Enhancement of Amorphous Celecoxib Stability by Mixing It with

Article pubs.acs.org/molecularpharmaceutics

Enhancement of Amorphous Celecoxib Stability by Mixing It with Octaacetylmaltose: The Molecular Dynamics Study K. Grzybowska,*,† M. Paluch,† P. Wlodarczyk,† A. Grzybowski,† K. Kaminski,† and L. Hawelek†,‡ †

Institute of Physics, University of Silesia, ul. Uniwersytecka 4, 40-007 Katowice, Poland Institute of Non Ferrous Metals, ul. Sowinskiego 5, 44-100 Gliwice, Poland

‡

D. Zakowiecki Department R&D, Pharmaceutical Works Polpharma SA, Pelplinska 19, 83-200 Starogard Gdanski, Poland

A. Kasprzycka Division of Organic Chemistry, Biochemistry and Biotechnology, Department of Chemistry, Silesian University of Technology, ul. Krzywoustego 4, 44-100 Gliwice, Poland

I. Jankowska-Sumara Institute of Physics, Pedagogical University of Cracow, ul. Podchoraz̨ ẏ ch 2, 30-084 Kraków, Poland ABSTRACT: In this paper, we present a novel way of stabilization of amorphous celecoxib (CEL) against recrystallization by preparing binary amorphous celecoxib−octaacetylmaltose (CEL−acMAL) systems by quench-cooling of the molten phase. As far as we know this is the first application of carbohydrate derivatives with acetate groups to enhance the stability of an amorphous drug. We found that CEL in the amorphous mixture with acMAL is characterized by a much better solubility than pure CEL. We report very promising results of the long-term measurements of stability of the CEL−acMAL binary amorphous system with small amount of stabilizer during its storage at room temperature. Moreover, we examined the effect of adding acMAL on molecular dynamics of CEL in the wide temperature range in both the supercooled liquid and glassy states. We found that the molecular mobility of the mixture of CEL with 10 wt % acMAL in the glassy state is much more limited than that in the case of pure CEL, which correlates with the better stability of the amorphous binary system. By dielectric measurements and theoretical calculations within the framework of density functional theory (DFT), we studied the role of acMAL in enhancing the stability of amorphous CEL in mixtures and postulated which interactions between CEL and acMAL molecules can be responsible for preventing devitrification. KEYWORDS: celecoxib, octaacetylmaltose, amorphous drug, molecular dynamics, glass transition, crystallization, devitrification, physical stability, secondary relaxations

■

INTRODUCTION Transformations of poorly water-soluble crystalline pharmaceuticals to the amorphous form is one of the most promising strategies to improve their oral bioavailability. In contrast to ordered crystals, amorphous solids are high-energy states containing no long-range order and presenting molecular arrangements similar to that of liquids. In the case of amorphous drugs, the structure of which is only short-range ordered, no energy is required to break up the crystal lattice during the dissolution process, and thus the enhancement of drug solubility and dissolution rate is usually achieved.1−3 However, amorphous solids are thermodynamically out of equilibrium states since they necessarily contain an excess of © 2012 American Chemical Society

Gibbs energy with reference to the crystalline phases. It can result in a decreased physical stability of the amorphous state, manifested by the tendency to change to a more stable state under recrystallization (the excess energy stored in the unstable state of an amorphous solid can release either completely through recrystallization associated with ΔG < 0 or partially by means of irreversible relaxation processes).4 The physical instability is the major disadvantage of amorphous drugs Received: Revised: Accepted: Published: 894

August 26, 2011 January 25, 2012 March 2, 2012 March 2, 2012 dx.doi.org/10.1021/mp200436q | Mol. Pharmaceutics 2012, 9, 894−904

Molecular Pharmaceutics

Article

acMAL system. To the best of our knowledge this is the first application of carbohydrate derivatives with acetate groups to enhance the stability of an amorphous drug. The amorphous solid dispersion CEL−acMAL is prepared by quench-cooling of the molten phase. By dielectric measurements and theoretical calculations within the framework of density functional theory (DFT), we study a molecular mechanism of crystallization inhibition of the amorphous CEL in acMAL matrix.

because they may undergo recrystallization over the time course of processing, storage, and use of the product. A key factor governing the stability of amorphous phases is molecular mobility.5−8 It is because of the fact that even below the glass transition temperature Tg, when the amorphous system is characterized by very high viscosity or by very slow structural relaxation times, there is enough mobility for an amorphous system to recrystallize for pharmaceutically relevant time scales. Recently, it has been reported that molecular mobility is an important factor in the large tendency toward recrystallization of the celecoxib (CEL) (Figure 1) in both the

■

EXPERIMENTAL METHODS Materials. The crystalline form of celecoxib (CEL) of 98% purity and molecular mass of Mw = 381 g/mol was supplied from Polpharma (Starogard Gdanski, Poland). Celecoxib, 4-[5(4-methylphenyl)-3-(trifluoromethyl)-1H-pyrazol-1-yl]benzenesulfonamide, selectively inhibits cyclooxygenase-2 (COX-2) enzymes and it is used in the treatment of osteoarthritis, rheumatoid arthritis, and management of pain. Octaacetylmaltose (acMAL) of molecular mass of Mw = 678.59 g/mol was synthesized at Silesian University of Technology (Division of Organic, Chemistry, Biochemistry and Biotechnology, Gliwice, Poland). The structure of the obtained compound and its purity (99%) was confirmed by nuclear magnetic resonance spectra. Method of Preparation of Amorphous Systems CEL with acMAL. The amorphous CEL, acMAL and binary systems CEL−acMAL with different amounts of acMAL were prepared by the quench cooling technique in the temperature and humidity controlled glovebox (PLAS LABORATORIES Inc. 890-THC-DT/EXP/SP) at the assured relative humidity RH < 5%. In order to obtain the homogeneous CEL−acMAL mixtures, first we thoroughly mixed crystalline powders of both compounds in appropriate proportions in a heat-resistant glass vial (weight of powder mixture was about 0.5 g). After that we put the magnetic stir bars into the vial with the mixture. Next, the crystalline mixture sample was melted in the vial on the hot plate magnetic stirrer (CAT M 17.5) at T = 443.15 K. The temperature inside the vial was controlled by using Pt-100 sensor. Only when the crystalline mixture CEL−acMAL was fully melted was the magnetic mixing (about 500 rpm) switched on (to avoid forming some crystalline powder deposit on the walls of the vial). After about 3−4 min of magnetic stirring of the liquid mixture we obtained homogeneous CEL− acMAL liquid solutions. Then we vitrified the solution by fast transfer of the vial from the hot plate to a very cold metal plate. The amorphous samples obtained in this way were analyzed immediately after the preparation to protect them from atmospheric moisture. We investigated several octaacetylmaltose mixtures of celecoxib with different concentrations of octaacetylmaltose collected in Table 1. Thermogravimetric Analysis (TGA). We performed the thermogravimetric measurements of the crystalline forms of CEL and acMAL to evaluate the temperature ranges of thermal

