Chain Order and Cross-Link Density of Elastomers As Investigated by Proton Multiple-Quantum NMR

Abstract

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.

NMR Reveals Non‐Distributed and Uniform Character of Network Chain Dynamics

“…Note that the proton dipolar reference value needed to convert D ress into S b suffers less from such changes in the model, due to a balance of multiple intra-and inter-group couplings along the backbone. [35] In any way, our qualitative argument is not affected, as the line shape in Figure 4(b) is the only one that does give a good match with the experiment after scaling and broadening. The super-Lorentzian line in Figure 4(d) can by no means describe the experimental data.…”

“…[32,33] The corresponding data and results discussed in this paper were published before, and the reader is referred to the respective literature for details. [33,35,46] In short, we used a dedicated MQ pulse sequence of Baum and Pines, which is applied to initial z magnetization twice for equal times t DQ , first for the excitation of mainly DQ coherences, and then their reconversion into final z magnetization that is detected after a final 90 8 pulse. Phase cycling of either the excitation or the reconversion block is used to filter out either the DQ coherences or a reference signal that comprises all signals that do not contribute to DQ coherences.…”

“…[33] are summarized in Figure 2 of these curves can be performed by using semi-analytical build-up functions that are reviewed in ref. [32,35] One can either use build-up functions derived on the basis of specific distribution models such as a Gaussian distribution, or a gamma distribution according to Equation (7). A third option is to use a numerical Tikhonov regularization procedure to estimate the distribution without assumptions on the shape.…”

Mechanical properties and cross-linking structure of cross-linked natural rubber

“…The magnetic dipole-dipole interaction of the cross-linked natural rubber was eliminated using the FMAS probe, with a rate 420 kHz. [8][9][10][11][12][13][14] The field-gradient FMAS probe enabled the application of various pulse sequences, such as distortionless enhancement by polarization transfer (DEPT), attached proton test (APT) and two-dimensional correlation measurements, to solid-state NMR spectroscopy. Moreover, the fieldgradient FMAS probe enabled the measurement of inverse correlations between 1 H and 13 C to detect the small signals from the small amounts of the cross-linking junctions, that is, the use of techniques such as heteronuclear multiple quantum correlation, heteronuclear single quantum correlation and heteronuclear multiple bond correlation.…”

Molecular weight distributions of irradiated siloxane-based elastomers: A complementary study by statistical modeling and multiple quantum nuclear magnetic resonance

“…The caveats and limitations of MQ-NMR-derived distributions have been discussed in detail elsewhere [28,30] and will not be repeated here, except to note that the uncertainly associated with distributions for p greater than 200 (roughly the degree of polym erization at M e ) and less than 10 is relativ ely large. This issue results from a combination of difficulties, including fitting faithfully MQ-NMR data in the plateau region (i.e., long MQ excitation times) and the inability to sufficiently sample at short excitation tim es.…”