qNMR. Part 1

Since the early 1960s the efficacy of NMR in quantitative measurements (qNMR) has been explored.  Although not a particularly sensitive technique, NMR (my technique of choice!) is ideal for quantification because:

(1) it is non-destructive; and
(2) if the sample is fully soluble, every component can be observed and has the same response factor.

Depending on experiment conditions and the external magnetic field strength (Bo), quantitative inaccuracies can be as low as 2.0% (not too shabby!) and can be validated with typical analytical parameters (e.g., precision, accuracy, linearity, reproducibility).

The premise of qNMR is that the observed signal intensity is proportional to the number of nuclei that give rise to that particular resonance.  Because each proton resonance has the same response factor (K) the relative quantity of each signal can be easily determined by comparative integration.  That is,

where     I is the observed integral
N is the number of nuclei per resonance
K is the response factor

Absolute quantification can also be used to determine the amount of analyte present in a sample.   This is most commonly done analytically through careful sample preparation with an internal standard.

where   I – observed integral
N – number of nuclei per resonance
MW – molecular weight
W – gravimetric weight
P – purity
x – analyte
std – standard

The infamous Internal Standard is not the only method – others can be used as well – including standard addition, calibration curves, external standards, electronic referencing methods (ERETIC), Quantification by Artificial Signal (QUANTAS), Pulse Into Gradient (PIG), Amplitude-corrected Referencing Through Signal Injection (ARTSI), and Pulse Length Based Concentration Determination (PULCON).

So, yes, all NMR IS quantitative, but just how quantitative the NMR you just measured actually is depends on a variety of factors of how you collected and/or processed your spectra.  This includes:

1) routine acquisition parameters e.g., pulse angle, sufficient relaxation delay, sufficient acquisition time, receiver gain, digital resolution etc.
2) S/N – for 1H qNMR is performed with a minimum S/N of 100:1.where             N – number of spins
γexc – gyrogmagnetic ratio of excited nuclei
γdet – gyrogmagnetic ratio of detected nuclei
B – external magnetic field
ns – number of scan
T2 – transverse relaxation time
T – sample temperature

3) correct processing – e.g., a good baseline and properly phased spectra.

I plan to discuss this topic in a little more detail over the next little while, and, if this is a topic that you’re interested in – there are many other useful NMR blogs that you should definitely check out.  They come highly recommended!
1) University of Ottawa – Glenn Facey
2) MNova – Mike Bernstein
3) MNova – Carlos
4) Process NMR – John Edwards

Bharti, S. K.; Roy, R. Trends. Anal. Chem. 2012, 35, 5