J. Phys. Chem. B 2007, 111, 7283-7287
7283
Effect of Physical Aging on Nucleation of Amorphous Indomethacin Sergey Vyazovkin* and Ion Dranca† Department of Chemistry, UniVersity of Alabama at Birmingham, 901 South 14th Street, Birmingham, Alabama 35294 ReceiVed: January 1, 2007; In Final Form: February 28, 2007
Differential scanning calorimetry has been used to study glassy indomethacin aged at 0 and -10 °C for periods of time up to 109 and 210 days, respectively. The results demonstrate the emergence of a small melting peak of the R-polymorph after aging for 69 days at 0 °C and for 147 days at -10 °C (i.e., ∼55 °C below the glass-transition temperature) that provides evidence of nucleation occurring in the temperature region of the β-relaxation. The evolution of an endothermic recovery peak temperature features a plateau at longer annealing times that suggests that the glass has made significant progress toward reaching the supercooled liquid state. It has been found that the melting peaks become detectable after the recovery peak has reached the plateau. The results highlight the importance of studying physical aging in the temperature region of the β-relaxation as a means of evaluating the physical stability of amorphous pharmaceutical materials.
Introduction Amorphous pharmaceuticals draw a great deal of interest because of their potential to enhance bioavailability. The downside of amorphous materials is their thermodynamic instability that unavoidably drives them toward the stable crystalline state. The rate of conversion from the amorphous to crystalline state depends on the molecular mobility that can be very slow at temperatures well below its glass-transition temperature, Tg. Under these conditions, the molecular mobility reduces to local, mostly noncooperative, motion that affords only very slow relaxation of an amorphous material. As a rule of thumb, it is frequently suggested that at Tg - 50 °C the relaxation is so slow that an amorphous material can be considered stable for most practical purposes.1 The local molecular mobility in this temperature region is still detectable in the form of the so-called β-relaxation2 or other low activation energy relaxation processes.3 These processes are most commonly studied by dielectric4 and mechanical spectroscopy.5 For instance, in indomethacin, which is frequently used as a model pharmaceutical compound, the β-relaxation has been detected by dielectric techniques.6,7 On the other hand, differential scanning calorimetry (DSC) can also be used for probing the sub-Tg relaxation processes and for estimating their activation energies.8,9 The resulting values are found to lie within 20% of the activation energies for the β-relaxation as measured by dielectric and mechanical spectroscopy.3 In particular, the activation energy derived by us9 from DSC runs on indomethacin has recently been confirmed by dielectric measurements.7 The temperature region of the β-relaxation is known10 to set the lower temperature limit to the process of sub-Tg relaxation or so-called physical aging. According to dielectric data,7 the β-relaxation becomes detectable in indomethacin at temperatures above -60 °C. That is, from above this temperature up to Tg, one can expect indomethacin to undergo physical aging, that is, to relax slowly from the amorphous glassy state toward the * To whom correspondence should be addressed. E-mail: vyazovkin@ uab.edu. † Present address: Department of Pharmaceutics, University of Minnesota, Minneapolis, Minnesota 55455.
