System Of Spherical Particles Research Articles

Shear viscosity of concentrated spherical silica suspension – effect of polymethylsiloxane surface treatment

In determining the formulation of cosmetics dispersed in powder, it is very important to discover the rheological behavior of the suspension. In the case of concentrated particle suspension, it is known that the remarkable behavior of the rheology, which is different from the dilution system, is shown in ways such as shear thickening. In this report, the rheological behaviors of a concentrated spherical silica particle system were investigated in terms of particle–particle and particle–medium interaction. In the case of an aqueous medium, shear thickening occurred under certain conditions. It is noteworthy that the pH of an aqueous medium far from the isoelectric point (pH 4) of silica particles resulted in a decrease in shear viscosity η due to an increase in the double‐layer repulsion. In addition, the rheological behaviors of suspension using the silica particles, which were treated with polydimethylsiloxane and methylhydrogen polysiloxane as the solvent system, were investigated. Shear thickening disappeared in all of the solvent systems, and polydimethylsiloxane system showed lower viscosity than the methylhydrogen polysiloxane system. The surface treatment, which affects the shear viscosity, is changed not only by the particle–particle interaction but also the particle–medium interaction.

Multiple scattering of light by densely packed random media of spherical particles: Dense media vector radiative transfer equation

The theory of light scattering by systems of spherical particles is applied to study the light scattering by discrete random media. A microphysical approach of statistical electromagnetics is used to derive the vector radiative transfer equation for semi-infinite densely packed media composed of identical spherical particles. The equation obtained corresponds to the sum of the ladder diagrams in the diagrammatic representation of the Bethe–Salpeter equation. The new vector radiative transfer equation is compared with that for sparse media. The effective refractive index as it enters in our equation is calculated from the known generalization of the Lorentz–Lorenz equation. Some numerical results of calculations of the reflection matrix are presented and compared with those for sparse media. The differences between the theoretical description of light scattering by closely packed and sparse media are discussed in detail.

Spin-echo small-angle neutron scattering for dense systems of spheres

This paper presents (spin-echo) SANS correlation functions describing small-angle scattering on dense systems of spherical particles. (Spin-echo) small-angle correlation functions and associated correlation lengths for a single sphere, a dumbbell, excluded volume and structure are introduced. It is shown that the correlation length is proportional to the cumulative scattering probability. This approach is applied to a hard-sphere liquid.

Correlation function of the excluded volume

The paper introduces a correlation function of the excluded volume necessary for a real-space description of scattering from dense systems of spherical particles.

Quantitative determination of the clustered silicon concentration in substoichiometric silicon oxide layer

We present an analytical methodology, based on electron energy loss spectroscopy (EELS) and energy-filtered transmission electron microscopy, which allows us to quantify the clustered silicon concentration in annealed substoichiometric silicon oxide layers, deposited by plasma-enhanced chemical vapor deposition. The clustered Si volume fraction was deduced from a fit to the experimental EELS spectrum using a theoretical description proposed to calculate the dielectric function of a system of spherical particles of equal radii, located at random in a host material. The methodology allowed us to demonstrate that the clustered Si concentration is only one half of the excess Si concentration dissolved in the layer.

Piling and avalanches of magnetized particles

We performed computer simulations based on a two-dimensional distinct element method to study granular systems of magnetized spherical particles. We measured the angle of repose and the surface roughness of particle piles, and we studied the effect of magnetization on avalanching. We report linear dependence of both angle of repose and surface roughness on the ratio f of the magnetic dipole interaction and the gravitational force (interparticle force ratio). There is a difference in avalanche formation at small and at large interparticle force ratios. The transition is at f(c) approximately 7. For f < f(c) small vertical chains follow each other at short times (granular regime), while for f > f(c) the avalanches are typically formed by one single large particle-cluster (correlated regime). The transition is not sharp. We give plausible estimates for f(c) based on stability criteria.

