Low Packing Fractions Research Articles

Active jamming: Self-propelled soft particles at high density

We study numerically the phases and dynamics of a dense collection of self-propelled particles with soft repulsive interactions in two dimensions. The model is motivated by recent in vitro experiments on confluent monolayers of migratory epithelial and endothelial cells. The phase diagram exhibits a liquid phase with giant number fluctuations at low packing fraction φ and high self-propulsion speed v(0) and a jammed phase at high φ and low v(0). The dynamics of the jammed phase is controlled by the low-frequency modes of the jammed packing.

An investigation of X-ray luminosity versus crystalline powder granularity

At the High-throughput Discovery of Scintillator Materials Facility at Lawrence Berkeley National Laboratory, scintillators are synthesized by solid-state reaction or melt mixing, forming crystalline powders. These powders are formed in various granularity and the crystal grain size affects the apparent luminosity of the scintillator. To accurately predict a ?full-size? scintillator?s crystal luminosity, the crystal luminosity as a function of crystal granularity size has to be known. In this study, we examine Bi4Ge3O12 (BGO), Lu2SiO5:Ce (LSO), YAlO3:Ce (YAP:Ce), and CsBa2I5:Eu2+ (CBI) luminosities as a function of crystalline grain size. The highest luminosities were measured for 600- to 1000-?m crystal grain sizes for BGO and LSO, for 310- to 600-?m crystal grain sizes for CBI, and for crystal grains larger than 165?m for YAP:Ce. Crystal grains that were larger than 1 mm had a lower packing fraction, and smaller grains were affected by internal scattering. We measured a 34percent decrease in luminosity for BGO when decreasing from the 600- to 1000- ?m crystal grain size range down to the 20- to 36-?m range. The corresponding luminosity decrease for LSO was 44percent for the same grain size decrease. YAP:Ce exhibited a luminosity decrease of 47percent when the grain size decreased from the 165- to 310-?m crystal grains to the 20- to 36-?m range, and CBI exhibited a luminosity decrease of 98percent when the grain size decreased from the 310- to 600-?m crystal grain range to the 36- to 50-?m range. We were able to very accurately estimate full-size crystal luminosities from crystalline grains that are larger than 90 ?m.

D-Cluster Converter Foil for Laser-Accelerated Deuteron Beams: Towards Deuteron-Beam-Driven Fast Ignition

A volumetrically-loaded ultra-high-density deuterium cluster material is described here for use as a deuteron beam source in laser matter interactions. Due to high volumetric loading, the material has potential to provide enough deuteron beam flux for the inertial confinement fusion (ICF) fuel ignition, avoiding depletion problem encountered by current proton-driven fast ignition (FI). In addition, accelerated deuterons can fuse with the ICF fuel (both D and T) to provide extra “bonus” energy gain, which further relaxes the laser-driver energy needed. Preliminary TRIDENT sub-Petawatt Laser experiments have provided some encouraging results showing that our cluster foils with a relative low packing fraction, can achieve a high yield of the accelerated deuterons even in the presence of an unwanted surface contaminant.

Propagating waves in a monolayer of gas-fluidized rods

We report on an observation of propagating compression waves in a quasi-two-dimensional monolayer of apolar granular rods fluidized by an upflow of air. The collective wave speed is an order of magnitude faster than the speed of the particles. This gives rise to anomalously large number fluctuations, ΔN~N(0.72±0.04), which are greater than ordinary number fluctuations of N(1/2). We characterize the waves by calculating the spatiotemporal power spectrum of the density. The position of observed peaks, as a function of frequency ω and wave vector k, yields a linear dispersion relationship in the long-time, long-wavelength limit and a wave speed c=ω/k. Repeating this analysis for systems at different densities and air speeds, we observe a linear increase in the wave speed with increasing packing fraction with almost no dependence on the air flow. We also observe that the parallel and perpendicular root-mean-square speeds of the rods are identical when waves are present, but become different at low packing fractions where there are no waves. Based on this apparent exclusivity, we map out the phase behavior for the existence of waves vs speed anisotropy as a function of density and fluidizing air flow.

