Analysis of Polymorphic Systems by Vibrational Spectroscopy

MSc Chemistry

Master Literature Study

Analysis of Polymorphic Systems by Vibrational

Spectroscopy

by

Joost van de Ven

12927635

March 2021 12 EC

February-March 2021

Supervisor/1st Examiner 2nd Examiner

Dr. F. Ariese Prof. Dr. S. Woutersen

Abstract

Quantification of polymorphic forms is important in various fields (e.g. pharmaceutical industry, polymer science) because changes in physicochem-ical properties are observed for different crystal structures. Both low- and mid-frequency Raman and infrared have been applied to quantify polymor-phic mixtures. But the low-frequency region is of higher interest since the lattice vibrates at these lower energies. Terahertz, far-infrared and low-frequency Raman spectroscopy are frequently applied to probe these low energy phonon modes. Between these three applications Terahertz spec-troscopy provides the most information rich data because of the coherent detection; enabling the determination the refractive index and absorption coefficient from the transient signals phase and amplitude. However, ad-vances in filter material technology have opened up the easy Rayleigh sup-pression by high volume Bragg gratings for low-frequency Raman and more efficient beamsplitters (Silicon solid substrate) at the lower frequencies for far-infrared spectroscopy. For both low-frequency Raman and far-infrared applications there are possibilities to convert the filters in conventional spec-troscopic systems to open up the low-frequency range, enabling the conve-nient detection of low-frequency spectra.

Contents

1 Introduction 3

2 Introduction to Polymorphic Systems 4

2.1 Description of Solid Crystal Structures . . . 4

2.2 Conformational Polymorphism . . . 7

2.3 Polymorphic Systems of Polymers . . . 9

2.4 Polymorphic Systems of Organic Compounds . . . 11

3 The Analysis of Polymorphic Systems by Vibrational Spectroscopy 12 3.1 Considerations for Sample Preparation . . . 13

3.2 Infrared Spectroscopy . . . 13

3.2.1 Mid-Infrared Spectroscopy . . . 13

3.2.2 Near-Infrared Spectroscopy . . . 17

3.2.3 Far-Infrared Spectroscopy . . . 17

3.3 Terahertz Spectroscopy . . . 19

3.4 Low- and Mid-Frequency Raman Spectroscopy . . . 22

3.5 Hyperspectral Imaging . . . 27

4 Discussion and Conclusion 29

1

Introduction

Many molecules can adept two or more different orientations in space in the solid state which are called polymorphs. Polymorphs do not differ in chemi-cal composition but only in molecular geometry and/ or can take on different molecular packing structures. The crystalline structure affects the physicochem-ical properties of the solid which can be altered to fit a specific purpose [1]. For example, polymers with a high degree of crystallinity tend to be more brittle than amorphous polymers and in the case of bio-polymers lower degradation rates are observed for more crystalline structure [2]. Besides polymers, polymorphs are also commonly observed for active pharmaceutical ingredients (APIs) [3]. Poly-morphic APIs often tend to have various solubility rates which affect the bio-availability, but stability and mechanical properties can also be different between polymorphs [4]. Often the most thermodynamically favourable conformation is found to have the lowest solubility which are seen in crystalline structures [5].

In the pharmaceutical industry fast and reliable process analytical technol-ogy (PAT) for the detection of polymorphic states are required to control and optimize production processes [6]. Established crystalline analysis tools like powder X-ray diffractionn (PXRD), differential scanning calorimetry (DSC) and solid-state NMR are not capable to be applied for in- or online measurements. However, spectroscopic applications such as near-infrared (NIR) and Raman spectroscopy are common in PAT. Investigation of fast and reliable vibrational spectroscopic applications for the analysis of polymorphic systems is of interest to characterize PATs. Especially the low-frequency spectral range is impor-tant because the intermolecular vibrations, called phonons, vibrate within this energy region. Directly probing the phonon modes by low-frequency Raman, far-infrared or Terahertz (THz) spectroscopy provides information about the crystal structure whereas detection by near-infrared (NIR), infrared (MIR) or mid-frequency Raman is only capable of indirectly detecting the global structure.

The aim of the literature study is to investigate the multiple opportunities to study polymorphic systems by vibrational spectroscopy. For both the direct and indirect measurement of the lattice vibrations common applications, considera-tions and recent advances will be discussed, guided by examples from literature. Furthermore, hyperspectral imaging is briefly discussed and the pros and cons of the different methods are summarized. However, first a basic introduction to polymorphic systems is described to provide context.

2

Introduction to Polymorphic Systems

A periodic crystal consists of numerous repeating structural units (e.g. atoms, molecules or ions) making up the spatial configuration of a crystalline solid. The location of the building blocks in three dimensional space can be represented by lattice points, resulting in an abstract scaffolding of the crystal structure. Within the lattice space, parallel sided unit cells are described by connecting several lattice points. The size and shape of a unit cell is described by lattice parameters with sidelengths (a, b, c) and angles (α, β, γ). Different combinations of the lattice parameters result in the seven possible crystal systems, shown in table 1.[7, 8]

Table 1: The seven crystal systems and their corresponding lattice parameter relation-ships. Table reproduced from Weller et al. (2014) [8]

Crystal system Lattice parameters

relationship Essential symmetries Triclinic a 6= b 6= c, α 6= β 6= γ 6= 90° None Monoclinic a 6= b 6= c, α = γ = 90°, β 6= 90°

One two-fold rotation axis and/ or mirror plane

Orthorhombic a 6= b 6= c, α = β = γ =

90°

Three perpendicular two-fold axes and/ or mirror planes

Rhombohedral a = b = c, α = β = γ 6=

90°

One three-fold rotation axis

Tetragonal a = b 6= c, α = β = γ =

90°

One four-fold rotation axis

Hexagonal a = b 6= c, α = β = 90°,

γ = 120°

One six-fold rotation axis

Cubic a = b = c, α = β = γ =

90°

Four three-fold rotation axes tetrahedrally arranged

In addition, the seven primitive (P) crystal systems can be expanded to greater symmetry. More detail on the unit cells is achieved by introduction of extra lattice points. A base-centred (C) orientation involves two lattice points at two opposite faces, in a face centred (F) orientation six additional lattice points are included at the centre of each side and a body centred (I) includes one lattice point at the heart of the primitive unit cell. The possible combinations of the seven primitive crystals systems and the additional details result in the fourteen Bravais lattices and are shown in Figure 1.

The structure of simple ionic solids can be useful as a basic descriptor to visu-alise a crystal structure. In a straightforward description the solid sodium chlo-ride ions can be described as solid spheres with positive and negative charges that interact mainly through Coulombic forces. In solid NaCl the electrostatic forces, originating from repulsion and attraction between the charged ionic species, cre-ate a face centred cubic (fcc) orientation, where Na+ and Cl-1 ions cover the lattice points. Focusing on a particular cation within the fcc crystal structure the nearest neighbours of the cation ion are six anions located at the face centres, the second nearest neighbours are 12 different cations at the middle of the edges. To complete the fcc structure eight anions are located at the unit cell corners, which are the third nearest neighbours. The close packed crystal structure is schematically presented in figure 2. If for the NaCl solid the cations and anions were switched in position the same structure is obtained because the ions are in a 1:1 ratio distributed. However, this is not valid for all ionic solids.[8]

The physical properties of solid sodium chloride can be calculated from the interactions between the Na+and Cl-1ions with respect to their spatial position. The potential energy in the crystal structure is minimized by optimal configu-rations of the intra- and intermolecular forces. The potential energy of an ionic lattice system is the sum of both attractive and repulsive Coulombic interactions that work on a particular reference point. The lowest energy for an ionic lat-tice can be calculated according to equation 1. Where L is Avogadro’s number (= 6.022 ∗ 10−23mol-1), |z+| and |z−| are the moduli of the positive and negative

charges, e is the charge on the electron (= 1.602 ∗ 10−19C), 0 is the permittivity

of a vacuum (= 8.854 ∗ 10−12 F m-1), r is the intermolecular distance between the ions and A is the Madelung constant.[10]

∆U (0K) = LA|z+||z−|e

2

4π0r

!

