Structural orderings of anisotropically confined colloids interacting via a quasi-square-well potential

We implement Brownian dynamics to investigate the static properties of colloidal particles confined anisotropically and interacting via a potential which can be tailored in a repulsive-attractive-respulsive fashion as the interparticle distance increases. A diverse number of structural phases are self-assembled, which were classified according to two aspects, that is, their macroscopic and microscopic patterns. Concerning the microscopic phases we found the quasicrystalline, triangular, square, and mixed orderings, where this latter is a combination of square and triangular cells in a $3\times 2$ proportion, i.e., the so-called $(3^3,4^2)$ Archimedian lattice. On the macroscopic level the system could self-organize in a compact or perforated single cluster surrounded or not by fringes. All the structural phases are summarized in detailed phases diagrams, which clearly show that the different phases are extended as the confinement potential becomes more anisotropic.

Figure 1

Representation of the interaction potential for the parameters $\alpha =1.5$ and $R=1.5$.

Figure 2

Schematic representation of a hypothetical small cluster formed by four particles which are represented by circles and indexed by numbers from 1 to 4. ${\theta }_{kl}^1$ represents the smallest angle made by the vectors ${\vec{r}}_{1k}$ and ${\vec{r}}_{1l}$, where $k,l=2,3,$ and 4 with $k\ne l$.

Figure 3

(a) Representative configuration obtained for a system with $N=336$ particles, $\gamma =0.6$, $\alpha =5.0$, and $R=4.1$, and (b) its corresponding contour shape (also known as the $\alpha$ shape), (c) concave hull, and (d) convex hull. The hatched surfaces on these two latter panels indicate, respectively, the areas of the concave and convex hulls.

Figure 4

Phase diagram $R\times \alpha$ indicating the regions in which the various types of microscopic ordering occur: (a) triangular (red region), (b) square (green region), and (c) mixed (orange region). Figures in the same columns have the same value of the anisotropy parameter. From left to right, $\gamma =0.2$, 0.4, 0.6, 0.8, and 1.0.

Figure 5

Representative configurations for the system with $N=336$ particles and $\gamma =0.4$. The configurations in the same row have the same value of $\alpha$. From the topmost line to the lowest, we have $\alpha =5.50$, 4.00, 3.30, 1.00. The $R$ values are indicated in each figure and have an increasing order from left to right.

Figure 6

$R\times \alpha$ diagrams showing the regions of (a) subclusters and (b) holes. In (c) we display the value of $\eta$ which provides an indication of how much the outer edge of the cluster is fringed. Panels that are in the same column have equal value of $\gamma$, and from left to right we have $\gamma =0.2$, $0.4$, $0.6$, $0.8$, and $1.0$.