Random and cooperative sequential adsorption

Abstract

Irreversible random sequential adsorption (RSA) on lattices, and continuum "car parking" analogues, have long received attention as models for reactions on polymer chains, chemisorption on single-crystal surfaces, adsorption in colloidal systems, and solid state transformations. Cooperative generalizations of these models (CSA) are sometimes more appropriate, and can exhibit richer kinetics and spatial structure, e.g., autocatalysis and clustering. The distribution of filled or transformed sites in RSA and CSA is not described by an equilibrium Gibbs measure. This is the case even for the saturation "jammed" state of models where the lattice or space cannot fill completely. However exact analysis is often possible in one dimension, and a variety of powerful analytic methods have been developed for higher dimensional models. Here we review the detailed understanding of asymptotic kinetics, spatial correlations, percolative structure, etc., which is emerging for these far-from-equilibrium processes.

Shapes for maximal coverage for two-dimensional random sequential adsorption

“…Rényi 2 introduced another famous one-dimensional RSA problem-the parking of cars along an unmarked curb. Feder 3 helped to make RSA a very popular tool for modeling monolayers obtained as a result of irreversible adsorption [4][5][6] . More recently, random packings generated by RSA have been of interest in a number of scientific fields, e.g., soft matter [7][8][9] , surface science 10 , mathematics 11 , telecommunication 12 and information theory 13 .…”

Aggregation of retail stores

“…Then, if it is profitable to do so, at low enough market coverages new sites can appear to cater to the unattended customers without interacting with the previous sites on the system. If these new sites appear randomly in the system, as long as their demand ranges still do not overlap, the problem can be mapped directly to a sequential adsorption problem with exclusion, for which a jamming transition occurs [10]. After this transition point, every new site will have a demand range that overlaps with the demand range of previous sites and interaction between different sites begins to play a rôle in the system.…”

Slow relaxation in granular compaction

“…We now propose a simple adsorption-desorption theory for granular compaction. The corresponding stochastic process was previously studied in the context of chemisorption [16][17][18] and protein binding [19]. The model is defined as follows: Identical spherical particles of unit diameter adsorb uniformly from the bulk to a substrate with rate k + and desorb with rate k − .…”