2.1.  Physical Properties

Name

Dimethyl Sulfone

Structure

+

Synonym

Methyl sulfone, Methylsulfonylmethane

CAS Registry Number

67-71-0

Molecular Formula

C₂H₆O₂S

Molar Mass [24], [25]

$94.136\mathrm{g}/\mathrm{mol}$, $u=0.005\mathrm{g}/\mathrm{mol}$

Melting point [26]

$109\mathrm{°C}$

Density

$\mathrm{1 450}\mathrm{kg}/{\mathrm{m}}^3$ [26]
$\mathrm{1 385}\pm 30\mathrm{kg}/{\mathrm{m}}^3$ [27]

Appearance

White crystalline powder

¹H NMR [28]

$\delta$ 3.14 (s, 6H)

¹³C NMR

$\delta$ 42.6

Figure 2 — ¹H NMR spectrum of DMSO₂ in D₂O: JEOL ECS-400 spectrometer with Royal probe.

2.2.  Solvent Compatibility

NMR solvents suitable for use with DMSO₂ include D₂O, DMSO-$d_6$, CD₃OD and CDCl₃. DMSO₂ is soluble at levels in excess of $10\mathrm{mg}{\mathrm{mL}}^{-1}$ in DMSO-$d_6$ and CD₃OD and in excess of $5\mathrm{mg}{\mathrm{mL}}^{-1}$ in D₂O and CDCl₃. [23]

2.3.  Quantification signal

The six magnetically equivalent methyl protons of dimethyl sulfone give rise to a singlet absorption at a chemical shift in the range $3.1\mathrm{ppm}$ – $3.2\mathrm{ppm}$ on the $\delta$ scale. The position of the resonance is a function of factors including, but not limited to, the solvent, temperature, pH, spectrometer and the concentration of DMSO₂ and analyte in the solution. The homogeneity of the spectrometer magnetic field should be optimized such that the full width at half maximum (FWHM) of the DMSO₂ resonance signal is less than $1\mathrm{Hz}$ when the base of the resonance retains a suitable Lorentzian peak shape.

2.4.  Impurities and artefact signals

In practice the main interferences in a qNMR solution using DMSO₂ as internal standard come from the residual non-deuterated solvent. The approximate chemical shifts of these signals are given in Table 1 below. In the case of solutions in D₂O the signal due to residual HDO could be attenuated if desired by the use of a (water) signal suppression pulse sequence, at the cost of introducing additional non-linearity into the signal responses. [29]

2.5.  Solvent recommendations and advisories

3.1.  Introduction

The first step in any purity assignment by qNMR should be the confirmation by qualitative NMR or other techniques of the identity of the analyte subject to purity assessment. In addition to confirming that the molar mass (M) and the number of nuclei (N) contributing to each signal subject to integration are appropriate, obtaining qualitative NMR spectra also provides a check for the occurrence and extent of any interfering signals in the sections of the NMR spectrum subject to integration.

Once the qualitative identity of the analyte has been appropriately established the input quantities that influence qNMR measurement results must be evaluated. These are identified from the measurement equation (Equation (1), Chapter 1). The purity of the internal standard used for the measurement, the source of traceability to the SI for the value assigned to the analyte, is established independently prior to the qNMR experiment.

The gravimetric procedure used for the preparation of the NMR solution has to be fully validated and fit for purpose, [30], [31] and the spectrometer performance, experimental parameters and the protocol for signal processing and integration must be optimized, [8], [9], [32] in order to produce a result for the ratio of the integral of the analyte and standard signals that accurately reflects the amount of substance fraction of the hydrogen nuclei giving rise to the signals. [33] Only when these conditions are met can the assigned mass fraction purity of the analyte also be regarded as properly traceable to the SI. [11], [12], [34] Some general guidance for recommended practice for these critical steps is given in the following sections.

3.2.  Internal standard

The internal standard used in qNMR should comply as far as possible with the criteria described in the Introduction regarding composition, physical characteristics, inertness, solubility, impurity profile and suitability for accurate gravimetry. In addition, in order to establish traceability of the result of the qNMR assignment to the SI, the material should comply with the requirements of a reference measurement standard, and in particular a reference material, as defined in the International Vocabulary of Metrology (VIM). [22]

To maintain SI-traceability the sources of the internal standard should be either a:

1. CRM [22] characterized for mass fraction purity and value assigned by an NMI;

2. CRM produced by a Reference Material Provider accredited to ISO 17034:2016 [35] requirements;

3. High-purity material subject to a validated measurement procedure for purity assignment by qNMR using as an internal standard a CRM of type 1) or 2).

