Molecular Dynamics of the Supercooled Pharmaceutical Agent

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Molecular Dynamics of Supercooled Pharmaceutical Agent Posaconazole Studied via Differential Scanning Calorimetry, Dielectric and Mechanical Spectroscopies K. Adrjanowicz, K. Kaminski, P. Wlodarczyk, K. Grzybowska, M. Tarnacka, D. Zakowiecki, G. Garbacz, M Paluch, and S. Jurga Mol. Pharmaceutics, Just Accepted Manuscript • DOI: 10.1021/mp4003915 • Publication Date (Web): 09 Sep 2013 Downloaded from http://pubs.acs.org on September 17, 2013

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Molecular Pharmaceutics

Molecular Dynamics of Supercooled Pharmaceutical Agent Posaconazole Studied via Differential Scanning Calorimetry, Dielectric and Mechanical Spectroscopies K. Adrjanowicz1, K. Kaminski2, P. Wlodarczyk3, K. Grzybowska2, M. Tarnacka2, D. Zakowiecki4, G. Garbacz5, M. Paluch2 and S. Jurga1,6 1

NanoBioMedical Centre, Adam Mickiewicz University, ul. Umultowska 85, 61-614 Poznan, Poland 2

Institute of Physics, University of Silesia, ul. Uniwersytecka 4, 40-007 Katowice, Poland 3

4 5 6

Institute of Non-Ferrous Metals, ul. Sowinskiego 5, 44-100 Gliwice, Poland

Pharmaceutical Works "Polpharma", Pelpińska 19, 83-200 Starogard Gdański, Poland

University of Greifswald, Institute of Pharmacy, Friedrich-Ludwig-Jahn-Strasse 17, Greifswald, Germany

Department of Macromolecular Physics, Adam Mickiewicz University, ul. Umultowska 85, 61-614 Poznan, Poland

Abstract This paper presents comprehensive studies on the molecular dynamics of pharmaceutically important substance, posaconazole. In order to characterize relaxation dynamics in the supercooled liquid and glassy states dielectric and mechanical spectroscopies were applied. Dielectric data have indicated multiple relaxation process that appear above and below glass transition temperature Tg (τα=100s) of posaconazole. From the curvature of the dielectric log10 (τ α ) versus inverse of temperature dependence we determine so-called ‘fragility’, being very popular parameter for classifying the structural dynamics of supercooled liquids and polymers. From the calculations we get m=150, which means that is one of the most fragile glass-forming liquids. In this paper, relaxation dynamics of supercooled posaconazole extracted from dielectric response function was also confronted with shear-mechanical relaxation. Finally, we have also presented a direct comparison of the fragility and the number of dynamically correlated molecules Nc determined from dynamic calorimetry curves, dielectric and mechanical spectroscopies, showing a clear deviation in the picture of glass-transition dynamics generated by calorimetric and spectroscopic techniques.

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AUTHOR INFORMATION Corresponding Author * Email: [email protected] Keywords: glass transition, molecular dynamics, dielectric relaxation, dynamic heterogeneity, fragility, amorphous pharmaceuticals

TOC GRAPHICS For Table of Contents Use Only

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Introduction The glass transition phenomenon is universal feature observed for a broad group of materials ranging from inorganic systems, organic substances like polymers, soft matter and even biological systems [1, 2, 3, 4]. Dynamical properties of supercooled liquids on approaching the glass transition are subject of detailed studies for a number of years. However, due to much complexity understanding of the supercooled liquids dynamics near the glass transition is still puzzling [5]. The glass transition phenomenon cannot be classified ‘strictly’ to the any of traditional thermodynamic phase transition definitions, however it resembles in some way second order transition. It is generally accepted to interpreted it as dynamic arrests of the system originating from underlying phase transition [6]. The relaxation process associated strictly with the dynamic liquid-glass transition event is termed as the structural relaxation. With decreasing temperature the structural relaxation dynamics becomes more and more cooperative and in most cases it has non-Arrhenius character, which means that the temperature dependence of α-relaxation times increases faster on approaching the glass transition temperature than predicted from the Arrhenius activation law (e.g.[5]). On approaching the glass transition temperature structural relaxation time exceed hundreds of seconds and become practically immeasurable below that point (Tg). The deviation from the Arrhenius formula is generally described by fragility parameter [7]

 d logτ α  m=   d (Tg / T )  T =Tg

(1)

that ranges from 16 up to 200, typically 80-90. Small values of fragility parameter indicates for more Arrhenius-like temperature dependence ( “strong” supercooled liquids), whereas large values of m are characteristic for “fragile” liquids which log10τα(T) dependences deviate strongly from the Arrhenius pattern. In that case lowering temperature by only a few degree results in increasing α-relaxation times by more than one order of magnitude. Non-Arrhenius data are often described in terms of the Vogel-Fulcher-Tammann equation [8,9, 10]

 DT   T − T 0  

τ α = τ ∞ exp

(2)

where τ ∞ , DT , T0 are constants. 3



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In recent years the concept of fragility has been much exploited, as it organizes glassforming materials in some logical scheme based on differences in their dynamics. The popularity and controversy related with fragility parameter stems from the fact that there had been observed attempts to correlate it to various structural parameters of glass-forming materials like nonexponentiality of the structural response (quantified using Kohlrausch-Williams-Watts exponent βKWW) [11] or dynamic heterogeneity [12,13]. Fragility was even suggested to be used as a measure of the physical stability of glass-forming materials (fragile systems should be physically more less in the glassy state than strong ones) [14,15,16]. However, variety of studies have indicated that there are many exceptions from the above correlations and none of them can be treated as rule of a thumb [17,18,19,20]. The separate problem related to fragility is the way of its quantification [21, 22]. In the past, various methods have been proposed to calculate parameter m, which based on conventional spectroscopic techniques, such as dielectric and mechanical spectroscopies, as well as thermal measurements. Fragility parameter determined from Eq. (1) refer solely to the structural relaxation which governs the dynamic on approaching the glassy state and it is termed as ‘kinetic fragility’. However, fragility of supercooled liquid can be also determined from calorimetric data, as the dependence of ∆S/∆Sm plotted versus T/Tm was found out to decrease in analogical way as log10 τα versus Tg/T [23]. This leads to ‘thermodynamic fragility’ concept that reflects the behavior displayed by the excess entropy, i.e., the difference between the entropy of the liquid and the entropy of the underlying crystal. Wang et al. demonstrated for more than 40 liquids that kinetic fragility can be predicted purely from thermodynamic quantities [24] using following equation

m = 56

∆C p Tg

(3)

∆H m

A very similar formula was also proposed by Lubchenko and Wolynes [25]

m = 34.7

∆C p Tm

(4)

∆H m

where ∆Cp and ∆Hm are heat capacity jump at Tg and ∆Hm is the fusion enthalpy, respectively. However, detailed experimental verification has showed that many-body molecular dynamics governing the kinetics of glass-forming liquids is unlikely to be totally governed by pure 4


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thermodynamic [26]. As suggested [27,

