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Polymorphic Phase Transition in 4’-Hydroxyacetophenone: Equilibrium Temperature, Kinetic Barrier and the Relative Stability of Z’ = 1 and Z’ = 2 Forms. Abhinav Joseph, Carlos E. S. Bernardes, Anna Ivanovna Druzhinina, Raisa M. Varushchenko, Thi Yen Nguyen, Franziska Emmerling, Lina Yuan, Valerie Dupray, Gérard Coquerel, and Manuel E. Minas da Piedade Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.6b01876 • Publication Date (Web): 21 Feb 2017 Downloaded from http://pubs.acs.org on February 24, 2017

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Crystal Growth & Design

Polymorphic Phase Transition in 4’-Hydroxyacetophenone: Equilibrium Temperature, Kinetic Barrier and the Relative Stability of Z’ = 1 and Z’ = 2 Forms

Abhinav Joseph,a Carlos E. S. Bernardes,a Anna I. Druzhinina,b Raisa M. Varushchenko,b,§ Thi Yen Nguyen,c Franziska Emmerling,c Lina Yuan,d Valérie Dupray,d Gérard Coquerel,d Manuel E. Minas da Piedadea,* a

Centro de Química e Bioquímica e Departamento de Química e Bioquímica, Faculdade de Ciências,

Universidade de Lisboa, 1649-016 Lisboa, Portugal; E-mail: [email protected]. b

Moscow State University, Department of Chemistry, 119991 Moscow, Russia.

c

BAM Federal Institute for Materials Research and Testing, Richard-Willstaetter-Strasse 11, 12489

Berlin, Germany. d

Normandie Université, Laboratoire SMS-EA3233, Université de Rouen, F-76821, Mont Saint Aignan,

France.

§

Deceased on December 30, 2012.

*Corresponding author. Tel. +351-21-7500866; Fax +351-21-7500088. E-mail address: [email protected] (M. E. Minas da Piedade)

RECEIVED DATE (to be automatically inserted after your manuscript is accepted if required according to the journal that you are submitting your paper to)

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Abstract

Particularly relevant in the context of polymorphism is understanding how structural, thermodynamic, and kinetic factors dictate the stability domains of polymorphs, their tendency to interconvert through phase transitions, or their possibility to exist in metastable states. These three aspects were investigated here for two 4’-hydroxyacetophenone (HAP) polymorphs, differing in crystal system, space group and, number and conformation of molecules in the asymmetric unit. The results led to a ∆ f G mo -T phase diagram highlighting the enantiotropic nature of the system and the fact that the Z’ = 1 polymorph is not necessarily more stable than its Z’ = 2 counterpart. It was also shown that the form II → form I transition is entropy driven and is likely to occur through a nucleation and growth mechanism, which does not involve intermediate phases, and is characterized by a high activation energy. Finally, although it has been noted that conflicts between hydrogen bond formation and close packing are usually behind exceptions from the hypothesis of Z’ = 1 forms being more stable than their higher Z’ analogues, in this case, the HAP polymorph with stronger hydrogen bonds (Z’ = 2) is also the one with higher density.

KEYWORDS: phase transition, polymorphism, high Z’, thermodynamics, kinetics, heat capacity, solubility, phase diagram, calorimetry, DSC, Raman spectroscopy, TR-SHG.


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Introduction Polymorphism is a common phenomenon in molecular organic solids, which consists in the existence of more than one crystal form of the same compound. Polymorphs may differ not only in their packing architecture but also, sometimes, in the conformation of the molecules that define the crystal lattice.1 These differences are frequently large enough to affect the stability of a material regarding chemical reactivity, compression, solubility, and various other properties that need to be strictly controlled in industry sectors such as pharmaceuticals.1-4 The industrial implications of polymorphism (e.g lack of reproducible product manufacture, variations in shelf-life, patenting of new forms)1-4 have fostered considerable efforts to devise strategies for the reproducible and selective preparation of crystal forms with the best properties for specific applications and manufacture processes using crystal engineering strategies This also raised some major challenges in terms of fundamental research, such as uncovering the structure-energetics features behind the relative stability of polymorphs and understanding how polymorphs may interconvert through phase transitions. Efforts in these directions led about a decade ago to the proposal that polymorphs with Z′ > 1 are metastable relative to their Z′ = 1 analogues.5,6 The suggestion was born from the idea that from a crystallographic point of view clean-cut symmetry expression and stability should go hand in hand. High Z′ structures might, therefore, correspond to arrested crystallization stages, originated by the non-equilibrium nature of the nucleation pathway, which would ultimately lead to a Z′ = 1 form if thermodynamic control could be achieved.5,6 A significant number of exceptions showed, however, that a rationale centered on a structural conjecture alone cannot provide a universal measure of stability, as emphasized in a recent seminal review on high Z′ crystal structures.7 Nevertheless, the fact that the exceptions are particularly common for certain types of compounds where there is difficulty in balancing close packing with hydrogen-bond (H-bond) formation,8-10 gives also important clues on how specific types of intermolecular forces may favor a given molecular organization in the solid state.


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Structure-stability discussions should not, however, be divorced from thermodynamics, which provides the appropriate theoretical framework to assess the relative stability of molecular systems in general and, therefore, also of polymorphs.1,11-13 Each crystalline form of a given molecule is characterized by a specific molar Gibbs energy value, Gm , which depends on the temperature (T) and pressure (p) considered. The most stable form under a given set of p-T conditions is the one with the lowest Gibbs energy, all other forms being metastable relative to that one. The Gm value is necessarily linked to structure and that relationship can be evidenced by recalling that:14

Gm = H m − T Sm

(1)

= U m + p Vm − T S m

(2)

where H m , U m , Vm and S m are the molar enthalpy, internal energy, volume and entropy functions. All these functions are related to structure. The molar volume is connected to the unit cell dimensions and the number of molecules it contains; the internal energy depends on the intra- and intermolecular interactions characteristic of the molecules in the lattice, which are intimately linked to the packing arrangement; this is also true for the enthalpy which further includes a volumetric dependency; and, in most cases, the entropy term is essentially determined by molecular and lattice vibration modes albeit other contributions (e.g. rotational, electronic) may also be present.15 Changing a particular molecular conformation or unit cell dimension will necessarily lead to a different Gm value and to a change in stability. Since stability increases as Gm decreases, the most stable structure will correspond to the packing arrangement that minimizes the U m and Vm terms and maximizes the S m contribution in eq 2. Adopting that crystalline arrangement will therefore involve an elaborate compromise between molecular constraints to close packing, maximization of attractive and minimization of repulsive


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intermolecular interactions, and maximization of entropy. It is conceivable that in some cases this will require a departure from close packing and the adoption of a lower crystal symmetry. Close molecular packing may imply unfavorable molecular interactions, such as charge or dipole repulsions, and a strong hydrogen bonding pattern may require a “loose” molecular packing. Thus, as previously pointed out, there seems to be no obvious relationship between crystal symmetry and enthalpy or entropy.16 The fact that polymorph stability is closely related to phase transitions can be evidenced by noting that when the molar Gibbs energies of two different crystalline forms Gm (cr I) and Gm (cr II) , are compared, the following relationships can be written:

Gm (cr II) − Gm (cr I) = ∆trsGm

(3)

∆trsGm = ∆ trsU m + p ∆ trsVm − T ∆trs Sm

(4)

where ∆trsGm , ∆ trsU m , ∆ trsVm , and ∆trs Sm represent the Gibbs energy, internal energy, volume and entropy changes associated with the cr I → cr II transformation under fixed p-T conditions, respectively. The notion that stability must be analyzed from a Gibbs energy point of view, should be stressed. Polymorph stability has frequently been discussed from lattice energy ( ∆ latU m ) considerations alone,5,17 with the lattice energy usually taken as the molar internal energy change of the process A(cr) → A(g), where a given crystalline solid A(cr) sublimes to an ideal gas state A(g).11 Note that ∆ latU m is related to the corresponding sublimation enthalpy ( ∆ sub H m ), which is typically the experimentally accessible quantity, by:11

∆ latU m = U m (g) − U m (cr) = ∆sub H m + RT


(5)

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where R is the gas constant. Although it can be easily concluded that the difference in lattice energies or enthalpies of sublimation of forms I and II is related to the ∆ trsU m term in eq 4 by ∆ trsU m =

