The sample was 1% ethylbenzene in CDCl3 which produces a cluster of aromatic peaks and well resolved signals for the CH2 and CH3 protons. In the graph below the experimental data are shown as points, while the lines show the relationship S/N = scans1/2 fitted to the experimental data. The aromatic resonances are red, the CH2 blue and the CH3 green.
Here the expected square root relationship seems to hold fairly well. The data were recorded with a two second relaxation delay between scans, probably long enough to allow equilibrium recovery of all three types of resonance before the next pulse. Unfortunately, because of the square root relationship doubling the experimental time gives at best a 41% S/N increase (21/2= 1.4142). This means that methods for increasing signal-to-noise in NMR are always being sought.
If signal-to-noise per unit time is our main consideration, and we are not concerned with accurate integration of the resonances, we can reduce the relaxation delay between scans. This will mean resonances with longer longitudinal relaxation times (T1s) will produce less signal than resonances with shorter T1s. In a simple 1D experiment we can compensate for this to some extent by using a less than 90o pulse so that the magnetisation will not take as long to return to equilibrium.
Using the ethylbenzene sample I recorded a series of spectra with pulse lengths ranging from 10-90o and relaxation delays between 0.25 and 2.0 seconds. The graph below shows the signal-to-noise of the aromatic resonances with the red line corresponding to a relaxation delay of 0.5 seconds, the blue a 1.0 second relaxation delay, and green a 2.0 second relaxation delay.
The data show that for a given relaxation delay the maximum signal-to-noise occurs around 4 μs, and as the relaxation delay is reduced this maximum shifts to shorter pulse widths. For this sample the 90o pulse was 9.1 μs, so the maximum signal-to-noise is obtained with close to a 30o pulse. The data also show that the longer the relaxation delay the greater the signal-to-noise, however, an experiment with a longer relaxation delay takes longer to record.
On our spectrometers the standard parameters for recording simple 1D experiments such as 1D 1H and 1D 13C spectra utilise a 30o pulse and a 0.5 second relaxation delay. While these parameters may produce spectra more rapidly, keep in mind that these parameters will not produce accurate integrals. For accurate integration you will need to increase the relaxation delay (D1) to five times the longest T1 of all the resonances in your spectrum.