Figure 1. Chemical structures of the investigated compounds (a) celecoxib and (b) octaacetylmaltose.

supercooled liquid and glassy states.9−12 Our study9 showed that the amorphous CEL prepared by quench-cooling of the melt of its crystalline form is physically unstable and it is easy to recrystallize below and above Tg. The degree of recrystallization of pure amorphous CEL reaches nearly 90% after 10 days of storage at room temperature (more than 30 K below the glass transition temperature of the drug). Based on results of the broadband dielectric spectroscopy measurements we concluded that the strong tendency of amorphous CEL toward crystallization is related to the large molecular mobility reflected in the three secondary relaxations (β, γ, δ). Among them the β-process can play an important role, because it is the true JG relaxation involving intermolecular motions of the entire molecule, and hence it is a precursor of the structural αrelaxation. At present, a great influence of molecular mobility reflected in secondary relaxations on nucleation and crystal growth in the glassy state of drugs is often considered.5−7,13−17Attempts have been also made to correlate physical instability of drug below and above Tg with the molecular motions reflected in the structural α-relaxation. We found that α-relaxation times at the temperature of storage of amorphous CEL correspond to the time of maximum rate of recrystallization of amorphous CEL at this temperature. Therefore, we concluded that besides secondary processes the structural relaxation can be also responsible for devitrification of the drug.9 The sensitivity of the α-relaxation times to temperature changes in the vicinity of Tg can be classified for various glassformers by the isobaric fragility concept. “Fragile” glass-formers are characterized by molecular mobility, which varies rapidly with temperature near Tg in contrast to that occurring in “strong” liquids. Therefore, it is often considered that strong liquids are more physically stable than fragile liquids.18−20 We found that the dynamic fragility parameter for CEL is marked by the large value mp = 110 (determined for Tg at α-relaxation time equal to 100 s), which allowed us to classify this drug as a fragile liquid.9 This finding correlates with the large tendency of CEL toward crystallization. In this paper, we analyze the stabilization effect of the low molecular weight excipient octaacetylmaltose (acMAL) on amorphous celecoxib (CEL) in the binary amorphous CEL−

Table 1. The Investigated Octaacetylmaltose Mixtures of Celecoxiba CW (wt %) xacMAL

0 0

10 0.06

30 0.19

50 0.36

100 1

a

CW: weight percentage concentration of octaacetylmaltose. xacMAL: mole fraction of octaacetylmaltose. 895

dx.doi.org/10.1021/mp200436q | Mol. Pharmaceutics 2012, 9, 894−904


Article

all samples were initially sonicated in an ultrasonic bath Sonorex RK 52 (Bandelin Electronic, Berlin, Germany) for few minutes, and then mechanically shaken at 180 rpm in a shaking water bath, Grant OLS200 (Grant Instruments Ltd., Cambridge, U.K.), at a temperature of 310 K. After two hours samples were withdrawn and filtered through a glass fiber membrane filter having pore size 1.0 μm (Pall). Solubility of CEL and CEL−acMAL systems, expressed as concentration of drug substance in solution after two hours of shaking (in micrograms per milliliter), was determined with the help of the liquid chromatographic method (UPLC). Separation was carried out using the ACQUITY UPLC system from Waters (Milford, MA, USA) and 50 mm columns with an internal diameter of 2.1 mm, packed with 1.7 μm ACQUITY UPLC BEH C18 particles from Waters (Wexford, Ireland). The column was thermostated at 298 K. UV absorbance data were collected at 265 nm with a data collection rate of 40 points per second. The mobile phase consisted of acetonitrile and a mixture of 1 mL of ortho-phosphoric acid 85% and 1 mL of triethylamine in 450 mL of purified water. The elution was carried out at a flow rate of 0.5 mL per minute and was completed in 5 min. The partial loop with needle overfill option was used, and the injection volume was 0.5 μL. Additionally, a syringe draw rate of 100 μL, needle overfill flush of 15 μL and both air gaps (preaspirate and postaspirate) of 0.3 μL were used. The needle was washed with 200 μL of acetonitrile (as a strong wash) and 600 μL of a mixture of water and acetonitrile (as a weak wash). Water and acetonitrile were mixed in a volume ratio of 1:1. Analysis data were acquired and calculated using the Empower Pro 2 software from Waters (Milford, MA, USA). Computational. Theoretical studies on the celecoxib were performed within the framework of density functional theory (DFT) in the orca program package.21 The geometry of the celecoxib molecule was optimized at the B3LYP/6-31G* level. Conformational interconversions were studied by performing relaxed geometry scans at the same level of theory. The optimized structure, which had the highest energy, was further optimized as a transition state by eigenvector following the method implemented in orca. The transition state was confirmed by performing frequency analysis. Vibrational frequencies were calculated numerically. The geometry of celecoxib dimer (CEL−CEL), as well as celecoxib−octaacetylmaltose complex (CEL−acMAL), was optimized at the PBE/6-31G* level of theory. The gradient PBE functional is quite good for describing hydrogen bond structures, especially for predicting binding strengths.22

