Gradients

Gradients have become an essential part of modern NMR spectroscopy. Nearly all probes now have pulsed field gradient capabilities and the vast majority of pulse sequences use gradient pulses. In this post, and those following, I will try and explain what gradients are and how they can be useful.

Normally in NMR one tries to make the magnetic field the same throughout the entire sample. This is the object of shimming the sample. Shimming is the process of adjusting the field in the three orthogonal directions, x, y and z, to produce a uniform magnetic field throughout the entire sample volume.

In the figure below a well-shimmed sample tube is shown on the left, with the red arrows representing identical nuclei experiencing the same magnetic field throughout the entire sample. The tube on the right shows the same well-shimmed tube after a gradient along the z-axis has been applied. Now, the nuclei near the top of the sample experience a stronger magnetic field, and those at the bottom experience a smaller one. By convention, the effect of the gradient is assumed to be zero at the center of the sample. A gradient creates a linear, position dependent change in magnetic field.

Recording a spectrum of the well-shimmed tube on the left would produce a spectrum with a single narrow peak, as all the nuclei in the sample experience the same magnetic field and precess at the same frequency. A spectrum of the tube on the right with the gradient applied would produce a broad peak with frequencies distributed around the position of the peak from the tube on the left. The nuclei at the top of the tube where the field is stronger would resonate at a higher frequency, while those at the bottom of the tube would resonate at a lower frequency.

A spectrum recorded in the presence of a gradient is in effect a one dimensional image of the sample. The distribution of the observed frequencies corresponds to the length of the sample and the intensity of the signal is proportional to the number of nuclei present. In the case of the tube on the right the image corresponds to the z-axis running vertically through the sample tube because a gradient was applied along the z-axis. Recording a spectrum in the presence of an x or y gradient would give a cross-sectional image of the sample. (See Figure 2 on this page for a good diagram.) This is how medical MRI scanners work. They use combinations of x, y and z gradients to build up images from within a sample, often a living person.

Recording NMR spectra in the presence of gradients broadens the signals so the gradient is typically turned on for 1 ms or so, then turned off to acquire the spectrum. Such "pulsed field gradients" allow gradients to be used without broadening the peaks. During an experiment that uses gradients one can see the effect of the gradients on the lock signal which repeatedly drops and recovers as the gradient is turned on and off.

So what can an NMR spectroscopist do with gradients? Gradients are typically used to select desired signals and eliminate unwanted ones. They can be used to reduce artifacts and the need for phase cycling, making experiments quicker. Gradients can be used for coherence selection in place of phase cycling, again making experiments quicker. In combination with selective pulses, gradients can be used to remove unwanted peaks, like those from solvents. And gradients can be used to measure how quickly molecules move in solution. The next few posts will discuss these applications.