Molecular Factors Governing the Liquid and Glassy States

Article pubs.acs.org/molecularpharmaceutics

Molecular Factors Governing the Liquid and Glassy States Recrystallization of Celecoxib in Binary Mixtures with Excipients of Different Molecular Weights K. Grzybowska,*,†,‡ K. Chmiel,†,‡ J. Knapik-Kowalczuk,†,‡ A. Grzybowski,†,‡ K. Jurkiewicz,†,‡ and M. Paluch†,‡ †

Institute of Physics, University of Silesia in Katowice, ul. Uniwersytecka 4, 40-007 Katowice, Poland Silesian Center for Education and Interdisciplinary Research, ul. 75 Pułku Piechoty 1a, 41-500 Chorzów, Poland

‡

ABSTRACT: Transformation of poorly water-soluble crystalline pharmaceuticals to the amorphous form is one of the most promising strategies to improve their oral bioavailability. Unfortunately, the amorphous drugs are usually thermodynamically unstable and may quickly return to their crystalline form. A very promising way to enhance the physical stability of amorphous drugs is to prepare amorphous compositions of APIs with certain excipients which can be characterized by significantly different molecular weights, such as polymers, acetate saccharides, and other APIs. By using different experimental techniques (broadband dielectric spectroscopy, differential scanning calorimetry, X-ray diffraction) we compare the effect of adding the large molecular weight polymerpolyvinylpyrrolidone (PVP K30)and the small molecular weight excipientoctaacetylmaltose (acMAL) on molecular dynamics as well as the tendency to recrystallization of the amorphous celecoxib (CEL) in the amorphous solid dispersions: CEL−PVP and CEL−acMAL. The physical stability investigations of the binary systems were performed in both the supercooled liquid and glassy states. We found that acMAL is a better inhibitor of recrystallization of amorphous CEL than PVP K30 deep in the glassy state (T < Tg). In contrast, PVP K30 is a better crystallization inhibitor of CEL than acMAL in the supercooled liquid state (at T > Tg). We discuss molecular factors governing the recrystallization of amorphous CEL in examined solid dispersions. KEYWORDS: celecoxib, amorphous drug, solid dispersion, molecular dynamics, glass transition, crystallization, devitrification, physical stability

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INTRODUCTION

crystalline drugs may act slowly, and high doses are necessary to reach the therapeutic effect. The problem is serious, because more than 70% of new drug candidates and 40% of the marked drugs are poorly soluble in water.1,2 The very promising method for solving this problem is the transformation of the crystal drug structure to the more disordered amorphous form. In contrast to the crystalline solids, to dissolve an amorphous drug any additional energy does not need to be provided to destroy the crystal lattice. This

Most drugs are formulated in the solid state. The same solid material can be crystalline or amorphous. It is well-known that crystalline solids have long-range atomic order. This is in contrast to the much more disordered amorphous solids, which have only short-range atomic order. It should be emphasized that a significantly greater number of solid drugs are nowadays prepared in the crystalline form because it is the most thermodynamically stable solid state. Consequently, properties of crystalline pharmaceuticals in general do not change during their long-term storage even if temperature or humidity is changing in the relatively wide range. However, it has been found that many drugs in the crystalline form are poorly watersoluble and their bioavailability can be strongly limited. Such © 2017 American Chemical Society

Received: Revised: Accepted: Published: 1154

November 21, 2016 February 16, 2017 February 27, 2017 February 27, 2017 DOI: 10.1021/acs.molpharmaceut.6b01056 Mol. Pharmaceutics 2017, 14, 1154−1168

Article

Molecular Pharmaceutics

role in the devitrification of CEL below its Tg due to the following correlation: the time scale of α-relaxation of CEL in the glassy state (at TRT = 20 °C) very well corresponds to the storage time of amorphous CEL after which the crystallization rate becomes maximal at TRT.11 This correlation indicates that the drug recrystallization deep in the glassy state can be controlled by the molecular motions reflected in the structural α-relaxation. Similar conclusions have been drawn not only for CEL but also for other drugs, i.e., indomethacin,23,24 ezetimibe,25 griseofulvin,26 itraconazole,27 trehalose.28 Nevertheless, a role of faster molecular motions reflected in various secondary relaxations in the CEL devitrification cannot be certainly excluded. Many efforts have been recently put into finding effective and efficient methods for preventing the recrystallization of amorphous pharmaceuticals. A very promising way to enhance the physical stability of amorphous drugs is to prepare amorphous compositions of a drug with certain excipients (crystallization inhibitors) which can be characterized by different molecular weights, including large molecular weight polymers and low molecular weight compounds such as saccharides, acetated saccharides, amino acids, or other drugs. The increase in the physical stability of the drug in such amorphous solid dispersions can be achieved by interplaying different factors,29−31 one being (i) antiplasticization effect of excipients on the drug. This factor mainly refers to polymers, because most polymeric excipients have a much higher Tg than Tg of drugs. Mixing of two compounds which have different Tg causes an increase in Tg of the binary mixture (drug−polymer) compared with Tg of pure API. The increase in Tg of the binary composition is associated with a decrease in the global molecular mobility of the mixture, and consequently with an enhancement of the physical stability of a drug in this amorphous binary system. However, the antiplasticization is not always sufficient to completely suppress the recrystallization.32 An important role in increasing the physical stability is often played by (ii) specif ic intermolecular interactions between molecules of drug and excipient such as hydrogen bonds or ionic interactions. Molecules of excipient which are able to specifically interact with the drug molecules prevent the recrystallization process of the drug.8,31−33 In this work, we examine and compare the effects of adding large molecular weight polymer polyvinylpyrrolidone (PVP K30) and low molecular weight octaacetylmaltose (acMAL) on the molecular mobility and the tendency to recrystallization of the amorphous CEL in the binary mixtures CEL−PVP and CEL−acMAL, respectively. It should be noted that these binary systems are interesting because earlier investigations showed that molecules of CEL can interact with the molecules of acMAL and PVP via hydrogen bonds formed between the same functional groups of drug and crystallization inhibitors (N−H··· CO).8,17 Moreover, the large molecular weight polymer PVP is a good antiplasticizer of CEL in contrast to the small molecular weight acMAL, because the value of Tg for PVP is much higher than that for CEL, while the values of Tg for acMAL and CEL are nearly the same.8,17 The investigations of physical stability and molecular dynamics of the binary compositions presented in this paper are performed in a wide temperature range in both the liquid and glassy states. There are still not many such studies, which are very important to gain better insights into correlations between molecular mobility and crystallization of pharmaceuticals above and below their Tg.

