Highly Ordered Monolayers of μm-Sized Polystyrene Spheres Studied by Grazing-Incidence Small-Angle X-ray Scattering, Simulations, and Geometrical Calculations.

Unraveling the two-dimensional (2D) structural ordering of colloidal particles assembled at a flat surface is essential for understanding and optimizing their physical properties. So far, grazing-incidence small-angle X-ray scattering (GISAXS) has been widely used to determine crystallographic information on 2D self-assembled structures of nanosize objects. However, solving the structure of 2D lattices consisting of micrometer (μm)-sized objects still remains a challenge using scattering methods. Here, a model 2D SCALMS (supported catalytically active liquid metal solution) template is fabricated from μm-sized polystyrene (PS) spheres that form a monolayer on top of the flat solid support. GISAXS patterns of the sample were collected for rotation angles around its surface normal in steps of 3°. For every rotation angle, different Bragg-type interference maxima along the out-of-plane ( q z ) direction were observed. On the basis of simulations of GISXAS patterns of single domains of ordered particle arrangements using the distorted wave Born approximation (DWBA) and validation against a simple geometrical scattering model, the interference maxima could nicely be interpreted to originate from a monolayer of the μm-sized spherical particles which are arranged in domains of hexagonal 2D paracrystalline order. This novel GISAXS evaluation technique serves as a proof of principle for determining the μm-size periodicity of 2D crystalline domains and demonstrates its potential to spatially resolve the relative orientations of such domains with respect to a reference direction.