# Nuclear Quadrupole Resonance (NQR)—A Useful Spectroscopic Tool in Pharmacy for the Study of Polymorphism

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## Abstract

**:**

^{14}N NQR can distinguish between the polymorphic crystalline phases of active pharmaceutical ingredients (APIs). In order to further stimulate

^{14}N NQR studies, we review here several results of API polymorphism studies obtained in Ljubljana laboratories: (a) In sulfanilamide, a clear distinction between three known polymorphs (α, β, γ) was demonstrated. (b) In famotidine, the full spectra of all seven different nitrogen positions were measured; two polymorphs were distinguished. (c) In piroxicam, the

^{14}N NQR data helped in confirming the new polymorphic form V. (d) The compaction pressure in the tablet production of paracetamol, which is connected with linewidth change, can be used to distinguish between producers of paracetamol. We established that paracetamol in the tablets of six different manufacturers can be identified by

^{14}N NQR linewidth. (e) Finally, in order to get an extremely sensitive

^{14}N NQR spectrometer, the optical detection of the

^{14}N NQR signal is mentioned.

## 1. Introduction

_{0}, NQR is based on the interaction between the tensor of the non-symmetric charge distribution e

**Q**of the nucleus with the nuclear spin I ≥ 1 and the tensor of internal electric field gradient (EFG)

**V,**leading to the quadrupole energy term in the Hamiltonian $\mathcal{H}=$ e

**QV**. The EFG is determined by the surrounding electric charge distribution at the site of a nucleus in the crystal lattice.

**V**, we have V

_{XZ}= V

_{YZ}= V

_{XY}= 0 for these EFG tensor components. If we choose |V

_{ZZ}| ≥ |V

_{XX}| ≥ |V

_{YY}|, define the asymmetry parameter η = (V

_{XX}− V

_{YY})/ V

_{ZZ}and write for the maximal component of the EFG tensor V

_{ZZ}= ∂

^{2}V/∂z

^{2}= eq, we obtain for the quadrupole Hamiltonian [4,5,6]

^{2}qQ/h = QCC is the quadrupole coupling constant, where eQ is the nuclear electric quadrupole moment, eq = V

_{zz}is the maximal component of the electric field gradient tensor, e is the elementary charge and h is Planck’s constant. The asymmetry parameter η is a measure of the deviation of the EFG tensor from axial symmetry; it takes values between 0 and 1.

^{14}N) with spin I = 1 is the most common quadrupole nucleus in organic chemical compounds and in APIs. Therefore, it is convenient to use the

^{14}N and its nuclear quadrupole interaction to obtain quadrupole energy levels and the allowed transitions between them. Figure 1 shows, schematically, the

^{14}N NQR energy levels with transitions between them. The corresponding quadrupole frequency set (QFS) is then written as [4,5,6]:

^{14}N NQR spectrum. The frequencies (${\nu}^{+}$, ${\nu}^{-}$, ${\nu}^{0}$) are determined by eQ, which is a property of the nitrogen nucleus, and by the EFG magnitude eq and asymmetry parameter η, which depend on the electric charge distribution in the chemical bond as well as on the arrangement of crystal forming entities (atoms, ions, molecules) in the vicinity of the nucleus. This gives rise to the unique connection between the

^{14}N NQR frequencies (Equation (2)) and the crystalline structure. Therefore, the quadrupole resonance spectrum is a fingerprint of a particular chemical compound and its crystalline structure. The relationship between NQR frequency and crystalline structure is often used in solid state physics. For example, almost every quadrupole nucleus can be and has been used in phase transitions research [8]. On the other hand, there are two applications where the quadrupole nucleus is most often nitrogen: the contactless (nondestructive) detecting of illicit materials (explosives, narcotics and counterfeit medicines) [9] and pharmaceutical applications [10].

^{35}Cl NQR [13] and

^{14}N NQR [14].

^{14}N NQR lines are found at very low frequencies (0.5–4 MHz). Hence, the signal-to-noise (S/N) ratio is in some cases very low and measurements may require the excessive averaging of the signal scans. In such cases, the indirect detection of

^{14}N NQR resonances is possible by measuring the proton NMR signal in various Nuclear Quadrupole Double Resonance experiments (NQDR). Although NQDR requires smaller samples, and spectra with good S/N can be acquired quickly, a significant line broadening is observed because an external magnetic field is required [17,18,19,20].

^{14}N NMR at high magnetic fields [21]. However, this method is limited to samples with a very small number of nonequivalent nitrogen atoms in the unit cell.

