Jamming and percolation of square objects of size k × k (k 2-mers) isotropically deposited on simple cubic lattices have been studied by numerical simulations complemented with finite-size scaling theory. The k 2-mers were irreversibly deposited into the lattice. Jamming coverage θ j,k was determined for a wide range of k (2 ≤ k ≤ 200). θ j,k exhibits a decreasing behavior with increasing k, being θ j,k→∞ = 0.4285(6) the limit value for large k 2-mer sizes. On the other hand, the obtained results shows that percolation threshold, θ c,k , has a strong dependence on k. It is a decreasing function in the range 2 ≤ k ≤ 18 with a minimum around k = 18 and, for k ≥ 18, it increases smoothly towards a saturation value. Finally, a complete analysis of critical exponents and universality has been done, showing that the percolation phase transition involved in the system has the same universality class as the 3D random percolation, regardless of the size k considered.

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Irreversible multilayer adsorption of semirigid k-mers on one-dimensional lattices of size L is studied by numerical simulations complemented by exhaustive enumeration of configurations for small lattices. The deposition process is modeled by using a random sequential adsorption algorithm, generalized to the case of multilayer adsorption. The paper concentrates on measuring the jamming coverage for different values of k-mer size and number of layers n. The bilayer problem (n 2) is exhaustively analyzed, and the resulting tendencies are validated by the exact enumeration techniques. Then, the study is extended to an increasing number of layers, which is one of the noteworthy parts of this work. The obtained results allow the following: (i) to characterize the structure of the adsorbed phase for the multilayer problem. As n increases, the (1 + 1)-dimensional adsorbed phase tends to be a "partial wall" consisting of "towers" (or columns) of width k, separated by valleys of empty sites. The length of these valleys diminishes with increasing k; (ii) to establish that this is an in-registry adsorption process, where each incoming k-mer is likely to be adsorbed exactly onto an already adsorbed one. With respect to percolation, our calculations show that the percolation probability vanishes as L increases, being zero in the limit L → ∞. Finally, the value of the jamming critical exponent ν j is reported here for multilayer adsorption: ν j remains close to 2 regardless of the considered values of k and n. This finding is discussed in terms of the lattice dimensionality.

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