Structure and Energetics of a New Hydrate of 4′-Hydroxyacetophenone

DOI: 10.1021/cg1001804

Published as part of a virtual special issue of selected papers presented in celebration of the 40th Anniversary Conference of the British Association for Crystal Growth (BACG), which was held at Wills Hall, Bristol, UK, September 6-8, 2009.

2010, Vol. 10 3070–3076

Structure and Energetics of a New Hydrate of 40 -Hydroxyacetophenone Carlos E. S. Bernardes,†,‡ M. F
atima M. Piedade,†,‡ and Manuel E. Minas da Piedade*,† †

Departamento de Quı´mica e Bioquı´mica, Faculdade de Ci^ encias, Universidade de Lisboa, 1649-016 Lisboa, Portugal, and ‡Centro de Quı´mica Estrutural, Complexo Interdisciplinar, Instituto Superior T
ecnico da Universidade T
ecnica de Lisboa, 1049-001 Lisboa, Portugal Received February 4, 2010; Revised Manuscript Received May 11, 2010

ABSTRACT: A new hydrate of 40 -hydroxyacetophenone (HAP), triclinic, space group P1, was isolated and characterized. Both the structure determination by single crystal X-ray diffraction at 150 K and the results of thermogravimetry analysis carried out in the temperature range 263-363 K indicated the H2O/HAP molar ratio to be 1.5. The water molecules line up in chains that reside in lattice channels (channel hydrate) and are sustained by OH 3 3 3 O hydrogen bonds. The chains also interact with the OH (donor) and CO (acceptor) groups of the HAP molecules through OH 3 3 3 O hydrogen bonds. The results suggest that the OH and CH3CO groups of the HAP molecules in the hydrate are in a syn orientation. This conformation is the same as that observed for the previously described anhydrous form II (orthorhombic, P212121). The dehydration process generates, however, the form I HAP polymorph (monoclinic, P21/c), where the anti conformation is preferred. From drop-sublimation Calvet microcalorimetry experiments it was possible to conclude that Δf H
m(HAP 3 1.5H2O, cr) = -812.5 ( 3.1 kJ 3 mol-1, at 298.15 K. Finally, thermodynamic analysis of the temperature and relative humidity effects on the dehydration process to yield HAP(cr I) and H2O(g) indicated that loss of water becomes favorable (ΔrGm < 0) at 298.15 K, for a relative humidity of ∼66%. This value is compatible with routine laboratory observations of the HAP 3 1.5H2O(cr) stability at ambient temperature. The analysis also suggested that, independently of the relative humidity, the hydrate will tend to decompose above ∼331 K, a temperature that closely matches the high limit of the dehydration range observed in the TG experiments.

Introduction It is well-known that a given organic compound can often crystallize with different structural architectures.1-3 These various forms, or polymorphs, may coexist under the same pressure and temperature conditions, and they normally exhibit significantly different physical properties. The control of polymorphism is, therefore, of considerable interest to the fine chemicals industry (e.g., pharmaceuticals), since it provides a means to alter the properties of a product in view of an application, without changing the molecule involved. This has fostered numerous recent efforts to develop systematic methodologies for the selective and reproducible preparation of polymorphic modifications.4 It may also happen that, in the course of crystallization from solution, solvent molecules cocrystallize with the solute, forming solvates (or hydrates if water is the solvent). The molecules of solvent may be simply entrapped in channels or voids within the lattice, or interacting with the solute via hydrogen bonds or van der Waals forces. Normally, the inclusion of solvent molecules in the crystal lattice also induces significant changes in the structure, physical properties, and solubility of a material, when compared with the corresponding unsolvated forms. The production of solvates is, therefore, another strategy of changing

the characteristics of a product in view of an application, when the presence of solvent molecules is not undesired.1-3 In the absence of kinetic barriers, metastable polymorphic modifications may evolve over time into the most thermodynamically stable one. Solvates can also transform into an unsolvated polymorph or an amorphous form, by losing solvent when changes in pressure, temperature, and amount of solvent present in the storage atmosphere (humidity in the case of hydrates) occur. Thus, a key issue once polymophs or solvates are identified is the thermodynamic characterization of their stability domains.1-3,5-11 We recently reported the isolation of a new polymorph of 40 hydroxyacetophenone, HAP (form I, monoclinic), that can be prepared in a reproducible way and stored at room temperature for long periods of time without apparent change.12 The structural differences between this and a previously known phase (form II, orthorhombic) were investigated by X-ray diffraction and computational chemistry methods, and their stability domains were characterized by several thermodynamic techniques. Here we describe the isolation of a new hydrate of HAP (triclinic, space group P1) and its structural and thermodynamic characterization relative to the anhydrous forms. Materials and Methods 1

