Random sequential adsorption of oriented rectangles with random aspect ratio

Abstract

We study saturated packings produced according to random sequential adsorption (RSA) protocol built of identical rectangles deposited on a flat, continuous plane. An aspect ratio of rectangles is defined as the length-to-width ratio, f = l/w. The rectangles have a fixed unit area (i.e., l × w = 1), and therefore, their shape is defined by the value of f (l = √ f and w = 1/ √ f ). The rectangles are allowed to align either vertically or horizontally with equal probability. The particles are deposited on a flat square substrate of side length L (measured in units of particle length, L ∈ [20, 1000]) and periodic boundary conditions are applied along both directions. The finite-size scaling effects are characterized by a scaled anisotropy defined as α = l/L = √ f /L. We showed that the properties of such packings strongly depend on the value of aspect ratio f and the most significant scaling effects are observed for relatively long rectangles when l ≥ L/2 (i.e. α ≥ 0.5). It is especially visible for the mean packing fraction as a function of the scaled anisotropy α. The kinetics of packing growth for low to moderate rectangle anisotropy is to be governed by ln t/t law, where t is proportional to the number of RSA iterations, which is the same as in the case of RSA of parallel squares. We also analyzed global orientational ordering in such packings and properties of domains consisting of a set of neighboring rectangles of the same orientation, and the probability that such domain forms a percolation.

Random sequential adsorption of aligned rectangles with two discrete orientations: finite-size scaling effects

“…For unoriented squares, the packing fraction equals 0.527 640 (18) [9,10], and for unoriented rectangles, it reaches the maximum at 0.549 632 (17) for a side length ratio of 1.492 (22) and then decreases monotonically with the growth of side length ratio [9,11]. It is worth noting, that the highest RSA packing fraction for this kind of system was recently reported for horizontally or vertically aligned rectangles with random side length ratio but constant surface area [12,13]. There, the packing fractions were up to 0.7, depending on the probability distribution used for choosing rectangles' anisotropy.…”

“…The parameter d is related to the number of particle degrees of freedom [16,17]. Among others, such behavior was also reported for RSA of freely oriented rectangles of fixed aspect ratio [11] and for horizontally or vertically aligned ones with random aspect ratio but fixed area [12,13]. On the other hand, for RSA of parallel squares, the kinetics of packing fraction takes the form [15] θ…”

“…To address all these phenomenons, we focus on the numerical study of RSA of rectangles placed on a continuous and flat plane that have two possible orientations: horizontal and vertical ones, but, in contrast to recent studies [12,13], fixed aspect ratio. Thus, the studied packings could allow us to effectively address all the abovementioned properties at the border between lattice and continuous packings built of oriented and unoriented elongated particles.…”

A random sequential adsorption model for the irreversible binding of Tenebrio molitor antifreeze protein to ice crystals

“…30 In the case of a binding ligand with a suitable size and orientation on an adsorption surface, the difference between the coverage obtained by simulation and the Palásti conjecture, which extended Rényi's one-dimensional random adsorption model, was only ∼0.7%. [31][32][33] This discrepancy is small enough to allow a reliable theoretical model of the TH activity to be developed based on the occupancy fraction of adsorbed TmAFP molecules on an ice crystal surface.…”

Two-stage random sequential adsorption of discorectangles and disks on a two-dimensional surface

“…The effects particle shape on structure of packing's have attracted great interest [4]. Continuous RSA problems for particles of various shapes, e.g., for disks [5,6], squares [6,7], cubic particles [8], rectangles [5,[9][10][11][12][13], oriented rectangles [14] discorectangles [4,5,11,15], rounded rectangles, isosceles and right triangles [16], ellipses [5,11,12,15,17,18], hard polygons [19], spheroids [20], and needles [11,12,18,21] were analyzed. For elongated particles, the non-monotonic dependencies of surface coverage φ J versus the aspect ratio ε (width to length ratio) have been typically observed [4].…”