Settling of particles in liquids: Effects of material properties

AbstractThis article presents a numerical study on the settling of uniform spheres in liquids by means of the discrete element method. The effects of particle and liquid properties, such as particle size, Hamaker constant, liquid density, and viscosity, on the formation of packed beds or cakes were studied in terms of packing fraction, radial distribution function (RDF), and coordination number (CN). The results showed that the packing fraction of a cake increases with increasing particle size but decreases with increasing the Hamaker constant, liquid density, and viscosity. RDF and CN also change correspondingly: packings with lower packing fraction generally have RDFs with fewer peaks and smaller mean CNs. A good correlation between packing fraction and other structural properties was identified. The analysis of the particle‐particle and liquid‐particle interactions showed that the packing properties are mainly affected by the ratio of the interparticle cohesion to the effective gravity of particles. The previously proposed equation linking packing fraction with the interparticle forces has been extended to incorporate the impact‐induced pressure force in a settling process. Based on the modified equation, the effects of key variables on the relationship between packing fraction and particle size were re‐examined for general application. © 2011 American Institute of Chemical Engineers AIChE J, 2012.

Two-Phase Synthesis of Monodisperse Silica Nanospheres with Amines or Ammonia Catalyst and Their Controlled Self-Assembly

A significant progress has recently been made in the synthesis of monodisperse silica nanoparticles less than 30 nm in diameter by using basic amino acids (e.g., lysine) as a base catalyst for hydrolysis of silicon alkoxide. Alternatively, a more versatile and economical amino acid-free method has been developed to synthesize uniform silica nanospheres (SNSs) with low polydispersity (<12%) in liquid-liquid biphasic systems containing tetraethoxysilane (TEOS), water, and primary amine (or ammonia) under precisely controlled pH conditions (pH 10.8-11.4). The diameter of the SNSs determined from scanning electron microscopy (SEM) can be tuned from ∼12 to ∼36 nm by simply changing the initial pH of the aqueous phase in the reaction mixtures. Furthermore, the as-synthesized sol was taken as the starting material for studying the influences of the type of base catalysts on the solvent evaporation-induced three-dimensional (3D) self-assembly of SNSs. X-ray diffraction (XRD) and nitrogen adsorption-desorption are used to characterize the degree of packing of the resulting 3D arrays. The assembled SNSs with large interparticle mesopores with the diameter of ca. 8.1 nm and low packing fraction of ca. 66.1% are observed upon solvent evaporation of as-synthesized sol in the presence of primary amine. This indicates that SNSs are loosely packed, compared with the packing fraction of 74% for a face-centered cubic array of ideal hard spheres. In contrast, with the aid of an organic buffer or lysine as additives, the assembly of SNSs having smaller mesopores (ca. 3.9 nm) and higher packing fraction of 70.5-71.5% are achieved. It is suggested that the chemical additives with the ability to maintain relatively strong repulsive interaction until the final stage of evaporation play a vital role in the fabrication of well-ordered SNSs arrays.

Investigating the effect of shape on particle segregation using a Monte Carlo simulation

A Monte Carlo simulation has been used to investigate the segregation potential of a range of particulate systems under conditions in which the particles undergo high amplitude low frequency shaking. These systems involve a wide range of binary powder mixtures in which complex particle shapes have been investigated, including plates and rods which represent the real world materials encountered in pharmaceutical systems such as those which include crystalline components. Previous simulations on the segregation propensity of systems with different shapes were limited to spheres and spherocylinders, with relatively low vibrational amplitude drops. A commercial computer application for particle packing—called MacroPac—has been successfully employed here, as it has been able to model systems that are more complex where the shape variation is much wider. These simulations apply to the case of macroscopic particles, in the absence of air resistance and inter-particle forces. For non-spherical shapes, an ‘effective size’ which relates to the radius of gyration of the particles is determined. Our studies indicate that with high amplitude low frequency shaking, in a mixture of particles with different shapes but with equal volumes, the particles with the larger ‘effective size’, which tend to have a lower packing fraction, segregate to the top.