*To whom correspondence should be addressed. E-mail: [email protected]. pubs.acs.org/crystal

Published on Web 06/01/2010

General. The H NMR spectra were obtained in CDCl3, at ambient temperature, on a Bruker Ultrashield 400 MHz spectrometer. GC-MS r 2010 American Chemical Society

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Crystal Growth & Design, Vol. 10, No. 7, 2010

experiments were performed on an Agilent 6890 gas chromatograph coupled to an Agilent 5973N mass detector. A TRB-5MS capillary column from Teknokroma (5% diphenyl/95% dimethylpolysiloxane; 30 m  0.25 mm i.d., 0.25 μm df) was used. The carrier gas was helium maintained at a constant pressure of 1.19 bar. A vaporization injector operating in the split mode (1:100), at 523 K, was employed, and the oven temperature was programmed as follows: 323 K (1 min), ramp at 10 K 3 min-1, 523 K (10 min). The transfer line, ion source, and quadrupole analyzer were maintained at 553 K, 503 K, and 423 K, respectively, and a solvent delay of 5 min was selected. Electron ionization mass spectra in the range 35-550 Da were recorded in the full-scan mode, at 70 eV electron energy, and with an ionization current of 34.6 μA. Data recording and instrument control were performed by means of the MSD ChemStation software from Agilent (G1701CA; version C.00.00). The identity of the analyzed compound was assigned by comparison of the mass-spectrometric results with the data in Wiley’s reference spectral databank (G1035B, Rev D.02.00), and its purity was calculated from the normalized peak areas, without using correction factors to establish abundances. X-ray powder diffraction experiments were carried out on a Philips PW1730 diffractometer with automatic data acquisition (APD Philips v.35B), operating in the θ-2θ mode. The apparatus had a vertical goniometer (PW1820), a proportional xenon detector (PW1711), and a graphite monocromator (PW1752). A Cu KR radiation source was used. The tube amperage was 30 mA and the tube voltage 40 kV. The diffractograms were recorded at ∼293 K in the range 10
e 2θ e 35
. Data were collected in the continuous mode, with a step size of 0.015
(2θ) and an acquisition time of 1.5 s/step. The samples were mounted on an aluminum sample holder. Scanning electron microscopy (SEM) images on Au/Pd-sputtered samples were performed in high vacuum, using a FEI Quanta

Figure 1. SEM image of the lamellar shaped crystals of HAP 3 1.5H2O.

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400 ESEM apparatus, with a resolution of 2 nm. The electron beam voltage was set to 8 kV. The HAP sample (Aldrich 98%) used as starting material for the synthesis of the hydrated form was purified by sublimation at 368 K and 13 Pa. 1H NMR (400 MHz, CDCl3/TMS): δ = 7.91 (d, CH, 2H), δ = 6.92 (d, CH, 2H), δ = 2.58 (s, CH3, 3H). These results are in accordance with those previously reported by us12 or published in a reference database.13 No impurities were detected by GC-MS. Synthesis of HAP 3 1.5H2O. A solution containing 3 g of HAP in 100 g of distilled and deionized water from a Millipore system (conductivity < 0.1 μS 3 cm-1) was kept at 308 K for 1 h and then slowly cooled to room temperature at a rate of 0.5 K 3 min-1 to yield lamellar shaped crystals of HAP 3 1.5H2O (Figure 1). The crystals were stable in air for ∼1 h at room temperature (typically 40-60% relative humidity, monitored with a TFA 30502 sensor) or for approximately 1 week when stored in a desiccator, over a saturated NaCl aqueous solution (94% relative humidity). No decomposition was detected in a sample kept in contact with the crystallization mother liquor, at ∼298 K, for more than 1 year. The stoichiometry of the hydrate was established by thermogravimetry and single crystal X-ray diffraction analysis (see below). Crystal Structure Determination. Single crystal X-ray diffraction analysis of HAP 3 1.5H2O was carried out at 150 K on a Bruker AXS APEX CCD area detector diffractometer, using graphitemonochromated Mo KR (λ = 0.71073 A˚) radiation. An empirical absorption correction was applied using SADABS,14 and the data reduction was performed with the SMART and SAINT programs.15 The structure was solved by direct methods with Bruker SHELXTL16 and refined by full-matrix least-squares on F2 using SHELXL97,17 that is included in WINGX-Version 1.70.01.18 Nonhydrogen atoms were refined with anisotropic thermal parameters. All hydrogen atoms were located in a Fourier map and their positions and isotropic displacement parameters, Uiso(H), refined freely, except those of the water molecules and of the hydroxyl group in HAP, which were refined using a riding model (1.5 times the attached oxygen atom). Graphical representations were prepared using Raster3D19 and Mercury 1.1.2.20 A summary of the crystal data, structure solution, and refinement parameters obtained at 150 K is given in Table 1. Differential Scanning Calorimetry (DSC) and Thermogravimetry (TG). The DSC and combined TG-DSC experiments were performed on a Setaram TG-DSC 111, under a flow of nitrogen of 10 cm3 3 min-1. In a typical TG-DSC run, the sample, with a mass in the range 9-21 mg, was removed from the mother liquor, quickly dried between two filter paper sheets, placed in an open aluminum crucible, and weighed with a precision of (0.01 mg with a Mettler XS205 balance. The crucible was suspended from the arm of the TG microbalance, surrounded by the oven, and subjected to the following temperature program: isothermal step for 300 s at a temperature in the range 263-298 K; ramp at a rate β = 1 or 2 K 3 min-1 to 363 K; isothermal step for 600 s at 363 K. No mass loss was observed in a control experiment where this procedure was applied to the anhydrous form I (monoclinic) of HAP at β = 2 K 3 min-1. Two DSC runs were carried out in the range 263-393 K, at β = 1 K 3 min-1, using sealed lid with punctured hole aluminum crucibles.

