Correlation between Glass-Forming Ability and Fragility of

Mar 17, 2015 - indomethacin, IDM, 357.8, 160.7, 45.1, Wako Pure Chemicals (Osaka, Japan). ketoconazole, KCZ, 531.4, 147.3, 43.9, Tokyo Chemical Indust...
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Correlation between Glass-Forming Ability and Fragility of Pharmaceutical Compounds Kohsaku Kawakami,*,† Takuji Harada,†,‡ Yasuo Yoshihashi,§ Etsuo Yonemochi,§,⊥ Katsuhide Terada,§ and Hiroshi Moriyama‡ †

International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan ‡ Faculty of Science and §Faculty of Pharmaceutical Sciences, Toho University, 2-2-1 Miyama, Funabashi, Chiba 274-8510, Japan ABSTRACT: Fragility is a measure of the departure from non-Arrhenius behavior for supercooled liquids and glasses, and various simple methods are available for its quantification. However, the obtained values usually do not agree with each other. One of the purposes of this study was to compare the fragility values obtained by different methodologies. Thermodynamic fragility (FT) is a simple concept that is evaluated from the heat capacity change at the glass transition temperature (Tg). Dynamic fragility is evaluated using three methodologies in this study: extrapolation of the configurational entropy (Sc) to the Kauzmann temperature (Tk) (FDC), ramp-rate dependence of Tg (FDTg), and that of the fictive temperature (Tf) (FDTf). FT and FDC of 19 pharmaceutical compounds were correlated, whereas FDTg and FDTf did not correlate with either of them. This result seems reasonable because both FT and FDC are calculated from thermodynamic parameters in the quasiequilibrium state, but FDTg and FDTf are likely affected by kinetics as well. Another goal of this study was to find the correlation between the glass-forming ability (GFA) and fragility. FDTg was shown to correlate with GFA, presumably because both were determined on the balance of thermodynamic and kinetic factors. This correlation suggests that fragile glass has low GFA. Furthermore, the relevance of fragility to isothermal crystallization is discussed. Compounds with small FDTg and FDTf tended to exhibit pressure-controlled crystallization, for which better storage stability can be expected relative to temperature-controlled compounds. Fragility was shown to be a useful parameter practically as well as scientifically.

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INTRODUCTION In the pharmaceutical industry, amorphization is an important formulation technology that helps the dissolution of drug molecules.1−4 However, several challenging problems hinder the general use of amorphization. In the case of the oral dosage forms, amorphous formulations are typically manufactured using either spray-drying or hot-melt extrusion, which are uncommon technologies compared with the manufacturing of conventional crystalline dosage forms. Low physical and chemical stability of the amorphous formulations is another obstacle to overcome. In addition to the low stability, the lack of prediction protocols is a problem that hinders the prompt development of amorphous formulations because the shelf life cannot be assured until the stability test at the storage conditions is completed.3−5 The manufacturability and storage stability of amorphous formulations appear to depend on the compounds. Terms such as glass-forming ability (GFA) and crystallization tendency are used to describe properties related to crystallization behavior.6−15 They are typically evaluated by observing the crystallization behavior during cooling from melt, which is not directly related to crystallization during isothermal storage. However, they help understand whether crystallization is © XXXX American Chemical Society

governed by temperature or pressure to provide basic information for predicting the isothermal crystallization behavior.16 Temperature-controlled compounds have characteristic crystallization temperature during cooling or reheating processes. In contrast, pressure-controlled compounds cannot crystallize during the cooling and reheating processes because of steric hindrance and intermolecular forces. Because isothermal crystallization of the temperature-controlled compounds is governed by temperature, their crystallization time is predictable only from their glass transition and storage temperatures. The isothermal crystallization of the pressurecontrolled compounds is expected to be slower than that of the temperature-controlled compounds. However, increase in the surface area may change the dominating factor from pressure to temperature.17 The GFA of organic compounds has attracted considerable attention.8−15 In general, compounds with high molecular weight are considered difficult to crystallize. Moreover, the number of benzene rings, the symmetry of the structure, the Received: September 24, 2014 Revised: March 5, 2015

