NMR Spectroscopy: Single-Pulse Experiment

Pulses

If a spin system has come to equilibrium in a fixed magnetic field B, how does one push the system away from equilibrium?

The approach employed in modern instruments is to apply a small magnetic field, B_ex, perpendicular to the primary static magnetic field B. This additional magnetic field is very weak: B_ex << B. Given the weakness of B_ex, one might wonder how it can make any difference at all.

In almost all circumstances, the effect of the small B_ex would be a very slight wobble in the bulk magnetization, too little to be useful. But there is one circumstance in which B_ex can have a profound impact. The key is to make B_ex an oscillating magnetic field and to make it oscillate at the Larmor frequency of the sample nuclei. If B_ex rotates at the same frequency as M precesses, then the influence of B_ex builds over time. The result is that M precesses about B_ex in the rotating frame.

In addition to detector coils along the x and y axes, NMR spectrometers also have RF transmission coils along these axes to generate B_ex for the purpose of manipulating the orientation of M. The RF coils are only turned on for brief periods of time (usually < 20 μsec). For the vast majority of time during an experiment, B_ex is zero and precession is solely about the z axis.

The NMR Experiment

The most basic NMR experiment is called a single-pulse experiment. The experiment begins with the system at equilibrium, which corresponds with M oriented along the z axis. The first step is a 90°_x pulse, which means an excitation field B_ex is applied along the x axis (in the rotating frame) by the RF coils. The bulk magnetization precesses about the x axis in response to B_ex. Instead of characterizing this precession by a frequency, the time required for M to rotate through a particular angle is used. For a 90° pulse, B_ex is applied just long enough for M to rotate 90°. Thus the effect of the 90°_x pulse is to reorient M from the z axis to the y axis.

After the pulse has been applied, the detection coils are monitored and the FID is acquired. Notice that detection is solely in the xy plane, because that is the plane containing the detection coils. The simulation below employs one detector placed on the x axis. However, two detection coils are usually used in tandem to provide phase-sensitive detection, known as quadrature detection, which allows one to distinguish between positive and negative frequencies. That is, one can tell which direction M is precessing during the FID.

The net pulse sequence is often written:       90°_x - FID

The simulation below begins with the system at equilibrium and allows one to step through the individual stages of the experiment.

Be aware that the time scale of the experiment is different during the 90°_x pulse and FID acquisition stages. In reality, for a ¹H experiment, the 90°_x might take 10 μsec, whereas the FID is usually acquired over several seconds.