System Of Spherical Particles Research Articles

On the Elastic Modulus of Powders

AbstractFor the design of silos and similar equipment for storage, handling and processing of particulate materials, a thorough understanding of the mechanical behaviour of powders is of great importance. Whereas strength properties of powders have been investigated by many workers, the elastic behaviour at small deformations has been much less in focus. In that respect, a simple preliminary theory of uniaxial elasticity has been derived for particles, based on a simple system of spherical and monosized particles of a homogenous and elastically isotropic material. The equation σ = Epϵel2 gives the relationship between stress, elastic modulus and elastic deformation for the unloading of a given powder at a specific consolidation stress/ compression level. Comparisons with experimental results of real powders in a uniaxial tester show surprisingly good agreement in many cases. The equation seems to describe the elasticity of powders fairly well, although it is only a preliminary derivation based on simple considerations.

Self-assembly of soft-matter quasicrystals and their approximants

The surprising recent discoveries of quasicrystals and their approximants in soft-matter systems poses the intriguing possibility that these structures can be realized in a broad range of nanoscale and microscale assemblies. It has been theorized that soft-matter quasicrystals and approximants are largely entropically stabilized, but the thermodynamic mechanism underlying their formation remains elusive. Here, we use computer simulation and free-energy calculations to demonstrate a simple design heuristic for assembling quasicrystals and approximants in soft-matter systems. Our study builds on previous simulation studies of the self-assembly of dodecagonal quasicrystals and approximants in minimal systems of spherical particles with complex, highly specific interaction potentials. We demonstrate an alternative entropy-based approach for assembling dodecagonal quasicrystals and approximants based solely on particle functionalization and shape, thereby recasting the interaction-potential-based assembly strategy in terms of simpler-to-achieve bonded and excluded-volume interactions. Here, spherical building blocks are functionalized with mobile surface entities to encourage the formation of structures with low surface contact area, including non-close-packed and polytetrahedral structures. The building blocks also possess shape polydispersity, where a subset of the building blocks deviate from the ideal spherical shape, discouraging the formation of close-packed crystals. We show that three different model systems with both of these features-mobile surface entities and shape polydispersity-consistently assemble quasicrystals and/or approximants. We argue that this design strategy can be widely exploited to assemble quasicrystals and approximants on the nanoscale and microscale. In addition, our results further elucidate the formation of soft-matter quasicrystals in experiment.

Numerical study of random lasing in three dimensional amplifying disordered media

In this paper, the lasing action in three-dimensional active random systems has been numerically investigated. Here, random systems of spherical dielectric particles imbedded in an active medium are considered. The quasi steady state approximation for the population inversion of the active medium is applied to solve three dimensional governing equations. Results show that when the density of particles increases to an upper limit, the intensity of lasing modes is enhanced. Also, the effects of pumping rate and particle size on the number of lasing modes and their intensity are studied. Lasing threshold of laser modes in different disordered systems is calculated and it is shown that by an appropriate selection of the central frequency of gain line-shape, the output power intensity of random lasers increases. These results are in agreement with the experimental results observed by others.

LIMIT DISTRIBUTIONS OF SOME STEREOLOGICAL ESTIMATORS IN WICKSELL'S CORPUSCLE PROBLEM

Suppose that a homogeneous system of spherical particles (d-spheres) with independent identically distributed radii is contained in some opaque d-dimensional body, and one is interested to estimate the common radius distribution. The only information one can get is by making a cross-section of that body with an s-flat (1 ≤ s ≤ d -1) and measuring the radii of the s-spheres and their midpoints. The analytical solution of (the hyper-stereological version of) Wicksell's corpuscle problem is used to construct an empirical radius distribution of the d-spheres. In this paper we study the asymptotic behaviour of this empirical radius distribution for s = d -1 and s = d - 2 under the assumption that the s-dimensional intersection volume becomes unboundedly large and the point process of the midpoints of the d-spheres is Brillinger-mixing. Of course, in stereological practice the only relevant cases are d = 3; s = 2 or s = 1 and d = 2; s = 1. Among others we generalize and extend some results obtained in Franklin (1981) and Groeneboom and Jongbloed (1995) under the Poisson assumption for the special case d = 3; s = 2.

Percolation-induced conductor-insulator transition in a system of metal spheres in a dielectric fluid

We develop a model to investigate the insulator-conductor transition observed in a system of spherical metal particles suspended in a quasi-two-dimensional viscous liquid between planar electrodes when the voltage of the electrodes is increased. Our model captures the main ingredients of the process in experimental system, and reveals the insulator-conductor transition at a well-defined critical voltage. Based on the simulation data we demonstrate that characteristic quantities of the system show power-law scaling in the vicinity of the critical point. These scaling analysis show clearly that the transition between the insulating and conducting phases is analogous to second-order phase transitions.

