Cryogenic Grinding of Indomethacin Polymorphs and Solvates: Assessment of Amorphous Phase Formation and Amorphous Phase Physical Stability KIERAN J. CROWLEY, GEORGE ZOGRAFI School of Pharmacy, University of Wisconsin-Madison, 777 Highland Avenue, Madison, Wisconsin 53705 Received 11 May 2001; revised 6 September 2001; accepted 11 September 2001 ABSTRACT: The effect of cryogenic grinding on ®ve crystal forms of indomethacin (IMC) was investigated with particular interest in the formation of amorphous phase. Powder X-ray diffraction (PXRD) and differential scanning calorimetry (DSC) demonstrated that amorphous phase formation took place for all three polymorphs (g, a, and d) and one solvate (IMC methanolate). In the latter case, a postgrinding drying stage was needed to remove desolvated methanol from the ground amorphous product because methanol destabilized amorphous IMC presumably via a plasticizing effect. The crystal structure of another solvate, IMC t-butanolate, was unaffected by grinding, indicating that amorphous phase formation on grinding does not occur in all cases. Ground amorphous materials possessed similar glass transition temperatures but signi®cant differences in physical stability as assessed by both isothermal and nonisothermal crystallization. It is argued that physical factors, namely residual crystal phase and speci®c surface area, determine the isothermal and nonisothermal crystallization behavior of ground amorphous samples as opposed to intrinsic differences in the structure of the amorphous phase. ß 2002 Wiley-Liss, Inc. and the American Pharmaceutical Association J Pharm Sci 91:492±507, 2002 Keywords: cryogenic grinding; polymorphs; solvates; amorphous phase; isothermal and nonisothermal crystallization INTRODUCTION Grinding is regularly used in pharmaceutical solid processing to reduce particle size. High levels of mechanical energy are used to generate suf®cient strain in solid substrate particles so as to cause crystal lattice disruption (defect formation), followed by crack formation, crack propagation, and particle fracture. Grinding is an inef®cient process in energetic terms, with the ratio of energy consumed in lattice bond breaking and crack formation versus mechanical energy input thought to be of the order of 1%.1 Large amounts of heat, sound, and vibrational energy Correspondence to: George Zogra® (Telephone: 608-2622991; Fax: 608-262-3397; E-mail: gzogra®@facstaff.wisc.edu) Journal of Pharmaceutical Sciences, Vol. 91, 492±507 (2002) ß 2002 Wiley-Liss, Inc. and the American Pharmaceutical Association 492 are also generated during grinding. The combination of grinding-induced crystal lattice disruption, also referred to in the pharmaceutical literature as process-induced disorder,2 mechanical activation,3 and the generation of excess energy can lead to additional physical and chemical changes in a crystalline solid. These include intra-and intermolecular chemical reactions, chemical complexation, polymorphic transition, and melting and amorphous phase formation,4 all of which can seriously affect the ef®cacy of a pharmaceutical solid dosage form.5 Formation of amorphous phase on grinding is the focus of this study. The term amorphous phase describes a condensed solid state without longrange three-dimensional molecular order. The amorphous state possesses greater molecular mobility compared to the more stable crystalline state, so it is often more susceptible to chemical JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 91, NO. 2, FEBRUARY 2002 CRYOGENIC GRINDING OF IMC POLYMORPHS AND SOLVATES degradation. The amorphous state can also offer pharmaceutical advantages, primarily an enhanced dissolution rate above the crystalline state. For this application, grinding provides an alternative method of preparing amorphous phase for materials that have heat or solvent sensitivities that preclude other preparation methods. Whether one is interested in amorphous phase formation on grinding from the perspective of the detrimental effect on stability or the bene®cial effect on drug dissolution, a better understanding of crystal to amorphous phase transformation is essential. Pertinent issues include: Which crystal properties determine whether transformation takes place? Under what conditions and at what rate does transformation take place? What are the properties of the amorphous phase formed and how do they compare to amorphous phase generated via other methods? The two leading theories of crystal to amorphous phase transformation have been described using the concepts of mechanical and thermodynamic destabilization.6,7 The mechanical mechanism describes how greater anharmonicity of lattice vibrations (phonons) under increased compression will eventually violate the Born stability criteria of a crystal lattice at a critical pressure, above which the lattice collapses to yield an amorphous structure.6 The thermodynamic mechanism declares that mechanical energy input continuously increases the concentration of defects in a crystal lattice to a critical limit, beyond which the amorphous phase has greater thermodynamic stability than the disordered crystal and so transformation takes place.7,8 Amorphous phase formation by mechanical energy input and by quench melting can be considered to occur by opposite routes in energetic terms, that is, energy input to the ground crystalline state and energy loss on cooling the high energy liquid state. Comparison of amorphous phases generated by mechanical energy input and those generated by quench melting have shown differences in con®gurational heat capacity,9 differences in vibrational spectra,10 and also ``memory'' effects that cause crystallization back to the original crystal phase.6 Such differences are unrelated to the rare phenomenon of polyamorphism.11 Instead, they emphasize that the amorphous state is not a tightly de®ned energetic state but can possess different dynamic and energetic properties according to the method of preparation and sample history. It is possible that amorphous phase formation on grinding can occur via a 493 quench melting mechanism if large increases in sample temperature take place. When attempting to investigate crystal to amorphous transformation on grinding, therefore, it is imperative that simultaneous melting to yield liquid phase is avoided, and so grinding must be performed at temperatures substantially below the melting temperature. The objectives of this study are to investigate cryogenic crystal to amorphous transformation in different crystal forms of indomethacin (IMC) and to establish the physical properties of the ground amorphous phase. IMC is a well-characterized glass-former with a glass transition temperature (Tg) of approximately 438C (measured for a rapidly quenched glass by thermal analysis at 108C/min).12 Previous work has shown that, below Tg, melt-quenched amorphous IMC crystallizes to the most stable g polymorph