supercooled liquid state. In our previous DSC study,9 we have been able to detect physical aging in indomethacin annealed at as low as -20 °C (i.e., around Tg - 65 °C), which is even lower than was observed in some other calorimetric studies1,11 that reported relaxation around Tg - 50 °C. However, a more important question is whether indomethacin would show any evidence of crystallization at temperatures that far below its Tg. Our preliminary aging experiments9 have provided evidence of crystallization after annealing indomethacin for 10 days at the annealing temperature, Ta ) 5 °C. Although it appears to be the lowest reported temperature for crystallization of indomethacin, it lies at the high-temperature end of the β-relaxation region. More definitive would be detection of crystallization on annealing at Ta ) -10 °C that had only exhibited9 ongoing physical aging after 31 days. Such evidence has been recently obtained12 and is reported in this paper. The paper also provides new data on a correlation of the processes of physical aging and crystallization. Experimental Section Indomethacin (indometacin) (1-(p-chlorobenzoyl)-5-methoxy2-methylindole-3-acetic acid) was purchased from MP Biomedicals, LLC and was used without further purification. The melting point measured by DSC was ∼160 °C that corresponds to the γ-form13 of indomethacin. About 10 mg of crystalline indomethacin was weighed in 40 µL Al pans and was hermetically sealed after quick melting in a furnace at 175 °C. The sealed samples were heated again and were quenched into liquid nitrogen. The quenched samples had the value of Tg ) 46 °C that was determined by DSC as a midpoint of the glass-transition step observed on heating at 10 °C min-1. The quenched samples were placed in freezers kept at 0 and 10 °C and annealed there for an extended period of time. During this period, some of the samples were individually removed from the freezers, placed in DSC, and heated at 10 °C min-1 to 200 °C. In order to avoid any significant heating above the annealing temperature, the samples were quickly transferred from the freezer to liquid nitrogen, from which they were transferred directly into the DSC cell precooled to -40 °C. Originally,9 it was a point of our
10.1021/jp0700027 CCC: $37.00 © 2007 American Chemical Society Published on Web 05/27/2007
7284 J. Phys. Chem. B, Vol. 111, No. 25, 2007
Figure 1. DSC curves obtained on heating at 10 °C min-1 of indomethacin after long-term annealing at Ta ) -10 °C. The numbers by the curves represent annealing time in days (d). Dash-dot line represents nonaged glass. Arrows show the location of the annealing peak. The melting region is circled. Inset shows a blow-up of the melting region.
concern that the use of liquid nitrogen might introduce significant thermal stress creating structure defects in amorphous samples and, therefore, promoting crystallization. However, we found that nonaged samples subjected to recurrent equilibrating at Ta and quenching into liquid nitrogen do not demonstrate any melting or crystallization peaks when heated in DSC at 10 °C min-1. To test reproducibility, we have also repeated the previously reported aging experiment at Ta ) 5 °C, as described earlier.9 The measurements were conducted by using a Mettler-Toledo heat flux DSC 822e in the atmosphere of nitrogen flow (80 mL min-1). The temperature and heat flow calibration were performed at 10 °C min-1 by using an indium standard. The standard DSC analysis software (Mettler-Toledo, STARe 7.01) has been used to determine the temperature of the endothermic recovery peaks, Tp, and the onset temperature of the melting peaks, Tm. Results and Discussion In our previous work,9 we detected crystallization of indomethacin annealed for 10 and 21 days at 5 °C. It was detected by DSC as the appearance of a small melting peak at the melting point of indomethacin that was observed on heating of the annealed samples. No such peaks were observed at shorter annealing times as well as in just-quenched samples. It was therefore concluded that indomethacin undergoes active nucleation during annealing, and the formed nuclei continue to grow on heating producing the crystalline phase, whose melting is detectable by DSC. In samples annealed at Ta ) -10 °C, no melting peaks are detected at annealing times, ta, less than 147 days (Figure 1). Very close examination may reveal some baseline fluctuations in the Tm area at shorter annealing times. However, any “overdetecting” is readily avoided by comparing the signal fluctuations against the detection limit, defined14 as 3 times the standard deviation of the blank signal. The average value of the detection limit estimated for the region 150-160 °C from three runs on nonaged samples is 0.006 W g-1. The aforementioned fluctuations do not exceed 0.005 W g-1, whereas the size of the detected melting peaks is ∼3 times lager (i.e., 0.013 and 0.018 W g-1). Therefore, the only effect that is reliably detected before 147 days is a shift in the position of the endothermic annealing (recovery) peak, Tp, with increasing the
Vyazovkin and Dranca
Figure 2. Variation of the Tp value with the annealing time at Ta ) -10 °C.
