Cross-linked poly(methyl methacrylate)s with various degrees of cross-linking were prepared, and their swelling, dynamic viscoelasticity and uniaxial extension behavior was investigated. For each sample, the values of molecular weight M c between cross-links (and trapped entanglements) evaluated from the equilibrium modulus G eq and the Mooney-Rivlin constants (C 1 +C 2 ) are comparable, while M c evaluated from the gel fraction is somewhat higher than those values. It is suggested from the data of excess storage modulus (G'−G eq ) and the Mooney-Rivlin constant C 2 that untrapped entanglement density decreases slightly while trapped entanglement density increases slightly with increasing degree of cross-linking. The strain-hardening tendency at constant strain rates becomes weaker with increasing crosslinking degree, and the strain-hardening does not appear when M c approaches the entanglement molecular weight M e . It is suggested for cross-linked polymers with rather high cross-linking density that chain breakage will occur before chain strands between cross-links stretch enough to result in the strain-hardening.

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For a lightly cross-linked poly (methyl methacrylate) (PMMA) with a gel fraction of 0.65, experimental studies are made on swelling, dynamic viscoelasticity, and uniaxial and biaxial extension at constant strain rates. The values of average molecular weight between cross-links, M c , (or between a cross-link and a trapped entanglement) are determined by four methods; swelling, the equilibrium modulus, the Mooney-Rivlin plot and the Young's modulus. These values are in the same order but somewhat smaller values are obtained from the latter two methods. The density of weakly attached or untrapped entanglement strands is evaluated from the plateau modulus of (G'−G eq ), where G' and G eq are the storage and equilibrium moduli. The entanglement molecular weight, M e , evaluated by this method is certainly smaller than M c , and is slightly larger than M e of uncross-linked atactic PMMA melt. In uniaxial extension, the stress growth coefficient shows stronger strain-hardening than that of uncross-linked PMMA melts with very high molecular weight component. On the other hand, in biaxial extension, the stress growth coefficient exhibits weak strain-softening followed by small upturn.