Reconstructing the fractal clusters of detonation nanodiamonds from small-angle X-ray scattering

Detonation nanodiamonds (DND) form fractal-like aggregates composed of polydisperse DND particles. We present a novel methodology for the visualisation and characterisation of fractal clusters of DND from one-dimensional small-angle X-ray scattering (SAXS) intensity. The fractal nature and polydispersity of DND are modelled by combining a diffusion-limited aggregation (DLA) process implemented in Monte Carlo simulations with the distribution of DND sizes measured from high-resolution transmission electron microscopy. The radius of gyration (42–44 nm), aggregation number (850–1150), and the maximum dimension (226–242 nm) of DND fractal clusters were obtained from the fitting of the synchrotron-based SAXS data (q∼0.11–4.75 1/nm) measured for two samples of commercialized DND powders by the developed theoretical model