Three-Dimensional Binary Superlattices of Oppositely Charged Colloids

We report the equilibrium self-assembly of binary crystals of oppositely charged colloidal microspheres at high density. By varying the magnitude of the charge on near equal-sized spheres we show that the structure of the binary crystal may be switched between face-centered cubic, cesium chloride, and sodium chloride. We interpret these transformations in terms of a competition between entropic and Coulombic forces.

Figure 1

Confocal image of substitutionally disordered rhcp lattice formed, after 23 hours, in a suspension with $\varphi =0.507$. The image, $8.2\mu \mathrm{m}$ away from a wall, depicts the close-packed $\{111\}$ plane. The larger spheres (component $A$) are shown in green and the smaller spheres ($B$) in red. The inset figure shows the $\{111\}$ face of a fcc unit cell of binary spheres with volume fraction ${\varphi }_c=0.55$.

Figure 2

Confocal image and model of cesium chloride superlattice (SG 221) formed, after 199 hours, in suspension with $\varphi =0.528$. (a) Confocal image of $\{100\}$ plane in polycrystalline sample, $7.2\mu \mathrm{m}$ below the cover slip. Colors as in Fig. 1. Note the square lattice of $A$ spheres around each $B$. Inset shows CsCl unit cell. (b),(c) Depiction of a slice through a CsCl crystal, parallel to the $\{100\}$ plane, at three different depths of focus (dashed lines). (b) Projection perpendicular to $\{100\}$ plane. (c) In-plane projection of $\{100\}$ plane. Note the in-plane projection (c) remains unchanged as the depth of focus is stepped down through the crystal. This agrees with the experimental observation that the symmetry of the confocal image (a) does not change as the depth of focus was varied.

Figure 3

Confocal image and model of sodium chloride superlattice (SG 225) formed, after 215 hours, in suspension with $\varphi =0.528$. (a) Confocal image of tilted $\{100\}$ plane at a depth of $10.4\mu \mathrm{m}$. Colors as in Fig. 1. Note the square lattice of $A$ spheres around each $B$. Inset shows NaCl unit cell. (b),(c) Depiction of a slice through a NaCl crystal, parallel to the $\{100\}$ plane, at three different depths of focus (dashed lines). (b) Projection perpendicular to $\{100\}$ plane. (c) In-plane projection of $\{100\}$ plane. Projection (b) reveals that the $\{100\}$ plane consists of vertical columns of alternate $A$ and $B$ spheres. Focusing down through the $\{100\}$ plane (c) causes a shift in the 2D square lattice of the face (shown in black) and a corresponding kink in the line of spheres. The same characteristic pattern is evident in the confocal image (white dashed line) confirming that the square lattice seen in (a) arises from a NaCl rather than a CsCl structure.