is why the amorphous drugs are usually characterized by significantly higher water solubility.3−10 For drugs characterized by low solubility but high permeability, which are classified to group II of biopharmaceutical classification system BCS-2, the enhanced aqueous solubility of a drug due to its amorphization will also lead to improvement of its bioavailability. Unfortunately, amorphous systems are not perfect due to their physical instability. Glassy materials are in a nonequilibrium state and may recrystallize during their storage or manufacturing, losing in this way their valuable properties coming from a disordered structure.11−14 One of the model drugs, which is characterized by the large tendency to recrystallization from the amorphous state, is celecoxib (CEL). The physical stability of the supercooled and glassy CEL has been already intensively studied.8,11,15−17 It has been established from calorimetric and dielectric measurements that the supercooled liquid state of CEL is highly unstable and recrystallizes under both nonisothermal11,15,17 and isothermal15,16 conditions (that is during heating of the liquid drug or during its storage at a fixed temperature T, which is higher that the glass transition temperature, Tg, and lower than the melting point, Tm). Moreover, long-term isothermal X-ray diffraction measurements (XRD) showed that the glassy state of CEL also easily recrystallizes during its isothermal storage at room temperature TRT = 20 °C, which is much lower (i.e., ∼30 °C) than Tg of the drug.11 It has been estimated that the maximum rate of crystallization of the initially fully amorphous celecoxib occurs after 100 h of its storage at TRT, whereas after 10 days of storage under the same conditions the sample becomes almost completely crystalline. It illustrates a large tendency of the glassy CEL to recrystallization. Probably the most important factor determining stability of amorphous drugs is their molecular mobility. Relatively large molecular mobility of amorphous pharmaceuticals can lead to their conversion to the stable crystalline state. Therefore, it seems to be essential to investigate molecular dynamics of amorphous drugs to reliably predict their tendency to recrystallization and to develop effective and efficient methods for their stabilization.18−22 However, the study of correlations between the molecular mobility of amorphous drugs and their physical stability is usually complicated. It should be noted that pharmaceuticals are often characterized by complex molecular structures of different conformations and intra- and intermolecular interactions, including specific interactions (e.g., hydrogen bonds of different strength or electrostatic forces). Consequently, the glass-forming pharmaceuticals usually exhibit complex molecular mobility reflected in several relaxation processes, which can be thoroughly explored by using broadband dielectric spectroscopy (BDS). Complex molecular dynamics has been also established for CEL, for which several dielectric relaxation processes can be observed in dielectric spectra. In the supercooled liquid state, the structural αrelaxation dominates. It reflects cooperative motions of many molecules together, and it is responsible for the liquid−glass transition, which is usually assumed to take place when the structural relaxation time τα = 100 s. In the glassy state, the αrelaxation becomes too long to be experimentally detected and only secondary relaxations can be measured. In the glassy CEL, as many as three secondary relaxations, β, γ, and δ, have been distinguished, which are much faster than the structural relaxation and reflect some local motions of whole molecules or reorientations of some parts of molecules. Our investigations showed that the structural relaxation may play an important 1155

DOI: 10.1021/acs.molpharmaceut.6b01056 Mol. Pharmaceutics 2017, 14, 1154−1168

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Molecular Pharmaceutics Table 1. Chemical Structures of Investigated Compounds

after preparing of the amorphous sample. The sample temperatures were controlled by Quatro System using a nitrogen gas cryostat. The temperature stability was better than 0.1 K. Differential Scanning Calorimetry (DSC). Calorimetric measurements of the nonisothermal cold crystallization of the investigated binary mixtures were carried out by MettlerToledo DSC apparatus equipped with a liquid nitrogen cooling accessory and an HSS8 ceramic sensor (heat flux sensor with 120 thermocouples). Temperature and enthalpy calibrations were performed by using indium and zinc standards. The amorphous form of each binary composition was prepared in an open aluminum crucible (40 μL) outside the DSC apparatus. 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 were sealed with the top with one puncture. Amorphous samples were scanned at fixed heating rate 10 K/min over a temperature range of 303 K to well above the respective melting points. Each measurement at given heating rate was repeated 3 times. For each experiment a new amorphous sample was prepared. To obtain the accurate temperature dependences of heat capacity Cp(T) for examined mixtures and temperature dependence of calorimetric structural relaxation times for pure PVP K30, a stochastic temperature-modulated differential scanning calorimetry (TMDSC) technique implemented by Mettler-Toledo TOPEM has been exploited. The samples were heated at a rate of 0.5 K/min. In the experiment, temperature amplitude of the pulses of 0.5 K was selected. To achieve higher accuracy of the heat capacity we adjusted our evaluations using a sapphire reference curve. The glass transition temperature Tg was determined as the temperature of the half step height of the temperature dependences of the quasi-static heat capacity Cp(T). X-ray Diffraction (XRD). The long-term isothermal X-ray diffraction measurements for the amorphous mixtures of CEL with 5% and 10% PVP were carried out at several temperatures near room temperature TRT = 293 K on the laboratory RigakuDenki D/MAX RAPID II-R diffractometer attached with a rotating anode Ag Kα tube (λ = 0.5608 Å), an incident beam (0

Our thorough analyses are mainly aimed at answering the following questions: (i) Which of the excipients (PVP or acMAL) more effectively impedes the recrystallization of glassy and supercooled CEL in the mixtures? (ii) Can we predict the physical stability of the glassy state of CEL in the solid dispersions based only on supercooled liquid crystallization kinetics? (iii) Which molecular factors may govern the recrystallization of amorphous CEL in the binary compositions with small and large molecular weight excipients (acMAL and PVP K30)?

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EXPERIMENTAL METHODS Materials. The crystalline form of the nonsteroidal antiinflammatory drug celecoxib (CEL) of 98% purity and molecular mass of 381g/mol was supplied from Polpharma (Starogard Gdanski, Poland). The amorphous form of polyvinylpyrrolidone (PVP K30) of molecular weight 40000 g/mol (number of monomer units: n ≈ 360) was purchased from Fluka (Switzerland). Beta-D-maltose octaacetate (acMAL) of molecular mass of 678.59 g/mol was supplied from Iris Biotech GMBH (Germany) in the crystalline form. Chemical structures of the examined materials are presented in Table 1. Method of Preparation of Amorphous Solid Dispersions CEL with PVP. The amorphous binary systems CEL−PVP and CEL−acMAL with different amounts of excipients were prepared by a simple quench-cooling of the molten phase of the binary mixtures. It is worth noting that both of excipients easily mix with CEL, when CEL is molten (that is, when the drug is in the liquid phase). The obtained amorphous binary solutions were homogeneous mixtures. Broadband Dielectric Spectroscopy Measurements (BDS). Isobaric measurements of the dielectric permittivity ε*(ω) = ε′(ω) − iε″(ω) were carried out using the NovoControl Alpha dielectric spectrometer over the frequency range 10−2−106 Hz and in the temperature range 120−523 K at ambient pressure. Nonisothermal measurements and kinetics of isothermal crystallization of CEL−PVP and CEL−acMAL mixtures were performed in a parallel-plate cell immediately 1156


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Molecular Pharmaceutics 0 2) graphite monochromator, and an image plate in the Debye−Scherrer geometry. The pixel size was 100 μm × 100 μm. Samples were placed inside 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.

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RESULTS AND DISCUSSION To answer the question “Which of the excipients (PVP or acMAL) more effectively impedes the recrystallization of glassy and supercooled CEL in the mixtures?” we investigated the binary compositions in a wide temperature range by using different experimental techniques such as BDS, DSC, and XRD. We studied the physical stability of the binary compositions in both the supercooled liquid (T > Tg) and glassy states (T < Tg) during their isothermal storage at a given temperature as well as under nonisothermal conditions, i.e., upon their heating at some rate. Such studies are important, because amorphous drugs are produced and stored under different thermodynamic conditions. The Experimental Evidence for the Better Physical Stability of the Supercooled Liquid State of CEL + PVP K30 than That of CEL + acMAL. Nonisothermal Investigations at T > Tg. The stability of the amorphous state is often defined as the resistance to recrystallization above its Tg upon reheating a drug from its glassy to liquid state. Thus, in fact, the physical stability of glassy drugs is established based on the physical stability of their supercooled liquid state.34,35 It is commonly considered that the crystallization process is related to molecular mobility, which increases with increasing temperature. Consequently, glass forming materials generally faster recrystallize above Tg in the metastable supercooled liquid state (where molecular mobility is relatively high) than below Tg in the unstable solid glassy state (where molecular mobility is strongly reduced). Since the physical stability measurements of the glassy state are often highly timeconsuming, most investigations of the devitrification of drugs are performed in the supercooled liquid state. The physical stability of the glassy state is then concluded based only on the crystallization tendency of the supercooled liquid. In this paper, we verify whether or not we can predict which of the crystallization inhibitors (PVP either acMAL) better stabilizes CEL in the amorphous solid dispersions only based on the physical stability investigations of the supercooled liquid state of both the binary mixtures. To characterize the molecular mobility of examined binary mixtures (CEL−PVP) as well as to find its relation with the physical stability of CEL in the binary compositions under nonisothermal conditions, the molecular dynamics measurements of CEL mixtures with different content of polymer PVP were performed by means of BDS. The selected dielectric spectra for pure CEL, CEL + 10 wt % PVP, CEL + 15 wt % PVP, and pure PVP obtained in the wide temperature range during heating of the samples are presented in Figure 1. It should be emphasized that the analogous study of the molecular dynamics of the binary mixtures of CEL (with various amounts of acMAL) has been recently published in ref 8. It is clearly seen that the dielectric spectra, and thus the molecular mobility of investigated systems, strongly depend on temperature. Above Tg, in the supercooled liquid state, all systems revealed well separated α-relaxation. When the sample