Effects of random pebble distribution on the multiplication factor in HTR pebble bed reactors

In pebble bed reactors the pebbles have a random distribution within the core. The usual approach in modeling the bed is homogenizing the entire bed. To quantify the errors arising in such a model, this article investigates the effect on k eff of three phenomena in random pebble distributions: non-uniform packing density, neutron streaming in between the pebbles, and variations in Dancoff factor. For a 100 cm high cylinder with reflective top and bottom boundary conditions 25 pebble beds were generated. Of each bed three core models were made: a homogeneous model, a zones model including density fluctuations, and an exact model with all pebbles modeled individually. The same was done for a model of the PROTEUS facility. k eff calculations were performed with three codes: Monte Carlo, diffusion, and finite element transport. By comparing k eff of the homogenized and zones model the effect of including density fluctuations in the pebble bed was found to increase k eff by 71 pcm for the infinite cylinder and 649 pcm for PROTEUS. The large value for PROTEUS is due to the low packing fraction near the top of the pebble bed, causing a significant lower packing fraction for the bulk of the pebble bed in the homogenized model. The effect of neutron streaming was calculated by comparing the zones model with the exact model, and was found to decrease k eff by 606 pcm for the infinite cylinder, and by 1240 pcm for PROTEUS. This was compared with the effect of using a streaming correction factor on the diffusion coefficient in the zones model, which resulted in Δ streaming values of 340 and 1085 pcm. From this we conclude neutron streaming is an important effect in pebble bed reactors, and is not accurately described by the correction factor on the diffusion coefficient. Changing the Dancoff factor in the outer part of the pebble bed to compensate for the lower probability of neutrons to enter other fuel pebbles caused no significant changes in k eff , showing that variations in Dancoff factor in pebble bed reactors can be ignored.

Journey of an intruder through the fluidization and jamming transitions of a dense granular media

We study experimentally the motion of an intruder dragged into an amorphous monolayer of horizontally vibrated grains at high packing fractions. This motion exhibits two transitions. The first transition separates a continuous motion regime at comparatively low packing fractions and large dragging force from an intermittent motion one at high packing fraction and low dragging force. Associated to these different motions, we observe a transition from a linear rheology to a stiffer response. We thereby call "fluidization" this first transition. A second transition is observed within the intermittent regime when the intruder's motion is made of intermittent bursts separated by long waiting times. We observe a peak in the relative fluctuations of the intruder's displacements and a critical scaling of the burst amplitudes' distributions. This transition occurs at the jamming point phi(J) defined as the point where the static pressure (i.e., the pressure measured in the absence of vibration) vanishes. Investigating the motion of the surrounding grains, we show that below the fluidization transition, there is a permanent wake of free volume behind the intruder. This transition is marked by the evolution of the reorganization patterns around the intruder, which evolve from compact aggregates in the flowing regime to long-range branched shapes in the intermittent regime, suggesting an increasing role of the stress fluctuations. Remarkably, the distributions of the kinetic energy of these reorganization patterns also exhibit a critical scaling at the jamming transition.

Statistics of contact force network in dense granular matter

We investigate the distribution of contact forces in a static granular system and in annular shear granular flow, using the discrete element method, and considering the influences of both packing fraction and friction coefficient. We find the existence of a critical packing fraction. If the packing fraction is lower than this critical value, all contact forces in granular system vanish. For shear granular flow, the critical packing fraction is significantly smaller than that for static granular system. The distribution of the contact forces also exhibits different forms, especially at lower packing fraction. We also investigate the spatial configuration of contact network using the angular distribution of contact forces. In static granular systems, the contact force network is approximately isotropic, while in shear granular flow, it exhibits a distinct anisotropy along the shear direction.

