Indomethacin - American Chemical Society

Aug 20, 2009 - Broadband dielectric measurements on the pharmaceutical indomethacin (IMC) were performed at ambient and elevated pressure. Data on ...
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J. Phys. Chem. B 2009, 113, 12536–12545

Broadband Dielectric Relaxation Study at Ambient and Elevated Pressure of Molecular Dynamics of Pharmaceutical: Indomethacin Z. Wojnarowska,† K. Adrjanowicz,† P. Wlodarczyk,† E. Kaminska,† K. Kaminski,*,† K. Grzybowska,† R. Wrzalik,† M. Paluch,† and K. L. Ngai‡ Institute of Physics, Silesian UniVersity, ul. Uniwersytecka 4, 40-007 Katowice, Poland, NaVal Research Laboratory, Washington, D.C. 20375-5320 ReceiVed: June 2, 2009; ReVised Manuscript ReceiVed: July 10, 2009

Broadband dielectric measurements on the pharmaceutical indomethacin (IMC) were performed at ambient and elevated pressure. Data on molecular dynamics collected at ambient pressure are in good agreement with that published in the literature. In the glassy state, there is a well-resolved secondary relaxation with Arrhenius activation energy Ea ) 38 kJ/mol. This commonly observed relaxation process (labeled γ) is of intramolecular origin because it is pressure-insensitive. Closer analysis of the ambient pressure dielectric spectra obtained in the vicinity of the Tg indicated the presence of one more secondary relaxation (β), which is slower than that commonly observed. Application of the CM predictions enabled us to classify it as a true JG relaxation. Pressure measurements confirmed our supposition concerning the origins of the two secondary relaxations in IMC. Moreover, we have found that IMC under pressure does not crystallize, even at very high temperatures of T g 372 K. This finding was discussed in the framework of the two-order parameter model proposed by Tanaka (Konishi, T.; Tanaka, H. Phys. ReV B 2007, 76, 220201), as well as the JG relaxation proposal by Oguni (Hikima T.; Hanaya M.; Oguni M. J. Mol Struct. 1999, 479, 245). We also showed that the shape of the R-relaxation loss peak is the same when comparing dielectric spectra with the same τR but obtained at ambient and elevated pressure. Additionally, we found out that the fragility of IMC decreases with increasing pressure. In addition, the pressure coefficient of the glass transition temperature, dTg/dP, was determined, and it is 255 K/GPa. Finally, we discuss the possibility of preparation of the amorphous state with higher density than by cooling of the liquid. Introduction Indomethacin (IMC) is a nonsteroidal, anti-inflammatory drug commonly used to reduce fever, pain, stiffness, and swelling. Its experimental solubility in water was determined to be 0.937 mg/L.1 Thus, one can classify this drug as almost completely insoluble in water. Consequently, a large dosage of indomethacin must be delivered to patients to have the desirable effects, and at the cost of possible undesirable side effects that can be toxic. This is the main reason for efforts to improve bioavailability of this API (active pharmaceutical ingredient). One of the simpler ways to do this is to prepare indomethacin in the amorphous form. In the literature, one can find a number of reports that show that such physical transformation from the crystalline to the amorphous state results in significant enhancement of the solubility of the drug.2-7 It was also confirmed for amorphous indomethacin (solubility ratio between glassy and crystal indomethacin was 4).7 However, it was also shown that amorphous IMC crystallizes when stored well below its glass transition temperature.3,8-10 This fact made indomethacin a model drug to study the kinetics of crystallization occurring below Tg and is the main reason why this API was studied over a wide range of temperatures by several experimental techniques: dielectric relaxation11,12 viscosity,13 calorimetric measurements,14-16 and thermally stimulated depolarized current.17 It is commonly believed that glasses are stable against crystallization.18 This belief is based on the dramatic increase in * Corresponding author. Email: [email protected]. † Silesian University. ‡ Naval Research Laboratory.

structural relaxation time and viscosity when temperature is lowered to below Tg such that molecular mobility becomes negligible and glass is unable to crystallize. However, recent experimental results show the opposite behavior. A few years ago, Oguni observed significant enhancement of crystal growth at and below the glass transition temperature in several glass formers.19-22 It should be pointed out that in many cases, the rate of the crystal growth was faster by about 1 order of magnitude at the Tg than aboVe the glass transition temperature. Recently, Tanaka proposed an explanation for this unexpected finding.23 He claimed that fluctuation of density leading to formation of the crystals can be relaxed by diffusion and hydrodynamic flow. Above Tg, density fluctuation can be transported by a pressure gradient following the Navier-Stokes equation. As a consequence, fluctuations of density are relaxed much more quickly than crystal can be formed. In such a case, crystallization is inhibited. In the glassy state, hydrodynamic transport is frozen because of the large viscosity. Thus, fluctuations of the density can be relaxed only by the diffusion. This in turn is too slow as compared with crystal formation. Hence, crystal growth is enhanced. The other interesting observation he made was that crystallization of the amorphous system can be closely related to the difference between the volume of the glass and crystal forms. The larger the difference, the greater the free volume that can be generated during crystallization. This implies greater local molecular mobility, which can lead to the enhancement of crystallization. Another explanation of the possible origin of crystallization of the amorphous systems was proposed by Oguni, He showed

