Field gradient diffusion, measurements

Mitra, P. P., and Halperin, B. I. (1995). Effects of finite gradient pulse widths in pulsed field gradient diffusion measurements. J. Magn. Reson. A 113, 94-101. 

Figure 3. High resolution proton NMR spectra of cheese, obtained by application of a Hahn spin echo pulse sequence with and without field gradient pulses. Measurements were performed on a Bruker MSL-300 spectrometer, operating at 300 MHz. The field gradient unit used with this spectrometer was home-built and the strength was calibrated to 0.25 T/m, using a 1-octanol sample for which the diffusion coefficient is known at several temperatures.

Diffusional motion. Many rotational and translational diffusion processes for hydrocarbons within zeolites fall within the time scale that is measurable by quasielastic neutron scattering (QENS). Measurements of methane in zeolite 5A (24) yielded a diffusion coefficient, D= 6 x lO" cm at 300K, in agreement with measurements by pulsed-field gradient nmr. Measurements of the EISF are reported to be consistent with fast reorientations about the unique axis for benzene in ZSM-5 (54) and mordenite (26). and with 180 rotations of ethylene about the normal to the molecular plane in sodium zeolite X (55). Similar measurements on methanol in ZSM-5 were interpreted as consistent with two types of methanol species (56). 

JE Tanner. Use of a Pulsed Magnetic-field Gradient for Measurements of Self-diffusion by Spin-Echo Nuclear Magnetic Resonance with Applications to Restricted Diffusion in Several Tissues and Emulsions. PhD dissertation, University of Wisconsin, 1966. 

The diffusion coefficients of water are in the range of 3.5 — 9.8 x 10 cm /s, which are of the same order of magnitude as the experimental value of about 2 X 10 cm /s measured by pulsed field gradient diffusion NMR [194]. Comparing this with the diffusion coefficient of 2.6 x 10 cm /s in a pure SPC/E water system, one can conclude that in the PSS/PDADMA PECs under study the water molecules diffuse about two orders of magnitude slower than in the pure water system. Therefore, the obtained results of the water diffusion lead to the same conclusion as our dielectric measurements water molecules inside PE mixtures exhibit a slow dynamics when compared to water molecules in a bulk environment. 

Hi) Use of pulse field gradients to measure molecular diffusion rates, particle and pore size distribution, and homogeneity of mixing (at low fields 1-10 MHz mainly for QC) and (iv) Peak ratio in low-field solution-state NMR spectra. 

Polymer concentration and temperature effects on solvent self-diffusion were examined by Pickup and Blum(25), who made pulsed-field-gradient NMR measurements on toluene 270 kDa polystyrene. Figure 5.2 shows representative measurements. At each temperature, D (c) of the solvent is a simple exponential for c < 0.4 (weight fraction) and a stretched exponential at larger c. The slopes of the exponentials as seen in the figixre are very nearly the same at all T, but v of the larger-c form increases with increasing T. 

We finish this section by comparing our results with NMR and incoherent neutron scattering experiments on water dynamics. Self-diffusion constants on the millisecond time scale have been measured by NMR with the pulsed field gradient spin echo (PFGSE) method. Applying this technique to oriented egg phosphatidylcholine bilayers, Wassail [68] demonstrated that the water motion was highly anisotropic, with diffusion in the plane of the bilayers hundreds of times greater than out of the plane. The anisotropy of... 

There are a number of NMR methods available for evaluation of self-diffusion coefficients, all of which use the same basic measurement principle [60]. Namely, they are all based on the application of the spin-echo technique under conditions of either a static or a pulsed magnetic field gradient. Essentially, a spin-echo pulse sequence is applied to a nucleus in the ion of interest while at the same time a constant or pulsed field gradient is applied to the nucleus. The spin echo of this nucleus is then measured and its attenuation due to the diffusion of the nucleus in the field gradient is used to determine its self-diffusion coefficient. The self-diffusion coefficient data for a variety of ionic liquids are given in Table 3.6-6. 

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

Johnson et al. [186] measured diffusion of fluorescein-labeled macromolecules in agarose gels. Their data agreed well with Eq. (85), which combined the hydrodynamic effects with the steric hindrance factors. Gibbs and Johnson [131] measured diffusion of proteins and smaller molecules in polyacrylamide gels using pulsed-field gradient NMR methods and found their data to fit the stretched exponential form... 

Hence, a series of measurements with several Tcp values will provide a data set with variable decays due to both diffusion and relaxation. Numerical inversion can be applied to such data set to obtain the diffusion-relaxation correlation spectrum [44— 46]. However, this type of experiment is different from the 2D experiments, such as T,-T2. For example, the diffusion and relaxation effects are mixed and not separated as in the PFG-CPMG experiment Eq. (2.7.6). Furthermore, as the diffusion decay of CPMG is not a single exponential in a constant field gradient [41, 42], the above kernel is only an approximation. It is possible that the diffusion resolution may be compromised. 

E. O. Stejskal, J. E. Tanner 1965, (Spin diffusion measurements Spin echoes in the presence of a time-dependent field gradient),/. Chem. Phys. 42 (1), 288—292. 

Fig. 4.5.5 Pulsed field gradient sequences to obtain velocity and diffusion data (a) spin-echo (PGSE) and (b) stimulated-echo (PGSTE). The application of imaging gradients C Gy and Gz allows the measurement of velcocity maps and spatially-resolved diffusion coefficients and size distribution in emulsions.

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