^{35}Cl NQR [22,23] and

^{14}N NQR [10,24] have shown that it is possible to distinguish between different polymorphic forms of APIs. Although nitrogen is the most prevalent quadrupole nucleus in solid APIs, the application of

^{14}N NQR is still scarce. Several comprehensive

^{14}N pure NQR studies of polymorphism in APIs conducted in recent years by research labs located in Ljubljana have shown that it is a viable complementary method to other spectroscopic methods.

^{14}N NQR research on polymorphism in sulfanilamide [25], famotidine [26], piroxicam [27,28] and paracetamol [15]. In all cases, polymorphism was confirmed by the X-ray diffraction (XRD) first.

## 2. Examples of ^{14}N NQR Studies of Polymorphism

#### 2.1. ^{14}N NQR in Sulfanilamide

^{1}H,

^{13}C

^{15}N) [40] and DTA [41,42] were used to further elucidate polymorphism in sulfanilamide.

^{14}N NQR. R. Blinc et al. [44] studied a group of sulfa drugs by

^{14}N NQR. The sulfanilamide β-polymorph and one other non-specified sulfanilamide polymorph were included, demonstrating the power of

^{14}N NQR in pharmaceutical research.

^{14}N NQR applications in pharmacy, and we systematically studied the

^{14}N NQR of α-, β- and γ-sulfanilamide polymorphs. The molecule of sulfanilamide (Figure 1b) has two chemically nonequivalent nitrogen atoms: the para amino nitrogen N(1) and the sulfonamide nitrogen N(2). Therefore, we expect two sets of three transition frequencies (${\nu}^{+},{\nu}^{-},{\nu}^{0})$ for each polymorph. The α- and β-polymorphs were prepared from different solvents and subsequent evaporation/crystallization [25,34,35,40,44]. Using different solvents can lead to the occurrence of different polymorphs, as was observed by several researchers [40,44,45]. The three polymorphs of sulfanilamide (α, β and γ) [35] were prepared by the recrystallization of commercially available sulfanilamide (Sigma-Aldrich): (i) in 3-methyl−1-butanol or n-butanol for the α-polymorph and (ii) in ethanol for the β-polymorph. At temperatures above approximately 400 K, these two polymorphs exist no more; only the γ-polymorph is left. The monotropic transition temperature from the α to γ form (at about 380 K) is slightly lower than from the β to γ form (at about 385 K) [34,35]. The third polymorph, γ, was prepared simply by the controlled heating of the β-polymorph at 403 K for approximately 30 min. All three polymorphs are stable at room temperature.

^{14}N NQR frequencies are clearly different for each polymorph and for each non-equivalent nitrogen molecule, as expected (Figure 2). For each polymorph, two sets of three lines (one for N(1) and one for N(2)) were obtained. In the lowest track of Figure 3, it can be seen that the sample prepared as the α -polymorph contained a small admixture of the β-polymorph. These measurements were taken with a standard pulse NQR spectrometer, operated from a PC. Technical details are published in [25] and [46]. All the results were obtained at room temperature and are presented in Table 1.

^{14}N NQR transition frequencies for the nitrogen atoms N(1) and N(2) for all three sulfanilamide polymorphs were measured in the temperature interval 210–330 K and are shown in Figure 4.

^{14}N NQR with their temperature dependences have been used to obtain, non-destructively, the following information [25]:

^{14}N NQR spectra were recorded. For easy quantitative interpretation, all the NQR spectra were measured at the room temperature. The measurements started with nominally pure sulfanilamide α-polymorph. The evolution of

^{14}N NQR spectra of the nitrogen N(2) and transitions between different polymorphic forms are shown in Figure 5. This Figure shows that the starting sample was a mixture of α- and a small amount of β-polymorph. Stepwise increase in the temperature of thermal treatment before each measurement triggers a gradual transition of α- polymorph to β-polymorph. The

^{14}N NQR line height for the α- polymorph is decreasing and the

^{14}N NQR line height for the $\beta $-polymorph is simultaneously increasing. At about 380 K the α- polymorph disappears completely. The areas under the

^{14}N NQR lines (line-shape integrals) of a studied sample were determined after a chosen temperature treatment. Assuming the validity of the expression (3), fractions all three polymorphs were obtained (Figure 6), where a, b, c are the coefficients, p

_{α}

_{,}p

_{β}

_{,}p

_{γ}are the line-shape integrals of the relevant lines, and the products ap

_{α}

_{,}bp

_{β}

_{,}cp

_{γ}are the fractions of different polymorphs

^{14}N NQR, is the same as the one obtained by the DSC measurement [38,42], the β- to γ- transition temperature obtained from

^{14}N NQR measurements is about 10 K higher. From Figure 3 and Figure 6 it is additionally evident that α-polymorph is not abundantly directly transformed to γ-polymorph, but preferably via the formation of intermediate β-polymorph that then transforms into γ-polymorph. We can notice that the scan at 363 K showed already the appearance of γ-polymorph, i.e., before all α-polymorph was transformed to β-polymorph”.

