Swelling of filler‐reinforced vulcanizates

A theory is developed to account for the restricted swelling in solvents of crosslinked elastomers containing reinforcing fillers. Assuming swelling to be completely restricted at the filler‐rubber interface due to adhesion, the following relation is obtained:\documentclass{article}\pagestyle{empty}\begin{document}$$ v_{ro} {\rm /}v_r {\rm } = {\rm 1} - [3c(1 - v_{ro} {}^{1/3}){\rm } + {\rm }v_{ro} - 1]\phi /(1 - \phi ), $$\end{document} where v r is the volume fraction of rubber in the swollen rubber phase, V ro is the same quantity referred to on otherwise analogous, unfilled vulcanizate, Φ is the volume fraction of filler, and c a parameter depending on the filler, but independent of Φ and V ro . This equation is shown to hold for a large volume of experimental data on carbon blacks, involving four rubbers, several sulfur vulcanizing systems, five solvents, and a wide range of crosslinking. Conformance with the theory indicates that carbon blacks are firmly bonded to the rubber and that, in the sulfur crosslinking systems investigated, they have no significant effect on the stoichiometry of vulcanization (although they may affect the rate of vulcanization). Illustrative examples of applications of the theory to problems in filler reinforcement and vulcanization are shown.