Random sequential adsorption and diffusion of dimers and k-mers on a square lattice (original) (raw)
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Slow dynamics of k -mers on a square lattice
Philosophical Magazine B, 2002
We have performed extensive simulations of random sequential adsorption and diOE usion of k-mers up to kˆ5 on a square lattice with particular attention to the case kˆ2. We observe that, for kˆ2; 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 diOE erent values of the diOE usion probability and deposition rate lead to diOE erent ®nal values of the coverage. We also give a brief account of the vacancy population dynamics.
The jamming and percolation for two generalized models of random sequential adsorption (RSA) of linear kkk-mers (particles occupying kkk adjacent sites) on a square lattice are studied by means of Monte Carlo simulation. The classical random sequential adsorption (RSA) model assumes the absence of overlapping of the new incoming particle with the previously deposited ones. The first model LK$_d$ is a generalized variant of the RSA model for both kkk-mers and a lattice with defects. Some of the occupying kkk adjacent sites are considered as insulating and some of the lattice sites are occupied by defects (impurities). For this model even a small concentration of defects can inhibit percolation for relatively long kkk-mers. The second model is the cooperative sequential adsorption (CSA) one, where, for each new kkk-mer, only a restricted number of lateral contacts zzz with previously deposited kkk-mers is allowed. Deposition occurs in the case when zleq(1−d)zmz\leq (1-d)z_mzleq(1−d)zm where zm=2(k+1)z_m=2(k+1)zm=2(k+1) ...
Impact of defects on percolation in random sequential adsorption of linear k-mers on square lattices
Physical review. E, Statistical, nonlinear, and soft matter physics, 2015
The effect of defects on the percolation of linear k-mers (particles occupying k adjacent sites) on a square lattice is studied by means of Monte Carlo simulation. The k-mers are deposited using a random sequential adsorption mechanism. Two models L(d) and K(d) are analyzed. In the L(d) model it is assumed that the initial square lattice is nonideal and some fraction of sites d is occupied by nonconducting point defects (impurities). In the K(d) model the initial square lattice is perfect. However, it is assumed that some fraction of the sites in the k-mers d consists of defects, i.e., is nonconducting. The length of the k-mers k varies from 2 to 256. Periodic boundary conditions are applied to the square lattice. The dependences of the percolation threshold concentration of the conducting sites p(c) vs the concentration of defects d are analyzed for different values of k. Above some critical concentration of defects d(m), percolation is blocked in both models, even at the jamming c...
Random sequential adsorption of partially oriented linear k-mers on a square lattice
Physical Review E, 2011
Jamming phenomena on a square lattice are investigated for two different models of anisotropic random sequential adsorption (RSA) of linear k-mers (particles occupying k adjacent adsorption sites along a line). The length of a k-mer varies from 2 to 128. Effect of k-mer alignment on the jamming threshold is examined. For completely ordered systems where all the k-mers are aligned along one direction (e.g., vertical), the obtained simulation data are very close to the known analytical results for 1d systems. In particular, the jamming threshold tends to the Rényi's Parking Constant for large k. In the other extreme case, when k-mers are fully disordered, our results correspond to the published results for short k-mers. It was observed that for partially oriented systems the jamming configurations consist of the blocks of vertically and horizontally oriented k-mers (v-and h-blocks, respectively) and large voids between them. The relative areas of different blocks and voids depend on the order parameter s, k-mer length and type of the model. For small k-mers (k 4), denser configurations are observed in disordered systems as compared to those of completely ordered systems. However, longer k-mers exhibit the opposite behavior.
Anisotropic random sequential adsorption of dimers on a square lattice
Physical Review A, 1992
The properties of the anisotropic random sequential adsorption of dimers on a square lattice are determined by Monte Carlo simulation and time-series expansion. The fractions of vertical and horizontal bonds occupied by dimers are calculated as a function of U, the probability of choosing vertical bonds to place dimers. In the limit v~0, the asymptotic fraction of vertical bonds occupied by dimers does not vanish but has the exact value e [1exp(-2e)]/2=0. 016046.. . .
Langmuir, 2000
The rigorous statistical thermodynamics of interacting linear adsorbates (k-mers) on a discrete onedimensional space is presented in the lattice gas approximation. The coverage and temperature dependence of the Helmholtz free energy, chemical potential, entropy, and specific heat are given. The chemical diffusion coefficient of the adlayer is calculated through collective relaxation of density fluctuations. Transport properties are discussed and related to features of the configurational entropy. The correspondence of the present model to adsorption in one-dimensional nanopores is addressed.
Random sequential adsorption on Euclidean, fractal, and random lattices
Physical Review E, 2019
Irreversible adsorption of objects of different shapes and sizes on Euclidean, fractal and random lattices is studied. The adsorption process is modeled by using random sequential adsorption (RSA) algorithm. Objects are adsorbed on one-, two-, and three-dimensional Euclidean lattices, on Sierpinski carpets having dimension d between 1 and 2, and on Erdos-Renyi random graphs. The number of sites is M = L d for Euclidean and fractal lattices, where L is a characteristic length of the system. In the case of random graphs it does not exist such characteristic length, and the substrate can be characterized by a fixed set of M vertices (sites) and an average connectivity (or degree) g. The paper concentrates on measuring (1) the probability W L(M) (θ) that a lattice composed of L d (M) elements reaches a coverage θ, and (2) the exponent νj characterizing the so-called "jamming transition". The results obtained for Euclidean, fractal and random lattices indicate that the main quantities derived from the jamming probability W L(M) (θ) behave asymptotically as M 1/2. In the case of Euclidean and fractal lattices, where L and d can be defined, the asymptotic behavior can be written as M 1/2 = L d/2 = L 1/ν j , and νj = 2/d.
Effects of impurities in random sequential adsorption on a one-dimensional substrate
Physical Review E, 1997
We have solved the kinetics of random sequential adsorption of linear k-mers on a one-dimensional disordered substrate for the random sequential adsorption initial condition and for the random initial condition. The jamming limits θ(∞, k ′ , k) at fixed length of linear k-mers have a minimum point at a particular density of the linear k ′-mers impurity for both cases. The coverage of the surface and the jamming limits are compared to the results for Monte Carlo simulation. The Monte Carlo results for the jamming limits are in good agreement with the analytical results. The continuum limits are derived from the analytical results on lattice substrates.