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 the domain ${|x|}^{2p}+{|y|}^{2p}+{|z|}^{2p}\ensuremath{\le}{R}^{2p}$, with $p\ensuremath{\in}(0,\ensuremath{\infty})$ being the deformation parameter. $0<p<0.5$ represents a family of hexapodlike (concave octahedral-like) particles, $0.5\ensuremath{\le}p<1$ and $p>1$ represent, respectively, families of convex octahedral-like and cubelike particles, with $p=1,\phantom{\rule{0.28em}{0ex}}0.5$, and $\ensuremath{\infty}$ 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 ${\ensuremath{\phi}}_{\ensuremath{\infty}}(p)$ and $\ensuremath{\nu}(p)$, the exponent that characterizes the kinetics of adsorption at long times $t$, ${\ensuremath{\phi}}_{\ensuremath{\infty}}(p)\ensuremath{-}\ensuremath{\phi}(p,t)\ensuremath{\sim}{t}^{\ensuremath{-}\ensuremath{\nu}(p)}$. Precise estimates of ${\ensuremath{\phi}}_{\ensuremath{\infty}}(p)$ and $\ensuremath{\nu}(p)$ are obtained and shown to be in agreement with the existing analytical and numerical results for certain types of superballs.