degradation of these compounds. The measurements were carried out using Perkin-Elmer Pyris 1 TGA instrument. The thermogravimetric curves were obtained during heating of the samples of weight about 2 mg at rate 10 K/min. Differential Scanning Calorimetry (DSC). Thermodynamic properties of crystalline and amorphous forms of CEL and acMAL have been investigated by differential scanning calorimetry. Calorimetric measurements were performed with Mettler-Toledo DSC apparatus equipped with a liquid nitrogen cooling accessory and a HSS8 ceramic sensor (heat flux sensor with 120 thermocouples). Temperature and enthalpy calibrations were carried out by using indium and zinc standards. The amorphous form of each of the compounds was prepared in an open aluminum crucible (40 μL) outside the DSC apparatus in the glow-box at RH < 5%. First, the crystalline sample was melted in the crucible on the heating plate (CAT M 17.5), and next the melt was immediately cooled to vitrify the sample. Crucibles with such prepared glassy samples as well as with their crystalline counterparts have been sealed with the top with one puncture. Crystalline and amorphous samples were scanned at a rate of 10 K/min over a temperature range of 298 K to well above the respective melting points. X-ray Diffraction. The long-term isothermal X-ray diffraction measurements for the amorphous mixture of CEL with 10 wt % acMAL were carried out at room temperature (T = 293 K) on the laboratory Rigaku-Denki D/MAX RAPID II-R diffractometer attached with a rotating anode Ag Kα tube (λ = 0.5608 Å), an incident beam (0 0 2) graphite monochromator and an image plate in the Debye−Scherrer geometry. The pixel size was 100 μm × 100 μm. The amorphous samples of the composition CEL−acMAL were placed inside Lindemann glass capillaries (1.5 mm in diameter). Measurements were performed for the sample filled and empty capillaries, and the intensity for the empty capillary was then subtracted. The beam width at the sample was 0.1 mm. The two-dimensional diffraction patterns were converted into the one-dimensional intensity data using suitable software. Broadband Dielectric Spectroscopy Measurements. Isobaric measurements of the dielectric permittivity ε*(ω) = ε′(ω) − iε″(ω) were carried out using the Novo-Control Alpha dielectric spectrometer over the frequency range from 3 × 10−3 to 3 × 106 Hz at ambient pressure. Dielectric measurements of CEL−acMAL mixtures were performed in a parallel-plate cell (diameter, 20 mm; gap, 0.1 mm) immediately after preparation of the amorphous sample. The sample temperatures in the range (120−423 K) were controlled by a Quatro System using a nitrogen gas cryostat. The temperature stability was better than 0.1 K. Water Solubility Study. Chemicals and Reagents. Acetonitrile of HPLC grade was supplied by Merck (Darmstadt, Germany). High purity water used in analytical procedures was obtained from a Millipore Milli-Q plus ultrapure water system (Bedford, MA, USA). Triethylamine anhydrous was supplied by POCH (Gliwice, Poland). Orthophosphoric acid 85%, used for pH adjustment, was purchased from Merck (Darmstadt, Germany). Equipment and Experimental Conditions. Aqueous solubility of CEL (crystalline, amorphous and quenched with acMAL) was determined in purified and deionized water. An excess amount of sample to be tested was added to 10 mL of pure water in a conical flask. In order to disintegrate any agglomerates, which can exist, especially in quenched material,

■

RESULTS AND DISCUSSION Merits of Using acMAL as a Stabilizer of Amorphous CEL. The first step of our study was checking if we can safely prepare (without thermal decomposition) the amorphous CEL−acMAL binary systems by quench cooling of their melt. In order to do it, we performed the calorimetric and thermogravimetric measurements for crystalline forms of CEL and acMAL to evaluate their melting temperatures as well as check whether these compounds do not undergo thermal degradation during the melting process. As can be seen in Figure 2 the melting endotherms of the crystalline forms of CEL (Tm = 435 K) and acMAL (Tm = 429 K) obtained from DSC measurements are situated far from the range of their thermal decomposition. TGA and DTG curves indicate that the onset of thermal decomposition of both 896



Article

Figure 3. The DSC thermogram of the amorphous forms of CEL and acMAL obtained during the heating at 10 K/min. The inset indicates the glass−liquid transitions for both compounds.

Figure 2. Thermal analysis of crystalline forms of CEL and acMAL. All thermograms have been obtained during heating at a rate of 10 K/min. The upper panel presents DSC scans, and the middle panel, curves obtained from thermogravimetric measurements, whereas the lower panel shows the first derivatives of TGA curves.

two hours for the amorphous mixtures of CEL with 10 wt % and 30 wt % of acMAL are about 6 times and 12 times respectively better than that for the crystalline CEL (see Figure 4). Gupta et al.25 also observed the increase in solubility of

compounds begins above 500 K whereas maximum rates of degradation for acMAL and CEL occur at 594 and 637 K, respectively. Therefore melting the crystalline forms of CEL and acMAL and preparing the amorphous composition based on both compounds by vitrification is safe. Because the melting temperatures of CEL and acMAL are similar, we were able to mix both compounds in their liquid states quickly and thoroughly without the hazard of components overheating. We found out that CEL and acMAL in the liquid states easily mix together in any weight ratio and form homogeneous solutions. This is the important advantage of acMAL over maltose, which easily caramelizes during the melting process,23 does not mix with liquid CEL, and consequently cannot be used as amorphous CEL stabilizer in the amorphous binary system prepared by vitrification. It is worth noting that preparation of the CEL−acMAL mixtures by quench cooling of the melt does not consume a lot of time and does not require using any additional solvents in contrast to the other amorphous binary mixtures (e.g., CEL with polyvinlpyrrolidone (PVP), CEL with hydroxypropylmethylcellulose (HPMC)) prepared by the solvent evaporation and precipitation techniques.24−28 However, more efforts are required to effectively scale up the vitrification method. The important feature of stabilizers of amorphous drug is a lack of tendency toward crystallization. DSC thermograms for acMAL and CEL obtained during heating of the amorphous samples (see Figure 3) indicate that acMAL does not crystallize in a wide temperature range (we did not observe any exothermic thermal effects) whereas pure CEL is characterized by a strong tendency toward crystallization. We also found from DSC measurements that values of the glass transition temperatures for CEL and acMAL are nearly the same, i.e. Tg(acMAL) = 332 K Tg(CEL) = 331 K. Therefore, one can suppose that the enhancement of physical stability by addition of acMAL to CEL will not be related to significant changes in Tg. This issue will be disused in the next sections. The next and one of the most important advantages of using acMAL as an amorphous CEL excipient is a significant enhancement of the water solubility of the drug in the acMAL matrix. Measurements of the aqueous solubility of the crystalline and amorphous CEL as well as amorphous CEL− acMAL binary systems showed that the solubilities reached in

Figure 4. Comparison of aqueous solubility of crystalline and amorphous CEL as well as the amorphous CEL−acMAL binary mixtures with 10 wt % and 30 wt % of acMAL at 310 K.

other amorphous binary systems: CEL−PVP in relation to pure amorphous and crystalline CEL. They found that the solubility reached in 2 h for amorphous CEL−PVP systems with 10 wt % is about 5 times better than that for crystalline CEL. For higher concentrations of PVP (20, 40, and 60 wt %), the values of solubility of CEL−PVP reached in 2 h are similar, and they are about 6 times better than that of crystalline CEL. Therefore, the results of solubility obtained for amorphous CEL−acMAL binary systems are promising from the therapeutic point of view. Isothermal Study of Amorphous CEL−acMAL System Stability below Tg. Recently, we presented the results of isothermal recrystallization studies of an amorphous form of pure CEL which has been stored several days at room temperature T = 293 K and under quasi-constant humidity conditions RH = 10%.9 These investigations have been performed by means of X-ray diffraction at specified time periods, starting from the moment of preparing of the amorphous sample. On the basis of the obtained diffraction patterns we evaluated the relative degree of crystallization Dc and plotted these values as a function of storage time. We found that the amorphous form of CEL is highly unstable and after 10 days of storage its recrystallization degree Dc achieves 87% (see Figure 5). Analogous long-term investigations of 897



