Random Sequential Adsorption on Imprecise Lattice

TL;DR

This paper demonstrates through simulations and analysis that even minimal imprecision in lattice site localization dramatically alters the convergence behavior to jamming in a one-dimensional RSA model, with implications for pattern-based deposition.

Contribution

It reveals that tiny imprecisions in lattice sites switch the convergence to jamming from exponential to power-law, a novel insight into RSA on imperfect substrates.

Findings

Imprecision causes a transition from exponential to power-law convergence.

Analytical and numerical methods confirm the impact of site imprecision.

Discontinuous jumps in jamming coverage occur at certain parameters.

Abstract

We report a surprising result, established by numerical simulations and analytical arguments for a one-dimensional lattice model of random sequential adsorption, that even an arbitrarily small imprecision in the lattice-site localization changes the convergence to jamming from fast, exponential, to slow, power-law, with, for some parameter values, a discontinuous jump in the jamming coverage value. This finding has implications for irreversible deposition on patterned substrates with pre-made landing sites for particle attachment. We also consider a general problem of the particle (depositing object) size not an exact multiple of the lattice spacing, and the lattice sites themselves imprecise, broadened into allowed-deposition intervals. Regions of exponential vs. power-law convergence to jamming are identified, and certain conclusions regarding the jamming coverage are argued for analytically and confirmed numerically.