Interpretation of Deviations from NEO-Hookean Elasticity by a Two-Network Model with Crosslinks and Trapped Entanglements

Abstract

Abstract Deviations from neo-Hookean elasticity in crosslinked rubbers, as measured by the ratio ψ=C2/(C1+C2) where C1 and C2 are the Mooney-Rivlin coefficients, have been found to be represented by a single function of fN, which is the ratio of network strands terminated by trapped entanglements to the total number of strands terminated by either trapped entanglements or crosslinks. It is assumed that the structure can be represented by a two-network model in which the crosslink network is neo-Hookean and the network of trapped entanglements is Mooney-Rivlin. The ratio fN is calculated from literature data for C1 and C2 and entanglement spacing derived from data on the uncrosslinked rubbers together with the Langley theory for the probability of entanglement trapping. Results are obtained for five polymers with different entanglement spacings over considerable ranges of degree of crosslinking and molecular weight before crosslinking, both of which influence the extent of entanglement trapping. The calculation is also applied to poly (dimethylsiloxane) networks crosslinked in the presence of diluent. The results show why, in various different investigations, C2 has been observed to increase, decrease, or remain approximately constant with increasing C1 or degree of crosslinking.