3.3.  Gravimetry and Sample Size

The realization of accurate and precise qNMR measurements relies on the application of a properly implemented gravimetric procedure for the mass determinations of the internal standard and analyte. Recommended practice in this area in the specific context of qNMR sample preparation has been described in a recent publication. [30] Achieving an overall relative standard measurement uncertainty for the result of a qNMR assignment of 0.1 % requires the relative uncertainty associated with individual gravimetric operations typically to be less than 0.03 %. If the combined standard uncertainty of a single mass determination is $3\mathrm{\mu g}$, a level achievable with modern electronic microanalytical balances, this corresponds to a minimum sample size of $10\mathrm{mg}$.

In addition to suitable control for each mass determination, if the receptacle used for the final solution preparation is not the same as that used for both mass determinations, the procedure for transfer of solids into the solution must address the assumption that the ratio of the gravimetric readings from the balance operations is equivalent to the ratio of the masses of each compound in the solution subject to the qNMR analysis.

For the examples reported in the Appendix A1.2 below, gravimetric operations were undertaken using a balance associated with a measurement uncertainty estimate of $1.3\mathrm{\mu g}$ for individual mass determinations. In this case a minimum sample size of $4\mathrm{mg}$ achieves a relative uncertainty in individual gravimetric operations below 0.03 %. In addition to the measurement uncertainty of the gravimetric operations, high accuracy measurements require additional correction for sample buoyancy effects [31] and the ¹H/²H isotope composition of the quantified signals. The value and associated uncertainty of the ¹H/²H isotope composition of each quantification signal can be obtained using an on-line calculator application. [25] As noted previously, because of the combination of the large number of hydrogens giving rise to the DMSO₂ quantification signal and its relatively small molar mass, when preparing a sample for qNMR in practice it can be problematic to use a sufficient mass of DMSO₂ such that the relative uncertainty of the gravimetric operation is below 0.03 %

As sample preparation for qNMR involves mass determinations in the milligram range using sensitive balances, the loss of minute (effectively invisible) quantities of powder during the gravimetric procedure will have a measurable influence on the balance reading and hence on the input quantities for the qNMR assignment. Environmental conditions for gravimetry and qNMR sample preparation should be controlled throughout the process, subject to minimum change and kept within the operating range recommended by the manufacturer. [36], [37] It is recommended that mass determinations be performed in an area where the humidity is maintained at a relatively stable level in the relative humidity range 30 % to 70 %.

The accumulation of surface electrostatic charges is another potential source of bias for mass determinations, particularly for high-polarity, hygroscopic compounds. In these cases, pre-treatment of the sample with an electrostatic charge remover or deioniser is advisable prior to the mass determination. Materials subject to qNMR analysis should be evaluated for their hygroscopicity, for example by measurement of the potential for change in the observed mass of a sample as a function of relative humidity using a dynamic sorption balance. [38] This allows for assessment of the likely impact of variation in the relative humidity in the local environment on the results of gravimetric operations for a given compound. A minimum of two independent gravimetric sample preparations should be undertaken.

3.4.  NMR spectrometer optimization

There is no specification of minimum NMR spectrometer field strength for purity measurements. Increasing the field strength enhances signal separation and sensitivity, both of which should increase the accuracy and precision of qNMR measurements. Careful optimization of the lineshape (shimming) is critical in order to achieve reliable qNMR results. [39] A general guidance is to choose the simplest signal in the sample, often the residual solvent peak, and to optimize the instrument shimming until this signal is symmetrical with a FWHM below at least $1\mathrm{Hz}$. Experience has shown that these lineshape requirements are more easily achieved using an inverse probe than a direct type. For lower field magnets ($<300\mathrm{MHz}$), this requisite might not be attainable which impacts on the level of measurement uncertainty associated with the assigned value. In no case should a signal from a labile, exchangeable hydrogen or one subject to dynamic tautomeric exchange be used for quantitative measurements.

Due to the relatively wide Lorentzian shape of NMR resonances the separation of the signals to be quantified from each other and from the remainder of the NMR signals in the spectrum should be considered carefully. Ideally there should be no interfering signals within a range one hundred times the FWHM on each side of each signal to be integrated.