Table 1. Crystal Data and Structure Refinement Parameters for HAP 3 1.5H2O at 150 K empirical formula formula weight T/K wavelength/A˚ crystal size/mm color of crystal crystal system space group a/A˚ b/A˚ c/A˚ R/deg β/deg γ/deg V/A˚3 Z

C8H11O3.5 163.17 150(2) 0.71073 0.40  0.33  0.20 colorless triclinic P1 5.7749(4) 7.2971(5) 10.2251(7) 76.308(4) 84.513(4) 77.722(4) 408.60(5) 2

Z0 Fcalcd/g 3 cm-3 μ/mm-1 F(000) θ limits/deg limiting indices

reflections collected/unique completeness to θ/% refinement method data/restraints/parameters GOF on F2 final R indices [I > 2σ(I)] R indices (all data) largest diff peak and hole/e 3 A˚-3

1 1.326 0.104 174 2.05-27.47 -7 e h e 7 -9 e k e 9 -13 e l e 13 12521/1835 [R(int) = 0.0260] 98.0 (θ = 27.47) full-matrix least-squares on F2 1835/1/134 1.088 R1 = 0.0470 R1 = 0.0645 0.435 and -0.378

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Bernardes et al. Table 2. Geometrical Parameters of the Structure of the Hydrate Form of 40 -Hydroxyacetophenone Obtained at 150 K bond distance/A˚

Figure 2. Raster3D19 drawing and labeling scheme of the 40 -hydroxyacetophenone and water molecules in the hydrate HAP 3 1.5H2O. Note that only half of the O2w water molecule is in the asymmetric unit. The samples had masses of 5.26 and 6.36 mg, respectively, and were handled as described for the TG-DSC experiments. Enthalpy of Decomposition Measurements. The enthalpy of decomposition of HAP 3 1.5H2O to give HAP(g) and H2O(g) was determined by using the electrically calibrated drop-sublimation Calvet microcalorimeter and the operating procedure previously described.21,22 The temperature, Tf, of the thermostatic jacket surrounding the calorimetric cells was in the range 348.0-348.1 K. In a typical experiment, the sample with 3.1-5.9 mg of mass was placed into a small glass capillary and weighed with a precision of 1 μg in a Mettler M5 microbalance. The capillary was equilibrated for ∼300 s at a temperature Ti in the range 298.1-301.3 K, inside a furnace placed above the entrance of the sample cell, and subsequently dropped into the cell under N2 atmosphere. The endothermic signal due to the heating of the capillary and the compound from Ti to Tf (with partial decomposition of the latter) was immediately observed, and before the measuring curve returned to the baseline, the sample and reference cells were simultaneously evacuated to 0.13 Pa. The massic enthalpy of the calorimetric process, Δrh, was obtained from
 1 A - Ab Δr h ¼ - mc cp, c ðTf - Ti Þ ð1Þ ms ε where ms and mc are the masses of the hydrate sample and of the glass capillary tube, respectively; A is the area of the measuring curve corresponding to the overall experiment; Ab is the area of the pumping background contribution for the observed process,21 which was determined in separate experiments where the cells containing only a nitrogen atmosphere were evacuated; ε is the energy equivalent of the calorimeter obtained from a set of electrical calibrations;21 and cp,c = 0.779 ( 0.001 J 3 K-1 3 g-1 is the mean value of the massic heat capacity of the capillary tube at constant pressure in the temperature range covered by the experiments, which was independently determined as previously described.22

