We characterize the jammed state structure of the random sequential adsorption of segments of two different sizes on a line. To this end, we define the size ratio as a dimensionless quantity measuring the length of the large segments in terms of the smaller ones. We introduce a truncated exponential as an {\it ansatz} for the probability distribution function of the interparticle distance at the jammed state and use it to reckon the first four cumulants of the probability distribution function. The sole free parameter present in the various analytical expressions is tied to the mean interparticle distance from Monte Carlo simulations, while the remaining three cumulants are computed without any free parameter and compared to Monte Carlo results. We find that the proposed {\it ansatz} provides results in good qualitative agreement with Monte Carlo ones.
Random sequential adsorption (RSA) is a standard method of modeling adsorption of large molecules at the liquid-solid interface. Here we consider jammed states of the RSA process of nonoverlapping dimers (objects occupying two nearest-neighbor lattice sites) in a hypercubic lattice of arbitrary space dimension $D \ge 2$. We show that each dimer in such a state belongs to a percolating cluster.
Random sequential adsorption (RSA) is a standard method of modeling adsorption of large molecules at the liquid-solid interface. Several studies have recently conjectured that in the RSA of rectangular needles, or $k$-mers, on a square lattice the percolation is impossible if the needles are sufficiently long ($k$ of order of several thousand). We refute these claims and present a strict proof that in any jammed configuration of nonoverlapping, fixed-length, horizontal or vertical needles on a square lattice, all clusters are percolating clusters.
An extension of the Random Sequential Adsorption (RSA) model has been proposed recently, motivated by the coverage of oil droplets by DNA-functionalized colloidal particles. Particles arrive to a flat substrate with a uniform flux F but they can only adsorb on patches. Patches diffuse on the substrate with a diffusion coefficient D if they are free and they remain immobile when attached to an adsorbed particle. The adsorption is considered irreversible and particles cannot adsorb on top of each other. Thus, the system reaches a jammed state, consisting of a monolayer where no more particles ca…
In random sequential adsorption (RSA), objects are deposited randomly, irreversibly, and sequentially; attempts leading to an overlap with previously deposited objects are discarded. The process continues until the system reaches a jammed state when no further additions are possible. We analyze a class of lattice RSA models in which landing on an empty site in a segment is allowed when at least $b$ neighboring sites on the left and the right are unoccupied. For the minimal model ($b=1$), we compute the full counting statistics of the occupation number. We reduce the determination of the full c…
A Generalized Model for Disordered Random Sequential Adsorption with Charge-Dependent Deposition
Centro de Ciências Exatas e Sociais Aplicadas, Universidade Estadual da Paraíba（帕拉伊巴州立大学精确科学与应用科学学院）；Departamento de Física, Universidade Federal de Pernambuco（伯南布哥联邦大学物理系）
Computer simulation was used to study the random sequential adsorption of identical discorectangles onto a continuous plane . The problem was analyzed for a wide range of discorectangle aspect ratios ($\varepsilon \in [1;100]$). We studied anisotropic deposition, i.e., the orientations of the deposited particles were uniformly distributed within some interval such that the particles were preferentially aligned along a given direction. The kinetics of the changes in the packing density $φ$ found at different values of $S_0$ are discussed. Partial ordering of the discorectangles significantly af…
The behavior of a system of two-dimensional elongated particles (discorectangles) packed into a slit between two parallel walls was analyzed using a simulation approach. The packings were produced using the random sequential adsorption model with continuous positional and orientational degrees of freedom. The aspect ratio (length-to-width ratio, $\varepsilon=l/d$) of the particles was varied within the range $\varepsilon \in [1;32]$ while the distance between the walls was varied within the range $h/d\in [1;80]$. The properties of the deposits when in the jammed state (the coverage, the order …
We study approach to the large-time jammed state of the deposited particles in the model of random sequential adsorption. The convergence laws are usually derived from the argument of Pomeau which includes the assumption of the dominance, at large enough times, of small landing regions into each of which only a single particle can be deposited without overlapping earlier deposited particles and which, after a certain time are no longer created by depositions in larger gaps. The second assumption has been that the size distribution of gaps open for particle-center landing in this large-time sma…
We introduce the theater model, which is the simplest variant of directed random sequential adsorption in one dimension with point source and steric interactions. Particles enter sequentially an initially empty row of $L$ sites and adsorb irreversibly at randomly chosen places. If two particles occupy adjacent sites, they prevent further particles from passing them. A jammed configuration without available empty sites is eventually reached. More generally, we investigate the class of models parametrized by $b$, the number of consecutive particles needed to form a blockage. We show analytically…