but forms the metastable a polymorph or a mixture of g and a above Tg.13±17 Crystallization of a third polymorph from supercooled IMC at 908C has been reported by Borka18 and will be classi®ed as d form in this article. The notations I, II, and IV were used for g, a, and d IMC, respectively, in the earlier study. To our knowledge, the only previous studies on IMC grinding were performed by Otsuka and coworkers.14,19 It was reported that grinding of IMC g and a polymorphs in the proximity of Tg yielded partially amorphous material but low temperature grinding yielded X-ray amorphous material. Interestingly, the starting crystal form affected the physical stability of ground amorphous material. In this study, cryogenic grinding was performed on three IMC polymorphs (g, a, and d) and two IMC solvates (methanol and t-butanol). Substrates were ground for different lengths of time and phase analysis was performed using powder X-ray diffraction (PXRD) and differential scanning calorimetry (DSC) accompanied by speci®c surface area analysis before and after grinding. The same methods were used to examine crystallization of ground Xray amorphous materials under both isothermal and nonisothermal conditions with reference to quenched IMC reference samples. EXPERIMENTAL Materials Gamma IMC obtained from Sigma (St. Louis, MO) was used without further treatment in grinding JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 91, NO. 2, FEBRUARY 2002 494 CROWLEY AND ZOGRAFI studies and also for preparation of all other crystal forms. Alpha IMC was precipitated from ethanol solution using distilled water as previously described.20 Delta IMC was prepared by desolvation of IMC methanolate under vacuum at 308C for 10 days.21 DSC analysis yielded melting temperature (Tm) and enthalpy (DHm) values of 157.98C (0.4) and 109.5 J/g (4.3) for g IMC, 151.48C (0.6) and 103.5 J/g (2.6) for a IMC, and 130.68C (0.3) for d IMC. DHm was not calculated for d IMC as immediate recrystallization took place on melting, affecting the enthalpy measurement. IMC methanolate (MeOH) and IMC t-butanolate (tBA) solvates were prepared as described by Joshi.21 Measurement of desolvation temperature (Td) and enthalpy (DHd) by DSC gave values of 82.98C (0.4) and 93.0 J/g (4.3) for MeOH and 86.18C (5.8) and 148.1 J/g (6.6) for tBA. Changes in DSC sample weight following desolvation of MeOH and tBA were 7.5% w/w (0.4) and 16.9% w/w (0.3), in good agreement with calculated solvent contents for 1:1 solvate stoichiometry (8.2 and 17.1 w/w, respectively). Meltquenched amorphous IMC was prepared by heating g IMC at approximately 1808C for 5 min and then rapidly cooling by immersion in liquid nitrogen. The amorphous product was then lightly ground using a pestle and mortar and passed through a 250 mm screen. Grinding Methodology Grinding was performed using a cryogenic impact mill (Model 6750; SPEX CertiPrep, Metuchen, NJ) consisting of a stainless steel vessel immersed in liquid nitrogen, within which a stainless steel rod is vibrated by means of a magnetic coil. Grinding of 2-g samples was performed at an impact frequency of 10 cycles per s for 2 min periods separated by 2 min cool-down periods. To assess the effect of grinding time on crystallinity, the sample vessel was removed at 6 min intervals, transferred to a glove bag purged with nitrogen gas, and allowed to warm to room temperature for sampling. When preparing amorphous IMC for investigation of isothermal and nonisothermal crystallization studies, the sample was kept in liquid nitrogen for a total grinding time of 60 min without intermittent removal of the sample vessel. Amorphous samples used in isothermal and nonisothermal crystallization studies were stored at 208C over P2O5 desiccant before analysis and the water content of each of these samples was shown to be below 0.1% w/w by Karl-Fisher JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 91, NO. 2, FEBRUARY 2002 titration (Aquastar C2000; EM Science, Cherry Hill, NJ). PXRD PXRD was used to examine changes in crystallinity and polymorphic/solvate form on grinding and on aging of ground samples. A PXRD method was sought that did not require additional sample trituration or mixing with a crystalline reference, steps that may further alter the properties of the processed sample. The equipment found to be most suited to this application was the General Area Detector Diffraction System (Siemens, Madison, WI). This equipment comprises a twodimensional detector that measures the entire cone of diffracted X-rays, providing diffraction data of reproducible peak intensity unaffected by preferred orientation, allowing more accurate and precise measurement of percentage crystal phase. Sample was gently packed into a glass capillary (2 mm i.d.; Charles Supper, Natick, MA), positioned in the X-ray beam path, and rotated through 3608 during the 5 min diffraction data collection. For quantitative measurement of crystal phase, calibration curves were constructed using duplicate PXRD measurements for physical mixtures of crystalline and amorphous IMC. Gamma and a IMC samples described in the Materials section were taken to be 100% crystalline based on the agreement of Tm and DHm data for both polymorphs with literature values.15,18,20 Raw data for g/amorphous IMC physical mixtures are given in Figure 1. The diffraction peak at 11.88 2y could be detected in mixtures containing as low as 2% crystal phase and so this peak was chosen for quantitative analysis of g IMC. The capability of detecting low levels of crystal phase arises from low detector noise and was of particular value for investigating the effects of grinding on IMC crystallinity. Although diffraction peak resolution was much lower than that of a conventional Bragg-Brentano powder diffraction apparatus, differences between diffraction patterns were suf®cient to permit identi®cation of all crystal forms of IMC used in this study. Diffraction peaks at 8.6, 9.8, 7.2, and 12.18 2y were used to quantify a, d, MeOH, and tBA, respectively, using peak height values corrected for the diffuse diffraction of the amorphous component. Calibration curves for g/amorphous IMC and a/amorphous IMC physical mixtures are shown in Figure 2. Isothermal crystallization studies were performed at 308C and approximately 0% relative humidity (RH) in CRYOGENIC GRINDING OF IMC POLYMORPHS AND SOLVATES 495 Figure 2. PXRD calibration plots of corrected peak height against percentage crystal phase for g/quenched amorphous and a/quenched amorphous physical mixtures. Figure 1. PXRD analysis of g/quenched amorphous IMC physical mixtures. temperature of the crystallization exotherm (Tp) was also recorded to permit kinetic analysis of the nonisothermal crystallization process. DSC numerical data reported in this article are the average of three measurements (with standard deviation in parentheses) and were obtained at a heating rate of 108C/min. Measurement of Speci®c