Figure 1. Dielectric loss spectra for pure CEL (a), binary compositions CEL + 10% PVP (b), CEL + 15% PVP (c), and pure PVP K30 (d) obtained at several temperatures during heating the amorphous samples.

is heated, the α-relaxation peak evidently shifts to higher frequencies and its magnitude is almost constant. It indicates that the global molecular mobility of examined systems 1157


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Figure 2. Temperature dependences of relative structural dielectric strength Δεα/Δεαmax obtained during heating the binary systems: (a) CEL + PVP and (b) CEL + acMAL. (c) Comparison of temperatures of the nonisothermal crystallization onsets Tc for the binary compositions of CEL + acMAL and CEL + PVP above Tg versus weight concentrations of excipients. (d) Comparison of the time scales of α-relaxation at temperatures of the nonisothermal crystallization onsets Tc for the binary compositions of CEL + acMAL and CEL + PVP above Tg versus weight concentrations of excipients.

10 wt % PVP is higher by 20 K than that for CEL + 10 wt % acMAL, and 1 wt % PVP exerts a considerably stronger effect on Tc of the compositions with CEL than 10 wt % acMAL; see Figure 2c). This is the first evidence that PVP K30 is a better nonisothermal crystallization inhibitor of CEL in the supercooled liquid state than acMAL. However, it is worth noting that the temperature Tc, commonly used to assess the tendency of various amorphous drugs to crystallization, is considered to be questionable if the glass transition temperatures Tg of examined systems are significantly different. In such cases, other methods should be applied to more reliably compare the physical stability of the amorphous systems. Based on BDS measurements, we propose to compare the time scales of the global molecular mobility at which the crystallization onset occurs during heating of the systems, i.e., τc = τα(Tc). This measure of the physical stability is suitable for any glass-forming liquid, because the time scale of α-relaxation at which the glass transition occurs is assumed to τα(Tg) = 100 s for all materials. Thus, τα(Tg) can be regarded as the same reference point for τc independently of the values of Tg for compared systems. As can be seen in Figure 2d, the relaxation times τc for the investigated supercooled binary mixtures CEL + PVP are shorter than those for the supercooled binary mixtures CEL + acMAL at the same weight concentration of excipients. For instance, the value of τc of CEL + 10 wt % PVP is about 1 decade shorter than that for CEL + 10 wt % acMAL. It means that the crystallization onset of the supercooled mixture CEL + 10 wt % PVP compared to CEL + 10 wt % acMAL takes place

increases. In other words, the time scale of molecular motions reflected in α-relaxation (i.e., α-relaxation times) becomes shorter with an increase in temperature. It can be also noted that the dielectric strength of the αprocess, Δεα, begins to rapidly decrease in the case of pure CEL and its mixtures with a small amount of PVP at some higher temperatures (e.g., T > 360 K for pure CEL and T > 387 for CEL + 10 wt % PVP) (see Figure 1a,b). Such a sudden drop in Δεα(T) is due to the sample recrystallization on heating and reflects the increasing degree of crystallinity. For the binary mixtures of CEL with more content of PVP (≥15 wt % PVP), we do not observe such a decrease in Δεα(T), which means that these supercooled systems are resistant to recrystallization upon their reheating. For supercooled CEL and its mixtures with PVP, which recrystallize during their heating, we determined temperatures Tc of the crystallization onset. In this study, Tc is defined as a temperature at which the relative structural dielectric strength Δεα/Δεαmax drops by 10%, which corresponds with the shelf life of the amorphous binary compositions (see Figure 2). In a similar way, the temperature Tc has been evaluated from the dielectric measurements of CEL + acMAL mixtures reported in ref 8. As a result, we established that the dependence of Tc vs weight concentration of crystallization inhibitor (and also the physical stability) much more rapidly increases for mixtures with PVP than that for mixtures with acMAL. It can be seen that Tc is much higher for CEL + PVP than CEL + acMal at the same percentage concentration weight of excipients (for example, Tc for CEL + 1158


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Figure 3. Representative DSC heating (10 K/min) curves for (a) pure CEL, binary mixtures of CEL with PVP K30, and pure PVP K30, as well as for (b) pure CEL, binary mixtures of CEL with acMAL, and pure acMAL. (c) The comparison of reduced crystallization temperatures Tred defined by eq 1 for binary compositions of CEL + acMAL and CEL + PVP versus weight concentrations of excipients.

Figure 4. Time dependences of normalized real permittivity ε′N for the binary mixtures (a) CEL + 10 wt % acMAL and (b) CEL + 10 wt % PVP, obtained from BDS measurements during isothermal storage of the binary compositions at different temperatures above Tg. (c) The temperature dependence of logarithm of the crystallization rate k for pure CEL (data taken from ref 16), and for the binary mixtures of CEL with 10 wt % PVP, 10 wt % acMAL, and 30 wt % acMAL.

dielectric study. In the DSC measurements, we do not observe any signs of crystallization in the mixture of CEL if the content of PVP is 10 wt % or larger (≥10 wt % PVP), whereas we need more than 30 wt % of acMAL in the mixture to stabilize the drug. In our DSC measurements, we found that CEL + 50 wt % acMAL certainly does not crystallize. Similarly to the BDS investigations of nonisothermal crystallization, these calorimetric results suggest that PVP is a better nonisothermal crystallization inhibitor of the supercooled binary systems than acMAL. This observation can be well quantified and verified by using the so-called reduced crystallization temperature Tred defined by Zhou et al.36 by the simple formula:

at the shorter time scale of the global relaxation with respect to the time scale of the glass transition. Thus, we can say that a supercooled system is more physically stable on heating if its cold crystallization occurs at a higher global molecular mobility. To confirm this result we also performed the nonisothermal calorimetric (DSC) measurements for both the examined binary mixtures (CEL + acMAL and CEL + PVP). In these investigations, the samples were heated from the glass to the supercooled liquid state at constant heating rate of 10 K/min. We found that temperatures (Tcryst_onset) of the crystallization onset manifested in DSC thermograms as an exothermal effect are increasing with increasing content of a given crystallization inhibitor in both the binary mixtures (see Figure 3a,b). Nevertheless, the increase in Tcryst_onset is much more pronounced for CEL + PVP mixtures than that for CEL + acMAL, similarly as the increase in Tc determined from the

Tred = 1159

Tcryst_onset − Tg Tm − Tg

(1) DOI: 10.1021/acs.molpharmaceut.6b01056 Mol. Pharmaceutics 2017, 14, 1154−1168

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Figure 5. Dielectric spectra of the real part of the complex dielectric permittivity collected during an isothermal crystallization of (a) CEL + 10% acMAL and (b) CEL + 10% PVP at different temperatures T > Tg but at the same α-relaxation times τα ≈ 4.28 μs of the binary mixtures. (c) Dielectric spectra of the imaginary part of the complex dielectric permittivity which illustrates the same time scale of the global molecular dynamics of the supercooled mixtures CEL + 10 wt % acMAL and CEL + 10 wt % PVP, obtained at temperatures 367 and 375 K, respectively. (d) Time dependence of normalized real permittivity ε′N for the binary mixtures CEL + 10 wt % acMAL and CEL + 10 wt % PVP, obtained during isothermal storage of the binary compositions at different temperatures T = 367 K and T = 375 K but at the same α-relaxation times τα ≈ 4.28 μs of the binary mixtures.