28

] the failure of such correlation might be related to

residual excess entropy at T0, which can be associated with the existence of all types of intramolecular motions that are not related to the α- process (secondary relaxations)]. Experimental [29,30] and theoretical [31,32] studies have shown that except of fragility, the very important aspects of glass transition dynamics is so-called dynamic heterogeneities, which refers to nanoscopic cooperative regions that consists of highly mobile and barely moving particles located just few nanometers away from each other [33]. A physical characterization of dynamical heterogeneities involves determining their typical lifetime, characteristic length scale ζ or the number of particles involved in correlated motion Nc. Direct measurement of dynamic heterogeneity is not so trivial, however there are some indirect means that can be used to qualitatively estimate the length scale of dynamic heterogeneity of supercooled liquids. One of the earliest formula to calculate ζ and Nc was given by Donth [6, 34]

ζ3 = Nc =

k B Tg2 ∆(CV−1 )

(5)

ρ (δT ) 2 RTg2 ∆ (CV−1 )

(6)

M (δT ) 2

where ρ is density, δT is the mean temperature fluctuation, CV is the isochoric heat capacity and M is molecular mass. Both equations derive from thermodynamic fluctuation theory and enable to estimate ζ and Nc in the glass transition region, but without taking into account the kinetic factor. In recent years a completely different approach was given by Berthier et al [12, 31,

35

],

which use the temperature derivative of two-point correlation function, Φ (t ) to approximate the four-point susceptibility χ 4 (t ) associated with the four-point correlation function G4 (r ; t ) that involve space-time correlations. The maximal value of dynamic susceptibility χ 4max was preidentified with a number of particles involved in correlated motion, N c on time scale of the order of t ~ τ α . If stretched exponential KWW function [ exp(− (t / τ α ) β KWW ) ] is used to describe Φ (t ) , then the number of molecules that are dynamically correlated during the structural relaxation of supercooled liquids can be simplified using formula proposed by Capaccioli and co-workers [36]

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2

2

Nc =

χ 4max

k k  β KWW   ∂ ln τ α   ∂Φ (t )  ≈ B T 2     = B  ∆C p ∆C p  e   ∂ ln T   ∂T 

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2

(7)

where ∆C p is heat capacity change at Tg, k B is the Boltzmann constant and β KWW stretched parameter varying from 0 to 1. The advantage given by this very simple formula is that based only on experimentally accessible quantities that characterize dynamic and thermodynamic properties of supercooled liquid, we can quantitatively probe the growing dynamic length scale on approaching glass transition. In this paper we present experimental studies on molecular dynamics of glass-forming liquid of much pharmaceutical interests, posaconasole. In order to do that we employed dielectric and shear-dynamic spectroscopies, being the most commonly applied techniques to study the supercooled liquids dynamics in the vicinity of the glass transition. Moreover, the glass-transition picture extracted from relaxation spectroscopies was supplemented by calorimetric data. Understanding if responses measured via different techniques display some universal features is still fundamental goal to reach that should help broaden our knowledge of the glass transition phenomenon. It was also of much interest to compare whether structural properties of supercooled liquid expressed in terms of fragility parameter m, as well as the number of dynamically correlated molecules at Tg estimated from different approaches provide much the same information about our system. We have also tested whether the number of dynamically correlated molecules calculated purely from heat capacity curves agrees with that estimated from Berthier et al. approach (that includes both, thermodynamic and kinetic factors). As a result we have found that both approaches gave back significantly different estimated number of dynamically correlated molecules at Tg. Finally, in terms of the four-point susceptibility function proposed by Berthier et al. we have shown that that slowing down of molecular dynamics of posaconazole is accompanied by approximately the same increase in dielectric and shearmodulus number of dynamically correlated molecules Nc. We also found out that in studied temperature range the Nc-ε/ Nc-G ratio is close to unity, which agrees with Dyre’s group finding for supercooled liquids that have similar stretching of the dielectric and shear response functions [37].

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2. Experimental 2.1. Material The

crystalline

sample

of

posaconazole

(IUPAC

Name:

4-(4-(4-(4-(((3R,5R)-5-(2,4-

difluorophenyl)-5-(1,2,4-triazol-1-ylmethyl)oxolan-3-yl)methoxy)phenyl)piperazin-1-yl)phenyl)2-((2S,3S)-2-hydroxypentan-3-yl)-1,2,4-triazol-3-one, C37H42F2N8O4 , 700.778 g/mol) was supplied from Pharmaceutical Works Polpharma (Poland) with purity greater than 99%, and used without further purification.

2.2. Methods 2.2.1. Dielectric Spectroscopy Complex dielectric permittivity measurements were carried out using the Novo-Control Alpha dielectric spectrometer over frequency range from 1·10-2 to 3·106 Hz at ambient pressure. Tested sample was placed between two stainless-steel electrodes (diameter: 20 mm, gap: 0.19 mm) and mounted on a cryostat. The temperature was controlled by Quatro System using a nitrogen gas cryostat, with stability better than 0.1 K. Dielectric measurements were performed on cooling from the melting point down to the glassy state, with different steps: every 10 K in the glassy state and every 2 K in the region above the glass transition temperature.

2.2.2. Mechanical Spectroscopy Dynamic mechanical measurements were performed by means of Ares rheometer (Rheometric Scientific). A plate–plate configuration (5 mm as well as 8mm diameter) was used in performed studies and gap between aluminum plates was set to be 1.0 mm and 2.3 mm, respectively. We suppose that due to tool compliance effects elastic plateau modulus for posaconazole in vicinity of the glass transition might be determined with a slight error. However, as we found out the instrument compliance does not affect the shape as well as the position of relaxation loss modulus peak measured in the glassy regime. Shear deformation was applied under conditions of controlled strain, always remaining in the range of the linear viscoelastic response. Experiments were made upon cooling in the temperature range from 341 to 329 K in the step of 2 K. The dynamic shear moduli G’ and G” at a constant temperature were collected in the frequency range from 0.001 to 100 Hz.

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2.2.3. Temperature-modulated Differential Scanning Calorimetry (TMDSC) Thermodynamic properties of posaconazole were investigated by DSC technique. 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 using indium and zinc standards while heat capacity Cp calibration was performed using a sapphire disc. The crystalline sample in aluminium crucible (40µL) was heated inside DSC apparatus and next immediately cooled to vitrify the liquid sample (50 K/min). Crystalline and amorphous forms of posaconazole were scanned at rate of 10 K/min over a temperature range from 298 K to well above respective glass transition point.

2.2.4. DFT calculations Posaconazole molecule was optimized on the B3LYP/6-31G** level of theory with use of Orca 2.9 package [cyt. Neese, F. ORCA – an ab initio, Density Functional and Semiempirical program package, Version 2.6. University of Bonn, 2008] . The x axis was matched with long axis of both molecules and afterwards, dipole moment calculations were carried out on the B3LYP/6-311G* level of theory. Finally, dipole moment vectors were plotted on the molecular structures with use of gOpenMol 3.0 – program for visualizations.