10.1021/jp905162r CCC: $40.75  2009 American Chemical Society Published on Web 08/20/2009

MD Study of Indomethacin that secondary relaxation observed in the glassy state by dielectric and mechanical spectroscopy can be responsible for crystallization. Recently, a similar explanation was proposed by Vyazovkin for indomethacin.15 He observed crystallization of the amorphous indomethacin aged at T ) 263 K (more than 50 K below Tg) for 167 days. He related a crystallization process of the IMC to the secondary relaxation which becomes visible in dielectric loss spectra at T ) 263 K. In his recent paper, Tanaka showed that crystallization observed by Oguni should not be related to the Johari-Goldstein secondary relaxation. He proposed that the translational diffusion mode is responsible for crystallization below Tg.24 On the basis of the literature data, Tanaka claimed that for a fragile liquid, great decoupling between structural relaxation time, τR, and the translational diffusion mode can be observed.25,26 Thus, in such liquids, the possibility of crystallization below the glass transition temperature is large. The opposite situation was observed for a strong liquid. In these systems, there is slight decoupling between the structural relaxation time and translational diffusion.27 Hence, this implies greater stability of the strong liquid against crystallization. One can mention silica, which stays amorphous for hundreds of years. On the other hand, the Johari-Goldstein secondary relaxation is much faster in fragile liquids than in strong liquids for the same τR,28 and thus, it is more effective in causing crystallization in fragile glassformers than strong ones. For silica, the JG relaxation time is close to or may be even identical to τR, and hence, this equally well explains why silica is stable against crystallization. The other point of view on crystallization of the IMC below Tg was presented by Andronis and Zografi. They performed dielectric measurements on indomethacin stored at 0, 56, and 86% relative humidity.29,30 They noted great influence of the absorbed water on the relaxation properties of this API. The change in the glass transition temperature was equal to 23 K between the supercooled indomethacin and that stored at 86% relative humidity. Thus, despite its hydrophobic character, IMC can absorb a significant amount of water. Consequently, an increase in molecular mobility is observed, which can make a sample more unstable to crystallization. Current research also shows that the manner of amorphization seems to be one of the most important factors controlling the stability of amorphous indomethacin. For example, the glassy state obtained by very slow cooling of the sample is stable against crystallization over 2 years,31 but quenched samples crystallize much more quickly.32 It may be due to the difference in densities of the glasses. Recently, a few papers about the preparation of the highly stable glass of indomethacin by vapor condensation were published.33,34 It was explained by vapor deposited glasses lying much lower on the potential energy landscape than the ordinary glasses Authors also argued that amorphous indomethacin prepared in such a specific way has a lower enthalpy (8 J/g) and is about 2% denser than that obtained via supercooling of the liquid. Moreover, they showed that kinetic stability of the freshly vapor-deposited IMC is equal to that of the 7-months-aged glass. In ref 35, it was also shown that vapor-deposited IMC absorbs a factor of 5 less water than that obtained by supercooling the melt. Recently, Carpentier et al. studied the molecular dynamics of IMC by means of dielectric and NMR spectroscopies.12 They found a presence of two secondary relaxations in the glassy state. The slower one is the Johari-Goldstein (JG) β-relaxation, and the faster one is the γ-relaxation. They discussed two scenarios that can be responsible for nucleation of indomethacin stored much below Tg. It was suggested that probably, motions

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Figure 1. Chemical structure of the indomethacin.

