Statistical characterization of microstructure of packings of polydisperse hard cubes

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.

Quantifying accuracy of stochastic methods of reconstructing complex materials by deep learning

Time and cost are two main hurdles to acquiring a large number of digital image I of the microstructure of materials. Thus, use of stochastic methods for producing plausible realizations of materials' morphology based on one or very few images has become an increasingly common practice in their modeling. The accuracy of the realizations is often evaluated using two-point microstructural descriptors or physics-based modeling of certain phenomena in the materials, such as transport processes or fluid flow. In many cases, however, two-point correlation functions do not provide accurate evaluation of the realizations, as they are usually unable to distinguish between high- and low-quality reconstructed models. Calculating flow and transport properties of the realization is an accurate way of checking the quality of the realizations, but it is computationally expensive. In this paper a method based on machine learning is proposed for evaluating stochastic approaches for reconstruction of materials, which is applicable to any of such methods. The method reduces the dimensionality of the realizations using an unsupervised deep-learning algorithm by compressing images and realizations of materials. Two criteria for evaluating the accuracy of a reconstruction algorithm are then introduced. One, referred to as the internal uncertainty space, is based on the recognition that for a reconstruction method to be effective, the differences between the realizations that it produces must be reasonably wide, so that they faithfully represent all the possible spatial variations in the materials' microstructure. The second criterion recognizes that the realizations must be close to the original I and, thus, it quantifies the similarity based on an external uncertainty space. Finally, the ratio of two uncertainty indices associated with the two criteria is considered as the final score of the accuracy of a stochastic algorithm, which provides a quantitative basis for comparing various realizations and the approaches that produce them. The proposed method is tested with images of three types of heterogeneous materials in order to evaluate four stochastic reconstruction algorithms.

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-based tortuosity and thermal conductivity of soft superball systems: shape dependence from octahedra via spheres to cubes

Understanding the effect of particle shape on the percolation threshold, tortuosity and thermal conductivity of soft (geometrical overlapping) particle systems is very crucial for the design and optimization of such materials, including colloids, polymers, and porous and fracture media. In this work, we first combine the excluded-volume theory with the Monte Carlo simulations to determine the percolation threshold for a family of soft superballs, the shape of which interpolates between octahedra and cubes via spheres. Then, we propose two continuum percolation-based models to respectively obtain the tortuosity and effective thermal conductivity of soft superball systems considering their percolation behavior, where monodisperse overlapping superballs are uniformly distributed in a homogeneous solid matrix. Specifically, both models cover the whole feasible range of superball volume fractions, including near the percolation threshold. Comparison with extensive experimental, numerical and theoretical results confirms that the present models are capable of precisely predicting the percolation threshold, tortuosity and thermal conductivity of such systems. Furthermore, we apply the proposed models to probe the influence of particle shape on these important parameters. Our results show that the decreasing percolation threshold and tortuosity as soft particles become more anisotropic is consistent with increasing conductivity. It suggests that the anisotropic-shaped inclusion phase is more conducting than the spherical inclusion phase. The present theoretical strategies and conclusions may provide sound guidance for the synthesis of colloidal and polymer superballs.

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.