Nucleation in suspensions of anisotropic colloids

We report Monte Carlo studies of liquid crystal nucleation in two types of anisotropic colloidal systems: hard rods and hard ellipsoids. In both cases we find that nucleation pathways differ strongly from the pathways in systems of spherical particles. Short hard rods show an effect of self-poisoning. This part of the article is based on a previous publication [T. Schilling, D. Frenkel, Self-poisoning of crystal nuclei in hard-rod liquids, Phys. Rev. Lett. 92 (2004) 085505]. When a crystallite forms, its surfaces are covered preferentially by rods which align perpendicular to the surface. Therefore subsequent growth is stunted. Hard, almost spherical ellipsoids can be compressed to very high densities without crystallization—in contrast to hard spheres, which crystallize easily. When forced to crystallize, ellipsoids form very loosely aggregated nuclei. In both cases nucleation pathways are complex and it is therefore difficult to define an appropriate reaction coordinate. The common strategies of investigation of nucleation problems (i.e. definition of a coordinate and then sampling barrier crossing with well-known techniques) fail in these systems.

An implementation of granular dynamics for simulating frictional elastic particles based on the DL_POLY code

We have modified Daresbury Laboratory's replicated data strategy (RDS) parallel molecular dynamics (MD) package DL_POLY (version 2.13) to study the granular dynamics of frictional elastic particles. DL_POLY [Smith and Forester, The DL_POLY_2 User Manual v2.13, 2001; Forester and Smith, The DL_POLY_2 Reference Manual v2.13, 2001] is a MD package originally developed to study liquid state and macromolecular systems by accounting for various molecular interaction forces. The particles of interest in this study are macroscopic grains in pharmaceutical powders, with sizes ranging from tens to hundreds of microns. We have therefore substituted the molecular interaction forces with contact forces (including linear-dashpot, HKK interaction forces and Coulombic friction) while taking advantage of the RDS scheme. In effect, we have created a parallel Discrete Element Simulation (DES) code. In this paper, we describe the modifications made to the original DL_POLY code and the results from the validation tests of the granular dynamics simulations for systems of monodisperse spherical particles settling under gravity. The code can also be utilized to study particle packings generated via uniaxial compaction and, in some cases, simultaneous application of shear, at constant strain.

The modelling of particle systems with real shapes.

The numerical modelling of particulate processes in environmental science increasingly requires an ability to represent the properties of individual natural particles. Considerable advances have been made in discontinuum modelling using spheres to represent particles. In this paper, we discuss recent developments that illustrate a way forward for tackling the complexity of realistically shaped bodies such as those exhibited by rock fragments. To address the validation of such approaches, we present a comparison of cube-packing experiments and their equivalent numerical simulation. Sensitivity to initial conditions, highlighted for non-spherical bodies, enters the discussion of problems with validation of numerical simulation. The algorithmic details behind these advances in modelling large systems of realistically shaped particles are summarized in our companion paper in this volume.

Motion of spheres along a fluid-gas interface.

A system of many spherical particles, suspended in a quiescent fluid and touching a planar free fluid-gas interface, is considered. Stick fluid boundary conditions at the sphere surfaces are assumed. The free surface boundary conditions are taken into account with the use of the method of images. For such a quasi-two-dimensional system, the one-sphere resistance operator is calculated numerically. Moreover, the corresponding friction and mobility tensors are constructed from irreducible multipole expansion. Finally, the long-distance terms of the two-sphere mobility tensor are evaluated explicitly up to the order of 1/r3, where r is the interparticle distance. Experiments which have motivated this work are outlined.

Liquid-liquid phase transitions for soft-core attractive potentials.

Using event-driven molecular dynamics simulations, we study a three-dimensional one-component system of spherical particles interacting via a discontinuous potential combining a repulsive square soft core and an attractive square well. In the case of a narrow attractive well, it has been shown that this potential has two metastable gas-liquid critical points. Here we systematically investigate how the changes of the parameters of this potential affect the phase diagram of the system. We find a broad range of potential parameters for which the system has both a gas-liquid critical point C1 and a liquid-liquid critical point C2. For the liquid-gas critical point we find that the derivatives of the critical temperature and pressure, with respect to the parameters of the potential, have the same signs: they are positive for increasing width of the attractive well and negative for increasing width and repulsive energy of the soft core. This result resembles the behavior of the liquid-gas critical point for standard liquids. In contrast, for the liquid-liquid critical point the critical pressure decreases as the critical temperature increases. As a consequence, the liquid-liquid critical point exists at positive pressures only in a finite range of parameters. We present a modified van der Waals equation which qualitatively reproduces the behavior of both critical points within some range of parameters, and gives us insight on the mechanisms ruling the dependence of the two critical points on the potential's parameters. The soft-core potential studied here resembles model potentials used for colloids, proteins, and potentials that have been related to liquid metals, raising an interesting possibility that a liquid-liquid phase transition may be present in some systems where it has not yet been observed.

