Morphology of Carbon-Black Aggregates: Fractal Versus Euclidean Geometry

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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...

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