Irreversible sequential adsorption of k-mers with diffusional relaxation on a one-dimensional lattice

Abstract

We consider the random sequential adsorption (RSA) of line segments with diffusional relaxation on a one-dimensional lattice by using Monte Carlo method. The line segments with a length k deposit with a probability p or diffuse up to a diffusion length l(l⩽k) with a probability 1−p. We observe a power-law behavior of the coverage fraction θ(t). For the dimer k=2, the empty area fraction decays according to 1−θ(t)=A(l)p0.68(1−p)−0.40(pt)−0.5, regardless of the diffusion length and the adsorption probability. The dynamics of empty area fraction of the dimers is equivalent to the diffusion-limited reaction (DLR), A+A→0, at the long time limits. A single empty site at the RSA corresponds to the reactants A at the DLR. For k⩾4, the empty area fraction decays according to the power law as 1−θ(t)=A(k,l)[(1−p)pt]−α(k,l). For k⩾4, the dynamics of empty area fraction is not interpreted by the kinetics of the diffusion-limited reaction, kA→0. For k⩾3, the model with l>1 stepping corresponds to reactions where the particles (gaps of size l) hop in a correlated way. Thus, our model of l-group-diffusion-limited k-particle reactions is different from those of the ordinary reaction kA→0. We found new power law behavior for l-group-diffusion limited k-particle reactions and the exponents of the power law depend on the hopping length l. We observed a mixed dynamics of the gap creations, splitting, and annihilations for the model at the long time.