3.5.  NMR acquisition parameters

The basic experiment to perform quantitative NMR experiments uses a simple 1D pulse sequence designed to minimize differences in the integrated signal intensities due to differential rates of relaxation. For highest accuracy assignments, use of broadband heteronuclear decoupling should in general be avoided as it can lead to undesired nuclear Overhauser effects introducing a bias in the intensities of individual measured signals. However in the common case of ¹³C-decoupling to remove satellite signals, the potential for bias is attenuated because of the low (1.1 %) natural abundance of the ¹³C isotopomer even though the decoupling efficiency for individual ¹³C satellite signals is variable. The potential for the introduction of additional bias due to ¹³C-decoupling is negligibly small in most cases.

The basic sequence for a qNMR measurement consists of a “delay-pulse-acquire” experiment. There are critical parameters associated with each phase of the sequence in order to achieve a reliable, unbiased and quantitative signal response. Assuming the experiment starts from an equilibrium magnetization state, the first phase in the experiment is the pulse, which itself is preceded by a delay.

In the pulse phase, the two critical parameters for good qNMR measurement results are the pulse offset and pulse length (also called pulse width or tip angle). When a single “hard” pulse is applied to the bulk magnetization of each compound, off-resonance effects can occur if the frequency offset of the initial pulse is relatively far from that of the signals of interest. Ideally the pulse offset should be positioned as close as possible to the midpoint between the two signals to be quantified. This will not eliminate off-resonance effects but should result in cancelling out in both signals.

Regarding the pulse length, $90\mathrm{°}$ pulses are recommended for quantitative analyses. A $30\mathrm{°}$ pulse experiment, providing a signal response approximately half that of a $90\mathrm{°}$ pulse, has the potential advantage of needing a significantly shorter relaxation time to re-establish equilibrium magnetization compared with a $90\mathrm{°}$ pulse while requiring only twice as many transients to achieve an equivalent total signal response. However this potential advantage is offset by the need for four times as many transients as a $90\mathrm{°}$ pulse to achieve the same signal to noise ratio. The accuracy of the results should not be impacted by the use of different pulse lengths but the acquisition time to achieve equivalent levels of precision will.

Additional parameters requiring optimization in the acquisition phase are the spectral window width, the acquisition time, the digital resolution and the relaxation delay time between acquisitions. The spectral window chosen will depend on the design and performance of the instrument used. The theoretical justification for the use of a large spectral window is that oversampling the FID will produce noise filtering. However, the efficiency of digital filters varies by instrument and the appropriate spectral window should be evaluated on a case-by-case basis.

The acquisition time should be at least $2.5\mathrm{s}$ to avoid truncation of the signals and to allow good digitisation of the spectrum. The ideal acquisition time is the smallest time for which no truncation is observed. Use of longer acquisition times than necessary primarily results in addition of noise to the spectrum. The digital resolution should not exceed $0.4\mathrm{Hz}/\mathrm{pt}$ in order to have accurately defined signals that will give accurate area measurements and suitable precision at typical sampling rates.

The relaxation delay between pulses in particular has to be carefully established for each sample mixture. To determine the optimum repetition time for a given qNMR measurement it is critical to determine the longest $T_1$ time constant of the signals to be quantified. This document presents some observed values measured for dimethyl sulfone in different solvents at the concentration and under the specific instrumental conditions used, but these should be regarded as indicative only, and in any event they are not the determining factor in cases where the $T_1$ of the analyte quantification signal is longer.

As the $T_1$ constant arises from a process of spin-lattice relaxation, its values are strongly dependent on the composition of the solution being measured and it should be determined for each signal to be quantified in each mixture on a case-by-case basis. The most commonly used method to determine the $T_1$ constant is the inversion-recovery sequence, which is generally available in the factory programmed pulse sequences installed with any NMR. The application of the inversion recovery experiment requires knowledge of the optimized $90\mathrm{°}$ pulse, which should also be determined for each mixture under investigation. The $90\mathrm{°}$ pulse is used for both the $T_1$ determination and the quantitative measurements.

The repetition time between pulses should correspond to the full loop time in the pulse sequence and not simply the relaxation delay. Since most of the time intervals involved in NMR measurement are negligible relatively to the $T_1$ values, the repetition time (RT) can be estimated as the sum of acquisition time (AQ) and relaxation delay (RD), where the RD is a multiple $T_1$. After a $90\mathrm{°}$ pulse, if available instrument time permits, a repetition time equivalent to 10 times $T_1$ of the signal with the longest relaxation time will lead to the recovery of > 99.99 % of the magnetization for all quantified signals. In cases where the $T_1$ of the quantified signals are similar in magnitude, a shorter relaxation delay may be sufficient for equivalent (even if incomplete) magnetization re-equilibration.

