Multi-dimensional1H NMR nuclear Overhauser spectroscopy under magic angle spinning: theory and application to elastomers

Bimodal 1H Double Quantum Build-Up Curves by Fourier and Laplace-like Transforms on Aged Cross-Linked Natural Rubber

The ¹H DQ Fourier and Laplace-like spectra for a series of cross-linked natural rubber (NR) samples naturally aged during six years are presented and characterized. The DQ build-up curves of these samples present two peaks which cannot be described by classical functions. The DQ Fourier spectra can be obtained after a numeric procedure which introduces a correction time which depends less on the chosen approximation, spin-½ and isolated CH₂ and CH₃ functional groups. The DQ Fourier spectra are well described by the distributions of the residual dipolar coupling correlated with the distribution of the end-to-end vector of the polymer network, and with the second and fourth van Vleck moments. The deconvolution of DQ Fourier spectra with a sum of four Gaussian variates show that the center and the width of Gaussian functions increase linearly with the increase in the cross-link density. The Laplace-like spectra for the natural aged NR DQ build-up curves are presented. The centers of four Gaussian distributions obtained via both methods are consistent. The differences between the Fourier and Laplace-like spectra consist mainly of the spectral resolution in the favor of Laplace-like spectra. The last one was used to discuss the effect of natural aging for cross-linked NR.

Molecular dynamics parameter maps by 1H Hahn echo and mixed-echo phase-encoding MRI

Residual dipolar couplings and averaged correlation time maps in soft matter were obtained by mixed echo phase-encoding solid imaging (MIPSI). Use of the mixed echo in soft matter NMR imaging experiments has two crucial advantages: the signal intensity is recovered with a weak incoherence losses, and second, the intervals during which the phase-encoding evolution due to the magnetic field gradients takes place can be chosen to be much larger than with all other spin echo experiments and hence, a higher special resolution can be achieved. The parameter maps are compared to those obtained by the Hahn-echo phase-frequency encoding method. For both MRI methods the density operator formalism is applied in the average Hamiltonian approximation to describe the encoding of the spin echoes by the molecular motions. The results of preliminary experiments are presented.

Versatility of the dipolar filter selection: from 1H nuclear spin diffusion experiment to the measurement of nuclear Overhauser effect in homopolymer melts

Dipolar filters select 1H magnetization according to local dipolar dephasing, which corresponds to site mobility in systems with heterogeneous molecular mobility. Combined with a conventional exchange experiment, it is usually applied to polymeric samples exhibiting structures on the nanometer length scale associated with a strong dynamic contrast. There, the resulting 1H nuclear spin diffusion experiment yields the size of the structure. When the same experiment is applied to homopolymer melts exhibiting a weak dynamic contrast and dynamic heterogeneities on significant shorter length scales, the recorded magnetization decay is in agreement with decays expected from a heterogeneous nanostructure. However, dipolar filters actually can also select mobile parts of the repeat unit, e.g. the end of the alkyl side chains and the subsequent magnetization transfer then can occur via cross relaxation due to non coherent zero-quantum transitions (nuclear Overhauser effect, NOE). The difficulties of distinguishing these two cases are examined and it is demonstrated that NOE experiments exploiting magnetization selection via the dipolar filter allow quantifying the local dynamics of the side chains. This opens new possibilities for measurements of local dynamics in non isotopically labeled homopolymer melts.

Enhanced sensitivity to residual dipolar couplings of elastomers by higher-order multiple-quantum NMR

The homonuclear and heteronuclear residual dipolar couplings in elastomers reflect changes in the cross-link density, temperature, the uniaxial and biaxial extension or compression as well as the presence of penetrant molecules. It is shown theoretically that for an isolated methyl group the relative changes in the intensity of the homonuclear double-quantum buildup curves in the initial time regime due to variation of the residual dipolar coupling strength is less sensitive than the changes in the triple-quantum filtered NMR signal when considering the same excitation/reconversion time. For a quadrupolar nucleus with spin I=2 the sensitivity enhancement was simulated for four-quantum, triple-quantum, and double-quantum buildup curves. In this case the four-quantum build-up curve shows the highest sensitivity to changes of spin couplings. This enhanced sensitivity to the residual dipolar couplings was tested experimentally by measuring 1H double-quantum, triple-quantum, and four-quantum buildup curves of differently cross-linked natural rubber samples. In the initial excitation/reconversion time regime, where the residual dipolar couplings can be measured model free, the relative changes in the intensity of the four-quantum buildup curves are about five times higher than those of the double-quantum coherences. For the first time proton four-quantum coherences were recorded for cross-linked elastomers.

Analysis of Proton−Proton Transfer Dynamics in Rotating Solids and Their Use for 3D Structure Determination

A detailed analysis of proton-proton-transfer dynamics under magic angle spinning NMR is presented. Results obtained on model compounds are evaluated under different experimental conditions and NMR mixing schemes. It is shown that the resulting buildup rates can be interpreted in terms of internuclear proton-proton distances provided that an appropriate theoretical description is chosen. As demonstrated in two test applications, these dependencies can be used in the context of a three-dimensional structure determination in the solid state.

Solid-state NMR spectroscopy under periodic modulation by fast magic-angle sample spinning and pulses: a review

Fast magic-angle spinning (MAS) holds promise for new approaches to pulsed high-resolution NMR in solids where homogeneous interactions dominate. Prerequisite for developing new pulse methods is the understanding of signal encoding by spin interactions under MAS conditions and of interferences between MAS and pulses. This review discusses corresponding strategies and techniques in a coherent way with particular concentration on homonuclear decoupling techniques for line-narrowing in solids.