Finite-Range Repulsive Systems of Finitely Many Particles

We consider the dynamics of finite systems of spherical particles where a fraction of the kinetic energy may be lost during collisions. We show that the set of initial configurations leading to infinitely many collisions in finite time can have positive measure, contrary to the hard-collision (energy conservation) case, in which this particular set is claimed to be empty. We also show that after sufficient time a system will decouple into maximal subsystems. This generalizes proofs that in the hard-sphere case there can be at most finitely many collisions for almost all initial configurations.

Compaction of confined mono-sized spherical particle systems under symmetric vibration: a suspension model

This paper presents a simulation study on the compaction of confined mono-sized spherical particle systems under symmetric vibration. In the model used, a random loose packing is confined between two fixed random granular boundary conditions and is submitted to symmetric vibrations of constant amplitude until complete transformation into a “suspension”. The granular system is then compacted by letting particles settle down until an equilibrium of minimum potential energy is reached. The influence of the vibration amplitude on the final packing density is studied. The increase in the vibration amplitude leads to an increase in the final packing density. Packing densities ranging from 0.57 up to 0.67 are obtained. For small vibration amplitude a linear relation is found between the final packing density and the vibration amplitude. For large vibration amplitude high packing densities are obtained and an order appears amongst the system. A suspension model is then presented which considers that, in the “suspension”, all the particles can move symmetrically upwards and downwards independently of the displacements of other particles in the system. It is shown that in these conditions, and for random systems, the vibration amplitude can be considered as a homogeneous contraction of the system during sedimentation. A relation is found between the final packing density, initial packing density and vibration amplitude. A very good agreement is obtained between the simulation results and this suspension model as long as the packing is random.

Computer Simulations of a Monolayer of Like-charged Particles Condensed on an Oppositely-charged Flat Area

A non-traditional approach to the computer simulation study of a class of quasi-two-dimensional Coulomb systems (charged particles confined to a layer near a charged planar surface) is presented. The essence of the approach lies in exploiting the fact that the charged confinement is of finite dimensions. The main consequence of such a finiteness is a non-zero potential gradient along the finite charged area that includes a non-zero tangential component of the electric field. A system of like-charged spherical particles confined by the planar surface that includes an oppositely charged squared area is considered as an example. We find that the like-charged particles, independent of their concentration, all become confined on the oppositely charged area, if the surface charge balances the total charge carried by the particles, and if the electrostatic coupling is sufficiently large. The local density of the particles above the charged area is not homogeneous; near the boundaries of the charged square a clear tendency of layer formation along the square sides is observed.

Invited article: Thermodynamic perturbation theory of the phase behaviour of colloid/interacting polymer mixtures

Thermodynamic perturbation theory is used to calculate the free energies and resulting phase diagrams of binary systems of spherical colloidal particles and interacting polymer coils in a good solvent within an effective one-component representation of such mixtures, whereby the colloidal particles interact via a polymer-induced depletion potential. Monte Carlo simulations are used to test the convergence of the high temperature expansion of the free energy. The phase diagrams calculated for several polymer-to-colloid size ratios differ considerably from the results of similar calculations for mixtures of colloids and ideal (non-interacting) polymers, and are in good overall agreement with the results of an explicit two-component representation of the same system, which includes more than two-body depletion forces.

The scattering spectra and color of disperse systems of weakly absorbing particles

The scattering spectra of weakly absorbing systems of spherical particles are calculated using various approximate and numerical methods. Comparative estimates are made for applicability of the single-scattering and mean-field approximations and the Monte Carlo computer simulation for different scattering multiplicities. The results of the calculations well agree with the experimental scattering spectra of the crystalline lens. Based on the spectral characteristics obtained, the chromaticity coordinates are calculated and regularities in variations of the color characteristics are analyzed as functions of the disperse system parameters.

