Cross-Link Density Estimation of PDMS Networks with Precise Consideration of Networks Defects

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Abstract

Two series of randomly cross-linked poly(dimethylsiloxane) (PDMS) networks with systematically varying and well-defined dangling chain and defect content were investigated by 1H double-quantum low-field NMR (DQ NMR), equilibrium swelling, and high-resolution magic-angle spinning NMR (MAS NMR) experiments in order to obtain information about the absolute molecular weight of the polymer chains between two cross-links, Mc, and its distribution. A comparison of the experimental results from swelling and DQ NMR experiments with the results of Miller–Macosko calculations, based upon the reaction turnover determined by MAS NMR, clarifies the importance of a precise estimation of the defect fraction of the polymer network for a reliable determination of Mc. In order to properly account for network defects in the evaluation of equilibrium swelling as well as DQ NMR experiments, we use the elastically effective polymer volume fraction ϕp,el (that can be obtained from DQ NMR or simple Hahn echo experiments on samples swollen in deuterated solvent) and the variable weight-averaged functionality fwa of the cross-links taken from Miller–Macosko calculations. On the basis of the dependence of the so-obtained Mc on fwa, we are able to confirm the validity of the phantom model of rubber elasticity, and find good agreement between the results from the different methods. Small deviations only pertain to a proportionality factor different from unity, which for the case of equilibrium swelling is attributed to the shortcomings of the Flory–Rehner theory. We further address the quantitative interpretation of the residual dipolar coupling constant as the central result of DQ NMR on dry samples, which is confirmed to be proportional to the inverse Mc, but is also subject to systematic errors.

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