Surface Area evacuated glass desiccators containing P2O5. Duplicate PXRD measurements were made at each time point. DSC DSC was performed using a Seiko SSC220C instrument (Haake, Paramus, NJ). Four- to sixmg samples were crimped in Seiko Al pans (SSCE030) with lids in a glove bag purged with nitrogen gas and accurately weighed. Pan lids were pierced for analysis of unground and ground solvate samples. DSC measurements were carried out from 10 to 1908C at heating rates of 5, 10, 20, and 308C/min with a nitrogen purge gas ¯ow rate of 100 mL/min. Temperature and enthalpy calibration was carried out at each heating rate using high purity indium and gallium (Aldrich, Milwaukee, WI). Tg was measured using the extrapolated onset temperature of the glass transition region. The extrapolated onset temperature was used to calculate Tc (crystallization temperature), Td, and Tm values. The peak Speci®c surface area measurements were made with the Quantasorb apparatus (Quantachrome, Boynton Beach, FL) using nitrogen adsorbate unless otherwise stated. Accurately weighed samples were degassed under a nitrogen purge for a minimum of 12 h at a temperature below 08C to avoid crystallization of amorphous sample. Monolayer desorption data were collected in triplicate for each sample. For samples with low speci®c surface area (< 1 m2/g), a modi®ed sample holder with a narrow bore diameter was used in order to minimize thermal diffusion effects. PXRD analysis was used to ensure that no crystallization had taken place during degassing and speci®c surface area measurement of each amorphous sample. RESULTS Effect of Grinding on c, a, and d IMC Polymorphs PXRD data for g, a, and d IMC following different grinding times are given in Figure 3a±c. A rapid JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 91, NO. 2, FEBRUARY 2002 496 CROWLEY AND ZOGRAFI Figure 3. PXRD analysis of IMC polymorphs and solvates following different grinding times: (a) g polymorph (b) a polymorph (c) d polymorph (d) methanol solvate (MeOH) (e) t-butanol solvate (tBA). PXRD for a 2/1 physical mixture of g/a IMC has been included in (d) to assist identi®cation of the phase composition following 60 min grinding. decrease in diffraction peak intensities was observed for all three IMC polymorphs during the ®rst 30 min of grinding. In each case, there was no detectable crystal phase present after 60 min, so all materials were classi®ed as X-ray amorphous. There was no evidence of polymorphic changes during g, a, or d IMC grinding, indicating direct crystal to amorphous phase transformation. Crystallinity reduction took place at comparable rates for each crystal form. The changes in speci®c surface area following 60 min grinding of g, a, and d IMC are given in Table 1. Grinding produced large increases in speci®c surface area for g JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 91, NO. 2, FEBRUARY 2002 and a IMC, but, surprisingly, a moderate decrease in speci®c surface area for d IMC. Figure 4a±c contains DSC heating data for g, a, and d IMC measured following varying grinding times. For each polymorph, formation of amorphous phase on grinding was con®rmed by the presence of a glass transition event in the temperature range of 39 to 458C, which was accompanied by an exothermic crystallization event between Tg and the melting region. As the quantity of amorphous phase increased on extended grinding, the enthalpy of crystallization (DHc) became larger, as re¯ected in the exotherm CRYOGENIC GRINDING OF IMC POLYMORPHS AND SOLVATES 497 Table 1. The Effect of 60 min Grinding on the Speci®c Surface Area and Phase Properties (Identi®ed by PXRD) of g, a, and d IMC, MeOH, tBA, and Quenched IMC Material Speci®c Surface Area Pregrinding [m2/g] Speci®c Surface Area Postgrinding [m2/g] g a d MeOH 0.38 (0.02)a 4.22 (0.15) 2.69 (0.01) 2.20 (0.30) TBA 0.17 (< 0.01)b 1.13 (0.14) Quenched/6 min ground 0.35 (< 0.01) 1.74 (0.02) Quenched/60 min ground 0.35 (< 0.01) 2.02 (0.03) 6.69 (0.09) 12.36 (0.86) 1.71 (0.05) 5.23 (0.11) Phase Properties Postgrinding X-ray amorphous X-ray amorphous X-ray amorphous X-ray amorphous if drying stage is followed by grinding No change (tBA intact even with drying stage) No change (remains X-ray amorphous) No change (remains X-ray amorphous) Standard deviation values are given in parentheses. a The speci®c surface area of g IMC measured using krypton sorption was 0.35 0.01 m2/g, con®rming that nitrogen adsorption data yield reasonably accurate data for samples with low speci®c surface area. b Measurement made using krypton adsorption. magnitude. For g and a, the peak temperature of nonisothermal crystallization (Tp) also rose on grinding by 10 to 158C (Figure 4a±b). DSC analysis of ground d IMC samples no longer identi®ed a d IMC melting event but two exothermic events following 12 and 30 min grinding that exhibited contrasting temperature relationships (Figure 4c). Increased grinding time caused a rise in the ®rst exotherm transition temperature but a fall in the second exotherm transition temperature. Most likely, the ®rst exotherm represented crystallization of amorphous phase and so exhibited a relationship with grinding time comparable to that observed for g and a substrates. The second exotherm was probably a phase transformation from d to the more stable g polymorph that took place before the d melting temperature was reached. Effect of Grinding on IMC Solvates The effects of grinding on solvate crystal structure and speci®c surface area are shown in Figure 3d±e and Table 1, respectively. Grinding of MeOH and tBA solvates did not produce X-ray amorphous phase. In the case of MeOH, signi®cant changes in PXRD data were apparent. A reduction in MeOH diffraction peak intensity took place after 12 min grinding. The diffraction peak at 7.28 2y, unique to MeOH, was almost absent by 30 min with g IMC the principal phase. Following 60 min grinding, a mixture of g and a IMC was present, with only a trace amount of MeOH remaining. For con®rmation of the phase composition at 60 min, a PXRD pattern of a 2/1 g/a physical mixture has been included in Figure 3d with diffraction peaks at 11.88 2y (g) and 8.68 2y (a) prominent. Changes in the nonisothermal desolvation behavior of ground MeOH were identi®ed by DSC analysis (Figure 4d). Grinding caused reduction in both Td and DHd in agreement with the loss of MeOH shown by PXRD. The d melting endotherm was no longer evident in ground MeOH samples, a change also seen with pure d IMC in Figure 4c. A small ``desolvation'' endotherm (now thought to be a desorption phenomenon) remained after 30 and 60 min grinding even though MeOH was undetected by PXRD and detectable weight loss was noted on DSC analysis. These observations indicated that desolvated methanol was still present in the sample. The effect of desolvated methanol on the outcome of cryogenic grinding was considered. With a melting temperature of 988C, methanol may be present