^{14}N NQR data convincingly differ for all three polymorphs. The view into the lattice dynamics of the N(1) and N(2) nitrogen atoms and their surroundings for the α- and β-polymorphs via the spin-lattice relaxation time, ${T}_{1}$, measurements is additional information. It is a valuable supplement to the

^{13}C and

^{15}N NMR magic angle spinning data (chemical shifts) as well as the corresponding ${T}_{1}$data for all three polymorphs [40].

^{14}N NQR studies demonstrate that we were dealing with the room temperature stable forms of all three polymorphs. We could repeat

^{14}N NQR measurements on all polymorphs during our several years lasting studies of sulfanilamide, provided the polymorph samples were thoroughly protected from the influence of laboratory environment. Prior to applying our experimental protocol, a mixture of α-and β-polymorphs was observed in our starting materials (Figure 3 and Figure 5). Having a stable mixture of sulfanilamide polymorphs, estimation of the contents of $\alpha $-, β- and γ-sulfanilamide polymorphs is possible, using

^{14}N NQR spectra”.

#### 2.2. ^{14}N NQR in Famotidine

^{14}N NQR spectra are much more complex for API molecules, which contain several non-equivalent nitrogen atoms [47], each of which contributes a quadrupole frequency set (QFS) of three characteristic

^{14}N NQR lines.

^{14}N NQR in famotidine study.

^{+}, ν

^{−}and ν

^{0}for each polymorph. Both famotidine polymorphs crystalize in monoclinic symmetry with four molecules per unit cell and are stable at room temperature.

_{1}and T

_{2}allowed the application of the MPSE technique [25,46,52] with up to 20 echoes in a single sequence. This multiplies the number of averages and improves the final S/N ratio.

^{14}N NQR frequencies belonging to seven non-equivalent nitrogen atoms in polymorphs A and B of famotidine, these steps were followed:

^{+}/ν

^{−}/ν

^{0}connections using pure NQR, careful frequency scans and numerous trials of the most probable combinations into tentative quadrupole sets were necessary. Measurement of the NQR lines shapes in a low magnetic field [56] was also performed to discriminate between the ν

^{+}/ν

^{−}character of the newly found lines, and to choose the probable region for further search for the missing lines.

^{14}N NQR transition frequencies at room temperature and the calculated EFG parameters are collected in Table 2.

- (i)
- (ii)
- the correlation between the two pairs ν
^{+}/ν^{−}of the two tentatively equivalent nitrogen sites of the polymorphs A and B, should agree with the same empirically confirmed ν^{+}/ν^{−}correlation, characteristic for many other molecules, containing the relevant structurally equivalent nitrogen surroundings [43,44,58,59,60,61] (cf. Figure 8)”.

^{a}, N

^{h}−> N

^{18}. The two highest QCC-s belong to the line sets N

^{a}of polymorph A and N

^{h}of polymorph B in the Table 2. Both tensors resemble those of the sulfonamide group in sulfanilamide and similar compounds [25,43,44,58]. Therefore, the QFS-s N

^{a}(polymorph A) and N

^{h}(polymorph B) – both lying near the frequencies ν

^{+}~3.5 MHz, ν

^{−}~2.5 MHz and ν

^{0}~1 MHz – are ascribed to the S

^{17}—N

^{18}H

_{2}nitrogen atom, located in the “sulfa” tail of the famotidine molecule (criterion (i))”.

^{6}on the “guanidine” side of the famotidine chain (group C

^{7}==

**N**—C

^{6}^{2}) and N

^{16}on the “sulfa” side (group C

^{14}==

**N**—S

^{16}^{17}). With our present understanding these two nitrogen atoms could only be alternatively connected with any of the remaining QFS-s N

^{f}or N

^{d}of polymorph A and with N

^{l}or N

^{j}of polymorph B”. For details, see reference [26].

