Irreversible deposition of extended objects with diffusional relaxation on discrete substrates

Abstract

Random sequential adsorption with diffusional relaxation of extended objects both on a one-dimensional and planar triangular lattice is studied numerically by means of Monte Carlo simulations. We focus our attention on the behavior of the coverage θ(t) as a function of time. Our results indicate that the lattice dimensionality plays an important role in the present model. For deposition of k-mers on 1D lattice with diffusional relaxation, we found that the growth of the coverage θ(t) above the jamming limit to the closest packing limit θ_CPL is described by the pattern θ_CPL-θ(t) ∝E_β[-(t/τ)^β], where E_β denotes the Mittag-Leffler function of order β∈(0,1). In the case of deposition of extended lattice shapes in 2D, we found that after the initial “jamming", a stretched exponential growth of the coverage θ(t) towards the closest packing limit θ_CPL occurs, i.e., θ_CPL - θ(t) ∝exp [-(t/τ)^β]. For both cases we observe that: (i) dependence of the relaxation time τ on the diffusion probability P_dif is consistent with a simple power-law, i.e., τ∝P_dif ^-δ; (ii) parameter β depends on the object size in 1D and on the particle shape in 2D.