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, 0(03)-0(t)-t-1'3, where 8 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-l", and the second by the t-1'3 law; the crossover occurs at a time that scales as E-"2 when e-+0, where E is a parameter of anisotropy. The influence of shape and elongation on the saturation coverage 0(03) is also discussed. Finally, for very elongated objects, we derive from scaling arguments that when the aspect ratio a of the objects becomes infinite, e(00) goes to zero according to a power law a-4 where p= l/(1+2fl). The fractal dimension of the system of adsorbed needles is also discussed.

Shapes for maximal coverage for two-dimensional random sequential adsorption

“…The lowest values are obtain for square dimer. In this last case the θ max is smaller than for rectangles (0.55) 16,18 as well as for disks (0.5470) 15 . In all cases it is smaller than value for ellipsoids or 16 .…”

“…Thus, for RSA of disks on two dimensional flat surface d = 2 but for anisotropic particles d = 3 as an orientation of a particle is an additional degree of freedom. It is worth noting, that even when particle anisotropy is very small, d = 3 describes the ultimate asymptotic behavior 16,22,29 .…”

“…Results obtained for anisotropic particles show that saturated random coverage fraction reaches its maximum for moderate anisotropy, i.e., when long-to-short particle axis ratio is approximately 1.5-2.0 16,19 . The highest saturated coverage fraction obtained was θ max = 0.583 ± 0.001, for both ellipsoids and spherocylinders 16,17 . Both of these are convex shapes.…”

Self-assembly of rodlike receptors from bulk solution

“…Again, attention should be called to the fact that there is some uncertainty about the value of J taken from Ref. 23. If we take M sat ͑meas͒ as corresponding to the definitive jamming limit, and assume that the rods are really lying with their long axes strictly parallel to the substratum, then J = M sat ͑meas͒ a ͑actual͒ / m = 0.56, a value that is far higher than the highest value found in Ref.…”

“…Approximate analytical expressions for the addition of elongated objects such as spherocylinders ͑cylinders with spherical ends͒ to a surface have been constructed, 23,24 and tested using numerical simulations, with fairly satisfactory results, but the model has apparently never been subjected to experimental test, despite its great practical value, since many nano-objects and micrometer-scale objects such as bacteria are highly elongated rather than spherical. Hence, a secondary purpose of the present work is to test the validity of this model.…”