A

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The Journal of Physical Chemistry B Table 1. List of Model Compounds Used in This Study compound

abbreviation

Mw

Tm (°C)

Tg (°C)

supplier

acetaminophen antipyrin bifonazole chlorpropamide cinnarizine clotrimazole D-salicin fenofibrate flurbiprofen ibuprofen indomethacin ketoconazole ketoprofen loratadine nifedipine phenobarbital procaine ritonavir tolbutamide

AAP ATP BFZ CPA CNZ CTZ DSL FFB FBP IBP IDM KCZ KPF LTD NDP PBB PCN RTV TLB

151.2 151.2 310.4 276.7 368.5 344.8 286.3 360.8 244.3 206.3 357.8 531.4 254.3 382.9 346.3 233.2 236.3 721.0 270.3

169.2 110.6 148.6 118.4 119.6 140.6 110.6 80.4 114.6 75.6 160.7 147.3 95.1 133.5 172.0 173.8 60.6 122.0 127.9

23.2 −24.6 16.1 16.9 6.8 28.3 57.7 −18.9 −5.4 −43.5 45.1 43.9 −3.0 35.1 45.5 41.9 −38.7 47.0 5.0

MP Biomedicals (Santa Ana, U.S.A.) Wako Pure Chemicals (Osaka, Japan) LKT Laboratories (St. Paul, U.S.A.) Sigma-Aldrich (St. Louis, U.S.A.) Sigma-Aldrich (St. Louis, U.S.A.) Wako Pure Chemicals (Osaka, Japan) Sigma-Aldrich (St. Louis, U.S.A.) Sigma-Aldrich (St. Louis, U.S.A.) Wako Pure Chemicals (Osaka, Japan) Hamari Chemicals (Osaka, Japan) Wako Pure Chemicals (Osaka, Japan) Tokyo Chemical Industry (Tokyo, Japan) Sigma-Aldrich (St. Louis, U.S.A.) Tokyo Chemical Industry (Tokyo, Japan) Alexis Biochemicals (San Diego, U.S.A.) Fujinaga Pharm (Tokyo, Japan) MP Biomedicals (Santa Ana, U.S.A.) LKT Laboratories (St. Paul, U.S.A.) Wako Pure Chemicals (Osaka, Japan)

namic fragility (FT) is a very simple concept that is evaluated from the heat capacity change at the glass transition temperature (Tg). Fragile materials generally exhibit large changes at Tg, whereas strong glasses show small changes. Nonetheless, exceptional behaviors are observed, notably for hydrogen-bonded materials.22 Dynamic fragility was evaluated using three methodologies in this study: extrapolation of the configurational entropy (Sc) to the Kauzmann temperature (Tk) (FDC), the ramp-rate dependence of Tg (FDTg), and that of the fictive temperature (Tf) (FDTf). The correlation between thermodynamic and dynamic fragility is still under discussion. A slightly negative correlation has been observed for small organic molecules.22 However, there is a lack of a sufficient number of data and data variations; therefore, further research is needed to reach meaningful conclusions on this matter. In this study, the correlation between fragility and GFA is discussed as well as the relevance of the fragility to isothermal crystallization behavior.

