Article pubs.acs.org/molecularpharmaceutics
Influence of Molecular Mobility on the Physical Stability of Amorphous Pharmaceuticals in the Supercooled and Glassy States Khushboo Kothari, Vishard Ragoonanan, and Raj Suryanarayanan* Department of Pharmaceutics, University of Minnesota, 308 Harvard Street SE, Minneapolis, Minnesota 55455, United States S Supporting Information *
ABSTRACT: We investigated the correlation between molecular mobility and physical stability in three model systems, including griseofulvin, nifedipine, and nifedipine−polyvinylpyrrolidone dispersion, and identified the specific mobility mode responsible for instability. The molecular mobility in the glassy as well as the supercooled liquid states of the model systems were comprehensively characterized using dynamic dielectric spectroscopy. Crystallization kinetics was monitored by powder X-ray diffractometry using either a laboratory (in the supercooled state) or a synchrotron (glassy) X-ray source. Structural (α-) relaxation appeared to be the mobility responsible for the observed physical instability at temperatures above Tg. Although the direct measurement of the structural relaxation time below Tg was not experimentally feasible, dielectric measurements in the supercooled state were used to provide an estimate of the α-relaxation times as a function of temperature in glassy pharmaceuticals. Again, there was a strong correlation between the α-relaxation and physical instability (crystallization) in the glassy state but not with any secondary relaxations. These results suggest that structural relaxation is a major contributor to physical instability both above and below Tg in these model systems. KEYWORDS: amorphous, glassy, crystallization, molecular mobility, nifedipine, griseofulvin
■
INTRODUCTION
state (T < Tg). Hence, from a practical standpoint, it is of importance to understand the role of structural mobility on the physical stability of glassy pharmaceuticals. In addition to the αrelaxation, it is recognized that local mobility (β-relaxations; fast noncooperative motions of individual molecules or parts of molecules), which is significant below the glass transition temperature, could also be influencing stability.4 This necessitates the measurement, ideally, or at the very least the calculation of the relaxation times of the different modes of mobility below Tg. The viscosity of a supercooled liquid and the time scale for molecular motions increase dramatically (typically 10−12 orders of magnitude between melting temperature and Tg) as the temperature is lowered toward Tg.13 Below Tg, the molecules are essentially “frozen in” due to the extremely
For drugs with poor aqueous solubility, formulation in the amorphous state offers a potential for enhanced oral bioavailability.1 However, the excess free energy and the associated thermodynamic instability can cause crystallization and may negate the bioavailability advantage brought about through the enhanced solubility.2,3 It is therefore critical to ensure that the drug is retained in the amorphous state during processing and storage. Extensive efforts have been directed toward understanding the causes of physical instability (i.e., crystallization tendency) in amorphous pharmaceuticals.4,5 In particular, several studies have investigated the possible correlation between molecular mobility and physical instability.4−8 Recently, Bhardwaj et al. established a correlation between the global mobility (structural or α-relaxation) and the physical stability of amorphous itraconazole and trehalose.9,10 Such a link has also been established for several other pharmaceuticals (indomethacin, felodipine, flopropione, and celecoxib) in the supercooled state (T > Tg).11,12 However, amorphous pharmaceuticals are usually stored in the glassy © 2014 American Chemical Society
Received: Revised: Accepted: Published: 3048
March 27, 2014 June 13, 2014 July 7, 2014 August 8, 2014 dx.doi.org/10.1021/mp500229d | Mol. Pharmaceutics 2014, 11, 3048−3055
Molecular Pharmaceutics
Article
demonstrated that the local dynamics were correlated with storage stability.26 Crystallization in amorphous fulvene and indomethacin at T < Tg was also circumstantially attributed to β-relaxation.27,28 On the other hand, in several glasses of pharmaceutical interest, including nifedipine, celecoxib and several macrolide antibiotics, structural relaxation times below Tg were closely coupled to crystallization.29−31 However, due to the extremely long time scales of these molecular motions, in none of these investigations, the α-relaxation times were directly measured. Therefore, different approaches have been attempted to estimate the structural relaxation time.29−32 For example, in nifedipine and griseofulvin, the structural relaxation time below Tg was calculated using the AGV model and the heating rate dependence of Tg characterized by calorimetry.30,32 Using dielectric spectroscopy, coupled with time temperature superposition, the structural relaxation time was determined in celecoxib, azithromycin, clarithromycin, and roxythromycin.29,31 While both α and β-relaxations can influence the physical stability in the glassy state, very few studies have systematically and comprehensively characterized all the mobility modes which may influence crystallization in the temperature range of interest. The first objective of our work was to characterize, using dielectric spectroscopy, both global and local motions in two model glasses (nifedipine and griseofulvin). Because the structural relaxation times in the glassy state could not be experimentally measured, they were calculated using eq 2. The second objective was to determine the potential correlation between each of these mobility modes and the crystallization kinetics in these systems. The use of highly sensitive synchrotron X-ray diffractometry enabled these quantitative studies. Finally, our investigations were extended to nifedipine−polyvinylpyrrolidone (PVP) solid dispersion. These studies enabled the development of correlation models which permit prediction of crystallization kinetics in glasses of interest. The ultimate goal of our investigation is to enable the development of stabilization approaches based on modulating the specific mobility responsible for physical instability.