Pattern formation of dipolar colloids in rotating fields: layering and synchronization

We report Brownian dynamics (BD) simulation and theoretical results for a system of spherical colloidal particles with permanent dipole moments in a rotating magnetic field. Performing simulations at a fixed packing fraction and dipole coupling parameter, we construct a full non-equilibrium phase diagram as a function of the driving frequency (ω0) and field strength (B0). This diagram contains both synchronized states, where the individual particles follow the field with (on average) constant phase difference, and asynchronous states. The synchronization is accompanied by layer formation, i.e., by spatial symmetry-breaking, similar to systems of induced dipoles in rotating fields. In the permanent dipole case, however, too large ω0 yields a breakdown of layering, supplemented by complex changes of the single-particle rotational dynamics from synchronous to asynchronous behavior. We show that the limit frequencies ωc can be well described as a bifurcation in the nonlinear equation of motion of a single-particle rotating in a viscous medium. Finally, we present a simple density functional theory, which describes the emergence of layers in perfectly synchronized states as an equilibrium phase transition.

Broad-band electrical conductivity of carbon nanofibre-reinforced polypropylene foams

The influence of foaming a semi-crystalline polymer reinforced with different concentrations of carbon nanofibres (0–20 wt.%) on the formation of an electrically conductive network was studied at room temperature using an impedance analyzer over a wide interval of frequencies (from 10 −2 to 10 6 Hz). Composites were prepared by melt-compounding using a twin-screw extruder, and later chemically foamed. Although composite materials displayed lower conductivities than expected, assuming a percolative behavior, foaming promoted a tunnel-like conduction at lower CNF concentrations than in the solids. At higher CNF concentrations, no great improvements were achieved as tunneling conduction decreased with increasing local crystallinity. Foams showed electrical conduction characteristics typical of a conductive random-distributed fibre-like system, while the behavior of the solids was closer to a system of spherical particles, related to CNF aggregation. The anisotropic cellular structure of the 20 wt.% CNF composite foamed by a physical foaming process disrupted the preferential in-plane CNF orientation attained during solid preparation, with these foams showing higher through-plane conductivity and more isotropic electrical properties than the chemically-foamed ones. It has been demonstrated that foaming PP–CNF composites resulted in the formation of a conductive network at lower CNF concentrations than in the solids, with foams showing the potential for use in conductive high-performance lightweight composite systems.

Static Light Scattering of Concentrated Particle Systems in the Rayleigh-Debye-Gans Regime: Modeling and Data Analysis

In this work we give an overview of the Rayleigh-Debye-Gans (RDG) theory applied to the analysis of static light scattering (SLS) data of different types of concentrated particle systems. First some useful models needed to analyze SLS data under the RDG regime for concentrated particle systems are presented. We consider monodisperse as well as polydisperse systems of spherical particles. Then we present some techniques for analyzing the SLS data in different contexts with the aim of gathering information about: particle size and shape, particle size distribution, particle concentration, and some other useful parameters characterizing the particle systems. Finally, we report an application of some of the models and methods illustrated previously. They were used to characterize a system of concentrated polymer particles embedded in a polymer matrix, formed as the result of a phase separation induced by polymerization in a polymer blend.

Effective mesopore tuning using aromatic compounds in the aerosol-assisted system of aluminium organophosphonate spherical particles

Spherical particles of ordered mesoporous aluminium organophosphonates (AOPs) were fabricated by spray-drying of precursor solutions containing Pluronic F127 (EO106PO70EO106) at low temperature. Expansion of the mesopores (10.5 nm) were investigated using the triblock copolymer by the addition of typical aromatic compounds such as 1,3,5-trimethylbenzene (TMB) and 1,3,5-triisopropylbenzene (TIPBz). 1,3,5-TIPBz was more useful than 1,3,5-TMB for obtaining spherical AOP particles with large mesopores (>20 nm) because 1,3,5-TIPBz with the boiling point (235 °C) much higher than the spray-drying temperature (~110 °C) was accommodated in the surfactant assemblies effectively. The boiling point of 1,3,5-TMB (165 °C) was not so high that it cannot stay completely in the surfactant assemblies during the spray-drying process, and thus smoothness of the surfaces was also deteriorated by evaporation of 1,3,5-TMB. Accordingly, the use of 1,3,5-TIPBz is effective for tuning uniform mesopores in the aerosol-assisted system of mesoporous AOP spherical particles with smooth surfaces.

