Random Sequential Adsorption on Fractals

TL;DR

This study investigates the irreversible adsorption of spheres on fractal collectors with dimensions between 1 and 2, using numerical RSA simulations to analyze coverage properties and kinetics, revealing that known properties extend to non-integer dimensions.

Contribution

It provides new numerical insights into RSA on fractals, improving the understanding of coverage ratios and autocorrelation functions in non-integer dimensions.

Findings

Maximal coverage ratio relates to collector dimension.

RSA kinetics are consistent across fractal dimensions.

Known properties of monolayers extend to non-integer dimensions.

Abstract

Irreversible adsorption of spheres on flat collectors having dimension $d<2$ is studied. Molecules are adsorbed on Sierpinski's Triangle and Carpet like fractals ($1<d<2$), and on General Cantor Set ($d<1$). Adsorption process is modeled numerically using Random Sequential Adsorption (RSA) algorithm. The paper concentrates on measurement of fundamental properties of coverages, i.e. maximal random coverage ratio and density autocorrelation function, as well as RSA kinetics. Obtained results allow to improve phenomenological relation between maximal random coverage ratio and collector dimension. Moreover, simulations show that, in general, most of known dimensional properties of adsorbed monolayers are valid for non-integer dimensions.