high viscosity of the glassy phase and the reorientation motion of the molecules cannot keep up with the decrease in temperature resulting in an observed deviation of the measured time scales of molecular motions from the “equilibrium supercooled liquid”. The α-relaxation times for supercooled liquids are usually in the nanosecond range, whereas below Tg, relaxation times are extremely long (>100 s) and often longer than the time scale of experimental observation.13,14 In supercooled liquids, the temperature dependence of the αrelaxation time can be described by the Vogel−Tamman− Fulcher−Hesse (VTFH) model (eq 1), whereas in the glassy state the relaxation behavior has been often described by the Adam−Gibbs−Vogel (AGV) model (eq 2).15−21
⎛ DT0 ⎞ τ = τ0exp⎜ ⎟ ⎝ (T − T0) ⎠
(1)
⎛ ⎞ ⎜ ⎟ DT0 ⎟ τ = τ0exp⎜ ⎜⎜ ⎛⎜T ⎛⎜1 − T0 ⎞⎟⎟⎞ ⎟⎟ Tf ⎠⎠ ⎠ ⎝⎝ ⎝
(2)
In the above equations, τ is the relaxation time, D is a measure of fragility of the system, τ0 is the pre-exponential relaxation factor, T0 is the zero mobility temperature, and Tf is the fictive temperature at which the glassy state will have the same macroscopic properties as the “equilibrium supercooled liquid”. The concept of Tf was introduced by Tool to explain the departure of the structural relaxation time from the equilibrium values below Tg.22,23 In contrast, β-relaxations generally obey an Arrhenius temperature dependence (eq 3).4,24 ⎛ Eaβ ⎞ τ = τ0exp⎜ ⎟ ⎝ (RT ) ⎠
(3)
where, R is the gas constant, and Eaβ is the activation energy for β-relaxations, which usually has a much smaller value than for α-relaxations. Molecular mobility measurement in the glassy state can be challenging. Bhattacharya and Suryanarayanan have listed the techniques available to measure molecular mobility in the glassy state and their advantages and limitations.4 Calorimetric techniques, in light of the ease of data collection and analyses, are very popular. Using isothermal microcalorimetry and differential scanning calorimetry (based on enthalpic recovery measurement), Bhugra et al. successfully predicted the crystallization time of several glassy pharmaceuticals near Tg but not at temperatures significantly below Tg.11,25 Calorimetric techniques provide an “average” measure of relaxation time and are unable to distinguish between the different modes of molecular motions. Because the physical stability may be correlated to a specific molecular mobility, this approach may not provide nuanced information. On the other hand, broadband dynamic dielectric spectroscopy (BDS, the terms dielectric spectroscopy and BDS have been used interchangeably throughout the manuscript), probes the reorientation of dipoles under an electric field applied at specific frequencies allowing a direct measure of the relaxation time. The wide frequency and temperature range enables a systematic analysis of the different mobility modes (primary and secondary motions) both above and below Tg. In the glassy regime, BDS has been extensively used to study local motions. Based on investigation of over 100 protein systems, Cicerone et al.