Figure 3. Temperature dependence of the enthalpy (H) and volume (V). During physical aging at Ta, the glass structure changes as shown schematically in the boxes related to (A) just-quenched, and (B) and (C) are extensively aged states. On aging, the local densities equalize and the overall density increases. Dash-dot lines illustrate an increase in Tp with the aging time (Tp is the peak temperature for dH/dT).
time of annealing. A similar effect was observed in long-term aging experiments by Chen,15 who provided an explanation to it. Briefly, when physical aging is performed well below Tg and for relatively short period, the respective enthalpy loss can occur at the expense of the faster part of the relaxation time spectrum. Reheating of the partially relaxed sample results in partial enthalpic recovery that gives rise to an endothermic annealing peak that appears before or during the main glass-transition step (cf. Figure 1). Ultimately, the annealing peak turns into well familiar “enthalpy overshoot” widely observed in glasses aged not far below Tg.16 Our experiments at Ta ) -10 °C demonstrate two noteworthy facts. First, the melting peaks emerge when the annealing peak turns into the enthalpy overshoot. Second, the melting point of the formed crystalline phase is ∼154 °C that corresponds to the R-form13 of indomethacin, which is different from the original γ-form used to produce the glassy samples. The amount of the crystalline phase formed is estimated to be less than 1% by comparing the heats derived from the melting peaks with the heat of melting of the neat R-polymorph.13 The first fact can be understood if we look at the evolution of the Tp value presented in Figure 2. It is seen that Tp increases with the annealing time until reaching some plateau value. An increase in Tp during physical aging reflects a progress of the glassy system toward metastable equilibrium (supercooled liquid) as shown in Figure 3. The closer the system approaches equilibrium the larger its characteristic relaxation
Physical Aging on Nucleation of Indomethacin
J. Phys. Chem. B, Vol. 111, No. 25, 2007 7285
Figure 4. Variation of the Tp value with the logarithm of the annealing time at Ta ) -10 (circles) and 0 °C (squares).
time becomes. For this reason, extensively aged glasses recover slower on reheating, demonstrating larger values of Tp. However, once the system reaches equilibrium, Tp stops shifting with increasing the annealing time and exhibits a plateau at some ultimate value characteristic of a given aging temperature. The value of Tp is known17 to increase in approximately linear fashion with the logarithm of the annealing time. An example of such behavior is seen in Figure 4. The behavior of Tp is similar to that of the enthalpy loss, which is commonly measured in aging studies of glassy materials. As a matter of fact, some recent data18 suggest that the evolution of both parameters is well correlated, and they reach equilibrium at the same time. That is, leveling off of the Tp value at larger values of log ta can generally be used to detect approaching equilibrium. The problem with determining the time to equilibrium by this or any other method is that in theory one intends to determine the point at which some physical parameters stop to evolve. In reality, one determines the point at which the difference in the consecutively measured values of the parameters becomes too small to be detected experimentally. In this regard, one can expect that measuring the enthalpy loss may be more reliable because the ultimate value of the enthalpy can be estimated by extrapolating the liquid-state values measured above Tg down to sub-Tg aging temperatures. However, such extrapolations are known18 to be quite dangerous and are associated with significant uncertainties especially when aging is performed well below Tg which is exactly our case. At any rate, it is generally believed that equilibrium cannot be reached on any reasonable time scale at temperatures significantly below Tg. The belief apparently originates from the argument put forward by Struik,10 who estimated the time scale as follows
t∞ ≈ 100 exp0.77(Tg - T)
(1)
where t∞ is the time to equilibrium in seconds. Equation 1 suggests that it would take about a year to reach equilibrium at 20 °C below Tg. The validity of eq 1 can be reasonably questioned because it was derived assuming that the temperature dependence of the relaxation time obeys the Williams-LandelFerry equation.19 However, below Tg the relaxation processes tend to follow2 the Arrhenius equation that predicts much weaker temperature dependence. In addition, the rate of aging can be significantly different for different materials. For example, the aging data20 for polycarbonate and polystyrene suggest that at similar Tg - T the former reaches equilibrium almost 10 times faster than the latter. In the view of the above discussion, the plateau in Tp observed in Figures 2 and 4 provides only necessary but not sufficient