number of rotatable bonds, the number of branches, and the number of electronegative atoms have been suggested to affect GFA.10−12 In addition, several physicochemical parameters, including melting enthalpy/entropy and temperature, the energy difference between the crystalline and amorphous state, Tg/Tm, and the viscosity above Tg, have been suggested to correlate with GFA.11 Fragility is a measure of the departure of physical characteristics including molecular mobility (relaxation time) and viscosity from non-Arrhenius behavior,18 and it is considered to correlate with GFA.6,7 These conclusions have mainly been reached based on observations using inorganic or polymeric materials. Low-molecular-weight organic compounds are extremely challenging materials because of the wide variation in their chemical structure. Although various methods have been developed to quantify fragility,19−26 the obtained values commonly do not agree with each other. For example, Andronis et al. determined strength parameters of indomethacin glass using shear viscosity, shear relaxation, dielectric relaxation, and heating rate dependence in the thermal analysis.20 The fragilities can be calculated as 95, 83, 71, and 83, respectively, from the parameters obtained in their study. Correia et al.23 and Moura Ramos et al.24 utilized thermally stimulated depolarization current for obtaining the fragility values of indomethacin glass as 51, 63, and 64, depending on the calculation methodology. As also supported by the results presented in this paper, inconsistency of the fragility value for the same sample is sometimes double and even more. In addition to the principle of evaluation, many factors can be an origin of the inconsistency, including the temperature range for the evaluation, morphology of the samples (powders, pellets, etc.), and how the sample atmospheres are controlled. We have analyzed only quenched pellet samples that were stored under a dried atmosphere. Thermal analysis is one of the convenient methods for obtaining the fragility value. Because thermal analysis can provide thermodynamic parameters of the crystalline/amorphous materials, the procedure for determining the fragility value can be simplified dramatically. One of the purposes of this study is to compare the fragility values based on thermal analysis but calculated by different methodologies. Thermody-

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MATERIALS AND METHODS

Materials. All of the model drugs used in this study are listed in Table 1 with their supplier, abbreviation, and basic characteristics. All of the compounds were used as supplied. Differential Scanning Calorimetry (DSC). DSC measurements were performed on a DSC Q2000 (TA Instruments, New Castle, DE, U.S.A.), which was periodically calibrated using indium and sapphire. Dry nitrogen was used as the inert gas at a flow rate of 50 mL/min. All evaluations were at least triplicated. Heat capacity measurements were conducted using a previously published protocol.27 In the modulated DSC mode, samples (ca. 10 mg) were heated in sealed T-zero aluminum pans at 2 °C/min with a 60 s period and 0.5 °C amplitude. Amorphous samples were prepared by quenching from above the melting temperature at 50 °C/min. Crystalline samples were prepared by partially melting the powder samples to allow recrystallization of the melted portion and enhance the thermal contact with the sample pans. Thermal Stability of Model Compounds. The thermal stability of each drug was investigated using thermogravimetry (TG) analysis on SDT Q600 (TA Instruments, New Castle, B

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The Journal of Physical Chemistry B DE, U.S.A.) and high-performance liquid chromatography (HPLC). TG analysis was made up to melting temperatures to observe weight loss due to decomposition and sublimation. The compounds that exhibited weight loss more than 0.01% in the TG study were subjected to the HPLC analysis on a Shimadzu Prominence (Shimadzu, Kyoto, Japan) equipped with a Cosmosil 5C18-AR-II (150 mmL × 5.0 mmID, Nacalai Tesque, Kyoto, Japan) with a flow rate of 1 mL/min. The column was equilibrated by acetonitrile/water = 5/95, and measurements were done with this mobile phase for 10 min, followed by a gradual change to 100/0 over 40 min and elution by acetonitrile for 10 min. The detection wavelength and injection volume were 210 nm and 2 μL, respectively. Thermodynamic Fragility. Thermodynamic fragility FT was evaluated from the heat capacity change at Tg22 FT =

FDT g =

−

ΔETg R

d log τ d(Tg /T ) =

= T=T g

d(ln q) d(1/Tg)

ΔET g 1 2.303Tg R

(6)

(7)

For determining fragility, the heating rate to observe Tg is generally set equal to the cooling rate from the melt in the preparation of the glass.28 However, this procedure posits strong constraints because slow cooling rates induce crystallization in most low-molecular-weight organic compounds. Thus, the effect of the cooling rate on fragility was investigated. Figure 1 shows the effect of the cooling rate on the middle

