Phase behavior of binary hard-sphere mixtures from perturbation theory

Using a first-order perturbation theory, we have studied the phase diagram of a binary mixture of hard spheres for different values of the size ratio. Recent models for the two-body depletion potential between large spheres are used to take into account the role of the small spheres. The theory predicts a complex phase diagram including a fluid-solid transition at high packing fraction of small spheres, metastability of fluid-fluid demixing, an isostructural solid-solid transition at high packing fraction of the large spheres for sufficiently small values of the size ratio q of the spheres, and the tendency to sticky-sphere behavior in the limit q-->0. The agreement with recent simulation results is quite good. We also show that this phenomenology was already implicit in the pioneering work of Asakura and Oosawa.     

Structural transitions in granular packs: statistical mechanics and statistical geometry investigations

We investigate equal spheres packings generated from several experiments and from a large number of different numerical simulations. The structural organization of these disordered packings is studied in terms of the network of common neighbours. This geometrical analysis reveals sharp changes in the network’s clustering occurring at the packing fractions (fraction of volume occupied by the spheres respect to the total volume, ρ) corresponding to the so called Random Loose Packing limit (RLP, ρ ～ 0.555) and Random Close Packing limit (RCP, ρ ～ 0.645). At these packing fractions we also observe abrupt changes in the fluctuations of the portion of free volume around each sphere. We analyze such fluctuations by means of a statistical mechanics approach and we show that these anomalies are associated to sharp variations in a generalized thermodynamical variable which is the analogous for these a-thermal systems to the specific heat in thermal systems.     

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The packing behaviors of pebble bed in blanket were investigated by packing experiment and discrete element modeling. The packing behaviors of cylinder mono-sized pebble beds show that the average packing factor is gradually increased with increase of the diameter ratio of the bed to pebbles. The experimental and simulated results of cylinder mono-sized pebble beds are in good agreement. Using binary-sized pebble packing and increasing the size ratio of binary pebbles can increase the packing factor of pebble bed, significantly. For binary-sized pebble bed, the average packing factor increases first and then decreases with the increase of the large pebble volume fraction. The maximum value is achieved when the larger pebble volume fraction is about 60%~80%. By optimizing the filling process of the pebble bed, the packing factor of the binary-sized pebble bed has reached 0.8, but the uniformity of the binary-sized bed is poor.     

固态氚增殖包层中球床堆积性能研究

基于球床堆积实验和离散元数值模拟对包层中球床的堆积性能做了初步研究。圆柱形一元(单尺寸颗粒)球床的堆积性能的结果显示随着球床直径与颗粒直径比的增大,球床的平均堆积因子逐渐增高,实验与模拟结果一致;采用二元颗粒(双尺寸颗粒)、提高颗粒粒度比可以显著提高球床的堆积因子,二元球床的堆积因子随着大颗粒体积分数的增加先增加后减小,在大颗粒体积分数约为60%~80%时达到最大。优化了二元球床的填充工艺,最终二元球床的堆积因子基本达到0.8,但球床的均匀性欠佳。     

Brownian dynamics of polydisperse colloidal hard spheres: Equilibrium structures and random close packings

Recently we presented a new technique for numerical simulations of colloidal hard-sphere systems and showed its high efficiency. Here, we extend our calculations to the treatment of both 2- and 3-dimensional monodisperse and 3-dimensional polydisperse systems (with sampled finite Gaussian size distribution of particle radii), focusing on equilibrium pair distribution functions and structure factors as well as volume fractions of random close packing (RCP). The latter were determined using in principle the same technique as Woodcock or Stillinger had used. Results for the monodisperse 3-dimensional system show very good agreement compared to both pair distribution and structure factor predicted by the Percus-Yevick approximation for the fluid state (volume fractions up to 0.50). We were not able to find crystalline 3d systems at volume fractions 0.50–0.58 as shown by former simulations of Reeet al. or experiments of Pusey and van Megen, due to the fact that we used random start configurations and no constraints of particle positions as in the cell model of Hoover and Ree, and effects of the overall entropy of the system, responsible for the melting and freezing phase transitions, are neglected in our calculations. Nevertheless, we obtained reasonable results concerning concentration-dependent long-time selfdiffusion coefficients (as shown before) and equilibrium structure of samples in the fluid state, and the determination of the volume fraction of random close packing (RCP, glassy state). As expected, polydispersity increases the respective volume fraction of RCP due to the decrease in free volume by the fraction of the smaller spheres which fill gaps between the larger particles.     

Collective motion of polar active particles on a sphere

Collective motion of active particles with polar alignment is investigated on a sphere. We discussed the factors that affect particle swarm motion and define an order parameter that can show the degree of particle swarm motion. In the model, we added a polar alignment strength, along with Gaussian curvature, affecting particles swarm motion. We find that when the force exceeds a certain limit, the order parameter will decrease with the increase of the force. Combined with our definition of order parameter and observation of the model, the reason is that particles begin to move side by side under the influence of polar forces. In addition, the effects of velocity, rotational diffusion coefficient, and packing fraction on particle swarm motion are discussed. It is found that the rotational diffusion coefficient and the packing fraction have a great influence on the clustering motion of particles, while the velocity has little influence on the clustering motion of particles.     