involved in the JG relaxation coupled with rotation of the chlorobenzyl groups (γ-relaxation) control crystallization kinetics of indomethacin. Summarizing all these studies, one can conclude that the density of the glass as well as the residual molecular mobility coming from secondary relaxation may be the important factors controlling crystallization kinetics in the glassy state. In lower density glasses, molecular mobility is higher. Thus, the probability of crystallization is larger than in the denser glasses. Hence, it is necessary to find an experimental way to produce glasses of higher density (lower mobility). This can be done by the application of pressure. In the literature, one can find a few reports that show that by compressing sample, it is possible to obtain glasses of higher density than by standard supercooling.36,37 Moreover, one can refer readers to the latest paper by Mierzwa et al.,38 in which the authors have shown that application of high pressures may be an effective tool in suppressing crystallization. Of course, in the literature, there are also examples showing that high pressure favors formation of the crystals, but these studies are concerned mainly with inorganic liquid and glasses.39-41 In these other systems, chemical bonding and interactions are completely different from that of pharmaceuticals, which are organic compounds. In this paper, we present for the first time high-pressure data obtained for indomethacin. The data are meaningful because the high-pressure measurements were done even at T g 372 K. It is the temperature region where indomethacin spontaneously crystallizes at ambient pressure. However, the application of pressure suppressed crystallization. We also observed that the shape of the R-relaxation peak is invariant to different pressure and temperature combinations that maintain constant structural R-relaxation time, τR. Furthermore, we found that the fragility of the indomethacin at high pressures decreases. This seems to be a very valuable finding that suggests more stable glass of indomethacin is formed at high pressure. Finally, our data obtained at high pressure revealed the presence of the slower secondary relaxation (almost invisible in data obtained at ambient data) and showed its relaxation time is sensitive to pressure. The latter proves that this secondary relaxation is intermolecular in character and is the JG β-relaxation of IMC, as was suggested in ref 12. Experimental Section Indomethacin (as the γ polymorph) was supplied by Sigma Aldrich. Its chemical structure is presented in Figure 1. Isobaric dielectric measurements at ambient pressure were carried out using a Novo-Control GMBH Alpha dielectric spectrometer (10-2-107 Hz). The samples were placed between two stainless steel, flat electrodes of the capacitor with a gap of 0.1 mm. The

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Figure 2. FTIR spectra collected during annealing of the IMC at 300, 350, 400, 415, 418, and 428 K. Dotted lines indicate bands undergoing subtle changes during annealing.

temperature was controlled by the Novo-Control Quattro system, with use of a nitrogen gas cryostat. Temperature stability of the samples was better than 0.1 K. In the case of high-pressure measurements, the capacitor filled with the test material was placed in a high pressure chamber and compressed using the silicone fluid via a piston in contact with a hydraulic press. The sample capacitor was sealed and mounted inside a Teflon capsule to separate it from the silicon oil. Pressure was measured by a Nova Swiss tensometric meter resolution of 0.1 MPa. Temperature was controlled within 0.1 K by means of liquid flow from a thermostatic bath. IR measurements were performed using a Bio-Rad FTS-6000 spectrometer equipped with a KBr beam splitter, a standard source, and a DTGS Peltier-cooled detector. The MIRacle diamond accessory with KRS5 prism was applied to collect spectra in the range 380-4000 cm-1, with a spectral resolution 2 cm-1. Results and Discussion I. Ambient Pressure Data. During melting of the indomethacin at 434 K, it was observed that this drug changes color from transparent to yellow. Such a finding might indicate that the γ polymorph of the indomethacin undergoes thermal degradation at the melting temperature Tm. Such a possibility was discussed in one of the recent papers.42 However, it was difficult to find information about induction time and the extent of degradation of the IMC at Tm. Thus, we performed IR measurements to check if the examined drug undergoes thermal decomposition. The applied FTIR technique is very sensitive to changes occurring in samples and is very often used to follow chemical reactions.43-47 Transmittance IR spectra were measured in the temperature range 300-428 K. In the first step, the sample was heated to 400 K, and the spectra were collected for succeeding temperatures (the temperature step was 20 K). After this, the sample was heated to the melting point, 418 K, and spectra were recorded every 15 min for 1 h. Later, the sample was heated again to 428 K and was kept at this temperature for 1 h; the spectra were collected every 15 min. Figure 2 shows the infrared spectra of indomethacine acid at room temperature, 300 K, and at temperatures of 350, 400, 418, and 428 K. The main changes observed in the spectra shape are due to the temperature effect (i.e., broadening of the bands and softening and hardening of several vibrational modes),