^{14}N NQR transition frequencies - one for each polymorph. The intensities of different

^{14}N NQR transition lines and also their relaxation properties are not equal. The best choice is to select a pair with the maximal intensity which allows the greatest number of echoes in a single multi-pulse sequence. According to reference [26] such pairs of lines are: 2603 kHz, 2862 kHz and 3455 kHz of polymorph A and 2587 kHz, 2887 kHz and 3462 kHz of polymorph B. Each of the three pairs of

^{14}N NQR transition lines can be observed simultaneously in the same spectral region for both polymorphic forms (Figure 9). From the

^{14}N NQR spectra it is possible to quantify the polymorphic form and its purity. Additionally, for samples of heterogeneous mixtures of polymorphs and excipients it is possible to determine the concentration of different polymorphs. This is of special interest in studying transitions from one polymorphic form to the other [26]”.

^{14}N NQR measurements of Ulfamid sample demonstrated the presence of famotidine polymorph B. The

^{14}N NQR lines were broader compared to the lines of powder famotidine (Figure 10). It was concluded that the deformation of grains during the tablets preparation process may be the reason for the linewidth increase”. The detailed study of this phenomenon is described in Section 2.4.

#### 2.3. ^{14}N NQR Study of Piroxicam

^{14}N NQR:

- (i)
- (ii)
- The quantitative determination of a particular piroxicam polymorph.

^{14}N NQR study of piroxicam. All the measurements were performed with the instruments described in [25,26].

^{14}N nuclei have a strong influence on the bonding orbitals and on the nitrogen EFG tensor. Each polymorphic form of piroxicam is defined by a set of nine characteristic

^{14}N NQR resonant frequencies. The set of nine lines of each polymorphic form consists of: 3 pairs (ν

^{+}

_{,}ν

^{−}) and 3 trivial low frequency lines (${\nu}^{0}={\nu}^{+}-{\nu}^{-})$. Each pair belongs to one of the three nonequivalent

^{14}N nuclei in the piroxicam molecule: the secondary amine N3 = N

_{keto}, pyridine N2 = N

_{pyr.}and benzothiazine nitrogen N1 = N

_{b.thiaz.}(Figure 11b and Table 3). Considering the published

^{14}N NQR data for molecules with aromatic, secondary and tertiary amines with bonded aromatic, keto- and sulfonyl- moieties, we can sort the size of

^{14}N quadrupole coupling constants and resonant frequencies [6,11]. Their magnitudes are ranked in the order N(sulfonyl) > N(pyridine) > N(keto). These observations have been compared to the measured

^{14}N NQR frequencies of piroxicam samples to assign the above frequency pairs to the proper nitrogen atoms N1 (=N

_{b.thiaz.}), N2 (=N

_{pyr.}) and N3 (=N

_{keto}) (cf. Figure 11 b and Table 3), knowing that benzothiazine N1 belongs to the sulfonyl structures”.

^{14}N NQR transition frequency to identify each piroxicam polymorph. In Figure 12, the ${\nu}^{+}$

^{14}N NQR transition frequencies of the nitrogen atom N2 were chosen.

^{14}N NQR lines, their intensities and linewidths in Figure 12 reveals that the polymorphs I and III were pure, while in this case, the polymorphs II and V were not pure—they contained the admixtures of the piroxicam polymorphs I and III [28].

^{14}N NQR research of piroxicam polymorphism was undertaken not much later. The results are described in [28]: “

^{14}N NQR confirmed the existence of four polymorphs, however, we could not prepare the polymorph V without small amounts of impurities of polymorphs I and/or II.

^{14}N NQR allows also a quantitative determination of these impurities. It is worth to mention that the similarity of polymorphs II and V was also reflected by the Raman and DSC measurements. We can therefore state that here the use of different measuring techniques demonstrated the high selectivity of NQR spectroscopy.

^{14}N NQR resonances of forms II and V are well separated and we can clearly resolve these two polymorphs. The measured

^{14}N NQR frequencies${\nu}^{+}$

_{,}${\nu}^{-}$ and ${\nu}^{0}$ enabled us to calculate the two NQR characteristic parameters QCC and η (Table 3). The QCC and η for all four polymorphic forms of piroxicam can be clearly associated with 3 different nitrogen atoms in the piroxicam molecule. The highest QCC and the smallest η is associated with the N1 atom of the benzo-thiazine ring, the middle QCC and the middle η is associated with the N2 atom of the pyridine ring and the smallest QCC and the biggest η is associated with the N3 atom of the amine nitrogen (=N

_{keto}). The values of quadrupole parameters (QCC, frequency and η) in Table 3 indicate the similarity in charge distribution for all four polymorphs of piroxicam. Higher deviation from average can be noticed only for the two QCC-s of N1 for polymorphs I and III (Figure 14a). On the other hand, again for polymorphs I and III higher deviation is seen in η of N3 (Figure 14b).

