Particle morphology effects in random sequential adsorption

Random sequential adsorption with correlated defects : A series expansion approach

The random sequential adsorption (RSA) problem holds crucial theoretical and practical significance, serving as a pivotal framework for understanding and optimizing particle packing in various scientific and technological applications. Here the problem of the one-dimensional RSA of k-mers onto a substrate with correlated defects controlled by uniform and power-law distributions is theoretically investigated: the coverage fraction is obtained as a function of the density of defects and several scaling laws are examined. The results are compared with extensive Monte Carlo simulations and more traditional methods based on master equations. Emphasis is given in elucidating the scaling behavior of the fluctuations of the coverage fraction. The phenomenon of universality breaking and the issues of conventional Gaussian fluctuations and the Lévy type fluctuations from a simple perspective, relying on the central limit theorem, are also addressed.

Random sequential adsorption of self-avoiding chains on two-dimensional lattices

Random sequential adsorption of extended objects deposited on two-dimensional regular lattices is studied. The depositing objects are chains formed by occupying adsorption sites on the substrate through a self-avoiding walk of k lattice steps; these objects are also called "tortuous k-mers." We study how the jamming coverage, θ_{j,k}, depends on k for lattices with different connectivity (honeycomb, square, and triangular). The dependence can be fitted by the function θ_{j,k}=θ_{j,k→∞}+B/k+C/k^{2}, where B and C are found to be shared parameters by the three lattices and θ_{j,k→∞} (>0) is the jamming coverage for infinitely long k-mers for each of them. The jamming coverage is found to have a growing behavior with the connectivity of the lattice. In addition, θ_{j,k} is found to be higher for tortuous k-mers than for the previously reported for linear k-mers in each lattice. The results were obtained by means of numerical simulation through an efficient algorithm whose characteristics are discussed in detail. The computational method introduced here also allows us to investigate the full-time kinetics of the surface coverage θ_{k}(t) [θ_{j,k}≡θ_{k}(t→∞)]. Along this line, different time regimes are identified and characterized.

Jamming and percolation of linear k-mers on honeycomb lattices

Numerical simulations and finite-size scaling analysis have been performed to study the jamming and percolation behavior of elongated objects deposited on two-dimensional honeycomb lattices. The depositing particle is modeled as a linear array of length k (so-called k-mer), maximizing the distance between first and last monomers in the chain. The separation between k-mer units is equal to the lattice constant. Hence, k sites are occupied by a k-mer when adsorbed onto the surface. The adsorption process starts with an initial configuration, where all lattice sites are empty. Then, the sites are occupied following a random sequential adsorption mechanism. The process finishes when the jamming state is reached and no more objects can be deposited due to the absence of empty site clusters of appropriate size and shape. Jamming coverage θ_{j,k} and percolation threshold θ_{c,k} were determined for a wide range of values of k (2≤k≤128). The obtained results shows that (i) θ_{j,k} is a decreasing function with increasing k, being θ_{j,k→∞}=0.6007(6) the limit value for infinitely long k-mers; and (ii) θ_{c,k} has a strong dependence on k. It decreases in the range 2≤k<48, goes through a minimum around k=48, and increases smoothly from k=48 up to the largest studied value of k=128. Finally, the precise determination of the critical exponents ν, β, and γ indicates that the model belongs to the same universality class as 2D standard percolation regardless of the value of k considered.

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 θ_{J} and on the temporal evolution of the coverage fraction θ(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 θ(t) to the jamming limit θ_{J} is found to be exponential, θ_{J}-θ(t)∼exp(-t/σ), for all lattice animals. It was shown that the relaxation time σ 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 σ≅m∈{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 θ_{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.

Random sequential adsorption on Euclidean, fractal, and random lattices

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 algorithm. Objects are adsorbed on one-, two-, and three-dimensional Euclidean lattices, on Sierpinski carpets having dimension d between 1 and 2, and on Erdős-Rényi 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, such a characteristic length does not exist, and the substrate can be characterized by a fixed set of M vertices (sites) and an average connectivity (or degree) g. This paper concentrates on measuring (i) the probability W_{L(M)}(θ) that a lattice composed of L^{d}(M) elements reaches a coverage θ and (ii) the exponent ν_{j} characterizing the so-called jamming transition. The results obtained for Euclidean, fractal, and random lattices indicate that the quantities derived from the jamming probability W_{L(M)}(θ), such as (dW_{L}/dθ)_{max} and the inverse of the standard deviation Δ_{L}, 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}}, with ν_{j}=2/d.