(1) In the sodium chloride example the Madelung constant incorporates the dif-ferent Coulombic forces acting on a single ion within the fcc crystal. Viewed from a particular cation the main contributing interactions to the structure are the attractive interactions of 14 anions, which are six nearest neighbours and eight third nearest neighbours, and repulsive interactions of 12 cations, which are second nearest neighbours. With increasing distance the electrostatic inter-action strength between the ions decreases, therefore the Madelung constant is determined by calculating the relative distances between the central point and the neighbours located differently in space. The nearest neighbours are at dis-tance r, the second nearest neighbours are at disdis-tance a = r√2, (a2 = r2+ r2), and the third nearest neighbours are b = r√3 from the central point. The spa-tial orientation of the different lattice points is shown in Figure 2. Equation 2 shows that the Madelung constant converges fast as the distance between two ions increases therefore interactions with ions beyond distance b are considered negligible.[10] A = 6 −  12√1 2  +  8√1 3  − ... (2)

Figure 2: The close packed crystal structure of sodium chloride. The distances between the ions are described by a, b and r. In this figure sodium is represented by the smaller spheres and chloride by the larger spheres. Figure reproduced from Pethrick (2007) [10]

Because electrostatic interactions are the main contributors to the crystal structure of NaCl it is fair to approximate the ions as spheres; therefore, sim-plifying the calculation. In a molecular solid multiple interactions (e.g. van der Waals, dipole-dipole, hydrogen bonding) determine the morphology, compli-cating the determination of the minimal lattice energy. Despite the increased complexity, often the additivity approach remains valuable for systems contain-ing multiple interaction types.[10]

2.2 Conformational Polymorphism

The previous paragraphs explained basic concepts of crystal structures accord-ing to an ionic model. Nevertheless, many polymorphic systems are observed in molecular solids and to gain a better understanding of these systems it is good to consider the concept of conformational polymorphism. The forces bestowed upon the solid state molecules by the crystal structure could determine its con-formation. Understanding the structural behaviour of a single molecule could give insight into the macromolecular structure, since it consists of many stacked molecules.

Most molecules have stereoisomeric structures arising from an infinite num-ber of short-lived spatial orientations of the atoms from different bond lengths, bond angles and torsion angles. Every unique conformation contains a different potential energy which can be approximated by computational methods. To re-duce the number of states, often the bond length and angle are fixed and only rotations along the bonds are allowed, in the so-called Rigid Rotor approxima-tion [11]. The energy mapping of all rotaapproxima-tions around a single bond results in a landscape with local and global energy minima. Any position on this potential energy surface (PES) translates to a unique conformation but a new conformer is

only obtained if an energy barrier is passed into a different energy minimum. Gas phase conformers of most neutral molecules are similar to the crystal conforma-tion although molecular conformaconforma-tions are affected by neighbouring molecules [12]. For a particular conformer the gas phase structure is accompanied by a small conformational adjustment to convert to the crystal phase conformation and a transition between two different conformers is a conformational change. Molecular conformations corresponding to different energy wells are considered to be conformational polymorphs. In Figure 3 an example of a PES is shown with the conformational adjustment and change illustrated.[13]

Figure 3: Illustration of a potential energy surface (PES) and the conformational adjustment and change schematicaly presented. Figure reproduced from Cruz-Cabeza and Bernstein (2014) [13]

Ideally one would like to predict polymorphism from the molecular conforma-tion. In a study, Cruz-Cabeza and Bernstein (2014) [13] evaluated structures in the Cambridge Structural Database (CSD) for conformational polymorphism in correlation to molecular features. From the available polymorphic data, obtained by Powder X-Ray Diffraction (PXRD), and accompanying molecular structures they assessed the existence of conformational adjustment or change. They pro-posed a decision tree to differentiate conformational adjustment from change of two crystal structures without energy calculations. Two conformations are conformational polymorphs if ∆θ > 90°, if not then the CSD distribution of molecular features can be examined and at last if required the rmsd(r)-crystal > 0.375˚A. Where ∆θ is the difference in torsion angle and rmsd(r)-crystal is the root-mean-square deviation of the distances between the two superimposed con-formations. If none of the requirements in the decision tree are fulfilled the two conformations are separated by a conformational adjustment. They concluded that generally it remains difficult to predict and control crystallization processes due to a lack of understanding of the relation between conformations and crystal

structure. Nevertheless, some regularities are observed that promote or reduce the likelihood of crystallization.[13, 14]

2.3 Polymorphic Systems of Polymers

Polymers are widely applied in a variety of fields, for instance from packaging to automotive to medical applications. Each application requires a different type of polymer which is determined by the demanded mechanical, thermal and degrad-able properties [2]. For a polymer the physio-chemical characteristics depend on the polymorphic structure; affected by thermodynamic stability, crystallization kinetics and molecular defects [1]. Polymer conformations in the crystalline state are defined by the stereoisomeric configurations along the chain and the minimal energy conformation of the chain similar to small molecular crystals [1]. In the case of polymers, stereoisomerism is determined by the orientation of the side groups along the backbone. If all stereoisomeric centres are configured identical the polymer chain is isotactic; however, if the orientation is alternated then it is syndiotactic. In the case of complete random distribution of the side group orientations the polymer backbone is considered atactic.

The definition of lifetime is determined by the application of the product. For instance, the lifespan of a plastic applied in a production process is in-fluenced by mechanical fail criteria like fracture toughness or ultimate stretch length. However, if the lifetime of a plastic is defined from synthesis to complete degradation into metabolic compounds its lifespan is obviously much longer than the mechanical lifetime. With rising concerns of plastic pollution in water, soil and food [15, 16] research towards polymers produced from sustainable sources has increased. In general, bioplastics can be divided into bio-based polymers which assemble from natural resources and biodegradable polymers which de-grade under normal environmental conditions [17]. These deterioration processes are hydrolytic (enzymatic or non-enzymatic), thermal, photo and/or oxidative degradation pathways [18]. The hydrolytic degradation of polymers is catego-rized by bulk and surface erosion which both are described by four variables. In polymers, erosion is the loss of material due to the dissolution and diffusion of monomers, oligomers and compounds formed upon degradation [19]. The parameters describing these types of erosion are rate of water diffusion into the polymer (D) and pseudo first-order rate of hydrolysis (λ’), and polymer thickness (L) and the critical polymer thickness (Lcrit =

p

D/λ0) [20]. If L > Lcritsurface

erosion prevails, resulting in the decrease of the material thickness but retaining average molecular weight and mechanical properties. On the other hand, bulk erosion occurs if L < Lcrit, reducing the average molecular weight due to chain

scissions which affect the mechanical properties of the polymer. The effect of both erosions over time on the average molecular weight and physical properties are shown Figure 4.