^{14}N NQR is illustrated in Figure 15 where the intensity of ${\nu}^{+}$

^{14}N NQR signal of N3 nuclei in the mixture of polymorph piroxicam I with pyridine monohydrate is shown”.

#### 2.4. Tablet Compaction Pressure vs. Linewidth

^{14}N NQR in drug research [15]: the linewidth of the

^{14}N NQR signal is correlated with the compaction pressure during the compression of particular tablets. The thermodynamically stable monoclinic paracetamol and the metastable orthorhombic polymorph were measured. In Figure 16, the relative

^{14}N NQR linewidth for the ν

^{+}and ν

^{−}lines of monoclinic paracetamol is shown as a function of compaction pressure during the tablet preparation. Subsequently, the

^{14}N NQR signals of the thermodynamically stable monoclinic paracetamol in different commercial paracetamol tablets available on the local market were measured. The results are shown in Figure 17a–b. It can be concluded that, in this way, the potential identification and authentication of the manufacturer is possible when needed, for instance, for the confirmation of fake drugs.

^{14}N NQR lines coming from different deformed grains. One can write for the above relation within the linear terms

^{+}, ν

^{-}, q and η are the non-shifted NQR line values and tensor components, whereas δν

^{+}, δν

^{-}, δq and δη are the corresponding shifts due to local deformations. One can also define standard deviations of the shifts of these values from the averages, like $<\delta {\nu}^{\pm}>=\sqrt{<{\left(\delta {\nu}^{\pm}\right)}^{2}>}=\mathsf{\Delta}{\nu}^{\pm}/2$. Taking into account the inaccuracy of the linewidth estimation, the actual ratio of the ${\nu}^{+}$ and ${\nu}^{-}$ linewidths is best explained by the following distribution width of the electric field gradient tensor components: $\mathsf{\Delta}q=2\sqrt{<{\left(\delta q\right)}^{2}>}\approx 0$ for all compaction pressures and $\mathsf{\Delta}\eta =2\sqrt{<{\left(\delta \eta \right)}^{2}>}$ growing from ~0.004 in powder to ~0.03 in model tablets, formed at 1.1 GPa, according to Figure 17.

^{14}N NQR signals was observed. No narrowing effect was observed either with commercial tablet samples after similar thermal annealing. Partial narrowing was obtained only after milling of tablets in “ball mill” (Fritsch). After 40 min milling (final grain size below ~50 mm) the linewidths of

^{14}N NQR signals of tablets prepared with 1.1 GPa pressure decreased to approximately half of the value obtained after tablet compaction. Yet, they remained much broader than those in the not pressed initial powder sample”.

#### 2.5. Instrumentation Improvements

^{14}N NQR measurements outside specialized laboratories may require substantial improvements in measuring speed and sensitivity. To accomplish that, several instrumentation improvements are being developed.

^{14}N NQR signals [33]. One can further improve the S/N ratio of a low frequency

^{14}N NQR measuring system by a combination of a standard pulsed

^{14}N NQR spectrometer, used today practically for all measurements, and an alkali metal optically pumped magnetometer (OPM) [73,74]. The latter will better detect the magnetic part of the

^{14}N NQR signal, as first mentioned in [32]. A comparison of the measured

^{14}N NQR signals by a classic pulsed NQR spectrometer and by a spectrometer combined with OPM [74] is shown in Figure 18.

## 3. Conclusions

^{14}N NQR is—in addition to NMR—a powerful contactless and non-destructive RF spectroscopic tool for detecting the appearance of polymorphism with a possibility to distinguish clearly and quantitatively among different polymorphs. This was demonstrated in several APIs containing

^{14}N nuclei in up to seven chemically nonequivalent sites. Different compaction pressures in the production of tablets are reflected in the different linewidths of the

^{14}N NQR lines.

^{14}N NQR measurements, an improved optical NQR measurement system is available.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**(

**a**) Quadrupole energy levels (schematic) and allowed transitions for the spin 1 nucleus. (

**b**) Sulfanilamide molecular structure (schematic). The para amino nitrogen N(1) and the sulfonamide nitrogen N(2) are marked.

**Figure 2.**

^{14}N NQR transition frequencies (ν

^{+}, ν

^{−}and ν

^{0}) at 295 K for the α-, β- and γ-sulfanilamide polymorphs. Vertical lines denote the nitrogen (N(1) and N(2)) quadrupole frequencies. Reproduced with permission from reference [25], Trontelj Z et al., Journal of Pharmaceutical Sciences; published by Elsevier, 2019.