Isothermal Investigations at T > Tg. We also tested how effectively both the crystallization inhibitors stabilize CEL in the supercooled binary mixtures (CEL + acMAL and CEL + PVP) in isothermal conditions. We performed isothermal measurements of crystallization kinetics of the supercooled binary compositions by means of the BDS. As a result, we obtained the dependences of the degree of crystallization vs storage time of the binary systems of CEL with different content of acMAL and PVP at given temperatures above Tg. The curves of crystallization kinetics are shown respectively in Figures 4a and 4b for CEL + 10 wt % acMAL and CEL + 10 wt % PVP as examples. In the BDS studies, the degree of crystallization can be accurately evaluated from a drop in the dielectric strength of the structural relaxation Δεα of a sample during its storage at a fixed temperature. The dielectric strength Δεα decreases, because the number of reorienting dipoles contributing to the α-relaxation decreases during crystallization. Figures 5a and 5b show the drops in Δεα for CEL + 10 wt % acMal at Tcr = 367 K and CEL + 10 wt % PVP at Tcr = 375 K as examples. The increase in the crystallization degree with time is usually expressed by the normalized real permittivity ε′N given by the following formula

This quantity represents a normalized measure of how far above Tg a compound must be heated before recrystallization occurs, which enable us to compare the tendencies to crystallization of materials having different Tg.36 It should be emphasized that Tred is often regarded as a measure of physical stability of drugs not only in the supercooled liquid state but also in the glassy state. A system is more stable if the value of Tred is closer to 1. We established that Tred is considerably higher for CEL + PVP than CEL + acMAL at the same percentage concentration weight of excipients. While Tred = 0.65 for CEL + 10 wt % acMAL, Tred → 1 for CEL + 10 wt % PVP, because the latter composition does not crystallize upon constant heating rate of 10 K/min. This is an additional argument for the more effective stabilization of supercooled CEL by PVP than acMAL. Since Tred is considered as a glass stability measure, this result could suggest that the glassy state of CEL + PVP would be also more stable than that of CEL + acMAL. We experimentally verify this prediction in the further part of the paper by analyzing measurements of the physical stability of investigated binary mixtures in their glassy state. 1160


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Figure 6. Temperature dependences of the α-relaxation times of the binary mixtures (a) CEL + PVP and (b) CEL + acMAL;8 the dependences log τα(1000/T) were fitted to the VFT equation given by eq 6 (solid black line). Comparison of the glass transition temperatures Tg (c) and fragility mp (d) of the binary compositions of CEL + acMAL8 and CEL + PVP versus weight concentrations of excipients, determined on the basis of the dielectric and calorimetric measurements.

ε′N (t ) =

ε′(0) − ε′(t ) ε′(0) − ε′(∞)

established by using the relation k = 1/τcr, which are shown in Figure 4c as functions of inverse temperature. From the isothermal crystallization kinetics study, we found that both the excipients PVP and acMAL reduce the tendency of the supercooled CEL to recrystallization, because the crystallization times τcr for the binary mixtures are longer than those for the drug (see Figure 4c where data for pure CEL are taken from ref 16). However, the slowest crystallization times at a given temperature have been observed by us for CEL with PVP. It shows that PVP is a better inhibitor of the isothermal crystallization of supercooled CEL than acMAL. Since the binary mixtures CEL + PVP and CEL + acMAL have significantly different values of Tg (as can be seen from the DSC thermograms in Figures 3a and 3b and will be also discussed later based on the BDS measurements), we investigate the crystallization kinetics of the mixtures at the same time scale of their molecular mobility defined by the structural relaxation time (τα = const). In Figure 5, such an analysis is presented at τα ≈ 4.28 μs, which characterizes the global molecular dynamics of the supercooled mixtures CEL + 10 wt % acMAL and CEL + 10 wt % PVP at temperatures 367 and 375 K, respectively. As shown in Figure 5d, the isothermal crystallization kinetics measured for the mixture of CEL with PVP at Tcr = 375 K is significantly slower than that for the mixture of CEL with acMAL at Tcr = 367 K. This observation is reflected in considerably different values of the crystallization times established for these supercooled binary systems in isochronal conditions (τα = const). The crystallization time for the supercooled mixture CEL + 10 wt % PVP (τcr = 10.7 h) is 7 h longer than that for the supercooled mixture CEL + 10 wt % acMAL (τcr = 3.7 h) at the same structural relaxation time τα ≈ 4.28 μs. The discussed results unambiguously show that PVP more effectively stabilizes CEL in the supercooled binary mixtures than acMAL in both the nonisothermal and isothermal

(2)

where ε′(0) is the static dielectric permittivity at the beginning of the crystallization, ε′(∞) is the long-time limiting value of the dielectric permittivity, and ε′(t) is the value of the dielectric permittivity at a given time of crystallization, t. This measure of the isothermal crystallization degree has been employed for the supercooled binary systems of CEL with different contents of acMAL and PVP. As examples, the isothermal crystallization kinetics quantified by ε′N(t) at different temperatures are presented in Figures 4a and 4b for the binary compositions with 10 wt % of excipients. From the shapes of the crystallization kinetics curves (shown in Figures 4a and 4b) is clearly seen that binary mixtures with 10 wt % PVP crystallize slower than the system with 10 wt % acMAL. To quantify the crystallization time scale for supercooled CEL and its binary mixtures with acMAL and PVP in isothermal conditions, we applied the method proposed by Avramov et al.37 Based on the first-order crystallization kinetics equation, ⎛ ⎛ t − t ⎞n ⎞ 0 ⎟ ε′N (t ) = 1 − exp⎜⎜ −⎜ ⎟⎟ ⎝ ⎝ τcr ⎠ ⎠

(3)

where τcr is a characteristic time for the isothermal overall crystallization, n is related to the dimensionality of the crystallization, and t0 is the induction time of crystallization, the authors suggested a more accurate method for evaluating the crystallization kinetics parameters instead of direct fitting the kinetic curves to eq 3. According to the Avramov approach, the characteristic crystallization time τcr can be determined as a time at the maximum of the first derivative of the normalized real permittivity dε′N(t)/(d ln t) versus ln t. Then, the temperature dependences of the crystallization rate k can be 1161


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where τ∞, T0, and D are fitting parameters, has been exploited to quantitatively describe the temperature dependence of αrelaxation times in the supercooled liquid up to the glass transition temperature Tg defined at τα(Tg) = 100 s. The latter relation has been used to determine the values of Tg from the dielectric data for investigated systems. It is worth noting (see Figure 6c) that these values of Tg have been found to be in accord to a good approximation with those established from the calorimetric TOPEM measurements. Role of Antiplasticization Effect on Physical Stability at T > Tg. As can be seen in Figure 6c, PVP is a very good antiplasticizer of CEL, because Tg of the binary systems CEL + PVP drastically increases with increasing content of polymer in the mixtures. On the other hand, the glass transition temperatures of the binary systems of CEL with acMAL are actually independent of the amount of acMAL in the mixtures due to the same values of Tg for CEL and acMAL. The increase in Tg of the binary mixture of CEL with polymer is associated with the decrease in the global molecular mobility of these systems. It means that the α-relaxation times of the supercooled mixtures CEL with PVP increase with increasing the polymer content in the compositions at a given temperature. In other words, the molecular mobility of supercooled CEL significantly slows after adding polymer to the drug, and consequently the physical stability of the systems CEL + PVP becomes better with increasing amount of PVP in the mixture. Thus, a higher resistance of the supercooled mixtures CEL + PVP to crystallization very well correlates with the strong antiplasticization effect of the polymer on CEL. This is in contrast to less stable supercooled binary mixtures with acMAL for which the global molecular dynamics seems to be independent of the content of acMAL in the mixture. Relation between Fragility and Physical Stability at T > Tg. Many attempts have been made to correlate some quantities characterizing α-relaxation in the supercooled liquid state with the tendency of drugs to recrystallization from both the supercooled liquid and glassy states as well as with the ability of supercooled liquids to glass formation.22 In this context, the fragility parameter has been often considered. The dynamic “fragility” mp has been defined43 as follows:

experiments (i.e., upon heating the compositions and during storage of the systems at a given temperature, respectively), as well as in isochronal conditions: when the global molecular mobility rate of the examined mixtures is fixed (i.e., at the same structural relaxation time). Correlations between Molecular Mobility and Physical Stability of the Binary Mixtures at T > Tg. To gain a better insight into molecular factors that may be responsible for the recrystallization tendency of the examined binary systems in the supercooled liquid state, we performed extensive investigations of the molecular mobility of the mixtures by means of the BDS. In this paper, we perform a comparative analysis of new measurements which were carried out by us for the mixtures of CEL with PVP and the dielectric data earlier reported by us for pure CEL11 and the mixtures of CEL with acMAL.8 To determine α-relaxation times at various temperatures for pure PVP and binary mixtures of CEL with different content of PVP, we fitted dielectric spectra to the following Havriliak− Negami38 (HN) formula: ε*(f ) = ε∞ +

