On the fluctuations of jamming coverage upon random sequential adsorption on homogeneous and heterogeneous media

TL;DR

This paper investigates how fluctuations in jamming coverage during random sequential adsorption decay with system size, revealing a power-law relationship influenced by substrate dimensionality and fractal properties, supported by analytical and numerical evidence.

Contribution

It provides a theoretical and numerical analysis of the decay of coverage fluctuations in RSA, introducing a formula linking the decay exponent to substrate dimensions and fractal characteristics.

Findings

Fluctuations decay as a power-law with system size.

The decay exponent depends on substrate dimension and fractal dimension.

Numerical simulations confirm the theoretical predictions.

Abstract

The fluctuations of the jamming coverage upon Random Sequential Adsorption (RSA) are studied using both analytical and numerical techniques. Our main result shows that these fluctuations (characterized by $\sigma_{\theta_J}$) decay with the lattice size according to the power-law $\sigma_{\theta_J} \propto L^{-1/ \nu}$. The exponent $\nu$ depends on the dimensionality $D$ of the substrate and the fractal dimension of the set where the RSA process actually takes place ($d_f$) according to $\nu = 2 / (2D - d_f)$.This theoretical result is confirmed by means of extensive numerical simulations applied to the RSA of dimers on homogeneous and stochastic fractal substrates. Furthermore, our predictions are in excellent agreement with different previous numerical results. It is also shown that, studying correlated stochastic processes, one can define various fluctuating quantities designed to capture either the underlying physics of individual processes or that of the whole system. So, subtle differences in the definitions may lead to dramatically different physical interpretations of the results. Here, this statement is demonstrated for the case of RSA of dimers on binary alloys.