Morphology of fine-particle monolayers deposited on nanopatterned substrates

We study the effect of the presence of a regular substrate pattern on the irreversible adsorption of nanosized and colloid particles. Deposition of disks of radius $r_0$ is considered, with the allowed regions for their center attachment at the planar surface consisting of square cells arranged in a square lattice pattern. We study the jammed state properties of a generalized version of the random sequential adsorption model for different values of the cell size, $a$, and cell-cell separation, $b$. The model shows a surprisingly rich behavior in the space of the two dimensionless parameters $\alpha =a∕2r_0$ and $\beta =b∕2r_0$. Extensive Monte Carlo simulations for system sizes of $500\times 500$ square lattice unit cells were performed by utilizing an efficient algorithm, to characterize the jammed state morphology.

Figure 1

Dashed lines delineate the square lattice unit cells. Adsorption of disks can only take place when their centers fall inside the solid squares, i.e., the allowed-landing cells.

Figure 2

A disk fails adsorption onto the substrate because (a) its center does not fall within an allowed-landing cell, or (b) it overlaps with a previously adsorbed disk.

Figure 3

The major subdivisions in the two-parameter space. For cell-cell separation $\beta <1$ we have the interacting cell-cell adsorption (ICCA), while for $\beta ⩾1$ we have the noninteracting cell-cell adsorption (NICCA). For cell sizes $\alpha <1∕\sqrt{2}$ we have a single-particle-per-cell adsorption (SPCA), while for $\alpha ⩾1∕\sqrt{2}$ we have multiparticle-per-cell adsorption (MPCA). Limiting cases of the model, as well as subregions with interesting properties, are discussed in the text.

Figure 4

(Color online) Typical configuration of a region of $25\times 25$ unit cells, for $\alpha =0.6$ and $\beta =1.2$, in the jammed state. This snapshot corresponds to the NICCA-SPCA upper-left region in Fig. 3.

Figure 5

(Color online) Configuration of a region of $25\times 25$ unit cells, for $\alpha =1.2$ and $\beta =1.2$, in the jammed state. Particles attempting adsorption never overlap previously adsorbed ones in different cells, but contrary to Fig. 4 each cell can now adsorb more than one particle. Since $\beta =1.2>1$, the kinetics of adsorption at each cell is decoupled from that at other cells.

Figure 6

(Color online) Coverage values obtained by Monte Carlo simulation of our RSA model (solid line, the jammed-state coverage) and by direct calculation for the close-packed configurations (dashed line), both for $\beta =1$. Notice the discontinuities in the values of the close-packed coverage as opposed to the smooth variation in the RSA case. The jammed-state coverages for $\beta =2$, calculated according to relation (5), are also shown for comparison (dotted line).

Figure 7

(Color online) Configuration of a region of $25\times 25$ unit cells, for $\alpha =0.2$ and $\beta =0.5$, in the jammed state. A particle attempting adsorption can overlap a previously adsorbed particle in a different cell. This excluded volume interaction is responsible for correlations which result in locally diagonal, semiordered domains as seen in this snapshot.

Figure 8

(Color online) Configuration of a region of $25\times 25$ unit cells, for $\alpha =1.2$ and $\beta =0.2$, in the jammed state. For this low $\beta$ value, the probability of a particle attempting adsorption to overlap with one in a neighboring cell is appreciable, thus building up a somewhat longer range diagonal semiordering than that seen for the parameter values of Fig. 7.

Figure 9

Plots of the distribution function for various values of $\alpha$, at fixed values of $\beta$: (a) $\beta =1.2$, with $\alpha =0.2$, 0.4, 0.8, and 1.4; (b) $\beta =0.2$, with $\alpha =0.2$, 0.4, and 1.2; (c) $\beta =0.8$, with $\alpha =0.2$, 0.4, 0.6, and 1.2.

Figure 10

The distribution function (a) for constant $\alpha =0.2$, with $\beta =0.2,0.5,1.2$; (b) for constant $\alpha =1.2$, with $\beta =0.2,0.4,0.6,0.8,1.2$; (c) along the diagonal line (0,0)—$(1∕\sqrt{2},1)$ in the ICCA-SPCA region of the $(\alpha ,\beta )$ “phase diagram,” Fig. 3, with $(\alpha ,\beta )=(0.2,0.28),(0.3,0.42),(0.5,0.70),(0.6,0.84)$.