**Figure 3.**Part of the

^{14}N NQR spectra of the nitrogen (N(1)) atoms with the frequency ν

^{+}for all three polymorphs of sulfanilamide (3393 kHz for the α-, 3426 kHz for the β- and 3343 kHz for the γ-polymorph). The measurements took place at 295 K with approximately the same amount of all sulfanilamide samples (~ 4 g). The presence of traces of the β-polymorph in the

^{14}N NQR scan of the α-polymorph is visible. To obtain this signal-to-noise (S/N) ratio, the measurement time for one polymorph was 20 minutes. Reproduced with permission from reference [25], Trontelj Z et al., Journal of Pharmaceutical Sciences; published by Elsevier, 2019.

**Figure 4.**Temperature dependence of the nuclear quadrupole resonance (NQR) lines for all three polymorphs, α-, β- and γ-, of sulfanilamide: (

**a**) ν

^{+}of nitrogen N(1), (

**b**) ν

^{+}of nitrogen N(2), (

**c**) ν

^{-}of nitrogen N(1) and (

**d**) ν

^{-}of nitrogen N(2). Polymorphs α-, β- and γ- are labelled with diamond, triangle and square symbols, respectively. Reproduced with permission from reference [25], Trontelj Z et al., Journal of Pharmaceutical Sciences; published by Elsevier, 2019.

**Figure 5.**Room temperature

^{14}N NQR spectra of the nitrogen N(2) (the highest frequency ν

^{+}line) for the initial α-polymorph (with traces of the β-polymorph). A sample of sulfanilamide was

**t**hermally treated at different temperatures, indicated at the left side of each

^{14}N NQR scan, prior to the

^{14}N NQR measurements. The starting temperature was 295 K (room temperature). Small variations in the

^{14}N NQR frequency, especially of the β-polymorph, are due to small variations in room temperature during time-separated thermal cycles. Reproduced with permission from [25], Trontelj Z et al., Journal of Pharmaceutical Sciences; published by Elsevier, 2019.

**Figure 6.**Estimated fractions of polymorphs α, β and γ- in a sulfanilamide sample, which was initially mainly composed of the α-polymorph with a small fraction of the β-polymorph. Polymorphs α, β and γ are labelled with diamond, triangle and square symbols, respectively. Error bars are shown if the estimated fraction uncertainty at a given temperature is higher than 0.02. Reproduced with permission from reference [25], Trontelj Z et al., Journal of Pharmaceutical Sciences; published by Elsevier, 2019.

**Figure 9.**Typical characteristic part of the

^{14}N NQR spectrum for a mixed sample of forms A and B of famotidine (approximately 75% form A and 25% form B). Reproduced with permission from reference [26], Lužnik J et al., Journal of Pharmaceutical Sciences; published by Elsevier, 2014.

**Figure 10.**Dependence of the

^{14}N NQR relative linewidth on the compacting pressure of tablet fabrication. The relative linewidth of the same

^{14}N NQR line recorded in “Ulfamid” is indicated by the dotted line. Reproduced with permission from reference [26], Lužnik J et al., Journal of Pharmaceutical Sciences; published by Elsevier, 2014.

**Figure 11.**(

**a**) Structural formula of the piroxicam molecule with numbered nitrogen atoms, according to the assignation of the

^{14}N NQR resonance lines ${\nu}^{+},{\nu}^{-},{\nu}^{0}$. (

**b**) Bar diagram of all

^{14}N NQR frequencies for the four studied polymorphs of piroxicam I, II, III and V. Reproduced with permission from reference [28], Lavrič et al., Journal of Pharmaceutical Sciences; published by Elsevier, 2015.

**Figure 12.**Superimposed

^{14}N NQR spectra in the 3370−3460 kHz RF-band for the four piroxicam polymorphs at room temperature (normalized, neglecting the weak signals of possible impurities). These NQR lines belong to the

^{14}N atoms of the pyridine fragment (N2, ${\nu}^{+}$). Reproduced with permission from reference [28], Lavrič Z et al., Journal of Pharmaceutical Sciences; published by Elsevier, 2015.

**Figure 13.**(

**a**) Dependence of the piroxicam polymorph portions, evaluated from

^{14}N NQR signals around 3.4 MHz at the time of heating at 140 °C of the initial form II. Note the decrease in the polymorph II portion and increase in that of polymorph I. (

**b**) Initial form III—dependence of the polymorph portions (obtained from

^{14}N NQR) at the time of 140 °C heating; final shock to 160 °C completes the transformation of the remaining intermediate form V to the polymorph I. (

**c**) Initial form V (unpure)—dependence of the polymorph portions (obtained from

^{14}N NQR) at the time of 140 °C heating; final shock to 160 °C causes an almost abrupt transformation of the starting form V to the polymorph I. Reproduced with permission from reference [28], Lavrič Z et al., Journal of Pharmaceutical Sciences; published by Elsevier, 2015.