The effect of multiple scattering in disperse media on polarization characteristics of scattered light

The effect of scattering of different multiplicity on polarization characteristics of scattered light is studied by the Monte Carlo computer simulation technique. The scattering multiplicity distribution versus the direction of scattering and dimensions of the scattering system is obtained for monodisperse systems of spherical particles of different size. The angular dependences of the elements of the light-scattering matrix (LSM) are calculated. It is shown that in a system of spherical particles, specific features of the LSM structure associated with multiple scattering have much in common with similar features of the LSM in systems of nonspherical particles under conditions of single scattering. The angular dependences of the degree of depolarization of the scattered light are studied.

Room temperature tunneling magnetoresistance of electron beam deposited (Co50Fe50)x(Al2O3)1−x cermet granular films

A series of (Co50Fe50)x-(Al2O3)1−x cermet granular thin films deposited on glass substrates by dual electron beam evaporation was studied for their structural, magnetotransport, and magnetic properties. Upon varying the magnetic volume fraction, x, from 0.07 to 0.52 the percolation threshold (xc) was determined from resistivity measurements to be ∼0.17. This value agrees well with the theoretical prediction for a three-dimensional system of spherical particles. Values of the isotropic tunneling magnetoresistance (TMR) as high as 10% at room temperature were found for films with x&amp;lt;0.16. The relationship between magnetotransport (maximum TMR) and the granular film topology (the percolation threshold) is discussed.

Modeling the “glass” Transition in Proteins

A model of a protein as a disordered system of identical spherical particles (which imitate protein side chains) interacting with each other via a repulsive soft sphere potential U(r) ∞ r−β is constructed. The particles undergo the conformational motion (CM) within their own harmonic conformational potentials around some mean equilibrium positions ascribed by the tertiary structure of the protein. A first principles calculation of the positional correlation functions for the CM is carried out. The general analysis is exemplified by the case in which the mean equilibrium positions of the particles form a cubic tightly-packed (face- centered) lattice (each particle has 12 nearest neighbors) with the step bhydr =6.6 A (the average distance between the centers of mass of hydrated protein subunits). The model yields dramatic slowing down of the relaxation with the decrease of temperature followed by a sharp glass transition at some crossover temperature Tc < 200 K. At the transition the liquidlike dynamic behavior (the correlation functions tend to zero with time) is altered by the glass-like one (the correlation functions tend with time to some non-zero limit). In the liquid-like region above the crossover temperature the relaxation exhibits distinct a-process following the β-one. The glass transition results from the interaction of the particles. Thus the model suggests that namely direct interactions of the fragments of protein structure rather than protein-solvent interactions are the origin of the phenomenon of the glass transition. The known increase of Tc up to 300 K at dehydration of the protein is attributed to the known concomitant compression of the globule upon drying by about 4–6% so that positions of individual atoms displace by about 0.6 A (modeled by the decrease of the step of the lattice b by 0.6 A so that bdehydr=6 A). The model suggests that the solvent influences the phenomenon of the glass transition indirectly determining the tertiary structure of the protein rather than via own freezing. In the model the transition from the liquid-like dynamic behavior to the glass-like one can be obtained even in a cluster containing a few particles. Thus the results of the model can be considered as an argument in favor of the point of view that the transition to the glassy behavior can take place for a very small domains of the protein comprising only several constituting fragments of its structure. The model predicts that for the dehydrated protein the a-relaxation process is strongly repressed.

Factors determining crystal--liquid coexistence under shear.

The interaction between an imposed shear flow and an order--disorder transition underlies a broad range of phenomena. Under the influence of shear flow, a variety of soft matter is observed to spontaneously form bands characterized by different local order---for example, thermotropic liquid crystals subjected to shear flow exhibit rich phase behaviour. The stability of order under the influence of shear flow is also fundamental to understanding frictional wear and lubrication. Although there exists a well developed theoretical approach to the influence of shear flow on continuous transitions in fluid mixtures, little is known about the underlying principles governing non-equilibrium coexistence between phases of different symmetry. Here we show, using non-equilibrium molecular dynamics simulations of a system of spherical particles, that a stationary coexistence exists between a strained crystal and the shearing liquid, and that this coexistence cannot be accounted for by invoking a non-equilibrium analogue of the chemical potential. Instead of such thermodynamic arguments, we argue that a balancing of the crystal growth rate with the rate of surface erosion by the shearing melt can account for the observed coexistence.