Wojnarowska et al. implying subtle structural changes in the molecule as the temperature increases. The comparison of the spectra for the solid state (300-400 K) and for the liquid phase (418 and 428 K) shows radical intensity changes of the bands assigned to the characteristic carbonyl and carboxyl group vibrations.48 It is easily seen for the bands at 1716 and 1689 cm-1 (connected with stretching CdO vibrations) and for hydroxyl group bands at 1281 (bending COH vibration), 1149 (wagging OH + rocking CH2 vibration), and 1174 cm-1 (bending COH + rocking CH2 vibration). This behavior is easily explained by breaking of hydrogen bonds at higher temperatures. Analysis of all the recorded spectra confirmed that IMC is stable up to its melting temperature at the time required for its complete melting. Hence, the change in color of the IMC during melting is not an effect of its chemical decomposition. It is worth adding that dissolution of the IMC in water or anhydrous ether at room temperature also results in a change in color of the solution (from transparent to yellow). Thus, one can suppose that this peculiar behavior of the indomethacin is an effect of the transition from the crystalline to the liquid phase. In Figure 3, dielectric loss spectra obtained above Tg (left panel) and below Tg (right panel) are presented. Here, Tg was defined as the temperature at which the dielectric, τR, equals 100 s. In the left panel, one can distinguish two dielectric processes. The first, appearing at lower frequencies, is the dc conductivity, which is closely connected to the translational motions of mobile ions present in the commercial sample. The other is a structural relaxation process, which is an effect of the cooperative motions of the IMC molecules. It gives us information about the reorganization of the structure of the liquid leading to viscous flow. As can be seen in Figure 3, both relaxation peaks move toward lower frequencies with decreasing temperature. Below Tg, τR exceeds the time scale of the experiment, and the structural R-relaxation cannot be monitored. Instead, the secondary relaxations become visible in the experimental window (right panel). What we can see is the loss peak of a secondary process (labeled by γ) moving toward lower frequencies on further decrease in temperature. To move this process over 8 decades, it is necessary to decrease the temperature by more than one hundred degrees from 263 to 133 K. Hence, this process is much less sensitive to temperature than the structural relaxation. The other interesting observation is the significant decrease in the amplitude of this γ-process with decreasing temperature. This fact can be explained in view of the island mobility concept, which says that with a decrease in the temperature, the number of islands of mobility (regions of glass of higher mobility) decreases. Consequently, a lower number of dipoles is involved in the motions. This observation also can be very useful in predicting the stability of the indomethacin, It is noteworthy that at T ) 263 K (the temperature at which Vyazovkin observed crystallization of the IMC), the maximum of the γ loss peak is located at megahertz frequencies and has the greatest amplitude. It means that the number of relaxing dipoles involved in this motion is significant and that molecular movements are relatively fast. Recently, the molecular origin of this relaxation process was identified by use of a combination of the dielectric and NMR spectroscopies.12 It was shown that rotational motions of the chlorobenzyl groups are hidden under the γ- relaxation peak. Thus, as can be seen from Figure 1, not a small part of the IMC molecule rotates. Hence, it cannot be excluded that this kind of motion can be in some way responsible for the

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Figure 3. Dielectric loss spectra of the IMC collected above (upper panel) and below (lower panel) the glass transition temperature.

dielectric or mechanical measurements is close to the Kauzmann temperature, which can be estimated from extrapolation of the cp curve of the liquid to the crystal one. Such agreement between both temperatures was found for various glass formers, such as sucrose, OTP, toluene, and sorbitol.52 However, Tanaka showed that the relation T0 ) TK is not always satisfied.53 He has proven that agreement between both temperatures depends on the fragility of the system. Furthermore, he found that the stronger the liquid (smaller fragility), the greater the difference between T0 and TK. From the VFT fit, the glass transition temperature Tg ) 314 K and steepness index m ) 83 were estimated. Both quantities are in great agreement with that reported in the literature.12,17,32 The steepness index was estimated from eq 2,

m ) d log10 τR /d(Tg /T) | (Tg/T))1 Figure 4. Relaxation map of the IMC. Blue circles and yellow squares denote structural and γ- relaxation times obtained at ambient pressure. Black squares and green triangles are, respectively, β and γ-relaxation times obtained from measurements carried out at p ) 400 MPa. Solid lines are VFT and Arrhenius fits to the temperature dependences of the structural and secondary relaxation times, respectively.

So indomethacin can be classified as an intermediate glassformer. Dependence of the γ-relaxation times vs reciprocal temperaure was fitted to the Arrhenius equation,

τγ ) τ0 exp(Ea/kBT) crystallization of the IMC, even at such low temperatures below the Tg, as also suggested by Carpentier et al. In Figure 4, a relaxation map constructed from the ambient pressure data shown in Figure 3 is presented. To determine Rand γ- relaxation times, the Havriliak-Negami49 and the Cole-Cole50 functions, respectively, were used. Dependences of the structural relaxation times vs temperature were fitted to the VFT equation,

(

τR ) τ∞ exp

DTT0 T - T0

)

(1)

where τ∞ ) -19.36, D ) 17, and T0 ) 234 K. Interestingly, in the case of indomethacin, T0 ) 234 K estimated from the VFT fit is very close to the Kauzmann temperature, TK ) 240 K.51 It was shown for various glass formers that T0 obtained from

(2)

(3)

The best fit was obtained for τ0 ) 2.69 × 10-14 and Ea ) 38 kJ/mol. It is interesting that activation energy determined from our dielectric data for γ-relaxation is significantly different from that reported in ref 12, Ea ) 56 kJ/mol. Unfortunately, we are not able to explain discrepancies between the activation energy reported in the article by Carpentier et al.12 and that determined from our dielectric data. Especially, that we have found that our data measured above glass transition temperature is in good agreement with that reported by Carpentier. In addition, it is worthwhile to mention that in the article by Correia et al.,17 the activation energy estimated for the γ-process from the thermally stimulated depolarization current study is in the range of 28-40 kJ/mol, nearly the same as in our case. In Figure 5, we present a dielectric loss spectrum of the IMC measured in the vicinity of the glass transition temperature. We fitted this spectrum to the sum of a Havriliak-Negami function

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Wojnarowska et al.

