Cross-link fluctuations: NMR properties and rubber elasticity

Abstract

A scale invariant model for the residual tensorial spin-spin couplings between nuclei has been used to investigate the NMR properties of deformed elastic networks. A general expression is derived which includes the effects of cross-link fluctuation dynamics and a non-isotropic deformation dependence of the fluctuation volume. The theoretical results are used to re-interpret the experimental results of Sotta and Deloche on the doublet structure observed in the ²H NMR spectra of deformed PDMS networks in terms of strain-dependent cross-link fluctuations. Previously, this feature has been used as evidence for an orientation-induced weak nematic network ordering. From the experimental results the magnitude of the junction fluctuations in the undeformed state is estimated to be approximately 1/3 of the phantom network result. Using a theory developed by Flory, these restricted junction fluctuations can be related to the elastic properties of the network. In particular, they were related to the deviations of the elastic modulus from the phantom chain result. When expressed in terms of the Mooney-Rivilin constants C₁ and C₂, the Flory theory together with the decuced value of the junction fluctuations obtained from the NMR results gives C₂/C₁=0.18. Using literature data, this value is in close agreement with the value C₂/C₁=0.21 obtained from mechanical measurements on almost identical networks.