Pulsed-field gradient nuclear magnetic resonance as a tool for ...

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PRICE
into another Ž 123, 124 . . Exact solutions to Eq.
119 are known only for some very simple cases
e.g., Refs. Ž 41, 124, 125. and generally, Eq. 119 must be evaluated numerically Ž 122, 124 . .
CONCLUDING REMARKS
Pulsed-field gradient experiments provide a
straightforward means of obtaining information
on the translational motion of nuclear spins.
However, the interpretation of the data is complicated
by the effects of restricting geometries and
the mathematical modeling required to account
for this becomes nontrivial for anything but the
simplest of geometries. Generally, we have to
resort to numerical methods andor approximations
to model diffusion within restricted geometries,
and the type of approximation that we
choose should be consistent with our experimen-
tal conditions. For example, to use the SGP approximation
we must ensure that the condition
holds.
In the present article we have presented the
underlying concepts of how PFGs may be used to
measure diffusion. The mathematical modeling
required to extract information from the attenuation
of the echo signal on the diffusion process
and structural information in restricting geometries
was presented in some detail, and both
isotropic and anisotropic systems were considered.
However, the experimental aspects and
complications were largely ignored. Further, we
presented only simple examples of restricting geometries
and have barely mentioned any of the
many applications that PFG NMR can be applied
to such as measuring polymer dynamics, obtaining
diffusion and structural information in porous
media with more complicated restricted geometries
and measuring exchange.
Figure 12 Example of an effective diffusion ellipsoid calculated using Eq. 116 . The
parameters used in the simulation were 20 ms, D 0.6 10 9 m 2 s 1 , D 1.2
xx yy
10 9 m 2 s 1 , D 1.5 10 9 m 2 s 1 . The extremely anisotropic diffusion parameters were
zz
chosen to allow easy visualization of the ellipsoidal shape.