A general algorithm using Mathematica 2.0 for calculting dlvo potential interactions and stability ratios in spherical colloidal particle systems

A general and numerical algorithm using Mathematica v. 2.0 is presented for calculating the stability ratios and interaction potential energy between two spherical colloidal particles according to the DLVO theory. The algorithm is applicable to electrolytes with any number of ionic species having any valence state and superficial potentials on the particles. The algorithm is versatile to allow change the values of the parameters that characterizes the colloidal system and is suitable to plot the stability curves for a given set of radii, Hamaker constant, superficial potential, electrolyte concentration range, and electrolyte valence. The algorithm was implemented on two models of DLVO interaction potential and is appropriate for analysis of coagulation tendencies of spherical colloidal particles.

On structural correlations in the percolation of hard-core particles

Percolation in colloidal suspensions is sometimes simulated by the random insertion of impenetrable particles into a box. However, configurations generated in this way are not representative of an equilibrated suspension. Here, we quantify the effect of the insertion method on the percolation threshold for systems of spherical particles.

Partition instability in water-immersed granular systems

It is well known that a system of grains, vibrated vertically in a cell divided into linked columns, may spontaneously move into just one of the columns due to the inelastic nature of their collisions. Here we study the behavior of a water-immersed system of spherical barium titanate particles in a rectangular cell which is divided into two columns, linked by two connecting holes, one at the top and one at the bottom of the cell. Under vibration the grains spontaneously move into just one of the columns via a gradual transfer of grains through the connecting hole at the base of the cell. We have developed numerical simulations that are able to reproduce this behavior and provide detailed information on the instability mechanism. We use this knowledge to propose a simple analytical model for this fluid-driven partition instability based on two coupled granular beds vibrated within an incompressible fluid.

Optical properties of two‐dimensional periodic arrays of metallodielectric nanosandwiches

AbstractWe report a theoretical study of two‐dimensional periodic arrays of composite particles, consisting of two metallic nanodisks separated by a dielectric spacer, using an efficient and accurate multiple‐scattering method, which was originally developed for systems of spherical particles and recently extended to non‐spherical shapes. In particular, we discuss the plasmonic excitations in such isolated nanosandwiches and study the influence of geometrical parameters like the thickness of the dielectric spacer. Moreover, we investigate the interaction between such composite particles as they approach each other in a two‐dimensional periodic lattice. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Local structures of fluid with discrete spherical potential: Theory and grand canonical ensemble Monte Carlo simulation

Grand canonical Monte Carlo simulation and theoretical calculations based on Ornstein-Zernike (OZ) integral equation and third order+second order perturbation density functional theory (DFT) are performed to study a system of spherical particles interacting through a core-softened (CS) potential combining a repulsive square soft core and an attractive square well. Both theoretical predictions and simulation results reveal peculiar homogeneous and inhomogeneous local structures originating from the discontinuous nature of the CS potential. The bulk radial distribution function displays discontinuities at the distances coinciding with the ranges of the successive repulsive and attractive parts in the CS potential function. The density profiles of confined CS fluid show the shapes arising from the complex interplay among the steric effects and the competition between the repulsive and attractive parts of the CS potential. Satisfactory agreement between the theoretical results and simulation data leads to the following conclusions: (i) a modified hypernetted chain approximation combined with a hard sphere bridge function, which has been recently proposed by one of the authors of this study, is sufficiently reliable for the structural studies of CS fluid, and (ii) the third order+second order perturbation DFT, which has proven successful for the study of inhomogeneous structure of model fluids with continuous intermolecular potential function, posses a high adaptability to be applied for various types of interaction potentials and performs well also in the case of discontinuous CS model.

Comment on "Long-Lived Giant Number Fluctuations in a Swarming Granular Nematic"

Narayan et al. (Reports, 6 July 2007, p. 105) reported giant number fluctuations attributed to curvature-driven active currents specific for nonequilibrium nematic systems. We present data demonstrating that similar results can be found in systems of spherical particles due either to inelastic clustering or persistent density inhomogeneity, suggesting two alternative explanations for their results.

Characterization of voids in spherical particle systems by Delaunay empty spheres

The pore space of mono-sized spherical particle systems of increasing density is characterized by Delaunay empty spheres. Periodic packings of densities ranging from 0.57 up to 0.70 are generated numerically by symmetric vibration. The Voronoi diagrams of these packings are then computed with an algorithm based on the research of Delaunay empty spheres. The voids distribution and the tortuosity of packings as a function of density are studied. As the density increases, the voids distribution becomes more narrow. For partly ordered packings of high density, the voids distribution presents two peaks corresponding to the size of Delaunay empty spheres of perturbed fcc or hcp packings. The tortuosity of disordered packings decreases slowly with density. However, when the system becomes partly ordered, a large increase in tortuosity is observed.