■
EXPERIMENTAL SECTION Materials and Methods. Griseofulvin (C17H17ClO6; Glaxo Laboratories, Canada; Purity >98%) and nifedipine (C19H16ClNO4; Laborate Pharmaceutical Ltd., India; purity >98%) were used without further purification. Polyvinylpyrrolidone (PVP) (K12 grade) was supplied by BASF Corporation. Preparation of Amorphous Materials. Amorphous drugs (nifedipine and griseofulvin) were prepared by melting in aluminum pans (∼5 °C above the melting point of the drug; 180 °C for nifedipine and 225 °C for griseofulvin) and then quenching on aluminum blocks precooled to −20 °C. The nifedipine−PVP solid dispersion was prepared by a solvent evaporation technique followed by melt quenching. Physical mixtures of nifedipine (97.5% w/w) and PVP (2.5% w/w) were dissolved in acetone, and the solvent evaporated at 40 °C under reduced pressure (IKA-HB10 digital system, Werke GmbH and Co. Staufen, Germany). The mixture was further dried under vacuum at room temperature for 24 h and then the melt was quenched from ∼5 °C above the melting point of the drug to obtain the solid dispersions. The melt-quenched materials were lightly crushed using a mortar and pestle in a glovebox at room temperature (RH < 5%). The amorphous materials were stored 3049
dx.doi.org/10.1021/mp500229d | Mol. Pharmaceutics 2014, 11, 3048−3055
Molecular Pharmaceutics
Article
Figure 1. (a) Dielectric loss behavior of griseofulvin in the temperature range of 97−115 °C and (b) nifedipine (50−70 °C). For the sake of clarity, the dielectric loss behavior at only select temperatures is shown.
at −20 °C in desiccators containing anhydrous calcium sulfate until further use. Karl Fischer Titrimetry. The water content in the amorphous materials was determined coulometrically using a Karl Fischer titrimeter (Model DL 36 KF Coulometer, Metler Toledo, Columbus, OH). Accurately weighed samples were directly added to the Karl Fischer cell and the water content was determined. Thermal Analysis. A differential scanning calorimeter (DSC) (Q2000, TA Instruments, New Castle, DE) equipped with a refrigerated cooling accessory was used. The instrument was calibrated with tin and indium. In a glovebox, the powder was accurately weighed and sealed hermetically in aluminum pans. All the measurements were done under dry nitrogen purge (50 mL/min) at a heating rate of 10 °C/min. Powder X-ray Diffractometry (XRD). A powder X-ray diffractometer (D8 ADVANCE; Bruker AXS, Madison, WI) equipped with a variable-temperature stage (TTK 450; Anton Paar, Graz-Straßgang, Austria), and a Si strip one-dimensional detector (LynxEye; Bruker AXS) was used. These isothermal crystallization studies were conducted in the nifedipine systems at four temperatures, all above Tg (55 to 70 °C). Samples were periodically exposed to Cu Kα radiation (40 kV × 40 mA) over an angular range of 6−27° 2θ with a step size of 0.04° and a dwell time of 0.5 s. Synchrotron XRD (SXRD). Isothermal crystallization studies below Tg were conducted in all the model systems at four temperatures (25−45 °C). The samples were stored at the desired temperature and then exposed to synchrotron radiation (17-BM-Sector; 0.72910 Å; Argonne National Laboratory, IL) in hermetically sealed DSC pans (in a glovebox maintained at RH< 5%). The sample to detector distance was set at 900 mm. The calibration was performed using Al2O3 (NIST; SRM-647a) standard. The two-dimensional (2D) data were integrated to yield one-dimensional (1D) d spacing (Å) or 2θ (deg) scans using the FIT2D software developed by A. P. Hammersley of the European Synchrotron Radiation Facility. Quantification of XRD Data. At each storage time point, the crystallinity index was calculated using eq 4. The crystallinity index can be equivalent to the % crystallinity in the sample, if the total integrated intensity (crystalline + amorphous) remains constant throughout the isothermal crystallization experiment.33 (Supporting Information, S1)
crystallinity index =
intensity of crystalline peaks total diffracted intensity
(4)
