Research Article
`
`Received: 13 March 2009
`
`Accepted: 19 July 2009
`
`Published online in Wiley Interscience: 9 September 2009
`
`(www.interscience.wiley.com) DOI 10.1002/jrs.2453
`
`Insights into phase stability
`of anhydrous/hydrate systems:
`a Raman-based methodology
`Mariela M. Nolasco,a∗
`Ana M. Amadob and Paulo J. A. Ribeiro-Claroa
`
`FT-Raman spectroscopy turns out to be a powerful technique to evaluate the amount of polymorphic and pseudopolymorphic
`forms in crystalline samples – which is particularly relevant in pharmaceutical sciences. This paper presents a methodology that
`allows successful quantitative evaluation of the solid-state hydration and dehydration processes, using FT-Raman spectroscopy.
`All the steps required for a reliable evaluation of the hydration/dehydration process are illustrated for the caffeine system, a
`particularly challenging system presenting limited spectral differences between the pseudopolymorphs. The hydration process
`of caffeine was found to occur in a single-step process with a half-life time of ca 13 h, while the dehydration occurs through a
`two-step mechanism. The critical relative humidity was found to be at ca 81 and 42% for anhydrous and hydrate caffeine forms,
`respectively. Copyright c(cid:1) 2009 John Wiley & Sons, Ltd.
`Supporting information may be found in the online version of this article.
`
`Keywords: Raman spectroscopy; hydration/dehydration; kinetics; phase stability; caffeine
`
`Introduction
`
`It has long been known that pharmaceutical solids can exist in more
`than one solid-state crystal form,[1] which can have significantly
`different pharmaceutical properties, such as solubility, dissolution
`rate and bioavailability.[2 – 5] In addition to polymorphs,[6,7] other
`examples of possible solid states are solvates and hydrates.[8]
`Different techniques ranging from thermal methods to spec-
`troscopic tools (nuclear magnetic resonance, X-ray diffraction and
`vibrational spectroscopy) can be applied to monitor pseudopoly-
`morphic transitions.[9 – 14] In the last few years, the investigation
`of pharmaceutical compounds by means of Raman spectroscopy
`has attracted much interest, and some exhaustive reports[15 – 17]
`have pointed out the pharmaceutical applications of Raman spec-
`troscopy. This technique, which provides an excellent method
`for probing solid-state hydrogen-bonding interactions between
`molecules (including polymorphs and solvates[9,10,15,18 – 23]),
`is
`more often associated with qualitative analysis. However, the
`application of Raman spectroscopy to monitor the solid-phase
`composition during polymorphic and pseudopolymorphic phase
`transitions has been described in recent publications.[24 – 35]
`It has been reported that approximately one-third of phar-
`maceutical solids are capable of forming a hydrate form,[36]
`depending on the environmental conditions (temperature and
`vapor pressure).[37] As the hydration state may affect the physical
`and chemical properties of the pharmaceutical product,[4,5] it is
`important to know the response of pharmaceutical solids to differ-
`ent environments of storage, namely humidity and temperature
`conditions, evaluating therefore the solid-state interconversion of
`such hydrates with their anhydrous forms that dictate the stability
`of a solid phase.
`In order to accomplish this purpose, a Raman spectroscopy
`methodology is presented and applied for caffeine – used as a
`model drug. This methodology was found to yield reliable kinetic
`
`data for systems that present large spectral changes between
`hydrate and anhydrous forms, such as theophylline[27] and
`niclosamide.[29] The applicability of the methodology in systems
`with less evident changes is well illustrated in this study with
`caffeine.
`Caffeine (1,3,7-trimethylpurine-2,6-dione; hereafter called CA,
`Fig. 1) is a methylated xanthine derivative that naturally occur
`in food products such as tea, coffee and chocolate and is
`one example of the many drugs sensitive to polymorphic and
`pseudopolymorphic transformations.[38 – 45] This compound finds
`a variety of medical applications, being routinely prescribed,
`for instance, as a central nervous system stimulant[46] and
`presents beneficial effects in preventing Parkinson and Alzheimer
`diseases.[47 – 49] CA is also known to cause diuresis,[50] and their
`administration seems to protect mice against whole-body lethal
`dose of γ -irradiation.[51]
`The solid-sate properties of CA have been widely investi-
`gated; it is known to crystallize into different crystalline states,
`namely as one crystalline nonstoichiometric hydrate,[40,52,53] here-
`after named as CAh, and a pair of anhydrous α- and β-
`polymorphs.[40,52,54 – 58] The anhydrous β-form, hereafter named
`as CAa (anhydrous CA), is stable at room temperature, whereas
`the α-form only occurs at higher temperatures.[44,45,56,59]
`The present paper has been organized as follows. Firstly,
`the methodology applied is described. Secondly, the results
`
`∗
`
`Correspondence to: Mariela M. Nolasco, CICECO, Chemistry Department,
`University of Aveiro, P-3810-193 Aveiro, Portugal. E-mail: mnolasco@ua.pt
`
`a CICECO, Chemistry Department, University of Aveiro, P-3810-193 Aveiro,
`Portugal
`
`b Química-Física Molecular, Chemistry Department, FCTUC, University of
`Coimbra, P-3004-535 Coimbra, Portugal
`
`J. Raman Spectrosc. 2010, 41, 340–349
`
`Copyright c(cid:1) 2009 John Wiley & Sons, Ltd.