∆ latU m (cr II) − ∆ latU m (cr I) = ∆sub H m (cr II) − ∆sub H m (cr I) , the comparison of ∆ latU m or ∆ sub H m values alone does not warrant a reliable stability measurement. Indeed as shown by eq 4, the tendency for spontaneous conversion of a given polymorph into a more stable one is determined by the Gibbs energy of the transformation, ∆trsGm , which, in addition to the ∆ trsU m term, further includes volume ( ∆ trsVm ) and entropic ( ∆trs Sm ) contributions. Thus, higher lattice energy does not necessarily imply higher stability. It is also often overlooked that, because the Gibbs energy varies with pressure (p) and temperature (T) the conclusion that a less stable polymorph should spontaneously transform into a more stable one ( ∆ trsG < 0), may be reversed if T and/or p change. In other words, the most stable polymorph may be different in different p-T domains. The investigation of enantiotropic systems involving two polymorphs with different Z′ is particularly interesting in the context of the structure-stability relationships mentioned above, since enantiotropy is characterized by the existence (at constant pressure) of a transition temperature before fusion at which the stability of the two forms is reversed. The determination of the accurate thermodynamic data needed for these studies usually requires slow painstaking procedures which are not devoid of pitfalls.11,13,18,19 One important complication that often arises is the existence of kinetic barriers associated with solid-solid phase transitions. The observation of an enantiotropic phase transition on heating a sample at constant pressure requires the nucleation and growth of the high temperature polymorph within the precursor low temperature form. Conversely, in the cooling mode, the low temperature polymorph must be generated from the high temperature phase. Two important points should be kept in mind: (i) some degree of superheating or supercooling, respectively, is necessary for nucleation to occur and (ii) the heating and cooling processes are not symmetrical. If true equilibrium conditions were achievable at a specific temperature ( Teq ), both phases would be present in ACS Paragon Plus Environment

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a proportion governed by the equilibrium constant of the process and no progress of the phase transition in the direct or reverse direction could be observed. Above Teq the low temperature polymorph will tend to transform into the high temperature one and below that temperature the opposite tendency prevails. According to classical nucleation theory the rates of the direct and reverse processes are both determined by the Gibbs energy barrier ( ∆Gc ) associated with the formation of a critical nucleus (i.e. a nucleus which further growth originates the new phase) and the activation energy ( Ea ) for that nucleus to grow by transfer of molecules from the mother to the daughter phase. This process, albeit criticisms have been raised,20 is generally considered to follow the Arrhenius relationship.12,21,22 The driving force for the formation of a critical nucleus increases as superheating or supercooling become more pronounced. In contrast, while heating favors overcoming Ea , the opposite occurs on cooling. This frequently leads to the observation of an enantiotropic phase transition well above its equilibrium temperature and without evidence of reversibility, when techniques such as differential scanning calorimetry (DSC) are used.19,23-29 It may also happen that the transition may be undetected because, once the equilibrium temperature is surpassed, polymorph conversion will slowly progress and become smeared throughout a large temperature range,26,30 or it is ultimately hindered up to fusion.28 Kinetic barriers are not exclusive of thermal activation processes and cases have been described where they were also most likely behind the detection of irreversible enantiotropic transformations of low-Z′ into high-Z′ polymorphs, using grinding or slurry tests.31-34 4’-Hydroxyacetophenone (HAP) has proved to be a rich system in terms of solid form diversity, with at least two polymorphs and three hydrates identified and characterized from structural,31,35-40 solid state stability,31,38,39 and crystallization points of view.39,41,42 The anhydrous polymorphs also provide an opportunity to study structure-energetics relationships behind the adoption of high-Z’ structures and their relative stability towards a Z’ = 1 counterpart, when solid state conversion through a phase transition is a one way process due to kinetic hindrances. Indeed, DSC and X-ray diffraction (XRD) ACS Paragon Plus Environment

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studies carried out at atmospheric pressure previously evidenced an irreversible phase transition between the two HAP polymorphs where packing, molecular conformation, and Z’ simultaneously change.31 On heating HAP form II (orthorhombic, space group P212121, Z’ = 2)31,35-37 from ambient temperature, an endothermic transformation into form I (monoclinic, P21/c, Z’ = 1)31 was observed at 351.2±2.7 K.31 The reverse process was not detected on cooling and both forms could be stored unaltered without strict control of laboratory temperature, pressure or humidity. This robustness towards interconversion was observed, even if the available thermal energy at 298 K (RT = 2.5 kJ.mol-1) was ∼5 times larger than the difference between the lattice energies of forms II and I at that temperature (0.49±0.13 kJ·mol-1) determined by solution calorimetry. The reduction of the number of molecules in the asymmetric unit from Z’ = 2 to Z’ = 1, was accompanied by a change in molecular conformation, since the relative orientations of the OH and C=O groups switched from Z in form II to E in form I (Figure 1).31 The Z conformations of the two molecules in the asymmetric unit of form II are very similar in terms of distances and dihedral angles. Moreover, altough in both cases the 1D packing motifs consisted of infinite linear chains C11 (8) sustained by “head-to-tail” bonding between the hydroxyl group of one molecule (donor) and the carbonyl group of an adjacent molecule (acceptor), the chains changed from helical in form II to linear in form I (Figure 1).31 It is finally worth mention that the higher lattice energy of the low temperature form II also corresponds to a slight density advantage, since the density of form II at 298 K (1.278 g⋅cm-3) is 2.4% larger than that of form I (1.247 g⋅cm-3), even though the packing fractions of both polymorphs are very similar (∼0.70).31 In this work the structure/energetics features behind the occurrence of Z’ = 1 or Z’ = 2 structures in HAP were investigated from various angles. The role of enthalpic and entropic contributions in determining the preference for the Z’ = 1 or the Z’ = 2 polymorphs in different temperature ranges was


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(Z)

(a)

(E) (b)

Figure 1.

Molecular conformations and 1D packing motifs of 4’-hydroxyacetophenone

polymorphs: (a) form II; (b) form I (see text).

elucidated based on DSC, adiabatic calorimetry, and solubility experiments. Insights about the activation barrier for the form II → form I transformation were also provided by DSC and temperatureresolved second harmonic generation (TR-SHG) experiments. The eventual presence of intermediate phases along the form II → form I transformation was probed by Raman spectroscopy and hot-stage microscopy. The overall results provided a detailed view of the thermodynamic/kinetic profile relating forms I and II HAP and of the major factors behind the preference of the Z′ = 1 or the Z′ = 2 polymorph in different temperature domains. ACS Paragon Plus Environment

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Experimental

Materials. Ethanol (Panreac, mass fraction 0.999) and acetonitrile (Fisher Scientific, HPLC grade, mass fraction 0.9999) were used as received. Form I HAP was obtained by sublimation of a commercial material (Fluka, mass fraction 0.98), at 368 K and 13 Pa. GC-MS analysis performed as previously reported31 indicated that the purified sample had a mass fraction >0.9999. The powder pattern recorded at 298±2 K was indexed as monoclinic, space group P21/c, a = 7.704(8) Å, b = 8.337(8) Å, c = 11.268(9) Å, β = 94.98(2)º. The indexation is in agreement with published single crystal X-ray diffraction data: a = 7.7200(15) Å, b = 8.3600(17) Å, c = 11.280(2) Å, β = 95.02(3)º.31 Form II was prepared by magnetically stirring a suspension of form I in ethanol or acetonitrile, below 300 K, for ~1 week. This procedure was suggested by the solubility studies carried out in this work (see below). The powder pattern of the obtained material, recorded at 298±2 K, was indexed as orthorhombic, space group P212121, a = 6.114(6) Å, b = 9.569(9) Å, c = 24.324(52) Å. These results are in agreement with previously reported single crystal X-ray diffraction data: a = 6.1097(11) Å, b = 9.5293(14) Å, c = 24.313(4) Å.31 Large form II single crystals (1-2 mm edge) were also obtained by the following procedure. A saturated ethanol solution of form I was prepared inside a Schlenk flask at ambient temperature (295±1 K) under magnetic stirring. The flask containing the solution was transferred to a thermostatic bath, where it was kept at 325 K for ∼2 h and then cooled to 275 K at a rate of ∼10 K⋅h-1. Crystals were collected by filtration after ∼24 h and dried under reduced pressure. Their identification as form II HAP was carried out by powder X-ray diffraction and DRIFT spectroscopy. The powders of forms I or II used in the DSC studies consisted of 88-250 µm particles and were obtained by grinding and sieving the original samples. Sieving was by means of a Scienceware minisieve micro sieve set (apertures 707, 500, 354, 250, 88 and 63 µm). The phase purity of the