Δεα [1 + (i 2πfτHN)αHN ]βHN

+

σdc i 2πfε0

(4)

where f denotes frequency, σdc is the dc conductivity, ε∞ is the high frequency limit permittivity, ε0 is the permittivity of vacuum, Δεα is the dielectric strength, τHN is the HN relaxation time, and αHN and βHN represent symmetric and asymmetric broadening of the dielectric spectrum. Then, the α-relaxation times can be determined by using the HN parameters.39 −1/ αHN ⎡ ⎛ πα ⎡ ⎛ πα β ⎞⎤1/ αHN ⎞⎤ HN ⎢sin⎜⎜ HN HN ⎟⎟⎥ ⎟⎟⎥ τα = τHN⎢sin⎜⎜ ⎢⎣ ⎝ 2 + 2βHN ⎠⎥⎦ ⎢⎣ ⎝ 2 + 2βHN ⎠⎥⎦

(5)

From the best fits of the dielectric spectra (see selected spectra in Figure 1), we found the temperature dependences of αrelaxation times for pure PVP and CEL + PVP mixtures (see Figure 6a). It should be noted that the identification of αrelaxation was difficult in the case of pure PVP due to an extremely high contribution of dc conductivity to the dielectric loss spectra. It was possible only in a narrow high temperature range, which means that we were able to determine only about 3 decades of dielectric relaxation times. To ensure that the dielectric process is indeed the segmental relaxation of the polymer, we performed the stochastic temperature modulated DSC (TOPEM). From the complex heat capacity of PVP, we determined calorimetric relaxation times at temperatures near Tg. The TOPEM analysis confirmed that the process distinguished from dielectric loss spectra of PVP is its segmental relaxation (responsible for the liquid−glass transition of the polymer), because the dielectric α-relaxation times can be successfully extrapolated to the calorimetric α-relaxation times. A comparison of the α-relaxation maps for the systems with PVP and acMAL is presented in Figures 6a and 6b. During vitrification, the α-process rapidly slows down in the case of all examined systems. The enormous increase in the αrelaxation times, τα, on isobaric cooling is the hallmark of the liquid−glass transition. An empirical Vogel−Fulcher−Tamman (VFT) equation,40−42 ⎛ DT0 ⎞ τα = τ∞ exp⎜ ⎟ ⎝ T − T0 ⎠

mp ≡

d log τα d(Tg /T )

T = Tg

(7)

It is worth noting that the dynamic fragility is closely related to the apparent activation enthalpy for α-relaxation ΔH at Tg,

mp =

ΔH(Tg) RTg ln(10)

(8)

where ΔH(T) ≡ R(d ln τα)/d(1/T) is defined44 at a constant pressure and R is the gas constant. It means that fragile liquids are characterized by a higher ratio ΔH(Tg)/Tg in comparison with strong materials. In the past two decades, the fragility parameter has become an appreciated measure of the sensitivity of molecular dynamics of supercooled liquids to changes in temperature near the glass transition. In terms of the value of mp, glass-forming liquids are classified as strong (mp ≤ 30), moderately fragile (30 < mp < 100), and fragile (mp ≥ 100). The molecular mobility of fragile liquids near the glass transition rapidly increases due to only a small temperature growth in contrast to that of strong materials. Thus, it is regarded that the more fragile materials

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bonds can be formed between small molecular weight particles of CEL (CEL···CEL), and CEL and acMAL (CEL···acMAL), as well as between small molecules of CEL and macromolecules of PVP (CEL···PVP). However, molecules of examined excipients cannot form H-bonds to each other. As a result, intermolecular interactions of small molecular weight acMAL and large molecular weight PVP are dominated by van der Waals forces. However, due to large sizes of PVP macromolecules and their complex topology, van der Waals forces are stronger and highly compounded in the polymer in comparison with the small acMAL molecules. Thus, the changes in the values of mp in the mixtures CEL + acMAL and CEL + PVP may result from the varying interplay and character of H-bonds and van der Waals forces of different strengths in the mixtures with changing content of excipients. In this context, it is interesting to note that the minimum in the dependence mp(wt % acMAL) is related to a saturation of H-bonds formed between molecules of acMAL and CEL, which takes place at about 37 wt % acMAL, i.e., 0.25 mole fraction of acMAL in the binary mixture CEL + acMAL. This evaluation is based on DFT calculations,8 which suggest that a single acMAL molecule having 8 H-bond acceptors can form H-bonds with 3 molecules of CEL. By adding an excipient (PVP or acMAL) to CEL, the population of H-bonded homodimers (CEL···CEL, favoring a crystalline structure formation) decreases, while the population of Hbonded heterogeneous molecular clusters (CEL···excipient) grows. It indicates that the antiplasticization effect of PVP on CEL can be strengthened by H-bonds formed between CEL and PVP, and the physical stability of CEL with PVP is more effectively improved. Nevertheless, the considerable increase in Tg of the binary systems CEL + PVP is mainly caused by van der Waals interactions between macromolecules of PVP, which become stronger with increasing content of PVP. Thus, the mobility of CEL molecules becomes more and more reduced due to their trapping in a more and more rigid polymeric matrix, which is reflected in the continuous decrease in mp(wt % PVP). In contrast to PVP, acMAL does not antiplasticize CEL and the decrease in mp(wt % acMAL) for small contents of acMAL comes from some kind of frustrations against crystallization. The frustrations are caused by the population of H-bonded heterogeneous molecular clusters (CEL···acMAL), which increases at the expense of the population of H-bonded homodimers of CEL···CEL molecules with adding acMAL to CEL. Independently of the examined crystallization inhibitor, when the content of excipient is sufficiently large, the interactions between the excipient molecules become dominant; hence the changes in mp in the mixtures with large contents of excipient are caused by the molecular interactions that dominate in the pure crystallization inhibitors, i.e., van der Waals forces. However, van der Waals interactions are weaker between small acMAL molecules than those between PVP macromolecules. Therefore, the dependence mp(wt % PVP) continuously decreases from about 100 to 70 for pure PVP, while mp(wt % acMAL) grows up to mp = 116 for pure acMAL. Concluding this part of our study devoted to the molecular mobility and the physical stability of CEL in the binary mixtures, we can claim that PVP is a more effective crystallization inhibitor of supercooled CEL than acMAL and a strong antiplasticization effect of PVP on the drug plays the primary role in the enhancement of the physical stability of CEL in the supercooled liquid state. In the next section, we verify whether the recrystallization tendency of the drug in the supercooled binary mixtures can be straightforwardly used to

should have a higher tendency to recrystallization (in both the supercooled liquid and glassy states) than the stronger ones, although there are known exceptions for this correlation.22,45−47 We test whether there is such a relation between mp of the investigated binary systems (CEL + acMAL and CEL + PVP) and the physical stability of CEL in the compositions. Based on the fragility definition (eq 7) and the VFT equation (eq 6), we determined the values of mp for examined systems from the following equation: mp =

D(T0/Tg) (1 − (T0/Tg))2 ln(10)

(9)

using the VFT equation parameters found from fitting experimental dependences log10 τα(1/T). To validate the values of mp determined on the basis of dielectric relaxation times (eq 9) (especially for pure PVP for which the dielectric τα(T) are measured in the relatively narrow range) we also used calorimetric measurements to evaluate mp based also on the definition eq 7. Exploiting the relation (eq 8) between mp and ΔH(Tg), we evaluated fragility parameters for pure PVP and the binary mixtures CEL + PVP by using an empirical relation48,49 between ΔH(Tg) and the glass transition width, ΔH*(Tg) = RC