`
`340
`
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`

`Insights into phase stability of anhydrous/hydrate systems
`
`Figure 1. Schematic representation of caffeine and atom numbering used
`in the text.
`
`obtained for the CA system are presented and discussed in four
`main sections, concerning (1) the selection of the most useful
`spectral regions; (2) the calibration procedure; (3) the underlying
`mechanisms and (4) the critical relative humidity (RH) conditions
`for both hydration and dehydration processes of CA forms.
`
`Methodology
`
`The Raman spectroscopy methodology here presented is based
`on the vibrational structural differences observed in most
`of hydrate/anhydrous systems as a result of the changes in
`intermolecular contacts. The different spectral Raman features
`(peak positions and intensities) observed in the spectra of distinct
`solid-sate forms are the key factors that allow monitoring the
`process during the phase transition.
`Water, being a component of the atmosphere which consider-
`ably varies from country to country and day to day, is the most
`critical parameter when substances may transform to hydrates
`under normal storage conditions. As water will be absorbed and
`desorbed with temperature and moisture changes, an experi-
`mental methodology that accounts for these factors is of utmost
`importance.
`Consider a hygroscopic pharmaceutical anhydrous compound,
`Xa, that display facile conversion to a hydrate form, Xh, by
`uptake of moisture into a solid dosage form upon equilibration
`with the ambient environment. Monitoring the amount of Xa
`and Xh forms at different RH and temperature conditions (see
`below, sample treatment) allows, by using this methodology,
`the investigation of hydration and dehydration kinetics of
`pharmaceutical compounds at various conditions of humidity and
`temperature. Additionally, the possible mechanisms underlying
`the hydration and dehydration processes of CA forms, as well as
`the critical RH conditions for both processes, can be determined.
`
`Quantification anhydrous/hydrate forms by peak area mea-
`surements
`
`In order to use Raman spectroscopy in the quantitative evaluation
`of Xa and Xh forms, it is firstly necessary to identify the distinct
`bands due to the different pseudopolymorphic forms intervening
`in the reaction pathway, i.e. reactant and product. Among a given
`pair of bands ascribed to the reactant and product, there will be a
`time-dependent intensity transfer during the reaction.
`The selected spectral regions, with spectral differences between
`anhydrous and hydrate, are evaluated for their suitability to be
`used in the relative quantification of the two forms, Xa and Xh, as a
`
`341
`
`Determination of kinetic parameters
`
`One crucial step in any kinetic study is finding the mechanism for
`the rate-determining reaction step that gives the best description
`of the studied process, and ultimately allows calculating mean-
`ingful kinetic parameters. In this context, once the fractional of
`conversion (αh and αa) has been obtained, a set of kinetics param-
`eters concerning the hydration and dehydration processes can
`be obtained by fitting different models to the data, which allow
`
`J. Raman Spectrosc. 2010, 41, 340–349
`
`Copyright c(cid:1) 2009 John Wiley & Sons, Ltd.
`
`www.interscience.wiley.com/journal/jrs
`
`function of the time of reaction (Xa hydration and Xh dehydration).
`Two main criteria should be considered. Firstly, the existence of
`an isosbestic point is required. Secondly, the number of bands
`required for the spectral deconvolution process should be the
`lowest to avoid ‘over-parameterization’ errors.
