Self-assembly of colloidal spheres on patterned substrates

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Abstract
We report here on the self-assembly of polystyrene colloidal spheres on patterned substrates. The substrate was a grating with a periodic one-dimensional-height profile. The two-dimensional (2D) arrays of colloidal spheres were obtained by the convective self-assembly method. It is shown that these structures strongly depend on the ratio between the diameter of the sphere (d) and the period of the grating (p) (x=d/p). When 1<x<1.15, and 1.15<x<2, the 2D array showed a centered-rectangular symmetry. For x=1.15 and 2, the ordered 2D array had a hexagonal symmetry structure. The angle between the grating groove direction and the crystal lattice vector (θ) is given by θ=sin−1(d/p). It is suggested that the variety of the 2D structures are formed by the capillary forces and the self-shadowing effects during the drying process.