Assessing the Mixing Quality of Hetero-Aggregates: Applying Mixing Theory to TEM Image Data

The hetero-aggregation of carbon black and colloidal silica in a spray flame is a promising approach to improve dispersibility and stability of carbon black. The mixing quality, i.e. homogeneity of local concentrations within the hetero-aggregate, is important for both properties, yet challenging to quantify. For this purpose, multiple TEM-EDX (Transmission Electron Microscopy with Energy Dispersive X-Ray Spectroscopy) scans are conducted on two distinct process conditions, leading to hetero-aggregates two different mixing qualities. By sampling cutouts of the images at randomized locations and applying principles adapted from classical mixing theory, hetero-aggregates are characterized with respect to mixing quality, irrespective of composition and primary particle size. Furthermore, correlation coefficient functions give insight to the length scale of primary particle clusters in the hetero-aggregates. In addition, on the basis of the intra-aggregate mixing state and the distribution of hetero-aggregate composition, a suitable description of the inter-aggregate mixing state is achieved. The developed methods present a generally valid, precise characterization of the mixing quality of hetero-aggregates.