O1-C1 C2-C1 C2-C3 C3-C4 C5-C4 C5-C6 C1-C6 C7-C4 C7-C8 C7-O2

1.356(2) 1.392(2) 1.383(4) 1.396(2) 1.401(2) 1.381(2) 1.399(2) 1.479(2) 1.505(2) 1.228(2)

bond angle/deg — O1-C1-C2 — O1-C1-C6 — C3-C2-C1 — C2-C3-C4 — C5-C4-C3 — C6-C5-C4 — C6-C1-C2 — C1-C6-C5 — C5-C4-C7 — C3-C4-C7 — C4-C7-C8 — O2-C7-C4 — O2-C7-C8

119.2(2) 121.0(2) 120.0(2) 121.0(1) 118.3(1) 121.3(2) 119.8(1) 119.6(2) 119.1(1) 122.6(1) 119.4(2) 120.4(1) 120.3(2)

Figure 3. Conformations of the molecule of 40 -hydroxyacetophenone in the hydrate (gray) and in the orthorhombic anhydrous form (yellow)12 suggested by the X-ray diffraction analysis.

Results and Discussion

Figure 4. Crystal packing of the hydrate phase of 40 -hydroxyacetophenone at 150 K showing the water chains parallel to the (002) plane.

Structure. Single crystal X-ray diffraction analysis carried out at 150 K confirmed that a previously unknown hydrate of HAP was obtained in this work. This new form is triclinic, space group P1, and has Z = 2 (Table 1). The ratio of HAP to water molecules in the asymmetric unit is 1:1.5. The Raster3D19 drawing with the labeling scheme is illustrated in Figure 2, and the bond angles and distances corresponding to the HAP unit in the hydrate are summarized in Table 2. These geometrical parameters are similar to those we previously found, at the same temperature, for the two anhydrous forms of 40 -hydroxyacetophenone.12 Moreover, as shown in Figure 3, the conformation of the HAP molecule in the hydrate suggested by the results is superimposable with that present in the anhydrous orthorhombic polymorph (form II). Computational chemistry calculations carried out at the B3LYP/6-31G(d,p) level of theory previously

indicated that, for an isolated molecule in the gas phase, this conformation, with the OH and CH3CO groups in a syn orientation, is more stable than that of the corresponding anti isomer, which is present in the crystals of the anhydrous HAP form I.12 Because the half water molecule (O2w) is located near an inversion center, another half is generated by symmetry, and therefore, the possibility of two slightly different crystal packings must be considered. In both cases, the water molecules form chains parallel to the (002) plane (Figure 4). As illustrated in Figure 5, these are sustained by three dissimilar hydrogen bonds, which exhibit a different alternancy in each packing: O1w-H1wb 3 3 3 O2w (dOH 3 3 3 O = 1.772 A˚), O1w-H1wb 3 3 3 O2w (dOH 3 3 3 O = 2.354 A˚), and O1w 3 3 3 O1w (dO 3 3 3 O = 2.775 A˚). The water chains are also connected to the HAP molecules through three other types of

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Figure 7. TG-DSC measuring curves for the decomposition of HAP 3 1.5H2O. The mass of sample was 18.80 mg and the heating rate β = 1 K 3 min-1. (;) TG trace; ( 3 3 3 ) DSC trace. Figure 5. Illustration of the three different hydrogen bonds sustaining the water chains, viewed in the bc plane: O1w-H1wb 3 3 3 O2w (dOH 3 3 3 O = 1.772 A˚), O1w-H1wb 3 3 3 O2w (dOH 3 3 3 O = 2.354 A˚), and O1w 3 3 3 O1w (dO 3 3 3 O = 2.775 A˚).

Figure 8. Differential scanning calorimetry measuring curve obtained for HAP 3 1.5H2O. Figure 6. View of the packing diagram of the hydrate phase of 40 -hydroxyacetophenone along the b axis, showing the channels containing the water molecules and the hydrogen bonds between HAP and H2O: d1 denotes O1-H1 3 3 3 O1w (dOH 3 3 3 O = 1.828 A˚); d2 represents O2w-H2wb 3 3 3 O1 (dOH 3 3 3 O = 1.784 A˚), and d3 refers to O1w-H1wa 3 3 3 O2 (dOH 3 3 3 O= 1.890 A˚). The diagram corresponds to packing 1 but is analogous to that of packing 2.

