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FAQ 2004-04.1: sample concentration and experimental time

FAQ 2004-04.1: Sample concentration and experimental time
Nearly every NMR user knows that the signal-to noise ratio of an NMR experiment increases with the square root of the number of transients (also called scans) of the experiment: the relevant parameter is nt. If nt is increased from 16 to 64 the s/n doubles.

Much more confusion seems to exist with regard to the effect of concentration and the length of an experiment to achieve a certain s/n ratio. In this case doubling the amount of material (doubling its concentration) will make it possible to achieve the same s/n with only 1/4 of transients which entails 1/4 of the experimental time (a). The total experimental time is proportional to the number of transients nt, this means the "double concentration" case takes 4 times less total experimental time.

Example. If 5 mg of compound A give a s/n of 100:1 with 64 transients in 4 minutes, then 10 mg of A dissolved in the same volume of solvent will provide 100:1 s/n in 16 transient (1 minute).

All this is of limited consequences for H1 NMR, because the inherent high sensitivity of H1 makes it easy to achieve a good s/n in a short time with fairly little sample. This does not apply to C13, however. The natural abundance of only 1% combined with its substantially lower inherent sensitivity result in a absolute sensitivity of only 0.000176 vs. 1.00 for H1 (b). This makes it much more time-consuming to obtain satisfactory C13 spectra with regard to s/n than H1. The consequence of this:

if availability and solubility are not limiting factors, make a concentrated solution for C13 experiments.

For H1 and F19 (c) it is preferred to stay below 100 mM, for C13 you can easily go beyond that. In general, the concentration in mM of a 0.7 mL sample is given by the formula

This is clearly not difficult math. If you are interested in calculating a sample concentration just type mM on the command line in VNMRJ and answer the two questions (what is the m.w. and how much sample do you have?). The above formula will then be applied to your input and the result will appear in the message window on top. No other action is taken by mM. By contrast, the EZ NMR S+A button "Calculate & Set nt" does first the calculation of the concentration and then sets nt to a reasonable number based on the sensitivity of the spectrometer and the technique chose. Most users are typically way too optimistic about the amount of compound (impurities including silica gel do add weight but not s/n!) so that for C13 and 31P no such estimation is made. Instead, these experiments run until stopped by the user.

(a) Phase cycling (i.e. rotating the pulses through x, y, -x, -y) to remove artifacts typically requires the acquisition of  4 transients minimum. Further phase cycling up to 16 transients improves the removal of artifacts even more with very little penalty in time, hence the smallest nt is 16 with a typical experimental time of ca. 1.5 minutes. However, if you really feel that 1.5 minutes is a waste of time you can reduce nt to 4 and save about a minute.

(b) The absolute sensitivity is the relative sensitivity (a property of the nucleus) multiplied by the natural abundance. Unfortunately, C13 is poor in both regards.

(c) F19 compares very well with H1; it is only marginally lower in absolute sensitivity at 0.83, the result of 100% abundance and a pretty good inherent sensitivity of this nucleus.