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 ${\left|x\right|}^{2p}+{\left|y\right|}^{2p}+{\left|z\right|}^{2p}\le R^{2p}$, with $p\in (0,\infty )$ being the deformation parameter. $0<p<0.5$ represents a family of hexapodlike (concave octahedral-like) particles, $0.5\le p<1$ and $p>1$ represent, respectively, families of convex octahedral-like and cubelike particles, with $p=1,0.5$, and $\infty$ 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 ${\varphi }_{\infty }\left(p\right)$ and $\nu \left(p\right)$, the exponent that characterizes the kinetics of adsorption at long times $t$, ${\varphi }_{\infty }\left(p\right)-\varphi (p,t)\sim t^{-\nu \left(p\right)}$. Precise estimates of ${\varphi }_{\infty }\left(p\right)$ and $\nu \left(p\right)$ are obtained and shown to be in agreement with the existing analytical and numerical results for certain types of superballs.

Figure 1

Packings of (a) concave superballs with $p=1/4$, (b) octahedral particles with $p=1/2$, and (c) cubelike particles with $p=5/4$. The packings are subject to periodic boundary conditions.

Figure 2

Maximum RSA packing fractions versus the deformation parameter $p$. For $p\ge 5$, the shape of particles approaches that of cubes with their maximum RSA packing fraction being $\sim 0.333$.

Figure 3

The kinetics of the RSA for various deformation parameters $p$. The asymptotic behavior of $log\left[\varphi \right(p,2t)-\varphi (p,t\left)\right]$ that exhibits the same scaling as $log[{\varphi }_{\infty }\left(p\right)-\varphi (p,t)]$ when plotted against $log\left(t\right)$ [Eq. (2)]. Purple, green, and orange indicate, respectively, cubes, spheres, and octahedra, while red represents hexapodlike particles with $p=1/4$.

Figure 4

The pair-correlation function $g_2\left(r\right)$ for the RSA packing of superballs at ${\varphi }_{\infty }$. Purple, green, and orange show, respectively, cubelike particles ($p=2$), spheres ($p=1$), and octahedra ($p=1/2$), while red represents the results for hexapodlike particles ($p=1/4$). The peak of $g_2\left(r\right)$ moves from left to right as the deformation parameter $p$ increases. For spherical particles, ${lim}_{r\to D^{+}}{g}_2\left(r\right)\sim -ln(r/D-1)$.