Quantification of signals in a sample

• Determination of the limiting T₁
  • T₁IR sequence or other preliminary sequence after optimizing the pulse angles
  • for a one-pulse 90° acquisition, it is necessary to wait for at least AQ + RD ≥ 5T₁ limiting
• N/S ratio must be sufficient
• No apodization (in practice, in exponential only if LB<FWHM)
• Baseline correction
• Integration (including good integral correction, complementary to baseline correction)
• Repeatability of integration: n_I1 integrations by the same operator for a given acquisition
• Repeatability of acquisition: n_A repeated identical experiments
• Reproducibility of integration: n_I2 integrations by another operator for a given acquisition
• If at least one characteristic signal of each component of the mixture is identified and spectrally isolated, the integration is trivial
  • Example: determination of the alcoholic strength of a mirabelle plum alcohol solution
• If the signals are not identified or partially overlaid, a DOSY experiment is possible to identify the components and to be in the previous case.
  • Example: spectral identification of two sugars in a mixture
• If identification is possible but integration is not trivial, a deconvolution treatment of the signals prior to the integration stage must be carried out
  • Example: determination of enantiomeric and diastereoisomeric excesses in an inseparable mixture of stereoisomers

Composition of a simple mixture by NMR: determination of the alcoholic strength of a solution of artisanal mirabelle plum alcohol by ¹H NMR

The alcoholic strength by volume (ASV), or alcoholic degree, defines the proportion of alcohol in a beverage. It is the ratio between the volume of ethanol in the mixture and the total volume of this mixture at a temperature of 20 °C

• Using the characteristic signals of the methyl and methylene groups, it is determined that each H of ethanol integrates for 1
• It can be seen that the most deshielded signal is the superposition of both the alcoholic proton signal of ethanol which integrates for 1, and the signal of the two equivalent protons of water which integrates for 11.4
• From this it can be deduced that for one mole of ethanol there is 11.4/2 times as much water in the mixture
• The conversion of the molar ratio to a volume ratio allows for deduction of an alcoholic titer equal to 37° at 20°C (ethanol density equal to 0.789, density of the alcoholic solution studied equal to 0.95);

Quantitative study of a mixture of inseparable constituents by 2H -{¹H} NMR

It is not always possible to differentiate the spectra of molecules that have close chemical structures such as diastereomers. In addition, it is intrinsically impossible to differentiate the NMR signals from a pair of enantiomers in an achiral solvent.
In contrast, in a chiral solvent, enantioselective solute-solvent interactions will allow for different spectral signatures for the two optical isomers. Then we can also better differentiate the signals of diastereoisomer pairs. If the solvent is otherwise liquid crystal, the quadrupolar interaction is no longer averaged to zero and it is possible to observe a quadrupolar doublet for each deuterium of the isomers considered. This reduces the possibility of observing line overlays, and increases the number of usable signals to quantify them.
If the signals are not sufficiently well separated, it is always possible to decompose them for a better quantification. The process must be repeated three to five times to obtain the uncertainty of repeatability, with an adequate signal-to-noise ratio.

• Objective: to determine e.e & d.e from a mix of inseparable stereoisomers mix d,l/ meso

Qualitative and quantitative study of a mixture by DOSY ¹H NMR: example of a mixture of sucrose and glucose

Molecules in solution have dynamic properties, particularly characterized by their diffusion coefficient, D. This coefficient depends on the size, molecular mass and shape of the molecule studied, as well as the temperature and viscosity 𝜂 of the solution. Stockes-Einstein’s model is the simplest and most common way to deduce an approximate size of the solvated molecule using its hydrodynamic radius R_h, and considering it in spherical form. More sophisticated models exist, including form factors, for example.

The DOSY experiment consists in separating the constituents of a mixture by playing on their abilities to diffuse differently in the solution in which they are involved. At the end of this experiment, a two-dimensional map is obtained. Its horizontal dimension is occupied by the mixture’s NMR 1D spectrum (generally ¹H), and the vertical dimension is a scale of diffusion coefficients, possibly presented in logarithmic form. Since diffusion is a movement that characterizes a given molecule, the set of NMR signals belonging to the same chemical species appears on the same line of the DOSY map.

Qualitative and quantitative study of the components of a mixture by DOSY ¹H NMR: example of a mixture of sucrose and glucose

See figure 14 in ref “Concepts in Magnetic Resonance, (2002), 14 (4), 225”

pK_A determination of a Brönsted acid/base couple: example of vitamin B1

• The chemical shifts of the nuclei of a molecule account for the chemical environment that each of them perceives. This environment is dependent on the solvent, possible impurities in solution, temperature and especially the pH of the NMR sample when the solute studied has acid-base properties (such as thiamine or vitamin B1).
• The chemical shift is a composite value in which each contribution does not evolve in the same way as a function of temperature or pH. It is, however, generally possible to track chemical shifts as a function of pH as observable NMR to determine the pK_A of an acid-base couple.
• The determination is carried out using the numerical adjustment of the curve or the function

Slow or fast exchange on the NMR time scale

When the solute studied possesses flexibility, the observed chemical shifts are modulated by the conformational distribution curve, and by the speed of the conformational exchange between the different conformers. The same is true when a site is in chemical exchange such as acidic protons of alcohols, acids or even amines.
The analysis of NMR signals as a function of temperature can help to determine the kinetic characteristics of the exchange studied. Using suitable models, such as the Eyring model, it is possible to trace back to thermodynamic data.

NB: If the two conformations are not at the same energy level, it is necessary to take into account the populations of each (reference OCP Hore)

• The exchange speed depends on the flexibility of the molecule, its symmetry and the sites studied. In the case of cis-decalin, sites 9 and 10 (cycle junction) are always in fast exchange at the selected temperatures. The alpha and beta sites of the cycle junction are in slow exchange below 12°C. Beyond the coalescence point, the fourth-order symmetry of the observed signals is greater than the second-order molecular symmetry, due to the rapid dynamics that modulate the observed signals.

Adapted from D.K. Dalling, D.M. Grant, L.F. Johnson, JACS, (1971), 93, 3678

Slow or fast exchange on the NMR time scale: detection of atropoisomeric chirality

• The two compounds constitute a pair of atropoisomers: their enantiomeric relationship stems from the steric bulk of the phenyl and naphthyl cycles relative to each other due to the hindrance of the alpha hydrogen atoms of the cycle junction. When the temperature is high enough to allow the molecular dynamics to bypass the activation barrier, the two enantiomers are no longer detectable.
• In a chiral solvent, different NMR signals can be observed for each enantiomer because of the enantio-selective solute-solvent interactions. To study this conformational exchange phenomenon, NMR in such a solvent is therefore well adapted. In addition, if the molecule is deuterated, it is possible to greatly simplify the observation of the atropoisomism phenomenon by observing ²H-{¹H} NMR spectrum.
• In a liquid crystal solvent, the deuterium’s quadrupolar nucleus of spin I=1 results in a quadrupolar doublet. If the liquid crystal solvent is chiral, a quadrupolar doublet for each enantiomer is observed if the exchange is slow.
• Temperature monitoring of the NMR signals allows the kinetics of the system to be determined. Using a model such as the Eyring model, it is possible to deduce the thermodynamic quantities that characterize the conformational exchange.