Figure 4: The influence of bulk (A) and surface (B) erosion on the average molecular weight, strength and mass of the polymer material. Figure reproduced from Bat et al. (2014) [19]

Poly(lactide) (PLA) is a common bioplastic that is both bio-based and biodegrad-able. The polymerization of pure poly(L-lactide) (PLLA) or poly(D-lactide) (PDLA) through condensation of lactic acid or ring-opening of lactide results in a stereoregular polymer with high modulus and strength [2]. The polymerization of a racemic mixture of L-lactide and D-lactide produces an amorphous poly-mer due to the random distribution of the stereoisopoly-mers. The lack of periodic structure improves the erosion rate of poly(D,L-lactide) (PDLLA) compared to the stereoregular forms of PLA [2]. Generally it is observed that an increased crystallinity lowers the degradation rate of (biodegradable) polymers because the structured packing reduces the diffusion rate of water into the polymer [20]. Since water is less readily available inside the polymer, the surface area that is available for hydrolytic cleavage is low and therefore the bulk degradation is slow. Thus the structure and reactivity of the amorphous regions control the degradation rate [20].

Controlling the erosion mechanism is an important aspect in tissue engi-neering. In this field, biodegradable polymers are used to regenerate soft tis-sue by temporarily scaffold implants and simultaneously removing the need for second surgery to remove the implant. For tissue engineering surface ero-sion is preferred over bulk eroero-sion because the polymer maintains mechani-cal properties. In addition, the rapid release of degradation products of bulk eroding polymers can be harmful to regenerated cells. Another application of surface-eroding polymers is the release and delivery of bio-active compounds be-cause of the predictable erosion rate. Examples of surface-eroding polymers are poly(anhydride)s, poly(orthoester)s, poly(trimethylene carbonate), poly(ethylene carbonate), poly(hydroxyalkanoate)s and poly(glycerol sebecate) while bulk ero-sion is observed in aliphatic polyesters.[19]

2.4 Polymorphic Systems of Organic Compounds

Polymorphic structures of small organic compounds are often observed in active pharmaceutical ingredients (APIs). In drug development and production, solid-state modifications can form during processing and storage, even mixtures of crystal forms are possible [4]. Changes to the crystalline structure of an API can affect the bio-availability which is often related to the solubility, stability of the polymorphic state. The most thermodynamically stable conformer may not always be the most suitable solid form with respect to pharmaceutical function [3].

The HIV drug Ritonavir is a commonly used example for conformational polymorphism in the pharmaceutical industry. Ritonavir is marketed as an oral liquid or semi-solid capsules because its solid form is not bio-available. Initially only one form of Ritonavir was identified, but while the drug was on the market some batches failed the dissolution quality control. Identification of the crystal structure of these batches indicated a second solid form (form II) which is less soluble in the hydroalcoholic solution than the original form (form I). While form I demonstrates no saturation effects upon dissolution, the alcohol water solution is 400% saturated in the same production process for form II. Due to the low solubility, and instability of form II it became practically impossible to manufacture Ritonavir and reformulation of the drug was required. Other examples of polymorphic APIs are Carbamazepine for treatment of epilespy and trigeminal neuralgia or Nabumetone which is an anti-inflamatory, analgesic, and antipyretic drug. [3, 21]

Co-crystals can be utilized to alter the physicochemical properties such as, permeability, bio-availability, solubility and stability of the drug without chang-ing the molecular structure and pharmacological properties of the API [5]. In the context of pharmaceutical compounds a co-crystal is defined as single-phase crystalline solid consisting of two or more different molecular and/or ionic com-ponents which interact through hydrogen bonding or other non-covalent and non-ionic interactions [5].

3

The Analysis of Polymorphic Systems by

Vibra-tional Spectroscopy

Powder X-ray diffraction (PXRD) is a powerful tool in polymorph analysis and is often seen as golden standard. In a PXRD experiment the sample is irradiated by an X-ray beam where the incident particles will elastically scatter. The angle and distribution of the scattering holds information about the crystal structure. The diffraction angle is inversely proportional to the lattice spacing according to Bragg’s law. Even though PXRD is a fundamental application in structure determinations, it offers no direct information about the force fields within the crystal structure. The ability to measure these force field energies is of interest to improve crystalline solid force field models and increase the understanding of structure and dynamics of large (bio)systems [22].

Intra- and intermolecular vibrations can be probed by a variety of vibrational spectroscopic techniques. High-frequency vibrations arise from covalent bonds and in organic compounds the upper limit is the stretch vibration of O-H or N-H. This stretch vibration frequency is determined by the small reduced mass, among other things. It is observed that hydrogen bonding is often different between polymorphs, and therefore vibrations of the affected functional groups shift and can be readily measured by mid-IR spectroscopy [3]. Low-frequency vibrations are observed mainly for intermolecular interactions and intramolecular backbone vibrations [23]. Shifts in the low-frequency lattice vibrations are caused by different crystal packing orders and can be detected by far-infrared (FIR), Terahertz (THz) and low-frequency Raman spectroscopy [3, 23, 24, 25]. In the upcoming paragraphs the principles of these vibrational spectroscopy techniques for the analysis of polymorphic systems are explained briefly to provide context. In addition, some interesting aspects to polymorphic analysis by vibrational spectroscopy are discussed on the basis of work published in literature.

Figure 5: The electromagnetic spectrum. Figure reproduced from Baxter et al. (2011) [26]

3.1 Considerations for Sample Preparation

In solids it is commonly observed that solid forms with a distribution in particle size could be separated during mixing, but grinding the solid powder in a mortar and sieving can improve the particle size uniformity. However, the absorbance in IR spectroscopy appears to be dependent on grind time and pressure with the matrix (e.g. potassium bromide (KBr)), and pressure and dwell-time of the KBr-disk compression [27]. Furthermore, light scattering is in relation to the particle size variation which can affect the acquisition of Raman events or IR absorption depending on the collection geometry [28]. While grinding and sieving generally improve the reproducibility one should be cautious that the sample handling does not affect the polymorphic forms.

3.2 Infrared Spectroscopy

3.2.1 Mid-Infrared Spectroscopy

The conventional infrared (IR) is considered the mid-IR (MIR) range, encom-passing 4000-400 cm-1 (2500-25000 nm), although the shorter wavelength is loosely defined by a factor of two. A MIR spectrum is obtained by illumi-nation of a sample with polychromatic MIR light, the absorption of the light reduces the intensities of the absorbed frequencies which are visualised in the spectrum upon detection. The emission intensity of the IR source is dependent on the wavelength therefore the spectrum of a sample is corrected by a back-ground measurement. The absorption of specific MIR frequencies translates to intramolecular vibrations and tables are available that relate specific absorption bands to specific vibrations between two or more atoms. Because the absorption energies of specific vibrations are well known, MIR is often applied to determine functional groups in a molecule. For example the carbonyl stretch vibration has a strong absorption band around 1700 cm-1. In a standard transmission mode MIR measurement the light travels through the sample towards the detector. However, no transmission is observed if all MIR light is absorbed by the sample and substrate and because of this a thin sample is needed in transmission mode. Alternatively, the high optical density of many materials require the dilution of the powdered sample in a mineral oil or KBr [29]. These preparations are labor intensive and may affect the physical structure of the sample which is unde-sired in polymorphic analyses [30]. Alternatives that do not experience trouble with complete absorption and require limited sample preparation are diffuse re-flectance infrared Fourier transform (DRIFT) and attenuated total reflection (ATR) IR.

