H. W. Spiess

Deuteron two-dimensional exchange NMR in solids

Abstract The deuteron two-dimensional exchange experiment for the study of slow molecular motions in polycrystalline and amorphous solids is presented. A pair of four-pulse sequences for obtaining pure phase 2D spectra of a spin I = 1 system and phase cycles for minimizing artifacts are derived from spin dynamics calculations. A comprehensive description of the experiment and the 2D data processing is given. The information content of 2D exchange spectra of powders is discussed. For discrete jump motions, 2D powder spectra exhibit characteristic ridge patterns originating from the singularities of the 2D lineshape. From the geometry of such ridge patterns the angles of reorientation of the electric field gradient tensors can be determined directly, thus yielding information about the type of motion. The method is illustrated by two examples: the two-site jump of dimethyl sulfone and the six-site jump of hexamethylbenzene.

DYNAMICS OF MOLECULAR REORIENTATIONS: DIRECT DETERMINATION OF ROTATIONAL ANGLES FROM TWO-DIMENSIONAL NMR OF POWDERS

Abstract Two-dimensional solid-state deuteron NMR spectroscopy has been applied to study rotational motions in powders. In general, tensorial interactions give rise to powder patterns producing 2D exchange signals with characteristic ridges which manifest the motional mechanism in a model-independent fashion. For deuterons in particular, the angles through which the molecules rotate are read directly from elliptical ridges in the 2D spectrum. Experimental data on the two-site exchange in dimethylsulphone are given as well as theoretical spectra for different types of molecular motion.

Two‐dimensional exchange NMR of powder samples. II. The dynamic evolution of two‐time distribution functions

Theoretical as well as experimental examples concerning the evolution of the two‐time distribution S2‖0 (ω1,ω2 ;tm) as a function of the mixing time tm are presented, where S2‖0 is identical with the two‐dimensional (2D) absorption spectrum rendered by 2D exchange NMR spectroscopy of static powder samples. The model calculations comprise standard models like isotropic rotational diffusion or overall isotropic reorientation combined with discrete internal rotational jumps to simulate the chain dynamics of polymers. In any case, the 2D spectrum directly reflects the main aspects of the underlying motional mechanism. An axially symmetric coupling (η=0) between spin and lattice is assumed throughout. Thus, the angular information contained in a 2D spectrum is completely specified by a one‐dimensional jump angle distribution supplied with each spectrum. In connection with the simulations the numerical mapping of a discrete distribution function into a space of new variables is discussed. In the experimental se...

Dynamics of molecular reorientations: Analogies between quasielastic neutron scattering and deuteron NMR spin alignment

The analogies between incoherent quasielastic neutron scattering and deuteron spin alignment in studying single particle reorientations are pointed out. Quasielastic neutron scattering measures the full van Hove correlation function for correlation times shorter than 10−8 s. Spin alignment represents an orientational single particle function for correlation times longer than 10−4 s. The analogy is based on the fact that geometrical information is obtained in both methods by manipulation of an appropriate phase factor. In neutron scattering this phase factor is Q⋅a in momentum space, where Q is the momentum transfer and a is a jump length. In spin alignment the phase factor is δQ⋅τ1 in time space where δQ specifies the strength of the quadrupole coupling and τ1 is a pulse spacing defining the evolution period. It is shown that the measurements of the elastic incoherent structure factor as a function of Q⋅R and the spin alignment echo height as a function of δQ⋅τ1, respectively, yields largely equivalent in...

Two‐dimensional exchange NMR of powder samples. I. Two‐time distribution functions

A systematic description of the two‐dimensional (2D) NMR exchange experiment for studying molecular motions in static powder samples is presented in terms of two‐time distribution functions. Various angular distributions and their transformation to the NMR frequency domain yielding 2D absorption spectra are discussed. The concept of jump angle distributions is introduced. General and isotropic reorientation as well as different symmetries of the tensorial interaction between spin and lattice are distinguished in the analysis. Special attention is directed to the question, to what extent can angular information be reextracted from a 2D exchange spectrum without referencing any model of reorientation. For tensorial interactions of axial symmetry, projections of the 2D spectrum are also calculated and their usefulness is compared to that of the complete 2D spectra. The close relationship between the dynamic exchange experiment and several static NMR experiments like 2D separated local field spectroscopy of p...