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grinded/sieved materials was assessed by powder X-ray diffraction and diffuse reflectance infrared Fourier transform (DRIFT) spectroscopy. X-ray powder diffraction (XRPD). XRPD analysis were carried out on a Philips PW1730 instrument operating in the θ-2θ mode. The apparatus included a vertical goniometer (PW1820), a proportional xenon detector (PW1711), a graphite monocromator (PW1752), and a Cu Kα (λ =1.54184 Å) radiation source set to 30 mA and 40 kV. The diffractograms were recorded at ~293 K, in the range 5º < 2θ < 35º. Automatic data acquisition (APD Philips v.35B) was performed in the continuous mode, with a step size of 0.015 º(2θ) and an acquisition time of 1.5 s per step. The samples were mounted on an aluminum sample holder. The program CELREF V343 was used to index the obtained powder patterns. Diffuse reflectance infrared Fourier transform (DRIFT). DRIFT spectra were collected in the 400 - 4000 cm-1 range using a Nicolet 6700 spectrometer equipped with a Smart Diffuse Reflectance (SDR) kit (Thermo Electron Corp.) and a deuterated triglycine sulfate (DTGS) detector. The wavenumber scale was calibrated with polystyrene film, the selected resolution was 2 cm-1 and 512 scans were used for both the background and sample runs. The background spectra were recorded with pure KBr (Sigma-Aldrich, FTIR grade). The samples were prepared by grinding the appropriate HAP and KBr quantities to obtain a spectral absorbance in a range compatible with the Kubelka-Munk transformation.44 The amount of sample in the sample-holder was consistent with infinite thickness conditions. Raman spectroscopy. The Raman spectroscopy study of the form II → form I transition was performed with a Raman RXN1 Analyzer (Kaiser Optical Systems) using NIR excitation at 785 nm and a sample irradiance of 6.4 W⋅cm-2. The spectra were collected at 30 s intervals using acquisition times of 4×4 s and a resolution of 4 cm-1. A single crystal of form II was placed in an acoustic levitation device45,46 and heated from 303 K to 363 K, in steps of 5 K using equilibration stages of ~600 s. The crystal temperature was maintained constant to ±1 K by a nitrogen stream that passed through a ACS Paragon Plus Environment

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thermostatized oven located immediately below the levitation device. The oven temperature was controlled by a Eurotherm unit connected to a JUMO K-type thermocouple (NiCr/NiAl) placed as close as possible to the sample.45 Hot-Stage Microscopy (HSM). An Olympus BX51 microscope equipped with a LTS350 Linkam hot stage and an Olympus SC-30 digital camera was used for visualizing the solid-solid phase transition of HAP. The temperature was controlled by a Linkam TMS 94 controller. The sample was placed on the hot stage, which was heated from 298 K to 373 K at 5 K⋅min-1. Images were recorded at regular intervals in polarized light. Temperature-Resolved Second Harmonic Generation (TR-SHG). Form II HAP crystallizes in the non-centrosymmetric space group P212121, which is SHG active, and form I crystalizes in the centrosymmetric space group P21/c, which is SHG inactive. TR-SHG experiments could, therefore, be used to follow the form II → form I phase transition in time. The apparatus and procedure have been described.47-49 In brief, 50 mg of a HAP powder sample were placed in a computer controlled thermal stage (Linkam THMS-600). The sample was then heated to the initial temperature at 20 K⋅min-1 and maintained at that temperature, within ±0.1 K, throughout the data collection. Runs at 343.15 K, 348.15 K, 353.15 K, 358.15 K, and 363.15 K were performed. Once the desired initial temperature was reached, the evolution of the SH signal was recorded versus time, every 5 min (for T =343.15 K and 348.15K) or every 2 min (for T = 353.15 K, 358.15 K, and 363.15 K), with an acquisition time of 3 s per measurement. The standard deviation of the recorded SH signal, due to laser fluctuations, was estimated to be ∼3%. It was ensured that the laser irradiated the same area of sample (4 mm2) throughout the experiment. The thermal effects induced by the laser were neglected. The conversion fraction was obtained from:

α = 1−

ISHG (t ) o ISHG

(6)


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o where I SHG and ISHG (t ) are the intensities of the SHG signal for α = 0 (recorded for form II HAP at

ambient temperature) and at time t, respectively. Differential

Scanning

Calorimetry

(DSC).

Differential

scanning

calorimetry

experiments on HAP were carried out with three different instruments: a DSC 204 F1-Phoenix from Netzsch, a TA Instruments 2920 MTDSC, and a DSC 7 from Perkin Elmer. They essentially involved three types of measurements: (i) conventional DSC scans on powders (subject or not to temperature annealing, see below) and single crystals; (ii) non-isothermal kinetic runs on annealed powder samples; and (iii) heat capacity determinations on liquid HAP to complement the heat capacity studies on the solid phases carried out by adiabatic calorimetry (see below). The samples were placed inside aluminum pans and all weightings were performed with a precision of ±0.1 µg in Mettler UMT2 or XP2U ultra-micro balances. The masses of sample used in the study of powders and in the determination of the heat capacity of liquid HAP were typically ∼5 mg. Single crystals had masses of 0.2-1.5 mg. The low temperature annealing of powdered HAP was performed as follows. Several form I or form II samples with a mass of ~5 mg, contained in sealed aluminum crucibles, were placed in the Netzsch calorimeter furnace. They were then subjected to three consecutive heating/cooling cycles in the temperature range 213 K to 268 K. In each cycle the samples were first cooled from 268 K to 213 K at 0.2 K·min-1 and then heated from 213 K to 268 K at 0.5 K·min-1. An isothermal 3 h step was inserted between each temperature ramp. The temperature and heat flow scales of the Netzsch apparatus were calibrated at the heating rate

β = 5 K⋅min-1 using a calibration kit from Netzsch (ref. 6.239.2-91.3.00), consisting of adamantane (mass fraction: ≥ 0.99, Ttrs = 208.65 K, ∆ trs h = 22.0 J·g-1), indium (mass fraction: 0.99999, Tfus = 429.75 K, ∆fus h = 28.6 J⋅g-1), tin (mass fraction: 0.99999, Tfus = 505.05 K, ∆fus h = 17.2 J·g-1), bismuth (mass fraction: 0.99999, Tfus = 544.55 K, ∆fus h = 53.1 J·g-1), zinc (mass fraction: 0.99999, Tfus = 692.65 ACS Paragon Plus Environment

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K, ∆fus h = 107.5 J·g-1) and cesium chloride (mass fraction: 0.99999, Ttrs = 749.15 K, ∆ trs h = 17.2 J·g1

). The fusion of indium was also selected to check the temperature calibration for all other heating rates

used throughout this work (β = 0.25, 0.5, 1, 2, 10, 12, 14, 16, 20, and 80 K⋅min-1). The purge and protective gas was nitrogen (Air Liquide N45), at flow rates of 20 cm3⋅min-1 and 50 cm3⋅min-1, respectively. The instrument control and data treatment were performed with the Netzsch Proteus V. 6.1.0 software. In the case of the TA apparatus, the temperature and heat flow scales were calibrated at 8, 10, and 14 K⋅min-1, as previously described.50 The purging gas was helium (Air Liquide N55), at a flow rate of 30 cm3⋅min-1. The Thermal Advantage V. 4.2 software and the TA Universal Analysis Software for Windows NT were used for experiment control and data treatment, respectively. The Perkin Elmer DSC 7 was calibrated at 2 K⋅min-1 by using indium (Perkin Elmer; mass fraction: 0.99999; Tfus = 429.75 K, ∆fus h = 28.45 J·g-1) and zinc (Perkin-Elmer; mass fraction 0.99999, Tfus = 692.65 K; ∆fus h = 107.5 J·g-1). The purging gas was nitrogen (Air Liquide N45), at a flow rate of 30 cm3⋅min-1. Instrument control and data acquisition were performed with the Pyris V. 7.0 software platform. Non-isothermal experiments on the kinetics of the form II → form I transition were carried out on the Netzsch apparatus, using powdered form II HAP samples that had been previously annealed as described above. This study was based on the determination of the II → I conversion fraction (α) as a function of temperature (T) at heating rates of 0.25, 0.5, 1 and 2 K·min-1. The α values were calculated from:

A0T α= ∞ A0

(7)


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where A0T is the area of the phase transition peak up to temperature T (heat flow versus temperature plot) and A0∞ is the total area of the peak. The full α-T curve at each selected heating rate was obtained with the Netzsch Proteus kinetics module software. Heat capacity measurements on liquid HAP, in the temperature range 385.3-400.1 K, were performed in the DSC 7 instrument, as described elsewhere.11,51 The heating rate was 2 K⋅min-1. Sapphire (Perkin Elmer α-Al2O3 disks, mass fraction: 0.9998) was used as reference. The molar heat capacity, Cp,m , at a given temperature was obtained from:

