For a number of different vulcanization systems, the equilibrium swelling ratios for carbon-black-filled and unfilled samples are shown to be linearly related, as found by Lorenz and Parks, indicating that the degree of crosslinking is not changed by incorporating carbon black. However, filled compounds swell less, and thus the apparent degree of crosslinking is significantly greater. For example, it is about twice as large for compounds containing 50 phr of HAF carbon black. This is confirmed by measurements of the elastic modulus of swollen samples. Relatively strong bonds appear to be formed between rubber molecules and the surface of carbon black particles - bonds that can withstand swelling stresses and temperatures of up to 120 °C. Bonding between rubber and carbon black is also indicated by the limited swelling of filled rubber compounds even before vulcanization, although in this case the apparent degree of crosslinking is smaller. Thus, vulcanization appears to enhance the contribution of rubber-particle bonding to the elastic modulus and restricted swelling of carbon-black-filled vulcanizates. Simple procedures are suggested for estimating the actual degree of crosslinking in filled rubber vulcanizates from measurements of equilibrium swelling or elastic modulus.
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