In the diffuse reflectance orientation the sample is irradiated through a small hole in an ellipsoid mirror. The diffuse components are collected by the ellipsoid mirror and focused onto the detector by a paraboloid mirror, while any reflected light returns through the hole. The paraboloid mirror reduces the magnification of the collected MIR beams to improves the beam intensity. While DRIFT does not affect the polymorphic structure of the sample and experiences no trouble with total absorption, its signal to noise ratio is relatively low and is dependent

on particle size [28, 31, 32]. The illumination and detection geometry of a DRIFT setup is shown in Figure 6.

Figure 6: Illumination and detection geometry of a Diffuse Reflectance Infrared Fourier Transform (DRIFT) setup. The position of the sample (S), detector (D), paraboloid (P) and ellipsoid (E) mirrors are shown. Figure reproduced from Fuller and Griffiths (1978) [29]

The illumination of the sample through an ATR crystal is based on the fact that the light penetrates the sample minimally upon total internal reflection in the crystal. In such a irradiation geometry the absorption is independent of sample thickness and often ATR crystals with high refractive indices are used to improve the total reflection [33]. As the light penetrates the sample minimally, approximately 1₂λ, light is absorbed at the sample materials’ surface. Because ATR is a surface absorption technique it can be affected by sample inhomogene-ity and should be treated with caution for polymorphic analyses [27, 31]. An advantage is that minimal sample amount and sample preparation is required for the measurement of the IR spectrum through an ATR crystal [31].

In the pharmaceutical setting FTIR is a widely applied analysis technique for the identification of materials because of requirements from regulatory bodies. Applications have been published for the measurement of polymorphic impurities in drug substances by transmission IR [27], DRIFT [28, 32] and ATR-FTIR [34, 35].

Mixtures of two polymorphic forms of the API imantinib mesylate as drug substance and tablet formulation were analysed by PXRD, differential scanning calorimetry (DSC) and ATR-IR in a study by Atici et al. (2015) [35]. They evaluated the quantitative performances of the three analysis techniques to de-termine the β-form impurity in the α-form of the cancer treatment drug. For all

three techniques they compared the data of the α- and β-form to determine dis-tinct signals corresponding to a particular form. In the IR spectrum the α crystal exhibits an extra peak at 1446 cm-1 that is not observed in the IR spectrum of the β-form. Additionally, the correlation improved by calculating the peak ratio versus the reference band 1630 cm-1. These distinct signals were applied to setup an univariate calibration curve from standards with different impurity levels. In Figure 7 the ATR-FTIR spectra of the α- and β-form are shown.

Figure 7: ATR-FTIR of α (black) and β (red) solid Imantab crystals in tablet formu-lation. Figure adapted from Atici et al. (2015) [35]

Evaluation of limit-of-detection (LOD) of the three methods revealed that both PXRD and DSC had similar LOD values however the performance of the IR application was much worse. PXRD and DSC were able to detect 1% and 4% of β-form in drug substance and tablet formulation, respectively, while ATR-IR was only capable of detecting the impurity upward of 12% in both types of sample. Although the ATR-IR application is the easiest and fastest of the tested methods, its poor performance limits the applicability. The high LOD is linked to the fact that the method is dependent on the selection of a transmittance band. If no clear absorption band for a specific form is available it affects the quantitative performance of the method which is the case for the IR measurement of imantinib mesylate β-form. Another univariate approach has been applied by Zhang et al. (2005) [36] to determine crystal modifications and thermal behaviour of poly(L-lactide acid) by MIR.

Multivariate approaches can provide an improved quantification method as opposed to univariate applications. Low level of polymorphic impurities in clopi-dogrel bisulphate were quantified by vibrational spectroscopy and chemometrics in a study performed by N´emet et al. (2009) [27]. They used form I and II of clopidogrel bisulphate as model compound of which the first is open for generic practices and the other is patented. The presence of form II in form I can be vi-sually detected based on the peak shift from 1035 cm-1to 1029 cm-1but the shift is barely visible below 15% form II, as shown in Figure 8. Furthermore, several

characteristic bands are present as shoulders at increasing concentrations of form II. The quantification performance of the FTIR application improves drastically if the impurity amount is determined by a chemometric model. They calculated the LOD and limit-of-quantification (LOQ) by multiplying the relative standard deviation (RSD) of a blank by 3.3 and 10, respectively, and dividing it by the slope of the calibration curve. By solving this calculation they reported and estimated LOD of 0.5% and LOQ of 1.7% for the quantification of form II in form I with chemometric modeling.

Figure 8: IR spectrum of Clopidogrel bisulphate; band shift from 1035 cm-1 _{to 1029}

cm-1 _{indicating increasing quantity of form II in form I. From top to bottom pure form}

I, 1%, 2%, 5%, 8%, 10%, 15% form II and pure form II. Figure adapted from N´emet et al. (2009) [27]

To determine polymorphic outliers from multivariate modelling objectively quality criteria are necessary. Rejections based on individual opinions lead to subjective predictions [32]. Common quality criteria in multivariate modeling are the Q-residuals and Hotelling-T2. The Q-residuals are in a sense indicators for the lack of fit of the regression and Hotelling-T2 evaluates the distances of the sample projections on the model space and centre [32]. ˇSaˇsi´c et al. (2018) [32] investigated low level polymorphic impurities by DRIFT and chemometrics. They especially examined the use of the above mentioned quality criteria to ob-jectively determine polymorphic outliers. It turned out there were no outliers in creation of the multivariate model according to a leave-one-out principle. The model creation appeared to be unbiased and was able to correctly predict the polymorphic impurity content in 10 independent batches containing no impu-rity, confirmed by PXRD. Nevertheless, further investigation showed that all predictions of the independent samples had a positive bias while a random dis-tribution around zero was expected. Furthermore, nearly all Q-residuals were

out of bounds even though the Hotelling-T2 were within limitations. Inclusion of several independent datapoints in the training set reduced the number of Q-residuals exceeding the limit threshold and the positive impurity prediction bias was slightly reduced. They concluded that application of Q-residuals and Hotelling-T2 could cast uncertainty on the predictions but without these criteria the predictions are prone to arbitrary considerations. Generally in chemomet-ric modelling it remains difficult to gather a representative training set for the complete sample range.

3.2.2 Near-Infrared Spectroscopy

Similar to MIR, polymorphic structures can be distinguished by near-infrared (NIR) but the detected vibrations are intrinsically different. In NIR the over-tones and combinational vibrations are probed by photons in the region of 13000-4000 cm-1 (770-2500 nm) [33]. These overtones are considered forbidden tran-sitions that have a change in vibrational level greater than one, for example from ground state directly to the second vibrational level. Changes in intensities are often minimal in NIR and absorption bands tend to be broad and overlap; requiring the use of multivariate approaches for quantitative purposes [31, 33]. For example, NIR spectroscopy has been applied to quantify polymorphs in pharmaceuticals [31, 37] or the inline quality control of polymerization processes [38]. The operation of NIR equipment and collection of NIR spectra is relatively straightforward, allowing for fast and non-destructive detection of polymorphs. Nevertheless, NIR nearly always requires multivariate modelling for quantita-tive purposes and the prediction performance of these models is often subpar to Raman applications [31]. Furthermore, the spectral resolution and information density of DRIFT surpasses that of NIR applications [32].

