Random sequential adsorption of lattice animals on a three-dimensional cubic lattice

The properties of the random sequential adsorption of objects of various shapes on simple three-dimensional (3D) cubic lattice are studied numerically by means of Monte Carlo simulations. Depositing objects are "lattice animals," made of a certain number of nearest-neighbor sites on a lattice. The aim of this work is to investigate the impact of the geometrical properties of the shapes on the jamming density theta(J) and on the temporal evolution of the coverage fraction theta(t). We analyzed all lattice animals of size n = 1, 2, 3, 4, and 5. A significant number of objects of size n >= 6 were also used to confirm our findings. Approach of the coverage theta(t) to the jamming limit theta(J) is found to be exponential, theta(J) - theta(t) similar to exp(-t/sigma), for all lattice animals. It was shown that the relaxation time sigma increases with the number of different orientations m that lattice animals can take when placed on a cubic lattice. Orientations of the lattice animal deposited in two randomly chosen places on the lattice are different if one of them cannot be translated into the other. Our simulations performed for large collections of 3D objects confirmed that sigma congruent to m is an element of {1, 3, 4, 6, 8, 12, 24}. The presented results suggest that there is no correlation between the number of possible orientations m of the object and the corresponding values of the jamming density theta(J). It was found that for sufficiently large objects, changing of the shape has considerably more influence on the jamming density than increasing of the object size.