Phase Cycling and Gradient Pulses - The James Keeler Group

absorption mode spectrum. We must also ensure that the two spectra we are
comparing have the same limiting resolution in the t 1
dimension, that is they
achieve the same maximum value of t 1
and, of course, the total experiment time
must be the same.
The detailed argument which is needed to analyse this problem is beyond the
scope of this lecture; it is given in detail in J. Magn. Reson Ser. A, 111, 70-76
(1994) † . The conclusion is that the signal-to-noise ratio of an absorption mode
spectrum generated by recombining P- and N-type gradient selected spectra is
lower, by a factor 1 2 , than the corresponding phase cycled spectrum with
SHR or TPPI data processing.
The potential reduction in sensitivity which results from selection with
gradients may be more than compensated for by an improvement in the quality
of the spectra obtained in this way. Often, the factor which limits whether or
not a cross peak can be seen is not the thermal noise level by the presence of
other kinds of "noise" associated with imperfect cancellation etc.
180°
δ δ
RF
∆
g τ τ
9.6.6 Diffusion
The process of refocusing a coherence which has been dephased by a gradient
pulse is inhibited if the spins move either during or between the defocusing and
refocusing gradients. Such movement alters the magnetic field experienced by
the spins so that the phase acquired during the refocusing gradient is not exactly
opposite to that acquired during the defocusing gradient.
In liquids there is a translational diffusion of both solute and solvent which
causes such movement at a rate which is fast enough to cause significant effects
on NMR experiments using gradient pulses. As diffusion is a random process
we expect to see a smooth attenuation of the intensity of the refocused signal as
the diffusion contribution increases. These effects have been known and
exploited to measure diffusion constants since the very earliest days of NMR.
The effect of diffusion on the signal intensity from the simple echo sequence
shown opposite is relatively simple to analyse and captures all of the essential
points. Note that the two gradient pulses can be placed anywhere in the
intervals δ either side of the 180° pulse. For a single uncoupled resonance, the
intensity of the observed signal, S, expressed as a fraction of the signal intensity
in the absence of a gradient, S 0
is given by
S ⎛ 2 2 2
= − G
⎛ τ
−
⎞ ⎞
exp⎜
γ τ ∆ D
S ⎝ ⎝
0
3⎠
⎟
[15]
⎠
where D is the diffusion constant, ∆ is the time between the start of the two
gradient pulses and τ is the duration of the gradient pulses; relaxation has been
ignored. For a given pair of gradient pulses it is diffusion during the interval
between the two pulses, ∆, which determines the attenuation of the echo. The
†
There is an error in this paper: in Fig. 1(b) the penultimate S spin 90° pulse should be phase y
and the final S spin 90° pulse is not required.
9–42