3.2.3 Far-Infrared Spectroscopy

In the spectral region of far-infrared (FIR), ranging from 400-100 cm−1, one can probe the intermolecular vibrations. Although FT-IR systems are com-mon lab equipment, FIR is not often used to measure the lattice interactions of polymorphs because most mid-IR systems are equipped with beamsplitters that absorb in the FIR range.

Suresh et al. (2019) [25] investigated FIR spectroscopy as a tool for poly-morph discrimination. In their study they compared mid-IR, FIR and THz spectra of 10 small pharmaceutical compounds to determine if FIR measure-ments provide benefit in the discrimination process of polymorphs. Both mid and FIR spectra were recorded with the same system, however, switching of the beamsplitters was required. The MIR system contained a KBr beamsplitter allowing for spectra to be obtained from 4000-400 cm−1 while the FIR measure-ments were recorded with a silicon solid substrate beamsplitter. Suresh et al. were able to distinguish polymorphs of the 10 different compounds investigated. Structural dissimilarities derive unique intermolecular, internal and external vi-brations that result in specific FIR features. Frequency shifts in the FIR spectra

allowed the simple differentiation of the multiple crystal systems and demon-strated that FIR could discriminated between distinct packing arrangements. FIR spectra of seven different compounds with multiple crystal structures are shown in Figure 9. Even though low-frequency Raman and Terahertz (THz) spectroscopy are more commonly reported for polymorphic analysis, the com-bination of analysis speed and easy conversion of a conventional FT-IR system to the low-frequency range makes FIR spectroscopy a suitable technique for the characterization and discrimination of polymorphs.

Figure 9: Far infrared spectra of seven polymorphic compounds. (a) mefenamic acid, (b) tolfenamic acid, (c) furosemide, (d) pyrazinamide, (e) nabumetone, (f ) sulindac, and (g) sulfamethazine. For clarity the spectra have been offset in the y-axis. Figure reproduced from Suresh et al. (2019) [25]

3.3 Terahertz Spectroscopy

High symmetry determines the observability of Terahertz modes which are most pronounced in crystalline structures due to the long range order, whereas the phonon frequencies of amorphous solids are broadened. The lack of long range or-der in amorphous solids is observed by THz spectroscopy as a featureless sloping baseline, while the higher symmetry in crystalline solids results in better defined THz modes. These THz modes are more detailed because the high ordered struc-ture restricts most vibrational modes due to the selection rule that requires the conservation of momentum upon optical transitions [23]. For the preservation of momentum the absorption of a photon requires a phonon event of similar fre-quency and momentum but these vibrational modes are limited by the reduced degrees of freedom in highly structured solids [23]. The observation of individual THz vibrational modes results in the reduction of peak broadening in the THz spectrum. While THz spectroscopy measures crystal lattice vibrations of similar energy or lower than FIR spectroscopy, its probing and detection mechanism is different from conventional IR applications. This different approach creates an advantage of THz spectroscopy over FIR in that the complete electric field is measured, allowing the determination of the THz pulses’ phase and amplitude. Knowing the phase and amplitude of the THz pulse, the refraction index and absorption coefficient can be calculated. Therefore, it enables the measurement of the complex permittivity without the need of time-resolved applications [39].

Figure 10: THz spectroscopy spectrum of air reference and a ZnO wafer sample in (a) time domain, and (b) frequency domain after Fourier transform. THz radiation emitted and detected by 1 mm thick ZnTe crystal and ∼100 fs optical pulse. Absorption features of water in atmosphere are visible at 1.1 and 1.6 THz for both measurements. Figure adapted from Baxter et al. (2011) [26]

In modern THz spectroscopy equipment a suitable semiconductor is irradi-ated with femtosecond (fs) laser pulses to generate picosecond (ps) electric field pulses in the THz range. A spectral range of 4 to 0.3 THz (133-10 cm-1) is ob-served for these systems but depending on fs laser pulse length and power, com-position of the semiconductor and emitter/ detection antenna arrangement [40]. Before THz frequency generation, the laser light is split into a probe and pump beam. The pump beam generates the THz radiation which is guided through the sample material prior to detection. The probe beam irradiates the detection

semiconductor after a variable delay in a photoconductive detection system. The photoconductive detection of the THz pulse employs a photoconductive antenna similar to the THz generation antenna. As the detection semiconductor is illumi-nated by light it generates short lived photoexited carriers that induce a current dependent on the interaction with the electric field from the THz pulse. The short lifetime of the exited state upon illumination by the probe beam and the fs optical pulse width result in a gated detection system and the complete THz pulse is measured in the time domain by scanning multiple optical delay times [26]. In Figure 10 an example is shown of the THz spectrum in both the time and Fourier transformed frequency domain. The highest electric field is obtained if the travel time of both the probe and pump beam match. The pump beam is delayed due to the permittivity of the THz radiation through the sample mate-rial. THz spectroscopy experiment with the variable probe beam pathlength is called THz time-domain spectroscopy (THz-TDS) and such a setup is schemati-cally visualised in Figure 11. Shorter optical pulses and reduced lifetimes of the photoexcited carriers in the antennas improve the measurements resolution [26]. Improving the lifetime of the semiconductor material benefits both the emitter and detector performance. Common semiconductor materials are GaAs, InAs, ZnTe and radiation-damaged Si-on-sapphire [40].

Figure 11: Schematic overview of a Terahertz time-domain spectrometer with photo-conductive detection. Figure reproduced from Smith et al. (2011) [40]

Optical rectification and free space electro optic sampling (FSEOS) are alter-natives to generate and detect THz pulses. In an electro-optic THz-TDS system again the laser pulse is split into a probe and pump beam. Pulsed THz radiation is obtained through frequency mixing of a short visible or NIR light pulse in a non-linear crystal (e.g. ZnTe, LiNbO3). While this THz radiation is detected

as the intensity of polarized light in the x- or y-plane in the probe beam. Af-ter the THz pulse propagates through the sample it is co-axially aligned with the planar polarized probe beam and sent through an electro-optic crystal. The THz-pulse influences the birefrigent properties of the crystal, therefore affecting

the orientation of the planar polarized light. The magnitude of the THz radia-tion determines the rotaradia-tion angle and the amplitude the rotaradia-tion direcradia-tion [39]. After the electro-optic crystal the planar polarized light is circular polarized and separated into two orthogonal components through a Wollaston polarizer. Both the components of the polarized light are detected and determine the magnitude of the THz radiation [40]. Contrary to the photoconductive detection, the THz electric field acts as a gated detection mechanism in the electro-optic systems. The electro-optic detection of the THz radation is presented in Figure 12.

Figure 12: Schematic overview of free space electro-optic sampling (FSEOS) in a terahertz time-domain spectrometer. Figure reproduced from Smith et al. (2011) [40]

In THz spectroscopy setups, photoconductive THz emission and detection are frequently combined with unamplified lasers while high energy pulsed lasers are coupled to electro-optics because the photoconductive antennas would be damaged by the high energy amplified lasers [26]. Amplified systems are reg-ularly applied to time-resolved THz applications where a third incident beam excites the sample to measure its photoconductivity. The lower repetition rate of amplified pulsed laser, opposed to oscillating lasers, allows for proper sample relaxation in between pulses [26]. Nevertheless, THz-TDS is more common for the analysis of polymorphic systems.

