Properties of random sequential adsorption of generalized dimers

Saturated random packing of particles built of two identical, relatively shifted spheres in two- and three-dimensional flat and homogeneous space was studied numerically using a random sequential adsorption algorithm. The shift between centers of spheres varied from $0.0$ to $8.0$ sphere diameters. Numerical simulations allowed the determination of random sequential adsorption kinetics, the saturated random coverage ratio, as well as the available surface function and density autocorrelation function.

Figure 1

Definition of anisotropy parameter $\epsilon$ and examples of three generalized dimers for $\epsilon =0.5$, $\epsilon =1.0$, and $\epsilon =1.5$.

Figure 2

Example coverages for three different values of $\epsilon$: $\epsilon =0.01$ (left), $\epsilon =0.5$ (middle), and $\epsilon =1.4$ (right) at the end of the simulation. The coverage ratio $\theta$ for presented snapshots are lower by about 0.5% from saturated random coverage ratio ${\theta }_{\max }$.

Figure 3

The power-law dependence of increments of the mean number of adsorbed particles on the dimensionless time for different anisotropy $\epsilon$. Inset shows the exponent in Eq. (4), determined using least squares fit method.

Figure 4

The dependence of saturated random coverage on dimer anisotropy. Dots correspond to measured data. Statistical error of ${\theta }_{\max }$ is approximately $0.0001$ and is smaller than the dot size. Lines have been drawn to guide the eye. Dashed line corresponds to saturated random coverage ratio for disks on a flat collector [23, 30].

Figure 5

The dependence of $C_1$ and $C_2$ (inset) coefficients on dimer anisotropy $\epsilon$. Dots are simulation data. Solid lines have been drawn to guide the eye.

Figure 6

Density autocorrelation function for several dimers of different anisotropy $\epsilon$. Distance (in $r_0$ units) is measured between centers of different disks, no matter whether they come from the same or different dimers. Autocorrelation function was obtained for layers at the end of simulations. Their coverage ratio was about $0.5\%$ smaller than ${\theta }_{\max }$.

Figure 7

Two exemplary generalized dimers ($\epsilon =0.5$) taken from saturated random coverage. Arrows point to distances between disks from different particles. In case (a) the distance is slightly higher than $2r_0$ whereas in cases (b) and (c) it is equal to about $3r_0$.

Figure 8

Saturated random coverage ratio measured for several dimers of different anisotropy $\epsilon$. The dashed line corresponds to ${\theta }_{\max }=0.3841$, which is the saturated random coverage ratio of spheres in three-dimensional space [23]. The solid line is to guide the eye. Inset shows the exponent in Eq. (4), determined using the least squares fit method dependence on particle anisotropy.