A custom-built program (using Fortran 77; Tucson, AZ) was used to quantify crystallinity. In this program, the amorphous intensity contribution was based on the experimental XRD pattern of the amorphous “reference” material (preparation method is provided above). The subtraction of the amorphous intensity from the total pattern yielded the intensity contribution from the crystalline peaks. The percent crystallinity was plotted as a function of time, and a characteristic crystallization time (tc) was obtained for a desired level of crystallization (either 0.5 or 10%). Dielectric Spectroscopy (BDS). Using a broadband dielectric spectrometer (Novocontrol Alpha-AK high performance frequency analyzer, Novocontrol Technologies, Germany), isothermal dielectric measurements were conducted over the frequency range of 10−2 to 107 Hz and between −100 and 150 °C. The Havriliak−Negami (HN) model (eq 5) was used to fit the dielectric data so as to obtain the average relaxation time (τHN) and shape parameters (αHN and βHN). ε*(ω) = ε∞ +
Δε (1 + (iωτHN)αHN )βHN
(5)
In the above equation, ω is the angular frequency, ε*(ω) is the complex dielectric permittivity consisting of real (ε′) and imaginary (ε″) components, and dielectric strength, Δε = εs − ε∞, where εs gives the low frequency limit (ω → 0) of ε′(ω) and ε∞ is the high frequency limit (ω → ∞) of ε′(ω). The shape parameters account for the symmetric (αHN) and asymmetric (βHN) peak broadening with 0 < αHN (or βHN) < 1. At higher temperatures, the contribution of conductivity was observed on the low frequency side of the dielectric spectra. This was taken into consideration by adding the conductivity component, σ0/iεsω to the HN equation where, σ0 is the dc conductivity. The powder was filled between two gold plated copper electrodes (20 mm diameter) using a PTFE ring (thickness: 1 mm; area: 59.69 mm2; capacitance: 1.036 pF) as a spacer. The spacer confined the sample between the electrodes Measurements were corrected for stray capacitance, spacer capacitance and edge compensation.
■
RESULTS AND DISCUSSION Characterization. The model amorphous materials were observed to be X-ray amorphous. The glass transition 3050
dx.doi.org/10.1021/mp500229d | Mol. Pharmaceutics 2014, 11, 3048−3055
Molecular Pharmaceutics
Article
Figure 2. Temperature dependence of α- and β-relaxation times in (a) griseofulvin and (b) nifedipine. Black circles represent the α-relaxation time at temperatures above Tg, and the blue dashed line is the calculated α-relaxation time in the glassy state. The β-relaxation times (red circles) in griseofulvin were also obtained experimentally (mean ± relative error; n = 3). In case of nifedipine, the β-relaxation times were obtained from the literature.36,39 The red dashed line is an extrapolation of the β-relaxation time.
temperatures, determined by DSC (griseofulvin: 90.2 ± 0.2 °C; nifedipine: 46.2 ± 0.4 °C; nifedipine−PVPK12: 46.6 ± 0.1 °C; determined using a 10 °C/min heating rate) were in excellent agreement with the literature values.30,34 The DSC heating curves are included in Supporting Information, S2. Karl Fischer titrimetry revealed a water content 1.2Tg. However, between Tg and 1.2Tg, the temperature range for the crystallization studies, the two motions were observed to decouple in several fragile liquids.40−44 In this temperature
Figure 4. (A) XRD patterns revealing progressive drug crystallization from nifedipine solid dispersion at 60 °C from 0−10 min. (B) % Crystallinity in nifedipine as a function of time. 3052
dx.doi.org/10.1021/mp500229d | Mol. Pharmaceutics 2014, 11, 3048−3055
Molecular Pharmaceutics
Article
Figure 5. (a) SXRD patterns in amorphous nifedipine at 40 °C as a function of time revealing progressive crystallization from the sample. (b) % Crystallinity in nifedipine as a function of time (mean ± SD; n = 3).
Figure 6. (a) Plot of characteristic crystallization time (τcry, inverse of the crystallization rate constant) versus α-relaxation time in griseofulvin. The crystallization data was obtained from ref 29. Plots of crystallization time (tc, time taken for 10% crystallization) versus α-relaxation time in (b) nifedipine and (c) nifedipine−PVP dispersion (mean ± relative error; n = 3).