ΔCpconf ΔCp

(1)

where ΔCconf is the heat capacity difference between the p supercooled liquid and crystal, that is, the configurational heat capacity, and ΔCp is the change in the heat capacity of the glass at Tg. Dynamic Fragility. Three methods were used for calculating the dynamic fragility.21,26 In the first method, the dynamic fragility (FDC) was obtained by extrapolating Sc to Tk. The temperature dependence of Sc is expressed as Sc =

∫T

T

k

⎛ ΔC conf (T ) ⎞ p ⎜ ⎟ dT ⎜ ⎟ T ⎝ ⎠

(2)

Figure 1. Middle point Tg of FFB as a function of heating and cooling rates. FFB was cooled from the melting temperature at 2 (●), 5 (△), 10 (×), and 20 (+) °C/min. Subsequently, the glassy FFB was heated at various heating rates (vertical axis) for determining Tg. The Tg’s obtained under the same heating and cooling rates are denoted with the open circles. The thick line represents the fitting to the data shown as open circles, from which FDTg is typically determined.

where T is the temperature. Assuming that TΔCconf p (T) is constant,21 the following equation can be obtained by integrating eq 2 up to the melting temperature using the configurational heat capacity at Tg ⎛ ⎞ ΔHm 1 1 ⎜ ⎟ 1 = + Tk Tm ⎜⎝ ΔCpconf (Tg)Tg ⎟⎠

(3)

point Tg of the FFB glass. For a fixed slow cooling rate (2 °C/ min), the slope of the data was much milder than that determined in the typical procedure, where an identical ramp rate was used in the cooling and subsequent heating. When the fixed cooling rate was faster than 10 °C/min, the slope almost agreed with that in the typical procedure. Because the fragility is determined from this slope, a fixed cooling rate faster than 10 °C/min seemed practically applicable. It was confirmed for other compounds as well, and the fragility values obtained using various cooling conditions are presented in Table 2. The effect of representative values for Tg was also investigated in this study, that is, either the onset or middle point Tg. Obviously, the use of a very slow cooling rate was problematic for all compounds. The fragility values obtained for cooling rates faster than 20 °C/min almost agreed with those obtained using the conventional methodology. The use of onset values, which are considered to be almost equal with Tf, also seemed practically inappropriate because of the large variation in the values. Thus, a constant cooling rate of 20 °C/min and the middle point Tg were used to obtain FDTg in this study. The fictive temperature (Tf) was also used in place of Tg for determining the dynamic fragility.25 In this procedure, the heating rate to observe Tf was set equal to the cooling rate from

where Tm and ΔHm are the melting temperature and melting enthalpy, respectively. The strength parameter, D, was calculated from the Vogel−Tammann−Fulcher (VTF) equation ⎛ DT0 ⎞ τ(T ) = τ0 exp⎜ ⎟ ⎝ T − T0 ⎠

(4)

where τ(T) and τ0 are the relaxation time and time scale of vibrational motions (ca. 10−14 s), respectively. T0 is a constant with almost the same value as Tk. Thus, the Tk value determined from eq 3 was substituted into T0 of eq 4, and τ at Tg was assumed to be 100 s to obtain D using eq 4. The fragility FDC was calculated as follows21,26 FDC =

DT0/Tg 2.303(1 − T0/Tg)2

(5)

The dynamic fragility (FDTg) was also estimated from the dependence of Tg on the ramp rate, q, in the DSC measurements using the following equations C

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The Journal of Physical Chemistry B Table 2. Dynamic Fragility Values (FDTg) Determined under Various Cooling Conditions IBP

IDM

FFB

DSL

cooling rate (°C/min)

onset

middle

onset

middle

onset

middle

onset

middle

2 5 10 20 30 = heating rate

51 64 68 80 77 77

55 60 68 68 68 68

66 61 74 78 98 83

71 69 72 83 80 85

55 65 76 85 82 97

62 68 81 86 81 82

48 66 63 78 77 73

48 59 62 72 72 74

the melt in the preparation process. The dynamic fragility, FDTf, was determined by best-fit to the following equation25 ⎛q⎞ ⎛ Ts ⎞ log⎜⎜ ⎟⎟ = FDT f ⎜1 − f ⎟ Tf ⎠ ⎝ ⎝ qs ⎠

