Packing of nonoverlapping cubic particles: Computational algorithms and microstructural characteristics

Packing of cubic particles arises in a variety of problems, ranging from biological materials to colloids and the fabrication of new types of porous materials with controlled morphology. The properties of such packings may also be relevant to problems involving suspensions of cubic zeolites, precipitation of salt crystals during ${\mathrm{CO}}_2$ sequestration in rock, and intrusion of fresh water in aquifers by saline water. Not much is known, however, about the structure and statistical descriptors of such packings. We present a detailed simulation and microstructural characterization of packings of nonoverlapping monodisperse cubic particles, following up on our preliminary results [H. Malmir et al., Sci. Rep. 6, 35024 (2016)]. A modification of the random sequential addition (RSA) algorithm has been developed to generate such packings, and a variety of microstructural descriptors, including the radial distribution function, the face-normal correlation function, two-point probability and cluster functions, the lineal-path function, the pore-size distribution function, and surface-surface and surface-void correlation functions, have been computed, along with the specific surface and mean chord length of the packings. The results indicate the existence of both spatial and orientational long-range order as the the packing density increases. The maximum packing fraction achievable with the RSA method is about 0.57, which represents the limit for a structure similar to liquid crystals.

Figure 1

(a) Salt suspension printed on a polyethylene terephthalate carrier. (b) Porous pattern formed by a cast vinyl film [43].

Figure 2

Packing of nonoverlapping equal-sized cubic particles generated by the ASC algorithm. The packing fraction is 0.97.

Figure 3

Packing of nonoverlapping equal-sized cubic particles with $N=2600$ and $d_0=0.05L$, where $N$ is the number of particles. The packing density is ${\varphi }_2=0.3$.

Figure 4

Dependence on the packing density ${\varphi }_2$ of the two-point probability function $S_2\left(r\right)$ for the solid phase. $r_{\mathrm{in}}$ is the radius of the cubes' insphere.

Figure 5

Dependence on the packing density ${\varphi }_2$ of the two-point cluster function $C_2\left(r\right)$. $r_{\mathrm{in}}$ is the radius of the cubes' insphere.

Figure 6

Dependence on the packing density ${\varphi }_2$ of the lineal-path function $L\left(z\right)$ for the pore phase of the packing. $r_{\mathrm{in}}$ is the radius of the cubes' insphere.

Figure 7

Dependence on the packing density ${\varphi }_2$ of the lineal-path function $L\left(z\right)$ for the solid phase of the packing. $r_{\mathrm{in}}$ is the radius of the cubes' insphere.

Figure 8

Dependence on the packing density ${\varphi }_2$ of the cumulative pore-size distribution function $F\left(\delta \right)$. $r_{\mathrm{in}}$ is the radius of the cubes' insphere.

Figure 9

Dependence on the packing density ${\varphi }_2$ of the scaled two-body contribution to the surface-surface correlation function $F_{\text{ss}}\left(r\right)$. $r_{\mathrm{in}}$ is the radius of the cubes' insphere.

Figure 10

Dependence on the packing density ${\varphi }_2$ of the scaled two-body contribution to the surface-void correlation function $F_{\text{sv}}\left(r\right)$. $r_{\mathrm{in}}$ is the radius of the cubes' insphere.