Comparison of Mean-Field Theory and 1 H NMR Transversal Relaxation of Poly(dimethylsiloxane) Networks

Abstract

We have estimated the mass fraction of elastic and pendant chains of model poly- (dimethylsiloxane) (PDMS) networks using transverse proton relaxation in nuclear magnetic resonance (1H NMR). These experiments were compared with theoretical estimations of the mass fraction of pendant chains predicted by mean-field calculations (MFC). A recursive approach, originally postulated by Miller and Macosko and extended by the authors to obtain information on several molecular parameters related to the molecular structure of the pendant chains, was employed for the theoretical calculations. A preliminary inspection of the results showed that proton relaxation measurements underestimate the mass fraction of pendant material. We speculate that trapped entanglements, in which long pendant chains are involved, may act as temporary cross-linking points in the time scale of the 1H NMR experiments. In this condition only portions of the pendant chains would be detectable by the experiments, justifying the observed differences between proton relaxation experiments and the MFC results. To verify this presumption, we formulated a modification of the recursive calculations to estimate the amount of entanglements in which pendant chains are involved. If entanglements are taken into consideration, a very good agreement between theoretical mass fraction of pendant chains calculated by the modified MFC and experimental values determined from proton relaxation is obtained.