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

## TL;DR

This paper introduces a universal simulation method for the random sequential adsorption of superballs, providing precise estimates of jamming fractions and adsorption kinetics, with implications for various scientific applications involving particle packing.

## Contribution

The paper presents a novel low-entropy algorithm for simulating superball adsorption, improving accuracy in estimating jamming fractions and kinetics compared to traditional methods.

## Key findings

- Accurate estimates of jamming fraction (p) for different superball shapes.
- Precise determination of the adsorption exponent ta(p) across shape parameters.
- Validation of the new algorithm against existing analytical and numerical results.

## 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 $0.5\leq p<1$ 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 $\phi_\infty(p)$ and $\nu(p)$, the exponent that characterizes the kinetics of adsorption at long times $t$, $\phi(\infty)-\phi(t)\sim t^{-\nu(p)}$. Precise estimates of $\phi_\infty(p)$ and $\nu(p)$ are obtained and shown to be in agreement, in some special limits, with the existing analytical and numerical results.