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

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PRICE
move the couplings. Signal-to-noise problems with
heteronuclei may also be alleviated by using inverse
detection and the like Žsee
Multiple Quantum
and Heteronuclear Experiments . .
Often solvent suppression will be a problem,
especially for low values of q, many possibilities
exist for removing the solvent signal, especially
those that can be placed before the PFG diffusion
sequence. Examples include presaturation or
water-PRESS Ž 113. and others Ž 114 . . As the value
of q increases, the solvent signal is almost never a
problem, since its intensity is reduced much faster
than that of the Ž more slowly moving. species of
interest by the PFG attenuation. This is, in fact,
the basis of another well-known method of water
suppression, DRYCLEAN Ž 115 . .
Typically, to obtain accurate diffusion coefficients
of freely diffusing samples, it is desirable to
record the echo attenuation over at least two
orders of magnitude, although if the signal-tonoise
ratio is very good, it is possible to determine
the diffusion coefficient from a signal attenuation
of only 1%. However, measuring to high degrees
of attenuation allows the effects of restricted
diffusion, if present, to be visualized. It might
seem advantageous to use absolute value Žalso
referred to as power or magnitude. spectra to
overcome eddy currentinduced phase instability
and the like. This is true only in the case of
first-order spectra or overlapped spectra Ž 4 . .Itis
preferable to correct the data in phase-sensitive
mode since, apart from the better spectral resolution,
phase changes related to the gradient parameters
are good indicators of eddy current effects
and their absence provides some confidence
that the data are artifact free.
Because of the dependence of the attenuation,
it is normally preferable to use high nuclei
as the probe nuclei. To set cogent values for , ,
and g in the experiment, it is worthwhile Žassum
ing the simplest case of a monodisperse single
species. to simulate the experiment using Eq.
2 with an approximate value for the diffusion
coefficient.
A very obvious way to analyze the data, especially
if a rough-and-ready analysis is acceptable,
Ž . 2 2 2 is simply to plot ln E versus g Ž 3, .
in which case the diffusion coefficient can be
obtained from the slope Ž i.e., D . . However, this
approach gives unequal weighting to the noise,
particularly as the signal approaches zero. For
this reason, when higher accuracy is called for, it
is better to use nonlinear regression of the relevant
attenuation equation onto the experimental
data. We note that von Meerwall and Ferguson
wrote a specialized computer program for analyzing
attenuation data with respect to a number of
pertinent models Ž 116 . .
CONCLUDING REMARKS
This article does not claim to be exhaustive in its
coverage of pulse sequences for measuring diffusion
and many other sequences exist e.g., Ž7,
117 .,
nor were special methods for measuring
diffusion in solids considered Ž 5 . . In passing, we
note that in particular, the review by Stilbs Ž 4.
also considered some experimental and technical
aspects. In the present article, we have introduced
some of the technical aspects related to
performing PFG diffusion measurements, and also
to their analysis for simple systems. The single
most important conclusion to draw from this article
is that the reliability of the diffusion measurements
depends on the spectrometer and gradient
system being well characterized and calibrated.
APPENDIX
Maple Worksheet for the Stejskal and
Tanner Equation, Including Gradient Pulses
with Infinitely Fast Rise Times and Long
Eddy Currents
Reset the system
> restart;
Define the integral used in determining F
> F(G, ti) int (G, t = ti..tf);
Define the time intervals and the relevant value
of g for each integral. Also calculate the value of
F for each interval remembering that it contains
the contribution from all of the intervals from the
start of the pulse sequence.
> l10;
> g10;
> F1F(g1, l1);
> l2t1;
> g2g;
> F2subs (tf = l2, F1) + F(g2, l2);
> l3t1 + delta;
> g3g*exp(- k*(t- l3));
> F3subs(tf = l3, F2) + F(g3, l3);