Thus the recommended pulse RT for high accuracy quantification is given by:

The number of transients (scans) should be determined according to the concentration of the sample, the nature of the signals and the available instrument time. To achieve small uncertainty a signal to noise (S/N) ratio of at least 1000 should be achieved for each signal subject to quantification. Smaller S/N values can still lead to acceptable results, but the reported measurement uncertainties increase as the S/N ratio decreases.

Table 2.  Recommended NMR Parameters for quantitative measurements.

Good practice for performing quantitative experiments is to prepare, in addition to the sample mixtures, one sample consisting of a solvent blank, one with the analyte only and one with the internal standard only in the same solvent. These additional NMR spectra should be acquired prior to the preparation of sample mixtures to check the suitability of the proposed mixture in terms of the absence of interferences from one compound (or impurities present in it) in the other. Other NMR techniques such as 2D HSQC or COSY may be applied to demonstrate the uniqueness of the signals used for quantification and the absence of overlapping contributions from impurities while aware that the sensitivity of such techniques is low and the absence of observable interferences does not guarantee a signal free of such interferences.

Each analyte/IS mixture should be measured at least three times in the NMR system. To correct for potential instrument drift, independent measurements for a particular sample mixture should be non-continuous. The sample tube should be ejected from the spectrometer probe and the measurement process (tuning, locking, shimming) repeated for each replicate for each sample. To avoid potential unwanted contributions due to spinning sidebands, it is recommended to undertake the measurement using sample spinning disabled. This presumes a high degree of field homogeneity has been achieved.

3.6.  NMR signal integration

In order to integrate in excess of 99.9 % of each quantified signal the integration range should extend from the centre of the signal at least seventy six times the FWHM on either side of the signal being measured. The limits of the integration range should be based on the outermost signals if a multiplet is subject to integration. An alternative rule-of-thumb that generally produces acceptable results is to use a range extending $30\mathrm{Hz}$ beyond the furthest ¹³C satellites as the start and end points for the integration ranges. A consistent approach should be employed for all signals subject to integration. It is also important to apply a suitable procedure for the baseline correction and check its validity by analysing standard samples. Practical experience has shown that manual baseline assignment currently works best when very high accuracy qNMR results are required. [32], [39] A window function can be applied as a final data treatment parameter to enhance the S/N ratio. [9] To avoid line broadening effects, an exponential multiplication factor not greater than $0.3\mathrm{Hz}$ should be used. The window function in use at the BIPM with the JEOL-ECS 400 was typically no greater than $0.05\mathrm{Hz}$ — $0.10\mathrm{Hz}$ and in some cases it was not used at all.

3.7.  Measurement uncertainty

Evaluation of the measurement equation previously presented (Equation (1)) allows for identification of individual factors potentially influencing the input quantities for the measurement uncertainty as shown in the diagram in Figure 3.

Figure 3 — Ishikawa diagram for input quantities considered for the measurement uncertainty estimation by qNMR

The observed repeatability of the integral area ratios, which incorporates contributions from the input factors for excitation, population, detection efficiency and data processing, is amenable to a type A statistical evaluation. [12], [32], [40] Since these measurements should come from at least two independent solutions each containing different sample masses, the area ratios will vary on a sample-by-sample basis.

The measurement uncertainty of the value obtained for each preparation can be evaluated separately and the individual purity results for each sample combined statistically. Another approach is to pool the purity values from the replicate results for the separate samples. Analysis of these combined data by ANOVA produces an assigned value and provides an estimate of the intermediate precision of the overall process. It also identifies if additional variance contributions from sample preparation and signal processing contribute significantly to the observed precision in the value assignment in addition to that arising from the method repeatability.

The final assigned value will be similar regardless of the approach used, although the contributions of the factors to the measurement uncertainty of the result may differ.

The standard uncertainties for the other major input quantities are type B estimates and are straightforward to evaluate. Molar masses and the ¹H/²H isotope distribution of the quantification signals, with their associated uncertainties, were calculated based on the values for atomic weights and hydrogen isotope distribution in the 2016 revision of the IUPAC Technical report of the Atomic weights of the elements, [24], [25] the uncertainties of individual gravimetric operations are based on balance performance characteristics corrected for buoyancy effects [31] and the uncertainty of the purity of the internal standard is assigned by the material provider.

Other approaches to the evaluation of measurement uncertainty for qNMR and the combination of results from qNMR with orthogonal techniques for purity evaluation have also been reported [8], [11], [12], [33] including recently a Bayesian approach using a Monte Carlo calculation of the results of replicate sample analysis. [41] Examples of measurement uncertainty budgets for qNMR analysis using DMSO₂ as the ISRM are provided in Appendix A1.2.