Figure 7. Plots of crystallization time [tc, time taken for 0.5% crystallization in (a) and 10% (b) and (c)] versus α-relaxation time in (a) griseofulvin, (b) nifedipine, and (c) nifedipine−PVP dispersion (mean ± relative error; n = 3).
coupling coefficient between crystallization and diffusion was found to be 0.82 (Supporting Information, S7). These results reveal that the physical stability of fragile liquids, in the temperature range of Tg to 1.2Tg, may be better coupled to translational rather than to rotational motions. Finally, we wanted to identify the specific mobility mode responsible for instability (crystallization) in the glassy state. This was accomplished in griseofulvin, where we determined the influence of the structural as well as the JG relaxation on the observed instability. The JG relaxation times could not be experimentally obtained in the temperature range (25−45 °C) where the physical stability was monitored. However, because
range, only the rotational motions and viscosity remain coupled. The Dtrans were observed to be an order of magnitude higher than that predicted by the Stokes−Einstein equation.13 Although the diffusion coefficient of nifedipine is not reported, it has been suggested that it would be close to that of indomethacin because the relaxation times of the two compounds are very close over a wide temperature range.45 Based on the bulk diffusivity of indomethacin, the coupling coefficient between translational diffusion and rotational motions in nifedipine was found to be 0.77 (Supporting Information, S7). This indicates that there exists a decoupling between these two kinds of motions between Tg and 1.2Tg. The 3053
dx.doi.org/10.1021/mp500229d | Mol. Pharmaceutics 2014, 11, 3048−3055
Molecular Pharmaceutics
■
ACKNOWLEDGMENTS K.K. was partially supported by the Center for Pharmaceutical Processing and Research and Doctoral Dissertation Fellowship, University of Minnesota. The project was partially funded by the William and Mildred Peters endowment fund. Parts of this work were carried out in the Characterization Facility, University of Minnesota, a member of the NSF-funded Materials Research Facilities Network (www.mrfn.org). This research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357. We thank Dr. Gregory Halder, Argonne National Laboratory, USA, for his help during the synchrotron data collection.
the JG is known to exhibit Arrhenius temperature dependence, the relaxation times could be obtained by extrapolation (Figure 2b). Using eq 6, we found an excellent coupling between the structural relaxation time and the crystallization kinetics in glassy griseofulvin (Figure 7a). Such a correlation did not exist with the JG relaxation (coupling coefficient: 2.6 ± 0.03). However, because the JG relaxation is an intermolecular relaxation involving motions of all the molecules in the system, it is believed to be a precursor to α-relaxation and may indirectly influence the physical stability.46−48 The indirect influence of the JG relaxation on the physical stability of amorphous celecoxib has also been recently highlighted.31 In nifedipine systems as well, the structural relaxation time was a very good predictor of physical instability with coupling coefficient values of 0.9 ± 0.2 for nifedipine and 1.2 ± 0.1 for the dispersion (Figure 7b,c). Although coupling coefficients can take values from 0−1, the observed higher value may be attributed to experimental errors. As mentioned earlier, the temperature dependence of JG relaxation could not be ascertained. However, at temperatures ≪Tg, secondary relaxations in amorphous nifedipine have been identified. Using the reported temperature dependence, we calculated the relaxation times at temperatures of interest to us.36,39 However, the coupling model revealed that the crystallization kinetics in the glassy state was not linked to these faster secondary motions observed in glassy nifedipine (coupling coefficient: 1.8 ± 0.07). In summary, our results reveal the strong influence of the cooperative α-relaxations on the physical stability of glassy nifedipine and griseofulvin systems. It has recently been established that surface crystallization is also an important driver of instability in both nifedipine and griseofulvin.34 This rapid surface crystallization may in turn then induce crystallization in the bulk. However, because our measurements in both BDS and XRD are carried out on bulk samples, it is therefore difficult to tease out the contribution of surface mobility.
