Page 134 - Environmental Nanotechnology Applications and Impacts of Nanomaterials

120 Principles and Methods

The differences between the various energy states is given by:
E 5 u gUH u where H is the magnetic field at the nucleus. The
N
Boltzmann distribution a 5 exps2 E/kTd gives the probability of
N b
higher and lower energy levels (N and N ). It is important, however, to
b
a
recall that the difference between high and low energy levels tends to
be very low. The increase or decrease of nucleus energy is due to absorp-
y
tion or emission of photons with a frequency , given by:
g
y 5 H . (4)
2p
NMR measures the frequency of this radiation, which is in the radio-
frequency range. Nuclei with various atomic arrangements absorb and
emit photons of slightly different frequencies due to shielding:

(1 ) (5)
H H 0
and

H 0
y 5 g s1 2 sd (6)
2p
The resonance frequencies are generally reported as chemical shifts (
..
which are described according to the following expression):
2 y
y sample standard 6
d 5 a y standard b 3 10 (7)

As with Mössbauer spectroscopy, NMR can provide valuable informa-
tion for identifying solid phases even in natural systems. For example,
naturally occurring nanoparticles such as imogolite or allophane can be
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identified using Si and Al solid-state NMR [Denaix et al., 1999]. On
the other hand, XRD is severely limited in its ability to provide such
information.
Sample preparation. For the analysis of nanoparticles using NMR, sam-
ples must be supplied as a homogeneous powder in a dry state.

Limitations. The sensitivity of NMR analysis is dependent on the abun-
dance of the given isotope in a sample. For example, the natural abun-
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27
dance of Si is 4.7 percent compared to Al, which is close to 100 percent.
With mixtures of different nanoparticles (e.g., Al and Si) the detection
of Si will be more difficult than Al. One possible solution to this prob-
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lem is to enrich the Si nanoparticle during the synthesis with Si.
Another strong limitation to NMR is that the presence of paramagnetic