data to claim that our system aged for 147 and 210 days has reached the state of metastable equilibrium corresponding to the liquid line (Figure 3). Nevertheless, it can be safely assumed that the system has made a significant progress toward the liquid state. This means that the glass has undergone significant structural relaxation toward assuming the structure of liquid. The initial just-quenched glass has a highly heterogeneous structure that contains areas of significantly different density (Figure 3). The existence of local density gradients stimulates translational diffusion of molecules from high to low density areas. This would ultimately lead to equalizing the density throughout the whole system so that it assumes a more homogeneous structure of a liquid. At the same time, the overall thermodynamic drive toward equilibrium causes a decrease in the volume of the whole system and an increase in its density. Therefore, as a glassy system ages, it undergoes two simultaneously occurring processes: density equalizing and densification. A question arises how these two processes may affect the rate of nucleation. Classical nucleation theory defines the rate as21,22
I)N
( ) ( ) ( ) kBT -ED -∆G* exp exp h kBT kBT
(2)
where I is the nucleation rate per unit volume, N is the number of atoms per unit volume, kB is the Boltzmann constant, h is the Planck constant, ED is the activation energy for diffusion across the phase boundary, and ∆G* is the maximum free energy necessary for the formation of the critical size nucleus. The ∆G* exponential term of the total rate represents the thermodynamic drive to the crystalline state. Because ∆G* is inversely proportional to the square of the difference between Tm and the actual temperature, the thermodynamic drive to crystallization below Tg is very large. As a matter of fact, one may expect it be even larger in the glassy state than in the liquid state at the same temperature. The height of the ∆G* barrier is inversely proportional to the difference in the volume free energy between the crystal and liquid.22 Since the free energy of the glassy state is larger than that of the liquid state, the ∆G* value may be expected to be smaller for crystallization from the glassy state. However, at temperatures close to Tg or below it, the nucleation rate is limited by the ED exponential term that represents diffusion. The rate of both rotational and translational diffusion decreases on aging.23 This would obviously suggest a decrease in the nucleation probability. Although the aforementioned factors are clearly not in favor of enhancing nucleation on aging, their relative contribution may be minor compared to other factors that favor nucleation. We have mentioned that aging is accompanied by density equalizing and densification. We believe that these processes can be the major factors of enhancing nucleation. Densification alone should promote intermolecular interaction and, therefore, the probability of nucleation. The effect should be similar to the well-known24 positive effect of the pressure on the rate of nucleation that is found in supercooled liquids25,26 and glasses.27 The effect can be linked to a decrease in the molar volume24,27 as well as in the interfacial energy.25 ∆G* in eq 2 is proportional to the square of the molar volume21 and to the cube of the interfacial energy.24 However, the largest contribution to enhancing nucleation is likely to be due to density equalizing. Structurally, a glass consists of high- and low-density regions that, respectively, demonstrate low and high molecular mobility. Measurements