3. Results and discussion 3.1. Theoretical calculations – relationship between shape of the molecule and its dynamics It is well-known that the shape of the molecule has an important impact on the intermolecular interactions, so in a consequence on its molecular dynamics as well. The chemical structure of posaconazole is presented in Figure 1 (a). It can be seen that a series of aromatic rings cause the molecule to be very stiff and ridged, just like typical liquid crystals. Very recently, we have carried out analogical studies on itraconazole (Figure 2(b)), an active pharmaceutical ingredient belonging to the same family of triazole antifungal agents as posaconazole, of roughly the same molecular structure. In that case, in dielectric loss spectra collected above glass transition temperature Tg an additional relaxation process of the Debye-type nature, labeled as α’-relaxation, was observed [38]. This relaxation process, labeled by us as α’relaxation, turned out to be sensitive to liquid-crystalline phase transitions that occur upon 8


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cooling of itraconazole from the melting point. Based on experimental evidence as well as theoretical predictions, given in terms of Letz et al. model [39], we have confirmed that itraconazole forms nanoscale domains of nematic order upon cooling. Therefore, the appearance of an additional process in the supercooled liquid state of itraconazole is due to the rotation of the whole molecule around one of its short axis. As posaconazole and itraconazole consists of the same molecular backbone it is of much interest to verify if the same scenario should be also valid in this case. In order to do that, DFT calculation were performed on posaconazole molecule, treated as a hard ellipsoid. From the calculations we get that semimajor axis of that ellipsoid is equal to 32 A, while semiminor axes are equal to 10 and 8 A. This gives the aspect ratio X0 equal to 4. Based on Lentz et al work [39], which suggests that when the aspect ratio is higher than 2 the glass transition is driven by a precursor of the nematic phase, we should also observe (same as for itraconazole (X0=3)) nematic ordering in the supercooled liquid state. As will be demonstrated in the further part of this paper, in the case of posaconazole we indeed observe experimentally a liquid-nematic like phase transition. From DFT calculation we also get insight into the magnitude of x, y and z components of the total dipole moment vector of posaconazole, as presented in Figure 2. We obtained that the dipole moment aligned along semimajor axis x is equal to – 1.50 D, while the ones parallel to semiminor axes y and z are equal to µ=2.70 D and µ= 1.93 D, respectively. Calculation of the average dipole moment yields to a value of 3.7 D and the dipole vector directed perpendicularly to the semimajor x axes.

3.2. Thermal properties of posaconazole Figure 3 shows DSC thermograms of posaconazole. As illustrated upon standard heating run of crystalline sample two endothermic events occur (=405.5K and =440.5 K). The first one is related with nematic-like phase transition, whereas the latter one with melting point. During heating of glassy sample, the glass transition (Tg=332 K) and cold-crystallization (Tc=416.3 K) events were observed. Immediately after cold-crystallization investigated material melts in one run at temperature of around 441 K. During standard heating run we haven’t observed endothermic events being characteristic for liquid-crystalline phase transitions taking place in the

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supercooled regime, just like in itraconazole. Detailed studies on the liquid-crystalline phase transitions that occur in the whole triazoles family will be given elsewhere. For the purpose of further comparison between dielectric and calorimetric data, we have also performed more precise calorimetric studies with the use of temperature-modulated calorimetry (TMDSC) technique (DSC curves are not shown herein). These results are listed in Table 1. ∆Cp (at Tg) is the heat capacity jump at Tg, i.e. that is the difference between heat capacities of the liquid and glass, whereas Cp-conf (at Tg) refer to the difference between heat capacities of the glass and crystal.

3.3. Characterization of the molecular mobility in the supercooled and glassy states of posaconazole 3.3.1. Dielectric studies In order to investigate relaxation dynamics of posaconazole dielectric measurements were performed in wide spectral and temperature ranges. Figure 4 shows raw dielectric loss spectra of posaconazole collected above and below its glass transition temperature (defined as temperature at which structural relaxation time reaches 100 seconds). As usual in the supercooled liquid state well pronounced structural relaxation and dc-conductivity are clearly visible. Apart from that, in the vicinity of the glass transition there is also a secondary relaxation, of much weaker amplitude. The dielectric loss spectra in the glassy state of posaconazole are depicted in the inset of Fig. 4. Two secondary relaxations clearly visible in the glassy region were denoted as β- and γrelaxations. In contrast to liquid-crystalline behavior of itraconazole, there is no Debye-type relaxation in the supercooled liquid state of posaconazole. This process is typically observed for materials having rod-like molecular structure and interpreted as due to rotational fluctuations of the whole molecule around one of the short axis. Its absence in the supercooled liquid state of posaconazole is quite surprising, especially because previous studies performed by some of us on rod-like shape analogue, itraconazole, showed good correlation between theoretical predictions and experiment. This clearly points out difficulties in any attempt to foreseeing dynamical properties of supercooled materials from any prediction that based on their molecular structure. The issue related with liquid-crystalline ordering in posaconazole, will be discussed in the future with the use of other techniques. 10


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Dielectric spectra collected in supercooled liquid state were fitted by the empirical Havriliak–Negami (HN) function given by [40]

ε * HN (ω ) = ε ' (ω ) − iε " (ω ) = ε ∞ +

∆ε [1 + (iωτ HN ) ]

a b

+

σ0 iωε 0

(8)

where ε ' and ε " are real and imaginary (dielectric loss) parts of the complex dielectric function, ∆ε is the dielectric strength, σ 0 is dc-conductivity, ε 0 is permittivity of the vacuum, a and b represents symmetric and asymmetric broadening of the loss peak, respectively [41]. By setting

b=1 one get the Cole-Cole function, used by us to describe secondary relaxation process in the glassy state. The characteristic time constant τ HN in HN function is related to the relaxation time at maximum of loss peak τ max by the following relation

τ max = τ HN [sin(πab/(2 + 2b)] -1/a [sin(πa /(2 + 2b))]1 / a

(9)

Figure 5 shows the temperature dependencies of the relaxation times of the α, β and γ processes for posaconazole. All relaxation times were determined from Eq. 9 using appropriate HN and Cole-Cole fitting parameters. The structural relaxation rate is well described by the empirical Vogel-Fulcher-Tamman (VFT) equation (Eq. 2). From τ α (T) dependence we have determined the glass transition temperature of posaconazole as 329.8 K (for τ α =100s). The value of the glass transition temperature calculated from dielectric data quantitatively coincidences with the Tg determined from calorimetric measurements (Tg=332 K). The temperature dependence of secondary β− and γ- relaxation times follows Arrhenius equation (AE) given by

 Ea    k BT 

τ = τ ∞ exp

(10)

where τ ∞ is high temperature limit of relaxation rate, k B is Boltzmann constant and Ea is activation energy. We obtain activation energy ( E a ) β = 83.7 kJ/mol and ( E a ) γ = 46.7 kJ/mol, which are quite similar to the values obtained for itraconazole ( ( E a ) β = 80.6 kJ/mol and ( E a ) γ = 36.2 kJ/mol). VFT and AE fitting parameters are collected in Table 2. High activation barrier for β-relaxation suggests that it might be attributed to motions that involve entire molecule or confomrational motions occurring within the molecule, whereas low value of the 11



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activation energy for γ-relaxation that it might be related with certain intramolecular motion. Nevertheless, in order to understand the exact intermolecular motion that stands beyond secondary γ- relaxation in the glassy state of posaconazole it will be very informative to perform in the future additional quantum mechanical calculations combined with NMR or IR measurements. In the next step the α-loss peak recorded at temperature of T=335 K was fitted by the oneside Fourier transform of the Kohlrausch-Williams-Watts (KWW) function expressed as [42,43]