`1. Different pseudopolymorphic forms (Xa and Xh) give rise
`to different Raman bands. The observed intensity of the band
`associated with a given pseudopolymorphic form (IXa and IXh) is
`directly proportional to the intrinsic intensity of the corresponding
`vibrational mode (δXa and δXh) and to the relative concentration
`of that pseudopolymorphic form in the sample (CXa and CXh):
`IXa = δXa × CXa
`IXh = δXh × CXh
`
`(1)
`(2)
`
`Additionally, the presence of a pseudo-isosbestic point in a
`specific spectral region of the Raman spectra is an indication that
`only two species exist in equilibrium and that they interconvert
`directly.[60,61] Therefore, the Raman data can be converted to a
`normalized form, called fractional of conversion (α), that ranges
`from 0 to 1 and is a measure of the progress of the reaction, in
`terms of intensity transfer from one band to the other, as a function
`of time.
`it is necessary to
`In order to apply the above procedure,
`determine the calibration relationships so that the relative
`proportions of hydrate (αh) and anhydrous (αa) in the samples
`could be determined without doubt. In fact, the relative intrinsic
`intensity of a particular mode may differ significantly depending on
`the considered pseudopolymorphic form. By preparing physical
`mixtures with well-known molar fractions ratio, the relative
`intrinsic intensities (δXh/δXa and δXa/δXh) of the considered
`vibrational mode can be determined by linear fitting of the
`predicted relative intensities (obtained by band deconvolution
`procedures) as a function of the known molar fractions ratio:
`
`IXa
`IXh
`
`= δXa
`δXh
`
`× χ Xa
`χ Xh
`
`(3)
`
`where χ Xa and χ Xh are the mole fraction of the anhydrous and
`hydrate forms, respectively.
`After the determination of the relative intrinsic intensities of
`the considered vibrational mode, the values of the fractional of
`hydration (αh) and of dehydration (αa) at a particular time of
`reaction t (time of exposure to RH conditions or time of storage at
`a given temperature) can be determined as
`(cid:1)
`αh(t) = IXh
`[IXh + (δXh/δXa)IXa]
`(cid:1)
`[IXa + (δXa/δXh)IXh]
`αa(t) = IXa
`respectively. By definition, αh + αa = 1.
`
`(4)
`
`(5)
`
`and
`
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`

`M. M. Nolasco, A. M. Amado and P. J. A. Ribeiro-Claro
`
`Rate-controlling mechanism
`
`Power law
`
`Power law
`
`Power law
`
`Power law
`One-dimensional phase boundary reaction (zero-order)
`
`Two-dimensional phase boundary reaction (cylindrical symmetry)
`
`Three-dimensional phase boundary reaction (spherical symmetry)
`(cid:2)
`Random nucleation (Mampel equation)
`Random nucleation (Avrami–Erofeev equation; n = 1
`(cid:2)
`Random nucleation (Avrami–Erofeev equation; n = 1
`(cid:2)
`Random nucleation (Avrami–Erofeev equation; n = 1
`(cid:2)
`Random nucleation (Avrami–Erofeev equation; n = 2
`Zero-order mechanism (Polany–Wigner equation)
`One-dimensional diffusion
`Two-dimensional diffusion
`
`2)
`
`3)
`
`4)
`
`3)
`
`Three-dimensional diffusion (Jander equation)
`
`α
`α2
`(1 − α) ln(1 − α) + α
`(cid:1)
`(1 − (1 − α)1
`(cid:1)
`3)2
`1 − (2α/3) − (1 − α)2
`M17
`Three-dimensional diffusion (Ginstling–Brounshtein equation)
`a α stands for Xa → Xh or Xh → Xa degree of conversion; k is the rate constant of the conversion reaction; t is time of exposure to RH conditions or
`time of storage at a given temperature.
`
`Table 1.
`
`Model
`
`M1
`
`M2
`
`M3
`
`M4
`M5
`
`M6
`
`M7
`M8
`
`M9
`
`M10
`
`M11
`
`M12
`M13
`M14
`M15
`
`M16
`
`1
`
`1
`
`1
`
`3
`
`α
`
`α
`
`α
`
`α
`
`4
`
`3
`
`2
`
`2
`
`Solid-state reaction rate equations and mechanisms[62 – 65]
`Equation, f (α) = kta
`(cid:1)
`(cid:1)
`(cid:1)
`(cid:1)
`1 − α
`(cid:1)
`1 − (1 − α)1
`(cid:1)
`1 − (1 − α)1
`− ln(1 − α)
`(cid:1)
`(− ln(1 − α))1
`(cid:1)
`(− ln(1 − α))1
`(cid:1)
`(− ln(1 − α))1
`(cid:1)
`(− ln(1 − α))2
`
`2
`
`3
`
`2
`
`3
`
`4
`
`3
`
`3
`
`identifying the mechanism underlying both Xa → Xh and Xh →
`Xa conversions. Different kinetic models f (α) = kt have been pro-
`posed for characterizing the solid-sate reaction mechanisms, such
`as the present pseudopolymorphic conversions (Table 1).[62 – 65]
`Some examples of hydration and dehydration kinetics studies
`described by such models can be found in the literature.[64,66]
`For example, dehydration of calcium oxalate monohydrate[67] was
`shown to follow geometrical contraction models (M6 and M7
`kinetic models of Table 1).
