Irreversible Sequential Adsorption of Line Segments with Diffusional Relaxation on a One-Dimensional Lattice

Abstract

We consider a random sequential adsorption of line segments(k‐mer) with diffusional relaxation. The line segments of a lenght k depsosit with a probability p or diffuse up to a hopping length l(l ⩽ k) with a probability 1 − p on a one‐dimensional lattice. For the dimer, the empty area fraction decays according to 1 − θ(t) ∼ [(1 − p)pt]−1/2, regardless of the diffusion length and the adsorption probability. For k ⩾ 3, the empty area fraction decays according to the power law as 1 − θ(t) = A(k,l)[(1 − p)pt]−α(k,l). The decaying exponents depend on the length of the line segment and the depositing probability p. The kinetics of the empty area fraction of the dimers is equivalent to the diffusion‐limited reaction, A + A → 0, at the long time limits. However, for k ⩾ 3, the model with l > 1 stepping corresponds to reactions where the particles (gaps of size l) hop in a correlated way. We found that 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.