either as a solid or liquid during grinding depending on the ability of the cryogenic mill to maintain low temperature. IMC may dissolve liquid methanol from which crystallization of IMC polymorphs could occur. With a Tg of 1708C,22 methanol could act as a potent plasticizer of any amorphous IMC formed during grinding. Plasticization could lower the Tg of IMC to below room temperature, resulting in rapid JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 91, NO. 2, FEBRUARY 2002 498 CROWLEY AND ZOGRAFI Figure 4. DSC analysis of IMC polymorphs and solvates following different grinding times: (a) g polymorph (b) a polymorph (c) d polymorph (d) methanol solvate (MeOH) (e) t-butanol solvate (tBA). JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 91, NO. 2, FEBRUARY 2002 CRYOGENIC GRINDING OF IMC POLYMORPHS AND SOLVATES crystallization from the amorphous state before PXRD and DSC analysis. The 8.2% w/w concentration of methanol in MeOH is low but signi®cant as the plasticizing effect is greatest at low solvent levels,23 and solvent will probably concentrate in amorphous regions of the partially ground sample. The formation of a IMC at longer grinding times gave a strong indication that phase changes took place above Tg, as the metastable a form is known to crystallize only above Tg unless a seeds are present.13 The Couchman-Karasz Equation (a modi®cation of the Gordon-Taylor Equation) can be used to estimate Tg of an ideal mixture of two components 1 and 224: Tg12 w1 Tg1 K w2 Tg2 w1 K w2 1 where w is weight fraction of each component and K DCp1/DCp2 (DCp represents the heat capacity change at Tg). Using Tg and DCp values of 458C and 0.41 J/g/8C for IMC, respectively,25 and 1708C and 0.81 J/g/8C for methanol, respectively,22 predicted Tg of an 8.2% w/w methanol in IMC mixture was 138C. A modi®ed grinding experiment was performed to establish if less stable amorphous phase was formed on cryogenic grinding of MeOH. MeOH was ground for 60 min using the same protocol as before except that sample was not brought to room temperature for intermittent analysis. Following 60 min grinding, sample was transferred directly to a freeze dryer precooled to 408C (Dura-Stop; FTS Systems, Stone Ridge, NY). This temperature should have been substantially below Tg of plasticized systems of 8.2% w/w methanol in IMC, even allowing for nonideal mixing. Ground samples were subjected to 24 h drying under vacuum at 50 mTorr. PXRD analysis of ground and dried MeOH identi®ed an X-ray amorphous product and a Tg value of 39.58C was measured by DSC analysis. No measurable weight loss was recorded following DSC analysis, con®rming that the drying step had been successful. The modi®ed grinding experiment con®rms that cryogenic grinding of MeOH formed an amorphous phase containing residual solvent that required solvent removal under high vacuum to yield an amorphous phase stable at room temperature. Grinding of tBA did not cause signi®cant changes in PXRD patterns (Figure 3e), suggesting that the solvate crystal structure remained intact throughout 60 min of processing. DSC analysis of 499 ground tBA identi®ed a reduction in both temperature and enthalpy of desolvation at an early grinding time (Figure 4e), but additional grinding did not cause further changes in desolvation behavior. The change in DSC nonisothermal desolvation behavior on initial grinding was probably due to particle size decrease that altered the rate and/or mechanism of desolvation.26 Thus, DSC analysis con®rmed that the tBA solvate lattice remained intact following grinding. The possibility that cryogenic grinding produced a less stable amorphous phase that immediately recrystallized prior to PXRD and DSC analysis must be considered. t-Butanol Tg and DCp values could not be found in the literature so eq. 1 could not be used to estimate the Tg of a t-butanol/IMC mixture. A crude estimate of t-butanol Tg can be made using its Tm of 299 K (268C) and the general rule that Tg/ Tm 0.7 for small organic glass-formers.27 Tg is predicted to be in the region of 209 K ( 648C), indicating that t-butanol could also plasticize IMC but to a lesser extent than methanol. tBA was also subjected to a two stage process of cryogenic grinding (without intermittent temperature increase) and vacuum drying identical to the process used to produce X-ray amorphous MeOH. In the case of tBA, combined grinding and drying failed to produce an amorphous phase, with tBA solvate found to be intact as shown by both PXRD and DSC. tBA appeared to resist desolvation or crystal to amorphous phase transformation on cryogenic grinding. Isothermal and Nonisothermal Crystallization Behavior of Ground Amorphous IMC The isothermal and nonisothermal crystallization behaviors of 60 min ground amorphous g, a, and d IMC polymorphs (abbreviated GA-g, -a, and -d) and 60 min ground and dried amorphous MeOH (abbreviated GDA-MeOH) are now presented. Crystallization was also investigated in two meltquenched amorphous IMC samples for reference purposes. The ®rst reference sample was prepared by grinding < 250 mm melt-quenched amorphous IMC for 60 min, providing a material with speci®c surface area and mechanical energy input that was comparable to ground amorphous materials. It was noted that the greatest changes in speci®c surface area took place during the early stages of grinding. Thus, it was possible to prepare a second reference sample with comparable speci®c surface area to all other ground materials following a much shorter grinding time and so JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 91, NO. 2, FEBRUARY 2002 500 CROWLEY AND ZOGRAFI having experienced much lower mechanical energy input. Six minute grinding of < 250 mm melt-quenched amorphous IMC achieved this objective, as seen by the similar speci®c surface areas for both reference samples (Table 1). The term ``quenched/ground'' is used to describe the reference samples. Isothermal crystallization of X-ray amorphous IMC samples was studied at 308C and 0% RH, conditions that are known to yield the g crystal form from melt-quenched amorphous IMC13,14 unless crystal seeds are present.15 Figure 5a±c contains plots of percent crystal phase versus time. Samples displayed in Figure 5a all crystallized to the g polymorph (GA-g, -d, and quenched/ ground reference samples) and percent crystal phase at the ®nal time points was greater than 90% w/w in each case. Quenched/ground reference samples that were subjected to different grinding times of 6 and 60 min exhibited comparable crystallization rates, reaching 90% w/w crystallinity following approximately 45±50 h. GA-g and GA-d samples both crystallized at faster rates relative to the quenched/ground IMC references, crystallizing to 90% w/w g IMC after approximately 13±15 h. Solid lines calculated by nonlinear regression analysis are shown for each data set, the details of which are described in the Discussion section. In Figure 5b, GA-a