Colloidal Ordering on a 2D Quasicrystalline Substrate

By using Monte Carlo simulations, we study the complex phase behavior of charged-stabilized colloidal particles in a two-dimensional substrate potential with quasicrystalline decagonal symmetry. In the regime where the strengths of the substrate and colloidal pair potential are comparable, we identify a novel and unexpected quasicrystalline phase with pure 20-fold bond order and a disordered structure without any apparent rotational symmetry. Furthermore, we demonstrate how phasonic displacements in the substrate potential induce phasonic flips in the colloidal monolayer.

Figure 1

(a) The colloidal potential corresponds to the interference pattern of five laser beams arranged symmetrically around the vertical. A small tilt angle is assumed so that the polarization vectors can be chosen all the same. (b) The five wave vectors of the beams projected along the vertical onto the $xy$ plane. (c) Gray-scale representation of the decagonal potential. White indicates a high laser intensity and therefore a potential minimum. The bar in the upper right corner marks the length scale $a_V=2\pi /|{\mathbf{G}}_j|$. The full and dashed lines indicate, respectively, the 10 bond directions for ${\psi }_{10}\ne 0$ and the additional bond directions for ${\psi }_{20}\ne 0$.

Figure 2

(a)–(c) Snapshots for particle positions and (d)–(f) direct correlation functions for (a),(d) the fluid, (b),(e) the phase with 20-fold bond order, and (c),(f) with 10-fold bond order. (g),(h) Phase diagrams for low (g) and high (h) colloidal densities depending on the potential strength $V_0$ (in units of $k_{B}T$) and the particle spacing $a_S$ (in units of $a_V=2\pi /|{\mathbf{G}}_j|$) in an ideal triangular lattice. For a detailed description, see the main text.

Figure 3

Pair correlation function $g(d)$ as a function of the particle distance $d$: (a) for colloids placed at the positions of all minima (solid line) or of all minima deeper than $-0.7V_0$ (dotted line) in the decagonal potential, (b)–(d) determined by Monte Carlo simulations in the low (b),(c) and high (d),(e) density cases. In each graph, $g(d)$ is drawn for constant $a_S/a_V$ and several strengths $V_0$. The inset tables give the values of ${\psi }_m$ for $m=6$, 10, and 20.

Figure 4

Colloidal ordering in the quasicrystalline phase for $a_S/a_V=0.65$ and $V_0/(k_{B}T)=1000$, (a) before and (b) after a phasonic displacement with $w_x=0.1a_V$. Note the flips of neighboring pentagons indicated by dotted circles.