Long-wavelength structural anomalies in jammed systems

The structural properties of static, jammed packings of monodisperse spheres in the vicinity of the jamming transition are investigated using large-scale computer simulations. At small wave number k , we argue that the anomalous behavior in the static structure factor, S(k) approximately k , is consequential of an excess of low-frequency, collective excitations seen in the vibrational spectrum. This anomalous feature becomes more pronounced closest to the jamming transition, such that S(0)-->0 at the transition point. We introduce an appropriate dispersion relation that accounts for these phenomena that leads us to relate these structural features to characteristic length scales associated with the low-frequency vibrational modes of these systems. When the particles are frictional, this anomalous behavior is suppressed providing yet more evidence that the jamming transitions for frictional spheres lie at lower packing fractions than for frictionless spheres. These results suggest that the mechanical properties of jammed and glassy media may therefore be inferred from measurements of both the static and dynamical structure factors.

On hydraulic permeability of random packs of monodisperse spheres: Direct flow simulations versus correlations

Hydraulic permeability is studied in porous media consisting of randomly distributed monodisperse spheres by means of computational fluid dynamics (CFD) simulations. The packing of spheres is generated by inserting a certain number of nonoverlapping spherical particles inside a cubic box at both low and high packing fractions using proper algorithms. Fluid flow simulations are performed within the interparticulate porous space by solving Navier–Stokes equations in a low-Reynolds laminar flow regime. The hydraulic permeability is calculated from the Darcy equation once the mean values of velocity and pressure gradient are calculated across the particle packing. The simulation results for the pressure drop across the packing are verified by the Ergun equation for the lower range of porosities (<0.75), and the Stokes equation for higher porosities (∼1). Using the results of simulations, the effects of porosity and particle diameters on the hydraulic permeability are investigated. Simulations precisely specified the range of applicability of empirical or semi-empirical correlations for hydraulic permeability, namely the Carman–Kozeny, Rumpf–Gupte, and Howells–Hinch formulas. The number of spheres in the model is gradually decreased from 2000 to 20 to discover the finite-size effect of pores on the hydraulic permeability of spherical packing, which has not been clearly addressed in the literature. In addition, the scale dependence of hydraulic permeability is studied via simulations of the packing of spheres shrunk to lower scales. The results of this work not only reveal the validity range of the aforementioned correlations, but also show the finite-size effect of pores and the scale-independence of direct CFD simulations for hydraulic permeability.

Generalized van der Waals theory for the twist elastic modulus and helical pitch of cholesterics

We present a generalized van der Waals theory for a lyotropic cholesteric system of chiral spherocylinders based on the classical Onsager theory for hard anisometric bodies. The rods consist of a hard spherocylindrical backbone surrounded with a square-well potential to account for attractive (or soft repulsive) interactions. Long-ranged chiral interactions are described by means of a simple pseudoscalar potential which is appropriate for weak chiral forces of a predominant electrostatic origin. Based on the formalism proposed by Straley [Phys. Rev. A 14, 1835 (1976)], we derive explicit algebraic expressions for the twist elastic modulus and the cholesteric pitch for rods as a function of density and temperature. The pitch varies nonmonotonically with density, with a sharp decrease at low packing fractions and a marked increase at higher packing fractions. A similar trend is found for the temperature dependence. The unwinding of the helical pitch at high densities (or low temperatures) originates from a strong enhancement of the local nematic order and the corresponding increase in the twist elastic resistance associated with near-parallel local rod configurations. This contrasts with the commonly held view that the increase in pitch with decreasing temperature as often observed in cholesterics is due to layer formation resulting from presmectic fluctuations. The increase in pitch with increasing temperature is consistent with an entropic unwinding as the chiral interaction becomes less significant than the thermal energy. The variation of the pitch with density, temperature, and contour length is in qualitative agreement with recent experimental results on colloidal fd rods.

