# The Analysis of Periodic Order in Monolayers of Colloidal Superballs
## 1 Introduction  
Colloidal monolayers are used in a wide variety of applications, such as anti-reflective coatings, photonic materials, photovoltaics and biosensors [1, 2]. Alternatively, the assembly of colloids into monolayers is often used as a step in colloidal syntheses in order to locally modify the particles in order, for example, to produce Janus colloids [3, 4, 5]. Various methods are known for the preparation of colloidal monolayers, such as drying methods, spin coating, the assembly on liquid interfaces and the horizontal and vertical deposition methods [2]. Each of these preparation methods have their own strengths and weaknesses. It was only recently shown, however, that colloidal monolayers could also be prepared by mechanically rubbing dried colloids between two sticky surfaces such as polydimethylsiloxane (PDMS) [6, 7]. This quick, simple and inexpensive method produces high-quality colloidal monolayers where the colloidal crystal grains align in the direction in which the mechanical rubbing was applied. So far, the unidirectional rubbing method has only been used for the monolayer formation of spherical particles. However, the shape of the colloidal particles can greatly influence the structures that are formed [8]. By employing the unidirectional rubbing method for the assembly of anisotropic colloids, colloidal monolayers that possess unique properties may be formed, which might be of interest in one of the many colloidal monolayer applications. Of specific interest are superball-shaped colloids, i.e., shapes varying from spheres via cubes with rounded edges to perfect cubes, because their variable shape allows smooth phase transitions to occur [9]. For instance, upon allowing superball-shaped colloids tosediment, plastic crystals and solid-solid phase transitions were observed [10; 11], whereas upon assembling these particles into monolayers using the horizontal and vertical deposition method both predicted densest packings were found as well as a continuous transition between the two lattice structures [12; 13]. Furthermore, upon the addition of depletants, the resulting crystal phases were found to depend on both the shape of the superballs and the radius of gyration of the added depletant relative to the size of the superballs [9; 14]. By employing the unidirectional rubbing method for the organization of colloidal superballs into monolayers it can be expected that monolayers with unique organizations can be achieved as a result of the directional force applied during its assembly. The periodic structures in colloidal monolayers can be studied, on the one hand, using microscopy techniques, which are superior in revealing local densely packed structures. On the other hand, to characterize long-range ordering on the colloidal scale, small-angle neutron scattering (SANS) [15] and small-angle X-ray scattering (SAXS) [16] are often applied. Although these two techniques are very similar in their general approach and theoretical models, there are many factors that determine which of these scattering techniques is most suitable for a certain study. For example, while for X-rays the scattering contrast is essentially determined by the total local electron density, which is approximately proportional to the mass density, neutron scattering contrast has much higher sensitivity to most lighter atoms with fewer electrons. Moreover, SANS offers great opportunities for contrast variation by using isotopes, most remarkably hydrogen/deuterium. This allows the revelation of minor structural details [17] or the minimization of multiple scattering [18]. In addition, the scattering of spin-polarized neutrons is sensitive to the magnetic ordering in the sample [19]. Wide opportunities can be opened by combining SANS with advanced spin-echo techniques, such as spin-echo small-angle neutron scattering (SESANS), which can access large-period structures [20] as well as nanostructures along with their nanosecond temporal dynamics [21; 22].