Field strength

Everybody knows bigger magnets make for better NMRs, right? But exactly what does a stronger magnetic field do for you in terms of the spectra you record? The short answer is increased sensitivity and resolution. Read on for more details.

The size of the signal generated by an NMR spectrometer is determined by the difference between the energy levels created when the nucleus is placed in a magnetic field. The stronger the field, the greater the difference and the bigger the signal. But how does the signal increase with field? How much more magnet is required to get a desired increase in sensitivity?

The expression below shows how signal to noise (S/N) is related to the number of nuclei present (n), the gyromagnetic ratios of the nuclei being excited (γ_e) and detected (γ_d), the magnetic field (B_o), and the time spent recording the data (t).

S/N ∝ nγ_e(γ_d³B_o³t)^½

Using this equation to plot S/N against field gives the graph below. Since S/N depends on B_o^1½ the graph is close to parabolic. Because of the curve of the graph, at lower fields a small increase is not as favourable as a similar increase at higher fields. This explains the drive to produce larger and larger magnets.

As the strength of the magnet increases the frequency at which nuclei resonate increases as well. For example, a proton resonating at 200 Hz in a 300 MHz magnet would resonate at 400 Hz in a 600 MHz magnet. This field dependence of peak position makes it difficult to compare spectra between instruments so the ppm scale was developed. The ppm scale expresses peak position as a fraction of the frequency at which the spectrum was recorded, making it independent of the field strength. This makes the number of hertz per ppm depend on the field used to record the spectrum. At higher field there is more Hz per ppm.

The width of an NMR signal depends on the J-coupling that splits the signal and its T₂ relaxation rate. Both of these are independent of field strength. A doublet that shows a J-coupling of 8 Hz at 300 MHz will show the same J-coupling at 600 MHz. However, at higher field the 8 Hz separation of the lines in the doublet occupies less ppm than it would at a lower field. In the figure below¹ spectra of menthol have been recorded at five different magnetic field strengths. It can be seen that the peaks are in the same place and show the same structure, no matter the field, but get narrower as the field increases. This is particularly obvious for peak n at 3.37 ppm.

The advantage of increased resolution afforded by higher field can be clearly seen with peak g at 1.10 ppm. At 200 and 250 MHz this peak overlaps the peaks just below 1 ppm, but at 500 and 600 MHz the peak is clearly resolved. Obviously, increased resolution allows larger molecules, with more signals, to be studied by NMR.

References
1. Jacobsen, Neil E.
"NMR spectroscopy explained"
John Wiley and Sons 2007 p43