## Self-assembly of micron-sized hollow silica cubes using convective assembly methods

##### Summary

Both simulations and experiments show interesting close-packed structures can be formed by superball-shaped particles. The arrangement of these particles depends on the roundness of the edges, which is defined by the deformation parameter m, where m = 2 for a sphere and m = ∞ for a perfect cube. Simulations predict that the highest packing density of superball/disk-shaped particles is obtained with two new Bravais lattices, called the Ʌ0 and Ʌ1 lattice. The maximum packing density(MPD) obtained with these lattices depends on the m-value of the particles. An experimental study with hollow silica cubes with m = 2.9 shows that hexagonal-like and square-like arrangements similar to the Ʌ0 and Ʌ1 lattices can be formed. For superballs of m > 2.6 the MPD of the Ʌ1 lattice is slightly higher compared to the Ʌ0 lattice and the difference increases with m. It is therefore expected that superballs with m-values >> 2.6 predominantly order on a Ʌ1 lattice.
In this experimental study dense structures of superballs with a high m-value are formed and analyzed. Therefore, micron-sized hollow silica cubes with m = 3.6 are synthesized and used in convective assembly(CA) experiments to form dense ordered structures. CA experiments are performed using the drying droplet(DD), horizontal deposition(HD) and flow-controlled vertical deposition(FCVD) method. The thickness and shape of the cube deposits are observed to strongly depend on the method used. SEM images show that ordered mono- and multilayers are formed with all methods. The shape of the growth start is found to have a significant influence on the size and orientation of the ordered domains. With the DD and the HD method deposits with a curved growth start are obtained, whereas with the FCVD method a relatively straight growth start is induced. Structure analyses of SEM images of the cube deposits demonstrate that large ordered domains of similar orientation can be formed with the FCVD method, while small ordered domains of different orientation are observed when the DD and the HD methods are used.
Using the translational coordinates and orientation of the cubes Interactive Data Language(IDL) is used to analyze to what extent the cubes order on Ʌ0 and Ʌ1 lattices. It is found that with all three CA methods Ʌ0 and Ʌ1 order is observed in both mono- and multilayers. The analyses show that the Ʌ1 lattice is slightly preferred over the Ʌ0 lattice. This is in agreement with simulations of superballs, since the MPD of cubes with an m -value of 3.6 is higher on the Ʌ1 lattice compared to the Ʌ0 lattice.
Since the growth start has a significant influence on the structure formation, patterned substrates are used to influence and study the behaviour of cubes at the growth start. Substrates with straight polymer lines are used to induce a straight growth start. With all three CA methods cubes are observed to align at the polymer lines, therefore inducing a straight growth start. In monolayers the cubes are orientated with their face side parallel to the polymer line. The orientation of the aligned cubes influenced the orientation of the neighbouring cubes. Patterned substrates are therefore promising since the behaviour and therefore the structures formed by the cubes can be influenced and controlled.