Tr =

C ΔET g 1 = end R − Tg

Tm − Tg

(10)

where Tc is the onset crystallization temperature. For determining Tr, a cooling rate of 5 °C/min was used. High Tr suggests low GFA. The Tc of some compounds rarely depends on the cooling rate, whereas other compounds do not. This difference can be elucidated by relative contribution of thermodynamic and kinetic factors for crystallization. Thus, it must be kept in mind that the kinetic factor for the crystallization cannot totally be eliminated from this parameter. The cooling rate dependence of the crystallization temperature d(ln q)/dTc was also evaluated as another measure of GFA (Figure 1b). Compounds with high GFA should exhibit strong cooling rate dependency, which means a small absolute value of d(ln q)/dTc. As a third measure of GFA, we used the crossing point of the cooling and heating rate dependencies of the crystallization temperature, as shown in Figure 1c. If the GFA is high, the crystallization temperature should depend strongly on the ramp rate. Thus, the crossing point (ln q) should decrease. The ramp rate at this point is defined as qx.

(8)

Another method sometimes used to evaluate fragility is observation of the glass transition width, for which the following equation is used21,26

Tgonset

Tc − Tg

(9)

where Tonset and Tend are the onset and end point of Tg, g g respectively. However, the material-dependent constant C is required for this calculation. Although a universal value of C = 5 is sometimes used, this method was not employed in this study owing to the low reliability of this assumption. GFA. Three methods were used in this study for assessing the GFA of pharmaceutical compounds, as shown in Figure 2. One was the reduced crystallization temperature Tr during cooling from melt (Figure 1a), which was defined as

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RESULTS AND DISCUSSION Thermal Stability of Model Compounds. Each drug was melted before assessing the heat capacity and crystallization behavior in the following experiments. If decomposition occurs, it can alter the heat capacity and crystallization behavior. Sublimation may influence the thermal contact of the sample because of the deposition of the sample on the lid and sidewalls of the pan. Thus, only compounds that were stable during preparation were used in this study. Table 3 shows the thermal Table 3. Thermal Stability of the Model Compounds degradation products (%)

a

compounds

weight loss (%)

CPA FBP PBB DSL TLB

0.14 0.11 1.28 0.34 0.02

a

1 min

10 min

0 0 0 0 0

41 17 0 0 0

(130 (130 (190 (130 (140

°C) °C) °C) °C) °C)

Determined by TG.

stability of compounds that lost mass during TG analysis. Sublimation appeared to be negligible because the largest mass loss was only 1.28%. HPLC analysis showed that CPA and FBP were not stable during the heating for 10 min; however, the problem was not significant during the 1 min heating, which was used in this study. Thus, all of the compounds used in this study appeared thermally stable.

Figure 2. Definition of GFA. All of the parameters take small values with increasing GFA. D

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Figure 3. Relation between the dynamic fragilities (a, FDC; b, FDTg, c, FDTf) and thermodynamic fragility, FT. Comparison of FDTg and FDTf is also presented (d), where a 45° line (solid) for confirming consistency of the values and a fitting line (dotted) drawn by ignoring two outliers, AAP and RTV, are presented.