`
`Spectral band deconvolution and mathematical data treat-
`ment
`
`For the evaluation of band intensity ratios, the integrated band
`intensities (IXh and IXh) can be determined by band-fitting
`procedures, using two Gaussian or two Lorentzian functions,
`after performing a linear baseline correction employing three
`points. For the determination of pseudo-isosbestic points, the
`procedure described by Girling and Shurvell[60] and Pemberton
`and Shurvell[61] should be considered.
`Different standard statistical criteria may be used to determine
`the aggregate deviation of a set of measured points from the
`calculated linear relationship. The most usually used are the
`correlation coefficient (R2) and the standard error of the slope
`of the regression line (sb). Some authors[62,68] have reported
`the inadequacies of using r-value as the sole determinant
`of the applicability of a particular kinetic model, particularly
`for distinguishing between mechanism that yield similar linear
`correlation coefficients (R2). Davies and Pryor[68] pointed out the
`advantages of using sb values instead. In this work, the quality of
`the linear fit obtained for each kinetic model tested (Table 1) is
`determined by considering both R2 and sb values.
`
`Experimental
`
`Materials
`
`CAa was obtained commercially (Sigma-Aldrich) and used without
`further purification (grain size between 125 and 250 µm). Hydrate
`◦
`C
`CA (CAh) was prepared by dissolving CAa in distilled water at 80
`until a supersaturated solution is prepared. When the solution
`was allowed to slowly cool to room temperature, the crystals that
`formed were filtered from the mother liquid, allowed to dry at
`ambient temperature and then gently milled to a fine powder
`(grain size between 125 and 250 µm). As CAh when exposed to
`ambient conditions, even for a short time period, tend to undergo
`partial dehydration, the fine powder was stored in a sealed vessel
`at 92% RH in the presence of a saturated solution of potassium
`nitrate.
`
`Sample treatment
`
`In order to monitor the hydration and dehydration kinetics
`by Raman spectroscopy, different types of experiments were
`In a first type of experiment, both anhydrous →
`performed.
`hydrate and hydrate→ anhydrous phase transitions were induced
`◦
`C ambient temperature. CAa
`by defined RH and studied at 22
`(commercial powder) and CAh samples (ca 0.1 g) were transferred
`to sealed vessels and exposed, for different time intervals, to
`the water atmosphere of 100 and 0% RH (without direct contact
`between the sample and the bulk liquid, Fig. 2), by considering
`pure water and anhydrous CuSO4, respectively. In a second type
`of experiment, the dehydration process was promoted by storing
`◦
`C) for
`the CAh samples at different temperatures (35, 45 and 60
`different time periods, under ambient RH conditions. In both the
`experiments, after the defined time intervals of exposure, the
`FT-Raman spectra of the different samples were recorded.
`
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`Copyright c(cid:1) 2009 John Wiley & Sons, Ltd.
`
`J. Raman Spectrosc. 2010, 41, 340–349
`
`342
`
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`
`

`

`Insights into phase stability of anhydrous/hydrate systems
`
`Figure 2. Schematic representation of the reservoir used for sample
`exposure to specific RH values.
`
`For the purpose of providing the critical RH values for both
`the anhydrous and hydrate forms, CAa and CAh samples (ca
`0.1 g) were exposed to different RH conditions. To control RH
`conditions, saturated salt solutions with deposits were used. The
`RH values considered (and salt used) were taken from Ref. [69]
`and were as follows: 9% (KOH), 13% (LiCl), 20% (KC2H3O2), 30%
`(CaCl2), 42% (Zn(NO3)2, 48% (KCNS), 52% (NaHSO4)), 58% (NaBr),
`61% (NH4NO3), 66% (NaNO2), 78% (Na2SO3), 79% (NH4Cl), 81%
`In all
`((NH4)2SO4), 84% (KBr), 86% (KHSO4) and 92% (KNO3).