hydrogen bonds (Figure 6): O1-H1 3 3 3 O1w (dOH 3 3 3 O = 1.828 A˚), O2w-H2wb 3 3 3 O1 (dOH 3 3 3 O = 1.784 A˚), and O1w-H1wa 3 3 3 O2 (dOH 3 3 3 O= 1.890 A˚). The arrangement of the water molecules in channels (Figure 6) suggests that they can be easily removed from the structure. This is consistent with the experimentally observed facile decomposition of HAP 3 1.5H2O crystals once separated from the mother liquor (see Materials and Methods) and with the TG-DSC results, which showed the onset of dehydration to occur at 298 ( 4 K (see below). The fairly easy loss of water is also probably the reason why the attempts to carry out a structural determination at ambient temperature using the available single crystal X-ray diffraction apparatus failed. In the course of these experiments, the crystals were observed to change from transparent to opaque with concomitant loss of the diffraction signal. Energetics. The 2005 IUPAC recommended standard atomic masses were used in the calculation of all molar quantities.23 Figure 7 illustrates a typical mass loss trace observed in the combined TG-DSC studies. These were carried out in the range 263-363 K and indicated that dehydration started at Ti = 298 ( 4 K and was completed at Tf = 331 ( 4 K. From these experiments it was also possible to conclude that the

H2O/HAP molar ratio in the hydrate was n = 1.5 ( 0.1. This result is in excellent agreement with the conclusions of the single crystal X-ray diffraction analysis. Note that the uncertainties assigned to Ti, Tf, and n correspond to twice the standard error of the mean of five determinations (see Supporting Information for details). The simultaneously recorded heat-flow curves (Figure 7, dotted line) show two unresolved peaks associated with the mass loss. This was further corroborated by the results of experiments where the calorimeter was operated in the DSC mode only (Figure 8). As shown in Figure 8, five thermal events were observed in the DSC study of the hydrate in the range 263-392 K. Peak a with Tmax = 273 K is probably related to the fusion of traces of nonlattice water present in the sample. This was not unexpected, since, as mentioned in the Materials and Methods section, to avoid decomposition, the HAP 3 1.5H2O crystals were collected from the mother liquor and quickly dried between two filter paper sheets previous to the calorimetric experiments. Peak b with Tmax = 286 K is tentatively assigned to a phase transition which occurs before the start of the dehydration process without modification of the HAP 3 1.5H2O stoichiometry. This is supported by two pieces of evidence: (i) no mass loss was observed at this temperature in the TG-DSC experiments; (ii) a powder X-ray diffraction pattern obtained for the hydrate at ∼293 K is different from that simulated using the program Mercury 1.4.2,20 based on the 150 K single crystal X-ray diffraction data obtained in this work (Figure 9). Unfortunately, the instability of the sample precluded structure determinations at temperatures immediately below and above 286 K. Peaks c and d with maxima at Tmax = 307 K and Tmax = 327 K correspond to

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Bernardes et al.

those already observed in the TG-DSC runs and can be assigned to the dehydration of the HAP 3 1.5H2O sample. The production of monoclinic HAP (form I) in the course of this process was inferred from three pieces of evidence: (i) the signature of the form II f form I phase transition occurring in anhydrous HAP at 351.2(2.7 K12 was always absent in the DSC measuring curves; (ii) the onset and maximum temperatures of the fusion peak, e, observed after complete dehydratation of the HAP 3 1.5H2O sample, Ton = 381.2 ( 0.6 K and Tmax = 382.2 ( 0.6 K (mean of two determinations), respectively, closely matched those reported for the anhydrous HAP form I (Ton = 381.9 ( 0.1 K and Tmax =382.8 ( 0.1 K);12 and (iii) as shown in Figure 10, the powder diffraction pattern of a dehydrated sample is in good agreement with that of form I HAP.12 The mean value of the massic enthalpy associated with the thermal decomposition of HAP 3 1.5H2O according to eq 2 in Scheme 1, determined by drop-sublimation Calvet microcalorimetry (see Supporting Information), was Δrh(2) = 1194.27 ( 7.16 J 3 g-1. This leads to ΔrH
m(2) = 194.9 ( 2.4 kJ 3 mol-1. These results were ascribed to the temperature

interval 298.15-348.1 K. Indeed, the enthalpic corrections due to the small differences 298.15 K - Ti and 348.1 K - Tf (recall that Ti and Tf represent the initial and final temperatures effectively determined in each experiment, respectively) are expected to be clearly within the experimental uncertainty of the measurements and were therefore neglected. Note that, following normal thermochemical practice, the uncertainty indicated for Δrh(2) refers to the standard error of the mean of six independent results and that ΔrH
m(2) is twice the overall standard error of the mean, including the contribution from the calibration. As shown in Scheme 1, ΔrH
m(2) is related with the standard molar enthalpies of dehydration processes 3 and 4 under isothermal conditions, at 298.15 K, through the following equations: Z 348:1K C
p, m ðHAP, gÞ dT Δr H
m ð3Þ ¼ Δr H
m ð2Þ Z - 1:5

