Siegfried Hafner

Solid-state nuclear magnetic resonance spectra of dipolar-coupled multi-spin systems under fast magic angle spinning

A general treatment of nuclear magnetic resonance (NMR) spectra under magic-angle spinning (MAS) conditions is provided that is applicable both to homogeneously and inhomogeneously broadened lines. It is based on a combination of Floquet theory and perturbation theory, and allows the factorization of the spin system response into three factors that describe different aspects of the resulting MAS spectrum. The first factor directly reflects the Floquet theorem and describes the appearance of sidebands. The other two terms give the integral intensities of the resulting sidebands and their line shapes and depend on the specific features of the considered interaction. The analytical form of these two factors is derived for multi-spin dipolar interactions under fast MAS. The leading term in the expansion of the integral intensities involves products of only two spin operators whereas the linewidths, which are found to be different for the different sideband orders, are determined predominantly by three-spin te...

Dipolar couplings and internuclear distances by double-quantum nuclear magnetic resonance spectroscopy of solids

The analysis of high-resolution double-quantum nuclear magnetic resonance spinning sidebands for measuring dipolar couplings and internuclear distances in dipolar solids is described. For this purpose, the response of a dipolar-coupled spin system in a rigid solid is investigated with respect to high-resolution multiple-quantum experiments using rotor-frequency synchronized pulse sequences. For isolated, magnetically equivalent spin-1/2 pairs, exact expressions for the double-quantum spinning-sideband patterns are derived. These patterns show spinning sidebands only at odd numbers of the rotor frequency. For longer excitation/reconversion cycles, the double-quantum spinning sidebands are sensitive to changes in the internuclear distances. Using this technique, the dipolar couplings for 13C spin pairs in double-labeled polyethylene were measured in crystalline and amorphous domains, respectively. In the former the dipolar coupling reflects the carbon–carbon distance, in the latter it is reduced due to mole...

Selective residual dipolar couplings in cross-linked elastomers by 1H double-quantum NMR spectroscopy

1H double-quantum (DQ) solid-state NMR spectroscopy under fast magic-angle spinning (MAS) is introduced as a new spectroscopic tool for the investigation of the structure and local chain dynamics of elastomers. Dipolar connectivities between the protons of the various functional groups can be directly established from the highly resolved DQ solid-state NMR spectra as is shown for a series of cross-linked poly(styrene-co-butadiene). More quantitatively, residual dipolar couplings within and between the functional groups are evaluated selectively from the build-up curves of the double-quantum signals in the limit of the spin-pair approximation. In particular, the CH-CH and the CH2-CH couplings of butadiene, which both act predominantly along the chain-segment direction, have been measured relative to the CH2 coupling. The total build-up intensity is correlated with the cross-link density.

Characterization of polymer networks using the dipolar correlation effect on the stimulated echo and field-cycling nuclear-magnetic resonance relaxometry

Chain dynamics in a series of styrene-butadiene rubbers (SBR) was studied with the aid of the dipolar correlation effect (DCE) and field-cycling NMR relaxometry (FCR). The typical time scales of the two techniques are t>10−4 s and t<10−3 s, respectively, and therefore complementary. The crosslink density of the polymer networks was varied in a wide range. In order to prevent sinusoidal undulations of the stimulated-echo attenuation curves due to spin exchange between groups with different chemical-shift offsets, the DCE of the samples was examined using a modified radio frequency pulse sequence with additional π pulses inserted in the free-evolution intervals. Residual dipolar couplings can thus be probed in samples where chemical-shift and dipolar interactions are of the same order. The dipolar correlations probed with the DCE in SBR networks turned out to exist on a time scale exceeding 300 ms. The short-time fluctuations (probed by FCR) and the long-time dynamics (probed by DCE) can be approached by po...