Hard-sphere fluids in annular wedges: Density distributions and depletion potentials

We analyze the density distribution and the adsorption of solvent hard spheres in an annular slit formed by two large solute spheres or a large solute and a wall at close distances by means of fundamental measure density-functional theory, anisotropic integral equations, and simulations. We find that the main features of the density distribution in the slit are described by an effective two-dimensional system of disks in the vicinity of a central obstacle. This has an immediate consequence for the depletion force between the solutes (or the wall and the solute) since the latter receives a strong line-tension contribution due to the adsorption of the effective disks at the circumference of the central obstacle. For large solute-solvent size ratios, the resulting depletion force has a straightforward geometrical interpretation which gives a precise "colloidal" limit for the depletion interaction. For intermediate size ratios of 5-10 and high solvent packing fractions larger than 0.4, the explicit density-functional results show a deep attractive well for the depletion potential at solute contact, possibly indicating demixing in a binary mixture at low solute and high solvent packing fraction besides the occurrence of gelation and freezing.

Dynamical arrest in low density dipolar colloidal gels

We report the results of extensive molecular dynamics simulations of a simple, but experimentally achievable model of dipolar colloids. It is shown that a modest elongation of the particles and dipoles to make dipolar dumbbells favors branching of the dipolar strings that are routinely observed for point dipolar spheres (e.g., ferrofluids). This branching triggers the formation of a percolating transient network when the effective temperature is lowered along low packing fraction isochores (phi<0.1). Well below the percolation temperature the evolution of various dynamical correlation functions becomes arrested over a rapidly increasing period of time, indicating that a gel has formed. The onset of arrest is closely linked to ongoing structural and topological changes, which we monitor using a variety of diagnostics, including the Euler characteristic. The present system, dominated by long-range interactions between particles, shows similarities to, but also some significant differences from the behavior of previously studied model systems involving short-range attractive interactions between colloids. In particular, we discuss the relation of gel formation to fluid-fluid phase separation and spinodal decomposition in the light of current knowledge of dipolar fluid phase diagrams.

Universal version of density-functional theory for polymers with complex architecture

We propose a density-functional theory for inhomogeneous polyatomic fluids with complex architecture by introducing a different representation for the polymers. This representation gives an efficient hierarchical algorithm to calculate the direct bonding connectivity integral for polymers with complex architecture, such as linear, star, branched, and dendritic structures. A comparison with the available simulated data for linear and star polymers confirms the accuracy of the present theory in reproducing the density profiles of the two types of polymer in the slits. By using the proposed algorithm, we also explore partitioning coefficients of polymers of different architectures in a slit, and find that the partitioning coefficients of branched, star, and dendrimer forms of 22-mers decrease to a minimum at extremely low packing fraction, and then increase monotonically with packing fraction. Moreover, it is found that it is more difficult for a linear polymer of 22-mers to enter the slit than for branched, star, and dendritic polymers. In addition, we also investigate the self-assembly of diblock copolymers with different tails in a slit. It is found that the linear copolymer self-assembles into a trilayer film structure, while copolymers with branched and dendritic tails self-assemble into a five-layer film structure. Interestingly, the copolymer with a star tail self-assembles into a trilayer film structure, and then the trilayer structure evolves into a five-layer structure with increase of the bulk packing fraction in the case studied.

Crystallization and gelation in colloidal systems with short-ranged attractive interactions

We systematically study the relationship between equilibrium and nonequilibrium phase diagrams of a system of short-ranged attractive colloids. Using Monte Carlo and Brownian dynamics simulations we find a window of enhanced crystallization that is limited at high interaction strength by a slowing down of the dynamics and at low interaction strength by the high nucleation barrier. We find that the crystallization is enhanced by the metastable gas-liquid binodal by means of a two-stage crystallization process. First, the formation of a dense liquid is observed and second the crystal nucleates within the dense fluid. In addition, we find at low colloid packing fractions a fluid of clusters, and at higher colloid packing fractions a percolating network due to an arrested gas-liquid phase separation that we identify with gelation. We find that this arrest is due to crystallization at low interaction energy and it is caused by a slowing down of the dynamics at high interaction strength. Likewise, we observe that the clusters which are formed at low colloid packing fractions are crystalline at low interaction energy, but glassy at high interaction energy. The clusters coalesce upon encounter.

