Slow dynamics of k-mers on a square lattice

We have performed extensive simulations of random sequential adsorption and diffusion of k-mers up to k = 5 on a square lattice with particular attention to the case k = 2. We observe that. for k = 2, 3, complete coverage of the lattice is never reached. because of the existence of frozen configurations that prevent isolated vacancies in the lattice from joining and we argue that complete coverage is never attained for any value of k. In particular the long-time behaviour of the coverage is not mean field and non-analytic, with t(-1/2) as the leading term. Morover different values of the diffusion probability and deposition rate lead to different final values of the coverage. We also give a brief account of the vacancy population dynamics.