[

φ (t ) = exp − (t / τ α )β

KWW

],

(11)

where βKWW ( 0 < β KWW ≤ 1 ) is the stretching parameter providing important information about the distribution of molecular relaxation times. As we found, for posaconazole βKWW is equaled to 0.5 which implies that the distribution of relaxation times is much broader than for classical Debyetype response ( β KWW =1). On the other hand, it is identical as that found for its triazole analogue, itraconazole. The inset presented in Figure 5 clearly shows that the KWW function describes well experimental data only in vicinity of maximum of α-peak. Deviation from the KWW fit, clearly visible on the high frequency flank of the structural relaxation peak, is due to secondary βrelaxation which has much lower amplitude than structural process, so it becomes partially covered by it. Herein, it is worth to note that when the secondary β-relaxation is located in very clove vicinity of α-relaxation it becomes hidden under the intense structural peak. In that case, so called ‘excess wing’ appears on the high frequency flank of structural relaxation. Experimentally, it is possible to transform excess wing into well-separated peak by physical aging or applying pressure [44,

45

]. Due to merging of α- and β- relaxations at high temperatures, the time-

temperature superposition (TTS) doesn’t apply to the entire dielectric loss of posaconazole. However, as illustrated in the inset of Figure 5 the mastercurve (constructed by horizontal shift of a few spectra) with respect to the structural relaxation shows that the α-component of the dielectric loss near Tg practically doesn’t change. This observation suggests that the α-process itself should follow TTS, but due to the presence of the β-relaxation it becomes obscure and distort in the temperature range where both processes merge.

3.3.2. Mechanical studies 12


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Dielectric spectroscopy is certainly a very powerful tool in studying relaxation dynamics of supercooled liquids, especially due to the wide range of temperatures and characteristic relaxation times that can be probed. However, it doesn’t provide strict information about mechanical relaxation process in the liquid state. It might also happen that relaxation process that appears in dielectric spectra isn’t observed by any other experimental response function (e.g. Debye relaxation in monoalcohols [46]), or where dielectric spectra of some supercooled liquids are strongly covered by dc-conductivity, which is not well-suited for monitoring the dynamics of supercooled liquid in vicinity of the glass transition. Therefore, another experimental techniques are needed to study the thermodynamic (DSC) and dynamic (rheology, DLS) effects accompanying the glass transition event. Understating if responses measured via different techniques display some universal features is still fundamental goal to reach that should help broaden our knowledge of the glass transition phenomenon. Except of dielectric relaxation studies, an additional information about α-relaxation in supercooled liquids and polymers can be obtained from mechanical relaxation measurements. In Figure 6 (a) we present real G’ (inset) and imaginary G” (main panel) parts of shear modulus as measured in vicinity of the glass transition between temperatures 341K and 329 K in frequency range covering approx. 5 decades of relaxation times. For the shear loss peak of posaconazole there is α-process clearly visible, that shifts to lower frequencies as temperature decreases. In close vicinity of the glass transition (T=329 K) we found some signs that may suggest presence of the excess wing, however the maximum of β-loss peak is expected to lie outside available dynamical range. The shape of the imaginary part of the response function presented on so-called ‘mastercurve’ (Figure 6 (b)) confirms that the shear α-peak, similarly as its dielectric analogue, essentially holds time-temperature superposition (TTS) rule when the system is cooled down. It is generally assumed that viscoelastic response has its analogy in dielectric relaxation. Moreover, the formalism used to describe the results of shear mechanical and dielectric experiments have many similarities [41]. Therefore, both shear and dielectric relaxations are often compared [47, 48,49]. As it is sometimes suggested, direct comparison between dielectric and shear relaxation data measured by different spectroscopic techniques should be given in terms of a unified representation [41,47]. In this context it is worth to note that dynamic susceptibility ε* 13



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refer to retardation process whereas modulus M* is related to relaxation process. In the frequency domain dielectric modulus M* and mechanical modulus G* are expressed as the inverse of the dielectric susceptibility ε* and shear mechanical compliance J*, respectively. Taking that into account, dielectric spectra of posaconazole presented and discussed in the previous part of this paper should be converted to modulus representation. However, it is also worth to stress that both representations are equivalent, but in the literature there is still no consensus which one should be used to analyze dielectric data. Therefore, we have provided a direct comparison between dielectric susceptibility ε and shear modulus G data, without introducing electric modulus M formalism. Analogously as other researchers, we believe that this approach have made the analysis presented in the further part of this paper not too much confused and complicated (e.g. [37], [49]). In addition, our aim was just to show how relaxation properties of supercooled posaconazole change once we shift from electrical to mechanical response function. Thus, more elaborated discussion on the validity of comparison between dielectric modulus/susceptibility and shear modulus relaxations is beyond the scope of this paper and can be found elsewhere (e.g. [50]). From the frequency that corresponds to the G” maximum the shear α-relaxation time was determined and its temperature dependence was compared with dielectric one, as demonstrated in Figure 6(c). As typically observed, for the same temperature the shear-mechanical relaxation of posaconazole is slightly faster than dielectric ((τα−ε”(T) > τα-G”(T)). However, this difference between shear and dielectric alpha relaxation times leads to only slightly different value of the glass transition temperature, that basically can be associated with various experimental setups for mechanical and dielectric studies (1.4 K difference). The glass transition temperature (Tg=T(τα=100s)) determined from mechanical relaxation studies was found to be Tg=328.4 K, whereas Tg estimated from the temperature dependence of dielectric relaxation times is Tg=329.8 K. In order to compare the shape of mechanical and dielectric loss spectra we have made use of βKWW parameter. In Figure 7 (a) we present comparison of alpha relaxation peaks in shear and

dielectric modulus responses which shows that in supercooled liquid state mechanical shearrelaxation (βKWW=0.46) of posaconazole is only slightly broader than dielectric one (βKWW=0.50). The motions that underlie structural relaxation and the glass transition phenomenon compose of both diffusion and reorientation. Dielectric and mechanical spectroscopies probe 14


Page 15 of 34

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slightly different aspects of the relaxation dynamics of supercooled liquid near Tg, i.e. dielectric spectroscopy provides information considering rotational part of α-process, whereas mechanical measurements about viscosity and shear relaxation times (translations). Therefore, both techniques combined together are very useful to probe the relationship between both types of motion. For posaconazole, τ α -dielectric has been plotted against τ α − shear − mech on a double-logarithmic plot, as illustrated in the upper inset of Fig. 6(c). In this representation a straight line with the slope s=1 indicates perfect coupling between the rotational and the translational properties of supercooled liquid. We obtain s=0.80 providing a clear evidence of the decupling between translational and rotational motions. Next, it is also very instructive to compare translational motions of rod-like molecules of posaconazole with translational motions of small ions that are also present in every sample. The latter one is usually described by the dc-conductivity term σ and can be determined from dielectric studies. In the lower inset of Fig. 6(c) we present the dielectric dc-conductivity plotted versus shear-mechanical relaxation times. The straight line with the slope s’=0.72 points out for a decoupling between dielectric and mechanical translational motions. The fact that translational motions of ionic species are enhanced when compared with translational motions of posaconazole molecules seems to be natural as small entities possess greater ability to move among elongated molecules.

