Irreversible deposition of extended objects with diffusional relaxation on discrete substrates

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 θCPL is described by the pattern θCPL - θ(t) ∝ Eβ[-(t/τ)β], where Eβ 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 θCPL occurs, i.e., θCPL - θ(t) ∝ exp[-(t/τ)β]. For both cases we observe that: (i) dependence of the relaxation time τ on the diffusion probability Pdif is consistent with a simple power-law, i.e., τ ∝ Pdif-δ; (ii) parameter β depends on the object size in 1D and on the particle shape in 2D