We present proton-proton multiple-quantum investigations on a series of monomodal and strongly bimodal end-linked poly͑dimethylsiloxane͒ model networks. A robust pulse sequence characterized by a well-defined double-quantum Hamiltonian along with a specific normalization approach is used to obtain double-quantum build-up curves. These curves are analyzed in terms of the spin dynamics of a local subsystem of monomer-fixed spins, where analytical fitting functions yielding residual dipole-dipole coupling constants are derived on the basis of exact solutions provided by simulations. Further employing the novel experimental strategy of double-quantum preselection of elastically active network chains, it is shown that the network response is purely heterogeneous, and that the data can be analyzed in terms of distributions of local dynamic order parameters using different models. The results yield consistent proof that local chain order in bimodal networks obeys a linear mixing law of short-and long-chain components. The order parameter distribution in a long-chain monomodal network is found to be surprisingly narrow, with a rather high average order parameter. Implications on the validity of present theories used to explain order and dynamics in networks are discussed.

No abstract

We present a study of the structure of Tetra-PEG model networks, using proton multiple-quantum NMR at low field in combination with computer simulations. Tetra-PEG is a novel high-performance hydrogel designed by combination of two symmetric tetra-arm macromonomers. In contrast to conventional hydrogels, which are highly heterogeneous due to fixed concentration fluctuations, Tetra-PEG exhibits a much less heterogeneous microstructure as indicated by previous light and small-angle neutron scattering studies. Here, the local-scale connectivity inhomogeneities, i.e., the sol and dangling polymer chains as well as the typical network connectivity defects resulting from the AÀB reaction of four-arm macromonomers, are quantified experimentally for the first time, studying as-prepared Tetra-PEG hydrogels, cross-linked at different polymer concentrations and stoichiometries. To this end, we developed a novel approach for the analysis of double-quantum buildup curves consisting of well-distinguishable components with different segmental dynamic order parameters, benefitting from the superb large-scale homogeneity of the samples. As a model for each component we suggest different connectivity modes between the macromonomers-mainly regular single links and double links between individual stars as well as other network defects with lower order parameters. To support the model, we report results from computer simulations with the bond-fluctuation model, which confirm the concentrationdependent trends of the network and double-link fractions.

We present a quantitative study of local segmental order in vulcanized natural and butadiene rubber far above the glass transition. Network chain order is dependent on the density of cross-links and is here derived from proton homonuclear residual dipolar couplings measured by static multiple-quantum NMR spectroscopy at low field. On the basis of a reasonable model of local chain structure and fast, uniaxially symmetric local motions, spin dynamics simulations are used to investigate the relationship between the experimentally determined residual coupling and the order parameter of the polymer backbone. The model is verified by site-resolved determinations of inter-and intraresonance residual couplings at high field. For both types of rubber, it is found that the distributions of the chain order parameter are rather narrow and in all cases well explained by the local coupling topology, thus excluding distributions of end-to-end separations or network chains lengths as important sources of broadening. This suggests that the NMR-detected order phenomenon cannot simply be captured with single-chain concepts. For natural rubber and poly(dimethylsiloxane), the relationship of the cross-link densities derived from the NMR-determined order parameter and from Flory-Rehner swelling experiments is linear as expected, yet the prefactors differ from the prediction by factors of 2 in different directions. We discuss the implications and the validity of the various models and approximations used for data analysis in light of recent results from computer simulations.

The dynamics of the polymer matrix in filled rubbers is modified by the presence of solid particles. We used low-field proton NMR to investigate model filled samples consisting of a dispersion of grafted silica particles into an elastomeric matrix. Exploiting magic-sandwich echo experiments, we were able to determine the fraction of polymer with slower dynamics and to correlate it to the silica specific surface. The presence of immobilized polymer;most probably due to a gradient of glass transition temperature around the solid particles;is detected whether there is a covalent bond between the filler and the matrix or not. Moreover, the fraction of immobilized polymer decreases in similar ways with either an increase of the temperature or the addition of solvent. In the case of covalent bonds between the silica and the polymer, multiple-quantum experiments reveal that the cross-link density of the elastomer matrix is locally increased in the vicinity of the particles. This is an observation that was not made in any conventional filled elastomer system and it can be attributed to the good particle dispersion and the covalent links in our model samples.