Two‐dimensional exchange nuclear magnetic resonance of powder samples. III. Transition to motional averaging and application to the glass transition

The two‐dimensional (2D) exchange nuclear magnetic resonance (NMR) experiment is applied to study ultraslow as well as faster motions in powdered solids. The theoretical framework required for the simulation of 2D exchange of the faster motions, and for the evaluation of the experimental data, is developed. Calculations are presented for two standard models: two‐site jump and isotropic rotational diffusion. For discrete jump motion, anisotropic spin‐lattice relaxation during the mixing time is also considered. The resulting, simulated 2D line shapes show new characteristics in the intermediate dynamic range. Experimental data are presented for two‐site exchange in the model compound polycrystalline dimethylsulphone. The technique is then applied to study the chain dynamics of linear polystyrene in the glass transition range. Close to Tg the correlation times extracted from 2D exchange NMR exhibit strong non‐Arrhenius behavior. This data together with correlation times obtained at higher temperatures from ...

Two-dimensional magic-angle-spinning NMR of partially ordered systems

Abstract A new two-dimensional NMR experiment is presented, which, when applied to rotor-synchronised magic-angle-spinning spectra of partially ordered solids, gives information both on the chemical shielding tensor orientation and on the degree of order in the sample, e.g., in partially ordered synthetic or biopolymers. Application of the experiment is demonstrated using samples of highly oriented polyethylene.

Transient States in [2 + 2] Photodimerization of Cinnamic Acid: Correlation of Solid-State NMR and X-ray Analysis

13C-CPMAS and other solid-state NMR methods have been applied to monitor the solid-state reactions of trans-cinnamic acid derivatives, which are the pioneer and model compounds in the field of topochemistry previously studied by X-ray diffraction, AFM, and vibrational spectroscopy. Single-crystal X-ray analyses of photoirradiated alpha-trans-cinnamic acid where the monomers are arranged in a head-to-tail manner have revealed the formation of a centrosymmetric alpha-truxillic acid photodimer. For a centrosymmetric dimer, however, two cyclobutane carbon signals and one carbonyl carbon signal were expected apart from other aromatic carbon signals. Instead, four cyclobutane and two carbonyl carbon signals were observed suggesting the formation of a non-centrosymmetric photodimer. Removing hydrogen bonds from the system by esterfication of alpha-truxillic acid yield a centrosymmetric photodimer. Careful analysis of the obtained products via solid-state NMR clearly showed that the observed peak splittings in the 13C-CPMAS spectra did not originate from packing effects but rather result from asymmetric hydrogen bonds distorting the local symmetry. Further evidence of this rather dynamic hydrogen-bonding stems from high-temperature X-ray data revealing that only the joint approach of both X-ray analysis and solid-state NMR at similar temperatures allows for the successful characterization of dynamic processes occurring in topochemical reactions, thus, providing detailed insight into the reaction mechanism of organic solid-state transformations.

Two‐dimensional exchange nuclear magnetic resonance of powder samples. IV. Distribution of correlation times and line shapes in the intermediate dynamic range

The two‐dimensional (2D) exchange nuclear magnetic resonance (NMR) experiment is applied to study ultraslow as well as faster chain motions in amorphous polymers in the glass transition range. Acquisition of the time domain data with a four‐pulse sequence leads to new characteristics in the corresponding 2H 2D line shapes if the correlation times of the motion are in the intermediate dynamic range. From the asymmetric 2D line shapes, the width of the correlation time distribution can be determined with higher accuracy than through conventional 1D NMR methods. Experimental data are presented on two amorphous polymers—atactic polypropylene and cis‐1,4‐polyisoprene—and are analyzed in terms of isotropic rotational diffusion. Deviations from this simple model due to the presence of conformational transitions within the polymer backbone are detected. Close to Tg, the mean correlation times extracted from 2D exchange NMR exhibit strongly nonArrhenius behavior usually described by the Williams–Landel–Ferry (WLF)...

Molecular dynamics at the glass transition: One dimensional and two dimensional nuclear magnetic resonance studies of a glass‐forming discotic liquid crystal

The molecular dynamics of the aromatic core as well as the hydrocarbon side chains have been studied in a new kind of glass‐forming discotic liquid crystal, based on a triphenylene core. It serves as a model compound in which only a limited number of degrees of freedom is activated at the glass transition. Slow motion with non‐Arrhenius temperature dependence (α process) is associated with the axial motion of the discs around the column axis. The geometry of this rotation is found to be neither a simple threefold jump as suggested by the pseudo threefold symmetry of the substituted triphenylene core nor does it correspond to small‐step rotational diffusion, established as a prominent feature of the rotational motions of polymers at the glass transition. Instead ill‐defined angular displacements with pseudo threefold symmetry are detected by two‐dimensional exchange NMR. A simple model combining small‐step diffusion and rotational jumps is presented that quantitatively accounts for the angular displacement...