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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 powders and NMR of oriented samples is pointed out. [ABSTRACT FROM AUTHOR]

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 information about the type of reorientational motion—although at different time scales. Therefore, both methods nicely supplement each other. Some examples (two-, four-, and six-fold jumps of dimethylsulfone, hexamethylenetetramine, and hexamethylbenzene as well as rotational diffusion of polystyrene in its viscous state) are discussed explicitly, where the geometry and time scale of slow molecular reorientations are identified directly. [ABSTRACT FROM AUTHOR]

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 CH[SUB2] 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 CH[SUB2] 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 dynamic order parameter along the chains is evaluated. It exhibits the remarkably high value of 〈P[SUB2]〉 ≈ 0.13 for the carbon-carbon bond connecting the CH and the CH[SUB2] groups in polybutadiene in the uncross-linked copolymer melt and only slightly increases with the cross-link density. [ABSTRACT FROM AUTHOR]

We present a new multidimensional NMR exchange experiment, three dimensional difference correlated exchange spectroscopy (DICO), which allows one to extract detailed information about the time scale as well as the geometry of rotational processes simultaneously. In contrast to experiments presently available the geometric information specified by a dynamic order parameter is independent of a specific model. Among others full isotropisation can be directly seen from the spectrum via a symmetry criterion. We apply this method to study the chain motion of polystyrene slightly above the glass transition. The DICO spectra prove that a typical chain segment performs small angle fluctuations as well as large angle jumps which can neither be described as random jumps nor tetrahedral jumps. A typical jump angle can be estimated to be of the order of 30°-40°. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

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 displacements observed. The motional behavior and the conformational order of the side chains were also studied. This shows that the high frequency β process detected previously by dielectric spectroscopy indeed can be associated with side chain motions. Moreover evidence is presented that the axial motion of the discs is a cooperative process, where adjacent molecules within the column rotate in a correlated fashion without changing the conformation of the side chains in the immediate neighborhood of the core. [ABSTRACT FROM AUTHOR]

A two-dimensional (2D) exchange NMR (nuclear magnetic resonance) experiment with sample flip during the mixing time (direction exchange with correlation for orientation-distribution evaluation and reconstruction, DECODER) is presented, which allows investigation of molecular order in great detail. For anisotropic NMR interactions with axial symmetry (η=0), the features of the orientation distribution of certain molecular axes are reflected directly in the distribution of the intensity in the 2D spectrum. The orientation distribution in terms of two angles can be largely reconstructed by a simple rearrangement of the spectral intensity. Analogies between this NMR experiment and wide-angle x-ray scattering (WAXS) techniques for pole figure analysis are identified. Practical aspects of the DECODER method are considered in detail, e.g., sample orientations that are particularly suited for elucidating biaxiality with high resolution, or that are convenient in terms of sample preparation. Even with spectral overlap and for η≠0, the degree of order can be read immediately from the spectrum. Simulations and experimental 2H NMR spectra for deuterated polyethylene serve to exemplify the method. [ABSTRACT FROM AUTHOR]

Theory and application are described of a new rotor-synchronized 3D-NMR (three-dimensional nuclear magnetic resonance) experiment, that correlates molecular structure, order, and dynamics in partially oriented solids. General expressions for the sideband intensities in three frequency dimensions are developed for uniaxially ordered samples undergoing ultraslow molecular motions. For an isotropic powder the exchange pattern is confined to a single plane perpendicular to one of the frequency axes. For a partially ordered solid without exchange the sideband pattern is confined to a cross-diagonal plane. Sidebands in the full 3D cube result only if the residue giving rise to the signal is involved in both, molecular order and dynamics. The experiment, therefore, correlates these two properties and relates them to the chemical structure. Moreover, it offers a means to exploit the superior information about the geometry of the molecular motions provided by partially ordered samples under high resolution magic angle spinning (MAS) conditions. The technique is illustrated by 3D MAS spectra of highly oriented poly(oxymethylene), where strong positive and negative sidebands in the full 3D cube result from the helical jump motion. [ABSTRACT FROM AUTHOR]

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 conventional T1 data follows the WLF equation over 11 orders of magnitude, from 10-6 to 1000 s. It is shown that 2D exchange NMR and spin-lattice relaxation probe the α and the β process, respectively, of the chain dynamics in the glass transition region. [ABSTRACT FROM AUTHOR]

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 section 2H NMR spectra of chain deuterated linear polystyrene above its glass transition temperature are shown, which are compared with the model calculations. [ABSTRACT FROM AUTHOR]