■
CONCLUSION In light of the challenges with the direct measurement of the structural relaxation times below Tg, dielectric measurements in the supercooled state provided a quick estimate of the αrelaxation times as a function of temperature in glassy pharmaceuticals. Crystallization kinetics in the supercooled state was investigated using a laboratory powder X-ray diffractometer, whereas synchrotron radiation enabled similar studies in the glassy state. There was a strong correlation between the cooperative α-relaxations and physical instability (crystallization) in both glassy and supercooled griseofulvin, nifedipine, and in nifedipine−PVP dispersion. ASSOCIATED CONTENT
S Supporting Information *
Quantification of XRD data, DSC heating curves, relaxation behavior, calculation of crystallization rate constants, and coupling coefficients. This material is available free of charge via the Internet at http://pubs.acs.org.
■
REFERENCES
(1) Vasconcelos, T.; Sarmento, B.; Costa, P. Solid Dispersions as Strategy to Improve Oral Bioavailability of Poor Water Soluble Drugs. Drug Discovery Today 2007, 12 (23−24), 1068−1075. (2) Hancock, B. C.; Zografi, G. Characteristics and Significance of the Amorphous State in Pharmaceutical Systems. J. Pharm. Sci. 1997, 86 (1), 1−12. (3) Murdande, S.; Pikal, M.; Shanker, R.; Bogner, R. Solubility Advantage of Amorphous Pharmaceuticals: II. Application of Quantitative Thermodynamic Relationships for Prediction of Solubility Enhancement in Structurally Diverse Insoluble Pharmaceuticals. Pharm. Res. 2010, 27 (12), 2704−2714. (4) Bhattacharya, S.; Suryanarayanan, R. Local Mobility in Amorphous PharmaceuticalsCharacterization and Implications on Stability. J. Pharm. Sci. 2009, 98 (9), 2935−2953. (5) Bhugra, C.; Pikal, M. J. Role of Thermodynamic, Molecular, and Kinetic Factors in Crystallization from the Amorphous State. J. Pharm. Sci. 2008, 97 (4), 1329−1349. (6) Johari, G. P.; Kim, S.; Shanker, R. M. Dielectric Studies of Molecular Motions in Amorphous Solid and Ultraviscous Acetaminophen. J. Pharm. Sci. 2005, 94 (10), 2207−2223. (7) Johari, G. P.; Kim, S.; Shanker, R. M. Dielectric Relaxation and Crystallization of Ultraviscous Melt and Glassy States of Aspirin, Ibuprofen, Progesterone, and Quinidine. J. Pharm. Sci. 2007, 96 (5), 1159−1175. (8) Tombari, E.; Ferrari, C.; Johari, G. P.; Shanker, R. M. Calorimetric Relaxation in Pharmaceutical Molecular Glasses and Its Utility in Understanding Their Stability against Crystallization. J. Phys. Chem. B 2008, 112 (35), 10806−10814. (9) Bhardwaj, S. P.; Arora, K. K.; Kwong, E.; Templeton, A.; Clas, S.D.; Suryanarayanan, R. Correlation between Molecular Mobility and Physical Stability of Amorphous Itraconazole. Mol. Pharmaceutics 2012, 10 (2), 694−700. (10) Bhardwaj, S. P.; Suryanarayanan, R. Molecular Mobility as an Effective Predictor of the Physical Stability of Amorphous Trehalose. Mol. Pharmaceutics. 2012, 9 (11), 3209−3217. (11) Bhugra, C.; Shmeis, R.; Krill, S. L.; Pikal, M. J. Prediction of Onset of Crystallization from Experimental Relaxation Times. II. Comparison between Predicted and Experimental Onset Times. J. Pharm. Sci. 2008, 97 (1), 455−472. (12) Dantuluri, A. K. R.; Amin, A.; Puri, V.; Bansal, A. K. Role of ARelaxation on Crystallization of Amorphous Celecoxib above Tg Probed by Dielectric Spectroscopy. Mol. Pharmaceutics 2011, 8 (3), 814−822. (13) Angell, C. A.; Ngai, K. L.; McKenna, G. B.; McMillan, P. F.; Martin, S. W. Relaxation in Glassforming Liquids and Amorphous Solids. J. Appl. Phys. 2000, 88 (6), 3113−3157. (14) Ediger, M.; Angell, C.; Nagel, S. R. Supercooled Liquids and Glasses. J. Phys. Chem. 1996, 100 (31), 13200−13212. (15) Adam, G.; Gibbs, J. H. On the Temperature Dependence of Cooperative Relaxation Properties in Glass-Forming Liquids. J. Chem. Phys. 1965, 43 (1), 139−146.