Figure 5. Dielectric loss spectra measured at T ) 317.5 K. Red line represents KWW fit with βKWW ) 0.59; black curve is a best fit constructed with superposition of the Havriliak-Negami and Cole-Cole functions.

for the R-relaxation and a Cole-Cole function for the γ-relaxation. At this point, we remind the readers that the molecular origin of the γ-process was revealed in ref 12. As can be seen, there is a rather poor description of the experimental data by the fit in the region of the minimum. Such a scenario may indicate the presence of another relaxation process, which has an amplitude too small to be resolved in dielectric loss spectra. It can be inferred that this process (β) is much slower that the γ-process which is clearly visible below Tg. This situation begs the question of the molecular origin of this unresolved β-relaxation. Is it the JG relaxation seen by Carpentier during isochronal measurements performed after rapid and deep quench of the IMC below Tg? One way to check this is to locate the JG relaxation by using the coupling model (CM) prediction on the JG β-relaxation time τJG.28 This theoretical tool is helpful in identification of the JG relaxation, particularly in the case when it is not resolved in the spectra. The primitive relaxation time, τ0, of the CM is a good estimate of τJG. This, together with the relation linking τR and τ0 given by the CM, leads to the following equation to calculate τJG.

τJG ≈ τ0 ) (tc)n(τR)1-n

(4)

Here tc ) 2 ps for small molecular glass formers, τR and (1 n) are the parameters of the Kohlrausch-Williams-Watts (KWW) function,

φ(t) ) exp[- (t/τR)1-n]

(5)

the one-sided Fourier transform of which fits the R-loss peak, as shown in Figure 5. Agreement between τ0 and the secondary relaxation times is a clear indication that the secondary process is the JG relaxation of intermolecular origin. Previous applications of CM had proven useful in identification of the JG βrelaxation in many glass formers and drugs.54-58 The best KWW fit to the relaxation peak of the IMC measured in the vicinity of the glass transition temperature was obtained with (1 - n) ) 0.59 (see Figure 5). It is worth mentioning that in a paper by Carpentier et al., βKWW estimated for indomethacin was the same as in our case. Thus, we again have found good agreement between data reported in ref 12 and ours.

Figure 6. Loss spectra of the IMC measured at 321, 319, 317, and 315 K. Vertical arrows indicate positions of the f0 calculated from eq 4.

From the known value of the stretch exponent, we calculated the primitive relaxation times for the dielectric spectra measured at T ) 321, 319, 317, and 315 (see Figure 6). One can see that the positions of the primitive relaxation frequencies, f0 ) 1/(2πτ0), indicated by the vertical arrows, are located exactly in the region of the minimum between the structural and γ relaxation peaks. Thus, one can suppose that the less than perfect description of this region by the sum of the HN and the Cole-Cole functions in Figure 5 is due to the contribution of the JG relaxation of very low amplitude to the loss spectra. This part of the paper on data taken at ambient pressure is summarized as follows: We have found the presence of the two secondary relaxations in the glassy state of the IMC. The faster one is of intramolecular character and was identified as a rotation of the chlorobenzyl groups. Surprisingly, the activation energy of this process determined by us is significantly different from that reported in ref 12. On the other hand, it is comparable to that estimated by Correia et al.17 The slower one is hardly detectable in the dielectric loss spectra. However, closer analysis of the dielectric loss spectra measured in the vicinity of the glass transition temperature together with application of the CM enabled us to identify it as the JG relaxation. We also speculated about the origin of crystallization of IMC observed during calorimetric measurements performed by Vyazovkin at T ) 263 K. B. Data Collected at Elevated Pressure. Isothermal and isobaric measurements were performed at T ) 338, 348, 372, and 386 K and at P ) 90, 136, and 226 MPa. However, in Figure 7, only representative isobaric (P ) 136 MPa) and isothermal (T ) 348 K) dielectric loss spectra are presented. During all high-pressure measurements, the frequency at the maximum of the structural relaxation loss peak was kept below 100 Hz to avoid crystallization. Despite that, it is worthwhile to mention that by application of pressure, it was possible to suppress crystallization of the IMC. At ambient pressure, indomethacin crystallizes spontaneously at temperatures T ) 372 and 386 K, whereas during high-pressure measurements performed at these temperatures, we did not observe crystallization throughout the time period of measurements (2 weeks). At this point, it is necessary to discuss this finding. Up to now, avoidance of the crystallization process was explained on the basis of a purely kinetic competition between a cooling rate and a nucleation rate.59,60 Recently, H. Tanaka proposed a new two-order parameter (TOP) model describing vitrification and