Effect of granulation scale-up on the strength of granules

Granulation is commonly used to enlarge particle size to impart desirable characteristics and functionality to the granules. In this work, the effect of operating scale of the granulator on the physical properties of granules is analysed. Three scaling up rules of constant tip speed, constant shear stress and constant Froude number have been evaluated using 1, 5 and 50 l Cyclomix high shear mixer granulators, calcium carbonate powder and Polyethylene glycol (PEG) as binder. The strength of granules produced in different granulator scales is analysed by side crushing test. The results indicate that the condition of constant tip speed for scale-up produces granules with relatively similar strength. When the condition of constant shear stress is used to scale-up the granulator, the granules produced in 5 and 50 l have relatively similar strength, but 1 l produces much weaker granules than those of 5 and 50 l. Work has also been carried out to analyse the flow field of granules in the granulator to provide a better insight into the velocity and stress profiles as a function of equipment scale. Positron Emission Particle Tracking (PEPT) analysis shows that under constant shear stress condition macroscopic flow field of 1 l and 5 l granulators are different, a feature which could affect the final structure of the agglomerates. The PEPT results are used to describe the velocity gradient in the Distinct Element Method (DEM) simulation of the agglomerate deformation under bulk shearing. DEM modelling of microscopic interactions in agglomerate behaviour within a shearing bed shows that flow conditions of 1 l granulator make the agglomerate with a higher elongation factor and lower packing fraction, indicating that the agglomerate would be weaker. This feature has also been observed experimentally.

Concentrating colloids with electric field gradients. I. Particle transport and growth mechanism of hard-sphere-like crystals in an electric bottle

This work concerns the use of electric field gradients to manipulate the local particle concentration in a hard-sphere-like suspension. Inside a specially designed "electric bottle," we observed our colloids to collect in the regions of lowest field strength ("negative dielectrophoresis"). This allows for the use of larger field gradients and stronger dielectrophoretic forces than in the original electric bottle design, which was based on positive dielectrophoresis [M. T. Sullivan et al., Phys. Rev. Lett. 96, 015703 (2006)]. We used confocal scanning laser microscopy to quantitatively follow the time-dependent change in the particle density and the suspension structure. Within a few days, the dielectrophoretic compression was seen to initiate a heterogeneouslike growth of large single crystals, which took place far out-of-equilibrium. The crystals had a random hexagonal close-packed structure and displayed an intriguing growth mechanism, during which the entire crystal was continuously transported, while growing both on the "high-field" and the "low-field" sides, although at different rates. After switching off the electric field, the compressed crystals were found to relax to a lower packing fraction and melt, at a much slower rate than the crystal growth. Besides revealing the particular (far out-of-equilibrium) crystal growth mechanism in these electric bottles, our observations also shed light on the role of the different particle transport processes in the cell and some of the relevant tuning parameters. This is useful for different types of experiments, for instance, focusing more on melting, homogeneous crystallization, or the glass transition.

Phase diagram for stimulus-responsive materials containing dipolar colloidal particles

Dipolar colloidal particles self-assemble into a rich variety of microstructures ranging from co-crystals of unusual symmetry, to open networks (gels) of cross-linked chains of particles. We use molecular dynamics computer simulation to explore the self-assembly, structure, crystallization and/or gelation of systems of colloid particles with permanent dipole moments immersed in a high-dielectric solvent. Particle-particle interactions are modeled with a discontinuous potential. The phase diagram in the temperature-packing fraction plane is calculated. Several types of phases are found in our simulations: ordered phases including face-centered-cubic, hexagonal-close-packed, and body-centered-tetragonal at high packing fractions, and fluid, string-fluid, and gel phases at low packing fractions. The very low volume fraction gel phases and the well-ordered crystal phases are promising for advanced materials applications.