7286 J. Phys. Chem. B, Vol. 111, No. 25, 2007 of diffusion rates on aging suggest23 that the high-density regions are primarily involved in slower rotational diffusion, whereas faster translational diffusion is associated with low-density regions. The latter, therefore, are the most likely regions for nucleation to occur. The high mobility regions or “mobility islands” were originally invoked28 to explain the β-relaxation processes that are found in a variety of glasses at sub-Tg temperatures. The local molecular mobility associated with the β-relaxation has been suggested29,30 to be the process determining the nucleation rate of several organic glasses below Tg. Recent studies31 of sub-Tg crystallization of metallic glasses in ultrasonic field also suggest that the process occurs via the local β-mobility and takes place in the high mobility regions. In eq 2, the rate of nucleation is proportional to the number of molecules per unit volume, N. In homogeneous media, N includes all molecules. However, in a glass the molecules of the structurally arrested high-density regions do not possess sufficient translation mobility to form a nucleus. That is, the rate of nucleation is proportional not to the total number of molecules but to a fraction of molecules found in the high mobility regions. In the process of density equalizing, the molecules from the structurally arrested regions diffuse into neighboring high mobility areas therefore increasing the fraction of molecules capable of nucleating. This is how density equalizing can contribute to increasing the rate of nucleation. It follows from above that an aged glass can provide a more favorable medium for nucleation than the just-quenched one. It is not, thus, surprising that crystallization in our experiments is detected in the glassy samples that have undergone significant structural relaxation toward assuming the structure of a liquid. The progress toward this state is measured in our experiments via the evolution of Tp that represents the process of enthalpy relaxation. Aging studies23 of polystyrene suggest that the rate of enthalpy relaxation correlates with the rate of translational diffusion occurring in the high mobility regions. Provided this correlation holds general, reaching a plateau in Tp value (Figures 2 and 4) is likely to indicate that the translational diffusion from the low to high mobility regions has significantly slowed down. That is, the number of molecules diffused into the high mobility regions (i.e., the value of N in eq 2) is getting close to its maximum. This would mean that the rate of nucleation is also approaching its maximum subject to the assumption that N really is the major factor contributing to the rate of nucleation in a glass. At this point, the glass is still relaxing toward equilibrium but primarily at the expense of rotational diffusion in the low mobility regions that is reported23 to be markedly slower compared to translation diffusion in high mobility regions. We believe that our data on detecting the melting peaks after prolonged aging make a convincing case that nucleation does occur during aging. Although an alternative interpretation could be that nucleation occurs not during aging but on heating of the extensively aged glasses from Ta to Tm, we consider it very unlikely. The process of heating is very fast. Our samples are heated at 10 °C min-1, that is, for example, it takes less than 6 min to get from Ta ) -10 °C to Tg ) 46 °C. This period is much shorter than the duration of the experimentally observed32 induction periods for crystallization of indomethacin. The induction period extends over weeks at 40 °C, and even above Tg (e.g., at 50 and 60 °C) it lasts days.32 That is, the time spent by the aged samples during heating through the respective temperature range is too short to induce any appreciable nucleation. Also, on heating above Tg, the aged indomethacin glass would quickly reach equilibrium. At that point, the structural changes that occurred on aging are erased, so that if
Vyazovkin and Dranca
Figure 5. DSC curves obtained on heating at 10 °C min-1 of indomethacin after long-term annealing at Ta ) 0 °C. The numbers by the curves represent annealing time in hours (h) and days (d). Arrows show the location of the annealing peak. The melting region is circled. Inset shows a blow-up of the melting region.
nucleation occurred above Tg it would be independent of the aging time. This means that the melting peaks would appear regardless of the aging time which is clearly not what we observe in our experiments (cf. Figures 1 and 5). The formation of the R-form of indomethacin crystals is another intriguing fact. According to the literature,13,33 heating of unaged amorphous samples tends to show two DSC melting peaks related to the R- and γ-forms, although the amount of the R-form appears to increase13 with the rate of quenching. Isothermal crystallization above Tg yields mixed polymorphs having markedly larger content of the R-form.13,32,34 Below Tg, the formation of the γ-form alone has been reported by Andronis and Zografi32 in the region 20-40 °C. However, the formation of the γ-form with inclusion of the R-polymorph have been observed by Wu and Yu35 in practically the same