`cases, the exposure time of the sample at the considered RH
`was 1 weak in order to guarantee the equilibrium moisture
`condition. After that period of exposure, the FT-Raman spectra
`of the different samples were recorded. All experiments were
`performed at ambient temperature.
`In order to determine the calibration relationship, physical
`mixtures of CAh/CAa with known compositions (CAh molar
`fractions of 0.00, 0.155, 0.165, 0.222, 0.500, 0.751 and 1.00) were
`prepared by smoothly mixing the samples in a mortar for 2 min to
`ensure mixing uniformity. Effects of particle size were examined
`by manually sieving samples to give particle size ranges between
`125 and 250 µm.
`
`this effect, a sample of CAh was exposed continuously to 500
`mW laser power for approximately 1 h and 40 min, and 20 records
`of 5 min each were collected. All the FT-Raman spectra reported
`on this work (using the conditions described above) have been
`collected in 25 min or less, after which period no spectral changes
`assignable to sample heating were observed on the exposure of
`CAh to the laser.
`
`Results and Discussion
`
`Selection of the most useful spectral regions
`
`Figure 3 compares the Raman spectra of CAa and CAh forms
`−1 and 2700–3400 cm
`−1 spectral regions.
`in the 100–1800 cm
`Selecting a suitable region for quantitative analysis would initially
`appear difficult since the FT-Raman spectra have very similar
`patterns, reflecting minor changes in the molecular vibrations due
`to different packing arrangements of the molecules.
`The spectral regions labeled with wavenumbers in Fig. 3 were
`found to be the most amenable for the present study, according to
`the criteria defined above: each pair presents a pseudo-isosbestic
`point and can be described in the spectral deconvolution process
`by only two single bands, avoiding the ‘over-parameterization’
`errors.
`According to our previous study,[72] these are related to the
`−1) and
`stretching mode of the oscillators C8 –H (3070–3150 cm
`CC + CN (1270–1310 cm
`−1).
`In the remaining regions, only
`slight intensity changes are observed. The complete vibrational
`assignment can be found in the reported study.[72]
`
`Calibration procedure
`
`FT-Raman spectroscopic experiments
`
`The FT-Raman spectra were recorded on an RFS-100 Bruker FT-
`spectrometer, using a Nd : YAG laser with excitation wavelength
`of 1064 nm, with laser power set to 300 mW. Each spectrum
`−1 resolution. As
`is the measurement of 100 scans with 2 cm
`emphasized in our previous work,[27] it is apparent that in some
`experiments the sample temperature can rise significantly due to
`laser exposure[70,71] and promote either loss of solvent molecules
`or polymorphic transformations. For the purpose of evaluating
`
`Figure 4 summarizes the calibration procedure for the stretching
`−1). Figure 4(a) shows
`mode of the oscillators C8 –H (3070–3150 cm
`−1.
`that this spectral region presents an isosbestic point at 3117 cm
`Figure 4(b) shows the plot of ICAa/ICAh versus χ CAa/χ CAh used to
`evaluate the required ratio δCAa/δCAh. This calibration procedure
`−1 spectral region, and the
`was also made for the 1270–1310 cm
`results are summarized in Table 2.
`The comparison between the FT-Raman spectra of CAa (solid
`line) and CAh (dashed line)
`forms in the 1270–1310 and
`
`343
`
`Figure 3. FT-Raman spectra of CAa and CAh in the 100–1800 cm
`differences between CA forms are marked.
`
`−1 and 2700–3400 cm
`
`−1 spectral regions. Some bands showing the most pronounced
`
`J. Raman Spectrosc. 2010, 41, 340–349
`
`Copyright c(cid:1) 2009 John Wiley & Sons, Ltd.
`
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`

`M. M. Nolasco, A. M. Amado and P. J. A. Ribeiro-Claro
`
`Mechanism for the CAa→CAh process
`The kinetics of anhydrous conversion form CAa to CAh by exposure
`to water-saturated atmosphere were monitored as described in
`the experimental section. Figure 6(a) and (b) show the sequential
`change of the CC+ CN stretching mode (1270–1310 cm
`−1 region)
`and the plot of the measured fractional of hydration (αh) as a
`function of time of exposure to RH = 100% conditions at 22
`◦
`C.
`−1
`The time-dependent intensities observed in the 3070–3150 cm
`spectral region present a similar behavior.
`The steepest increase is observed around ca 960 min (16 h), and
`after 25 h of exposure the anhydrous form was totally transformed
`to the hydrate (situation referred to in Fig. 6(a) as CAh), which is in
`accordance with the results of X-ray diffraction and hygroscopicity
`measurements published by Pirttim¨aki and Laine.[43] Larger times
`of exposure did not give rise to any further observable spectral
`change.
