Random sequential adsorption: Series and virial expansions

Abstract

We introduce an operator formalism for random sequential adsorption on lattices and in continuous space. This provides a convenient framework for deriving series expansions for the deposition rate dθ/dt in powers of t. Several specific examples—the square lattice with nearest-neighbor exclusion, and with exclusion extended to next-nearest neighbors, and disks and oriented squares on the plane—are considered in detail. Precise estimates for θ(t) and the jamming coverage are obtained via Padé approximant analysis. These are found to be in excellent agreement with simulation results. A diagrammatic expansion for dθ/dt is derived, and its relation to the equilibrium Mayer series is elucidated.