crystallization produced both g and a polymorphs. Only a IMC crystallization was identi®ed at early time points (0±11 h) after which time its rate of formation decreased. Gamma IMC was ®rst identi®ed at 11 h and crystallized to a value of 38% w/w after 100 h, by which time crystallization of both a and g appeared to have slowed greatly. At 100 h, the concentration of a IMC was measured at 23% w/ w, therefore the total percent crystal phase was in the region of 60% w/w. PXRD analysis following 2 months aging identi®ed minor changes in the levels of a (18% w/w) and g (48% w/w), demonstrating that a signi®cant portion of amorphous phase present in GA-a resisted crystallization over extended time periods. These ®ndings are consistent with crystallization data for GA-a previously reported.14 Crystallization from GDAMeOH also produced a mixture of g and a (Figure 5c). The rate of g formation was much greater than that observed for GA-a, although it was again found that a portion of amorphous GDA-MeOH did not crystallize after 100 h, with concentrations of g and a leveled off at values of 83% w/w and 2% w/w, respectively. Thus, samples JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 91, NO. 2, FEBRUARY 2002 Figure 5. Isothermal crystallization of ground amorphous IMC samples at 308C and 0% RH. (a) Quenched/ ground for 6 min, quenched/ground for 60 min, GA-g and GA-d. (b) GA-a: ^ crystallizing to g polymorph; } crystallizing to a polymorph. (c) GDA-MeOH: ^ crystallizing to g polymorph; } crystallizing to a polymorph. Solid lines represent KJMA kinetics (®t to eq. 2). CRYOGENIC GRINDING OF IMC POLYMORPHS AND SOLVATES 501 DISCUSSION that crystallized to produce a mixture of polymorphs both possessed a quantity of amorphous phase that resisted crystallization during the time scale of this investigation. Nonisothermal crystallization data (Tc, Tp, and DHc values) measured by DSC analysis for ground and quenched/ground amorphous materials are reported in Table 2 along with Tg values. Differences in nonisothermal crystallization behavior were evident with Tp values for ground amorphous materials (GA-g, -a, and -d and GDAMeOH) equal to or less than the quenched/ground references. A direct correlation between Tp and speci®c surface area was evident. On grinding, it was found that Tp varied as the ratio of crystalline to amorphous phase changed (Figure 4a±c). Amorphous samples undergoing isothermal crystallization below Tg will also contain different ratios of crystalline and amorphous phase. To see if Tp was altered in partially crystalline sample formed on isothermal crystallization, DSC analysis was performed on GA-a following different aging times at 308C and 0% RH. DSC data presented in Figure 6 show an expected decrease in DHc as isothermal crystallization proceeded, but there was little variation in Tp. Comparing Figures 4b and 6 demonstrates that the nonisothermal crystallization behavior of partially crystalline samples varies according to how the partially crystalline sample was prepared: by generating amorphous phase in a crystal substrate on grinding or by isothermal crystallization of an amorphous substrate. Otsuka et al.19 ®rst demonstrated that low temperature grinding of g and a IMC produced Xray amorphous material. The current work extends the earlier ®ndings in reporting that d IMC and the methanol solvate MeOH are also rendered X-ray amorphous by such treatment, although ground solvate requires additional lowtemperature vacuum drying to stabilize the amorphous phase. An increase in speci®c surface area accompanies crystal to amorphous phase transformation for most materials following 60 min grinding, with the exception of d IMC (see Table 1). It is assumed that these increases in speci®c surface area are brought about by reduction in particle size. The surprising decrease in speci®c surface area seen on d IMC grinding was dif®cult to explain. Delta IMC was prepared by isothermal desolvation of a solvate while all other crystal substrates (g and a IMC, MeOH and tBA) were prepared by crystallization from solution. We speculate that d IMC prepared by desolvation may possess more coarse crystal surfaces compared to those harvested from solution, a property that could counter the effect of particle size reduction on speci®c surface area and produce an overall decrease in this parameter. Alternatively, d IMC crystals prepared by desolvation may exhibit different fracture behavior on grinding. Another explanation is that the presence of low levels of residual methanol in the d IMC sample interfered with the N2 gas desorption signal and affected the accuracy of speci®c surface area calculation. Table 2. DSC Analysis of 60 min Ground IMC and Quenched/Ground IMC References (6 and 60 min Grinding): Tg and Nonisothermal Crystallization Behavior (Tc, Tp and DHc). Speci®c Surface Areas of Ground Materials are Also Listed Material Quenched/6 min ground Quenched/60 min ground GA-g GA-a GA-d GDA-MeOH Crystallized Phase Surface Area Postgrinding [m2/g] Tg [8C] Tc [8C] 44.3 (0.1) 87.3 (0.1) 94.0 (0) 68.1 (2.7) a 1.74 43.1 (0.4) 84.8 (0.1) 90.8 (0.1) 72.4 (0.3) a 2.02 41.8 41.0 41.1 39.5 68.5 (0.1) 67.6 (0.4) 84.7 (0) 72.2 (0.5) 77.6 73.1 90.8 78.4 46.5 45.8 74.2 49.7 a a a a 6.69 12.36 1.71 5.23 (0.6) (0.1) (0.9) (0.3) Tp [8C] (0.1) (0.1) (0.1) (0) DHc [J/g] (3.0) (3.2) (0.1) (0.6) Standard deviation values are given in parentheses. JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 91, NO. 2, FEBRUARY 2002 502 CROWLEY AND ZOGRAFI Figure 6. DSC analysis of GA-a following isothermal aging at 308C and 0% RH. Only the temperature region 20±1008C is shown to facilitate visualization of Tg and Tp. The differing behavior of MeOH and tBA solvates on grinding is of particular interest. Grinding of MeOH causes desolvation and formation of a mixture of IMC polymorphs. Grinding followed by drying of MeOH leads to amorphous phase formation. In contrast, no phase changes are observed on tBA grinding or following the twostage grinding and drying process. Solvate lattice properties are likely to be a factor in determining susceptibility to amorphous phase formation on grinding. Previous work has demonstrated that MeOH and tBA exhibit different rates and mechanisms of isothermal desolvation.21 Optical microscopy demonstrated anisotropic desolvation of MeOH but not tBA that points to the presence of distinct solvent channels in the crystal structure of MeOH but not tBA. The more ready desolvation of MeOH under isothermal conditions and ease of crystal structure collapse on grinding may be related. Once amorphous phase is generated on grinding, different solvents will exert different plasticizing effects based on the solvent Tg and miscibility of JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 91, NO. 2, FEBRUARY 2002 the two amorphous components. The large differences in Tg and size of methanol and t-butanol molecules could also contribute to the different