`The fractional of hydration (αh) measured for the two considered
`regions were fitted to the different kinetic models listed in Table 1,
`in order to choose the model giving the best statistical fit. As
`already emphasized in this work, the most usually used statistical
`criteria are the correlation coefficient (R2) and the standard error
`of the slope of the regression line (sb). Thus, the quality of the
`linear fit obtained for the different kinetic models was determined
`by considering both of them (Table S1, Supporting Information).
`Table 3 shows the best kinetic results obtained for CAa hydration.
`Although the R2 and sb values for M9 and M13 kinetic models
`are somewhat similar (Table 3), M9 was assumed to yield a better
`description of the overall results (two spectroscopic regions).
`Within this assumption, it was found that the hydration of CAa
`follows a one-step random nucleation process, described by the
`Avrami–Erofeev equation of exponent 1/2 with a rate constant of
`ca (1.14±0.05)×10
`−3 min
`−1. The time required for half-hydration
`(t1/2) was ca 750 min (≈13 h) with the completion of CAa hydration
`after ca 3030 min (≈51 h).
`Although these results are not in accordance with the studies
`of Pirttim¨aki and Laine,[43] which suggest that CAa hydration
`involves two steps with a 50% hydration achieved after 26 h, these
`discrepancies can be explained by the different history of the CAa
`samples used. In this work, commercial CAa samples were used,
`while in the reported study[43] the CAa samples were obtained by
`dehydration of CAh samples. This situation can lead to significantly
`different samples morphologies (e.g. grain size and crystal defects),
`which can affect the hydration behavior.
`Mechanism for the CAh→CAa process
`The kinetics of the conversion of CAh to CAa by exposure to very
`low water vapor pressure conditions were monitored. Figure 7(a)
`
`Figure 4. Calibration
`procedure.
`(a) FT-Raman
`spectra,
`in
`the
`−1, of physical mixtures of CAa and CAh with well-known
`3070–3150 cm
`composition (CAh molar fractions of 0.00, 0.155, 0.165, 0.222, 0.500, 0.751
`−1;
`and 1.00 were used). A pseudo-isosbestic point is observed at 3117 cm
`(b) plot of ICAa/ICAh versus χ CAa/χ CAh (error bars included).
`
`−1 spectral regions, after scaling in order to reflect
`3070–3150 cm
`their relative intrinsic intensities, is shown in Fig. 5.
`
`Mechanisms underlying hydration/dehydration processes of
`CA forms
`
`The dehydration process of CAh has been studied in
`detail,[40 – 43,52,73,74] but significantly less research has been done
`on the reverse process, from anhydrous caffeine to hydrate
`caffeine.[43,74]
`
`Table 2. Results obtained for the plot of ICAa/ICAh versus χ CAa/χ CAh
`
`Band centre
`(wavenumbers in
`−1)
`cm
`
`Spectral region
`
`Vibrational
`modea
`
`CAa
`
`CAh
`
`bb
`
`b
`
`sb
`
`R2b
`
`b
`
`δCAa
`δCAh
`
`−1
`3070–3150 cm
`−1
`1270–1310 cm
`
`3113
`1285
`
`3122
`1290
`
`νC8 – H
`νCC + νCN
`a In accordance with Ref. [72]; ν stands for stretching.
`b b and sb stand for slope and slope standard deviation of the linear regression line, respectively; R2 for the correlation coefficient; δCAh and δCAa stand
`for intrinsic intensities of the mode for the CAh and CAa forms, respectively.
`
`1.4632
`0.6147
`
`0.14057
`8.27 × 10
`−2
`
`0.9991
`0.9922
`
`1.46
`0.62
`
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`
`Copyright c(cid:1) 2009 John Wiley & Sons, Ltd.
`
`J. Raman Spectrosc. 2010, 41, 340–349
`
`344
`
`Merck Exhibit 2241, Page 5
`Mylan v. Merck, IPR2020-00040
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`

`

`Insights into phase stability of anhydrous/hydrate systems
`
`−1 and 3070–3150 cmFigure 5. Comparison of the FT-Raman spectra of CAa (solid line) and CAh (dashed line) forms in the 1270–1310 cm
`
`
`regions, after scaling in order to reflect their relative intrinsic intensities.
