Diffusion line-shape analysis

The transition from single- to many-chain behavior already becomes obvious qualitatively from a line shape analysis of the NSE spectra (see Fig. 60) [116]. For dilute solutions (c = 0.05) the line shape parameter (3 is equal to about 0.7 for all Q-values, which is characteristic of the Zimm relaxation. In contrast, in semi-dilute solutions (e.g. c = 0.18), ft-values of 0.7 are only found at larger Q-values, whereas P-values of about 1.0, as predicted for collective diffusion [see Eq. (128)] are obtained at small Q-values. A similar observation was reported by [163]. 

Abstract As a non-invasive technique, NMR spectroscopy allows the observation of molecular transport in porous media without any disturbance of their intrinsic molecular dynamics. The space scale of the diffusion phenomena accessible by NMR ranges from the elementary steps (as studied, e.g., by line-shape analysis or relaxometry) up to macroscopic dimensions. Being able to follow molecular diffusion paths from ca. 100 nm up to ca. 100 xm, PPG NMR has proven to be a particularly versatile tool for diffusion studies in heterogeneous systems. With respect to zeolites, PFG NMR is able to provide direct information about the rate of molecular migration in the intracrystalline space and through assemblages of zeolite crystallites as well as about possible transport resistances on the outer surface of the crystallites (surface barriers). 

Diffusion measurements fall into two broad classes. Under macroscopic equilibrium, i.e. if the overall concentration within the sample remains constant, molecular diffusion can only be studied by following the diffusion path of the individual molecules ( microscopic measurement by quasielastic neutron scattering (QENS) [48,183,184], nuclear magnetic relaxation and line-shape analysis, PFG NMR) or by introducing differently labelled (but otherwise identical) molecules into the sample and monitoring their equilibration over the sample ( macroscopic measurements by tracer techniques) [185,186]. The process of molecular movement studied under such conditions is called self-diffusion. 

Application of continuous wave techniques and line shape analysis to wide-line n.m.r. spectra Cf D-xylose, D-mannose, D-glucose, D-fructose, and D-sorbose suggests that the lattice is effectively rigid in all except possibly D-fructose. Previously published C n.m.r. data for arabinosides and ribosides have been tabulated with correlation diagrams constructed in such a way that the data on new compounds can be used to assign the anomerlc configurations and ring size. Measurements of self-diffusion coefficients of carbo-... 

Although the characteristic functions for n-butane can be accurately fitted using two diffusion coefficients the fits with 2-butyne at low frequencies in Figure 15 are poor suggesting fliat some other factor may be additionally involved. Using NMR line shape analysis[21] 2-butyne sorbate molecules were found to perform a 90 flip motion with a correlation time 10" s which was not observed with n-butane molecules. This slower, molecular reorientation process may be reason for the poor fit at low frequencies. 

Line Shape Analysis for Nitroxide Spin Probes. Nitroxide radicals as spin probes and labels are useful for the determination of the motional mechanism, rotational correlation time, to, and local polarity. Figure 2a demonstrates that the relative line widths and line heights depend on the rotational correlation time to, which is inversely proportional to the diffusion constant of rotational diffusion. 

EPR Line shape analysis of nitroxide undergoing jump diffusion 79Mor2... 

Using dynamic solid-state CP MAS NMR spectroscopy, the kinetics of the degenerate intermolecular double and quadruple proton and deuteron transfers in the cyclic dimer of N labelled polycrystalline 3,5-diphenyl-4-bromopyrazole (DPBrP) and in the cyclic tetramer of N labelled polycrystalline 3,5-diphenylpyrazole (DPP) have been studied in a wide temperature range at different deuterium fractions in the mobile proton sites. Rate constants were measured on a millisecond time scale by line shape analysis of the doubly N labelled eompounds and by magnetisation transfer experiments on a second timescale of the singly N labelled compounds in order to minimise the effeets of proton-driven N spin diffusion. The Arhenius curves of all processes were found to be nonlinear and indicated tunneling processes at low temperatures. In a preliminary analysis, they were modelled in terms of the Bell-Limbach tuimeling model. 

Internal and overall motions that take place on a dynamic scale from 10 to 10 s can affect the line shape of NMR powder spectra. This is often the case for phenyl ring rotations or chain isomeriza-tions in polymeric liquid crystals and for rotational diffusion in discotic mesophases. Line shape analysis allows different types of motions to be discriminated and the relative kinetic parameters to be obtained. Moreover multidimensional exchange NMR can be applied to characterize molecular details of dynamical processes when the correlation times range between 10 and 10 s. 

The steady-state methods involve theoretical analysis of magnetic resonance spectra observed under steady-state conditions. This typically involves assumptions regarding the adequacy of magnetic resonance line shape theory, some model for molecular motions and distances of closest approach on collision, and a comparison of calculated spectra for various assumed diffusion constants, and observed spectra. In general, the agreement between diffusion constants calculated using the transient and steady-state methods has been excellent. 

We emphasize the line shape problem perhaps a little more than usual in the spectroscopic literature. Collision-induced spectra have little structure. Yet, the diffuse line and band spectra extend over wide frequency bands and must often be subtracted, say from the complex spectra of planetary or stellar atmospheres, for a more detailed analysis of other, less well known components. The subtraction requires accurate knowledge of the profile and its variation with temperature, composition, etc., often over frequency bands of hundreds of cm-1. 

A different approach to probe the ion-neutral potential involves the analysis of collision-broadened ion cyclotron resonance line shapes. For ions undergoing elastic collisions, the power absorption curve is Lorentzian in shape with a half-width at half-maximum equal to the collision frequency (J, which is then simply related to the reduced collision frequency, the diffusion cross section, and the ion mobility. For a series of nonreactive alkyl cations in methane, excellent agreement is found between experimental values for these quantities and theoretical values predicted from the Langevin model.H Unexpectedly, this finding may be interpreted to suggest that other mechanisms for collision broadening, namely inelastic collisions and, specifically, collisions involving complex formation, appear to be unimportant. ... 

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