Table 4. Fragility and GFA Values of Model Compounds dominating factor for crystallization temperature

local pressure

compounds

FT

FDC

FDTg

ATP CPA FBP NDP TLB AAP BFZ CNZ DSL PBB

1.08 1.11 1.17 1.26 1.10 1.08 1.16 1.14 1.21 1.52

63 90 59 94 95 79 56 76 69 155

81 219 88 112 122 77 76 84 118 96

CTZ FFB IBF IDM KCZ KPF LTD PCN RTV

1.32 1.04 1.07 1.04 1.33 1.25 1.20 1.17 1.15

91 73 51 67 118 61 78 129 75

63 82 75 85 97 67 72 90 86

Correlation between Thermodynamic and Dynamic Fragilities. Figure 3a−c shows the relation between thermodynamic and dynamic fragilities, and Figure 3d presents correlation between FDTg and FDTf. The numerical data are given in Table 4. Ideally, the thermodynamic and dynamic fragilities should be correlated, and the dynamic fragility values should agree with each other. In this study, FT showed

FDTf

127

Tr

d(ln q)/dTc

ln qx

0.45 0.69 0.43 0.44 0.61

0.1506 0.0863 0.3027 0.1995 0.1518

3.42 2.91 2.47 2.87 4.40

134 94 71 62 28 62 47 61 38 50 28 64 142

correlation with FDC but not with FDTg and FDTf. This may be reasonable because both FT and FDC were calculated from thermodynamic parameters in the quasi-equilibrium state, whereas FDTg and FDTf should also be affected by kinetics, as summarized in Table 5. The values for the dynamic fragilities did not agree with each other. Correlation between FDC and FDTg (FDTf) is expected only when the amorphous materials E

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mobility, the fragility and Tr should be positively correlated. One factor that may disturb the correlation is the temperature range of the investigation. Although the fragility values were determined based on the analysis of the glass transition behavior, the observations of the crystallization behavior were made in a much higher temperature range where the effect of local pressure is less important. The dominating factors in the determination of GFA are summarized in Table 5. FT and FDC are purely thermodynamic parameters, whereas kinetics is involved in the determination of FDTg and FDTf. Among GFA, thermodynamics should have a larger contribution for Tr despite considerable the influence of kinetics as well, whereas the other parameters are dominated by kinetics. Tr and FDTg are the only parameters for each property that are determined on the basis of a balance of thermodynamics and kinetics. The successful correlation between these parameters is attributed to the similar background. As mentioned in the Materials and Methods section, the kinetic factor for crystallization cannot totally be eliminated from Tr. The relative importance of the kinetic factors can be understood from −d(ln q)/dTc values, from which FBP and NDP are relatively sensitive to the cooling rate. As a matter of fact, these compounds fail to crystallize at a cooling rate of 20 °C/min. In the correlation between Tr and FDTg, only the data of these compounds can be found below the correlation line. Thus, the deviation of the plot may be explained by the difference in the weight of the kinetic factor for the crystallization. Although GFAs determined from the cooling rate dependence of Tc and ln qx also consider kinetic factors in the crystallization, they did not show any correlation with FDTg. Because Tc is much higher than Tg, the relative contribution of the frustration experienced by the molecules should be much larger in the glass transition process. Moreover, the crystallization involves transition in the molecular structure, whereas the glass transition is not associated with such obvious molecular transition. Thus, the kinetic factors for fragility and GFA have different origins, and it may explain the absence in the correlation between FDTg and those GFA parameters. Relevance of Fragility to Isothermal Crystallization. The crystallization behavior during isothermal storage must be well understood for developing the amorphous dosage forms. However, it is obvious that the crystallization behavior during isothermal storage is not directly correlated with the GFA during cooling from melt. On the basis of the assumption made in the previous section, a much larger contribution of the intermolecular frustration should be considered for under-