3.3.3. Fragility of posaconazole determined from dielectric, rheological and calorimetric studies The concept of fragility is very popular for classifying the structural dynamics of supercooled liquids and polymers. In the classical way, it can be calculated from the curvature of the log10 (τ α ) versus inverse of temperature dependence, using Eq. (1). According to literature data, the highest ever reported value of the fragility parameter for supercooled liquid was that reported for very compact molecule decahydroisoquinoline (DHIQ), m= 158 [51], which stands as classical example of supercooled liquid with large fragility. As there are only few examples of supercooled liquids with very large fragility index, studies on that matter are potentially very interesting. Using Eq. 1 we have estimated fragility of supercooled posaconazole from dielectric data. Value of m =150±10 allows us to classify it as very fragile glass-former. This is a bit higher value than reported by us for its triazole analogue, itraconazole, m=135.6 ([38]). However, 15



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Page 16 of 34

taking into account uncertainties involved in determination of fragility index for such a steep τα(T) dependence, both values suggest that triazoles seems to be very fragile systems. By

comparing the size of posaconazole and DHIQ we may get to the conclusion that the molecule of the former compound is significantly larger than the latter one. On the other hand, they both have something in common, i.e. ridged backbone that contains of aromatic rings and broad αdispersion in the dielectric spectrum (βKWW=0.35 [51]). However, DHIQ rather obey the general correlation between fragility and non-exponentially, quantified using βKWW parameter [11], whereas posaconazole not

m = 250(±25) - 320 β KWW

(11)

Deviation from this rule can be treated as an exception, although examples of the failure of fulfilling Eq. 11 are also known for other non-fragile glass-formers [52, 53]. Fragility of posaconazole defined in terms of Eq. 1 was also calculated from the temperature dependence of shear-mechanical alpha relaxation times. In this case, we have obtained m=192±10, which is certainly higher than that calculated for dielectric data, but confirms that posaconazole is indeed very fragile glass-former. As we have found out, discrepancy between values of the fragility index determined from dielectric and shearmechanical relaxations can be directly related to the degree of decoupling between translational and rotational motions in posaconazole. This becomes more evident once we calculate the fragility ratio mdiel/mshear-mech=0.78. Fragility determined in the way as that presented above refers solely to the structural relation, which governs the dynamic on approaching the glassy state. However, m can be also determined from calorimetric measurements. In that case, we termed it thermodynamic fragility as it reflects the behavior displayed by the excess entropy, i.e., the difference between the entropy of the liquid and the entropy of the underlying crystal. In order to calculate fragility of posaconazole purely from thermodynamic properties we have used Eq. (3) and (4) which based on the magnitude of the heat capacity increment at the glass transition, ∆Cp (Tg). The exact value of ∆Cp (Tg) =0.48 for posaconazole was determined from thermally modulated calorimetry. Fragilities obtained for stable form of posaconazole are collected in Table 3. As demonstrated, using Angel and Wang equation we get m=126±7, whereas from very similar Lubchenko and Wolynes formula the value of fragility is bit lower and equals 104±7. Now, by comparing 16


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fragility index of posaconazole derived from dielectric, mechanical and from differential scanning calorimetry measurements we get that they are generally different. However, in view of uncertainties involved in determination of the curvature of the τ α (T) dependence near Tg for such extremely fragile glass-former (changes in in temperature by one degree might result in increase of relaxation times by orders of magnitude) we can conclude that dynamic fragility of posaconazole determined from spectroscopic measurements agree reasonably well with those derived from thermodynamic properties (Wang and Angell empirical formula). Therefore, we concluded that very fragile nature of examined glass-former can be indeed detected by different in its nature experimental techniques.

3.3.4. Dynamic heterogeneity from dielectric, calorimetric and rheological studies As already mentioned dynamic heterogeneity is an active field of glass-transition research. However, due to experimental problems its direct determination in supercooled liquids is very limited, which has led to different ways of its estimation [6,12,54]. Now, having all experimental data gather together it is also very instructive to take a close look at dynamical heterogeneity aspect viewed in terms of different approaches. In order to do that we have followed spatially heterogeneous dynamics of posaconazole by the number of particles involved in correlated motion Nc using two different methods of its approximation. Let’s start with the formula proposed by Berthier et al. (Eq. 7). This requires to determine ∆Cp from calorimetric measurements, βKWW(T) and τα(Τ) dependences from spectroscopic

techniques. At first, we have estimated the temperature dependence of Nc based on dielectric response data. Since we

have found

that

the structural dielectric relaxation peak of

posaconazole has essentially the same shape in studied temperature range, we used constant value of stretching parameter (βKWW= 0.5) to calculate dielectric Nc(T) dependence. The behavior of Nc upon cooling calculated using dielectric τα(T) dependence is presented in Figure 8(a). By extrapolating Nc(T) up to 100 seconds we get that the number of dynamically correlated molecules at the glass transition temperature is N c -ε ≅ 440 at Tg. Then, analogical procedure was applied to shear-mechanical relaxation data. Obtained in this way results were plotted together with dielectric data, showing that the growth of Nc-G and Nc-ε is practically identical upon lowering temperature/slowing down of molecular dynamics (Fig 7.(b)). Thus, mechanical and 17



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Page 18 of 34

dielectric Nc evolve in rather similar way as their τα(T) dependences. By extrapolating shear Nc(T) up to 100 seconds we get that the number of dynamically correlated molecules at the glass transition temperature is N c -G ≅ 550 at Tg. Therefore, at the glass transition temperature the Nc-ε /Nc-G ratio is close to 0.8, which suggest that the degree of decoupling between dielectric and mechanical relaxations is portrayed in some way in the difference between the number of molecules dynamically correlated over τα determined from various probes methods. These results corresponds to experimental finding that the number of dynamically correlated molecules determined for dielectric Nε and shear-modulus NG data are proportional and in general for most of conventional supercooled liquids (except of hydrogen bonding liquids and polymers) the Nε/ NG ratio is close to unity [37]. Dynamic heterogeneity determined from Berthier equation takes into account thermodynamic (∆Cp) and kinetic (τα, βKWW) properties of investigated system. However, the number of dynamically correlated molecules as well as characteristic length scale can be determined purely from calorimetric experiment. Since dynamic heterogeneity is one of the key features of supercooled liquid dynamics it is essential to compare its approximate value determined from different experimental approaches. Thus, we have compared the number of dynamically correlated molecules estimated from Berthier expression for dielectric and shearmechanical data with that given by Donth and coworkers. According to this approach, the breadth of the calorimetric transition is inversely related to the size of heterogeneous region, whereas in dielectric loss response the broader peak implies more heterogeneous dynamics. Based on calorimetric measurements we have determined the number of molecules involved in correlated dynamics from Eq. 6. The mean temperature fluctuation we determined as

δT =

∆T 2.5

(12)

where ∆T is temperature interval in which Cp changes from 16-84% of the total ∆Cp step at Tg. The value of ∆(CV−1 ) is defined as ∆ (CV−1 ) = CVg − CVl -1

-1

(13) 18


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-1

where CVg and CVl

-1

are the values of the glassy and liquid Cv extrapolated to Tg, respectively.

This difference is either neglected or accounted via the following equation

( )

∆(CV−1 ) = (0.74 ± 0.22)∆ C p−1

(14)

As we get, the resulting value at the glass transition temperature is ~92, which is drastically lower than those reported from dielectric and shear mechanical spectroscopies (440 and 550, respectively). One can add that similar number of correlated molecules at Tg was estimated also for other glass formers such indomethacin, sorbitol, maltitol using Donth approach. On the other hand we found that Nα calculated from Berthier equation yields completely different number of correlated molecules for posaconazole at Tg. Hence, one may ask question do these models refer to the same quantity called usually dynamic heterogeneities or cooperatively rearranging regions? Our data presented herein indicate that both approaches can give us completely different results. Thus, in fact further studies should be performed to clarify this issue.

