Abstract
Self-diffusion or translational displacements of molecules as a consequence of Brownian motions [88] is to be distinguished from interdiffusion [104] of molecules of different species which are initially separated. Both phenomena can favorably be investigated by magnetic-resonance methods.
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Notes
The 90° — τ1 — 180° Hahn echo two-pulse sequence may be interpreted as a 90° — τ1— 90° — τ2 — 90° three-pulse sequence in the limit τ2 → 0.
Apart from propagator, the probability density for a displacement r may also be called Green’s function, i.e., the response to an initial distribution given by a delta function.
Note that in NMR diffusometry experiments carried out with unidirectional field gradients, only one displacement component, say x, is probed. The corresponding probability density is then \( p(x,t) = \frac{1}{{{{{(4\pi Dt)}}^{{ \frac{\hbox{$\scriptstyle 1$}}{\hbox{$\scriptstyle 2$}} }}}}}\exp \left\{ { - \frac{{{{x}^{2}}}}{{4Dt}}} \right\} \) where \( \int\limits_{{ - \infty }}^{{ + \infty }} {p(x,t)dx} = 1 \). Figure 18.1 shows representative displacement distributions as expected for water self-diffusion.
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© 1997 Springer-Verlag Berlin Heidelberg
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Kimmich, R. (1997). Survey of NMR Diffusometry. In: NMR. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60582-6_18
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DOI: https://doi.org/10.1007/978-3-642-60582-6_18
Publisher Name: Springer, Berlin, Heidelberg
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