Tonset g

TgonsetTgend Tgend − Tgonset

(10)

Tend g

where and denote respectively temperatures of the onset and endset of the glass transition in DSC thermogram, while the constant C = 5. As can be seen in Figure 6d, the values of mp for pure PVP and its mixtures with CEL evaluated independently from dielectric and calorimetric data are in accord to a good approximation. From the comparison of the dependences of mp on the content of crystallization inhibitor in the mixtures CEL + PVP and CEL + acMAL (see Figure 6d), we can see that the dependence mp(wt % PVP) considerably decreases in a monotonic way from mp ≈ 100 for pure CEL to mp ≈ 70 for pure PVP K30, while the dependence mp(wt % acMAL) changes nonmonotonically. Initially, the adding of acMAL to CEL also results in a decrease in mp of the binary mixture. However, the dependence mp(wt % PVP) more rapidly drops than mp(wt % acMAL), which well correlates with the more effective stabilization of CEL by PVP than by acMAL in the supercooled liquid state. In case of higher content of crystallization inhibitors in the binary mixtures, the dependence mp(wt % PVP) continuously decreases, whereas mp(wt % acMAL) reaches a minimum, and then it starts increasing (although the physical stability of both the supercooled CEL + acMAL and CEL + PVP mixtures continuously increases with growing content of excipients in the mixtures). Thus, the values of mp enable prediction of the physical stability of the supercooled binary mixtures of CEL with PVP in the whole range of PVP content, while it is possible only in the limited range of small amounts of acMAL in the binary compositions CEL + acMAL. The nonmonotonic behavior of mp vs wt % acMAL may result from a different character of intermolecular interactions in the mixtures of CEL with large and small content of acMAL. As was discussed in refs 8 and 17, molecules of CEL have both H-bond donor and acceptor groups, whereas molecules of both the crystallization inhibitors acMAL and PVP have only Hbond acceptors (−CO group). Consequently, hydrogen 1163


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Figure 7. X-ray diffraction patterns of the initially fully amorphous binary compositions of CEL with 5 wt % PVP (a) and 10 wt % PVP (b) recorded during their storage at room temperature. (c) Comparison of the dependences of relative degree of isothermal glassy state recrystallization Dc of the binary mixtures: CEL + 5 wt % PVP and 10 wt % PVP, CEL + 10% acMAL,8 and pure CEL11 as a function of storage time ts of the systems at room temperature TRT = 293 K.

From the dependences Dc(ts) obtained from XRD measurements at several temperatures below Tg for pure CEL, as well as for the unstable binary mixtures CEL + 5 wt % PVP and CEL + 10 wt % PVP, we determined temperature dependences of crystallization times τcryst of the systems. Since the crystallization in the glassy state takes a long time, the values of τcryst were evaluated as a time after which Dc reaches 10%. As can be seen in Figure 8, the crystallization times τcryst in the glassy state

predict the physical stability of CEL in the glassy state in the examined binary systems. The Experimental Evidence for the Better Physical Stability of the Glassy State of CEL + acMAL than That of CEL + PVP K30. Isothermal Study at T < Tg. We performed the long-term XRD isothermal measurements of the binary mixtures CEL + 5 wt % PVP and CEL + 10 wt % PVP during storage of the systems at room temperature TRT = 293 K (which is much below their values of Tg). From XRD diffraction patterns (Figures 7a and 7b), we found that the binary mixtures of CEL with 5 and 10 wt % PVP are not stable and recrystallize from their glassy state over time. For both compositions, we evaluated the values of the relative degree of crystallization Dc which are plotted as a function of storage time ts. Figure 7 shows the comparison of the newly obtained dependences of Dc(ts) for the binary compositions (CEL + 5 wt % PVP and CEL + 10 wt % PVP) with those recently reported for pure CEL11 and for CEL + 10% acMAL.8 It is clearly seen that the fastest crystallization process is observed for pure CEL; the degree of crystallization Dc of the pure amorphous CEL reaches nearly 90% after only 10 days of the drug storage. Crystallization of CEL in PVP matrix is significantly slowed down compared to the pure drug; the degree of crystallization of the glassy mixtures CEL + 5 wt % PVP and CEL + 10 wt % PVP reaches 25% and 15% after 50 days of storage, respectively. It turns out that acMAL is a better inhibitor of the CEL glassy state recrystallization than PVP, because the amorphous mixture of CEL with 10% of acMAL has not revealed any tendency to crystallization for more than one year of its storage. Thus, acMAL f ully suppresses the recrystallization of the glassy state of CEL, whereas PVP only reduces the recrystallization tendency of the glassy state of CEL (crystallization times become longer after adding PVP to the drug). It indicates that a small molecular weight crystallization inhibitor, which does not act as antiplasticizer on a drug, is able to more effectively stabilize the drug in the glassy state than strongly antiplasticizing polymer. It is worth noting that the tendency to crystallization for examined systems evaluated at TRT is analogous to what we found at other temperatures TRT < T < Tg, that is, at T = 303 K and T = 310 K.

Figure 8. Comparison of temperature dependences of the crystallization times of examined systems determined for Dc = 10% in both supercooled liquid (solid stars) and glassy (open stars) states with the temperature dependences of time scales of α-relaxation (τα) measured by BDS in the supercooled liquid state (solid circles) as well as τα predicted in the glassy state by constructing the master plot (open circles).

(open stars) of the binary mixtures CEL + PVP are longer about 1 decade from those for pure CEL, wherein the values of τcryst for CEL + 10 wt % PVP are slightly longer than those for CEL + 5 wt % PVP. However, CEL in the binary composition with 10 wt % acMAL was physically stable in the investigated temperature range TRT < T < Tg. 1164


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recrystallization process in the glassy state of pure CEL and the mixtures CEL + PVP due to τα ≈ τcryst. Then, one could suggest that the coupling parameter s between τcryst and τα would even tend to 1. Nevertheless, approximately the same order of magnitudes of τcryst and τα does not ensure that the slopes of the inverse temperature dependences of log10 τcryst and log10 τα are actually the same. This could be verified only if we were able to establish the values of τα for pure CEL and the mixtures CEL + PVP below Tg in the same temperature range in which the values of τcryst were determined near the room temperature TRT < Tg. In the case of the mixture CEL + acMAL at T < Tg, we also could not exclude a role of structural relaxation in the recrystallization process, which would be characterized by very long crystallization times if the process occurred after a longterm storage (τα ≪ τcryst). It should be emphasized that the antiplasticization effect of the polymer on CEL strongly influences the predicted α-relaxation times in the glassy mixture CEL + 5 wt % PVP, whereas the predicted dependence τα(T) for the composition CEL + 10 wt % acMAL in glass is nearly the same as that for pure CEL. These findings are crucial. They indicate that one can estimate how long pure CEL as well as CEL mixed with the antiplasticizing polymer PVP will be physically stable in the glassy state at a given temperature based on the value of α-relaxation time evaluated below Tg. However, this procedure is ineffective for the mixtures of CEL with the small molecular weight acMAL, which does not act as an antiplasticizer, but effectively stabilizes the drug by specific molecular interactions. This stabilization effect is not reflected in changes in α-relaxation times (compared to those for pure CEL) in both the supercooled liquid and glassy states. In the next step, we analyze whether secondary relaxations of the systems are able to reflect the finding that acMAL more effectively than PVP suppresses some molecular mobility of CEL responsible for the recrystallization of the drug in the glassy state. Local Molecular Mobility−Secondary Relaxations. Our investigations show that the better physical stability of the glassy state of the binary mixtures of CEL with acMAL than that of the glassy systems CEL + PVP is reflected in secondary relaxations of the systems. Figure 9 presents the comparison of the dielectric spectra of pure CEL and its binary mixtures with