4. Summary and Conclusions In this paper molecular dynamics of pharmaceutical, posaconazole was studied in the supercooled liquid and glassy states. In our studies we have utilized dielectric and mechanical spectroscopies combined with calorimetric measurements and DFT calculations. Quantum mechanical calculations reveal that rod-like molecule of posaconazole has very large value of the dipole moment (3.7 D) and due to the aspect ratio (semimajor axis to semiminor axis) greater than 2 its supercooled dynamics should be dominated by nematic like ordering. Due to broad range of available relaxation times and temperatures, dielectric spectroscopy was used to characterize molecular dynamics in the liquid and glassy states of posaconazole. Multiple relaxation process were observed: primary α-relaxation detected above glass transition temperature and secondary relaxations: β- and γ- in vicinity and below glass transition temperature of posaconazole. Dielectric and shear mechanical studies have confirmed that posaconazole is extremely fragile glass-former (m=150±10 from dielectric and m=192±10 from 19



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Page 20 of 34

shear-mechanical dataragility of posaconazole determined solely from calorimetric measurements were bit lower. Nevertheless, taking into account uncertainties related with determination of the curative of the τα(T) dependence near Tg, we can assume that they corresponds rather well to dielectric and mechanical fragilities (especially m=126±7 calculated from Wang and Angel empirical equation). In this paper we have also made an attempt determine and compare dynamic heterogeneity of posaconazole, quantified by the number of dynamically correlated molecules Nc, based on different approximation approaches, i.e form Berthier equation (that involves thermodynamic and kinetic properties of investigated material) and Donth equation (which bases only on calorimetric measurements). As we get, dielectric and mechanical Nc, which were determined from Berthier equation, are approximately the same and their temperature dependences evolve in rather similar way. On the other hand, the characteristic number of correlated molecules at the glass transition calculated from calorimetric data (Donth equation) is drastically lower than those reported from relaxation spectroscopies (Nc-calor.= 92, Nc-ε= 440, Nc-G = 550). This points out for an essential divergence upon calculation of dynamical heterogeneity of supercooled liquid without including correction for the kinetic factor. Finally, our studies have demonstrated that in supercooled posaconazole there is a decoupling between translational and rotational motions (s=0.80). Its degree has direct influence on the difference between dielectric and mechanical relaxation times, fragilities as well as the number of dynamically correlated molecules determined from dielectric and mechanical probes methods.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. Notes 20


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The authors declare no competing financial interest.

Acknowledgments We would like to thank Dr. G. Nowaczyk (NanoBioMedical Centre) for helpful discussion and support during rheological measurements. K. A and S. J. acknowledge financial assistance from National Centre for Research and Development (Nanomaterials and their potential application in nanobiomedicine). K.A is also deeply grateful for financial support from POKL and FNP START (2013) programs. M. P and K. G are deeply greatful for the financial support by the National Science Centre within the framework of the Opus 3 project (Grant No. DEC2012/05/NZ3/03233).

Figures and Tables

(a)

(b) 21



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Figure 1. Chemical structure of selected triazoles: (a) posaconazole, (b) itraconazole

a)

b)

22


Page 22 of 34

Page 23 of 34

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c)

d)

Figure 2. Schematic illustration of the x (a), y (b) and z (c) components of the dipole moment vector. Panel (d) present the resultant dipole moment orientation. The x component (-1.50 D) of the total dipole moment is directed towards strongly electronegative F atoms. Semiminor y and z components are equal to µ=2.70 D and µ= 1.93 D, respectively. The total dipole moment of posaconazole is equal to 3.7 D and its vector is directed likely towards y axis.

23



5

Tm=440.5 K

Heating of the sample 10 K/min 1.0

4

3

glass heating Heat Flow [W/g]

Heat Flow [W/g]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 34

Tm=441 K

0.5

Tg= 332 K

TC=416.3 K

0.0

2 -0.5 320

340

360

1

380

400

420

440

460

T [K]

T1=405.5 K

0

-1 320

340

360

380

400

420

440

460

T [K]

Figure 3. DSC thermograms of posaconazole obtained upon heating (10 K/min) of the crystalline and glassy samples.

24


Page 25 of 34

. p m e t

. p m e t n o i t a x a l e r β

ε"

K 3 6 2

10

K 3 6 1

0,01

n o i t a x a l e r -

K 0 2 = T

γ

∆

1

-2

-1

10

0

10

ε"

10

1

10

2

10

Freq. / Hz

3

10

4

10

5

10

6

10

0,1 T=337 K T=345 K T=331 K ∆T=2K

10-2

10-1

n o i t a x a l e r -

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


α 100

101

102

103

104

105

106

107

Freq. / Hz

Figure 4. Dielectric loss spectra of posaconazole collected above (main panel) and below (inset) its glass transition temperature.

25



1

α−relaxation

T=347 K T=337 K T=337 K T=333K T=331 K

ε"

2

K 8 . 9 0 2 5 3 1 = = T gm

0

secondary β−relaxation

log10 [τ/s]

0.1

β KWW =0.5

-2

at 331 K 10

-4

10

-2

0

10

10

2

10

4

10

6

10

8

Freq. / Hz

-4

l o m / J k 7 . 3 8 = E β

-6

l o m / J k 7 . 6 4 = E

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 34

τα

γ

τβ τγ

-8 0.0032

0.0040

0.0048

0.0056

0.0064

Temp.[K] Figure 5. Thermal activation plots of the structural (α) and secondary (β and γ) relaxation processes for posaconazole. Solid line represents temperature dependence of structural relaxation times fitted by the VFT equation, whereas dotted line represents fits by the Arrhenius equation. The inset presents superposition of loss spectra at few various temperatures above Tg. Solid line represents the best fit of experimental data to the KWW function, with βKWW=0.5.

26


Page 27 of 34

2

0.32

0

0.08

10-3 10-2 10-1 100

101

102

Freq (Hz)

0.06

0.04

T=329 K T=331 K T=333 K T=335 K T=337 K T=339 K T=341 K

0.02

G"/G"max

0.00

0.6

-2.6

-4

-6 0.2

10-3

0.0

-1.3

0.0

1.3

log10 [τα-G"/s]

τα from G"

τα from ε"

-14.0

10-1

-8 101

103

f/fmax

Freq (Hz)

-14.4 -14.8 -15.2 -3.5

βKWW=0.48 10-3 10-2 10-1 100 101 102 103

s=0.80

-2

0.4

0.00

1.3

-1.3

0.8

log10 [τα/s]

G' (GPa)

0.16

log10 [τα−ε"/s]

1.0

0.24

0.08

T=329 K T=331 K T=333 K

log10 σdc [S/cm]

0.12

0.10

(c)

(b)

(a)

G" [GPa]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


s'=0.72 -3.0

-2.5

-2.0

-1.5

log10 [τα-G"/s]

330 340 350 360 370 380

Temp. [K]

Figure 6. The (a) real (inset) and imaginary (main) parts of the shear response for posaconazole; (b) Shear relaxation loss spectra scaled by the maximum of G”max plotted as a function of frequency divided by the frequency of peak maximum. Solid line indicates KWW fit of loss spectrum recorded at 331 K with stretching parameter βKWWW=0.46; (c) Mechanical and dielectric relaxation times plotted as a function of temperature. Solid lines corresponds to VFT fits of experimental data. The upper inset shows plot of dielectric relaxation times against shearmechanical relaxation times. The data were described using single value of the fractional exponent, s=0.80. The lower inset shows plot of dc-conductivity versus shear-mechanical relaxation times with decoupling parameter, s’=0.72.

