PHILOSOPHICAL MAGAZINE B, 2002, VOL. 82, NO. 4, 375±381 Slow dynamics of k-mers on a square lattice C. Fuscoy }, P. Galloy , A. P etri ‡k and M. Roverey y Dipartimento di Fisica, UniversitaÁ di Roma Tre, and Istituto Nazionale per la Fisica della Materia, UnitaÁ di Ricerca Roma Tre, Via della Vasca Navale 84, I-00146 Roma, Italy z Consiglio Nazionale delle Ricerche, Istituto di Acustica `O.M. Corbino’, Area della Ricerca di Roma Tor Vergata, Via del Fosso del Cavaliere 100, 00133 Roma, and Dipartimento di Fisica and Istituto Nazionale per la Fisica della Materia, UniversitaÁ `La Sapienza’, Piazzale Aldo Moro 2, 00189 Roma, Italy Abstract We have performed extensive simulations of random sequential adsorption and diŒusion of k-mers up to k ˆ 5 on a square lattice with particular attention to the case k ˆ 2. We observe that, for k ˆ 2; 3, complete coverage of the lattice is never reached, because of the existence of frozen con®gurations 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 ®eld and non-analytic, with t 1=2 as the leading term. Morover diŒerent values of the diŒusion probability and deposition rate lead to diŒerent ®nal values of the coverage. We also give a brief account of the vacancy population dynamics. } 1. Introduction The random sequential adsorption (RSA) process has been known for a long time and is employed to model a wide range of irreversible phenomena in physics, chemistry and biology (for an extensive review see Evans (1993)). It consists of the deposition of hard particles on a substrate until the jamming situation is reached, that is no more locations for further deposition are available. The temporal evolu- tion of the coverage …t† and its jamming value  J depend on the nature of the substrate, on the particle shape and on the dimensionality of the system. Several cases have been investigated mostly through numerical means, since exact analytical solutions are available only in a few cases. In many experimental situations the process of adsorption is not completely irreversible, because particles can also diŒuse on the substrate. This has led to con- sideration of the mechanism of diŒusional relaxation (DR) besides particle deposi- tion in the above models, and to a study of its eŒects on …t† and …1† (Privman 2000). Most of the available results are related to the random sequential adsorption with diŒusion (RSAD) of particles on a one-dimensional lattice; for the case of dimers it was shown by numerical simulations (Privman and Nielaba 1992, de Oliveira and Petri 1998) and analytical results (Grynberg and Stinchcombe 1995) Philosophica l Magazine B ISSN 1364±2812 print/ISSN 1463±6417 online # 2002 Taylor & Francis Ltd http://www.tandf.co.uk/journals DOI: 10.1080 /1364281011008493 9 } Present address: Department of Theoretical Physics, University of Nijmegen, Toernooiveld 1, 6525 ED Nijmegen, The Netherlands. k Author for correspondence. Email: alberto@idac.rm.cnr.it