From the comparison of the crystallization tendency of the binary mixtures CEL + acMAL and CEL + PVP in both the supercooled liquid and glassy states, one can conclude that we are not able to predict the physical stability of the glassy state of CEL in the examined solid dispersions based only on the supercooled liquid crystallization kinetics. Correlations between Molecular Mobility and Physical Stability of the Binary Mixtures at T < Tg. Global Molecular Mobility: α-Relaxation. To discuss correlations between the global molecular mobility of the examined systems and their tendency to crystallization in the glassy state, the temperature dependences of time scales τα of the global molecular mobility and the crystallization times τcryst (for Dc = 10%) are collected in Figure 8, which shows the time scales in both the supercooled liquid and glassy states. Since α-relaxation times in the glassy state are too long to be measured, the dependence τα(T) below Tg has been predicted by a construction of socalled master plot based on the experimental dielectric relaxation data measured at T > Tg. The master plot has been obtained by the horizontal shifting of a well-shaped α-loss peak measured in the liquid state near Tg to lower frequencies to overlap loss spectra collected at T < Tg, where only high frequency flanks of the α-loss peak can be measured.11,22 It is worth noting that each spectrum of α-process collected in the nonequilibrium glassy state was measured after a prior return to the equilibrium supercooled liquid state to avoid the aging effect on α-loss peak. We predicted τα(T) in the glassy state for pure CEL and the binary mixtures CEL + 10 wt % acMAL and CEL + 5 wt % PVP, whereas a large conductivity contribution to dielectric spectra disabled the master plot construction for the mixtures of CEL with higher contents of PVP. It seems to be reasonable that the molecular motions characterized by time scales which do not exceed crystallization time scales can influence the crystallization process. As can be seen in Figure 8, the time scales of the global molecular mobility of examined systems and the crystallization times differ approximately as many as 9 decades in the supercooled liquid state in the considered crystallization temperature range. Such a considerably less time scale τα compared to τcryst suggests that the global molecular mobility can affect the recrystallization process in the supercooled liquid state of the tested systems. Moreover, values of the coupling parameter s between τcryst and τα (which is the slope of the linear correlations (not shown here) between log10 τcryst and log10 τα) are relatively high above Tg, i.e., s = 0.70 ± 0.04 and s = 0.73 ± 0.04 for pure CEL and the mixture CEL + 10 wt % acMAL, respectively. Nevertheless, to determine these log−log linear correlations between τcryst and τα, the values of τα have had to be extrapolated to higher temperatures by using fits to the VFT equation (eq 6), because the crystallization times have been able to be evaluated at relatively high temperatures. The same procedure has been applied to the mixture CEL + PVP at even higher temperatures (due to considerably increasing crystallization times of this binary mixture with decreasing temperature), and consequently we have obtained a smaller value of the coupling parameter, s = 0.55 ± 0.02, which most likely reflects a gradually increasing role of the thermodynamic factor compared with the kinetic factor in the crystallization process at such high temperatures as the crystallization theory typically predicts at the temperature increasing from the glass transition to the melting point. In the glassy state, τα and τcryst become convergent, excluding the mixture CEL + 10 wt % acMAL that does not crystallize below Tg. Thus, the global molecular mobility can play a role in the

Figure 9. Comparison of dielectric spectra of the pure CEL11 and its mixtures with 10 wt % acMAL,8 as well as with 10 wt % PVP and 15 wt % acMAL measured deep in the glassy state of the systems at T = 273 K. 1165


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H−N−H in CEL molecule. Thus, heterogeneous molecular clusters CEL···PVP less effectively than CEL···acMAL hinder the formation of homogeneous clusters CEL···CEL in the glassy state. It is worth noting that the secondary β-relaxation of CEL in the glassy state is similarly suppressed by adding both acMAL and PVP (see Figure 9). It shows that the reduction in the JG local molecular mobility often considered as a precursor of the global relaxation certainly favors the lower tendency of CEL in the amorphous binary mixtures to recrystallization, but it does not enable one to distinguish which of these crystallization inhibitors better stabilizes the amorphous CEL. It should be emphasized that PVP less effectively than acMAL stabilizes CEL against recrystallization in the glassy state despite the combined antiplasticization and H-bonding impact exerted by PVP on CEL. It has turned out that acMAL much better protects the glassy CEL against devitrification. This strong stabilization influence of acMAL on CEL is achieved by the effective H-bonding network between molecules of the drug and the crystallization inhibitor in the glassy state. The role of H-bond formation in the physical stabilization of the drug in the glassy state can be more important than that in the supercooled liquid, because both the number and strength of H-bonds increases with decreasing temperature in the supercooled liquid and reaches a nearly constant high level in the glassy state.50 It also may explain a worse physical stability of CEL + acMAL compared to CEL + PVP in the supercooled liquid state (T > Tg) where the role of H-bonds is smaller than in the glassy state (T < Tg).

PVP (CEL + 10 wt % PVP, CEL + 15 wt % PVP), and with acMAL (CEL + 10 wt % acMAL) measured below Tg of the systems at 273 K. As already discussed,8,11 the dielectric spectra for pure CEL obtained at temperatures below its Tg reveal three secondary relaxations: (i) β-process, reflecting small-angle reorientations of intermolecular origin of the whole drug molecule, which has been classified as a so-called Johari− Goldstein (JG) relaxation that is considered as a precursor of the structural relaxation; (ii) faster γ-process, reflecting rotation of the phenyl ring with the sulfonamide group (Ph−SO2NH2), which is able to form H-bonds with other CEL molecules or with molecules of excipients (acMAL and PVP); (iii) δ-process, reflecting rotations of the phenyl ring with the methyl group (Ph−CH3), which does not form external hydrogen bonds with other molecules of CEL or our excipients. From Figure 9, it is clearly seen that, after addition of acMAL to CEL, the significant (or even complete) decrease in the dielectric strength of γ-process is observed. It indicates that 10 wt % acMAL in the binary mixture with CEL causes the f reezing of motions of the molecular group Ph−SO2NH2 in CEL, reflected in the γ-process. On the other hand, acMAL does not influence the fastest δ-relaxation of the drug. It means that acMAL does not modify the mobility of the molecular group Ph−CH3 in CEL (δ-relaxation in the mixture of CEL with acMAL is characterized by the same relaxation times as those observed for pure CEL). Analyzing the dielectric data measured for the binary mixtures of CEL with PVP in the glassy state, we observe that the addition of PVP (10 wt %) to CEL almost does not modify the dielectric spectra of CEL: we can distinguish 3 secondary relaxations with almost the same relaxation times as in pure CEL. Thus, 10 wt % PVP does not ef fectively suppress the mobility of the molecular group Ph−SO2NH2 in CEL. As can be seen in Figure 9, even 15 wt % PVP does not immobilize this molecular group in CEL, although a decrease in the magnitude of the secondary γ-relaxation is observed for the mixture CEL + 15 wt % PVP. Such a behavior can be related to a smaller number of molecular groups Ph−SO2NH2 in CEL in the binary mixture of CEL with the larger concentration of PVP. The differences in the secondary γ-relaxation behavior in the binary mixtures of CEL with acMAL and PVP can be explained by the different a character of H-bonds formed between molecules of the excipients and CEL molecules. Although molecules of CEL can interact with the molecules of acMAL and PVP via hydrogen bonds formed between the same functional groups of drug and crystallization inhibitors (−N− H···OC−), molecules of CEL with acMAL can create a stronger network of hydrogen bonds, and consequently can form stronger H-bonded heterogeneous molecular clusters (CEL···acMAL) in the glassy state than CEL with PVP. Density functional theory (DFT) calculations8 indicate that the mobility of the molecular group NH2 of CEL can be fully suppressed by double H-bonds (−CO···H−N−H···OC−) which can be formed by two −CO groups of a single acMAL molecule with the group H−N−H in a single CEL molecule. Moreover, it has been found that a single acMAL can bind (by the double H-bonds) as many as 3 molecules of CEL, which suggests that the molecular structure of the binary mixture CEL + acMAL is dominated by strongly H-bonded (CEL···acMAL) heterogeneous molecular clusters. On the other hand, Gupta and coworkers17 suggest that the mobility of the group NH2 of CEL can be suppressed by only a single H-bond (H−N−H···O C−) between the group −CO in PVP unit and the group