Table 5. Dominating Factors for Fragility and GFA fragility

GFA

FT FDC FDTg, FDTf Tr d(ln q)/dTc ln qx

thermodynamic

kinetic

dominant dominant involved dominant hardly involved hardly involved

no contribution no contribution involved involved dominant dominant

show perfect fit to the VTF equation, which is not likely for most materials. Although FDTf was expected to have almost the same value with FDTg, it was not likely according to Figure 3d. This discrepancy can partially be explained by relaxation of the amorphous materials because the Tf value decreases if the recovery peak is found in the DSC curve. Because the relaxation is more promoted at slower cooling/heating rates, FDTf for the compounds that tend to relax effectively should be smaller than FDTg. A change in the cooperative rearranging region during the thermal treatment26 can also influence FDTf. Because the impact of these factors on the middle point Tg is less significant, FDTg may be a better parameter to describe fragility than FDTf. Nevertheless, FDTg and FDTf seem to have correlation, if we ignore some outliers such as AAP and RTV. Correlation between Fragility and GFA. Figures 4−6 show the relations between fragilities and GFA. The numerical values for GFA are also presented in Table 4. Note that compounds that do not crystallize during cooling cannot be included in this evaluation. Compounds that easily crystallize during cooling could not be used as well because the fragility could not be determined. The former group can be regarded as the compounds that exhibit pressure-controlled crystallization, whereas crystallization of the latter compounds is dominated by temperature. Thus, evaluation was done only for the compounds wherein the crystallization is initiated on a balance of temperature and pressure domination; hence, the results discussed below were obtained using compounds with a limited range of characteristics. FT and FDC did not exhibit correlation with any GFA indexes; however, FDTg showed correlation with Tr. This correlation is not very high but proper scientifically. It means that fragile glass has low GFA, which agrees with an earlier observation made for metallic glasses using the critical cooling rate as an indicator of GFA.6,7 The larger the fragility, the higher the molecular mobility relative to that expected from the Arrhenius equation. Thus, if the temperature totally dominates the crystallization, that is, if the crystallization is governed by the molecular

Figure 4. Relation between GFA and FT. F

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Figure 5. Relation between GFA and FDC.

Figure 6. Relation between GFA and FDTg.

understanding the fragility of drug candidates may clarify their suitability for amorphous dosage forms with respect to physical stability. Additives that improve physical stability are used in practice. However, information on the physical stability of the drug molecules is also important because it can provide the worst case of the stability, which is of great interest to the pharmaceutical industry. Last, it must be stressed that the methodology used for determining fragility must be considered well when its relevance with other properties is discussed because, as noted in the Introduction, the fragility values may significantly depend on the methodologies employed.

standing isothermal crystallization, in addition to the intramolecular frustration that requires consideration in the case of hot crystallization. In a previous study, we showed that the initiation time of the isothermal crystallization can be expressed as a function of only the reduced temperature regardless of the chemical structure if the crystallization is dominated by temperature (i.e., thermodynamics).16,17 Exceptional compounds, wherein the crystallization is controlled by local pressure (kinetics), exhibited slower crystallization due to the high energetic barrier for nucleation. However, the dominant factor may change from pressure to temperature if the energetic barrier is lowered by increasing surface area and/or allowing water adsorption. In Table 4, the compounds are separated in two groups based on the dominant factor for the crystallization. Obviously, the temperaturecontrolled compounds tend to have large FDTg and FDTf values. This tendency appears to be clearer than the correlation of the fragility with the hot crystallization behavior. Thus, their FDTg or FDTf may be used as an indicator of the isothermal crystallization behavior. That is, compounds with small FDTg or FDTf may be expected to have better physical stability than those with large FDTg. RTV exhibited exceptionally large FDTf, although its crystallization behavior is totally dominated by pressure.16,17 RTV is one of the most difficult compounds for determining Tf because of a relatively large recovery enthalpy and the dependence of the cooperative rearranging region on the thermal program, which can be detected as a change in width of the glass transition region. Thus, much care is required for assuming the crystallization behavior from FDTf of such compounds. Fragility has been a well-defined concept that enables the quantitative description of non-Arrhenius behavior in glassy materials. In this study, we showed that it might have practical application in addition to scientific significance. That is,