C p ,m = k

M ∆φ mβ

(8)

where m and M are the mass and the molar mass of the compound, respectively, β is the heating rate, ∆φ is the difference in heat flow rate between the main and blank runs at a given temperature, and k is a calibration factor obtained from an analogous run carried out with sapphire. Heat capacity measurements were also carried out on form I HAP (data given in the Supporting Information) to assess the accuracy of the method against adiabatic calorimetry. The agreement between the two determinations in the range covered by the DSC measurements (324-374 K) was within ∼1 %. Adiabatic Calorimetry. The heat capacities of forms I and II HAP in the temperature ranges 79-373 K and 294-329 K, respectively, were obtained with a fully automated setup consisting of a vacuum adiabatic calorimeter and an AK-9.02 control and data acquisition system connected to a computer. The apparatus and method have been described.52-54 During the calorimetric measurements the sample with a mass of 302.19 mg (form I) or 377.57 mg (form II) was contained in a cylindrical titanium cell of ∼1 cm3 internal volume, tightly fitted into a


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copper sleeve containing a ~300 Ω heater, surrounded by an adiabatic shield. Weightings were performed with a precision of ±0.05 mg using a Mettler balance. The temperature of the adiabatic shield, Tshield , was monitored with an accuracy of ±3 mK using a rhodium-iron resistance thermometer (R0 ≈ 50 Ω) which had been calibrated according to ITS-90 over the temperature range 5-373 K. The temperature difference between the adiabatic shield and the cell, ∆Ts-c , was maintained at ±3 mK with an eleven-junction [(Cu+0.1 wt% Fe)–Chromel] thermocouple. The temperature of the sample (assumed identical to that of the calorimetric cell) was obtained by combining the Tshield and ∆Ts-c values and its uncertainty was ±0.01-0.02 K. A typical experiment consisted of six periods: (i) fore period where the sample was heated to the desired initial temperature; (ii) equilibration period (10 min) to attain a steady reading at that temperature; (iii) initial baseline recording (6 min); (iv) main period (4 min), where a known electrical energy (∼3 J ) was supplied to the calorimeter through the heater, at heating rate β = 0.3 K⋅min-1; (v) equilibration period (10 min) to attain a steady temperature reading; (vi) final baseline recording (6 min). Further data points were obtained by repeating steps (iii)-(vi) in different temperature ranges. This procedure had been previously validated by measuring the heat capacity of copper (mass fraction 0.99995) and n-heptane (chromatographically pure). The obtained accuracy in the temperature range 80-373 K was ~0.2%. Solubility Measurements. Equilibrium solubility measurements on HAP, in ethanol and acetonitrile, were carried out by gravimetry, using the previously described glass cell set-up and procedure.55 The determinations were performed in the range 283-312 K, using ascending and descending temperature sequences with ~2 K steps. The temperature of the mixture inside each glass cell was controlled to ±0.01 K by circulating water from a thermostatic bath through the cell jacket, and monitored with a resolution of ±0.01 K by a Pt100 sensor.

In a typical

experiment, a suspension of form II HAP in 70 cm3 of solvent was initially equilibrated at 283.2


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K for one week. After the equilibration period, three samples of the supernatant liquid (3 cm3 each) were extracted using a preheated syringe adapted to a micro filter (WhatmanPuradisc 25 TF, 0.2 µm PTFE membrane). The corresponding masses of solvent and solute were determined by weighing the samples before and after being taken to dryness. Based on these determinations, the mole fraction of HAP in the saturated solution, xHAP, could be determined as the mean value from the three samples. At each equilibration temperature, a sample of the solid phase was also collected and analyzed for phase identification by DRIFT spectroscopy.

Results and Discussion

As substantiated below, DSC, adiabatic calorimetry and solubility studies showed that, in the case of HAP, the relative thermodynamic stabilities of the Z’ = 1 and Z’ = 2 polymorphs depend on the temperature range considered. Solubility studies demonstrated that form II is the most stable phase below 300.1±0.4 K (see section on solubility studies) and becomes less stable than form I above this threshold. Only the form II (Z’ = 2) → form I (Z’ = 1) transition could be observed in the solid state both for powders and under single crystal to single crystal conditions (as shown by HSM experiments). The process requires form II to attain considerable metastability (i.e. a wide metastable zone width in the terminology of crystallization science)56 as, depending on the heating rate, the corresponding onset temperature is typically 30 K to 70 K above the value corresponding to equilibrium conditions (300.1±0.4 K) given by solubility studies. DSC and TR-SHG experiments indicate that the transition is hindered by a large activation barrier. It is nevertheless possible to interconvert the two forms under thermodynamic control if (as in the solubility studies) the phase transition is mediated by a dissolution/crystallization process. Detailed results of the DSC, adiabatic calorimetry, and solubility measurements are given in the Supporting Information. All uncertainties quoted for thermodynamic ACS Paragon Plus Environment

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quantities in the present work correspond to twice standard deviation of the mean of the number of independent determinations stated. Differential Scanning Calorimetry. When a sample consisting of polymorph I HAP in powder form (88-250 µm particles) was heated at different rates (1, 10, and 80 K⋅min-1) in the temperature range 293-418 K no phase transition other than fusion, with onset Ton = 382.0±0.2 K and ∆fus Hm = 18.1±0.2 kJ⋅mol-1, was observed. These results, which represent means of the ο

corresponding values obtained at the three heating rates (see Supporting Information), are similar to those previously obtained at 1 K⋅min-1 (Ton = 381.9±0.1 K; ∆fus Hm = 18.08±0.07 ο

kJ⋅mol-1).31 Different patterns were, however, evidenced when the experiments were repeated with form II HAP powder. As illustrated in Figure 2a, for β = 1 K⋅min-1 the measured curve

(a)

(b)

Figure 2. Differential scanning calorimetry curves obtained for HAP powders (a) and single crystals (b) at different heating rates.


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showed the II → I phase transition at Ton = 356.8±4.8 K, followed by fusion of form I at Ton = 381.71±0.04 K. No signature of the reverse I → II process was noted when a form II sample was heated above the phase transition range without melting and then cooled to 213 K, thus indicating that the transition was irreversible. For β = 10 K⋅min-1, the II → I phase transition peak was absent. In this case, fusion of form II was observed at Ton = 377.2±0.2 K, followed by the crystallization of metastable liquid HAP into form I, which subsequently melted at Ton = 381.9±0.2 K. A run at β = 80 K⋅min-1 was also made in an attempt to observe a clean fusion of form II. In this case, however, a broad peak with onset at Ton = 378.8±0.2 K was obtained, indicating that fusion of form II could not be decoupled from the two subsequent processes noted at 10 K⋅min-1. When similar experiments were carried out with single crystals of form II (one crystal of 1-2 mm edge inside the crucible), using heating rates of 1-20 K·min-1, the three following patterns were observed (Figure 2b). In most cases, independently of the heating rate, the measured curve evidenced the II → I phase transition followed by fusion of form I. While the fusion temperature of form I was fairly insensitive to the heating rate, with a mean value for all heating rates of 382.1±0.1 K, the onset of the phase transition increased from 351 K to 371 K on increasing β from 1 K⋅min-1 to 20 K⋅min-1. In a few cases where β = 8, 10, or 14 K⋅min-1, either ο (i) a single sharp peak corresponding to the fusion of form II (Ton = 377.7±0.2 K; ∆fus Hm =

19.1±0.6 kJ⋅mol-1) was detected or (ii), as in the case of powders, the DSC curve showed the fusion of form II followed by crystallization of metastable liquid into form I and finally the fusion of form I. The effect of subjecting the samples to low temperature annealing (see Materials and Methods section) on the DSC patterns was also studied. When an annealed powder sample (88250 µm particles) of polymorph I HAP was heated at 1 K⋅min-1, in the temperature range 293ACS Paragon Plus Environment