region (2240 °C). Extrapolation of data by Andronis and Zografi32 down to our temperature region would suggest that the γ-form should be preferred thermodynamically. However, some care must be exercised when such extrapolation is done to significantly lower temperatures, that is, for the medium of a higher density. The R-form has a larger density than that the γ-form,13 so that its formation may have energetic advantages as the density of the amorphous medium is increasing. This conjecture is consistent with the exclusive formation of the R-polymorph in crystallization under pressure.33 Assuming that the data by Andronis and Zografi32 can be extrapolated to our aging temperatures, we need to consider an important difference in our respective experiments. Andronis and Zografi have used polarized light microscopy to observe the formation of the fully blown crystals, that is, the entities whose size is no less than tens of micrometers. The respective degrees of crystallinity were no less than 5%.32 We consider that the development of the fully blown crystals is very unlikely under our conditions. Recall that the degrees of crystallinity estimated from the melting peaks are less than 1%. We believe that under our conditions one can only expect the formation of nuclei, that is, the nanometer size entities.9 The nuclei are too small to develop any distinct shape and are typically treated as spherical particles. However, they would serve as crystallization centers when nucleated indomethacin is heated to higher temperatures, especially to the temperatures corresponding to the maximum crystal growth rate that is around 80 °C32 for the R-form. As a result, at elevated temperatures, the R-form (the form preferentially13,32 growing above Tg) may start growing on the nuclei formed during aging. Therefore, our detecting the melting peaks
Physical Aging on Nucleation of Indomethacin at Tm of the R-form does not necessarily contradict the conclusion of Andronis and Zografi32 that crystallization of indomethacin below Tg results in the formation of the γ-polymorph. To confirm the effect observed at Ta ) -10 °C, we have performed a series of long-term annealing runs at 0 °C. Figure 5 displays the shift of the annealing peak and the emergence of the melting peak as a function of the annealing time. It is seen that the melting peak becomes noticeable in the samples annealed longer than 50 days. Again, detection of melting correlates with the moment when the annealing peak turns in the overshoot and the value of Tp reaches a plateau. Figure 4 shows that the plateau value of Tp is reached at ∼60 days. The melting point estimated from the melting peaks observed after 69 and 109 days of annealing is ∼154 °C that corresponds to the formation of the R-form of crystalline indomethacin. The amounts of the crystalline phase formed are around 1-2% as estimated from the heats of melting. Undoubtedly, the results of the annealing runs at Ta ) 0 °C are phenomenologically identical to the results derived from the runs at Ta ) -10 °C. A comment needs to be made about reproducibility of the reported results. Our experiments were not designed as a quantitative study of the relaxation and crystallization kinetics. The idea rather was to probe either qualitative or semiquantitative correlation between relaxation and crystallization. For this reason, performing repetitive runs in a systematic fashion, that is, at every aging time, was not deemed necessary. Nevertheless, occasional repetitive runs have been performed, always confirming the same qualitative trend, which is the absence of the melting peaks before reaching the plateau in Tp and the appearance of the melting peaks after the plateau is reached. We have also repeated the previously reported9 aging experiment at Ta ) 5 °C. In that experiment,9 the melting peak developed between the 2nd and 10th day of aging, that is, the peak did not appear after 2 days of aging but was detected after 10 days. In a new series of measurements, the melting peak has developed between the 7th and 20th day of aging. This is considered as evidence of reproducibility in a semiquantitative sense. From the quantitative viewpoint, a significant difference has been noted in the size of the melting peaks. The previous series of runs at Ta ) 5 °C yielded the heats of melting 1.2 and 7.4 J g-1 at 10 and 22 days of aging, respectively.9 The new experiment has resulted in smaller values of the melting heats that are 0.3 and 0.6 J g-1 for 20 and 35 days of aging, respectively. However, the results of five recurring runs at the same aging time have demonstrated that