Random sequential adsorption with two components: asymptotic analysis and finite size effects

Abstract

Abstract. We consider the model of random sequential adsorption (RSA) in which two lengths of rod-like polymer compete for binding on a long straight rigid onedimensional substrate. We take all lengths to be discrete, assume that binding is irreversible, and short or long polymers are chosen at random with some probability. We consider both the cases where the polymers have similar lengths and when the lengths are vastly different. We use a combination of numerical simulations, computation and asymptotic analysis to study the adsorption process, specifically, analysing how competition between the two polymer lengths affects the final coverage, and how the coverage depends on the relative sizes of the two species and their relative binding rates. We find that the final coverage is always higher than in the one-species RSA, and that the highest coverage is achieved when the rate of binding of the longer polymer is higher. We find that for many binding rates and relative lengths of binding species, the coverage due to the shorter species decreases with increasing substrate length, although there is a small region of parameter space in which all coverages increase with substrate length.

Effects of competition between random sequential nucleation of point-sized seeds and island growth by adsorption of finite-sized grains

“…Denoting the units or dimensions of a term by [·], and considering the terms in Eq. (6), we note that [x] = 1/[t], which is consistent with the term e xt in (28 , which is consistent with the prefactor on the right-hand side of Eq. (30).…”

“…We have solved this model analytically determining an ansatz for the gap size distribution function (14) and hence an expression for the jamming coverage θ(m). Remarkably, an explicit asymptotic approximation (28), for the gap size distribution in the early timescale can be found using Laplace transforms. This shows how the delta function initial conditions (17) evolve to the intermediate dynamics and motivate the form of the ansatz (14) which explains the behaviour of the system in the approach to jamming.…”

“…Later, the deposition of competitive binary mixture of finite sized particles was been considered [25,26]. The RSA of mixture of particles of different uniform sizes has been studied [27,28]. The RSA model in presence of precursor-layer diffusion and desorption has also been studied where accelerated RSA and growth-and-coalescence has been considered as a special case [29,30].…”

Competitive random sequential adsorption of binary mixtures of disks and discorectangles

“…The different variant of RSA model with deposition of binary mixtures or particles with size distributions were also analyzed [17][18][19][20][21][22]. For multicomponent mixtures the competitive and multistep RSA models were investigated.…”