■
■
Article
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest. 3054
dx.doi.org/10.1021/mp500229d | Mol. Pharmaceutics 2014, 11, 3048−3055
Molecular Pharmaceutics
Article
(16) Debenedetti, P. G.; Stillinger, F. H. Supercooled Liquids and the Glass Transition. Nature 2001, 410 (6825), 259−267. (17) Hodge, I. M. Effects of Annealing and Prior History on Enthalpy Relaxation in Glassy Polymers. 6. Adam-Gibbs Formulation of Nonlinearity. Macromolecules 1987, 20 (11), 2897−2908. (18) Scherer, G. W. Theories of Relaxation. J. Non-Cryst. Solids 1990, 123 (1−3), 75−89. (19) Vogel, H. The temperature dependence law of the viscosity of fluids. Phys. Z. 1921, 22, 645−646. (20) Fulcher, G. S. Analysis of recent measurements of the viscosity of glasses. J. Am. Ceram. Soc. 1925, 8, 339−355. (21) Tammann, G.; Hesse, W. The dependancy of viscosity on temperature in hypothermic liquids. Z. Anorg. Allg. Chem. 1926, 156, 245−257. (22) Moynihan, C. T.; Easteal, A. J.; De Bolt, M. A.; Tucker, J. Dependence of the Fictive Temperature of Glass on Cooling Rate. J. Am. Ceram. Soc. 1976, 59 (1−2), 12−16. (23) Tool, A. Q. Relation between Inelastic Deformability and Thermal Expansion of Glass in Its Annealing Range. J. Am. Ceram. Soc. 1946, 29 (9), 240−253. (24) Johari, G. P. Localized Molecular Motions of β-Relaxation and Its Energy Landscape. J. Non-Cryst. Solids 2002, 307−310 (0), 317− 325. (25) Bhugra, C.; Shmeis, R.; Krill, S.; Pikal, M. Predictions of Onset of Crystallization from Experimental Relaxation Times ICorrelation of Molecular Mobility from Temperatures above the Glass Transition to Temperatures Below the Glass Transition. Pharm. Res. 2006, 23 (10), 2277−2290. (26) Cicerone, M. T.; Douglas, J. F. β-Relaxation Governs Protein Stability in Sugar-Glass Matrices. Soft Matter 2012, 8 (10), 2983− 2991. (27) Alig, I.; Braun, D.; Langendorf, R.; Voigt, M.; Wendorff, J. H. Simultaneous Ageing and Crystallization Processes within the Glassy State of a Low Molecular Weight Substance. J. Non-Cryst. Solids 1997, 221 (2−3), 261−264. (28) Vyazovkin, S.; Dranca, I. Physical Stability and Relaxation of Amorphous Indomethacin. J. Phys. Chem. B 2005, 109 (39), 18637− 18644. (29) Adrjanowicz, K.; Zakowiecki, D.; Kaminski, K.; Hawelek, L.; Grzybowska, K.; Tarnacka, M.; Paluch, M.; Cal, K. Molecular Dynamics in Supercooled Liquid and Glassy States of Antibiotics: Azithromycin, Clarithromycin and Roxithromycin Studied by Dielectric Spectroscopy. Advantages Given by the Amorphous State. Mol. Pharm. 2012, 9 (6), 1748−1763. (30) Aso, Y.; Yoshioka, S.; Kojima, S. Molecular Mobility-Based Estimation of the Crystallization Rates of Amorphous Nifedipine and Phenobarbital in Poly(Vinylpyrrolidone) Solid Dispersions. J. Pharm. Sci. 2004, 93 (2), 384−391. (31) Grzybowska, K.; Paluch, M.; Grzybowski, A.; Wojnarowska, Z.; Hawelek, L.; Kolodziejczyk, K.; Ngai, K. L. Molecular Dynamics and Physical Stability of Amorphous Anti-Inflammatory Drug: Celecoxib. J. Phys. Chem. B 2010, 114 (40), 12792−12801. (32) Zhou, D.; Zhang, G. G. Z.; Law, D.; Grant, D. J. W.; Schmitt, E. A. Thermodynamics, Molecular Mobility and Crystallization Kinetics of Amorphous Griseofulvin. Mol. Pharmaceutics 2008, 5 (6), 927−936. (33) Nunes, C.; Mahendrasingam, A.; Suryanarayanan, R. Quantification of Crystallinity in Substantially Amorphous Materials by Synchrotron X-Ray Powder Diffractometry. Pharm. Res. 2005, 22 (11), 1942−1953. (34) Zhu, L.; Jona, J.; Nagapudi, K.; Wu, T. Fast Surface Crystallization of Amorphous Griseofulvin Below Tg. Pharm. Res. 2010, 27 (8), 1558−1567. (35) Zhou, D.; Grant, D. J. W.; Zhang, G. G. Z.; Law, D.; Schmitt, E. A. A Calorimetric Investigation of Thermodynamic and Molecular Mobility Contributions to the Physical Stability of Two Pharmaceutical Glasses. J. Pharm. Sci. 2007, 96 (1), 71−83. (36) Goresy, T. E.; Böhmer, R. Dielectric Relaxation Processes in Solid and Supercooled Liquid Solutions of Acetaminophen and Nifedipine. J. Phys.: Condens. Matter 2007, 19 (20), 205134.
