Gradient Spin-Echo NMR

Consider the situation where the local magnetic field at position r is the sum of a uniform field and a nonuniform field Bg(r, t), that is, 

We will be principally concerned with the situation where the molecules move a sufficiently small distance that the field experienced by a particular spin i can be expressed in terms of the zeroth and first order term in a Taylor expansion, that is, 

This use of Eq. (13) has no meaning whenever the applied nonuniform magnetic field is on the order of or larger than the main magnetic field. While the small inhomogeneous field approximation will be useful in a wide class of experiments, we will find it useful to retain the more general treatment represented by Eq. (11). 

Our general Hamiltonian will be written in terms of spin operators 

Following the usual practice, we use the density matrix p(t) to describe the state of the system, where 

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Meerwall v., E. D. Self-Diffusion in Polymer Systems. Measured with Field-Gradient Spin Echo NMR Methods, Vol. 54, pp. 1—29. 

O-FID Oxygen-specific flame ionisation PGSE Pulsed gradient spin-echo (NMR)... 

The solvent mobility in atactic polystyrene-toluene solutions has been studied as a function of temperature using NMR. The local reorientation of the solvent was studied using deuterium NMR relaxation times on the deuterated solvent. Longer range motions were also probed using the pulsed-gradient spin-echo NMR method for the measurement of diffusion coefficients on the protonated solvent. The measurements were taken above and below the gel transition temperatures reported by Tan et al. (Macromolecules, 1983. 16, 28). It was found that both the relaxation time measurements and the diffusion coefficients of the solvent varied smoothly through the reported transition temperature. Consequently, it appears that in this system, the solvent dynamics are unaffected by gel formation. This result is similar to that found in other chemically crossed-linked systems. 

Umecky, T, Kanakubo, M., and Ikushima, Y., Self-diffusion coefficients of l-butyl-3-methylimidazolium hexafluorophosphate with pulsed-field gradient spin-echo NMR technique. Fluid Phase Equilib., 228-229, 329, 2005. 

Self-Diffusion in Polymer Systems, Measured with Field-Gradient Spin-Echo NMR Methods... 

Toonkool, P., Regan, D. G., Kuchel, P. W., Morris, M. B., and Weiss, A. S. (2001a). Thermodynamic and hydrodynamic properties of human tropoelastin. Analytical ultracentrifuge and pulsed field-gradient spin-echo NMR studies. / Biol. Chem. 276, 28042-28050. 

Abstract We use Nuclear Magnetic Resonance relaxometry (i.e. the frequency variation of the NMR relaxation rates) of quadrupolar nucleus ( Na) and H Pulsed Gradient Spin Echo NMR to determine the mobility of the counterions and the water molecules within aqueous dispersions of clays. The local ordering of isotropic dilute clay dispersions is investigated by NMR relaxometry. In contrast, the NMR spectra of the quadrupolar nucleus and the anisotropy of the water self-diffusion tensor clearly exhibit the occurrence of nematic ordering in dense aqueous dispersions. Multi-scale numerical models exploiting molecular orbital quantum calculations, Grand Canonical Monte Carlo simulations, Molecular and Brownian Dynamics are used to interpret the measured water mobility and the ionic quadrupolar relaxation measurements. 

A Multiscale Analysis of 1H Pulsed Gradient Spin-Echo NMR Measurements. 

Gao, P. and Fagerness, P., Diffusion in HPMC gels. I. Determination of drug and water diffusivity by pulsed-field-gradient spin-echo NMR, Pharmaceutical Research, Vol. 12, No. 7, 1995, pp. 955-964. 

Using pulsed field gradient spin echo NMR, Guering and Lindman [14] and, independently, Clarkson et al. [15] measured the self-diffusion coefficients of the components of microemulsions of sodium dodecyl sulfate (SDS), toluene, butanol, and NaCl brine. The results (Fig. 8) establish unequivocally the existence of bicontinous microemulsion. 

Diffusion coefficients derived from pulsed gradient spin echo NMR-studies show lower values for the encapsulated guest identical to those of the host, see Frish, L. Matthews, S. E. Bohmer, V. Cohen, Y. J. Chem. Soc., Perkin Trans. 2 1999, 669-671. 

Figure 5.1 Pulsed-gradient spin-echo NMR sequence for the measurement of self-diffusion coefficient.

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