Article

Figure 5. The relative degree of isothermal recrystallization Dc of amorphous CEL and CEL + 10% acMAL as a function of storage time tS at room temperature T = 293 K. The insets present the diffraction patterns for pure CEL and the CEL + 10% acMAL system after 10 and 270 days of storage, respectively. The data for pure CEL presented here for the readers’ convenience has been already published by us in ref 9. Solid lines are only guides for the eyes.

stability were performed for the CEL−acMAL binary amorphous system with the smallest amount of 10 wt % of acMAL during 9 months of storage at the same conditions as pure amorphous CEL. The diffraction patterns for pure CEL and the CEL + 10% acMAL system measured immediately after their vitrification had a form of broad amorphous halos (not shown here) which confirms the lack of three-dimensional long-range ordered structure. However, as storage time goes on, the area of sharp peaks for CEL increases with time, indicating the increase of degree of recrystallization, whereas diffraction patterns of CEL + 10% acMAL systems remain unchanging and degree of recrystallization of the systems equals zero even after 9 months of storage (see Figure 5). It indicates that 10 wt % of additive of acMAL fully suppressed a recrystallization of the amorphous CEL during its storage at normal condition. Molecular Dynamics of CEL−acMAL Systems. To find the molecular origin of the effect of acMAL as a good recrystallization inhibitor for the amorphous CEL, we performed measurements of molecular dynamics of several CEL−acMAL binary amorphous systems with different contents of acMAL by using broadband dielectric spectroscopy. Representative dielectric spectra for CEL, CEL + 10% acMAL, CEL + 30% acMAL, CEL + 50% acMAL and acMAL measured at ambient pressure and in the wide temperature ranges are presented in Figure 6a−d. As can be seen in Figure 6 the relaxation spectra of all the examined mixtures are strongly dependent on temperature. Above the glass−liquid transition temperatures (about 330 K), in the supercooled liquid states, all systems reveal one well-separated α-relaxation process with large amplitude. The dominant α-process is a structural relaxation related to the glass transition. During vitrification, the α-process enormously slows down shifting to lower frequencies. Such an extremely rapid increase in the structural relaxation times on system cooling is a main feature of the liquid−glass transition, whereas, in the glassy state, the αrelaxation is too slow to be experimentally observed. In this region, faster processes with smaller amplitudes called secondary relaxations come to play a main role and provide us with information on molecular dynamics in glasses. As can be seen in Figure 6 dielectric spectra obtained in both the liquid and glassy states significantly depend on the content of acMAL. This will be the main subject of further analysis. To describe

Figure 6. Dielectric loss spectra for pure CEL (a) and binary mixtures CEL + 10% acMAL (b), CEL + 30% acMAL (c), CEL + 50% acMAL (d), and pure acMAL (e) at several temperatures and ambient pressure obtained during heating of the amorphous systems. The data for pure CEL (a) and acMAL (e) shown here for the readers’ convenience have been already published in refs 9 and 33, respectively.

relaxation processes and determine their relaxation times we performed a numerical fitting analysis of the entire dielectric spectra as a superposition of the Havriliak−Negami (HN) function describing the broad and asymmetric α peak, and the 898



Article

proportional to the total amount of relaxing units participating in the structural process. It is clearly seen that with an increase in the amount of acMAL in the CEL−acMAL binary mixture the onset of a system's recrystallization occurs at higher temperature and the degree of crystallization becomes smaller and smaller (the drop of Δεα values becomes less rapid). It indicates that the stability of CEL−acMAL systems in their supercooled liquid states monotonically increases as acMAL is gradually added to the mixture. The system becomes fully stable if the weight concentration of acMAL is larger than 30 wt %. Based on the analysis of dielectric spectra obtained for CEL− acMAL systems at T > Tg, we evaluated structural relaxation times τα for each temperature. The temperature dependences of α-relaxation times for all systems were fitted to the Vogel− Fulcher−Tamman equation29 in the same temperature range. We used the VFT parameters to evaluate values of the isobaric fragility mp as well as the glass transition temperatures Tg for all examined systems. By extrapolation of the VFT fits to τα = 10 s, we determined the glass transition temperatures of the mixtures

Cole−Cole (CC) functions which appropriately describe symmetric secondary relaxations. The complex permittivity ε*(ω) data of quenched investigated systems are fitted to the following formula: ε*(ω) = ε′(ω) − iε″(ω) = ε∞ +

∑

Δεk

ξk δk k [1 + (iωτk ) ] (1)

Here ε∞ is the high frequency limit permittivity and k denotes the primary and the secondary processes. Δεk is the relaxation strength, τk is the HN relaxation time, and ξk and δk are the HN exponents of the relaxation processes. For secondary relaxation processes, δk = 1, so that the HN function becomes the CC function. Above the glass transition temperature Tg, spectra have been satisfactory fitted by a superposition of ionic conductivity and one HN function, whereas to describe dielectric spectra in the glassy state a superposition of three CC functions has been applied for pure CEL and one CC function for the rest of the investigated systems. Molecular Dynamics of the Supercooled Liquid: Structural Relaxation, Nonisothermal Crystallization, Glass Transitions, and Fragilities. In this section, we examine the effect of addition of acMAL into CEL on structural relaxation behavior in the liquid state of the binary mixtures. As we have already reported in ref 9, the amorphous CEL not only easily recrystallizes in the glassy state during its isothermal storage at temperatures much below Tg but also recrystallizes on heating in the liquid state at temperatures T ≥ 365 K. By analyzing the structural relaxation presented in Figure 6, we found that a small amount of acMAL in the CEL−acMAL binary mixture does not fully protect a supercooled CEL against crystallization. For all investigated systems shown in Figure 6 we observe that the structural relaxation speeds up on heating. However, the α-process peaks with nearly constant amplitude Δεα ≈ const for pure CEL, CEL + 10% acMAL, and CEL + 30% acMAL moving toward higher frequencies on heating up only to some temperature Tc. Above Tc the dielectric strength of the α-process, Δεα, begins to rapidly decrease, which is caused by the onset of the mixture recrystallization on heating and reflects the increasing degree of crystallinity (see Figure 6a−c). In Figure 7 we plotted the temperature dependence of dielectric strength Δεα of the α-process which value is

Table 2. The Isobaric Fragilities mp and Glass Transition Temperatures Tg for Investigated Systems Obtained from Dielectric Measurements

a

material

Tga (K)

mpa

CEL CEL + 10% acMAL CEL + 30% acMAL CEL + 50% acMAL acMAL

331 330 329 329 331

89 80 74 76 100

For τα = 10 s.