Control of Ceramic Material Microstructure with Super High Magnetic Field

A new control method of the particle orientation structure with super high magnetic field is studied for Al2O3 ceramics. Al2O3 slurry was made with two types of Al2O3 particles, which one was spherical shape of, and the other one was elongated shape of. The Al2O3 ceramics of orientation structure was fabricated by drying the Al2O3 slurry under the super high magnetic field, cold isostatic pressing (CIP) and sintering. Effects of particle shape, particle size, the solid loading, slurry viscosity, dispersant content and the magnetic field strength on the particle orientation structure were examined in detail. The experimental results indicate that even the spherical Al2O3 particles can align under the magnetic field; the particle orientation degree changes with the particle shape and the solid loading under same magnetic field strength conditions, and the elongated particle system is easier to align than the spherical particle system; the particle orientation degree of the Al2O3 ceramics can be controlled by adjusting the particle shape, particle size, solid loading, slurry viscosity, dispersant content and magnetic field strength.

Effects of fiber curvature on the microstructure of the interfacial transition zone in fresh concrete

The study on the interfacial transition zone (ITZ) of concrete has received lots of attention in the last decade. However, no information is available on the influence of the curvature of a rigid surface on the microstructure of ITZ. This paper employed computer simulation technology to study the influence of fiber curvature on the initial microstructure of ITZ in concrete. For the sake of simplification, the investigation was first focused on the mono-size spherical particle packing system around a cylindrical fiber with different diameters. An algorithm of serial cylindrical sectioning was developed. The curve of the solid volume fraction versus the distance to the surface of the fiber was used as a parameter to characterize the microstructure of the ITZ. Then, the influence of the ratio of fiber diameter to particle diameter on the initial ITZ’s microstructure was studied. These curves were compared with the ones from flat aggregate surface on which mono-size spherical particles were packed. Furthermore, the multi-size spherical particles system was further investigated. The simulation results demonstrate that no matter whether the spherical particle system is mono-size or multi-size, the fresh ITZ’s microstructure is irrelevant to the curvature of the fiber. The shape of the curve of solid volume fraction versus the distance from the surface of the fiber is similar to that around a flat aggregate surface. In all cases, the horizontal coordinates of the first peak of the curves are located at around half the mean weight diameter of the particles. The thickness of ITZ reduces slightly with the decrease in water/cement ratio. Therefore, one may use the ITZ’s microstructure around a flat aggregate surface to represent the ITZ’s microstructure around a cylindrical fiber in the fresh state, and vice versa.

Tunable colloids: control of colloidal phase transitions with tunable interactions.

Systems of spherical colloidal particles mimic the thermodynamics of atomic crystals. Control of interparticle interactions in colloids, which has recently begun to be extensively exploited, gives rise to rich phase behaviours as well as crystal structures with nanoscale and micron-scale lattice spacings. This provides model systems in which to study fundamental problems in condensed matter physics, such as the dynamics of crystal nucleation and melting, and the nature of the glass transition, at experimentally accessible lengthscales and timescales. Tunable control of these interactions provides reversible control. This will enable quantitative studies of phase transition kinetics as well as the creation of advanced materials with switchability of function and properties.

Non-Gaussian energy landscape of a simple model for strong network-forming liquids: Accurate evaluation of the configurational entropy

We present a numerical study of the statistical properties of the potential energy landscape of a simple model for strong network-forming liquids. The model is a system of spherical particles interacting through a square-well potential, with an additional constraint that limits the maximum number of bonds Nmax per particle. Extensive simulations have been carried out as a function of temperature, packing fraction, and Nmax. The dynamics of this model are characterized by Arrhenius temperature dependence of the transport coefficients and by nearly exponential relaxation of dynamic correlators, i.e., features defining strong glass-forming liquids. This model has two important features: (i) Landscape basins can be associated with bonding patterns. (ii) The configurational volume of the basin can be evaluated in a formally exact way, and numerically with an arbitrary precision. These features allow us to evaluate the number of different topologies the bonding pattern can adopt. We find that the number of fully bonded configurations, i.e., configurations in which all particles are bonded to Nmax neighbors, is extensive, suggesting that the configurational entropy of the low temperature fluid is finite. We also evaluate the energy dependence of the configurational entropy close to the fully bonded state and show that it follows a logarithmic functional form, different from the quadratic dependence characterizing fragile liquids. We suggest that the presence of a discrete energy scale, provided by the particle bonds, and the intrinsic degeneracy of fully bonded disordered networks differentiates strong from fragile behavior.