298:15K 348:1K

C
p, m ðH2 O, gÞ dT

ð5Þ

298:15K

Δr H
m ð4Þ ¼ Δr H
m ð3Þ - Δsub H
m ðcr IÞ

ð6Þ

where C
p,m(HAP,g) and C
p,m(H2O, g) are the standard molar heat capacities of gaseous HAP and water, respectively, and ΔsubH
m(cr I) is the standard molar enthalpy of sublimation of monoclinic HAP at 298.15 K. The temperature dependencies of the heat capacities of gaseous HAP and water were evaluated from (C
p,m in J 3 K-1 3 mol-1)

C
p, m ðHAP, gÞ ¼ - ð1:9376  10 - 4 ÞT 2 þ 0:5596T þ 6:8932 ð7Þ C
p, m ðH2 O, gÞ ¼ ð1:8177  10 - 5 ÞT 2

Figure 9. Comparison of the experimental powder X-ray diffraction pattern of HAP 3 1.5H2O at 293 K with that simulated from the single crystal X-ray diffraction results obtained in this work at 150 K.

- ð6:4164  10 - 3 ÞT þ 33:898

ð8Þ

Equation 7, valid between 200 and 400 K, has been reported by us,12 and eq 8 was derived from a least-squares fit to published C
p,m(H2O, g) data in the range 200-500 K.24 Eqs 5-8 together with the value of ΔrH
m(2) indicated above and ΔsubH
m(cr I) = 103.2 ( 0.8 kJ 3 mol-1 12 lead to ΔrH
m(3) = 184.0 ( 2.4 kJ 3 mol-1 and ΔrH
m(4) = 80.8 ( 2.5 kJ 3 mol-1. The standard molar enthalpy of formation of HAP 3 1.5H2O(cr) at 298.15 K can also be obtained as ΔfH
m(HAP 3 1.5H2O, cr) = -812.4 ( 3.1 kJ 3 mol-1 from Δf H
m ðHAP 3 1:5H2 O, crÞ ¼ - Δr H
m ð4Þ þ Δf H
m ðHAP, cr IÞ þ 1:5Δf H
m ðH2 O, gÞ ð9Þ

Figure 10. Comparison of the experimental diffraction pattern of a dehydrated HAP 3 1.5H2O sample with that of the monoclinic form I of HAP reported in ref 12.

by using ΔfH
m(HAP, cr I) = -368.9 ( 1.9 kJ 3 mol ΔfH
m(H2O, g) = -241.826 ( 0.040 kJ 3 mol-1.25

Scheme 1

-1 12

and

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Despite the endothermic nature of reaction 4 (Scheme 1), as mentioned above, the hydrate species HAP 3 1.5H2O(cr) is not very stable when removed from the crystallization mother liquor at ∼298 K, decomposing after ∼1 h in air of 40-60% relative humidity or after a week if kept in a desiccator under air of 94% relative humidity. The thermodynamic driving force for the decomposition of HAP 3 1.5H2O at 298.15 K, in a closed system, according to reaction 4, can be analyzed in terms of the corresponding Gibbs energy change: pðH2 OÞ ð10Þ Δr Gm ð4Þ ¼ Δr G
m ð4Þ þ 1:5RT ln p
with Δr G
m ð4Þ ¼ Δr H
m ð4Þ - TΔr S
m ð4Þ

ð11Þ

Figure 11. Variation of the Gibbs energy of reaction 4, ΔrGm(4), at 298.15 K, with the water pressure, p(H2O), over the hydrate, predicted from eq 10.

In eqs 10 and 11, ΔrG
m(4), ΔrH
m(4), and ΔrS
m(4) are the standard molar Gibbs energy, enthalpy, and entropy of the process, respectively, p(H2O) is the partial pressure of water in equilibrium with the hydrate, p
= 105 Pa is the standard pressure, and R = 8.314472 J 3 K-1 3 mol-1 is the gas constant. The value ΔrH
m(4) = 80.8 ( 2.5 kJ 3 mol-1 has been obtained above, and ΔrS
m(4) can be calculated from the standard molar entropies of H2O(g), HAP(cr I), and HAP 3 1.5H2O(cr), at 298.15 K, by using Δr S
m ð4Þ ¼ 1:5S
m ðH2 O, gÞ þ S
m ðHAP, cr IÞ - S
m ðHAP 3 1:5H2 O, crÞ