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ο 418 K, no phase transition other than fusion (Ton = 381.52±0.06 K and ∆fus Hm = 17.8±0.1

kJ⋅mol-1) was observed. Moreover, submitting the sample to cooling and heating cycles in the range 213-268 K (where form II is the thermodynamically stable phase) during the annealing process did not induce the I → II transformation. These results suggest that low temperature annealing has no significant effect on the fusion temperature and enthalpy values and that it is also unable to promote the reversibility of the II →I phase transition. In contrast, when similar experiments were carried out with annealed form II powder samples (88-250 µm particles), at a heating rate of 1 K⋅min-1, a significant improvement in the reproducibility of the phase transition onset was observed. Figure 3 shows the DSC profiles of five experiments carried at 1 K·min-1 using non-annealed (Figure 3a) and annealed samples (Figure 3b) of the same original batch. A much larger Ton dispersion is noted for the nonannealed (Ton= 356.8±4.8 K) than for the annealed (Ton= 356.9±0.8 K) samples. Also the peak profile seems to be broader and rougher in the first case. This is not unexpected, since a crystallized substance often exhibits defects within the crystals which lead to lattice strain.57

(a)

(b)

Figure 3. DSC curves obtained for different powder samples of form II HAP at 1 K·min-1: (a) non-annealed samples (b) annealed samples. ACS Paragon Plus Environment

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Annealing tends to remove the lattice strain and reduce the number of defects in the crystallites and, as a result, the phase transition becomes smoother and the onset temperature more reproducible. The fact that samples stored at ambient temperature for different periods of time did not show indication of spontaneous isothermal annealing, suggests that the lattice strain release is promoted by the alternate contraction and expansion processes associated with the successive cooling-heating cycles. Overall, the DSC patterns observed at different heating rates using powders (annealed and non-annealed) and single crystals led to the following conclusions: (i) The fact that a clean fusion of form II could only be observed with single crystals probably reflects a more hindered nucleation of form I on a form II crystal of higher perfection. This is in agreement with previous results for p-dichlorobenzene.58 (ii) Both for single crystals and powders, whenever fusion of form II was not present, and regardless of the heating rate, the DSC curve always evidenced the II → I phase transition followed by fusion of form I. This indicates that, as should be expected, once the transition is observed, the formation of the thermodynamically stable form I will always be preferred to the fusion of form II into a metastable liquid. (iii) Increasing the heating rate shifted, however, the onset of the phase transition to a higher temperature (e.g. Figure 2b). This is typical of thermally induced nucleation and growth processes (in this case the crystallization of form I from form II), where a widening of the metastable zone width is normally observed on increasing the heating/cooling rate. (iv) The three peak endo → exo → endo pattern exemplified by the 10 K⋅min-1 curve in Figure 2a, corresponds to cases where the heating rate is sufficiently high to allow the temperature of fusion of form II to be reached (first endothermic peak) before the nucleation and growth of form I becomes significant. The metastable liquid resulting from that process then recrystallizes into the thermodynamically stable form I, which finally undergoes fusion to a stable liquid phase. (v) The observation that


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the enthalpy of fusion obtained for form II ( ∆fus Hm = 19.1±0.6 kJ·mol-1) is larger than that ο

obtained for form I ( ∆fus Hm = 18.2±0.2 kJ·mol-1) is in accordance with Burger’s heat of fusion ο

rule, which states that in an enantiotropic system the higher melting polymorph will have the lowest enthalpy of fusion.1,23,24 (vi) The fact that the II → I process was found to be endothermic, irreversible, and with an onset that increased with the heating rate gave a good indication that, even at the lowest heating rate (β = 1 K⋅min-1), the phase transition temperature (Ton = 356.8±4.8 K) was most likely higher than the “true” equilibrium value. Further evidence that this was indeed the case (large metastable zone width) was provided by the adiabatic calorimetry and by the solubility results discussed below. The latter, in particular, allowed the assignment of the equilibrium transition temperature to 300.1±0.4 K. This is in agreement with Burger’s enthalpy of transition rule which indicates that if an endothermic solid-solid phase transition is observed in a DSC trace, then the corresponding equilibrium temperature must be at, or below, the temperature of the experimentally detected peak.1,23,24 It may also be recalled that, as mentioned in the Introduction, some degree of superheating (heating mode) or supercooling (cooling mode) is always necessary for the occurrence of a nucleation process. That degree significantly depends on the activation energy of the process. The large metastable zone width found in the present work, therefore, suggests that a significant activation barrier should be associated to the II → I phase transition. This conclusion is also consistent with the notable irreversibility of the process, because the thermal energy available to overcome Ea and promote any diffusion process necessary to molecular rearrangement decreases as the system is being cooled below 300.1±0.4 K. It should also be pointed out that a sample of form I that has been kept in the laboratory for ∼6 years at 294±4 K did not show any signs of conversion into form II when analyzed by DRIFT and XRPD. Quantitative insights into the size of the II → I activation barrier were provided by the DSC and TR-SHG kinetic studies discussed below. ACS Paragon Plus Environment

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(vii) Thermal annealing of form I within the thermodynamic stability domain of form II had no effect on the fusion parameters and could not induce the I → II phase transition. A similar treatment of form II considerably improved the reproducibility of the II → I temperature onset and the shape of the transition peak. This is a good indication that lattice defects play an important role in promoting the transition, as should be expected for a nucleation and growth process. Adiabatic Calorimetry. The heat capacity measurements on forms I and II HAP by adiabatic calorimetry (Figure 4) provided further support for the picture resulting from the DSC observations. Form I was studied in the range 299.20-369.79 K. As illustrated in Figure 4a (black solid line, open triangles), no evidence of phase transitions was obtained. Form II was subjected to the following measuring sequence: (i) heating from 294.38 K to 373.11 K; (ii) cooling to 79.12 K (without data recording) and (iii) re-heating from 79.12 K to 373.25 K. As shown in Figure 4a (blue solid line, open squares), when the sample was first heated from 294.38 K to 373.11 K the presence of the II → I phase transition was clearly apparent in the range 328.51-336.49 K. After the phase transition, the heat capacity curve followed that obtained for form I within ∼0.15%. On re-heating the sample from 79.12 K and to 373.25 K (Figure 4b), the high temperature part of the recorded heat capacity curve (Figure 4a, red line, open circles) matched that obtained for form I (Figure 4a, black line, open triangles) within ∼0.1%. It can be concluded from these results that: (i) as observed in the DSC experiments, the endothermic form II → form I transition is irreversible; (ii) the onset of the phase transition is observed at Ton ∼ 328 K, c.f. ∼30 K below that observed in the DSC runs performed on nonannealed powders at the lowest heating rate (1 K⋅min-1); (iii) although the endothermic nature the phase transition is clear in Figure 4a, the corresponding peak is composed of a series of exothermic and endothermic events.


23

230

225

220

200

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175

210 Cºp,m/J.K-1.mol-1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Cºp,m/J.K-1.mol-1


200 190

150 125 100

180

75

170

50 290

310

330

350

370

390

50

150

250

350

450

T/K

T/K (a)

(b)

Figure 4. Heat capacity of the two polymorphs of 4’-hydroxyacetophenone measured by adiabatic calorimetry. (a) Overlay of form I and form II data: heating of form I in the range 299.20-369.79 K (black solid line, open triangles); heating of form II from 294.38 K to 373.11 K (blue solid line, open squares) evidencing the form II → form I phase transition; and final section of a second run where the form I sample resulting from the phase transition was cooled from 373.11 K to 79.12 K and re-heated to 373.25 K (red solid line, open circles). (b) Full data of the previous run in the range 79.12-373.25 K. Note that the data points in the temperature region of the phase transition (figure 4a, blue curve), where the system is not under thermodynamic equilibrium, should be regarded as “apparent” heat capacities given by Q/∆T, where Q is the heat introduced into the calorimeter and ∆T is the resulting temperature change.


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The adiabatic calorimetry experiments, where the lowest Ton value was observed, were carried out by a slow stepwise process in which the heating steps were separated by equilibration periods. This observation and the irreversible nature of the phase transition noted in both types of calorimetric experiments suggest that the true equilibrium temperature of the form II → form I transition should be even lower than Ton ∼ 328 K, obtained in the adiabatic calorimetry experiments. This was in fact confirmed in the equilibrium solubility studies described below, which, as already mentioned, allowed the assignment of that transition temperature to 300.1±0.4 K. The few exothermic “sparks” observed throughout the phase transition range are perhaps originated by the release of internal strains accumulated within the crystalline material while the less dense form I grows from the more dense form II. This effect was also noted in DSC experiments carried out at the lowest heating rate with non-annealed samples. Its relationship with strain release was suggested by the fact that subtle movements of crystals undergoing the phase transition could be detected by hot stage microscopy. Solubility.

