Random sequential adsorption on euclidean, fractal and random lattices

Abstract

Irreversible adsorption of objects of diferent 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 Sierpin- ski carpets having dimension d between 1 and 2, and on Erdos-Renyi random graphs. The number of sites is M = Ld for Euclidean and fractal lattices, where L is a characteristic length of the sys- tem. In the case of random graphs it does not exist such characteristic length, and the substrate can be characterized by a xed set of M vertices (sites) and an average connectivity (or degree) g. The paper concentrates on measuring (1) the probability WL(M)( ) that a lattice composed of Ld(M) elements reaches a coverage , and (2) the exponent 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 WL(M)( ) behave asymptotically as M1=2. In the case of Euclidean and fractal lattices, where L and d can be de ned, the asymptotic behavior can be written as M1=2 = Ld=2 = L1= j , and j = 2=d.