(Table 2). Then, their fragility parameters are calculated by using the following formula: m≡

d log τα d(Tg /T )

= T = Tg

D(T0/Tg ) (1 − (T0/Tg ))2 ln(10)

(2)

The values of Tg and mp are plotted against the molar fraction of acMAL (Figure 8). As can be seen in Figure 8 we found an unusual, nonmonotonic behavior of the function of isobaric

Figure 7. Temperature dependence of the dielectric strength Δεα of αrelaxation for supercooled mixtures of CEL−acMAL with 0, 10, 30 and 50 wt % acMAL content. The inset shows the changes of the crystallization onset temperatures with addition of acMAL to the mixtures. Solid lines are guides for the eyes.

Figure 8. Dependences of isobaric fragility mp and glass transition temperatures Tg for the CEL−acMAL binary systems versus mole fraction of acMAL in the mixture. Values of mp and Tg have been evaluated at τα = 10 s. 899



Article

fragility mp for the considered mixtures CEL + acMAL vs mole fraction of acMAL. It is often considered that a weaker molecular mobility near Tg in the case of strong liquids results in the smaller nucleation and growth rate of crystals, and consequently a weaker tendency toward crystallization than fragile liquids. As can be seen in Figure 8, pure CEL and acMAL are the most fragile liquids from the investigated systems, whereas their mixtures belong to the stronger glass-formers. It indicates that, near Tg, the structure of CEL−acMAL mixtures changes with temperature to a smaller extent than those for pure components. It could suggest a better stability of the binary mixtures. However, mp(xacMAL) reaches a minimum and then it starts increasing. Thus, the stability of CEL−acMAL mixtures, which continuously increases with adding acMAL, cannot be rather correlated with the mixtures' fragility. Figure 8 can also suggest a nonmonotonic behavior of the dependence of Tg(xacMAL) and its deviation from the line predicted by the Gordon−Taylor (G−T) equation.30 However, the values of Tg vary only within the range of 2 K, and despite small Tg error bars, it cannot lead us to the conclusion that acMAL plasticizes CEL in the binary system. The very small differences in the values of Tg of the binary systems, pure CEL and acMAL also do not correlate with the significant enhancement of physical stability by adding acMAL to CEL. Molecular Dynamics of the Glassy States of CEL− acMAL Systems: Secondary Relaxations. As it has been recently reported by us,9 a high degree of molecular mobility found in the glassy state of pure CEL can be responsible for its strong tendency toward crystallization. In the dielectric spectra of CEL, we distinguished as many as three secondary relaxations, i.e., the slower β-process, faster γ-process, and the fastest δ-process. On the basis of the extended coupling model,31,32 we classified the β-process as a Johari−Godstein (JG) relaxation, which confirms its intermolecular nature. It indicates that the β-process characterized by a large value of activation energy (ΔEβ = 80 kJ/mol) reflects some fast local motions of the whole CEL molecules which trigger the structural relaxation, and thus the β-process can play an important role in devitrification of the drug. Moreover, the faster secondary relaxations (γ and δ) with smaller values of energy activation (ΔEγ = 51 kJ/mol and ΔEδ = 21 kJ/mol) have been ascribed to intramolecular motions of side groups of the CEL molecule. Therefore, we have not assigned a significant role of γ- and δ-processes in the physical stability of amorphous celecoxib.9 Now, we will analyze the effect of adding acMAL into CEL on the secondary relaxations of the binary mixtures in the glassy state to find molecular factors responsible for stabilization of amorphous CEL in acMAL dispersions. By using eq 1 we performed the analysis of dielectric spectra obtained for CEL− acMAL binary systems at T < Tg, to evaluate secondary relaxation times. Unfortunately, we could not evaluate secondary relaxation times in the case of all CEL−acMAL binary systems. As can be seen in Figures 5, 8 and 9, the dielectric spectra of pure CEL exhibit three secondary relaxation processes (β, γ, δ), whereas pure acMAL exhibits only one secondary relaxation, herein called the μacMAL-process (which originates from the intramolecular rotations of the acetyl moiety (C−O−(COCH3)), of the acMAL molecule.33 As acMAL is added to CEL, we observe a significant increase in the contribution of the μacMAL-process to dielectric spectra of the binary mixtures, which indicates that a molecular dynamics

Figure 9. Comparison of dielectric spectra of all investigated systems measured at T = 193 K.

of mixtures in the glassy state is gradually dominated by acMAL (see Figure 9). The amplitude of the μacMAL-process increases with increasing acMAL content while the dielectric strength of the δ-process is nearly invariable. Consequently, a wellseparated δ-process is visible only for the binary system with the smallest amount of acMAL (CEL + 10% acMAL), whereas, in the case of the acMAL-rich mixtures (30 wt % and 50 wt %), δ- and μacMAL-secondary processes are strongly coupled to each other. It results in very broad dielectric spectra, without separated maxima of individual relaxation processes. Since a determination of relaxation times of secondary processes for CEL + 30% acMAL and CEL + 50% acMAL binary systems would be highly speculative, we focused on the analysis of secondary relaxations for the mixture with the smallest content of acMAL (CEL + 10% acMAL). A comparison of selected dielectric spectra obtained for two systems (pure CEL and CEL + 10% acMAL) in the glassy state is presented in Figure 10. We found that the addition of 10 wt

Figure 10. Comparison of dielectric spectra of the pure CEL and its mixture CEL + 10% acMAL measured at T = 193 K (a) and T = 273 K (b). Solid lines indicate fits of the entire dielectric spectra based on superposition of Cole−Cole functions which describe the individual secondary processes (dotted lines).

