Confinement effects on the random sequential adsorption packings of elongated particles in a slit

The behavior of a system of two-dimensional elongated particles (discorectangles) packed in a slit between the two parallel walls was analyzed using a simulation approach. The packings were produced using the random sequential adsorption model with continuous positional and orientational degrees of freedom. The aspect ratio (length-to-width ratio, $\varepsilon =l/d$) of the particles was varied within the range $\varepsilon \in [1;32]$ while the distance between the walls was varied within the range $h/d\in [1;80]$. The properties of deposits in jammed state [the coverage, the order parameter, and the long-range (percolation) connectivity between particles] were studied numerically. The values of $\varepsilon$ and $h$ significantly affected the structure of the packings and the percolation connectivity. Particularly, the observed nontrivial dependencies of the jamming coverage $\phi \left(\varepsilon \right)$ or $\phi \left(h\right)$ were explained by the interplay of the different geometrical factors related to confinement, particle orientation degrees of freedom and excluded volume effects.

Figure 1

A schematic picture of the of RSA packing of elongated particles between the two parallel walls with the distance $h$ between them. The walls and particles (cores) are assumed to be impenetrable. The cores of particles are discorectangles with the length $l$ and width $d$. The space between particles can be treated as pores. Periodic boundary conditions are applied in $y$ direction. For connectivity analysis along the $x$ and $y$ axes, the particles were covered with shells of thickness $\delta$. The particles of different shades correspond to the different clusters.

Figure 2

Examples of packing patterns (top), and profiles of the scaled coverage $g\left(x\right)=\phi \left(x\right)/\langle \phi \rangle$ and the order parameter, $S\left(x\right)$ (bottom), for the value of the aspect ratio $\varepsilon =2$ and the distance between walls $h=4$ (a) and $h=10$ (b). The corresponding mean values, averaged through the slit, are $\langle \phi \rangle =0.518\pm 0.01$ and $\langle S\rangle =0.54\pm 0.01$ (a) and $\langle \phi \rangle =0.558\pm 0.01$ and $\langle S\rangle =0.26\pm 0.01$ (b). Here $x_m$ corresponds to the positions of the extremum in ${\phi }^{*}\left(x\right)$ (maxima) or $S\left(x\right)$ (minima) dependencies.

Figure 3

Position of the extremum $x_m$ in spatial distribution of the coverage $\phi$ or the order parameter $S$ versus the aspect ratio $\varepsilon$ in a slit with different distances between walls $h$ (a) and $x_m$ versus $h$ at different values of $\varepsilon$ (b). Inset shows the enlarged part of $x_m\left(h\right)$ dependence (b).

Figure 4

The mean coverage $\langle \phi \rangle$ versus the aspect ratio $\varepsilon$ in slits with different distances $h$ between the walls (a) and versus the $h$ for different values of $\varepsilon$ (b).

Figure 5

The mean order parameter $\langle S\rangle$ versus the aspect ratio $\varepsilon$ in slits with different distances $h$ between the walls (a) and versus the $h$ for different values of $\varepsilon$ (b).

Figure 6

Thickness of the connectivity shell $\delta$ versus the aspect ratio $\varepsilon$ along $x(\leftrightarrow )$ and $y(\updownarrow )$ axes for different distances between walls $h$.

Figure 7

Examples of the coverage $\phi$ versus the inverse length of a slit $1/L$ at different distances between its walls $h$ and the aspect ratio of particles $\varepsilon$. Inset shows $\phi /{\phi }_{\infty }$ versus $1/L$, where ${\phi }_{\infty }$ corresponds to the limit $L\to \infty$. The value of ${\phi }_{\infty }$ was determined using linear approximation for $\phi (1/L)$ dependence.

Figure 8

Examples of the packing patterns for the values of the aspect ratios $\varepsilon =5$ and $\varepsilon =20$, and distances between the walls $h=2$ and $h=20$.

Figure 9

Examples of the profiles of the scaled coverage $g\left(x\right)=\phi \left(x\right)/\langle \phi \rangle$ and the order parameter, $S\left(x\right)$ for the the different values of the aspect ratio $\varepsilon$ and distances between the walls $h$: $\varepsilon =5, h=2$ (a); $\varepsilon =5, h=10$ (b); $\varepsilon =20, h=2$ (c); and $\varepsilon =20, h=10$ (d). Here $x_m$ corresponds to the positions of the extremum in the $g\left(x\right)$ (maxima) or $S\left(x\right)$ (minima) dependencies, and $\langle \phi \rangle$ is the mean value of the coverage, averaged across the slit.