Random sequential adsorption of anisotropic particles. I. Jamming limit and asymptotic behavior

Abstract

We study the random sequential adsorption (RSA) of unoriented anisotropic objects onto a flat uniform surface, for various shapes (spherocylinders, ellipses, rectangles, and needles) and elongations. The asymptotic approach to the jamming limit is shown to follow the expected algebraic behavior, θ(∞)−θ(t)∼t−1/3, where θ is the surface coverage; this result is valid for all shapes and elongations, provided the objects have a nonzero proper area. In the limit of very small elongations, the long-time behavior consists of two successive critical regimes: The first is characterized by Feder’s law, t−1/2, and the second by the t−1/3 law; the crossover occurs at a time that scales as ε−1/2 when ε→0, where ε is a parameter of anisotropy. The influence of shape and elongation on the saturation coverage θ(∞) is also discussed. Finally, for very elongated objects, we derive from scaling arguments that when the aspect ratio α of the objects becomes infinite, θ(∞) goes to zero according to a power law α−p, where p=1/(1+2√2). The fractal dimension of the system of adsorbed needles is also discussed.