**Figure 14.**Graphic comparison of QCCs (

**a**) and corresponding asymmetry parameters η (

**b**) in successive polymorphs of piroxicam. Reproduced with permission from reference [28], Lavrič Z et al., Journal of Pharmaceutical Sciences; published by Elsevier, 2015.

**Figure 15.**ν

^{+}(2587 kHz)

^{14}N NQR signal intensity dependence on the volume fraction (W

_{V/V}) of piroxicam I (resonating

^{14}N NQR quadrupolar nuclei N3) in mixture with pyridine monohydrate. Reproduced with permission from reference [27], Lavrič Z et al., Journal of Pharmaceutical Sciences; published by Elsevier, 2010.

**Figure 16.**Relative

^{14}N NQR ${\nu}^{+}$ and ${\nu}^{-}$ linewidths in monoclinic paracetamol versus the compacting pressure of tablet preparation. Reproduced with permission from reference [15], ], Lužnik J et al., Applied Magnetic Resonance; published by Springer, 2013.

**Figure 17.**Normalized

^{14}N NQR ν

^{+}and ν

^{−}NQR signals from different monoclinic paracetamol commercial tablets for (

**a**) 1921 kHz and (

**b**) 2564 kHz lines. For comparison, the

^{14}N NQR lines of an uncompressed powder sample are also included. Reproduced with permission from reference [15], Lužnik J et al., Applied Magnetic Resonance; published by Springer, 2013.

**Figure 18.**Aminotetrazole monohydrate

^{14}N NQR line at 1.2132 MHz. Signal obtained with the K-OPM improved NQR spectrometer, panel (

**a**), and classic NQR spectrometer, panel (

**b**). Signals in the frequency (upper two panels) and in temporal domains with real parts (thick line) and imaginary parts (thin line) (lower two panels). Reproduced with permission from reference [74], Begus S et al., Journal of Physics D: Applied Physics; published by IOP Publishing Ltd, 2017.

**Table 1.**Measured

^{14}N NQR transition frequencies, with the corresponding temperature coefficients, quadrupole coupling constants (QCC), asymmetry parameters η and spin-lattice relaxation time T

_{1}of the α-, β- and γ-sulfanilamide polymorphs at 295 K. The upper rows belong to the N(1) and the lower rows to the N(2) atoms in the sulfanilamide molecule. Reproduced with permission from reference [25], Trontelj Z et al., Journal of Pharmaceutical Sciences; published by Elsevier, 2019.

Polymorph | Atom | ν^{+}(kHz) | dν^{+}/dT(kHz/K) | ν^{−}(kHz) | dν^{−}/dT(kHz/K) | ν^{0}(kHz) | QCC(kHz) | η | T_{1}(ms) |

A | N(1) | 3393 | −0.17 | 2416 | −0.12 | 977 | 3873 | 0.50 | 25 |

N(2) | 3049 | −0.23 | 2516 | −0.25 | 533 | 3710 | 0.29 | 400 | |

Β | N(1) | 3426 | −0.35 | 2496 | −0.32 | 930 | 3947 | 0.47 | 25 |

N(2) | 3074 | −0.40 | 2565 | −0.39 | 509 | 3743 | 0.29 | 400 | |

Γ | N(1) | 3343 | −0.19 | 2400 | −0.13 | 944 | 3829 | 0.49 | 25 |

N(2) | 3041 | −0.95 | 2541 | −1.17 | 500 | 3721 | 0.27 | 25 |

**Table 2.**

^{14}N NQR transition frequencies at room temperature for the polymorphic forms A and B of famotidine belonging to all seven different nitrogen positions in each of the two crystal unit cells. Reproduced with permission from reference [26], Lužnik J et al., Journal of Pharmaceutical Sciences; published by Elsevier, 2014.