27



(a) (a)

(b)

400

420

1 Nc

280

300

140

Nc

G"/G"max and ε"/ε"max

ε

" " G

200

0 -6

-4

-2

0

2

log10[τα/s]

100 0.1 Nc (dielectric)

0

Nc (mechanical)

10-2

100

102

104

106

108

330

1010

340

(a) (a)

360

370

380

(b)

ε

560

500 420

1 Nc

400

280 140

300

Nc

G"/G"max and ε"/ε"max

350

Temperature [K]

f/fmax

" " G

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 34

0

200

-6

-4

-2

0

2

log10[τα/s]

100

0.1

0 10-2

100

102

104

106

108

Nc (dielectric) Nc (mechanical)

330

1010

340

350

360

370

380

Temperature [K]

f/fmax

Figure 7 (a) Comparison of normalized shear and dielectric α-relaxation peaks at the same temperature T= 331 K. (b) Evolution of the number of dynamically correlated molecules for shear and dielectric responses plotted versus temperature and the logarithm of structural relaxation times (inset) 28


Page 29 of 34

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Table 1. Thermodynamic properties of posaconazole

Tg (DSC)

∆Cp

Cp-conf

[K]

(at Tg) [Jg-1K-1]

Tm [K]

∆Hm [J/g]

∆Hm

Trecryst

(at Tg)

(initial

[J/g]

[K]

[Jg-1K-1]

crystal)

(after

Degree of recryst.

416.3

22%

recryst.) 332 ± 2 K

0.48 ± 0.02

0.21

440.5 ± 1

70.63 ± 5

15.36

Table 2. Parameters of the VFT fits of the τ α (T) and the Arrhenius fits of the τ β (T) and τ γ (T) dependences

Arrhenius VFT log10( τ ∞ /s)

-11.14 ± 0.07

D

1,26 ± 0.02

T0 (K)

β-relaxation

γ-relaxation

Ea (kJ/mol)

83.7 ± 1.4

46.7 ± 0.9

log10 (τ ∞ /s)

-18.9 ± 0.3

-18.0 ± 0.2

300,8 ± 0.4

Table 3. Comparison of the fragility and the number of dynamically correlated molecules at Tg determined from calorimetric, dielectric and shear-mechanical measurements for posaconazole

mp

mp

mp

mp

Nc-εε

Nc-G

Nc-calor

from Eq. 3

from Eq. 4

from BDS

from mech.

from Eq.7

from Eq.7

from Eq. 6

(τα=100s)

(τα=100s)

150±10

192±10

440±98

550±128

92±9

126±7

104±7

29



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Page 30 of 34

References 1. Elliott, S. R. Amorphous semiconductors. Nature 1979, 282, 560–560. 2. Demetriou, M. D.; Launey, M. E.; Garrett, G.; Schramm, J. P.; Hofmann, D. C.; Johnson, W. L.; Ritchie, R. O. A damage-tolerant glass. Nature Materials 2011, 10, 123–128. 3. Levine, H. Amorphous food and pharmaceutical systems; Royal Society of Chemistry: Cambridge, 2002. 4. Storey, K. B.; Storey, J. M. Natural freezing survival in animals. Ann. Rev. Ecol. Syst. 1996, 27, 365–386.

5. Dyre, J. C.; The glass transition and elastic models of glass-forming liquids. Rev. Mod. Phys.,

2006, 78, 953-972. 6. Donth, E.; The Glass Transition, Springer Berlin, 1st edn, 2001. 7. Angell, C. A., Strong and fragile liquids, Relaxations in Complex Systems, edited by K. L. Ngai and G. B. Wright (U.S. GPO, Washington, D.C) 3–11, 1985. 8. Vogel H.; The law of the relation between the viscosity of liquids and the temperature, Physikalische Zeitschrift 1921, 22, 645-6.

9. Fulcher, G.; Analysis of recent measurements of the viscosity of glasses, J. Am. Cer. Soc.

1925, 8, 339 – 355. 10. Tammann, G.; Hesse, W.; Die Abhängigkeit der Viscosität von der Temperatur die unterkühlten Flüssigkeiten, Zeitschrift für anorganische und allgemeine Chemie, 1926, 156, 245 – 257.

11. Böhmer, R.; Ngai, K. L.; Angell, C.A.; Plazek, D. J.; Nonexponential relaxations in strong and fragile glass formers, J. Chem. Phys. 1993, 99, 4201. 12. Berthier, L.; Biroli, G.; Bouchaud, J-P.; Cipelletti, L.; El Masri, D.; L’Hote, D.; Ladieu, F.; Pierno, M.; Direct Experimental Evidence of a Growing Length Scale Accompanying the Glass Transition, Science 2005, 310, 1797. 13. Qiu, X. H.; Ediger, M. D.; Length Scale of Dynamic Heterogeneity in Supercooled DSorbitol: Comparison to Model Prediction, J. Phys. Chem. B 2003, 107, 459.

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14. Kim, AI., The role of viscoelastic properties in physical stability of freeze-dried solids: Crystallization of mannitol, 1998 Purdue University AAT 9939376. 15. Tanaka, H.; Two-order-parameter description of liquids. I. A general model of glass transition covering its strong to fragile limit. J. Chem. Phys. 1999, 111, 3163–3175. 16. Tanka, H.; Two-order-parameter model of the liquid–glass transition. I. Relation between glass transition and crystallization. J. Non-Cryst. Solids 2005, 351, 3371–3384. 17. Paluch, M.; Ngai, K.L.; Hensel-Bielowka, S.; Pressure and temperature dependences of the relaxation dynamics of KDE: Evidence of contributions from thermodynamics and molecular interactions, J. Chem. Phys. 2001, 114, 10872. 18. Adrjanowicz, K.; Wojnarowska, Z.; Grzybowska, K.; Hawelek, L.; Kaminski, K.; Paluch, M.; Kasprzycka, A.; Walczak, K.; Molecular dynamics and crystallization phenomenon of supercooled and glassy DNA and RNA nucleosides:β-adenosine,β-thymidine, andβ-uridine, Phys. Rev. E. 2011, 84, 051507. 19. Hong, L.; Gujrati, P. D.; Novikov, V. N.; Sokolov, A. P.; Molecular cooperativity in the dynamics of glass-forming systems: A new insight, J. Chem. Phys. 2009, 131, 194511. 20. Adrjanowicz, K.; Kaminski, K.; Paluch, M.; Ngai, K. L.; Yu, Y.; Study of dynamics and crystallization kinetics of 5-methyl-2-[(2-nitrophenyl)amino]-3-thiophenecarbonitrile at ambient and elevated pressure. J. Chem. Phys. 2012, 136, 234509. 21. Angell, C. A. ; Relaxation in liquids, polymers and plastic crystals – strong/fragile patterns and problems, J. Non-Cryst. Solids 1991, 131–133, 3-31. 22. Richert, R.; Angell, C. A.; Dynamics of glass-forming liquids. V. On the link between molecular dynamics and configurational entropy, J. Chem. Phys. 1998, 108, 9016. 23. Ito, K.; Moynihan, C. T.; Angell, C. A.; Thermodynamic determination of fragility in liquids and a fragile-to-strong liquid transition in water, Nature 1999, 398, 492. 24. Wang, L-M.; Angell C. A.; Response to ‘‘Comment on ‘Direct determination of the fragility indices of glass-forming liquids by differential scanning calorimetry: Kinetic versus thermodynamic fragilities” J. Phys. Chem. 2003, 118, 10353.

