Pair distribution function analysis of nano-object assemblies

The atomic pair distribution function (aPDF) analysis technique, also known as the total scattering method, which considers both Bragg and diffuse scattering, has been used extensively to probe local atomic arrangements in crystalline and disordered materials. In contrast, there have been limited applications of the PDF in self-assembled nanomaterials, which represent a class of materials built from nanoscale objects, such as nano-colloids, micelles and proteins. As distinguished from atoms, nano-objects have polydispersity in size and shape, and such form-factor effects complicate the application of PDF analysis to nano-systems. Herein, the application of the PDF is extended to spherical nano-object assemblies and the formulae for the nano-PDF (nPDF) are derived, showing some differences from the aPDF. By numerical simulations, the properties of the nPDF (peak broadening and pattern profile) are studied systematically as a function of structural features, such as nano-object parameters (size and size polydispersity) and assembly structural features (size, shape, structure type and lattice disorder), and of data processing parameters (q cut-off and ‘missing’ data in ultra-small-angle regions). The nPDF analysis method is found to provide an effective route to revealing not only nanoscale but also mesoscale structural properties, for example the morphology of a nano-assembly.