(37) Crowley, K. J.; Zografi, G. The Use of Thermal Methods for Predicting Glass-Former Fragility. Thermochim. Acta 2001, 380 (2), 79−93. (38) Ngai, K. L.; Capaccioli, S. Relation between the Activation Energy of the Johari−Goldstein B Relaxation of Glass Formers. Phys. Rev. E 2004, 69 (3), 031501. (39) Gnutzmann, T.; Kahlau, R.; Scheifler, S.; Friedrichs, F.; Rossler, E. A.; Rademann, K.; Emmerling, F. Crystal Growth Rates and Molecular Dynamics of Nifedipine. CrystEngComm 2013, 15 (20), 4062−4069. (40) Tarjus, G.; Kivelson, D. Breakdown of the Stokes−Einstein Relation in Supercooled Liquids. J. Chem. Phys. 1995, 103 (8), 3071− 3073. (41) Champion, D.; Hervet, H.; Blond, G.; Le Meste, M.; Simatos, D. Translational Diffusion in Sucrose Solutions in the Vicinity of Their Glass Transition Temperature. J. Phys. Chem. B 1997, 101 (50), 10674−10679. (42) Cicerone, M. T.; Ediger, M. Enhanced Translation of Probe Molecules in Supercooled O-Terphenyl: Signature of Spatially Heterogeneous Dynamics? J. Chem. Phys. 1996, 104 (18), 7210−7218. (43) Fujara, F.; Geil, B.; Sillescu, H.; Fleischer, G. Translational and Rotational Diffusion in Supercooled Orthoterphenyl Close to the Glass Transition. Zeitschrift für Physik B Condensed Matter 1992, 88 (2), 195−204. (44) Roessler, E.; Tauchert, J.; Eiermann, P. Cooperative Reorientations, Translational Motions, and Rotational Jumps in Viscous Liquids. J. Phys. Chem. 1994, 98 (33), 8173−8180. (45) Brian, C. W.; Yu, L. Surface Self-Diffusion of Organic Glasses. J. Phys. Chem. A 2013, 117 (50), 13303−13309. (46) Johari, G. P.; Goldstein, M. Viscous Liquids and the Glass Transition. II. Secondary Relaxations in Glasses of Rigid Molecules. J. Chem. Phys. 1970, 53 (6), 2372−2388. (47) Johari, G. P.; Power, G.; Vij, J. K. Localized Relaxation in a Glass and the Minimum in Its Orientational Polarization Contribution. J. Chem. Phys. 2002, 117 (4), 1714−1722. (48) Ngai, K. L. Relation between Some Secondary Relaxations and the α-Relaxations in Glass-Forming Materials According to the Coupling Model. J. Chem. Phys. 1998, 109 (16), 6982−6994.
■
NOTE ADDED AFTER ASAP PUBLICATION This paper was published ASAP on August 8, 2014, without an Acknowledgments section. The corrected version was reposted on September 2, 2014.
3055
dx.doi.org/10.1021/mp500229d | Mol. Pharmaceutics 2014, 11, 3048−3055