What do we learn from the local geometry of glass-forming liquids?

We examine the local geometry of a simulated glass-forming polymer melt. Using the Voronoi construction, we find that the distributions of Voronoi volume P(v(V)) and asphericity P(a) appear to be universal properties of dense liquids, supporting the use of packing approaches to understand liquid properties. We also calculate the average free volume along a path of constant density and find that extrapolates to zero at the same temperature T0 that the extrapolated relaxation time diverges. We relate to the Debye-Waller factor, which is measurable by neutron scattering.     

The equation of state of a system of hard spherocylinders

Using the Monte Carlo method, we have computed the equation of state of a system of hard spherocylinders (cylinders with a hemisphere at each end), of length-to-breadth ratio equal to 3, in the isotropic liquid phase. We obtain a pressure slightly smaller than that predicted by the scaled-particle theory (SPT). The SPT predicts a liquid to nematic transition when the density is increased; we have observed that the isotropic liquid phase is stable up to densities significantly higher than the SPT transition density. Using the free-volume theory, we have also determined the behaviour of the pressure at very high densities, for any value of the length-to-breadth ratio γ. Moreover, we have shown that the packing fraction (number density times the volume of one spherocylinder) corresponding to the beginning of the fusion of the solid is an increasing function of γ.     

Fluctuating particle motion during shear induced granular compaction

Using a refractive index matching method, we investigate the trajectories of particles in three dimensional granular packing submitted to cyclic shear deformation. The particle motion observed during compaction is not diffusive but exhibits a transient cage effect, similar to the one observed in colloidal glasses. We precisely study the statistics of the step size between two successive cycles and observe that it is proportional to the shear amplitude. The link between the microscopic observations and the macroscopic evolution of the volume fraction during compaction is discussed.     

A Stochastic Description of Transition Between Granular Flow States

Two-dimensional granular flow in a channel with small exit is studied by molecular dyhamics simulations. We firstly define a key area near the exit, which is considered to be the choke area of the system. Then we observe the time variation of the local packing fraction and flow rate in this area for several fixed inflow rate, and find that these quantities change abruptly when the transition from dilute flow state to dense flow state happens. A relationship between the local flow rate and the local packing fraction in the key area is also given. The relationship is a continuous function under the fixed particle number condition, and has the characteristic that the flow rate has a maximum at a moderate packing fraction and the packing fraction is terminated at a high value with negative slope. By use of the relationship, the properties of the flow states under the fixed inflow rate condition are discussed in detail, and the discontinuities and the complex time variation behavior observed＇in the preexisting works are naturally explained by a stochastic process.     

Depletion forces and packing models

In binary colloidal suspensions, due to the depletion forces, large spheres tend to pack together so as to make entropy maximum. Based on the complexities of depletion forces and phase behaviors in binary mixtures, two packing models, named nucleation and non-nucleation packing, are proposed in this Letter. Numerical results show that, when the volume fraction is small, the nucleation is possible. As a result, the large spheres tend to pack into a larger and larger cluster. However, when the volume fraction is very large in a way, the hard-spheres will proceed in the non-nucleation packing fashion. The numerical results also show that differences between the two packing models decrease with the decrease of volume fraction.     

Packing of elastic wires in spherical cavities

We investigate the morphologies and maximum packing density of thin wires packed into spherical cavities. Using simulations and experiments, we find that ordered as well as disordered structures emerge, depending on the amount of internal torsion. We find that the highest packing densities are achieved in low torsion packings for large systems, but in high torsion packings for small systems. An analysis of both situations is given in terms of energetics and comparison is made to analytical models of DNA packing in viral capsids.     

Pfaffian pairing wave functions in electronic-structure quantum Monte Carlo simulations

We investigate the accuracy of trial wave functions for quantum Monte Carlo based on Pfaffian functional form with singlet and triplet pairing. Using a set of first row atoms and molecules we find that these wave functions provide very consistent and systematic behavior in recovering the correlation energies on the level of 95%. In order to get beyond this limit we explore the possibilities of multi-Pfaffian pairing wave functions. We show that a small number of Pfaffians recovers another large fraction of the missing correlation energy comparable to the larger-scale configuration interaction wave functions. We also find that Pfaffians lead to substantial improvements in fermion nodes when compared to Hartree-Fock wave functions.     

The influence of the packing density of absorbing inclusions into a dispersive medium on its absorption coefficient

Using an approach that is similar to the approximation of anomalous diffraction of physical optics, we have obtained analytical relations for the absorption coefficients of homogeneous and dispersive media that contain equal amounts of light absorbing matter. We show that these relations depend on the packing density of inclusions, which is characterized by the fraction of the area or volume that they occupy. It has been found quantitatively that differences between absorption coefficients of the homogeneous and dispersive media increase with increasing optical size of inclusions and decrease at large packing densities. We note that it is important to take into account the obtained dependences in spectroscopic investigation of the dispersive medium near intense absorption bands of its components. Theoretical and experimental results are compared with each other, and it is shown that they reasonably agree with each other qualitatively and quantitatively. Our study may be useful for specialists in biomedical optics, ocean physics, physics of the Earth’s surface, and scientific and applied photography.     