More detailed reviews of THz generation and detection are provided by Ki-taeve et al. (2008) [41] and Sizov et al. (2010) [42], respectively.

Prior to analysis the pathway of the THz radiation must be purged by N2

to reduce THz absorption from rotational transitions by water vapour which is also observed for FIR spectroscopy [43]. Water absorbs THz frequencies in the range of 1-3 Thz, limiting the applicability of THz-spectroscopy and FIR for the measurement of samples with high moisture content [26]. However, there have been studies that applied THz spectroscopy to determine hydration states in for

instance biomolecules [26].

3.4 Low- and Mid-Frequency Raman Spectroscopy

Raman spectroscopy is often perceived as a sister technique to IR spectroscopy because both methodologies are able to measure molecular vibrations [31]. In Raman the vibrations are detected as inelastic scattering of the incident light whereas in IR the non absorbed light is measured. Upon inelastic scattering the photon exchanges energy with the vibrational mode of the molecule if its polariz-ability changes during that vibration. In the case the energy of the observed light decreases the Stokes lines are obtained and for an increase in energy anti-Stokes lines. The probability of Raman scattering is very low since most scattering photons undergo elastic scattering; no loss or gain of energy. To obtain sufficient signal many Raman setups irradiate the sample with lasers because the high laser power increases the inelastic scattering yield. Furthermore, the development of more sensitive detectors improves the detection of Raman scattering.

Whereas conventional Raman systems probe internal molecular vibrations, low-frequency Raman spectroscopy detects the low energy, long range phonon modes corresponding to the frequency band of 0-50 cm-1 [4]. Since the energies of the phonon Stokes lines are low, their wavelengths are close to the excitation wavelength. Detection of these low-frequency Raman bands requires the removal of Rayleigh scattering by ultra-narrow band filters [4]. High efficiency volume Bragg gratings (VBG) are able to narrowly filter light, down to a FWHM (full width at half maximum) of 3 cm-1[44]. In low-frequency Raman setups reflecting Bragg gratings (RBGs) are applied to reflect the specific narrow frequency of the Rayleigh scattering while the low-frequency (anti-)Stokes shifts are able to propagate through the filter. It is observed by angular scans that the optical density (OD) of the RBG is dependent on the incident angle. The angular alignment is a key RBG parameter to obtain optimal suppression of elastic light scattering and can be as critical as 0.1°; see Figure 13. For Raman spectroscopy most systems require a Rayleigh light suppression of 60 dB (OD = 6) or more [44]. Since a single RBG filter often provides insufficient Rayleigh suppression, the sequential configuration of multiple RBGs can increase the combined optical density to a satisfactory Rayleigh rejection level.

Besides the precise suppression of the Rayleigh light, the RBG filters are also able to remove amplified spontaneous emission (ASE); reflect the beam onto the sample material without loss of intensity unlike beam splitters [45]; enable the detection of both Stokes and anti-Stokes scattering and remove the need for multi stage spectrometers [44]. Because volume Bragg gratings allow low-frequency Raman to be measured by single stage spectrometers the complexity of the system is reduced [44]. Older techniques using double monochromators [46] or triple grating [24] are also capable of accurately suppressing the laser wavelength but tend to be more complex to operate and outperformed by VBGs [45].

Figure 13: Optical density dependency of the incident light angle for reflecting volume Bragg gratings at (a) 633 nm and (b) 488 nm. Figure reproduced from Glebov et al. (2012) [44]

DRIFT, diffuse reflectance FT-NIR (DR-FT-NIR) and mid-Raman spectroscopy were directly compared in a quantitative analysis of binary polymorphic mixtures performed by Guo et al. (2017) [28]. They demonstrated that the DRIFT pro-vided the most accurate quantification of fusidic acid form I in form III while mid-frequency Raman performed least well. Form III is the most thermodynami-cally stable polymorph of the antibiotic fusidic acid and form I was considered an impurity in this model compound. Since the NIR and Raman samples were not sieved and ground, the poor quantitative performance of the Raman and NIR applications could be linked to the broad distribution of particle sizes and poly-morph inhomogeneity [28]. This possibly indicates the importance of uniform particle size distribution but the risk remains that altering the solid material affects the crystalline structure.

Paiva et al. (2020) [45] presented a wide angle illumination method for low-frequency Raman to reduce the measurement error due to large particle size distribution and sample inhomogeneity. They demonstrated the application of an adjustable wide laser illumination in combination with sample rotation to reduce the spectral band broadening effects. Both the larger spot size and sample rotation increase the sampling area and because of that small inconsistencies are averaged. The reported setup allows for laser spot size adjustment from 3 to 3000 µm and VBGs were applied as ultra-narrow notch filters and to reduce ASE from the laser. However, with increasing spot size the laser intensity decreases and therefore high power lasers are required to improve the Raman scattering events [45]. The use of a parabolic mirror with a central hole, rather than a beam splitter, allowed the excitation by the laser’s full power and minimal loss of photons scattered towards the detector. The Raman spectrophotometer is schematically presented in Figure 14. The optical lens (4) is responsible for the larger spot size and variation of the focal length influences this size. The meniscus lens (4) causes the collimated laser beam to diverge and therefore the focus is longer than the focal length, as shown in Figure 14b. This setup enables the convenient acquisition of LF-Raman spectra from both micro and macro

spot sizes by the adjustment the optical lens’ (4) focal length. Furthermore, the large spot size improves the reproducibility and the measurement needed only short integration times (e.g. 2-10 s). Fast detection is possible due to the fact that the laser’s power is used to its full potential for excitation. The versatility of the macro and micro spot size sampling is shown in Figure 15. Indicating the possibility to map the sample inhomogeneity with the micro laser spot size and the higher signal to noise ratio obtained for the macro spot size.

Figure 14: (a) Photo image of LF-Raman spectrophotometer. (b) Schematic of laser spot size dependecy on a collimating or diverging laser beam. (c) Schematic represen-tation of the LF-Raman setup (1) 785 nm laser, (2) ASE filter, (3) dichroic mirror, (4)-100 mm meniscus lens, 5) 2” silver coated parabolic mirror with 4” of focus angle and 3.2 mm central hole, (6) dichroic mirror, (7) 2” aspheric sample lens, (8) sample pellet, (9) 600 µm slit, 10) collimator lens, 11) ultra-narrow notch filters, 12) focusing lens and 13) 100 µm optic fibre. (d) Rotating sample holder. Figure reproduced from Paiva et al. (2020) [45]

In a study, Lipi¨ainen et al. (2018) [4] evaluated the added benefit of low-frequency Raman to mid-low-frequency Raman for the quantitative determination of polymorphic mixtures. Piroxicam, a non-steroidal anti-inflammatory drug, acted as model drug of which the crystalline solid has five anhydrous forms, and one monohydrate (MH) crystal. For the evaluation ternary mixtures con-taining the two most stable anhydrous crystals (α2, β), and the monohydrate form were prepared at different concentrations, as shown in Figure 16. The sam-ples were measured by a home-built low-frequency (LF-785) Raman, commercial

Figure 15: (a) LF-Raman spectra at 3 different concentrations of Paracetamol in tablet acquired with 2 s integration time and 1000 µm laser spot size. (b) LF-Raman spectra of one 5% w/w Paracetamol sample in tablet probed at three different locations with 2 s integration time and 3 µm laser spot size. Figure adapted from Paiva et al. (2020) [45]

low-frequency (LF-830) Raman and FT-Raman setup. Partial least squares re-gression (PLSR) was applied for polymorph quantification. The LF-785 was capable of simultaneously measuring the low- (8-200 cm-1) and mid-frequency (700-1700 cm-1_{) Raman spectra but at the cost of spectral resolution (5-7 cm}-1_).