behavior of MeOH and tBA on grinding and on grinding/drying. Interestingly, 60 min grinding produces a large increase in tBA speci®c surface area from 0.17 to 1.13 m2/g, presumably due to particle size reduction. Changes in DSC desolvation temperature are in agreement with such particle size decrease. It is anticipated that grinding of tBA leads to formation of defects prior to crack formation, propagation, and particle fracture, in which case defect formation in tBA is not accompanied by amorphous phase formation. Such behavior can be explained using either the thermodynamic or mechanical destabilization mechanisms of crystal to amorphous phase transformation. In terms of the thermodynamic mechanism, grinding produces some lattice disorder but the critical concentration of defects is not reached. In terms of the mechanical mechanism, the mechanical energy generated on grinding does not exceed the lattice stability limit. As both CRYOGENIC GRINDING OF IMC POLYMORPHS AND SOLVATES transformation theories can be used to explain these ®ndings, identi®cation of the most applicable mechanism of amorphous to crystal phase transformation is not possible. Sixty minute ground amorphous IMC samples (GA-g, -a, and -d and GDA-MeOH) possess Tg values ranging from 39.5 to 41.88C, slightly below the Tg values for the reference quenched/ground samples of 43.1 and 44.38C. These small differences can be explained by differing enthalpy relaxation behavior at the glass transition that affects Tg calculation, indicating variation in amorphous phase energetics according to processing history but not inherent structural differences. Despite similar Tg values, isothermal stability of ground amorphous materials differs both in terms of polymorph selection and rate of crystallization. Crystallization kinetics are often described using the Kolmogorov-Johnson-MehlAvrami (KJMA) Equation:28 x 1 exp k t t o n 2 where x represents the fraction crystallized following time t and induction time to, yielding a rate constant k and exponent n that re¯ects the dimension of transformation. KJMA crystallization rate constants were calculated using nonlinear regression analysis (SigmaPlot 5TM) for samples that crystallized to a single polymorph, namely, quenched/ground references GA-g and GA-d. KJMA k and n values and R2 regression coef®cients are reported in Table 3 solid lines in Figure 5a represent calculated KJMA kinetic pro®les. In all cases, crystal phase is present by the ®rst time point and so to is zero. KJMA crystallization rate constants of 503 3.3 10 2 h 1 and 3.1 10 2 h 1 were calculated for 6 and 60 min quench/ground reference samples, respectively, and 1.62 10 1 h 1 and 1.00 10 1 h 1 for GA-g and GA-d, respectively. Values of n fall between 1.0 and 2.7, a range that is lower than predicted for classic nucleation mechanisms (n 4 for continuous nucleation, n 3 for nucleation from a ®xed number of nuclei or via a site-saturated mechanism).28 Considering both the wide range of n and the absence of a trend linking GA-g and GA-d samples and/or quenched/ ground reference samples, mechanistic interpretation of KJMA n is not possible. KJMA n calculated for amorphous state crystallization is often reduced relative to the predicted value, suggesting deviation from KJMA theory, which demands that nucleation is random and that nucleation and growth rate constants do not change during the isothermal crystallization process.29 Nonrandom nucleation (due to chemical impurities, residual crystal phase, or mechanical strains) or the changing energy difference between amorphous and crystalline phases (due to enthalpic relaxation of amorphous phase) may have contributed to the apparent deviation from KJMA kinetics. Consequently, eq. 2 is utilized solely for calculation of a crystallization rate constant in this work. An effect of speci®c surface area on isothermal crystallization below Tg is known for meltquenched amorphous IMC.15,17 Previous crystallization studies performed at 308C and 0% RH show that the larger surface area of a triturated sample screened to < 250 mm gives a KJMA rate constant of 3.7 10 3 h 1 (KJMA n 1.2), an order of magnitude above 2.9 10 4 h 1 (KJMA n 2.8) for an undisturbed ®lm. KJMA rate constants for the quenched/ground reference Table 3. KJMA Analysis of Isothermal Crystallization Data Measured at 308C and 0% RH for 60 Min Ground Amorphous IMC and Quenched/Ground IMC References (6 and 60 Min Grinding). Speci®c Surface Area Data for Amorphous Samples are Also Shown Material Quenched/6 min ground Quenched/60 min ground GA-g GA-a GA-d GDA-MeOH Crystallized Phase KJMA k KJMA n KJMA R2 Surface Area Postgrinding [m2/g] g 0.033 1.7 0.990 1.74 g 0.031 2.0 0.996 2.02 g a and g g a and g 0.162 n.a. 0.100 n.a. 1.0 n.a. 2.7 n.a. 0.971 n.a. 0.993 n.a. 6.69 12.36 1.71 5.23 n.a., not applicable due to g and a cocrystallization. JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 91, NO. 2, FEBRUARY 2002 504 CROWLEY AND ZOGRAFI samples reported in this work are in agreement with the earlier studies, with further reduction in particle size causing further increase in k. These results are to be expected as IMC crystallization at 308C and 0% RH is known to occur via surface nucleation.16 Different grinding times of 6 and 60 min have little effect on KJMA k for quenched/ ground reference samples, demonstrating that the lengthy grinding process does not introduce chemical impurities or create high energy surfaces that affect the site or rate of nucleation in ground amorphous IMC. Differences in speci®c surface area failed to explain the differences in crystallization rates between ground amorphous and quenched/ ground reference samples. There is a threefold difference in KJMA k between GA-d and both reference samples despite comparable speci®c surface areas (1.71 vs. 1.74±2.02 m2/g). One possible explanation is that small quantities of crystal phase are present in the ground amorphous samples below the limit of detection of PXRD. Such residual crystal phase can provide secondary nuclei for the growth of the same polymorphic form or heterogeneous nuclei for the growth of a different polymorph. We hypothesize that formation of g IMC on isothermal crystallization of GA-g occurs via secondary nucleation of undetected g phase. In the case of GA-d, residual d IMC acts as an heterogeneous nucleating agent of g. Alternatively, residual d IMC undergoes a polymorphic change to g and thus also affects crystallization by secondary nucleation. It was not possible to prove the presence of such residual crystal phase as we know of no technique capable of identifying less than 2% w/w crystal phase in amorphous phase. Microscopic examination using cross-polarized light failed to identify crystal phase although this method was limited by the small particle size and agglomerated nature of ground amorphous samples, which reduced the intensity of transmitted light. KJMA k values were not calculated