Precise dipolar coupling constant distribution analysis in proton multiple-quantum NMR of elastomers

Abstract

In this work we present an improved approach for the analysis of (1)H double-quantum nuclear magnetic resonance build-up data, mainly for the determination of residual dipolar coupling constants and distributions thereof in polymer gels and elastomers, yielding information on crosslink density and potential spatial inhomogeneities. We introduce a new generic build-up function, for use as component fitting function in linear superpositions, or as kernel function in fast Tikhonov regularization (ftikreg). As opposed to the previously used inverted Gaussian build-up function based on a second-moment approximation, this method yields faithful coupling constant distributions, as limitations on the fitting limit are now lifted. A robust method for the proper estimation of the error parameter used for the regularization is established, and the approach is demonstrated for different inhomogeneous elastomers with coupling constant distributions.

Linking Network Microstructure to Macroscopic Properties of Siloxane Elastomers Using Combined Nuclear Magnetic Resonance and Mesoscale Computational Modeling

“…Indeed, these data are consistent with previous observations for a chain molecular weight ratio of 20 (the present materials have a ratio of 16); 32 and only for more disparate parent chain lengths (with a ratio on the order of 60) has a distinct bimodality in RDC been observed. 31 …”

Effect of entanglements in the microstructure of cured NR/SBR blends prepared by solution and mixing in a two-roll mill

“…5 shows the distributions obtained after the numerical inversion procedure of I nDQ for pure samples based on NR and SBR, respectively. This regularization analysis is able to discriminate between located network heterogeneities with phase separated morphology and randomly (homogeneously) distributed network heterogeneities as it has been demonstrated [31]. The studied rubber blends show a phase separated morphology (see TEM images in Fig.…”

“…Normalization procedure applied to the double quantum intensity (I nDQ ) effectively separates the effect of temperature dependent dynamics from the time-independent effect of network structure. The subsequent analysis of I nDQ by using a numerical inversion procedure based on a modified Fast Tikhonov Regularization [31], has been used to obtain a quantitative picture of the actual distribution function of residual couplings. Regularization procedure and data analysis for NR and SBR samples were widely explained in a cursory way elsewhere [16][17][18][19]21,31].…”

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

“…In these works, a "bu ild-up" of thes e multiple qu antum (MQ) coherences is measured through a suitable NMR experim ent, and the RDC distrib ution is typically ex tracted from this data in a model-free way using T ikhonov regularization software, FTIKREG [20]. This program is able to derive a series of possible normalized RDC distributions that would m anifest the observed NMR response; and through a detail ed statistical treatment of many such distributions, a "m ost likely" candidate can be chosen [27].…”

“…Multiple quantum nuclear m agnetic resonance (MQ-NMR) has been used with much success over the past decade to reveal detailed information on polymer dynamics, microstructure, and degradation [20][21][22][23][24][25][26][27]. In m any of these studi es, relative changes in polym eric properties are tracked in c onsiderable detail, a llowing for the extraction and the id entification of otherwise subtle or invisible chem ical and physical pheno mena.…”