Therefore, the LF-830 system was used to measure the low-frequency Raman at better resolution (2 cm-1) to be similar to the resolution of the FT-Raman setup. In both the low- and mid-frequency region they were able to distinguish the dif-ferent solid mixtures but most importantly the RMSEP (prediction error) was the lowest for the low-frequency model and better than the mid-frequency model. From the PLSR loading weights it appeared that the sub-100 cm-1 provides the most significance and the score plots are highly similar to the triangular ternary mixture design. The score and loading plots of the 8-200 cm-1 and 8-1700 cm-1 models are shown in Figure 17. The improved performance of the low-frequency models compared to the mid-frequency models is probably linked to the high peak intensity and signal to noise ratio in the low spectral region and that the intermolecular vibrations are more intense at lower frequencies [4].

Figure 16: Mixture design for partial least squares regression model (calibration) and test (validation) set for the quantitative determination of Piroxicam polymorphs. Figure adapted from Lipi¨ainen et al. (2018) [4]

Figure 17: From top to bottom: score plot, loadings plot and Raman spectra of both low- (8-200 cm-1; left) and broad-frequency (8-1700 cm-1; right) models for the analysis of Piroxicam polymorphs: form β, form α2 and monohydrate (MH). Figure reproduced from Lipi¨ainen et al. (2018) [4]

3.5 Hyperspectral Imaging

In the previous paragraphs the different vibrational spectroscopy techniques available for polymorph analysis were discussed. These spectroscopic methods can be applied for the spatial detection of the polymorphic distribution in a solid which can be of interest to improve production processes or gain insight in the relationship between polymorphic forms and physicochemical properties. For instance, the distribution of an API and possible polymorphic impurities in tablet formulation or the dissolution of such a formulation could be visualised [33, 37]. The two- or three-dimensional visualisation can either be acquired through imaging or mapping approaches. In spectroscopic mapping each pixel is measured individually and the collection of all pixels creates the chemical image. Generally, the mapping approach results in high quality pixels with better signal to noise ratio and spectral resolution. But the downside is that each point has to be detected by a moving sample stage separately which can be time consuming. Faster integration times per pixel can immensely reduce the total measuring time since numerous pixels need to be acquired to construct the whole chemical im-age. On the contrast, with spectroscopic imaging a spectrum is recorded in two dimensions simultaneously using a charged coupled device (CCD) for example. Fewer recordings are required to complete the whole profiling of the chemical im-age which can be optimal for monitoring dynamic processes [33]. Nevertheless, the faster image acquisition comes often at the cost of reduced image quality.

Similar to univariate quantifacation methods, spectral images can be con-structed from single band intensities. Here the intensity of a particular band represents the quantity of a certain polymorphic form as shown in a study by Ajito et al. (2011) [47]. In their study they demonstrated THz-TDS imaging for the localisation of famotidine polymorphic forms in drug tablets, which is a histamine H2-receptor antagonist. However, as seen for the polymorphic quan-tification by vibrational spectroscopy, spectral features are often not clear cut and quantification can be improved by multivariate approaches.

Piqueras et al. (2014) showcased the combination of Raman point mapping and a multivariate curve resolution approach. They studied the spatial polymor-phic transformation of Carbamazepine upon heating. The hyperspectral image contained 20 x 20 pixels with a 10 µm resolution and 1349 spectral channels (100 to 1650 cm-1). The acquisition of the complete image required 40 min. To construct the spectral image the acquired spectra for all pixels were subjected to a multivariate curve resolution (MCR) protocol which is able to extract the pure compound contributions of spectra originating from mixtures. These pure compound spectra can be applied to plot distribution maps of the three differ-ent polymorphs separately. In Figure 18 the hyperspectral image and Raman spectra are shown at different temperatures. In Figure 18a the global intensity of carbamazepine as a function of temperature is shown, whereas in Figure 18b the process change upon heating is presented.

Figure 18: Hyperspectral images (20x20 pixels; 10 µm pixel resolution) of Carba-mazepine at different temperatures obtained by Raman point mapping. In (a) the pure spectral contribution is shown whereas in (b) the process evolution upon heating is visu-alised. Each pixel represents the global intensity were blue indicates a low intensity and the more red the higher the global intensity. The global intensities are obtained by de-termining the mean values of the distribution maps calculated by the multivariate curve resolution protocol. Figure reproduced from Piqueras et al. (2014) [48]

4

Discussion and Conclusion

The various vibrational spectroscopy techniques for the analysis of polymorphs can be divided in direct and indirect detection of the lattice vibrations. NIR, MIR and mid-frequency Raman intrinsically detect the local structure whereas these techniques often detect the intermolecular due to peak shifts arising from differences in hydrogen bonding [43, 6]. The specific vibration energy of the hydrogen bridging bonds is considered to be influenced by the crystalline struc-ture [3]. The direct detection of the low energy lattice vibrations is possible by FIR, THz and low-frequency Raman spectroscopy because these vibrational modes are affected by the crystal packing [3]. Each vibrational spectroscopic techniques has its strong and weak points therefore the advantages and disad-vantages between the different techniques are discussed below and summarized in Table 2.

Arguably, both near- and mid-infrared spectroscopy are the applications that require the least expertise and are widely applied in chemical analysis as they are common equipment in laboratories. Since these kind of systems have been com-mercialized for some time the acquisition of spectra is relatively easy and fast. In addition, the possibility to use ATR or diffuse reflectance illumination geome-try reduces the need for sample preparation. Since in ATR the evanescent wave minimally penetrates the sample a good surface contact is required. For optimal sensitivity and accuracy the solid powder is compressed on the ATR crystal. However one should be cautious of pressure induced polymorph transformation [37].

IR detects the vibrations associated with the absorption of infrared, and mid-Raman is capable of probing similar molecular vibrations through inelastic scattering events. Raman requires minimal sample preparation, can measure the sample through a container and due to the fact that water is a weak scat-tering molecule Raman is only slightly affected by moisture in the sample or atmosphere. Generally, the Raman scattering efficiency is very low but with the introduction of high power lasers relatively fast detection of Raman spectra is possible. Raman spectroscopy has become a more common chemical analysis tool because of advances in lasers, since the number of Raman events increases with the number of emitted photons. However, the higher photon intensity of lasers introduces the chance of photodegradation or thermal degradation, which could change the crystal packing. Furthermore, in Raman experiments fluores-cence interferences can be observed due to the excitation of the sample or matrix material by the laser. Fluorescence can be suppressed in Raman spectroscopy by time-gated detection since the lifetime of the fluorescence emission is much longer than that of Raman scattering but this gating mechanism complicates the setup.

