Entanglement Effects in Elastomers: Macroscopic vs Microscopic Properties
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Abstract
This Perspective highlights how entanglement effects on rubber elasticity can be unveiled by a combination of different macroscopic and microscopic methods, taking advantage of new developments in proton low-field NMR spectroscopy as applied to bulk and swollen rubbers. Specifically, the application of a powerful yet routinely applicable double-quantum method, combined with a back-extrapolation procedure over results measured at different degrees of swelling, allows one to characterize the recently introduced "phantom reference network" state, which only reflects contributions of actual cross-links and topologically trapped entanglements. We further present an assessment of the qualitative yet popular Mooney–Rivlin analysis of mechanical data, where the influence of entanglement contributions on the fitted, purely empirical parameters C1 and C2 is reconsidered in the context of different tube models of rubber elasticity. We also review the impact of entanglements on results of equilibrium swelling experiments and address the validity of the common Flory–Rehner approach, where we stress its qualitative nature and the need to use NMR observables for a correct estimation of the relevant volume fractions. We discuss semiquantitative estimations of the cross-link density from these macroscopic experiments with its microscopic determination by NMR on the example of lowly cross-linked synthetic and natural poly(isoprene) rubber prepared by a novel UV-based curing protocol of dried latex based upon thiol–ene chemistry, which in contrast to previously studied thermally peroxide-cured natural rubber contain only small amounts of short-chain defects. We find that the entanglement effects in these samples can best be described by the Heinrich–Straube tube model with positive scaling exponent ν > 0.3 as well as by the slip-link model of Ball et al./Edwards–Vilgis with a slip parameter η > 0.1. A comparison with literature results demonstrates that these findings are not universal in that the apparent entanglement contribution depends significantly on the sample (in)homogeneity, i.e., of the NMR-determined fraction of inelastic defects and spatial cross-linking inhomogeneities. This means that conclusions on the validity or invalidity of specific tube theories cannot be drawn without careful consideration of the network microstructure.