2.1.  Physical Properties

Name

Dimethyl terephthalate

Structure

+

Synonym

Dimethyl 1,4-benzenedicarboxylate

CAS Registry Number

120-61-6

Molecular Formula

C₁₀H₁₀O₄

Molar Mass [19]

$194.186\mathrm{g}/\mathrm{mol}$, $u=0.009\mathrm{g}/\mathrm{mol}$

Melting point [20]

$141\mathrm{°C}$

Density

$\mathrm{1 075}\mathrm{kg}/{\mathrm{m}}^3$ [20]
$\mathrm{1 200}\mathrm{kg}/{\mathrm{m}}^3$ [21]

Appearance

White crystalline powder

¹H NMR [22]

$\delta 8.1\text{ (S},4\text{H) ; }3.94\text{ (s},6\text{H) ppm}$

¹³C NMR

$\delta 166.2;134.0;129.6,52.4\text{ ppm}$

Figure 2 — ¹H NMR spectrum of DMTP in CDCl₃

2.2.  NMR Solvent Compatibility

NMR solvents suitable for use with DMTP are CDCl₃ and DMSO-$d_6$. DMTP is soluble at levels in excess of $5\mathrm{mg}{\mathrm{mL}}^{-1}$ in CDCl₃ and in excess of $2\mathrm{mg}{\mathrm{mL}}^{-1}$ in DMSO-$d_6$. qNMR studies using DMTP as ISRM can also be undertaken in as solutions in acetone-$d_6$ or CD₃CN.

DMTP is moderately soluble in CD₃OD. The formation in situ of mono- and di-transesterification artefacts from exchange of CH₃O- by CD₃O- at the methoxycarbonyl substituents restricts its use for qNMR in this solvent to quantifications based on the aromatic proton signal. [23]

2.3.  NMR quantification signals

The four magnetically equivalent aromatic and six equivalent methyl ester protons of DMTP are observed as singlets at a chemical shift of approximately $8\mathrm{ppm}$ and $4\mathrm{ppm}$ respectively. The position of the resonance is a function of factors including but not limited to the solvent, temperature and the concentration of DMTP and other analytes in the solution. For optimal quantification results the homogeneity of the spectrometer magnetic field should be optimized such that the full width at half maximum (FWHM) of the signal(s) used for quantification are less than $1\mathrm{Hz}$ while the base of each resonance retains a suitable Lorentzian peak shape.

2.4.  Impurities and artefact signals

Samples of DMTP analysed in our laboratory show some evidence of the presence of small levels of related structure impurities in the material. These are most likely either isomeric (dimethyl phthalate) or homologous (diethyl terephthalate) in structure.

As noted above, artefacts form if DMTP is taken up in solution in CD₃OD due to transesterification exchange. An NMR spectrum showing the appearance of free methanol in a solution of DMTP in CD₃OD subsequent to its preparation is shown in Appendix A1.3.

In practice the main interferences in a solution containing DMTP come from residual non-deuterated solvent. The chemical shifts of these signals are given in Table 1 below.

2.5.  Solvent recommendations & 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)). The mass fraction purity of the internal standard used for the measurement, the source of traceability to the SI for the value to be assigned to the analyte, is established by independent measurements undertaken prior to the qNMR experiment.

The gravimetric procedure used for the preparation of the NMR solution has to be fully validated and fit for its intended purpose, [24], [25] and the spectrometer performance, experimental parameters and the protocol for signal processing and integration must be optimized, [4], [7], [26] in order that the observed ratio of the integrals of the analyte and standard signals accurately reflects the molar ratio of the hydrogen nuclei giving rise to the signals. [27] When these conditions are met the assigned mass fraction purity of the analyte can be regarded as traceable to the SI. [9], [28], [29] Some general guidance for recommended practice for these critical steps is given in the following sections.

3.2.  Internal standard

At least one of the internal standards listed in Figure 1 above should be suitable for use as the ISRM for a qNMR purity assignment. The material used should comply as far as possible with the criteria described in Chapter 1 above regarding composition, physical characteristics, inertness, solubility, impurity profile and relative hydrogen content by mass. In order to establish traceability of the result to the SI, the material should comply with the requirements of a reference measurement standard, and in particular of a Certified Reference Material, defined in the International Vocabulary of Metrology (VIM). [30]

For SI-traceability the internal standard should consist of one of the following:

1. Certified Reference Material (CRM) characterized for mass fraction purity and value assigned by a National Metrology Institute;

2. CRM provided as a high purity organic material by a Reference Material Producer accredited to ISO 17034:2016 [31] 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

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. [24] Achieving an overall relative standard measurement uncertainty for a qNMR assignment of 0.1 % will typically require the relative uncertainty associated with individual gravimetric operations be less than 0.03 %. If the combined standard uncertainty of a mass determination is $3\mathrm{\mu g}$, a level achievable with modern electronic microanalytical balances, this corresponds to a minimum sample size of $10\mathrm{mg}$. Care should be exercised to include an appropriate allowance for the uncertainty of each gravimetric operation within the overall uncertainty budget for a qNMR purity assay. It must take into account the contribution due to gravimetric uncertainty introduced as a consequence of the aliquot sample sizes and the performance characteristics of the balance used.