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Figure 7. Loss spectra obtained (upper panel) during isothermal measurement carried out at T ) 348 K (p ) 65-135 MPa) and (lower panel) isobaric measurements performed at p ) 136 MPa (T ) 372-352 K).

crystallization process.61-63 This model considers the liquidglass transition as an effect of the competition between longrange density ordering, leading to formation of the crystals, and short-range bond ordering, favoring formation of the locally preferred structures. In the case of formation of a locally favored structure (LFS) with a geometry different from the equilibrium crystal, the system becomes frustrated. Consequently, inhibition of the crystallization rate is expected. One can state that a larger degree of frustration gives rise to a greater glass-forming ability of the liquid. The degree of frustration can be linked to the bond order parameter, S. Its average value can be expressed by the following equation ∼

S ∝ S0 exp[β(∆E - P∆Vs)]

(6)

where β ) 1/kBT, ∆E is the energy gain, ∆Vs is the volume change upon the formation of a locally favored structure, and P is the pressure. One can mention that the specific volume of the LFS should be smaller than that of the normal liquid. Hence, in such a situation, we have ∆Vs < 0. This implies an increase

in the average value of the bond order parameter (system becomes more frustrated). Furthermore, a decrease in the fragility is expected. It is obvious that compression of the system leads to a significant decrease in the volume of the liquid. Thus, the average value of the bond order parameter should also increase. In such a situation, the degree of frustration becomes greater. According to the predictions of the TOP model, the fragility of the investigated system should be lower. In other words, the higher the degree of frustration, the stronger the liquid. As will be shown later, in fact, the fragility was lowered by pressure. Of course, inhibition of crystallization of the IMC at T ) 372 and T ) 386 K at high pressures can also be related to the increase in the viscosity of the investigated drug with respect to the measurements performed at the same temperatures at ambient pressure. However, it was shown that during 4 days of storage of the IMC at ambient pressure and temperatures close to its Tg (T ) 313-343 K), a large amount of the γ and R polymorphs form. It should be added that IMC at temperatures T ) 313-343 K has a viscosity comparable to that measured at T ) 372 (P ) 136-236 MPa) and T ) 386 K (P ) 236-316 MPa). This information can be deduced directly from the observation that the structural relaxation times lie in the same range of frequencies. Hence, suppression of crystallization of the IMC during high pressure measurements cannot be related to the differences in viscosities between samples measured at ambient and high pressures. It should also be mentioned that modification of the tendencies toward crystallization in IMC can be done by grinding of the supercooled indomethacin. It was shown that increasing the milling intensity has the same effect as decreasing the temperature.64 As can be seen in Figure 7, the increase in the pressure brings about the same effect on the structural relaxation process as lowering its temperature; that is, the structural relaxation peak moves toward lower frequencies with increasing pressure. It is also observable that the low-frequency side of the γ-relaxation appears at higher frequencies when the structural peak approaches th glass transition temperature. Moreover, it is seen that there is greater contribution of the dc conductivity to the loss spectra as compared with that presented in Figure 3. This fact can be easily explained. First, dc conductivity is mainly a thermally activated process that exhibits only weak sensitivity to pressure. Second, all high-pressure measurements were performed at temperatures T g 338 K. Thus, under this condition, it is justified to expect a greater contribution of the dc conductivity to the loss spectra. In Figure 8, we presented superposed dielectric loss spectra obtained at different thermodynamic conditions (P, T). These spectra were chosen to have almost the same τR, One can see that distribution of the relaxation times of the structural relaxation peak is invariant to different pressure and temperature conditions. Hence, in the case of IMC, as in other glass-forming liquids, the main factor controlling the shape of the structural relaxation peak is τR, or vice versa.65,66 Obviously, in the literature, one can find examples, mainly highly hydrogen bonding systems, such as glycerol,67 sorbitol,68 m-fluoroaniline,69 and the dimer of propylene glycol,70 for which there is a P-T superposition breakdown. However, in these peculiar systems, the breakdown may be related to the different population of the hydrogen bonds at different thermodynamic conditions. From analysis of the dielectric relaxation spectra obtained at isobaric and isothermal conditions (R-dispersion was fitted to the Havriliak-Negami function), structural relaxation times were determined. Next, we constructed the relaxation map

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Figure 8. Mastercurve constructed from the loss spectra obtained at different T, P conditions. All loss spectra were chosen to have almost the same τR.

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Figure 10. Dependence of the isobaric fragility estimated from eq 2 vs pressure.

