# Random sequential adsorption on Euclidean, fractal and random lattices

## TL;DR

This study investigates irreversible object adsorption on various Euclidean, fractal, and random lattices using RSA, revealing how jamming probabilities scale with system size and dimension, and deriving a universal exponent relation.

## Contribution

It introduces a comprehensive analysis of RSA on diverse lattice types, establishing scaling laws and the jamming transition exponent for Euclidean, fractal, and random structures.

## Key findings

- Jamming probability scales as M^{1/2} across lattice types.
- The jamming exponent _j relates to lattice dimension as _j=2/d.
- Universal scaling behavior observed in different lattice geometries.

## Abstract

Irreversible adsorption of objects of different shapes and sizes on Euclidean, fractal and random lattices is studied. The adsorption process is modeled by using random sequential adsorption (RSA) algorithm. Objects are adsorbed on one-, two-, and three-dimensional Euclidean lattices, on Sierpinski carpets having dimension $d$ between 1 and 2, and on Erdos-Renyi random graphs. The number of sites is $M=L^d$ for Euclidean and fractal lattices, where $L$ is a characteristic length of the system. In the case of random graphs it does not exist such characteristic length, and the substrate can be characterized by a fixed set of $M$ vertices (sites) and an average connectivity (or degree) $g$. The paper concentrates on measuring (1) the probability $W_{L(M)}(\theta)$ that a lattice composed of $L^d(M)$ elements reaches a coverage $\theta$, and (2) the exponent $\nu_j$ characterizing the so-called "jamming transition". The results obtained for Euclidean, fractal and random lattices indicate that the main quantities derived from the jamming probability $W_{L(M)}(\theta)$ behave asymptotically as $M^{1/2}$. In the case of Euclidean and fractal lattices, where $L$ and $d$ can be defined, the asymptotic behavior can be written as $M^{1/2} = L^{d/2}=L^{1/\nu_j}$, and $\nu_j=2/d$.