for GA-a or GDA-MeOH as these samples form a mixture of polymorphs on crystallization and so neither polymorph approaches x & 1. Visual inspection of Figure 5a±c suggests that GA-a has the slowest overall rate of crystallization among the samples studied despite possessing the largest speci®c surface area. The formation of a IMC at early time points followed by g crystallization can again be explained by the presence of undetected crystal phase. In this instance, residual a IMC in GA-a appears to cause secondary nucleation of a to JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 91, NO. 2, FEBRUARY 2002 detectable levels. The formation of a delays the onset of g crystallization and also reduces its rate of crystallization, suggesting that the mechanism of g crystallization has changed. Bulk nucleation of g has been observed below Tg in quenched amorphous IMC but at lower rates compared to surface nucleation.16 It is possible that a formation reduces or prevents surface nucleation and so crystallization of g can only occur via the slower bulk mechanism. If true, we have an interesting scenario whereby the seeded system exhibits greater stability than the nonseeded system due to redirection of the route of crystallization. Isothermal crystallization of GA-a does not form a completely crystalline sample even following 2 month storage at 308C and 0% RH. The fact that a portion of amorphous phase fails to crystallize in this sample is con®rmed by DSC analysis after 2 months aging, recording a Tg of 51.68C. The increase in Tg from 41.0 to 51.68C (a trend also apparent in Figure 6) represents enthalpic relaxation of amorphous IMC to a lower energy state. The decreased energy difference between amorphous and crystalline states that drives crystallization would be expected to reduce the crystallization rate but not to the extent that remaining amorphous phase is stabilized. It is known that amorphous IMC contains a wide distribution of relaxation times30 that are thought to arise from heterogeneous dynamic behavior. Such dynamics imply the presence of nanoscale domains exhibiting different levels of molecular motion.31 Crystallization from a heterogeneous amorphous IMC phase could be favored in regions where molecular mobility is greater, leaving uncrystallized phase with lower molecular mobility and so greater physical stability. The longer relaxation times of the remaining amorphous phase would produce a higher Tg. An alternative explanation for the stabilization of residual amorphous phase in GA-a is that the cocrystallized mixture of g and a generates elastic strains at amorphous/crystal interfaces that alter the interfacial energies and impede further crystallization.32 DSC analysis of amorphous materials provides important information regarding glass structure (via glass transition behavior) and glass stability (via nonisothermal crystallization behavior). Tp represents the temperature at which a known percentage of transformation has taken place (approximately 63%)33,34 and so can be used to assess nonisothermal stability provided a constant heating rate is used. DSC data for ground CRYOGENIC GRINDING OF IMC POLYMORPHS AND SOLVATES amorphous IMC samples given in Table 2 show variation in Tp that directly correlates with speci®c surface area. Samples with a larger speci®c surface area have a lower Tp so they are less stable. This relationship is the same as that seen for quenched amorphous IMC under isothermal conditions but not for ground amorphous samples. The factor that overrides the effect of speci®c surface area on isothermal crystallization of ground amorphous samples (thought to be residual crystal phase) has no effect on the rate of nonisothermal crystallization. One reason for this could be that different IMC polymorphs crystallize above and below Tg (g < Tg > a).13±16 Crystallization of g, which has been shown to occur via both surface and bulk nucleation below Tg, may be more readily in¯uenced by residual crystal phase than a crystallization above Tg (for which only surface nucleation has been observed).16 It was not possible to identify the polymorphic form that crystallizes under nonisothermal conditions from single DSC heating analyses because further phase transformations took place between Tp and Tm resulting in mixtures of a and g detected in the melting region. Changes in heating rate do not overcome this problem so it is not possible to interpret nonisothermal crystallization behavior from nonisothermal melting behavior. Additional DSC experiments were performed using open pans with the intention of isolating the crystallized phase, adjusting the temperature program so that the heating ramp was terminated at a temperature between 5 and 108C above Tp (close to the crystallization offset temperature) followed by rapid cooling to room temperature at 408C/min. The solid product of nonisothermal crystallization was shown to be a IMC for each ground amorphous and quenched/ground reference sample. Therefore, the polymorph formed under nonisothermal conditions also appears to be insensitive to the property of ground amorphous IMC that affects isothermal crystallization. DSC measurements presented in Figure 6 were carried out at different time points during the isothermal crystallization of GA-a, so they comprise mixtures of amorphous and crystalline phase. Both Tp and the shape of crystallization exotherms were unaffected by increasing isothermal aging time, a variable that increases the quantity of crystalline phase in the starting sample. It is interesting to compare this ®nding to the DSC data obtained at different grinding times as these samples are also mixtures of crystal and 505 amorphous phase but are generated by a different route, namely, generating amorphous phase in a crystalline sample. Increasing grinding time causes a rise in Tp despite the fact that speci®c surface area is also increasing on grinding (Figure 4a±c). These data indicate that partially crystalline mixtures formed by grinding have reduced nonisothermal stability compared to partially crystalline samples formed on aging. The possible explanations for the reduced nonisothermal stability of partially crystalline samples generated by grinding are numerous, including differences in crystal size, shape, and surface properties, or lattice defect concentration that promotes seeding effects or varying degrees of relaxation of the amorphous component. Traditionally, prediction of the behavior of low levels of amorphous phase in intimate contact with crystal phase is based upon the properties of an X-ray amorphous material often prepared by a method other than grinding. DSC data presented in this work demonstrate that such approaches may be inappropriate as the behavior of small quantities of amorphous phase created by grinding differs from the behavior of X-ray amorphous phase prepared by grinding or other methods. CONCLUSIONS We have demonstrated that