Packing of nonoverlapping cubic particles: Computational algorithms and microstructural characteristics

Microstructural characterization of DEM-based random packings of monodisperse and polydisperse non-convex particles

Understanding of hard particles in morphologies and sizes on microstructures of particle random packings is of significance to evaluate physical and mechanical properties of many discrete media, such as granular materials, colloids, porous ceramics, active cells, and concrete. The majority of previous lines of research mainly dedicated microstructure analysis of convex particles, such as spheres, ellipsoids, spherocylinders, cylinders, and convex-polyhedra, whereas little is known about non-convex particles that are more close to practical discrete objects in nature. In this study, the non-convex morphology of a three-dimensional particle is devised by using a mathematical-controllable parameterized method, which contains two construction modes, namely, the uniformly distributed contraction centers and the randomly distributed contraction centers. Accordingly, three shape parameters are conceived to regulate the particle geometrical morphology from a perfect sphere to arbitrary non-convexities. Random packing models of hard non-convex particles with mono-/poly-dispersity in sizes are then established using the discrete element modeling Diverse microstructural indicators are utilized to characterize configurations of non-convex particle random packings. The compactness of non-convex particles in packings is characterized by the random close packing fraction fd and the corresponding average coordination number Z. In addition, four statistical descriptors, encompassing the radial distribution function g(r), two-point probability function S2(i)(r), lineal-path function L(i)(r), and cumulative pore size distribution function F(δ), are exploited to demonstrate the high-order microstructure information of non-convex particle random packings. The results demonstrate that the particle shape and size distribution have significant effects on Z and fd; the construction mode of the randomly distributed contraction centers can yield higher fd than that of the uniformly distributed contraction centers, in which the upper limit of fd approaches to 0.632 for monodisperse sphere packings. Moreover, non-convex particles of sizes following the famous Fuller distribution of the power-law distribution of the exponent q = 2.5, have the highest fd (≈0.761) with respect to other q. In contrast, the particle shapes have an almost negligible effect on the four statistical descriptors, but they are remarkably sensitive to particle packing fraction fp and size distribution. The results can provide sound guidance for custom-design of granular media by tailoring specific microstructures of particles.

Two-stage random sequential adsorption of discorectangles and disks on a two-dimensional surface

The different variants of two-stage random sequential adsorption (RSA) models for packing of disks and discorectangles on a two-dimensional (2D) surface were investigated. In the SD (sticks+disks) model, the discorectangles were first deposited and then the disks were added. In the DS (disks+sticks) model, the disks were first deposited and then discorectangles were added. At the first stage the particles were deposited up to the selected concentration and at the final (second) stage the particles were deposited up to the saturated (jamming) state. The main parameters of the models were the concentration of particles deposited at the first stage, aspect ratio of the discorectangles ɛ (length to diameter of ratio ɛ=l/d) and disk diameter D. All distances were measured using the value of d as a unit of measurement of linear dimensions, the disk diameter was varied in the interval D∈[1-10], and the aspect ratio value was varied in the interval ɛ∈[1-50]. The dependencies of the jamming coverage of particles deposited at the second stage versus the parameters of the models were analyzed. The presence of first deposited particles for both models regulated the maximum possible disk diameter D_{max} (SD model) or the maximum aspect ratio ɛ_{max} (DS model). This behavior was explained by the deposition of particles in the second stage into triangular (SD model) or elongated (DS model) pores formed by particles deposited at the first stage. The percolation connectivity of disks (SD model) and discorectangles (DS model) for the particles with a hard core and a soft shell structure was analyzed. The disconnectedness was ensured by overlapping of soft shells. The dependencies of connectivity versus the parameters of SD and DS models were also analyzed.