ð12Þ

where S
m(H2O, g) = 188.834 ( 0.042 J 3 K-1 3 mol-1 24 and S
m(HAP, cr I) = 191.8 J 3 K-1 3 mol-1.12 The value of S
m(HAP 3 1.5H2O, cr) is not known but may be estimated based on the additivity hypothesis: S
m ðHAP 3 1:5H2 O, crÞ  S
m ðHAP, cr IIÞ þ 1:5S
m ðH2 O, crÞ ð13Þ

-1

-1 12

Note that in this case S
m(HAP, cr II) = 190.3 J 3 K 3 mol was considered, since the conformation of the HAP molecule in HAP 3 1.5H2O is that of the orthorhombic HAP polymorph (form II). The term S
m(H2O, cr) = 41.39 J 3 K-1 3 mol-1 at 298.15 K was calculated from S
m ðH2 O, crÞ  S
m ðH2 O, cr, 273:15 KÞ þ C
p, m ðH2 O, cr, 273:15 KÞ ln

298:15 273:15

ð14Þ

where S
m(H2O, cr, 273.15 K) = 38.07 J 3 K-1 3 mol-1 26 and C
p,m(H2O, cr, 273.15 K) = 37.89 J 3 K-1 3 mol-1 26 represent the standard molar entropy and heat capacity of ice at 273.15 K, respectively. Hence, from eq 13 S
m(HAP 3 1.5H2O, cr) = 252.4 J 3 K-1 3 mol-1 can be derived. Substitution of this result and the values of S
m(H2O, g) and S
m(HAP, cr I) indicated above in eq 12 yield ΔrS
m(4) = 222.7 J 3 K-1 3 mol-1. The obtained ΔrH
m(4) and ΔrS
m(4) finally lead to ΔrG
m(4) = 14.4 kJ 3 mol-1 at 298.15 K. From this value and eq 10 it is possible to predict the variation of ΔrGm(4) with the water pressure in the gas phase, at 298.15 K, illustrated in Figure 11. The saturation pressure of water at this temperature, p(H2O)sat = 3.17 kPa, and the pressure at which ΔrGm(4) = 0, p(H2O) = 2.08 kPa, are specifically indicated in the figure. The value of p(H2O)sat was obtained from27 pðH2 OÞsat ln pc ¼

Tc ða1 ϑ þ a2 ϑ1:5 þ a3 ϑ3:0 þ a4 ϑ3:5 þ a5 ϑ4:0 þ a6 ϑ7:5 Þ ð15Þ T

Figure 12. Combined influence of temperature and relative humidity on the Gibbs energy of reaction 4, ΔrGm(4).

where pc = 22.064 MPa and Tc = 647.096 K are the critical pressure and temperature of water, respectively, a1 = -7.85951783, a2 = 1.84408259, a3 = -11.7866497, a4 = 22.6807411, a5 = -15.9618719, a6 = 1.80122502, and ϑ = (1 - T/Tc). Figure 11 suggests that, as expected, the decomposition of HAP 3 1.5H2O(cr) according to reaction 4 is favored by a decrease of p(H2O), becoming thermodynamically favorable (exergonic) for p < 2.08 kPa. This corresponds to a relative humidity Φ = 100p(H2O)/p(H2O)sat ∼ 66%, a value which is compatible with the dehydration behavior observed in practice at ambient temperature, particularly in view of the approximations involved in the calculations. In fact, the hydrate was found to partially decompose (see the Materials and Methods section) when stored for a week under a somewhat higher relative humidity (Φ ∼ 94%). It should be noted, however, that a decrease as small as ∼1.8% in the estimated S
m(HAP 3 1.5H2O, cr) value is, for example, enough to make ΔrGm(4) < 0 at Φ ∼ 94%. Further insight regarding the combined influence of temperature and relative humidity on the thermodynamic stability of the hydrate was obtained as follows. First, ΔrG
m(4) at a temperature in the range 273-343 K (that approximately covered in the dehydration studies by TG-DSC, Figure 7) was calculated from eq 11 based on the assumption that ΔrH
m(4) and ΔrS
m(4) are constant and identical to their values at 298.15 K. Second, p(H2O)sat at that temperature was obtained from eq 15 and used to calculate the partial pressure of water over the hydrate, p(H2O), corresponding to a given value of Φ. Substitution of p(H2O) and ΔrG
m(4) into eq 10 finally leads to ΔrGm(4) for a specified temperature and

