Scaling behavior of jamming fluctuations upon random sequential adsorption

Abstract

It is shown that the fluctuations of the jamming coverage upon Random Sequential Adsorption ($σ_{θ_J}$), decay with the lattice size according to the power-law $σ_{θ_J} \propto L^{-1 / ν_J}$, with $ν_{J} = 2 / (2D - d_f)$, where $D$ is the dimension of the substrate and $d_{\rm f}$ is the fractal dimension of the set of sites belonging to the substrate where the RSA process actually takes place. This result is in excellent agreement with the figure recently reported by Vandewalle {\it et al} ({\it Eur. Phys. J.} B. {\bf 14}, 407 (2000)), namely $ν_J = 1.0 (1)$ for the RSA of needles with $D = 2$ and $d_f = 2$, that gives $ν_J = 1$. Furthermore, our prediction is in excellent agreement with different previous numerical results. The derived relationships are also confirmed by means of extensive numerical simulations applied to the RSA of dimers on both stochastic and deterministic fractal substrates.