three polymorphs of IMC and IMC methanolate can be made X-ray amorphous by cryogenic grinding. Solvent removal under vacuum was required to stabilize GDA-MeOH, probably by increasing the Tg of amorphous IMC plasticized by residual methanol. The solvate structure of IMC tBA remained intact on grinding and also on grinding followed by vacuum drying, demonstrating that crystal-amorphous transition on grinding does not readily occur for all crystal forms of a drug molecule. Properties of both the solvate lattice and solvent are likely to determine solvate susceptibility to amorphous phase formation on grinding. Comparison of X-ray amorphous IMC samples prepared by crystal grinding and quenched/ground references demonstrated comparable Tg values and thus comparable amorphous phase structure. Undetected crystal structure was thought to determine the isothermal crystallization behavior of ground amorphous samples below Tg, in most cases enhancing crystallization rates compared to quenched/ground reference samples via a seeding JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 91, NO. 2, FEBRUARY 2002 506 CROWLEY AND ZOGRAFI effect. Such an effect was not evident under nonisothermal conditions, with peak nonisothermal crystallization temperature correlating with speci®c surface area. It is concluded that variation in the physical stability of amorphous IMC generated by grinding and by quench melting is not indicative of different amorphous phase structure but instead re¯ects the sensitivity of the nucleation step to other factors, primarily residual crystal structure and speci®c surface area. ACKNOWLEDGMENTS The Purdue-Wisconsin Program on the Physical and Chemical Stability of Pharmaceutical Solids is gratefully acknowledged for ®nancial support. Professor Juan DePablo, Department of Chemical Engineering, UW-Madison, and group members are thanked for access to PXRD equipment. REFERENCES 1. Parrott EL. 1990. Comminution. In: Swarbrick J, Boylan JC, editors. Encyclopedia of Pharmaceutical Technology. New York: Marcel Dekker, pp. 101±121. 2. York P. 1983. Solid-State Properties of Powders in the Formulation and Processing of Solid Dosage Forms. Int J Pharm 14:1±28. 3. Huttenrauch R, Fricke S, Zielke P. 1985. Mechanical Activation of Pharmaceutical Systems. Pharm Res 2:302±306. 4. Shakhtshneider TP, Boldyrev VV. 1999. Mechanochemical Synthesis and Mechanical Activation of Drugs. In: Boldyreva E, Boldyrev V, editors. Reactivity of Molecular Solids. Chichester, U.K.: Wiley, p. 271±311. 5. Byrn SR, Pfeiffer RR, Stowell JG. 1999. Solid State Chemistry of Drugs. West Lafayette: SSCI, Inc. 6. Tse JS. 1992. Mechanical Instability in Ice Ih. A Mechanism for Pressure-Induced Amorphization. J Chem Phys 96:5482±5487. 7. Johnson WL, Li M, Krill CE. 1993. The Crystal to Glass Transformation in Relation to Melting. J Non-Cryst Solids 156±158:481±492. 8. Fecht HJ. 1992. Defect-Induced Melting and SolidState Amorphization. Nature 356:133±135. 9. Tsukushi I, Yamamure O, Suga H. 1994. Heat Capacities and Glass Transitions of Ground Amorphous Solid and Liquid-Quenched Glass of tri-Omethyl-b-cyclodextrin. J Non-Cryst Solids 175: 187±194. 10. Fan GJ, Guo FQ, Hu ZQ, Quan MX, Lu K. 1997. Amorphization of Selenium Induced by HighEnergy Ball Milling. Phys Rev B 55:11010±11013. JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 91, NO. 2, FEBRUARY 2002 11. Ha A, Cohen I, Zhao X, Lee M, Kivelson D. 1996. Supercooled Liquids and Polyamorphism. J Phys Chem 100:1±4. 12. Fukuoka E, Makita M, Yamamura S. 1986. Some Physicochemical Properties of Glassy Indomethacin. Chem Pharm Bull 34:4314±4321. 13. Imaizumi H, Nambu N, Nagai T. 1980. Stability and Several Physical Properties of Amorphous and Crystalline Forms of Indomethacin. Chem Pharm Bull 28:2565±2569. 14. Otsuka M, Kaneniwa N. 1988. A Kinetic Study of the Crystallization Process of Noncrystalline Indomethacin under Isothermal Conditions. Chem Pharm Bull 36:4026±4032. 15. Yoshioka M, Hancock B, Zogra® G. 1994. Crystallization of Indomethacin from the Amorphous State Below and Above its Glass Transition Temperature. J Pharm Sci 83:1700±1705. 16. Andronis V, Yoshioka M, Zogra® G. 1997. Effects of Sorbed Water on the Crystallization of Indomethacin from the Amorphous State. J Pharm Sci 86: 346±350. 17. Andronis V, Zogra® G. 2000. Crystal Nucleation and Growth of Indomethacin Polymorphs from the Amorphous State. J Non-Cryst Solids 271: 236±248. 18. Borka L. 1974. The Polymorphism of Indomethacin. Acta Pharm Suecica 11:295±303. 19. Otsuka M, Matsumoto T, Kaneniwa N. 1986. Effect of Environmental Temperature on Polymorphic Solid-State Transformation of Indomethacin During Grinding. Chem Pharm Bull 34:1784±1793. 20. Kaneniwa N, Otsuka M, Hayashi T. 1985. Physicochemical Characterization of Indomethacin Polymorphs and the Transformation Kinetics in Ethanol. Chem Pharm Bull 33:3447±3455. 21. Joshi V. 1998. Physical Transformations in Solvated Pharmaceuticals. PhD Dissertation. Purdue University. 22. Privalko VP. 1980. Excess Entropies and Related Quantities in Glass-Forming Liquids. J Phys Chem 84:3307±3312. 23. Hancock BC, Zogra® G. 1994. The Relationship Between the Glass Transition Temperature and the Water Content of Amorphous Pharmaceutical Solids. Pharm Res 11:471±477. 24. Couchman PR, Karasz FE. 1978. A Classical Thermodynamic Discussion of the Effect of Composition on Glass-Transition Temperatures. Macromol 11:117±119. 25. Crowley KJ, Zogra® G. 2001. The Use of Thermal Methods for Predicting Glass-Former Fragility. Thermochim Acta, in press. 26. Taylor LS, York P. 1998. Effect of Particle Size and Temperature on the Dehydration Kinetics of Trehalose Dihydrate. Int J Pharm 167:215±221. 27. Gujrati PD, Goldstein M. 1980. Viscous Liquids and the Glass Transition. 9. Noncon®gurational CRYOGENIC GRINDING OF IMC POLYMORPHS AND SOLVATES Contributions to the Excess Entropy of Disordered Phases. J Phys Chem 84:859±863. 28. Price CW. 1990. Use of Kolmogorov-Johnson-MehlAvrami Kinetics in Recrystallization of Metals and Crystallization of Metallic Glasses. Acta Metall Mater 38:727±738. 29. Christian JW. 1975. The Theory of Transformations in Metals and Alloys. London: Pergamon. 30. Hancock BC, Shamblin SL, Zogra® G. 1995. Molecular Mobility of Amorphous Pharmaceutical Solids Below Their Glass Transition Temperatures. Pharm Res 12:799±806. 507 31. Sillescu H. 1999. Heterogeneity at the Glass Transition. J Non-Cryst Solids 243:81±108. 32. Schmelzer J, Pascova R, Moeller J, Gutzow I. 1993. Surface-Induced Devitri®cation of Glasses: The In¯uence of Elastic Strains. J Non-Cryst Solids 162:26±39. 33. Ozawa T. 1970. Kinetic Analysis of Derivative Curves in Thermal Analysis. J Thermal Anal 2:301±324. 34. Henderson DW. 1979. Thermal Analysis of NonIsothermal Crystallization Kinetics in Glass Forming Liquids. J Non-Cryst Solids 30:301±315. JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 91, NO. 2, FEBRUARY 2002
© Copyright 2026 Paperzz