Random Sequential Adsorption Of K-mers Research Articles

Random sequential adsorption of k-mers on the fully-connected lattice: probability distributions of the covering time and extreme value statistics

We study the random sequential adsorption of k-mers on the fully-connected lattice with N = kn sites. The probability distribution Tn(s,t) of the time t needed to cover the lattice with s k-mers is obtained using a generating function approach. In the low coverage scaling limit where with the random variable t − s follows a Poisson distribution with mean ky2/2. In the intermediate coverage scaling limit, when both s and n − s are , the mean value and the variance of the covering time are growing as n and the fluctuations are Gaussian. When full coverage is approached the scaling functions diverge, which is the signal of a new scaling behaviour. Indeed, when , the mean value of the covering time grows as nk and the variance as n2k, thus t is strongly fluctuating and no longer self-averaging. In this scaling regime the fluctuations are governed, for each value of k, by a different extreme value distribution, indexed by u. Explicit results are obtained for monomers (generalized Gumbel distribution) and dimers.

Random sequential adsorption of polyatomic species on fractal substrates

Random sequential adsorption of k-mers of different sizes and shapes deposited on two types of fractal surfaces (deterministic and statistical) is studied. These kinds of substrates present intrinsic heterogeneities. As a consequence, the average coordination number depends on the topology that characterizes the adsorbent. For discrete models, at the late stage the surface coverage evolves according to θ(t)=θ(j)-Aexp[-t/σ], where θ(j) is the jamming coverage while A and σ are fitting parameters. A detailed analysis of how these main quantities [θ(j), σ] depend on the relationship between the geometry of the adsorbate and the adsorbent is presented. The results obtained suggest that the symmetry of the substrate may exert a decisive influence on the adsorption kinetics of polyatomic species.

Random sequential adsorption of polyatomic species with the presence of impurities

Random sequential adsorption of k-mers (particles occupying k adsorption sites on the substrate) of different sizes and shapes deposited on square lattices is studied. Heterogeneous surfaces caused by impurities previously and randomly deposited are considered. Thus, an adsorption site occupied by an impurity is considered as forbidden for the deposition of adsorbent. As a consequence, the average coordination number for each available element depends on the concentration of impurities. For discrete models, at the late stage the surface coverage evolves according to θ(t)=θ(∞)−Aexp[−tσ], where θ(∞) is the jamming coverage while A and σ are fitting parameters. The dependence of the terminal relaxation time σ (which determines how fast the lattice is filled up to the jamming coverage) on the parameters of the problem is established.

Random sequential adsorption of polyatomic species

Random sequential adsorption of k-mers (particles occupying k adsorption sites on the substrate) of different sizes and shapes deposited on two-dimensional regular lattices is studied. For discrete models at the late stage the surface coverage evolves according to , where θ(∞) is the jamming coverage while A and σ are fitting parameters. In the present paper, the dependence of the terminal relaxation time σ (which determine how fast the lattice is filled up to the jamming coverage) on the parameters of the problem is established through a theoretical approach. In addition, a strategy for determining σ by means of a computational algorithm is presented.

Monte Carlo simulation of the percolation process caused by the random sequential adsorption of k-mers on heterogeneous triangular lattices

Abstract Mixed site-bond percolation is studied for a random sequential adsorption process of k-mers on heterogeneous lattices with variable connectivity by means of Monte Carlo simulation. The percolation phase diagrams are built to render evidence about complex structures. Critical exponents are also calculated to show that the universality class corresponding to ordinary percolation in two dimensions is preserved.

Random sequential adsorption of k-mers on a square lattice: The large k regime.

The random sequential adsorption of k-mers on a two-dimensional lattice is studied in the regime of large k, up to infinity where the coverage has a finite limit. A simple and accurate representation of the coverage as a function of the time is given for any value of k. Its parametrization is a consequence, through the master equations, of the particular behavior that we find for the deposited clusters in Monte Carlo simulations of the process. The parameters are fixed by matching a seventh-order time series expansion. \textcopyright{} 1996 The American Physical Society.

Pair correlation function in random sequential adsorption processes

An analytical expression of the pair distribution function is derived for the car-parking problem and for the random sequential adsorption of K-mers onto a one-dimensional lattice. Both on a lattice and in the continuum limit, super-exponential decay of the distribution function is observed. A comparison of the spatial correlations with those at equilibrium demonstrates the influence of the irreversibility of the RSA process.

On irreversible deposition on disordered substrates

For original paper see Milosevic et.al., ibid., vol.26, p.1061 (1993) The kinetics of random sequential adsorption of k-mers on a one-dimensional lattice, occupied initially by point impurities with a random distribution, is solved exactly. The solution of the process on a continuum substrate is also derived from the discrete case.