■

CONCLUSIONS Our investigations showed that both the examined excipients acMAL and PVP are relatively good recrystallization inhibitors of CEL, because they slow down the drug crystallization. However, we established that the investigated excipients are characterized by different stabilization efficiencies in the supercooled liquid and glassy states of their binary mixtures with CEL. These differences result from an interplay between molecular factors such as H-bonds (formed by molecules of the crystallization inhibitors PVP and acMAL with molecules of CEL) and a strong antiplasticization effect of PVP on CEL. We found evidence that the polymer PVP K30 more effectively stabilizes the drug in the supercooled liquid state than small molecular weight acMAL. This finding well correlates with the strong antiplasticization effect of the added polymer on the supercooled CEL. Thus, the antiplasticization effect of PVP on CEL (associated with the decrease in the global molecular mobility) is a key factor increasing the physical stability of the drug in the supercooled liquid state of binary mixtures (CEL + PVP). Moreover, the better stability of supercooled CEL in the mixture with PVP is revealed in the more rapid drop in the dependence of mp(wt % PVP) than mp(wt % acMAL) in the monotonic way, wherein the dependence mp(wt % acMAL) decreases only for small content of acMAL, and then behaves nonmonotonically. In the supercooled liquid state, the effect of hydrogen bonding on the physical stability of the examined binary compositions of CEL is less than that in the glassy state, because H-bonds are more easily broken at higher temperatures. However, in the glassy state, the role of hydrogen bonding in the physical stability of the binary mixtures increases. We found that acMAL fully suppresses the glassy state of CEL against recrystallization most likely due to 1166


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drug solubility in discovery and development. Pharmacol. Rev. 2013, 65, 315−499. (2) Di, L.; Fish, P. V.; Mano, T. Bridging solubility between drug discovery and development. Drug Discovery Today 2012, 17, 486−495. (3) Craig, D. Q.; Royall, P. G.; Kett, V. L.; Hopton, M. L. The relevance of the amorphous state to pharmaceutical dosage forms: glassy drugs and freeze dried systems. Int. J. Pharm. 1999, 179, 179− 207. (4) Murdande, B. S.; Pikal, M. J.; Shanker, R. M.; Bogner, R. H. Solubility Advantage of Amorphous Pharmaceuticals: I. A Thermodynamic Analysis. Pharm. Res. 2010, 27, 2704−14. (5) Murdande, B. S.; Pikal, M. J.; Shanker, R. M.; Bogner, R. H. Solubility Advantage of Amorphous Pharmaceuticals, Part 3: Is Maximum Solubility Advantage Experimentally Attainable and Sustainable? J. Pharm. Sci. 2011, 100, 4349−4356. (6) 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. (7) Hancock, B. C.; Parks, M. What is the True Solubility Advantage data for the melting point, heat of fusion, and heat capacity of for Amorphous Pharmaceuticals? Pharm. Res. 2000, 17, 397−404. (8) Grzybowska, K.; Paluch, M.; Wlodarczyk, P.; Grzybowski, A.; Kaminski, K.; Hawelek, L.; Zakowiecki, D.; Kasprzycka, A.; JankowskaSumara, I. Enhancement of amorphous celecoxib stability by mixing it with octaacetylmaltose: the molecular dynamics study. Mol. Pharmaceutics 2012, 9, 894−904. (9) 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. (10) 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, 100, 2642−2657. (11) Grzybowska, K.; Paluch, M.; Grzybowski, A.; Wojnarowska, Z.; Hawelek, L.; Kołodziejczyk, K.; Ngai, K. L. Molecular Dynamics and Physical Stability of Amorphous Anti-Inflammatory Drug: Celecoxib. J. Phys. Chem. B 2010, 114, 12792−12801. (12) Adrjanowicz, K.; Kaminski, K.; Wojnarowska, Z.; Dulski, M.; Hawelek, L.; Pawlus, S.; Paluch, M.; Sawicki, W. Dielectric relaxation and crystallization kinetics of ibuprofen at ambient and elevated pressure. J. Phys. Chem. B 2010, 114, 6579−93. (13) Kothari, K.; Ragoonanan, V.; Suryanarayanan, R. Influence of Molecular Mobility on the Physical Stability of Amorphous Pharmaceuticals in the Supercooled and Glassy States. Mol. Pharmaceutics 2014, 11, 3048−3055. (14) Karmwar, P.; Graeser, K.; Gordon, K. C.; Strachan, C. J.; Rades, T. Investigation of properties and recrystallization behavior of amorphous indomethacin samples prepared by different methods. Int. J. Pharm. 2011, 417, 94−100. (15) Gupta, P.; Bansal, A. K. Devitrification of Amorphous Celecoxib. AAPS PharmSciTech 2005, 6 (2), E223−E230. (16) Dantuluri, A. K. R.; Amin, A.; Puri, V.; Bansal, A. K. Role of α − relaxation on crystallization od amorphous celecoxib above Tg probed by dielectric spectroscopy. Mol. Pharmaceutics 2011, 8, 814−822. (17) 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. (18) 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. (19) Shamblin, S. L.; Tang, X.; Chang, L.; Hancock, B. C.; Pikal, M. J. Characterization of the time scales of molecular motion in pharmaceutically important glasses. J. Phys. Chem. B 1999, 103, 4113−4121.

effectively immobilizing the molecular group NH2 of CEL by double H-bonds (−CO···H−N−H···OC−) formed by two CO groups of a single acMAL molecule with the group H−N−H in a single CEL molecule, which is reflected in vanishing of the dielectric secondary γ-process after adding 10 wt % acMAL to CEL. On the other hand, PVP only reduces the tendency of the glassy CEL to crystallization (crystallization times of glassy CEL become longer after adding PVP to the drug), although PVP exerts the combined antiplasticization and H-bonding effect on CEL. However, H-bonds formed between molecules of CEL and PVP seem to be less effective than those between CEL and acMAL. They do not fully immobilize the group NH2 of CEL, because only a single H-bond (H−N−H··· OC−) is formed between the group −CO of the PVP unit and the group H−N−H of the CEL molecule. Consequently, in the glassy mixture of CEL with 10 wt % PVP, we still observe mobility of the group NH2 of CEL, which is reflected in the dielectric secondary γ-process similarly as in the case of pure CEL. Since molecules of CEL with acMAL can create stronger H-bonded heterogeneous molecular clusters (CEL···acMAL) in the glassy state than CEL with PVP, acMAL better protects CEL against crystallization at T < Tg. We established that the secondary β-relaxation of CEL in the glassy state is similarly suppressed by adding both acMAL and PVP. The reduction in the JG local molecular mobility certainly favors the lower tendency of CEL in the amorphous binary mixtures to recrystallization. However, we cannot consider the behavior of the JG relaxation of CEL as a factor distinguishing the efficiencies of the physical stabilization of amorphous CEL by mixing with acMAL and PVP. The stabilization effect of acMAL on CEL is not reflected in changes in α-relaxation times (compared to those for pure CEL) in both the supercooled liquid and glassy states in contrast to that exerted by antiplasticizing PVP. We found that the crystallization times are close to the α-relaxation times in the case of the mixtures CEL + PVP in the glassy state, which shows that the physical stability of the mixtures of CEL with PVP can be predicted from the evaluated values of τα below Tg. However, this method does not yield proper results for the compositions of CEL with the small molecular weight acMAL, which has no antiplasticization effect on CEL, but effectively stabilizes the drug by specific molecular interactions in the glassy state.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

K. Grzybowska: 0000-0002-0691-3631 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS K.G., K.C., J.K., A.G., and M.P are grateful for the financial support received within the Project No. 2015/16/W/NZ7/ 00404 (SYMFONIA 3) from the National Science Centre, Poland.

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