Random sequential adsorption on fractals

Abstract

Irreversible adsorption of spheres on flat collectors having dimension d < 2 is studied. Molecules are adsorbed on Sierpinski's triangle and carpet-like fractals (1 < d < 2), and on general Cantor set (d < 1). Adsorption process is modeled numerically using random sequential adsorption (RSA) algorithm. The paper concentrates on measurement of fundamental properties of coverages, i.e., maximal random coverage ratio and density autocorrelation function, as well as RSA kinetics. Obtained results allow to improve phenomenological relation between maximal random coverage ratio and collector dimension. Moreover, simulations show that, in general, most of known dimensional properties of adsorbed monolayers are valid for non-integer dimensions.

Continuum random sequential adsorption of polymer on a flat and homogeneous surface

“…Feder's law was confirmed for RSA of spheres in several collector dimensions [23], including nonintegral [24,27], as well as for elongated particles [6,25]. The analysis of exponent in (6) estimated using coverage ratio growth presented in Fig.3 reveals at least three things worth noticing.…”

Properties of random sequential adsorption of generalized dimers

“…The above relation, known as Feder's law, has been also proved numerically for one-to eightdimensional collectors [23] as well as for fractal collectors having 1 < d < 3 [24,25]. It is also valid for RSA of anisotropic particles on a flat collector [7,12,26,27], however, in this case, d = 3, which could be explained by additional degree of freedom of an adsorbate particle [6,[28][29][30].…”

Scaling Properties of the Number of Random Sequential Adsorption Iterations Needed to Generate Saturated Random Packing

“…Moreover, packing fraction decreases with the growth of packing dimension [14,17], which additionally spoils statistics in numerical simulations. Additionally, it is worth noting that Feder's law (1) seems to be valid also for fractional packing's dimensions [15,16]. As its derivation bases on the same assumption as made here, namely (2), presented results should be valid also for fractional d's.…”

“…The relation (1) was tested numerically to be valid for large enough, but finite packings [1,[14][15][16]. It is commonly used to estimate the number of particles at jamming, however it does not give any hints related to the number of RSA iterations needed to saturate a packing.…”