Morphology and kinetics of random sequential adsorption of superballs: From hexapods to cubes

Superballs represent a class of particles whose shapes are defined by the domain |x|^{2p}+|y|^{2p}+|z|^{2p}≤R^{2p}, with p∈(0,∞) being the deformation parameter. 0<p<0.5 represents a family of hexapodlike (concave octahedral-like) particles, 0.5≤p<1 and p>1 represent, respectively, families of convex octahedral-like and cubelike particles, with p=1,0.5, and ∞ representing spheres, octahedra, and cubes. Colloidal zeolite suspensions, catalysis, and adsorption, as well as biomedical magnetic nanoparticles are but a few of the applications of packing of superballs. We introduce a universal method for simulating random sequential adsorption of superballs, which we refer to as the low-entropy algorithm, which is about two orders of magnitude faster than the conventional algorithms that represent high-entropy methods. The two algorithms yield, respectively, precise estimates of the jamming fraction ϕ_{∞}(p) and ν(p), the exponent that characterizes the kinetics of adsorption at long times t, ϕ_{∞}(p)-ϕ(p,t)∼t^{-ν(p)}. Precise estimates of ϕ_{∞}(p) and ν(p) are obtained and shown to be in agreement with the existing analytical and numerical results for certain types of superballs.

Continuum percolation of congruent overlapping polyhedral particles: Finite-size-scaling analysis and renormalization-group method

The continuum percolation of randomly orientated overlapping polyhedral particles, including tetrahedron, cube, octahedron, dodecahedron, and icosahedron, was analyzed by Monte Carlo simulations. Two numerical strategies, (1) a Monte Carlo finite-size-scaling analysis and (2) a real-space Monte Carlo renormalization-group method, were, respectively, presented in order to determine the percolation threshold (e.g., the critical volume fraction ϕ_{c} or the critical reduced number density η_{c}), percolation transition width Δ, and correlation-length exponent ν of the polyhedral particles. The results showed that ϕ_{c} (or η_{c}) and Δ increase in the following order: tetrahedron < cube < octahedron < dodecahedron < icosahedron. In other words, both the percolation threshold and percolation transition width increase with the number of faces of the polyhedral particles as the shape becomes more "spherical." We obtained the statistical values of ν for the five polyhedral shapes and analyzed possible errors resulting in the present numerical values ν deviated from the universal value of ν=0.88 reported in literature. To validate the simulations, the corresponding excluded-volume bounds on the percolation threshold were obtained and compared with the numerical results. This paper has practical applications in predicting effective transport and mechanical properties of porous media and composites.

Shape-dependent effective diffusivity in packings of hard cubes and cuboids compared with spheres and ellipsoids

We performed computational screening of effective diffusivity in different configurations of cubes and cuboids compared with spheres and ellipsoids. In total, more than 1500 structures are generated and screened for effective diffusivity. We studied simple cubic and face-centered cubic lattices of spheres and cubes, random configurations of cubes and spheres as a function of volume fraction and polydispersity, and finally random configurations of ellipsoids and cuboids as a function of shape. We found some interesting shape-dependent differences in behavior, elucidating the impact of shape on the targeted design of granular materials.

Statistical characterization of microstructure of packings of polydisperse hard cubes

Polydisperse packings of cubic particles arise in several important problems. Examples include zeolite microcubes that represent catalytic materials, fluidization of such microcubes in catalytic reactors, fabrication of new classes of porous materials with precise control of their morphology, and several others. We present the results of detailed and extensive simulation and microstructural characterization of packings of nonoverlapping polydisperse cubic particles. The packings are generated via a modified random sequential-addition algorithm. Two probability density functions (PDFs) for the particle-size distribution, the Schulz and log-normal PDFs, are used. The packings are analyzed, and their random close-packing density is computed as a function of the parameters of the two PDFs. The maximum packing fraction for the highest degree of polydispersivity is estimated to be about 0.81, much higher than 0.57 for the monodisperse packings. In addition, a variety of microstructural descriptors have been calculated and analyzed. In particular, we show that (i) an approximate analytical expression for the structure factor of Percus-Yevick fluids of polydisperse hard spheres with the Schulz PDF also predicts all the qualitative features of the structure factor of the packings that we study; (ii) as the packings become more polydisperse, their behavior resembles increasingly that of an ideal system-"ideal gas"-with little or no correlations; and (iii) the mean survival time and mean relaxation time of a diffusing species in the packings increase with increasing degrees of polydispersivity.