Correlation of vulcanizate properties with polymer–black interaction

The specific surface activity of carbon black, as indicated by amount of rubber bound to the black during the mixing process, has been found to be the major factor in determining the modulus of the vulcanizate at high extensions. However, modulus at low extension is independent of specific surface activity and mostly influenced by other black characteristics, such as “structure” and surface area. Further, a relationship of the Guth‐Gold type based upon elastic theory was applied for predicting modulus of filled vulcanizates at high extension from that of an identically cured gum vulcanizate. The relationship is\documentclass{article}\pagestyle{empty}\begin{document}$M = M_0 (1 + 2.5\Phi + 14.1\Phi^2)$\end{document} where Φ is the reinforcement volume or volume fraction of filler plus volume fraction of bound polymer. This relationship was also used to calculate the actual elongation in a filled vulcanizate to compensate for that portion that does not elongate at all, and this actual extension ratio (α') was utilized in the Mooney‐Rivlin equation. The Mooney‐Rivlin equation is the theoretical expression for the modulus of a vulcanizate as it changes with elongation and cure level (or number of effective chains per unit volume). The equation has been successfully used previously for gum vulcanizates, but not for filled vulcanizates. With the use of the corrected elongation (α'), experiment and theory are in much better agreement than previously, and a general concept of the influence of black upon vulcanizate properties can be postulated.