The properties of the random sequential adsorption of objects of various shapes on a two-dimensional triangular lattice are studied numerically by means of Monte Carlo simulations. The depositing objects are formed by self-avoiding lattice steps, whereby the size of the objects is gradually increased by wrapping the walks in several different ways. The aim of this work is to investigate the impact of the geometrical properties of the shapes on the jamming density θ_{J} and on the temporal evolution of the coverage fraction θ(t). Our results suggest that the order of symmetry axis of a shape exerts a decisive influence on adsorption kinetics near the jamming limit θ_{J}. The decay of probability for the insertion of a new particle onto a lattice is described in a broad range of the coverage θ by the product between the linear and the stretched exponential function for all examined objects. The corresponding fitting parameters are discussed within the context of the shape descriptors, such as rotational symmetry and the shape factor (parameter of nonsphericity) of the objects. Predictions following from our calculations suggest that the proposed fitting function for the insertion probability is consistent with the exponential approach of the coverage fraction θ(t) to the jamming limit θ_{J}.

In the preceding paper, Budinski-Petković et al (2016 J. Stat. Mech. 053101) studied jamming and percolation aspects of random sequential adsorption of extended shapes onto a triangular lattice initially covered with point-like impurities at various concentrations. Here we extend this analysis to needle-like impurities of various lengths. For a wide range of impurity concentrations p, percolation threshold θ * p is determined for k-mers, angled objects and triangles of two dierent sizes. For suciently large impurities, percolation threshold θ * p of all examined objects increases with concentration p, and this increase is more prominent for impurities of a larger length. We determine the critical concentrations of defects p * c above which it is not possible to achieve percolation for a given object, for impurities of various lengths. It is found that the critical concentration p * c of finite-size impurities decreases with the length of impurities. In the case of deposition of larger objects an exception occurs for point-like impurities when critical concentration p * c of monomers is lower than p * c for the dimer impurities. At relatively low concentrations p, the presence of small impurities (but not point-like) stimulates the percolation for larger depositing objects.

Percolation properties of two-component mixtures are studied by Monte Carlo simulations. Objects are deposited onto a substrate according to the random sequential adsorption model. Various shapes making the mixtures are made by self-avoiding walks on a triangular lattice. Percolation threshold θ p for mixtures of objects covering the same number of sites is always lower than θ p for the more compact object, and it can be even lower than θ p for both components. Mixtures of percolating and non-percolating objects almost always percolate, but the percolation threshold is higher than θ p for the percolating component. Adding a shape of high connectivity to a system of compact nonpercolating objects, makes the deposit percolate. Lowest percolation thresholds are obtained for mixtures with elongated angled objects. Dependence of θ p on the object length exhibits a minimum, so it could be estimated that the angled objects of length 6 10 give the largest contribution to the percolation.

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The percolation properties in anisotropic irreversible deposition of extended objects are studied by Monte Carlo simulations on a triangular lattice. Depositing objects of various shapes and sizes are made by directed self-avoiding walks on the lattice. Anisotropy is introduced by imposing unequal probabilities for placing the objects along different directions of the lattice. The degree of the anisotropy is characterized by the order parameter p  determining the probability for deposition in the chosen (horizontal) direction. For each of the other two directions adsorption occurs with probability . It is found that the percolation threshold increases with the degree of anisotropy, having the maximum values for fully oriented objects. Percolation properties of the elongated shapes, such as k-mers, are more affected by the presence of anisotropy than the compact ones. Percolation in anisotropic deposition was also studied for a lattice with point-like defects. For elongated shapes a slight decrease of the percolation threshold with the impurity concentration d can be observed. However, for these shapes, significantly increases with the degree of anisotropy. In the case when depositing objects are triangles, results are qualitatively different. The percolation threshold decreases with d, but is not affected by the presence of anisotropy.