Figure 11. Dependences of the glass transition temperature vs pressure. Solid lines represent the best Andersson and Andersson (eq 7) fit.

defined as a temperature at which τR ) 100 s. We used these values to plot Tg vs pressure (see Figure 10). As can be seen, the pressure coefficient of the glass transition temperature is linear only in the low pressure range, whereas at higher pressure, dTg/dP decreases. One can mention that this behavior is commonly observed for the glass-forming liquids.71 To describe the dependence of the Tg vs pressure, we used the empirical relation proposed by Andersson and Andersson.72

(

Tg ) k1 1 +

Figure 9. Structural relaxation times obtained during isobaric (upper panel) and isothermal measurements (lower panel) Solid lines are temperature VFT and its pressure counterpart fits.

depicted in Figure 9. Isobaric and isothermal dependences were fitted to the temperature VFT equation (eq 1) and its pressure counterpart, respectively. From the former fit, glass transition temperatures at pressures P ) 90, 136, and 226 MPa were calculated. It should be noted that the Tg in this case was also

)

k2 P k3

1/k2

(7)

The best fit (solid line in Figure 10) was obtained for the k1 ) 315 ( 1, k2 ) 3.14 ( 0.5, and k3 ) 1238 ( 87. By dividing k1/k3, one can estimate the value of the pressure coefficient of the glass transition temperature in the limit of low pressures limPf0 dTg/dP. It is equal to 254 K/GPa for IMC. It is a rather large value, comparable to that obtained for polymers and typical van der Waals glass-formers. In the case of hydrogen bonding systems, dTg/dP is much smaller, for example, for glycerol (40 K/GPa),73 tripropylene glycerol (37 K/GPa),74 and sorbitol 43K/ GPa.75 It is interesting that using the above classification, indomethacin can be regarded as a typical van der Waals liquid, despite the ability of this drug to form weak hydrogen bonds.

MD Study of Indomethacin From the VFT fits to temperature dependences of the structural relaxation times at different isobaric conditions, we also determined the steepness index, m (eq 2). This quantity is very often used to characterize temperature dependence, the structural relaxation time of the examined systems. One can say that it is a single parameter that provides information about how quickly the glass transition temperature is approached during cooling of the liquid. A larger value of fragility means that the deviation from the typical Arrhenius behavior is greater. In Figure 11, we plotted m vs pressure. One can see that the fragility of the IMC decreases with pressure. Taking into account the range of the applied pressures, the change of m seems rather to be significant. One can mention that similar behavior can be found for the van der Waals liquid as well as ionic liquids,76 although in the case of H-bonded systems, the opposite scenario is observed.71,77 At this point, one can remind the readers that according to Tanaka’s TOP model predictions, greater stability of the glassformer against crystallization can be reached when the degree of frustration increases. This implies that the considered liquid becomes stronger. It is consistent with what we observed in our experiments. Thus, greater stability of the IMC at high pressures can be very well explained in view of the TOP model predictions. Lest one forget, it is also consistent with the JG relaxation explanation. As a final point, we performed isobaric measurements at P ) 400 MPa over a wide range of temperatures to see the effect of pressure on the secondary relaxations in IMC. The dielectric spectra acquired during these measurements are presented in the upper panel of Figure 12. One can observe the dominant γ-relaxation peak moving to lower frequencies with decreasing temperature. Moreover, in the region of minimum between γ and R-relaxation processes, another peak emerges. This new relaxation mode was not seen in the dielectric loss spectra obtained at ambient pressure. This relaxation process becomes more separated and visible with lowering of the temperature. This suggests that the activation energy of this new secondary process is much greater than that of the γ-one. Analysis of the loss spectra presented in Figure 12 with the use of superposition of two Cole-Cole functions enabled us to determine relaxation times of the two secondary relaxations, and the results are shown in Figure 3. One can see that times of the γ-relaxation obtained from measurements carried out at P ) 400 MPa (green squares) are identical to that estimated from the loss spectra measured at ambient pressure. This is a clear indication that γ-relaxation is insensitive to pressure and is of intramolecular origin. In addition, we found that activation energy estimated for the β-relaxation process is equal to Ea ) 73 kJ/mol. Hence, one can suppose that this process is not related to the motions of a part of the IMC molecule. Thus, this relaxation can be the true JG β-relaxation already inferred from the loss spectra obtained at ambient pressure. To additionally confirm our identification of the intermolecular nature of the β-relaxation, we perform additional pressure measurements on the sample of IMC. In the lower panel of Figure 12, we compare two dielectric spectra measured in the glassy state but with different thermal-pressure history. The black one is obtained from a typical ambient pressure experiment. The sample at ambient pressure was simply cooled down to a temperature of 264 K. The red curve was obtained in the following way: The sample at T ) 310 K was initially compressed to pressure 400 MPa, then the temperature of the sample was decreased to 264 K at a constant pressure (400 MPa). Finally, when we achieved this temperature, we reduced the pressure to the ambient pressure and measured the dielectric