`
`−1 spectral
`
`345
`
`−1 region, of CAa samples as a function of time of exposure to RH = 100% conditions; (b) plot of theFigure 6. (a) FT-Raman spectra, in the 1270–1310 cm
`
`fractional of hydration (αh, %) as a function of time of exposure to the RH = 100% conditions (22
`◦
`C); (c) Fitting of the αh values to the Avrami–Erofeev
`random nucleation (n = 0.5) equation.
`
`and (b) show the sequential change of the C8 –H stretching mode
`−1) and the plot of the measured
`spectral region (3070–3150 cm
`fractional of dehydration (αa) as a function of time of exposure
`to RH = 0% conditions at 22
`◦
`C. The time-dependent intensities
`−1 spectral region present a similar
`observed in the 1270–1310 cm
`behavior.
`The CAh dehydration promoted by RH = 0% conditions is
`consistent with a two-step process, also suggested by Pirttim¨aki
`and Laine.[43] The first evidences of the CAh → CAa conversion are
`detectable after 2 h (120 min) of exposure to RH = 0% conditions,
`with the complete dehydration observed after 24 h (situation
`referred to in Fig. 7(a) as CAa).
`After fitting the αa data to the different kinetic models (Table
`S2, Supporting Information), the best kinetics results (Table 4)
`reveal that, for the two spectroscopic regions, the first step of CAh
`dehydration can be described by the Avrami–Erofeev equation
`of exponent 2/3, with a rate constant of ca (5.6 ± 0.5) × 10
`−3
`
`−1, which corresponds to a half-life time of ca 141 min. For
`min
`the second step, we can assume that it is best represented by the
`three-dimensional diffusion mechanism (Jander equation) with a
`rate constant of ca (7.7 ± 0.1) × 10
`−5 min
`−1.
`Griesser and Burger,[42] by applying microscopic and various
`thermoanalytical techniques, also suggested the same mechanism
`for CAh dehydration at low water vapor pressure (RH between
`0 and 13%),
`in which it was assumed that water leaves the
`crystal through the channel structure.[40,42,74] As their CAh sample
`preparation was the same as in the present work, this similarity
`reinforces the idea that the experimental conditions are critical in
`these studies.
`The dehydration of CAh samples was also monitored at
`◦
`C. Figure 8 shows the plot of the measured
`35, 45 and 60
`−1
`fractional of dehydration (αa), derived from the 3070–3150 cm
`spectral region, as a function of time of storage at 35, 45 and
`◦
`C.
`60
`
`J. Raman Spectrosc. 2010, 41, 340–349
`
`Copyright c(cid:1) 2009 John Wiley & Sons, Ltd.
`
`www.interscience.wiley.com/journal/jrs
`
`Merck Exhibit 2241, Page 6
`Mylan v. Merck, IPR2020-00040
`
`

`

`M. M. Nolasco, A. M. Amado and P. J. A. Ribeiro-Claro
`
`Table 3. Values of rate constant of hydration (k), standard deviation of the slope (sb), correlation coefficient (R2) and times of half-hydration (t1/2)
`and complete hydration (th), obtained for the best linear fits f (α), considering two different spectral regions (CAa → CAh conversion induced by
`RH = 100% conditions)
`
`Spectral region
`−1)
`(cm
`
`3070–3150
`1270–1310
`1270–1310
`
`Kinetic
`modela
`
`M9
`M9
`M13
`
`f (α)
`−0.07654 + 0.00128t
`0.04400 + 0.00100t
`−0.06597 + 0.00068t
`
`k
`−1)
`(min
`1.28 × 10
`−3
`1.01 × 10
`−3
`6.8 × 10
`−4
`
`sb
`5.0 × 10
`−5
`5.0 × 10
`−5
`8.0 × 10
`−5
`
`R2
`
`0.9903
`0.9870
`0.9789
`
`b
`t1/2
`(min)
`
`711
`789
`832
`
`c
`th
`(min)
`
`2711
`3349
`1567
`
`a Kinetic model described in Table 1.
`b Time for half-hydration f (α) is equal to 0.833 and 0.5 for M9 and M13, respectively, using (α = 0.5).
`c Time for total hydration (f (α) equal to 3.393 and 0.99999 for M9 and M13, respectively, using α = 0.99999).
`
`−1 region, of CAh samples as a function of time of exposure to RH = 0% conditions; (b) plot of theFigure 7. (a) FT-Raman spectra, in the 3070–3150 cm
`
`fractional of dehydration (αa, %) as a function of time of exposure to the RH = 0% conditions (22
`◦
`C).