% acMAL to CEL significantly modifies relaxation dynamics of the amorphous CEL, i.e., (i) 10 wt % of acMAL in the binary mixture suppresses the β (JG)-relaxation. In contrast to pure CEL, for the CEL + 10% acMAL system, we cannot distinguish the β-process from spectra (see Figure 10b). It indicates that the β900



Article

in refs 9. and 33, respectively. As can be seen in Figure 11, the values of activation energies ΔEδ as well as δ-relaxation times are nearly the same for pure CEL and CEL + 10% acMAL. This finding confirms that acMAL does not influence the δrelaxation of CEL. DFT Simulations: Conformations of CEL. We have studied the conformations and the possible interconversion pathways of the celecoxib molecule in order to identify its secondary relaxation modes, observed by means of dielectric spectroscopy. We have studied rotations of three groups, i.e., Ph−SONH2, CF3, and Ph−CH3 (where Ph denotes phenyl ring). Simulations of rotations performed for a single molecule within the framework of density functional theory enabled us to determine activation energies which are shown in Table 3. The

relaxation becomes slower in the mixture than that in pure CEL and shifts toward lower frequency. It can be one of the important reasons for stabilization of the amorphous form of CEL in CEL−acMAL binary systems. (ii) 10 wt % of acMAL in the binary mixture causes the freezing of some molecular motions reflected in the γprocess. After adding acMAL to CEL one can observe the significant (or even complete) decrease in the dielectric strength of the γ-process (see Figure 10a,b). It is important to recognize the molecular origin of the γprocess for pure CEL, because some specific interactions between CEL and acMAL, which suppress the molecular motions that underly the γ-process, may prevent devitrification of CEL. Such an analysis based on density functional theory (DFT) simulations will be presented in the next section. (iii) In dielectric spectra of the mixture CEL + 10% acMAL at T < Tg, we observe only one well-separated secondary relaxation (δ-process) which is characterized by the same relaxation times as those observed for pure CEL (i.e., 10% acMAL in the mixture does not influence the δrelaxation which originates from pure CEL). Thus, the molecular mobility of the mixture of CEL + 10% acMAL in the glassy state is much more limited than that in the case of pure CEL. The suppressed molecular mobility of the amorphous CEL in the matrix of acMAL can be responsible for preventing devitrification of the drug. The temperature dependence of δ-relaxation times determined for the CEL + 10% acMAL system and its comparison with secondary relaxation times for pure CEL and acMAL are shown in Figure 11. The experimental temperature dependence

Table 3. Activation Energies for Rotations of Side Groups of the CEL Molecule Determined on the Basis of Simulations Performed for a Single Molecule within the Framework of Density Functional Theory type of conformational interconversion

act. energy ΔE (kJ/mol)

Ph−CH3 rotation Ph−SO2NH2 rotation CF3 rotation

17 (HB independent) 16 (HB dependent) 1.5 (HB dependent)

rotation of the CF3 substituent is connected with very small fluctuations of dipole moment despite the fact that the fluorine is the most electronegative atom of all. Contrary to this situation, movements of Ph−CH3 or Ph−SONH2 cause a large fluctuation of the dipole moment of the molecule from 2.8 to 7.4 D (see Figure 12), therefore only these two conversions could be observed by means of dielectric spectroscopy which is sensitive to the change of dipole moment. The rotations of both phenyl ring are not independent, i.e., while one of the phenyl rings is rotating and when the rings become perpendicular to each other, the second phenyl ring is being repulsed. Thus, the rotation of the low polar Ph−CH3 group causes a large fluctuation of dipole moment because of the repulsion of the Ph−SONH2 substituent during conversion. As can be seen in Table 3, both group rotations have activation energies about 20 kJ/mol. However, calculations are performed for the isolated molecule, without external hydrogen bonds (HB). The sulfonamide group from the Ph−SONH2 part is a great HB former. Nitrogen atoms from the amino group can act as proton donors or proton acceptors. Therefore, in the real system, one can be certain that the NH2 fragment is a part of a HB network. In such a situation, the activation energy calculated for the rotation of the Ph−SONH2 part is in fact higher by a factor related to the value of HB energy, while the activation energy for the Ph−CH3 part can be compared directly with experiment. On the basis of DFT calculations, we postulate that the origin of dielectric γ-relaxation is the rotation of the Ph− SONH2 group of CEL. Moreover, characteristics of this movement highly depend on the HB dynamics in the system due to the ability of the NH2 group to form hydrogen bonds. The fastest δ-relaxation probably originates from the rotation of the Ph−CH3 part of CEL. Moreover, this rotation is independent of hydrogen bonding in the system, because the CH3 substituent is unable to form hydrogen bonds. DFT Simulations: Comparison of CEL−CEL and CEL− acMAL Complexes. In order to better understand the stabilization of celecoxib in the amorphous state by adding

Figure 11. Comparison of relaxation maps for the pure CEL, its mixture CEL + 10% acMAL, and pure acMAL. Solid lines indicate fits of the entire dielectric spectra based on superposition of Cole−Cole functions which describe the individual secondary processes (dotted lines). Crossed open symbols denote structural relaxation times determined in the recrystallization range during heating of the systems in the supercooled liquid state. Relaxation maps for pure CEL and acMAL have been already published in refs 9 and 33, respectively.

of τδ for CEL + 10% acMAL has been described by the Arrhenius equation, τ(T) = τ∞ exp(ΔE/kT), where τ∞ is preexponential factor, ΔE is energy barrier and k is Boltzmann constant. As a result we obtained the following fitting parameters: log τ∞δ(CEL+10%acMAL) = −12.23, ΔEδ(CEL+10%acMAL) = 22 kJ/mol for the δ-process. Fitting parameters for secondary relaxations for pure CEL and acMAL has been already reported 901



Article

Figure 12. Diagrams represent energy and dipole moment fluctuations during certain conformational interconversions of the CEL molecule. The left diagram represents rotation of the phenyl ring with the methyl group, while the right one represents rotation of the phenyl ring with the attached sulfonamide group.

equal to 148°. Despite the fact that the hydrogen bonds are more curved, binding energy between CEL and acMAL molecules is quite high, i.e., 58 kJ/mol. This value is even higher than the CEL−CEL binding energy, which is quite surprising. Moreover, a single acMAL molecule is large enough to bind three CEL molecules. In summary, the CEL−acMAL connection is concurrent with the CEL−CEL one, because of the similar binding energy. Therefore, acMAL molecules effectively form hydrogen bonds with CEL molecules.

