Hahn spin echoes in porous
media
with large internal fields
NMR dephasing behavior of the nuclear spins of a fluid confined in
a porous material can be investigated by Hahn spin echoes. Previous
experimental
results on water in a magnetically doped clay have shown a nonmono
exponentially
decaying magnetization, which can be understood neither by the known
dephasing
rate of freely diffusing spins in a uniform gradient nor by spins
diffusing
in a restricted geometry. For a better understanding of NMR
measurements
on these systems, a systematic survey was performed of the various
length
scales that are involved. The standard length scales for the situation
of a uniform gradient are diffusing length, structural length and
dephasing
length. We show that for a nonuniform gradient, a new length scale has
to be introduced: the magneticfield curvature length. When a particle
diffuses less than this length scale, it experiences a local uniform
gradient.
In that case the socalled Local Gradient Approximation (LGA) can
describe
the spinecho decay. When a particle diffuses over a longer distance
than
the structure length, the spinecho decay can be described by the
motional
averaging regime. For both regimes, scaling laws are derived. We have
used
a randomwalk model to simulate the dephasing effect of diffusing spins
in a spherical pore in the presence of a magnetic dipole field. By
varying
the dipole magnitude, situations can be created in which the dephasing
behaviour scales according to the motional averaging regime or
according
to the LGA regime, for certain ranges of echo times. Two model systems
are investigated: a spherical pore in the vicinity of a magnetic point
dipole and a spherical pore adjacent to a magnetic dipolar grain of the
same size as the pore. The simulated magnetization decay curves of both
model systems confirm the scaling laws, see figure 1.
Figure 1 – The dephasing rate Rd as a function
of the magnetic dipole strength for three pore sizes.
The solid lines
represent the scaling laws for the motional averaging regime (slope=2)
and the LGA situation (slope=2/3).
The LGA, characterized by a nonmonoexponential magnetization
decay,
is also investigated by calculating the spatially resolved
magnetization
in the pore, see figure 2. For this regime, the magnetization is found
to be inhomogeneously distributed within the pore, whereas it is
homogeneously
distributed in the motional averaging regime.
Figure 2 – The isomagnetization
surface M0 /2
for four successive spinecho times.
The magnetic dipole (m
=10^14 Am^2) is situated
at
the top of the pore with a radius of 3 mm.

An extensive description can be found in:
R.M.E. Valckenborg, H.P. Huinink, J.J. v.d. Sande, and K. Kopinga,
Random walk simulations of NMR dephasing effects due to uniform
magnetic
field gradients in a pore, Phys. Rev. E. 65, 021306
(2002)
R.M.E. Valckenborg, H.P. Huinink and K. Kopinga; NMR Dephasing
Effects
due to a magnetic dipole in a spherical pore, Journal of Chemical
Physics
118,
32433251 (2003)
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