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 mass determinations the procedure for transfer of solids into the solution must be validated to address the assumption that the ratio of the 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 balance reading, for high accuracy measurements correction for sample buoyancy effects and the contribution to the overall measurement uncertainty associated with this correction should also be taken into consideration. [25]

As sample preparation for qNMR involves mass determinations in the milligram range using sensitive balances, the loss of even minute (almost 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. [32] It is recommended that mass determinations be performed in an area where the relative humidity is maintained in the range 30 % to 70 %.

The accumulation of surface electrostatic charges is a 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. Where possible materials subject to qNMR analysis should be evaluated for their hygroscopicity, for example by measurement of the change in observed mass as a function of relative humidity using a dynamic sorption balance. 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 when assigning the purity of a compound by qNMR.

3.4.  NMR spectrometer optimization for quantitative measurements

There is no specification of minimum NMR spectrometer field strength for purity measurements. Increasing field strength results provides enhanced signal separation and increases sensitivity, both of which should increase the accuracy and precision of qNMR measurements. Careful optimization of the lineshape (shimming) is mandatory and critical in order to achieve reliable qNMR results. [33] 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 recommendation might not be attainable. If the lineshape is broader the level of measurement uncertainty associated with the assigned value will increase. 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 signal 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 the range one hundred times the FWHM either 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 minimise differences in the integrated signal intensities due to effects related to incomplete relaxation of the quantification resonances. For highest accuracy assignments use of broadband heteronuclear decoupling should be avoided if possible 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, this potential contribution to bias in a qNMR result is attenuated to a negligible level because of the low (1.1 %) natural abundance of the ¹³C isotopomer.

The recommended 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 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 them 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 signal response. However this potential practical 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 (trueness) of the results should not be impacted by the use of different pulse lengths but the acquisition times to achieve equivalent levels of signal precision (repeatability) 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 meaningful area measurements and suitable repeatability 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 DMTP 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 generally available in the factory programmed pulse sequences installed with any NMR. The application of the inversion recovery experiment requires knowledge of the optimized $90\mathrm{°}$ pulses for each quantified signal, which should also be determined for each mixture under investigation. The optimized $90\mathrm{°}$ pulse values can be 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 RT is a multiple $T_1$. After a $90\mathrm{°}$ pulse, if the available instrument time permits, 10 times $T_1$ of the signal with the longest relaxation time will lead to the recovery of > 99.995 % 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 will be sufficient for equivalent (even if incomplete) magnetization re-equilibration. At least 10 $T_1$ should be used as a minimum where highest accuracy results are sought.

Thus the pulse RT is given by:

The number of transients (or scans) should be determined according to the concentration of the samples, 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 for 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 but it is important to be 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 independently weighed analyte/IS mixture (a minimum of two samples) should be measured at least three times in the NMR system. Independent measurements for a particular sample mixture should be non-continuous, where the tube is removed and the measurement process (tuning, locking, shimming) repeated each time for each sample.

3.6.  NMR signal integration

The integration range should extend on each side ideally at least seventy six times the FWHM of the signal being measured in order to integrate in excess of 99.9 % of the signal. The estimation of signal width should be done for the outer signals if a multiplet signal is subject to integration. A generally acceptable approximation is to use a range extending $30\mathrm{Hz}$ beyond the furthest ¹³C satellites as the start and end points for the integration range, as this generally exceeds the above described width. In a complex spectrum where other signals are adjacent to one or both of the quantification signals and quantification over the full range is not possible apply a consistent approach to the integration of both signals.

It is important to apply a suitable algorithm for the baseline correction and check its validity by analysing standard samples. Practical experience has shown that currently manual baseline assignment is the most reliable general approach when high accuracy qNMR results are required. [31] A final data treatment parameter that can be applied is an adequate window function. For ¹H NMR, exponential multiplication by a factor not greater than $0.3\mathrm{Hz}$ should be used. The exponential multiplication factor in use at the BIPM with the JEOL-ECS 400 is typically no greater than $0.05\mathrm{Hz}-0.10\mathrm{Hz}$ and in some cases is not used at all.

3.7.  Measurement uncertainty

Evaluation of the measurement equation previously presented (Equation (1)) identifies the factors 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. [24], [34] Since these measurements come from at least two independent solutions each containing different sample masses, the observed absolute 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 this 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 exist in addition to that due to the method repeatability. [9]

The final assigned value will be similar regardless of the approach used, although the contribution 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 their uncertainties are estimated based on the “conventional” values for atomic weights given in Table 3 of the 2016 revision of the IUPAC Technical report of the Atomic weights of the elements, [19] the uncertainties of mass determinations are based on balance performance characteristics and are corrected for buoyancy effects [26] 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. [28], [35] Examples of “best case” measurement uncertainty budgets for qNMR analysis are provided in the examples given in Appendix A1.2.