and modeling of liquid bridges formed in complex gas-solid-liquid flows.

A contact detection algorithm for deformable tetrahedral geometries based on a novel approach for general simplices used in the discrete element method

We present an extended particle model for the discrete element method that on the one hand is tetrahedral in shape and on the other hand is capable to describe deformations. The deformations of the tetrahedral particles require a framework to interrelate the particle strains and resulting stresses. Hence, adaptations from the finite element method were used. This allows to link the two methods and to adequately describe material and simulation parameters separately in each scope. Due to the complexity arising of the non-spherical tetrahedral geometry, all possible contact combinations of vertices, edges, and surfaces must be considered by the used contact detection algorithm. The deformations of the particles make the contact evaluation even more challenging. Therefore, a robust contact detection algorithm based on an optimization approach that exploits temporal coherence is presented. This algorithm is suitable for general \(\mathbb {R}^{\text {n}}\) simplices. An evaluation of the robustness of this algorithm is performed using a numerical example. In order to create complex geometries, bonds between these deformable particles are introduced. This coupling via the tetrahedra faces allows the simulation bonding of deformable bodies composed of several particles. Numerical examples are presented and validated with results that are obtained by the same simulation setup modeled with the finite element method. The intention of using these bonds is to be able to model fracture and material failure. Therefore, the bonds between the particles are not lasting and feature a release mechanism based on a predefined criterion.

Controllable synthesis of α-Bi2O3 and γ-Bi2O3 with high photocatalytic activity by α-Bi2O3→γ-Bi2O3→α-Bi2O3 transformation in a facile precipitation method

Rod-like α-Bi2O3 and tetrahedral γ-Bi2O3 particles have been controlled fabricated by a facile solution crystallization method, which was performed at a mild reaction condition without any surfactants and/or templates. By combining the results of X-ray powder diffraction, high resolution transmission electron microscope, scanning electron microscopy, X–ray photoelectron spectra, and UV-visible absorption spectra, the morphology and crystalline phase evolution of Bi2O3 was studied versus reaction time and reaction temperature. It is interesting to note that the phenomenon of α-Bi2O3 → γ-Bi2O3 → α-Bi2O3 transformation was found. The nanorod α-Bi2O3 phase formed in a short time, while α-Bi2O3 could transform to tetrahedral γ-Bi2O3 crystals upon enough reaction time. However, γ-Bi2O3 may transform into rod-shape α-Bi2O3 with further increasing the reaction time. Moreover, it can be deduced that high reaction temperature promoted the transformation from α-Bi2O3 to γ-Bi2O3, and then from γ-Bi2O3 to α-Bi2O3. The photocatalytic activities of Bi2O3 with different crystalline phases were evaluated by the photocatalytic degradation of rhodamine B as a model pollutant. The γ-Bi2O3, which exhibits lower electrons-holes recombination rate than that of α-Bi2O3, showed excellent photocatalytic activity as compared with the α-Bi2O3.

Dodecagonal quasicrystalline order in a diblock copolymer melt

We report the discovery of a dodecagonal quasicrystalline state (DDQC) in a sphere (micelle) forming poly(isoprene-b-lactide) (IL) diblock copolymer melt, investigated as a function of time following rapid cooling from above the order-disorder transition temperature (TODT = 66 °C) using small-angle X-ray scattering (SAXS) measurements. Between TODT and the order-order transition temperature TOOT = 42 °C, an equilibrium body-centered cubic (BCC) structure forms, whereas below TOOT the Frank-Kasper σ phase is the stable morphology. At T < 40 °C the supercooled disordered state evolves into a metastable DDQC that transforms with time to the σ phase. The times required to form the DDQC and σ phases are strongly temperature dependent, requiring several hours and about 2 d at 35 °C and more than 10 and 200 d at 25 °C, respectively. Remarkably, the DDQC forms only from the supercooled disordered state, whereas the σ phase grows directly when the BCC phase is cooled below TOOT and vice versa upon heating. A transition in the rapidly supercooled disordered material, from an ergodic liquid-like arrangement of particles to a nonergodic soft glassy-like solid, occurs below ∼40 °C, coincident with the temperature associated with the formation of the DDQC. We speculate that this stiffening reflects the development of particle clusters with local tetrahedral or icosahedral symmetry that seed growth of the temporally transient DDQC state. This work highlights extraordinary opportunities to uncover the origins and stability of aperiodic order in condensed matter using model block polymers.

Effects of particle shape on the thermoelastoplastic behavior of particle reinforced composites

Particle shape effects in thermoelastoplastic ductile matrix composites are evaluated systematically. This is done by studying generic, periodic, multi-inhomogeneity volume elements that contain 20 volume percent of randomly positioned and, where applicable, randomly oriented, identical particles taking the form of spheres, regular octahedra, cubes, or regular tetrahedra. The Finite Element method is used for obtaining the responses of the initially stress-free volume elements to single, stress controlled loading cycles at four fixed macroscopic stress triaxialities, viz., loading by shear, uniaxial, in-plane hydrostatic, and hydrostatic applied stresses. In addition, a thermal loading cycle and the effects of residual stresses on shear loading are considered. Results are evaluated as ensemble averages over five phase arrangements of each type. They are presented in terms of macroscopic responses as well as the evolution of the phase-level averages and standard deviations of the microscopic stress and strain fields. Consistent shape effects are predicted for all load cases considered, with the responses of cube-shaped and octahedral particles being fairly similar and lying between the predictions obtained for spherical and tetrahedral inhomogeneities. Among the shapes studied, tetrahedral particles are found to give rise to the stiffest responses under mechanical loading.