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1
An R1 Distribution Study of Hydrated Randomly
Close Packed Synthetic Soils
C.L. Bray1, S. Iannopollo1, G. Ferrante3, N.C.
Schaller2, D.Y. Lee1, J.P. Hornak1 1 Magnetic
Resonance Laboratory and 2Computer Science
Department, RIT, Rochester, NY 14623 USA 3 Stelar
s.r.l, Mede (PV) 27035, Italy
Motivation The relationship between pore size and
the NMR spin-lattice relaxation rate (R1) has
been the focus of many studies.1,2 We are
interested in the relationship between the
particle size distribution in hydrated soils and
the proton R1 of the water within voids between
the particles. An earlier study displayed
biexponential R1 behavior in some natural soil
samples.3 This NMR study examines the R1
distribution of water in hydrated randomly close
packed4 synthetic soils as a function of particle
diameter (d) and magnetic field strength.
Results Discussion A mono-modal R1 distribution
was obtained for all particle diameters and field
strengths. At 300 MHz, where the largest range
of d values were studied and the most repetitions
performed, R1 values increased with decreasing
particle diameter from the bulk water value at
large particle diameters to a value of 1.36 s-1
at the smallest diameter. (See Fig. 1.) A
similar trend was seen at 10, 1, and 0.01 MHz.
These results are consistent with a fast exchange
between structured and bulk water environments
where the structured to bulk water fraction
increases as particle diameter decreases. R1
values increase with decreasing field strength as
expected.
Methods Sample Preparation Mono-dispersed glass
bead samples (Quackenbush, Crystal Lake, IL, and
Whitehouse Scientific, Ltd., Chester, UK) ranging
from 0.025 lt d lt 2 mm were cleaned with 2 molar
KOH followed by multiple rinses with 18 MW water.
Beads were placed in either 5 mm or 1 cm
diameter NMR tubes, and hydrated with the 18 MW
water. Samples were centered in the RF coil and
occupied less than 90 of the RF coil length to
minimize variation in the rotation angle across
the sample. 300 MHz Acquisitions Proton NMR
spectra were recorded at 23 ºC using DRX-300
(Bruker, Billerica, MA) NMR spectrometer. An
inversion recovery sequence was used at 300 MHz.
A logarithmic distribution of 127 inversion time
values between 25 ms lt TI lt 15s, with the denser
sampling at low TI values,6 a 15s repetition
time, and eight phase cycling averages per TI
value were used. Magnetization recovery curves
were produced from the area of the water peak.
The TI15 s point was repeated twice, once at the
beginning and end of the acquisition, to detect
drift during the 5 hr acquisition. Relaxation
curves with drift were discarded. Field Cycling
Acquisitions Field cycling studies were performed
at 0.01, 1.0, and 10.0 MHz using a Spinmaster
FFC-2000 (Stelar, Mede, Italy) NMR spectrometer
using the standard field stepping procedure.5
The same logarithmic distribution of 127 stepping
time values between 25 ms lt TI lt 15s, a 15s
repetition time, and eight phase cycling averages
per TI value were used. Analysis All
magnetization recovery curves were converted to
exponential decays with an intentional 5 DC
offset. The distribution of R1 between 1x10-4
and 1x104 s-1 was estimated using CONTIN.7 The
5 offset converted the any uncertainty in the
equilibrium (long TI) signal8 into an R1 peak at
5x10-4 s-1 in the CONTIN output. (See Appendix.)
Conclusions The results of this study suggest
that prediction of particle size in simple
monodispersed systems can be made based on R1 and
perhaps field strength. Bi-modal R1 recoveries
seen in prior work with real soil samples3 may be
attributed to sample packing inhomogeneities and
not because of slow exchange between the
structured and bulk water environments. Future
studies are planned to examine the relationship
between the packing geometry,4 void size, and R1.
Appendix Uncertainty in the equilibrium
magnetization is a major cause of error in
fitting exponential recovery data.8 The
uncertainty can be removed by adding an offset,
d, to all curves before CONTIN analysis. As a
validation of this procedure, synthetic mono
exponential decay curves with R10.333 s-1 and 0
lt d lt 0.3 as defined by Eqn. 1 were analyzed with
CONTIN. 1 The offset did not affect the
calculation of the actual R1 of the decay. (See
Table 1.) The offset was represented by an
additional peak in the CONTIN output located at
R1?5x10-4 s-1. The location of this additional
peak is much less than the smallest possible R1
value for water. Table 1. Comparison of actual
R1 values from synthetic data with various
offsets.
References 1. G. Liu, et al., Chem. Phys. 149165
(1990). 2. E.W. Hansen, et al. J. Phys. Chem. B
101 9206 (1997). 3. C.L. Bray, et al., A Fast
Field Cycling Study of Soil, 6th International
Conference on Magn. Reson. in Porous Media, Ulm,
Germany, 2002. 4. A.R. Kansal, et al., Phys.
Rev. E., 55 041109 (2002). 5. E. Anoardo, G.
Galli, G. Ferrante, Appl. Magn. Reson. 20365
(2001) 6. G.C. Borgia, R.J.S. Brown, et al.,Mag.
Res. Imaging 16549 (1998). 7. S.W. Provencher,
Phys. Comm. 27229 (1982). 8. J. Gong, J.P.
Hornak, J. Magn. Reson. Imag. 10623 (1992).
For an electronic copy of this poster, please
see http//www.cis.rit.edu/people/faculty/hornak
/conf-proc/enc-2004/
ENC-2004