Form A* | ν^{+} (kHz) | ν^{−} (kHz) | ν^{0} (kHz) | QCC (kHz) | η |

N^{a} | 3455 | 2443 | 1012 | 3932 | 0.51 |

N^{b} | 2862 | 2065 | 797 | 3285 | 0.49 |

N^{c} | 2819 | 2080 | 739 | 3266 | 0.45 |

N^{d} | 2738 | 2274 | 464 | 3341 | 0.28 |

N^{e} | 2735 | 2030 | 705 | 3177 | 0.44 |

N^{f} | 2603 | 1971 | 632 | 3049 | 0.41 |

N^{g} | 1979 | 1457 | 522 | 2291 | 0.46 |

Form B* | ν^{+} (kHz) | ν^{−} (kHz) | ν^{0} (kHz) | QCC (kHz) | η |

N^{h} | 3462 | 2472 | 990 | 3956 | 0.50 |

N^{i} | 2887 | 2364 | 523 | 3501 | 0.30 |

N^{j} | 2848 | 2234 | 614 | 3388 | 0.36 |

N^{k} | 2787 | 2043 | 744 | 3220 | 0.46 |

N^{l} | 2649 | 2133 | 516 | 3188 | 0.32 |

N^{m} | 2587 | 1765 | 822 | 2901 | 0.57 |

N^{n} | 1982 | 1339 | 643 | 2214 | 0.58 |

^{a,b,c,…}in order of descending ${\nu}^{+}$.

**Table 3.**

^{14}N NQR Frequencies, Quadrupole Coupling Constants (QCC) and Asymmetry Parameters η of Piroxicam Polymorphs I, II, III and V at room temperature. Reproduced with permission from Reference [28], Lavrič et al., Journal of Pharmaceutical Sciences; published by Elsevier, 2015

v^{+}[kHz] | v^{−}[kHz] | v^{0}[kHz] | QCC [kHz] | η | ||
---|---|---|---|---|---|---|

I | N1 | 3928 | 3686 | 242 | 5076 | 0.0954 |

N2 | 3439 | 2983 | 456 | 4281 | 0.213 | |

N3 | 2587 | 1972 | 615 | 3039 | 0.405 | |

II | N1 | 3852 | 3600 | 252 | 4968 | 0.101 |

N2 | 3399 | 2946 | 455 | 4230 | 0.215 | |

N3 | 2533 | 2081 | 452 | 3076 | 0.294 | |

III | N1 | 4008 | 3763 | 245 | 5181 | 0.0946 |

N2 | 3392 | 2967 | 425 | 4239 | 0.201 | |

N3 | 2592 | 2085 | 507 | 3118 | 0.325 | |

V | N1 | 3849 | 3587 | 262 | 4957 | 0.106 |

N2 | 3419 | 2956 | 463 | 4250 | 0.218 | |

N3 | 2532 | 2075 | 457 | 3071 | 0.298 |

**Table 4.**

^{14}N NQR transition frequencies $\nu $, linewidths $\mathsf{\Delta}\nu $, and relaxation times T

_{1}in two polymorphs of paracetamol at room temperature. Reproduced with permission from reference [15], Lužnik J et al., Applied Magnetic Resonance; published by Springer, 2013.

Monoclinic | Orthorhombic | ||||
---|---|---|---|---|---|

ν | Δν | T_{1} | ν | Δν | T_{1} |

[kHz] | [Hz] | [s] | [kHz] | [Hz] | [s] |

2564 | 1400 | 11 | 2570 | 2300 | 6 |

1921 | 1800 | 5 | 1955 | 3000 | 3 |

643 | 615 |

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Trontelj, Z.; Pirnat, J.; Jazbinšek, V.; Lužnik, J.; Srčič, S.; Lavrič, Z.; Beguš, S.; Apih, T.; Žagar, V.; Seliger, J.
Nuclear Quadrupole Resonance (NQR)—A Useful Spectroscopic Tool in Pharmacy for the Study of Polymorphism. *Crystals* **2020**, *10*, 450.
https://doi.org/10.3390/cryst10060450

**AMA Style**

Trontelj Z, Pirnat J, Jazbinšek V, Lužnik J, Srčič S, Lavrič Z, Beguš S, Apih T, Žagar V, Seliger J.
Nuclear Quadrupole Resonance (NQR)—A Useful Spectroscopic Tool in Pharmacy for the Study of Polymorphism. *Crystals*. 2020; 10(6):450.
https://doi.org/10.3390/cryst10060450

**Chicago/Turabian Style**

Trontelj, Zvonko, Janez Pirnat, Vojko Jazbinšek, Janko Lužnik, Stane Srčič, Zoran Lavrič, Samo Beguš, Tomaž Apih, Veselko Žagar, and Janez Seliger.
2020. "Nuclear Quadrupole Resonance (NQR)—A Useful Spectroscopic Tool in Pharmacy for the Study of Polymorphism" *Crystals* 10, no. 6: 450.
https://doi.org/10.3390/cryst10060450