the lowest and largest values of the melting heat differ about 3 times. Conclusions Physical aging of indomethacin has been studied at temperatures down to Tg - 56 °C or 0.83Tg that corresponds to the temperature region of the β-relaxation. The study demonstrates that indomethacin undergoes nucleation in this temperature region. To our knowledge, this represents the lowest temperatures for which evidence of nucleation has been reported. Although the process is quite slow, detecting it is very important because prenucleated amorphous pharmaceuticals would crystallize faster when the storage temperature is increased. Clearly, studies of the kinetics of the sub-Tg relaxations should play a key role in estimating the physical stability of amorphous pharmaceuticals. Another finding of this work is that nucleation becomes detectable after glassy indomethacin has reached a
J. Phys. Chem. B, Vol. 111, No. 25, 2007 7287 significant extent of relaxation defined as a plateau in the plot of the aging peak temperature against aging time. The significance of this correlation is that it could be used for estimating the lifetimes of amorphous pharmaceuticals as the time of reaching the aforementioned plateau, because this period appears to determine the time to nucleation. However, whether this correlation is a common feature of crystallizable glasses remains to be seen in our ongoing investigation. Acknowledgment. This work was partially supported by the Boehringer-Ingelheim Cares Foundation. References and Notes (1) Hancock, B. C.; Shamblin, S. L.; Zografi, G. Pharm. Res. 1995, 12, 799-806. (2) Donth, E. The Glass Transition: Relaxation Dynamics in Liquids and Disordered Materials; Springer: Berlin, 2001. (3) Vyazovkin, S.; Dranca, I. Thermochim. Acta 2006, 446, 140-146. (4) Hedvig, P. Dielectric Spectroscopy of Polymers; Wiley: New York, 1977. (5) McCrum, N. G.; Read, B. E.; Williams, G. Anelastic and Dielectric Effects in Polymeric Solids; Dover: New York, 1991. (6) Correia, N. T.; Ramos, J. J. M.; Descamps, M.; Collins, G. Pharm. Res. 2001, 18, 1767-1774. (7) Carpentier, L.; Decressain, R.; Desprez, S.; Descamps, M. J. Phys. Chem. B 2006, 110, 457-464. (8) Vyazovkin, S.; Dranca, I. J. Phys. Chem. B 2004, 108, 1198111987. (9) Vyazovkin, S.; Dranca, I. J. Phys. Chem. B 2005, 109, 1863718644. (10) Struik, L. C. E. Physical Aging in Amorphous Polymers and Other Materials; Elsevier: Amsterdam, 1978. (11) Shamblin, S. L.; Tang, X.; Chang, L.; Hancock, B. C.; Pikal, M. J. J. Phys. Chem. B 1999, 103, 4113-4121. (12) First evidence was obtained after 147 days of annealing and was presented in our talk at 33rd NATAS Conference, Universal City, CA, Sept. 19th, 2005. (13) Yoshioka, M.; Hancock, B. C.; Zografi, G. J. Pharm. Sci. 1994, 83, 1700-1705. (14) Skoog, D. A.; Holler, F. J.; Nieman, T. A. Principles of Instrumental Analysis, 5th ed.; Brooks/Cole Pub Co.: Florence, KY, 1998. (15) Chen, H. S. J. Non-Cryst. Solids 1981, 46, 289-305. (16) McKenna, G. B.; Simon, S. L. In Handbook of Thermal Analysis and Calorimetry, v.3; Cheng, S. Z. D., Ed.; Elsevier: Amsterdam, 2002; p 49. (17) Hodge, I. M. J. Non-Cryst. Solids 1994, 169, 211-266. (18) Hutchinson, J. M.; Kumar, P. Thermochim. Acta 2002, 391, 197217. (19) Williams, M. L.; Landel, R. F.; Ferry, J. D. J. Am. Chem. Soc. 1955, 77, 3701-3707. (20) Rault, J. J. Phys. Condens. Matter 2003, 15, S1193-S1213. (21) Turnbull, D.; Fisher, J. C. J. Chem. Phys. 1949, 17, 71-73. (22) Christian, J. W. The Theory of Transformations in Metals and Alloys, 3rd ed.; Elsevier: Amsterdam, 2002. (23) Thurau, C. T.; Ediger, M. D. J. Chem. Phys. 2002, 116, 90899099. (24) Landau, L. D.; Lifshitz E. M. Statistical Physics, 3rd ed.; Butterworth: 1980. (25) Gutzow, I.; Durschang, B.; Russel, C. J. Mater. Sci. 1997, 32, 5389-5403. (26) Maris, H. J.; Caupin, F. J. Low Temp. Phys. 2003, 131, 145-154. (27) Fuss, T.; Ray, C. S.; Kitamura, N.; Makihara, M.; Day, D. E. J. Non-Cryst. Solids 2003, 318, 157-167. (28) Johari, G. P.; Goldstein, M. J. Chem. Phys. 1970, 53, 2372-2388. (29) Hikima, T.; Hanaya, M.; Oguni, M. Bull. Chem. Soc. Jpn. 1996, 69, 1863. (30) Hatase, M.; Hanaya, M.; Hikima, T.; Oguni, M. J. Non-Cryst. Solids 2002, 307-310, 257. (31) Ichitsubo, T.; Matsubara, E.; Yamamoto, T.; Chen, H. S.; Nishiyama, N.; Saida, J.; Anazawa, K. Phys. ReV. Lett. 2005, 95, 245501-1245501-4. (32) Andronis, V.; Zografi, G. J. Non-Cryst. Solids 2000, 271, 236248. (33) Okumura, T.; Ishida, M.; Takayama, K.; Otsuka, M. J. Pharm. Sci. 2006, 95, 689-700. (34) Wu, T.; Yu, L. J. Phys. Chem. B 2006, 110, 11694-15699. (35) Wu, T.; Yu, L. Pharm. Res. 2006, 23, 2350-2355.
