Morphology of Carbon Black Aggregates on Nanoscales

The structure or amount of specific voids of the three grades is almost the same and differs between 1 cm3/g and 1.2 cm3/g, only. Since the specific weight of carbon black is almost twice that for DBP, this corresponds to a factor of 2 for the void volume as compared to the solid volume of the aggregates. It means that about 2/3 of the aggregate volume is empty space, i.e., the solid fraction E p of the primary aggregates is relatively small (Op 0.33). 

It is shown below that p fulfills a scaling relation which involves the size and mass fractal dimension of the primary aggregates. Due to significant deviations of the solid fraction p from 1, the filler volume fraction of carbon black in rubber composites has to be treated as an effective one in most applications, i.e., 0eff=0/0p (compare [22]). 

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