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CONCLUSIONS Fragility can be determined by various methods, but the obtained values do not agree with each other. We investigated 19 pharmaceutical compounds with correlated FT and FDC, whereas FDTg and FDTf did not correlate with either of them. This result seemed reasonable because both FT and FDC were calculated from thermodynamic parameters in the quasiequilibrium state, whereas FDTg and FDTf should be affected by kinetic factors as well. FDTg was shown to correlate with Tr, the reduced crystallization temperature during cooling, presumably because both of them are determined on a balance of thermodynamic and kinetic factors. This correlation suggests that fragile glass has a low GFA. Compounds with large FDTg and FDTf tended to exhibit temperature-controlled crystallization during isothermal storage. Fragility was shown to be a useful parameter not only from a scientific viewpoint but also from a practical standpoint.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel. +81-29-8604424. Fax. +81-29-860-4708. G

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(17) Kawakami, K. Surface Effects on the Crystallization of Ritonavir Glass. J. Pharm. Sci. 2015, 104, 276−279. (18) Angell, C. A. Relaxation in Liquids, Polymers and Plastic Crystals  Strong/Fragile Patterns and Problems. J. Non-Cryst. Solids 1991, 131−133, 13−31. (19) Hancock, B. C.; Dalton, C. R.; Pikal, M. J.; Shamblin, S. L. A Pragmatic Test of a Simple Calorimetric Method for Determining the Fragility of Some Amorphous Pharmaceutical Materials. Pharm. Res. 1998, 15, 762−767. (20) Andronis, V.; Zografi, G. The Molecular Mobility of Supercooled Amorphous Indomethacin as a Function of Temperature and Relative Humidity. Pharm. Res. 1998, 15, 835−842. (21) Crowley, K. J.; Zografi, G. The Use of Thermal Methods for Predicting Glass-Former Ability. Thermochim. Acta 2001, 380, 79−93. (22) Huang, D.; McKenna, G. B. New Insights into the Fragility Dilemma in Liquids. J. Chem. Phys. 2001, 114, 5621−5630. (23) Correia, N. T.; Moura Ramos, J. J.; Descamps, M.; Collins, G. Molecular Mobility and Fragility in Indomethacin: A Thermally Stimulated Depolarization Current Study. Pharm. Res. 2001, 18, 1767−1774. (24) Moura Ramos, J. J.; Correia, N. T.; Taveira-Marques, R.; Collins, G. The Activation Energy at Tg and the Fragility Index of Indomethacin, Predicted from the Influence of the Heating Rate on the Temperature Position and on the Intensity of Thermally Stimulated Depolarization Current Peak. Pharm. Res. 2002, 19, 1879−1884. (25) Wang, L. M.; Velikov, V.; Angell, C. A. Direct Determination of Kinetic Fragility Indices of Glassforming Liquids by Differential Scanning Calorimetry: Kinetic versus Thermodynamic Fragilities. J. Chem. Phys. 2002, 117, 10184−10192. (26) Kawakami, K. Dynamics of Ribavirin Glass in Sub-T g Temperature Region. J. Phys. Chem. B 2011, 115, 11375−11381. (27) Harada, T.; Kawakami, K.; Yoshihashi, Y.; Yonemochi, E.; Terada, K.; Moriyama, H. Practical Approach for Measuring Heat Capacity of Pharmaceutical Crystals/Glasses by Modulated-Temperature DSC. Chem. Pharm. Bull. 2013, 61, 315−319. (28) Moynihan, C. T.; Easteal, A. J.; Wilder, J.; Tucker, J. Dependence of the Glass Transition Temperature on Heating and Cooling Rate. J. Phys. Chem. 1974, 78, 2673−2677.

⊥

E.Y.: Institute of Medicinal Chemistry, Hoshi University, 2-441 Ebara, Shinagawa, Tokyo 142-8501, Japan. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was in part supported by the World Premier International Research Center (WPI) Initiative on Materials Nanoarchitectonics, MEXT, Japan, and the Low-carbon Research Network, Japan.

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DOI: 10.1021/jp509646z J. Phys. Chem. B XXXX, XXX, XXX−XXX