Morphology and Kinetics of Random Sequential Adsorption of Superballs: From Hexapods to Cubes

Abstract

Superballs represent a class of particles whose shapes are defined by ${|x|}^{2p}+{|y|}^{2p}+{|z|}^{2p}\le R^{2p}$, with $p\in (0,\infty )$ being the "deformation parameter". $0<p<0.5$ represents a family of hexapodlike (concave octahedrallike) particles, while for $0.5\le p<1$ and $p>1$ one has, respectively, families of convex octahedrallike 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 "low-entropy" algorithm, in contrast with the conventional algorithm that represents a "high-entropy" method. The two algorithms yield, respectively, precise estimates of the jamming fraction ${\varphi }_{\infty }(p)$ and $\nu (p)$, the exponent that characterizes the kinetics of adsorption at long times $t$, $\varphi (\infty )-\varphi (t)\sim t^{-\nu (p)}$. Precise estimates of ${\varphi }_{\infty }(p)$ and $\nu (p)$ are obtained and shown to be in agreement, in some special limits, with the existing analytical and numerical results.

13 pages, 4 figures, 1 table, Submitted to Physical Review Letters