Spin echo diffusion limits

The first direct spin-echo diffusion measurement in a polymer melt was reported by McCall, Douglass, and Anderson34) in low-molecular weight polyethylenes. Because of the limitations of the SGSE method the authors found themselves restricted (D > 1(T7 cm2/sec) to molecular weights M < 10 and to temperatures T above 130 °C. They observed an Arrhenius behavior ... 

This experiment has two limitations (a) nuclei with short T2 are difficult to be detected and (b) multiplets produce a distorted signal phase after n pulse which inverts the coupled spin states. Both limitations are partially overcome by the stimulated echo experiment (STE).64,65 The main difference with the experiment previously described is that the echo attenuation due to the diffusion competes with Tx rather than with T2. The equation analogous to Equation (13) is now ... 

By the pulsed field gradient spin echo method (1) it is possible to measure mean diffusion lengths ( /(l2)) for molecules in a given time interval in systems without a concentration gradient. The application of the method is limited to... 

The self-diffusion coefficients described below were measured by the pulsed-field technique proposed by Stejskal and Tanner. The pulse sequence applied is a modification of the classical Hahn spin-echo experiment for the determination of the spin-spin relaxation time,72- Fourier transformation of the second half of the spin-echo permits the simultaneous study of complex mixtures. The limit for the number of compounds that can be measured in one experiment is set solely by the requirement that there is at least one... 

Fig. 23 Variation of the diffusivity of n-alkanes in zeolite Na,Ca-A with the carbon number at 473 K as observed with different techniques [QENS spin-echo technique (NSE), 12 carbon atoms per cavity x PFG NMR, 1 molecule per cavity A, (more recent data), 2 molecules per cavity ZLC, limit of vanishing concentration , o (more recent data)]. From [176], with permission...

Abstract Neutron scattering was first used to derive the self-diffusivities of hydrocarbons in zeolites, but transport diffusivities of deuterated molecules and of molecules which do not contain hydrogen atoms can now be measured. The technique allows one to probe diffusion over space scales ranging from a few A to hundreds of A. The mechanism of diffusion can, thus, be followed from the elementary jumps between adsorption sites to Lickian diffusion. The neutron spin-echo technique pushes down the lower limit of diffusion coefficients, traditionally accessible by neutron methods, by two orders of magnitude. The neutron scattering results indicate that the corrected diffusivity is rarely constant and that it follows neither the Darken approximation nor the lattice gas model. The clear minimum and maximum in diffusivity observed by neutron spin-echo for n-alkanes in 5A zeolite is reminiscent of the controversial window effect . 

In contrast with chemical diffusion, the self- (or intra-or tracer-) diffusion of ions simply is the manifestation of Brownian motion. It can be visualized by labeling a small amount of ions and observing their displacement in an environment of nonlabeled ions of the same type. Nuclear magnetic resonance (NMR) spin-echo experiments use spin labeling radioactive tracers are used in closed capillary methods. At infinite dilution the self-diffusion of an ion X, is linked to its limiting ion conductivity Eq. (43), and its generalized mobility a>,, Eq. (15), (F = CoNa, Earaday constant) ... 

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