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Figure 12. Dielectric loss spectra obtained from (upper panel) isobaric measurements p ) 400 MPa performed at T) 372-264 K. (lower panel) Comparison of the dielectric loss spectra obtained at p ) 0.1 MPa, T ) 264 K. The first one was collected after supercooling of the melt (9). The red curve was obtained in the following way: The sample at T ) 310 K was initially compressed to pressure 400 MPa, then the temperature of the sample was decreased to -9 °C at constant pressure (400 MPa). Finally, after we achieved this temperature, pressure was reduced to the p ) 0.1 MPa.

spectrum. In this case, although T and P are the same, the densities of the samples are different. The sample is surely denser in the second case. It can be seen that the positions of the γ-relaxation peaks in the loss spectra obtained via different thermodynamic conditions are the same. It is also observed that β-relaxation becomes more separated from the γ-peak. Such a finding indicates that γ-relaxation is not sensitive to the density of the sample. The opposite behavior is observed for β-relaxation. In this case, it is obvious that the considered mode is sensitive to the density of the sample and, thus, intermolecular interactions. One can add that a similar scenario was observed in leucrose.37 In this disaccharide, slower secondary relaxation was identified as a JG relaxation coupled with twisting motions of the glucose and fructose units around a glycosidic linkage. Hence, one can suppose that the β-relaxation seen in IMC can be classified as a JG relaxation. Finally, it is worth mentioning that by application of high pressure, it was possible to obtain a glass with greater density than by standard supercooling of the melt. It is worthwhile to mention that very recently, it was shown that by compression of the crystals of the IMC up to P ) 6 GPa, the amorphous form of this drug can be obtained.78 Surprisingly, a Raman

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spectrum of the so-produced amorphous IMC differs significantly from that measured for the supercooled indomethacin. The authors of ref 78 claimed that compressing crystals of the IMC to the high pressures yields a denser amorphous form of the IMC than that which can be obtained via supercooling of the melt. Moreover, it was also shown that after decompressing of the IMC amorphous form of higher density relaxed to that of lower density (glass obtained on thermal way). Such an observation was a clear indication about the presence of two different amorphous states of the indomethacin. Such a finding reported in ref 78 is in good agreement with our observation. However, there is one difference. We did not observe transformation of the higher density glass to that of lower density at the time of our experiment. Finally, it should be stressed that in view of the current research, density may be one of the most important parameters controlling crystallization kinetics. Greater density implies lowering of the diffusion coefficient and molecular mobility, as well as changing the JG relaxation. Hence, one can speculate that more densely packed glass should be more stable against crystallization. This issue will be examined in the future. Conclusions In this paper, we presented dielectric loss spectra on IMC obtained at ambient and elevated pressures. Our data collected above the glass transition temperature at ambient pressure are in good agreement with that published in the literature. In the glassy state of the IMC, we found two secondary relaxations. The faster one was seen by others. However, we noted a difference between the activation energy of this relaxation determined by Carpentier et al. and by us. Moreover, detailed analysis of the dielectric loss spectra measured in the vicinity of the Tg enabled us to suggest the presence of a slower secondary relaxation having very low amplitude in IMC. Therefore, this mode cannot be observed as a separate peak in the loss spectra. Application of the CM predictions enabled us to identify this relaxation as a JG β-relaxation. High-pressure measurements showed that by compressing indomethacin, it is possible to suppress its crystallization very effectively. To explain this finding, we used the two order parameter model proposed by Tanaka. We have found great agreement between predictions of the TOP model and what we observed in our experiment. However, the JG relaxation mechanism cannot be excluded. We also found that dispersion of the structural relaxation peak is invariant to variations of T and P combinations, as long as the structural relaxation time is maintained constant. Moreover, high-pressure data indicated that γ- relaxation is insensitive to pressure. This confirms its local character (motions of the chlorobenzyl groups). On the other hand, a lowfrequency side of the γ- process, a new β-process, has emerged. Its activation energy was determined to be equaled to Ea ) 73 kJ/mol. Furthermore, pressure measurements revealed that this process is sensitive to the density of the sample. Consequently, it indicates that this β-process can be regarded as a true JG β-relaxation. Finally, we show that by application of the high pressure, one can obtain glass of greater density than by supercooling the liquid. It is worth pointing out that the same observation was derived from the high-pressure data obtained from Raman measurements on IMC. In the future, we will try to verify if there is a relation between density of the amorphous state and its stability against crystallization. Acknowledgment. The authors are deeply thankful for the financial support within the framework of the project entitled

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