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

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Figure 13 An example of a temperature calibration plot for a 5-mm multinuclear inverse
probe for a Ž standard bore. Bruker DRX 300 Spectrometer. Generally, the set and actual
temperatures correspond well around ambient temperature using methanol Ž closed squares.
and ethylene glycol Ž closed circles . . Note the kink between the temperature measured with
methanol and ethylene glycol. This results from imperfect calibration of the chemical shifts
of these compounds with respect to temperature. The solid line represents the ideal case of
perfect correspondence between the set and actual temperature. The correlation between
the two temperatures can be improved by increasing the flow rate of the coolingheating
gas and moving the thermocouple closer to the sample Ž see, for example, Fig. 4 . . However,
shimming generally becomes more problematic as the thermocouple becomes closer to the
sample.
Ž .
ents 65 . The thermal gradient, T, can be estimated
directly from the linewidth,
linewidth Ž ppm.
Ž 1
T Kcm . 24 1.45 rf coil height Ž cm.
The most fundamental means for minimizing
convection problems is to have good temperature
control, which to some extent is generally improved
by increasing the airflow, although this
will depend strongly on the probe construction
Že.g., the separation between the outside of the
sample and the insert glass in the probe . . Convection
is also reduced through the use of short and
narrow samples, since the walls retard the onset
of convective flow. If convection is still a problem,
modified PFG diffusion sequences which rely
upon gradient moment nulling Ž 64. can be used.
To see how this method works, it is necessary to
understand the connection between flow and
phase. The phase shift at time t of a nuclear spin
following a path rŽ t. in a gradient gŽ t. is given
by
t
H
0
Ž t. gŽ t. rŽ t. dt 25 Only the component of the spin’s motion in the
direction of the gradient, zt, Ž. is relevant, and
this can be expanded in a Taylor series Ž 66.
ž / ž /
z 1 2 z
Ž .
2
z t z0 t t
2
t 2 t
t0 t0
26
The terms on the right-hand side of Eq. 26
correspond to the position z , velocity
0 0
Ž . Ž 2 2 zt and acceleration a zt .
t0 0 t0,
etc., and thus, Eq. 25 can be rewritten as
1
Ž t. z M M a M 27 0 0 0 1 0 2
2
where
H
t n
n
0
z
M g Ž t.Ž t. dt 28 M is termed the nth moment of g Ž.
n z t with
respect to t Žn.b.,
this should not be confused
with macroscopic magnetization . . Equation 27 provides the basis of so-called gradient moment