acetylmaltose to the system, we have optimized geometries of CEL−CEL dimer and CEL−acMAL complex. As can be seen in Figure 13 there are strong hydrogen bonds in both systems. In the CEL−CEL dimeric structure, there are two major hydrogen bonds. The first one, NH···F, has length 2.30 Å, and the NHF angle is equal to 160°. The second one NH···N has length 2.05 Å, and the angle NHN is equal to 173°. Binding energy between two molecules, which is the sum of van der Waals and hydrogen bond interactions, is equal to 56.5 kJ/mol, which well corresponds to the value of the activation energy of the dielectric γ-relaxation of pure CEL (see Figure 11). Octaacetylmaltose as a pure sample is unable to form hydrogen bonds. Despite the fact that there are HB acceptor sites in the acMAL molecule, i.e., oxygen atoms with lone electron pairs, there are no proton donors. However, if acMAL is mixed with CEL, the acMAL molecule can accept a HB from a CEL molecule created by the NH2 group. Therefore, one can see two major NH···OC hydrogen bonds in Figure 13. The first one has length equal to 2.23 Å and NHO angle equal to 140°. The second one has length equal to 2.24 Å and NHO angle

■

CONCLUSIONS In this paper, we presented a novel way of stabilization of amorphous CEL against recrystallization by preparing an amorphous binary mixtures of CEL with octaacetylmaltose by using a simple quench cooling technique. acMAL has several merits to be used as an amorphous drug excipient: (i) it is nontoxic, (ii) it reveals no tendency toward crystallization (iii) it does not undergo thermal decomposition during the melting process (in contrast to the natural maltose, acMAL does not caramelize), and (iv) it easily mixes with CEL, when both 902



Article

responsible for nucleation and crystal growth in the solid structure of the amorphous pharmaceuticals. Such a suppression of these fast small-angle reorientations of entire CEL molecules by acMAL can reduce the ability of the amorphous CEL to form critical nuclei and devitrify the system. (ii) Moreover, 10 wt % of acMAL in the binary mixture causes the freezing of some molecular mobility reflected in the γ-process. We observe this phenomenon as a rapid decrease in the dielectric strength of γ-process after adding acMAL to CEL. Based on DFT calculations, we can postulate that the γ-relaxation involves rotations of the −Ph−SONH2 group of CEL, which are arrested by strong H-bonds formed between the −Ph−SONH2 group of CEL and the −CO group of acMAL. It is worth noting that the same molecular mechanism of the amorphous CEL stability enhancement has been reported by Gupta et al.9 for the CEL−PVP binary system where hydrogen bonds are formed between the −NH2 group of CEL and the −CO group of PVP. However, PVP has a strong antiplasticizing effect on the amorphous CEL and significantly increases the Tg of the system, whereas the Tg of CEL−acMAL binary systems are lower than that for pure CEL.

Figure 13. Optimized structures of the CEL−CEL dimer and the CEL−acMAL complex. Two major hydrogen bonds are marked for each structure. Protons from the sulfonamide group are donors, while the oxygens in the case of acMAL and nitrogen and fluorine in the case of the second CEL molecule are acceptors. Hydrogen bonds in the CEL−CEL dimer are closer to the linear form. Hydrogen bonds in the CEL−acMAL complex are curved.

■

AUTHOR INFORMATION

Corresponding Author

*Institute of Physics, University of Silesia, ul. Uniwersytecka 4, 40-007 Katowice, Poland. E-mail: katarzyna.grzybowska@us. edu.pl.

components are in the liquid state, forming a homogeneous binary system which can be effortlessly vitrified by rapid cooling from the liquid state. Moreover, we established that the water solubility of amorphous CEL in the acMAL matrix is significantly better than those for the crystalline and amorphous forms of pure CEL. It is an important benefit for therapeutic effects. We found that acMAL characterized by the same value of Tg as CEL is a good inhibitor of the amorphous drug recrystallization. Long-term isothermal measurements of stability of the amorphous binary system of CEL with only 10 wt % acMAL show that there are no signs of the sample recrystallization after 9 months of storage at room temperature (degree of recrystallization of pure amorphous CEL reaches nearly 90% after 10 days of storage at the same conditions). However, 10 wt % of acMAL does not protect the CEL− acMAL binary system against crystallization during its heating in the supercooled liquid state. We found that the stability of the supercooled CEL−acMAL binary liquid is continuously enhanced with increasing acMAL content in the mixture. Supercooled liquid crystallization is fully suppressed if the weight concentration of acMAL is larger than 30 wt %. The monotonic increase in the CEL−acMAL system stability does not correlate with the nonmontonic behavior of the acMAL content dependences of mp and Tg. We found that the molecular mobility of the mixture of CEL + 10% acMAL in the glassy state is much more limited than that in the case of pure CEL. It correlates with the better stability of the binary system. The protection of the amorphous CEL against devitrification by adding acMAL can be related to some specific interactions of acMAL with CEL molecules, which significantly affect secondary relaxations: (i) The addition of 10 wt % acMAL to CEL slows down some local molecular motions reflected in the β (Johari− Goldstein) relaxation, which are often considered as

Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors are deeply thankful for the financial support of their research within the framework of the project entitled “From Study of Molecular Dynamics in Amorphous Medicines at Ambient and Elevated Pressure to Novel Applications in Pharmacy” (Contract No. TEAM/2008-1/6), which is operated within the Foundation for Polish Science Team Programme cofinanced by the EU European Regional Development Fund.

■

REFERENCES

(1) Adrjanowicz, K.; Kaminski, K.; Paluch, M.; Wlodarczyk, P.; Grzybowska, K.; Wojnarowska, Z.; Hawelek, L.; Sawicki, W.; Lepek, P.; Lunio, R. Dielectric relaxation studies and dissolution behavior of amorphous verapamil hydrochloride. J. Pharm. Sci. 2010, 99, 828−839. (2) Adrjanowicz, K.; Grzybowska, K.; Kaminski, K.; Hawelek, L.; Paluch, M.; Zakowiecki, D. Comprehensive studies on physical and chemical stability in liquid and glassy states of telmisartan (TEL): solubility advantages given by cryomilled and quenched material. Philos. Mag. 2011, 91, 1926−1948. (3) Kaminski, K.; Adrjanowicz, K.; Wojnarowska, Z.; Grzybowska, K.; Hawelek, L.; Paluch, M.; Zakowiecki, D.; Mazgalski, J. Molecular dynamics of the cryomilled base and hydrochloride ziprasidones by means of dielectric spectroscopy. J. Pharm. Sci. 2011, 2642−2657. (4) Hilfiker, R. Polymorphism in the Pharmaceutical Industry; WILEYVCH: Weinheim, Germany, 2006; pp 259−285. (5) Bhattacharya, S.; Suryanarayanan, R. Local mobility in amorphous pharmaceuticals--characterization and implications on stability. J. Pharm. Sci. 2009, 98, 2935−2953. (6) Bhugra, C.; Pikal, M. J. Role of thermodynamic, molecular, and kinetic factors in crystallization from the amorphous state. J. Pharm. Sci. 2008, 97, 1329−1349.

