Irreversible Adsorption of Colloidal Particles

Abstract

A (1+1)-dimensional adsorption model has been analyzed to investigate the influence of diffusion and sedimentation on the structure of monolayers of particles irreversibly adsorbed on a line (Faraudo & Bafaluy 1996). The relative influence of both effects is measured by the dimensionless particle radius defined as R* ≡ R((4πgΔρ)/(3k _B T))^1/4. For R* ≫ 1 the motion is deterministic, whereas if R* ≪ 1 brownian motion predominates. We focus our attention on the dependence of the radial distribution function g(r) and the saturation coverage θ _∞ on R*. First, we study the adsorption probability onto an available interval using approximate solutions of the transport equation and brownian dynamics simulations. In these simulations, the particle motion is discretized in time, and at every time step the particle performs sequentially the deterministic motion (sedimentation) and the random displacement (from a Gaussian distribution) corresponding to brownian motion. If a collision with an adsorbed particle occurs during the deterministic displacement, the incoming particle rolls over the pre-adsorbed one. The collision rule for the Brownian motion is a perfect reflection of the particle trajectory. The simulation results agree with our approximate solutions and with numerical solutions (Choi 1995) of the transport equation. The predicted scaling behavior for the probability of adsorption when R* ≫ 1 is shown to hold for R* larger than ~ 2.3. Combining our results with an approximate general formalism, we obtain θ _∞ and the gap density at the jamming limit. In this calculation we neglect the interaction with third neighbors, which plays a minor role, as shown by control simulations. The saturation coverage has also been obtained, as well as g(r), performing 10³ simulations for each R* with lines of length 200R with periodic boundary conditions. For R* ≤ 1, θ _∞(R*) and g(r) are close to the R* = 0 form (θ _∞ ≃ 0.751). For R* ≥ 1, θ _∞(R*) grows quickly with R*. The peaks in g(r) increase and are steeper when R* grows reflecting the tendency of large particles to pack closer than smaller ones due to the increasing effect of the rolling mechanism. For large gravity, θ _∞ approaches the ballistic limit (θ ^BD_∞ = 0.808...) following a power law, θ ^BD_∞ − θ _∞(R*) ∝ (R*)^−8/3, which is independent of the system dimension, as has been observed in simulations (Ezzeddine et al. 1995).