Contruction of 3D Models From USAXS on Aggregate Structures*

An accurate 3D model of aggregate structures is desirable for comparison with TEM micrographs and as an input to computer simulations of aggregate transport and growth. For example, we have used such 3D models for polymer nanocomposites with carbon black and silica. Ultra-small angle X-ray scattering was coupled to a hierarchical scattering model, the unified scattering function, to obtain topological parameters that describe 9 average features of aggregates including details of the branched structure. A simple diffusion limited aggregation model was simulated and use to generate aggregates using two free parameters, the degree of aggregation, z, and the sticking probability, p [1]. USAXS measurements resulted in z for input to the simulation and the single parameter p was varied from 0 to 1 until a value that could reproduce the 8 remaining USAXS aggregate descriptors was found. The simulated average aggregates agreed well with TEM micrographs of the same samples. This approach can be used to depict complex morphological differences in ceramic oxide and carbon black aggregates and has the potential to be applied to a wide range of other aggregated materials.

1 Mulderig, A. et al. J. Aerosol Sci. 2017, 109 (March), 28–37.