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Crystal Growth & Design, Vol. 10, No. 7, 2010

relative humidity. The obtained results are illustrated in Figure 12, where the solid black line corresponds to T-Φ conditions for which ΔrGm(4) = 0. This approximate analysis therefore leads to the conclusion that independently of the relative humidity the hydrate will tend to decompose above ∼331 K, a temperature that closely matches the high limit of the dehydration range observed in the TG experiments. It also shows that, as should be expected, the compound becomes more stable as the temperature decreases and the relative humidity increases. ~o Acknowledgment. This work was supported by Fundac-a para a Ci^encia e a Tecnologia, Portugal, through Project PTDC/ QUI-QUI/098216/2008 and a postdoctoral grant (SFRH/BPD/ 43346/2008) awarded to C. E. S. Bernardes. Thanks are also due to Prof. J. M. Nogueira (FCUL, Portugal) for the GC-MS analysis, Janine Schwiertz and Henning Urch for the recording of the SEM images at Professor Matthias Epple laboratory (University of Duisburg-Essen, Germany), and Professor Juliana Boerio-Goates (Brigham Young University, USA) for helpful discussions. Supporting Information Available: CIF file with the crystallographic parameters and structural data for HAP 3 1.5H2O at 150 K. Tables S1 and S2 with the details of the TG-DSC and dropsublimation Calvet microcalorimetry experiments. This material is available free of charge via the Internet at http://pubs.acs.org.

References (1) Brittain, H. G. Polymorphism in Pharmaceutical Solids; Marcel Dekker: New York, 1999. (2) Bernstein, J. Polymorphism in Molecular Crystals; Oxford University Press: Oxford, 2002. (3) Hilfiker, R. Polymorphism in the Pharmaceutical Industry; Wiley-VCH: Weinheim, 2006. (4) Brittain, H. G. J. Pharm. Sci. 2008, 97, 1–26.

Bernardes et al. (5) Westrum, E. F., Jr.; McCullough, J. P. Thermodynamics of Crystals; In Physics and Chemistry of the Organic Solid State; Fox, D., Labes, M. M., Weissberger, A., Eds.; Interscience: New York, 1963; Vol. I. (6) Giron, D. Thermochim. Acta 1995, 248, 1–59. (7) Giron, D. J. Therm. Anal. Calorim. 2001, 64, 37–60. (8) Yu, L. J. Pharm. Sci. 1995, 84, 966–974. (9) Yu, L.; Huang, J.; Jones, K. J. J. Phys. Chem. B 2005, 109, 19915– 19922. (10) Toscani, S. Thermochim. Acta 1998, 321, 73–79. (11) Grunenberg, A.; Henck, J.-O.; Siesler, H. W. Int. J. Pharm. 1996, 129, 147–158. (12) Bernardes, C. E. S.; Piedade, M. F.; Minas da Piedade, M. E. Cryst. Growth Des. 2008, 8, 2419–2430. (13) Saito, T.; Hayamizu, K.; Yanagisawa, M.; Yamamoto, O.; Wasada, N.; Someno, K.; Kinugasa, S.; Tanabe, K.; Tamura, T.; Hiraishi, J. Spectral Data Base for Organic Compounds (SDBS); http://www.aist.go. jp/RIODB. (14) SADABS; Area-Detector Absorption Correction; Bruker AXS Inc.: Madison, 2004. (15) SAINT: Area-Detector Integration Software (Version7.23); Bruker AXS Inc.: Madison, 2004. (16) Sheldrick, G. M. Acta Crystallogr. 2008, A64, 112–122. (17) Sheldrick, G. M. SHELXL-97: Program for the Refinement of Crystal Structure; University of G€ ottingen: Germany, 1997. (18) Farrugia, L. J. J. Appl. Crystallogr. 1999, 32, 837–838. (19) Merritt, E. A.; Bacon, D. J. Methods Enzymol. 1997, 277, 505–524. (20) Macrae, C. F.; Edgington, P. R.; McCabe, P.; Pidcock, E.; Shields, G. P.; Taylor, R.; Towler, M.; van de Streek, J. J. Appl. Crystallogr. 2006, 39, 453–457. (21) Kiyobayashi, T.; Minas da Piedade, M. E. J. Chem. Thermodyn. 2001, 33, 11–21. (22) Bernardes, C. E. S.; Santos, L. M. N. B. F.; Minas da Piedade, M. E. Meas. Sci. Technol. 2006, 17, 1405–1408. (23) Wieser, M. E. Pure Appl. Chem. 2006, 78, 2051–2066. (24) Chase, M. W., Jr. NIST-JANAF Thermochemical Tables, 4th ed.; J. Phys. Chem. Ref. Data 1998, Monograph 9. (25) CODATA Key Values for Thermodynamics; Cox, J. D., Wagman, D. D., Medvedev, V. A., Eds.; Hemisphere: New York, 1989. (26) Giauque, W. F.; Stout, J. W. J. Am. Chem. Soc. 1936, 58, 1144–1157. (27) Wagner, W.; Pruss, A. J. Phys. Chem. Ref. Data 2002, 31, 387–535.