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Abstract Based on the concepts of the occlusion of rubber and random packing of spheres whose volume is equivalent to that permeated by individual aggregates, an equation was deduced to estimate the distance between carbon-black aggregates in filled rubber. It was found that when the interaggregate distance reaches a critical point which is approximately identical for all carbon blacks investigated (furnace blacks), the elastic modulus measured at very low strain deviates from the modified Guth-Gold equation. Tan δ and resilience are mainly determined by the distance between aggregates. These phenomena are related to filler networking which is determined by the attractive potential and the distance between individual aggregates. Since the factor S f , used to characterize the strength of secondary filler networks in hydrocarbon rubbers and measured by means of inverse gas chromatography, is approximately the same for all furnace blacks, the interaggregate distance seems to determine filler networking. A comparison of fillers with different S f (graphitized vs. nongraphitized carbon blacks, carbon black vs. silica) shows that at the same interaggregate distance, a lower S f leads to higher tan δ of the filled vulcanizates.
Wang et al. (Sat,) studied this question.