As mentioned above, the results of the DSC and adiabatic calorimetry

experiments suggested that, for kinetic reasons, the onset temperatures of the II → I phase transition observed for different heating regimes did not correspond to equilibrium values. The thermodynamic equilibrium temperature, Ttrs, was, therefore, determined from solubility studies in ethanol and acetonitrile, where the nature of the solid phase in equilibrium with the solution at each temperature was monitored by DRIFT analysis (Figure 5).25 These experiments allow overcoming the energy barrier hindering the direct conversion of the two solid phases, through a solution mediated process, where the phase which is metastable at a given temperature dissolves and the thermodynamically stable one subsequently precipitates.


25


-0.5 Form I

Form II

-1.0 Ethanol -1.5

ln x

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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-2.0

Acetonitrile

-2.5

Ttrs=300.1 K

-3.0 3.1

3.2

3.3

3.4

3.5

3.6

1000/(T/K)

(a)

(b)

Figure 5. (a) Mole fraction solubilities of HAP in ethanol and acetonitrile. (b) DRIFT spectra of the solid phase in equilibrium with the solution throughout the solubility measurements in ethanol. The spectra obtained up to 299.7 K correspond to form II (red lines) and those above this temperature (in blue) refer to form I.

The mole fraction (x) solubility determinations were carried out in the range 283-312 K. Linear least squares fits of eq 9

ln x = A +

B (T / K)

(9)

to the obtained x vs. T data (see Supporting Information) led to the results indicated in Table 1, where Trange denotes the temperature range of the measurements and R2 is the regression


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Table 1. Parameters of Eq. 9 Corresponding Temperature Ranges of Application (Trange), and Regression Coefficients (R2) Solvent ethanol acetonitrile

Phase form I form II form I form II

−A 1505.8±194.0 1731.9±51.4 3268.2±246.3 2661.6±197.4

B 3.84±0.63 4.60±0.18 8.92±0.80 6.86±0.67

Trange/K 300.25-312.18 283.25-299.35 300.81-312.29 283.12-299.84

R2 0.92 0.99 0.98 0.96

coefficient for 95% probability. As shown in a Table 1 and Figure 5a for all solvents the ln x vs. 1/T curves exhibit a slight slope shift at 300.1±0.4 K originated by the II → I phase transition. The occurrence of the phase transition at this temperature was confirmed by the DRIFT analysis of the solid phase in contact with the solution, as illustrated in Figure 5b for ethanol. The thermodynamic equilibrium temperature was therefore taken as Ttrs = 300.1±0.4 K. This value is ∼30 K lower than the II → I onset temperature observed in the adiabatic calorimetry experiments and ∼60-70 K lower than the corresponding temperatures measured by DSC at different heating rates. A key result from the solubility studies was the fact that, independently of the solvent, interconversion of the two polymorphs could be observed simply by raising or lowering the temperature of the solid+solution slurry around Ttrs = 300.1 K. This unequivocally indicated that a Z′ > 1 form is not necessarily less stable than the corresponding Z′ = 1 form, thus lending quantitative support to an equivalent statement made in a recent review.7 Raman spectroscopy. The Raman spectra collected for a single crystal of HAP form II, suspended on an acoustic levitator, as a function of temperature are shown in Figure 6. The figure evidences that the form II → form I transition initiates above 348 K. This observation is signaled by the appearance of a peak at 1658 cm-1 (marked with an asterisk in Figure 6) which corresponds to the stretching frequency of the carbonyl group in form I.40 As in the case of ACS Paragon Plus Environment

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infrared spectra,40 the major spectral differences associated with the occurrence of the phase transition are noted in the 1659 cm-1 to 1575 cm-1 range: (i) the ν% (C = O) frequency changes from 1642 cm-1 to 1658 cm-1, reflecting modifications in the hydrogen bond pattern; (ii) the two

ν% (C &&& − C) ring frequencies at 1584 cm-1 and 1598 cm-1, typical of the Z molecular conformation present in form II, change into values that are characteristic of the E conformation present in

Figure 6

Raman spectra evidencing the transformation of an acoustically levitated form II

HAP single crystal into form I when heated in the range 318 K to 363 K. The red and blue spectra refer to forms II and I, respectively. The green spectra correspond to mixtures of the two phases.


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form I, namely 1575 cm-1 and 1603 cm-1. No significant broadening of the peaks along the heating process, which could be indicative of an amorphous intermediate, is also noted. The Raman spectroscopy results, therefore, suggest that the phase transition directly occurs from form II to form I, without any detectable intermediate phase. This conclusion is consistent with the hot stage microscopy results discussed in the next section. Hot Stage Microscopy. Hot stage microscopy observations made on heating a form II single crystal in the range 298-373 K, at β = 5 K⋅min-1, revealed the smooth movement of a well-defined interface corresponding to the growth of a form I crystal within the original form II mother phase (Figure 7). This single crystal to single crystal phase transformation could only be evidenced when regular crystals with clear-cut faces were used in the HSM experiments. The process was completed within ~1 min after the interface propagation was initiated and the onset was detected at Ton ~ 370 K. This temperature is well above the equilibrium value of 300.1 K determined in the solubility studies and also on the high end of the values obtained in the DSC experiments carried out on single crystals at the same heating rate (on average Ton = 362.5±5.8 K). Such finding is not unexpected since more perfect crystals should, in principle, lead to increased nucleation hindrance and consequently to a larger difference between the onset temperature of the phase transition and its “true” equilibrium value obtained from the solubility studies, or in other words to a wider metastable zone width (MZW). The HSM results, therefore suggest that the form II → form I transition occurs through a nucleation and growth mechanism involving an edgewise mode of interface motion.12 This is in agreement with the combined evidence of the DSC, adiabatic calorimetry, and solubility experiments. The MZW widening with the heating rate is typical, for example, of crystal nucleation from liquids or solutions.56


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Figure 7. Hot-stage microscopy images showing the progressive growth of a form I crystal within the form II mother phase, along the form II → form I phase transition in 4HAP, when heated from 298 to 373 K at 5 K⋅min-1. The images were recorded in polarized light.

Kinetic Studies. The overall activation barrier, Ea , of the form II → form I phase transition was investigated by differential scanning calorimetry (non-isothermally) and temperature-resolved second harmonic generation (isothermally). Attempts to carry out isothermal DSC experiments were ACS Paragon Plus Environment

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unsuccessful, since at the low end of the temperature range where the transition is observed (e.g. 330350 K) the obtained peaks spread over a large time interval and were difficult to separate from the baseline making impossible to extract any reliable kinetic information from the α-t data; at higher temperatures the phase transition started while heating the sample to isothermal conditions and the α-t curve could not be defined. The non-isothermal DSC determinations were carried out with powder samples of form II that had been annealed as above described. The heating rates were 0.25, 0.5, 1 and 2 K·min-1. Higher heating rates could not be used because the obtained DSC pattern often showed the fusion of form II without detection of the II → I phase transition. Triplicate measurements were performed at each heating rate, and typical results are illustrated in Figure 8. The Ea determination from those data was based on the isoconversional approaches proposed by Starink59 and Vyazovkin60,61 (integral methods), and Friedman62 (differential method), which do not require any mechanistic assumptions and are recommended as the most reliable procedures for determination of Ea as a function

Figure 8. Results from the non-isothermal DSC kinetic study of the form II → form I transition carried out using temperature annealed form II powdered samples. ACS Paragon Plus Environment

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of the conversion fraction from non-isothermal data.63,64 In the case of the integral procedures, T-α curves were first obtained for each heating rate from experimental DSC plots such as those in Figure 8, by using eq 7. Then, the temperatures, Tα , corresponding to conversion fractions separated by 0.1 units in the range α = 0.1-0.9 were calculated at the different heating rates. The Starink procedure relies on the equation:59

ln

β 1.92

Tα

= m − 1.0008

Ea,α

(10)

RTα

where β is the heating rate, Tα is the temperature corresponding to a given α at that heating rate, m is a constant, R is the gas constant, and Ea,α is the activation energy at the α value considered. Linear least squares fits of eq 10 to plots of ln( β / Tα1.92 ) against 1/ Tα for α values in the range 0.1 to 0.9 led to the activation energies shown in Figure 9a (data given in the Supporting Information), where the error bars correspond to the standard error of the mean of three determinations. No significant change of Ea with α can be inferred from Figure 9 given the error bars of the determinations. The mean value of the Starink analysis results in Figure 9 is Ea = 240±16 kJ·mol-1, where the uncertainty is the average absolute deviation. According to Vyazovkin’s method the activation energy at a specific conversion fraction, α, is obtained by determining the Ea value that minimizes the equation:60,61

n

n

I ( Ea,α , Tα ,i ) β j

∑∑ I ( E i =1 j ≠i

a,α

, Tα , j ) β i

= min

(11)


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(a)

(b)

(c)

(d)

Figure 9. Activation energy, Ea, as a function of the conversion fraction, α, obtained from isoconversional analysis of the non-isothermal DSC results by using: (a) Starink’s method, eq 10; (b) Vyazovkin’s method eqs 11, 12; (c) Friedman’s method, eq 13. (d) Analysis of SHG results using the standard isoconversional method for isothermal experiments, eq 14.


