Random sequential adsorption of partially ordered discorectangles onto a continuous plane

A computer simulation was used to study the random sequential adsorption of identical discorectangles onto a continuous plane. The problem was analyzed for a wide range of discorectangle aspect ratios ($\varepsilon \in [1;100]$). We studied the anisotropic deposition, i.e., the orientations of the deposited particles were uniformly distributed within some interval such that the particles were preferentially aligned along a given direction. The kinetics of the changes in the packing fraction found at different values of such the alignment are discussed. Partial ordering of the discorectangles significantly affected the packing fraction at the jamming state, ${\phi }_{\text{j}}$, and shifted the cusps in the ${\phi }_{\text{j}}\left(\varepsilon \right)$ dependencies. The structure of the jammed state was analyzed using the adsorption of disks of different diameters into the porous space between the deposited discorectangles. The analysis of the connectivity between the discorectangles was performed assuming a core-shell structure of particles.

Figure 1

An illustration of the RSA model of the packing of discorectangles on a 2D substrate. Intersections of the particle cores are forbidden. For the connectivity analysis, each particle is assumed to be covered by a soft (penetrable) shell with thickness $\delta$.

Figure 2

Actual order parameter, $S$, versus the packing fraction, $\phi$, at different values of the aspect ratio $\varepsilon$. Examples for the preassigned order parameters $S_0=0.5$ and $S_0=0.9$. The values of ${\phi }_{\text{j}}$ correspond to jamming states.

Figure 3

Examples of the jamming patterns for aspect ratio $\varepsilon =10$ at $S_0=0$ (random orientation) and $S_0=1$ (complete alignment along the horizontal direction) (a), and for aspect ratio $\varepsilon =2$ at $S_0=0$ (b). For the latter case, the void space between the discorectangles is filled with reference disks with diameters $d_{\circ }=0.3l$ and $d_{\circ }=0.55l$. Fragments with size of $9l\times 9l$ are shown.

Figure 4

Packing fraction, $\phi$, (a) and time derivative $d\phi /d{log}_{10}t$ (b) versus the deposition time, $t$, for the disordered RSA packing ($S_0=0$) of discorectangles with aspect ratio $\varepsilon$. Here ${\phi }_{\text{j}}$ is the jamming coverage and $\tau$ is the characteristic deposition time.

Figure 5

Packing fraction at the jamming state, ${\phi }_{\text{j}}$, (a) and characteristic deposition time, $\tau$, (b) versus the discorectangle aspect ratio, $\varepsilon$, at different values of the preassigned order parameter, $S_0$.

Figure 6

Minimal reduced thickness of shell, $\delta /d$, required for infinite connectivity between particles (formation of a spanning path through the system), versus the packing fraction, $\phi$, at different aspect ratios $\varepsilon$. The preassigned order parameter is $S_0=0.0$. The inset shows the $\delta /d$ versus $\varepsilon$ dependencies at $\phi =0.4$ and $\phi ={\phi }_{\text{j}}$ (jamming state).

Figure 7

Packing fraction of reference disks, $\varphi$, versus the deposition time, $t$. Here discorectangles with an aspect ratio of $\varepsilon =2$ and random orientations ($S_0=0$) were preliminarily deposited to the jamming state (${\phi }_{\text{j}}\approx 0.582$), and then RSA packing of reference disks with different diameters $d_{\circ }$ into the confined void spaces between the discorectangles was applied. The value ${\varphi }_{\text{j}}$ corresponds to the jamming coverage of the reference disks.

Figure 8

Jamming packing fraction of reference disks in the void space between discorectangles, ${\varphi }_{\text{j}}$, versus reduced diameter of the disks $d_{\circ }/l$. The data are presented for completely disordered ($S_0=0$, filled symbols, solid lines) and completely aligned ($S_0=1$, open symbols, dashed lines) discorectangles with different aspect ratios of $\varepsilon$. The value of $d_{\text{m}}/l$ corresponds to the maximum diameter of the reference disks. Inset shows the $d_{\text{m}}/l$ versus $\varepsilon$ dependencies for different values of the preassigned order parameters, $S_0$.