A model of binary assemblies of spheres

We propose a theoretical model of random binary assemblies of spheres at any packing fraction. We use the notion of geometrical neighborhood between grains that is defined through two generalizations of the Vorono? tessellation: the radical (or Laguerre) tessellation and the navigation map. The model is tested on different numerical packings. We find a weak local segregation for high packing fraction. We also find that the higher the size ratio of the particles, the more important the segregation. Received 19 February 2001 and Received in final form 27 June 2001     

Density functional theory for molecular orientation of hard rod fluids in hard slits

A density functional theory (DFT) is used to investigate molecular orientation of hard rod fluids in a hard slit. The DFT approach combines a modified fundamental measure theory (MFMT) for excluded-volume effect with the first order thermodynamics perturbation theory for chain connectivity. In the DFT approach, the intra-molecular bonding orientation function is introduced. We consider the effects of molecular length (i.e. aspect ratio of rod) and packing fraction on the orientations of hard rod fluids and flexible chains. For the flexible chains, the chain length has no significant effect while the packing fraction shows slight effect on the molecular orientation distribution. In contrast, for the hard rod fluids, the chain length determines the molecular orientation distribution, while the packing fraction has no significant effect on the molecular orientation distribution. By making a comparison between molecular orientations of the flexible chain and the hard rod fluid, we find that the molecular stiffness distinctly affects the molecular orientation. In addition, partitioning coefficient indicates that the longer rodlike molecule is more difficult to enter the confined phase, especially at low bulk packing fractions.     

Dense packing of binary and polydisperse hard spheres

The packing of binary and polydisperse unimodal and bimodal ensembles of hard spheres in the limit of high pressure is studied using a sequential addition algorithm. Upon fixing the number of particles, and their size distribution, the average (maximum) packing fraction is determined for systems of up to 20 000 particles. The structures obtained correspond to amorphous states close to the dense random close packing density. Binary distributions obtained are denser than the equivalent monodisperse distribution and agree with the theoretical prediction for an infinite size ratio limit. Unimodal normal and lognormal polydisperse distributions obtained compare favourably with available simulation and experimental data. Results for bimodal lognormal distributions are presented. In all cases it is seen how an increase in polydispersity increases the packing fraction of the system. The results can be employed to gain insight into optimal formulations for dense emulsions.     

Intermolecular overlap geometry gives two classes of fulleride superconductor: electronic structure of 38 K Tc Cs3C60

Superconductivity emerges for the A15 polymorph of the fulleride Cs3C60 upon compression to a pressure of approximately 4 kbar. Using density functional theory we study the bonding in the A15 phase as a function of unit cell volume comparing it to that in the fcc polymorph. We find that, despite its smaller packing density, the bcc-derived A15 phase has both a substantially wider bandwidth for the partially occupied t1u band and a higher density of states at the Fermi level. This result can be traced to the striking differences in the nature of the interanion Tc--the two sphere packings (body centered versus face centered) observed experimentally produce two electronically distinct classes of fulleride superconductors.     

Effects of short-range attraction on Jamming transition

Enormous progresses to understand the jamming transition have been driven via simulating purely repulsive particles which were somehow idealized in the past two decades. While the attractive systems are both theoretical and practical compared with repulsive systems. By studying the statistics of rigid clusters, we find that the critical packing fraction φ_c varies linearly with attraction μ for different system sizes when the range of attraction is short. While for systems with long-range attractions, however, the slope of φ_c appears significantly different, which means that there are two distinct jamming scenarios. In this paper, we focus our main attention on short-range attractions scenario and define a new quantity named "short-range attraction susceptibility" χ_p, which describes the degree of response of the probability of finding jammed states pjto short-range attraction strength μ. Our central results are that χ_p diverges in the thermodynamic limit as χ_p ∝|φ-φ_c~∞|~(-γ_p), where φ_c~∞ is the packing fraction at the jamming transition for the infinite system in the absence of attraction. χ_p obeys scaling collapse with a scaling function in both two and three dimensions, illuminating that the jamming transition can be considered as a phase transition as proposed in previous work.     

Creep and fluidity of a real granular packing near jamming

We study the internal dynamical processes taking place in a granular packing below yield stress. At all packing fractions and down to vanishingly low applied shear, a logarithmic creep is observed. The experiments are analyzed using a viscoelastic model which introduces an internal, time-dependent, fluidity variable. For all experiments, the creep dynamics can be rescaled onto a unique curve which displays jamming at the random-close-packing limit. At each packing fraction, we measure a stress corresponding to the onset of internal granular reorganization and a slowing down of the creep dynamics before the final yield.