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where

Tα  E  I ( Ea,α , Tα ) = ∫ exp  − a,α dT 0  RT 

(12)

In the previous equations, Ea,α and Tα represent the activation energy and temperature, respectively, corresponding to fraction α at different i and j heating rates. The calculation procedure was implemented in a MS Excel macro.65 The application of Vyazovkin’s procedure led to a variation of Ea with α (Figure 9b, data given in the Supporting Information) identical to that obtained by Starink’s method and also to an identical mean activation energy and corresponding average absolute deviation, namely Ea = 240±16 kJ·mol-1. Friedman’s differential method is based on the equation:62

Ea,α  dα  ln   = n− RTα  dt α

(13)

where (dα / dt ) α , Tα , and Ea,α denote the rate, the temperature, and the activation energy of the process corresponding to a fixed α, and n is a constant. In this case, the values of (dα / dt ) α and Tα , corresponding to a given α conversion were obtained for all heating rates used. Linear least squares fits of eq 13 to ln (dα /dt )α vs. 1/ Tα plots afforded the variation of the activation energy with α shown in Figure 9c (data given in the Supporting Information) where, as for the integral methods, the error bars represent the standard error of the mean of three determinations. The mean value of the results obtained by Friedman’s method in Figure 9c corresponds to Ea = 211±29 kJ⋅mol-1, where the assigned uncertainty corresponds to the average absolute deviation. ACS Paragon Plus Environment

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Independent support for the DSC results was provided by temperature-resolved second harmonic generation experiments. The II(P212121) → I(P21/c) phase transition is accompanied by a change from a SHG active non-centrosymmetric space group (P212121) to a SHG inactive centrosymmetric space group (P21/c). The kinetics of the form II to form I conversion could therefore be followed by monitoring the decrease in the SHG signal over time in a series of isothermal runs carried out at 343.15 K, 348.15 K, 353.15 K, 358.15 K, and 363.15 K. The conversion fractions, α, were calculated from the SHG intensities recorded as a function of time by using eq 6. The obtained α-t data were analyzed by a standard isoconversional method64 which relies on the equation:

− ln tα = −

Ea,α RT

+p

(14)

where tα is the time at which a given conversion α is attained for a run carried out at the temperature T and p is a constant. The procedure used to obtain Ea,α from eq 14 was as follows: (i) the t-α data obtained at the different temperatures were fitted to polynomial functions; (ii) these functions were then used to calculate tα values corresponding to a series of conversions separated by 0.05 increments in the α = 0.1-0.9 range; (iii) finally least squares fits of eq 14 to − ln tα vs. 1/Tα plots were performed and the Ea,α values were calculated from the slopes of the obtained equations.

The variation of Ea with α obtained from the SHG experiments (see

Supporting Information) is given in Figure 9d. Albeit the results are closer to those of Friedman’s method, the general agreement is remarkable given the difficulty of the experiments. The mean value of the SHG results, Ea = 209±31 kJ⋅mol-1 (the assigned uncertainty corresponds to the average absolute deviation) is also in good agreement with the above mentioned Ea = 240±16 kJ·mol-1 (Starink and Vyazovkin equations) and Ea = 211±29 kJ⋅mol-1 (Friedman ACS Paragon Plus Environment

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equation). The average of these three values, Ea = 220±30 kJ⋅mol-1, will be taken as representative of the activation energy of the form II → form I transition. The corresponding error bar was arbitrarily assumed to be analogous to the largest uncertainty of the individual Ea data. Overall, it can be concluded that: (i) for a given conversion the various isoconversional approaches lead to activation energies which are in agreement within their combined uncertainty intervals. The fact that the results refer to two completely different experimental methodologies (DSC and SHG) is a good indication of their consistency. (ii) There seems to be an apparent decrease of Ea,α with α, which is independent of the experimental technique and of the selected data treatment method, but this trend is overshadowed when the error bars of the data points are considered. This gives some support to the application of the integral isoconversional methods, which require constancy of the activation energy with α.66 (iii) Last but not the least, the Ea,α results obtained by the different methods vary in the range 157-265 kJ⋅mol-1, which corresponds to values 1.5-2.6 times larger than the lattice enthalpy of form II HAP, as measured by its enthalpy of sublimation, ∆ sub H mo (HAP, crII) = 104.3±0.4 kJ⋅mol-1.31 A survey of reported activation energies for solid-solid phase transitions and sublimation enthalpies of the compounds involved in the processes shows that Ea values considerably higher than ∆ sub H mo are not uncommon. Thus, in the case of 1,1-diamino-2,2-dinitroethylene (FOX-7), while the

estimated enthalpies of sublimation for an unspecified polymorph lie in the range ∆ sub H mo = 109-116 kJ⋅mol-1,67,68 the experimentally obtained activation energies of the β → γ and γ → δ transitions are

Ea (β → γ) = 215 kJ·mol-1

69

and

Ea (γ → δ) = 647 kJ·mol-1,69 respectively; for 2,4,5,6-

tetrachlorobenzene-1,3-dicarbonitrile (chlorothalonil) ∆ sub H mo = 107 kJ⋅mol-1

70

and Ea (α → β) = 650

kJ·mol-1;71 for 2-(2,3-dimethylphenyl)aminobenzoic acid (form I), ∆ sub H mo (cr I) = 133 kJ⋅mol-1


72

and

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Ea (I → II) = 300-362 kJ·mol-1;73-75 and in the case of the widely studied octahydro-1,3,5,7-tetranitro1,3,5,7-tetrazocine (HMX) system ∆ sub H mo = 162 kJ⋅mol-1

76

and Ea (β → δ) = 204-510 kJ⋅mol-1.77-81

The significance of these large activation energies (larger than the sublimation enthalpies) is impossible to assess without a detailed information about the phase transition mechanism, which in the above examples, as in the case of HAP, is essentially unknown. The HAP results suggest, nevertheless, a complex nucleation and growth process consisting of several elementary steps characterized by their own individual Ea that add up to a large overall value (also dubbed apparent activation energy). Furthermore, the large metastable zone width (30-70 K) observed for the onset of the II → I phase transition in the adiabatic calorimetry and DSC experiments carried out at different heating rates (1-20 K⋅min-1) seems compatible with a high contribution from the nucleation barrier (although not necessarily larger than the lattice energy) to the overall Ea value. Stability Domains of Forms I (Z’ = 1) and II (Z’ = 2) HAP and Activation Energy Profile of the II → I Phase Transition. The thermodynamic data obtained in this work allowed the re-evaluation of the ∆ f Gmo -T diagram illustrating the stability domains of forms I and II HAP at ambient pressure (1 bar). The kinetic studies also provided an activation energy profile of the II → I transition. Critical for the building of the ∆ f Gmo -T diagram using a previously reported methodology31 were the heat capacities of solid (forms I and II) and liquid HAP obtained by adiabatic calorimetry and DSC, and the equilibrium temperature of the phase transition (Ttrs = 300.1±0.4 K) given by the solubility studies. The obtained

C po,m values (See Supporting Information) were fitted to polynomial equations of the type:

C po,m /J⋅mol-1⋅K-1 = a’ +b’(T/K) + c’(T/K)2


(15)

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by the least squares method. The corresponding parameters, range of application and regression coefficients (R2) for 95% probability are summarized in Table 2. Also included in Table 2 for comparison purposes are the previously reported parameters for the heat capacity of gaseous o HAP.31 The reliability of the C p,m measurements by DSC was tested by comparing the

corresponding values obtained for form I (see Supporting Information) with analogous results from adiabatic calorimetry calculated from eq 15 and the parameters in Table 2. The agreement between the two determinations in the range covered by the DSC measurements (324-374 K) was within ∼1 %. The obtained ∆ f Gmo -T diagram is illustrated in Figure 10a, evidencing that at ambient pressure (1 bar) form II (Z’ = 2) is the stable phase up to Ttrs = 300.1 K and above that temperature form I (Z’ = 1) prevails until fusion occurs at 381.9 K. The phase transition temperatures obtained in the adiabatic calorimetry (∼328 K) and DSC (351 K to 371 K on increasing the heating rate from 1 K⋅min-1 to 20 K⋅min-1) experiments, therefore, correspond to situations where the nucleation of form I within a considerably metastable form II starts. Figure 10b shows the temperature dependence of the thermodynamic functions corresponding to the II → I phase transition, namely ∆ trs Gmo , ∆ trs H mo and ∆ trs S mo . As should be

Table 2.