903



Article

(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, 1159−1175. (8) Wojnarowska, Z.; Grzybowska, K.; Adrjanowicz, K.; Kaminski, K.; Paluch, M.; Hawelek, L.; Wrzalik, R.; Dulski, M.; Sawicki, W.; Mazgalski, J.; Tukalska, A.; Bieg, T. Study of the Amorphous Glibenclamide Drug: Analysis of the Molecular Dynamics of Quenched and Cryomilled Material. Mol. Pharmaceutics 2010, 7, 1692−1707. (9) 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, 12792−12801. (10) P. Gupta, P.; Chawla, G.; Bansal, A. K. Physical stability and solubility of advantage from amorhous celecoxib: the role of thermodynamic quantities and molecular mobility. Mol. Pharmaceutics 2004, 1 (6), 406−413. (11) Kaushal, A. M.; Bansal, A. K. Thermodynamic behavior of glassy state of structurally related compounds. Eur. J. Pharm. Biopharm. 2008, 69, 1067−1076. (12) Dantuluri, A. K. R.; Amin, A.; Puri, V.; Bansal, A. K. Role of αRelaxation on Crystallization of Amorphous Celecoxib above Tg Probed by Dielectric Spectroscopy. Mol. Pharmaceutics 2011, 8 (3), 814−822. (13) Johari, G. P.; Kim, S.; Shanker, R. M. Dielectric study of equimolar acetaminophen-aspirin, acetaminophen-quinidine, and benzoic acid-progesterone molecular alloys in the glass and ultraviscous states and their relevance to solubility and stability. J. Pharm. Sci. 2010, 99, 1358−1374. (14) Alie, J.; Menegotto, J.; Cardon, P.; Duplaa, H.; Caron, A.; Lacabanne, C.; Bauer, M. Dielectric study of the molecular mobility and the isothermal crystallization kinetics of an amorphous pharmaceutical drug substance. J. Pharm. Sci. 2004, 93, 218−233. (15) Hikima, T.; Hanaya, M.; Oguni, M. β-Molecular Rearrangements Process, But Not an α-Process, as Governing the Homogenous Crystal-Nucleation Rate In a Supercooled Liquid. Bull. Chem. Soc. Jpn. 1996, 69, 1863−1868. (16) Paladi, F.; Oguni, M. Anomalous generation and extinction of crystal nuclei in nonequilibrium supercooled liquid o-benzylphenol. Phys. Rev. B 2002, 65, 144202−144207. (17) Paladi, F.; Oguni, M. Generation and extinction of crystal nuclei in an extremely non-equilibrium glassy state of salol. J. Phys.: Condens. Matter 2003, 15, 3909−3917. (18) Hancock, B. C.; Shamblin, S. L. Molecular mobility of amorphous pharmaceuticals determined using differential scanning calorimetry. Thermochim. Acta 2001, 380, 95−107. (19) Tanaka, H. Relationship among glass-forming ability, fragility, and short-range bond ordering of liquids. J. Non-Cryst. Solids 2005, 351, 678−690. (20) Shintani, H.; Tanaka, H. Frustration on the way to crystallization in glass. Nat. Phys. 2006, 2, 200−206. (21) Neese, F. ORCAan ab initio, Density Functional and Semiempirical program package, Version 2.6; University of Bonn: Bonn, 2008. (22) Rabuck, A. D.; Scuseria, G. E. Performance of recently developed kinetic energy density functionals for the calculation of hydrogen binding strengths and hydrogen-bonded structures. Theor. Chem. Acc. 2000, 104, 439−444. (23) Wlodarczyk, P.; Kaminski, K.; Adrjanowicz, K.; Wojnarowska, Z.; Czarnota, B.; Paluch, M.; Ziolo, J.; Pilch, J. Identification of the slower secondary relaxation’s nature in maltose by means of theoretical and dielectric studies. J. Chem. Phys. 2009, 131, 125103-1−125103-7. (24) Gupta, P.; Thilagavathi, R.; Chakraborti, A. K.; Bansal, A. K. Role of Molecular Interaction in Stability of Celecoxib − PVP Amorphous Systems. Mol. Pharmaceutics 2005, 2, 384−391. (25) Gupta, P.; Kakumanu, V. K.; Bansal, A. K. Stability and Solubility of Celecoxib−PVP Amorphous Dispersions: A Molecular Perspective. Pharm. Res. 2004, 21, 1762−1769.

(26) Zhuang, H.; Gao, P. Stable Amorphous Celecoxib Composite and Process Therefor. United States Patent US 6,864,373 B2, 2005. (27) Taylor, L. S.; Zografi, G. Spectroscopic characterization of interactions between PVP and indomethacin in amorphous molecular dispersions. Pharm. Res. 1997, 14, 1691−1698. (28) Kakumanu, V. K.; Bansal, A. K. Enthalpy relaxation studies of celecoxib amorphous mixtures. Pharm. Res. 2002, 19, 1873−1878. (29) Vogel, H. Das Temperaturabhangigkeitgesetz der Viskosität von Flüssigkeiten. J. Phys. Z. 1921, 22, 645−646. Fulcher, G. S. Analysis of Recent Measurements of the Viscosity of Glasses. J. Am. Ceram. Soc. 1925, 8, 339−355. Tammann, G.; Hesse, W. Die Abhängigkeit der Viscosität von der Temperatur bie unterkühlten Flüssigkeiten. Z. Anorg. Allg. Chem. 1926, 156, 245−257. (30) Gordon, M.; Taylor, J. S. Ideal copolymers and the second-order transitions of synthetic rubbers 1: Non-crystalline copolymers. J. Appl. Chem. 1952, 2, 493−498. (31) Ngai, K. L. An extended coupling model description of the evolution of dynamics with time in supercooled liquids and ionic conductors. J. Phys.: Condens. Matter 2003, 15, S1107. (32) Ngai, K. L.; Paluch, M. Classification of secondary relaxation in glass-formers based on dynamic properties. J. Chem. Phys. 2004, 120, 857−873. (33) Kaminski, K.; Wlodarczyk, P; Hawelek, L.; Adrjanowicz, K.; Wojnarowska, Z.; Paluch, M.; Kaminska, E. Comparative dielectric studies on two hydrogen-bonded and van der Waals liquids. Phys. Rev. E 2011, 83, 061506-1−061506-9.

904


Enhancement of Amorphous Celecoxib Stability by Mixing It with

Recommend Documents