Also the direct detection of phonon modes has been used to study polymorphic systems by probing their low-frequency vibrations. Absorption of far-infrared light corresponds to these vibrational energies, which can be measured by the

convenient swapping of the potassium bromide beamsplitter in a mid-infrared spectrophotometer to a silicon (Si) solid substrate beamsplitter [25]. The perfor-mance of Si beamsplitter is better in the far-infrared frequencies than the usual beamsplitters (e.g. KBr or PET) used in MIR instrumentation. The higher re-fractive index of Si beamsplitters improves the efficiency of the beamsplitter at the lower frequencies. These splitters can also be employed in the mid-infrared range but have a reduced resolution (∼= 1 cm-1) opposed to PET beamsplitters in this spectral region [49]. Silicon solid substrate beamsplitters appear to offer an convenient method to measure lattice vibrations with standard IR instru-mentation, nevertheless, THz and low-frequency Raman spectroscopy are more commonly reported for the detection of phonon modes [25].

THz spectroscopy has been widely applied to the analysis of polymorphic forms of pharmaceuticals [43]. The emission and detection of THz irradiation is mainly performed by electro-optics or photoconductive antennas, where the for-mer is reported to be less complicated to implement and achieve wider detection bandwidths [40]. THz spectroscopy detects the particular wave characteristics allowing for the calculation of the refractive index and absorption coefficient and below 3 THz the signal to noise ratio is better for THz spectroscopy than FIR [26, 50]. Even though the data obtained by THz spectroscopy is dense in information, it lacks the applicability for online process control unlike NIR or Raman [6]. Unlike Raman, both FIR and THz spectroscopy do not suffer from fluorescence obstruction but the low frequency irradiation is absorbed by water molecules. Therefore, the optical pathway of the THz or FIR radiation requires to be purged from atmospheric moisture to reduce absorption bands originating from rotational transition of water prior to acquisition [43].

Low-frequency Raman spectra were considered difficult to acquire because of the alignment of triple grating Raman spectrometers but with the development of volume Bragg gratings the low-frequency region has become more convenient for Raman spectroscopy [43]. VBGs are able to suppress Rayleigh scattering relatively easy, enabling the simple direct detection of lattice vibrations. Similar to FIR, it has been reported that low-frequency spectral region was achieved in commercial Raman instrumentation by conversion of the conventional Raman filters to ultra-narrow notch filters [51, 6]. Using ultra-narrow notch filters (e.g. high volume Bragg gratings) it is also possible to detect simultaneously both inter and intramolecular frequencies; at the cost of spectral resolution [4]. In addition, these spectral filters enable the possibility to detect both Stokes and anti-Stokes which cannot be realized with edge filters. The application of VBGs does require the accurate calibration of the incident angle because the filters’ optical density is dependent on this angle [44]. An added benefit of low-frequency Raman over mid-frequency Raman is that interfering fluorescence is less severe in the former because the phonon Stokes shifts are outside of the fluorescence spectral window [6].

The univariate quantification of polymorphic forms has been reported for MIR [35] and Raman [46]. Single parameter regression models simplify the quantifi-cation process but have shown to be then outperformed by PXRD or DSC

appli-cations [35]. Furthermore, simple linear regression requires the change in peak shift or intensity of a particular band which does not necessarily has to be ob-served between different polymorphs. The assessment of the spectral pattern in multivariate modelling strategies can be more effective for the quantification of polymorphic structures. Chemometrics improve the quantification performances of the vibrational spectroscopic methods but could be considered more challeng-ing than univariate regression [27]. One of the key challenges in chemometrics is to objectively interpret the predictions; requiring quality assessment criteria like Q-residuals and Hotelling-T2 [32]. Multivariate curve resolution appears to be an interesting approach to study the different polymorphic structure in the sample because this algorithm is able to extract pure compound spectra of the different forms or visualize transitions between forms in dynamic measurements [48].

An interesting observation was the dependency of the distribution in particle size on the reproducibility of all investigated vibrational spectroscopic methods. Nearly all investigated studies reported the sieving and/ or milling of the solid powder to improve particle size uniformity and therefore improve the repro-ducibility [28]. In the case for THz spectroscopy the measurement of particles smaller than the THz wavelength was reported to reduce baseline offsets be-cause of non-resonant light scattering [22]. However, physical altering the solid could possibly result in transformation of the polymorphic forms. An alterna-tive approach to lowering the effect of particle size distribution is to increase the illumination spot size and rotation of the sample [45].

To conclude, various techniques under the vibrational spectroscopy umbrella have been applied to measure crystalline solids. Where older methods tend to use NIR or MIR, novel developments in hardware have pushed the application of the direct detection of the phonon modes by THz, FIR or low-frequency Raman spectroscopy. Improvements for the detection of low-frequency vibrations have for one been incentivized by process analytical technologies that required fast and reliable analysis of polymorphs compared to the golden standard PXRD [6]. The advancement in ultra-narrow notch filters has simplified and improved the setups of low-frequency Raman and the development of faster lasers and better THz emitters and detectors improved the performance of THz spectroscopy. These two spectroscopic applications have been proven to be useful for the measurement of polymorphic systems and appear to be applied more often than FIR [25]. However, FIR appears also an interesting methods for the detection of phonon modes because existing mid range IR equipment can be converted to the low-frequency range by the conversion of certain filters, similar to low-low-frequency Raman.

Table 2: Advantages and disadvantages of vibrational spectroscopic techniques for the analysis of polymorphic systems. Table adapted from Bunaciu et al. (2015) [31], Lipi¨ainen et al. (2018) [4], Roy et al. (2013) [6], Guo et al. (2017) [28], Smith et al. (2011) [40], Paudel et al. (2015) [52], Han et al. (2018) [53], Peiponen et al. [54]

Technique Information Advantages Disadvantages

Near-Infrared

- Vibrational overtones - 13000-4000 cm-1 - 4 cm-1 resolution

- Short acquisition times

- No sample preparation required - Possible to penetrate glass container - Availability fiber optic probes

- Low sensitivity and selectivity - Severe baseline slope

- Nearly always requires chemometrics - Affected by moisture levels

- Affected by particle size variations Mid-Infrared

- Intramolecular vibrations - 4000-400 cm-1

- 4 cm-1 _resolution

- Relatively short acquisition times - Commercially availalble intruments - Availability of spectral libraries

- ATR or DRIFT can induce solid-state transform - Interference of moisture in atmosphere or sample - Affected by particle size variations

Mid-Frequency Raman - Intramolecular vibrations - 4000-400 cm-1 - 2 cm-1 resolution - Insensitive to water

- No sample preparation required - Possible to measure through container - Availability fiber optic probes

- Fluorescence - Photodegradation

- Laser induced thermal decomposition - Affected by particle size variations Far-Infrared

- Lattice vibrations - 400-100 cm-1 - 4 cm-1 resolution

- Available through conversion of MIR beamsplitter - Interference of atmospheric moisture - Lower spectral resolution than MIR - Affected by particle size variations Terahertz

- Lattice vibrations - 133-10 cm-1

- Spectral resolution dic-tated by step size of the de-lay line

- Determination of complex refraction index and adsorp-tion coefficient

- THz radiation is insensitive to multiple polymeric com-pounds

- THz radiation is insensitive to multiple polymeric com-pounds

- Interference of atmospheric moisture - Affected by particle size variations

Low-Frequency Raman - Lattice vibrations - 400-8 cm-1 - 2 cm-1 _resolution

- See mid-frequency Raman

- VBGs enable simultaneous measurement of Stokes and anti-Stokes lines

- Less fluorescence observed than mid-frequency Raman

- Photodegradation

- Laser induced thermal decomposition - Affected by particle size variations

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