Morphology of Carbon-Black Aggregates: Fractal Versus Euclidean Geometry

Abstract

Abstract A study has been made comparing the utility of fractal and Euclidean geometry in the characterization of carbon-black aggregates. The fractal models used were the perimeter-area relationship, P∼ADp/2, and the mass fractal, M∼RDm. Values of the perimeter fractal, Dp, and the mass fractal, Dm, were determined for nineteen different grades of carbon black from a sampling of 1000 aggregates per grade. The perimeter (P), area (A), mass (M), and size (R) of the aggregates were all measured by on-line transmission-electron-microscopy/automated-image-analysis (TEM/AIA) which enabled rapid sampling. Values of Dp and Dm ranged from 1.05 to 1.23 and 2.85 to 2.47 respectively and were shown to correlate with carbon-black colloidal properties such as dibutyl-phthalate absorption (DBPA) and Euclidean size and shape parameters from TEM/AIA. These parameters were also used to classify aggregates into different shape categories using discrimination analysis techniques. Both perimeter and mass fractals were nearly constant within each shape category. Four carbon blacks of similar particle size and varied DBPA range were also used to show the effects on Dp and Dm upon high-shear mixing of the carbon-black aggregates into rubber and CAB composites.