`
`The general results obtained for the different temperatures
`are consistent with a two-step process,
`like the dehydration
`promoted by RH = 0% conditions, and after 1440 min (24 h) the
`◦
`C, the first step of CAh
`CAh dehydration is complete. At 45 and 60
`dehydration is too fast to allow a kinetic study with this technique.
`In fact, the time required to achieve 75% dehydration is of the
`◦
`C, respectively. In the
`order of 100, 30 and 5 min at 35, 45 and 60
`◦
`C experiment, according to the best kinetic results
`case of the 35
`(Table 5 and Table S3, Supporting Information), we can assume
`that the first step of CAh dehydration is described by zero-order
`mechanism (Polany–Wigner equation) with a rate constant of ca
`(7.15±0.74)×10
`−3 min
`−1, which corresponds to a half-life time of
`ca 67 min. The second step can be described by random nucleation
`(Mampel equation) with a rate constant of ca. (4.89± 0.68)× 10
`−3
`−1.
`min
`
`Critical RH conditions for hydration/dehydration processes of
`CA forms
`
`The stability of a solid drug substance in the presence of
`atmospheric moisture is of concern to the pharmaceutical industry,
`
`as it has practical implications for processing and storage.[5] It is
`sometimes the case that an anhydrous crystal is stable below a
`certain critical RH but at higher RH it will convert to a crystalline
`hydrate[75] and vice versa. As this hydration or dehydration aging
`phenomena can affect several drug properties, the knowledge of
`a critical RH of a particular drug is essential to obtain a stable final
`dosage.
`
`Critical RH for CAa→CAh process
`The information concerning the critical RH for CAa → CAh
`conversion is scarce, but the occurrence of this phase transition at
`high humidity has been reported.[76]
`−1,Figure 9(a) shows the Raman spectra, in the 3070–3150 cm
`
`obtained for CAa samples stored at different RH values for 1 week
`◦
`C. The corresponding plot of the measured fractional of
`at 22
`hydration (αh) as a function of RH values is shown in Fig. 9(b).
`Spectral evidences of the presence of CAh form occur only for RH
`> 81%, while evidences of the presence of the CAa form completely
`vanish for RH ≥ 90%. After 1 week at RH = 86% the amount of
`sorbed water still very low, approximately 23% hydration. These
`
`www.interscience.wiley.com/journal/jrs
`
`Copyright c(cid:1) 2009 John Wiley & Sons, Ltd.
`
`J. Raman Spectrosc. 2010, 41, 340–349
`
`346
`
`Merck Exhibit 2241, Page 7
`Mylan v. Merck, IPR2020-00040
`
`

`

`Insights into phase stability of anhydrous/hydrate systems
`
`Table 4. Values of rate constant of dehydration (k), standard deviation of the slope (sb), correlation coefficient (R2) and time of half-dehydration
`(t1/2) obtained for the best linear fits f (α), of the first and second step data, considering two different spectral regions (CAh → CAa conversion induced
`by RH = 0% conditions)
`
`First step data
`
`Second step data
`
`Spectral region
`(wavenumbers in cm
`
`−1)
`
`Kinetic
`modela
`
`3070–3150
`1270–1310
`1270–1310
`
`3070–3150
`1270–1310
`
`M12
`M12
`M8
`
`M16
`M16
`
`f (α)
`−0.01119 + 0.00521t
`0.03597 + 0.00597t
`−0.03305 + 0.00668t
`0.22545 + 0.000080t
`0.29064 + 0.000074t
`
`k
`−1)
`(min
`5.21 × 10
`−3
`5.97 × 10
`−3
`6.68 × 10
`−3
`8.0 × 10
`−5
`7.4 × 10
`−5
`
`sb
`9.2 × 10
`−4
`1.2 × 10
`−4
`1.11 × 10
`−4
`1.0 × 10
`−6
`1.2 × 10
`−6
`
`R2
`
`0.9868
`0.9868
`0.9882
`
`0.9804
`0.9722
`
`b
`t1/2
`(min)
`
`152
`129
`108
`
`–
`–
`
`a Kinetic model described in Table 1.
`b Time for half-dehydration (f (α) is equal to 0.78 and 0.69 for M12 and M8, respectively, using α = 0.5).
`
`When stored at RH > 61%, CAh shows good stability, whereas
`with a decrease in humidity it starts to dehydrate. According to
`our results, while at RH= 42% the Raman spectrum of CAh already
`shows the presence of small amounts of CAa, the full dehydration