Multiple-pulse assisted line-narrowing by fast magic-angle spinning

Combined rotation and multiple-pulse experiments (CRAMPS) are reported that are performed under the conditions of fast magic-angle spinning. Quasi-static conditions, as are required for CRAMPS experiments, can be fulfilled approximately also for fast sample spinning conditions when windowless or semiwindowless sequences are applied. In order to allow direct detection for these cases also, appropriately timed detection windows are introduced without loss of resolution. In contrast to conventional CRAMPS experiments, high-speed MAS was found to play an important role also in the averaging of residual dipolar contributions. The resolution achieved in these first experiments is comparable to that of conventional CRAMPS experiments and the demands with respect to spectrometer hardware and tuning are much lower.

Spin dynamics under magic angle spinning by Floquet formalism

A new analytical method is presented for studying in a uniform way the spin dynamics in NMR experiments performed under the conditions of magic angle spinning. It was derived on the basis of the formalized Floquet theory and consists in transforming the Fourier-state representation of the NMR signal into an integral one. The integral representation proves to be well suited in combination with Rayleigh-Schrodinger perturbation theory for both the fast and the slow spinning regimes. The corresponding perturbation expansions can be readily extended to higher-order correction terms, which also allows the inclusion of more moderate spinning speeds. Explicit expressions of the perturbation series were derived for both spinning regimes and applied to the case of isolated dipolar-coupled spin-1/2 pairs for which the results can be compared with those obtained by the exact evaluation of the equation of motion.

Two-dimensional proton magnetization-exchange NMR spectroscopy in cross-linked elastomers

Solid‐state two‐dimensional proton magnetization‐exchange NMR is used to investigate intergroup residual dipolar couplings in a cross‐linking series of poly(styrene‐cobutadiene) elastomers. The magnetization‐exchange process between the CH and the CH2 group in the regime of short mixing time provides valuable insight regarding molecular order. A three‐spin model is employed, in which the CH and CH2 protons are considered to be coupled by residual dipolar interactions. The spin‐system response reflects well‐localized dipolar interactions. The time scale in which the exchange process takes place justifies these assumptions as well as the interpretation of various NMR relaxation experiments previously performed on this class of polymers. The residual intergroup dipolar couplings are measured along the average polymer‐chain direction and correlated with the dynamic storage modulus. It is shown that they are sensitive to both cross‐link points and nonpermanent geometric constraints of the chain motion. The dyn...

Magic echoes and NMR imaging of solids

Solid state NMR imaging techniques based on magic echoes are reviewed. The theoretical background of magic echoes in general and their spatial encoding in particular is treated. The magic-echo imaging pulse sequences presently in use are described and discussed. Particular emphasis is devoted to those techniques, which allow the incorporation of spectroscopic or parameter-selective information. The applicability of these methods for the investigation of materials is demonstrated and perspectives for materials science are outlined.

Slice-selective polarization transfer for localized solid-state NMR spectroscopy

A new method of spatial localization in solids using the high off-resonance sensitivity of heteronuclear polarization transfer is presented in theory and experiment. Application in imaging and volume-selective spectroscopy are discussed and test experiments to this end are reported.

Multi-dimensional 1H NMR Nuclear Overhauser Spectroscopy under Magic Angle Spinning: Theory and Application to Elastomers

The process of cross-relaxation between different protons (nuclear Overhauser effect) is investigated in soft solids by 2- and 3-dimensional NMR under the conditions of fast magic-angle spinning. The cross-relaxation rates are found to depend weakly on fast motions in the Larmor frequency range and strongly on slow motions of the order of the spinning frequency W R. Explicit expressions for the W R dependent cross-relaxation rates are derived for different motional models. These findings were tested experimentally on elastomers, i.e., on a cross-linking series of styrene-butadiene rubbers where the cross-relaxation was studied as a function of W R. Short mixing times as are required for extracting the relaxation rates could be realized conveniently using a pulsed magnetic-field gradient for coherence pathway selection. As in solution NMR, relative couplings between chemically resolved spins can be determined from the peak intensities. By combining cross-relaxation measurements with T 1 measurements, the d...