Coefficients of Eq 15 for Different HAP Phases, Corresponding Temperature

Ranges of Application (Trange), and Regression Coefficients (R2)a Phase a' b' HAP, cr I 24.821±0.935 0.51426±0.00275 HAP, cr II 35.776±2.307 0.47390±0.00740 HAP, l 157.49±0.07 0.34625±0.00017 HAP, ga 6.8932 0.5596 a Ref 31, see text.

c'

−1.9376×10-4


Trange/K 298-373 294-327 385-400 298-347

R2 0.998 0.993 0.999

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(a)

(b)

Figure 10. (a) ∆ f Gmo -T diagram for the solid and liquid phases of 4’-hydroxyacetophenone at pº = 1 bar. (b) Thermodynamic functions of the form II → I phase transition.

expected, the ∆ trs Gmo curve indicates that below 300.1 K the II  I equilibrium will be shifted towards form II ( ∆ trs Gmo > 0) and above that temperature form I will prevail ( ∆ trs Gmo < 0). A more interesting insight is, however, provided by the inspection of the ∆ trs H mo and ∆ trs S mo trends, which clearly indicate that the process is entropy driven. Indeed the enthalpy curve shows that the II → I process is endothermic, within the temperature range considered, with an approximately constant ∆ trs H mo value. The enthalpy of form II is, therefore, always smaller than that of form I and, on enthalpy grounds alone, it would be concluded that form II was the stable polymorph, even above 300.1 K. Nonetheless, because the entropy change of the phase transition is also positive the formation of polymorph I becomes favorable once T ∆ trs S mo overcomes ∆ trs H mo and thus ∆ trs Gmo < 0.


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An approximate profile of the kinetic barrier associated with the II → I phase transition can be drawn by combining the Gibbs energy of formation of forms I and II HAP at that temperature,

∆f Gmo ( HAP, cr I ) = −461.6 kJ⋅mol-1 and ∆f Gmo ( HAP, cr II ) = −461.5 kJ⋅mol-1, and taking ∆‡Gmo ∼ Ea = 220±30 kJ⋅mol-1. The corresponding diagram at 350 K is illustrated in Figure 11, where the activation curve is just a qualitative representation of a typical profile. This temperature was selected since it is representative of the onset typically found in the DSC experiments and also of the range covered by the kinetic measurements.

Figure 11.

Gibbs energy of activation profile of the form II → form I transition at 350 K (see text).

The activation curve represents a typical profile and has no quantitative meaning.


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Conclusion

The present study suggests that the form II → form I phase transition relating two 4’hydroxyacetophenone polymorphs, differing not only in crystal system and space group but also in the number of molecules in the asymmetric unit and their conformation is entropy driven, and occurs through a nucleation and growth mechanism characterized by a large metastable zone width (MZW), and a large overall activation energy barrier. The large MZW and activation barrier are present despite the fact that, as previously found,31 the lattice energies of the two forms differ only by 0.49±0.13 kJ·mol1

. Raman spectroscopy experiments suggested that the transition does not involve intermediate phases

and hot stage microscopy observations revealed that it may occur under single crystal to single crystal conditions. Solubility measurements unequivocally showed that at atmospheric pressure form II HAP (orthorhombic, Z’ = 2) is more stable (smaller Gibbs energy) than form I (monoclinic, Z’ = 1) up to 300.1±0.4 K and that the stability is reversed above that temperature. The fact that interconversion of the two polymorphs could be observed in the solubility studies under thermodynamic control indicates that the assumption of Z′ > 1 forms being necessarily less stable than the corresponding Z′ = 1 form cannot be universally true, thus lending quantitative support to an equivalent statement made in a recent review.7 The solubility studies further suggested a simple method for the selective and reproducible preparation the two known 4’-hydroxyacetophenone polymorphs, which seems particularly suitable for scale-up. It consists in keeping a suspension of the compound in a given solvent (in this work ethanol and acetonitrile were used) under continuous magnetic stirring, a few degrees below (form II) or above (form I) 300.1 K. The enantiotropic nature of the system was confirmed by the solubility studies, but the equilibrium temperature of the phase transition was found to lie ∼70 K below than previously assumed from DSC results. This information, together with that obtained from accurate heat capacity


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determinations by adiabatic calorimetry allowed a redefinition of the relative stability domains of both polymorphs in the form of a ∆ f Gmo -T phase diagram. As mentioned in the Introduction, it has been pointed out in the literature that exceptions to the conjecture that Z′ = 1 polymorphs are more stable than their higher Z′ counterparts are particularly common for compounds where there is difficulty in balancing close packing with hydrogen-bond (Hbond) formation. For the HAP system experimental evidence indicates that the presence of two molecules in the unit cell of form II (Z’ = 2) does seem to favor the formation of stronger H-bonds compared to form I. Indeed, (i) DRIFT spectroscopy results showed that the OH stretching band is shifted to a lower wavenumber in form II (3124 cm-1) than in form I (3308 cm-1)40 and (ii) comparative analysis of single crystal X-ray diffraction data for both polymorphs suggests that the OH⋅⋅⋅O bond distances/angles are more compatible with stronger hydrogen bonds in form II than in form I.31,40 In this case, however, the adoption of a higher Z’ structure does not imply a deviation from close packing, since the density at 298 K is larger for form II (1.278 g⋅cm-3) than for form I (1.247 g⋅cm-3).31 It can finally be pointed out that the results obtained in this work clearly show that polymorph stability should not be analyzed from structural arguments alone, but rather through thermodynamics. The differences between polymorphic structures normally involve complex and subtle compromises between optimization of attractive/repulsive intermolecular interactions and maximization of entropy. In most cases, these compromises do not translate into obvious structure-stability relationships, albeit searching for such relationships is clearly an important endeavor. The stability hierarchy of different crystal forms can, on the other hand, be unambiguously quantified by comparing their Gibbs energies. It should nevertheless be kept in mind that (i) a given stability hierarchy may change if p or T conditions are changed and (ii) as in the case of HAP, kinetic barriers may allow the existence of metastable polymorphs for long periods of time without any signs of transformation into a more stable form.


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Acknowledgements. This work was supported by Fundação para a Ciência e a Tecnologia (FCT), Portugal through project UID/MULTI/00612/2013 and grants awarded to A. Joseph (SFRH/BD/90386/2012) and C. E. S. Bernardes (SFRH/BPD/101505/2014). Thanks are also due to PARALAB (Portugal) for providing the Netzsch DSC 204 F1-Phoenix apparatus. Finally, we also acknowledge the COST action CM1402.

Dedication. This article is dedicated to the memory of Professor Raisa M. Varushchenko that sadly passed away while the work was in progress.

Supporting Information Available. Tables S1 and S2 with the indexation of the powder diffraction patterns of the form I and form II samples studied in this work. Tables S3-S7 with the results of the heat capacity measurements by DSC and adiabatic calorimetry. Tables S8-S11 with the results of the DSC studies on the II → I phase transition and fusion of forms I and II. Table S12 with the solubilities of HAP in ethanol and acetonitrile. Table S13 with the activation energies of the II → I phase transition obtained by DSC and SHG measurements. Table S14-S17 with the data used in the calculation of the ∆ f Gmo -T phase diagram. This material is available free of charge via the Internet at http://pubs.acs.org.


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Polymorphic Phase Transition in 4’-Hydroxyacetophenone: Equilibrium Temperature, Kinetic Barrier and the Relative Stability of Z’ = 1 and Z’ = 2 Forms Abhinav Joseph, Carlos E. S. Bernardes, Anna I. Druzhinina, Raisa M. Varushchenko, Thi Yen Nguyen, Franziska Emmerling, Lina Yuan, Valérie Dupray, Gérard Coquerel, Manuel E. Minas da Piedade*

Synopsis: Solid-solid phase transitions are a key aspect of polymorphism in molecular organic solids. The interplay of structural, thermodynamic, and kinetic factors behind the interconversion and relative stability of the Z’ = 1 and Z’ = 2 polymorphs of 4’-hydroxyacetophenone was investigated by a variety of methods including calorimetry, solubility measurements, hot-stage microscopy, Raman spectroscopy, temperature-resolved second harmonic generation.

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Equilibrium Temperature, Kinetic Barrier, and the ... - ACS Publications

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