Analytical and numerical study of particles with binary adsorption

Random sequential adsorption on mobile patches

An extension of the random sequential adsorption 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 can adsorb. We performed Monte Carlo simulations to study the adsorption kinetics and jammed-state morphology on a one-dimensional lattice. We show that, while the time-dependence of the coverage depends on F and D, the jammed-state coverage depends solely on the ratio F/D. This result is grasped by a simple mean-field calculation. We also report two different regimes for the functional dependence of the jammed-state coverage on the size of the particles, for low and high density of patches.

Random sequential adsorption of polydisperse mixtures on lattices

Random sequential adsorption of linear and square particles with excluded volume interaction is studied numerically on planar lattices considering Gaussian distributions of lateral sizes of the incident particles, with several values of the average μ and of the width-to-average ratio w. When the coverage θ is plotted as function of the logarithm of time t, the maximum slope is attained at a time t_{M} of the same order of the time τ of incidence of one monolayer, which is related to the molecular flux and/or sticking coefficients. For various μ and w, we obtain 1.5τ<t_{M}<5τ for linear particles and 0.3τ<t_{M}<τ for square particles. At t_{M}, the coverages with linear and square particles are near 0.3 and 0.2, respectively. Extrapolations show that coverages may vary with μ up to 20% and 2% for linear and square particles, respectively, for μ≥64, fixed time, and constant w. All θ vs logt plots have approximately the same shape, but other quantities measured at times of order t_{M} help to distinguish narrow and broad incident distributions. The adsorbed particle-size distributions are close to the incident ones up to long times for small w, but appreciably change in time for larger w, acquiring a monotonically decreasing shape for w=1/2 at times of order 100τ. At t_{M}, incident and adsorbed distributions are approximately the same for w≤1/8 and show significant differences for w≥1/2; this result may be used as a consistency test in applications of the model. The pair correlation function g(r,t) for w≤1/8 has a well defined oscillatory structure at 10t_{M}, with a minimum at r≈μ and maximum at r≈1.5μ, but this structure is not observed for w≥1/4.