31



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 32 of 34

25. Lubchenko V.; Wolynes, P. G.; Barrier softening near the onset of non-activated transport in supercooled liquids: Implications for establishing detailed connection between thermodynamic and kinetic anomalies in supercooled liquids, J. Chem. Phys. 2003, 119, 9088. 26. Ngai, K. L.; Yamamuro, O.; Thermodynamic fragility and kinetic fragility in supercooling liquids: A missing link in, J. Chem. Phys. 1999, 111, 10403. 27. Cangialosi, S.; Alegria, A.; Colmenero, J.; A thermodynamic approach to the fragility of glass-forming polymers, J. Chem. Phys. 2006, 124, 024906. 28. Scopigno, T.; Cangialosi, D.; Ruocco, G.; Universal relation between viscous flow and fast dynamics in glass-forming materials, Phys. Rev. B 2010, 81,100202 (R). 29. Tracht, U.; Wilhelm, M.; Heuer, A.; Fend, H.; Schmidt-Rohr, K.; Spiess, H. W.; Length Scale of Dynamic Heterogeneities at the Glass Transition Determined by Multidimensional Nuclear Magnetic Resonance, Phys. Rev. Lett. 1998, 81, 2727. 30. Vidal Russell E.; Israeloff, N. E.; Direct observation of molecular cooperativity near the glass transition, Nature 2000, 408, 695-698. 31. Dynamical heterogeneities in glasses, colloids and granular media, ed. L. Berthier, G. Biroli, J-P. Bouchaud, L. Cipeletti, and W. van Saarloos (Oxfrod Univ. Press, Oxford, 2011) 32. Bennemann, C.; Donati, C.; Baschnagel, J.; Glotzer, S.C.; Growing Range of Correlated Motion in a Polymer Melt On Cooling Towards the Glass Transition, Nature, 1999, 399, 246. 33. L. Hong, P. D. Gujrati, V. N. Novikov, and A. P. Sokolov, Molecular cooperativity in the dynamics of glass forming systems: A new insight, J. Chem. Phys. 2009, 131, 194511. 34. Donth E.; Characteristic length of the glass transition, J. Pol. Sci. Part B 1996, 34(17):288192. 35. Berthier, L.; Dynamic heterogeneity in amorphous materials, Physics 2011, 4, 42. 36. Capaccioli, S.; Ruocco, G.; Zamponi, F.; Dynamically Correlated Regions and Configurational Entropy in Supercooled Liquids, J. Phys. Chem. B 2008, 112, 10652-10658. 37. Maggi, C.; Jakobsen, B.; Dyre, J. C.; Unique Dynamic Length in Supercooled Liquids, 2010, arXiv:1003.0341v1 [cond-mat.soft] 1 Mar 38. Tarnacka, M.; Adrjanowicz, K.; Kaminska, E.; Kaminski, K.; Grzybowska, K.; Kolodziejczyk, K.; Wlodarczyk, P.; Hawelek, L.; Paluch, M.; Garbacz, G.; Weitschies, W.; Molecular dynamics of itraconazole at ambient and high pressure (under revision) 32


Page 33 of 34

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


39. Letz, M.; Schilling, R.; Latz, A.; Ideal glass transitions for hard ellipsoids, Phys. Rev. E 2000, 62, 5173.

40. Havriliak, S.; Negami, S.; A complex plane representation of dielectric and mechanical relaxation processes in some polymers, Polymer 1967, 8, 161. 41. Kremer F.; Schönhals, A.; Broadband Dielectric Spectroscopy, Springer, Berlin, 2003. 42. Williams. G.; Watts, D. C.; Non-symmetrical dielectric relaxation behavior arising from a simple empirical decay function, Trans. Faraday Soc., 1970, 66, 80 – 85. 43. Kohlrausch R.; Nachtrag über die elastiche Nachwirkung beim Cocon und Glasladen, Ann. Phys. (Leipzig) 1987, 72, 393.

44. P. Lunkenheimer, R. Wehn, Th. Riegger, A. Loidl, J. Non-Cryst. Solids 2002, 307–10, 336– 344. 45. Hensel-Bielowka, S.; Paluch, M.; Ngai, K. L.; Emergence of the genuine Johari-Goldstein secondary relaxation in m-fluoroaniline after suppression of hydrogen-bond-induced clusters by elevating temperature and pressure, J. Chem. Phys. 2005, 123, 014502. 46. Jackobsen, B.; Maggi, C.; Christensen, T.; Dyre, J.C.; Investigation of the shear-mechanical and dielectric relaxation processes in two monoalcohols close to the glass transition, J. Phys. Chem. 2008, 129, 184502.

47. Paluch, M; Dielectric and mechanical relaxation in epoxy systems with molecules of different topology, J. Phys.: Condens. Matter 2000, 12, 9511. 48. Gainaru, C.; Hecksher, T.; Olsen, N. B.; Böhmer, R.; Dyre, J. C. Dyre, Shear and dielectric responses of propylene carbonate, tripropylene glycol, and a mixture of two secondary amides, J. Chem. Phys, 2012, 137, 064508.

49. Niss, K.; Jakobsen, B.; Olsen, N. B.; Dielectric and shear mechanical alpha and beta relaxation in seven glass-forming liquids, J. Chem. Phys. 2005, 123, 234511. 50. Niss, K.; Jakobsen, B.; Olsen, N. B.; Dielectric and shear mechanical relaxations in glassforming liquids: A test of the Gemant-DiMarzio-Bishop model, J. Chem. Phys. 2005, 123, 234510. 51. Richert, R.; Duvvuri, K.; Duong, L.-T.; Dynamics of glass-forming liquids. VII. Dielectric relaxation of supercooled tris-naphthylbenzene, squalane, and decahydroisoquinoline J. Chem. Phys. 2003, 118, 1828. 33



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 34 of 34

52. Paluch, M.; Ngai, K. L.; Henel-Bielowka, S.; Pressure and temperature dependences of the relaxation dynamics of cresolphthalein-dimethylether: Evidence of contributions from thermodynamics and molecular interactions, J. Chem. Phys. 2001, 114, 10872. 53. Roland, C. M.; Paluch, M.; Rzoska, S. J.; Departures from the correlation of time- and temperature-dependences of the α-relaxation in molecular glass-formers. J. Chem. Phys. 2002, 119, 12439.

54. Kremer, F.; Huwe, A.; Arndt, M.; Behrens, P.; Schwieger, W. ; How many molecules form a liquid?, J. Phys. Condens. Matter 1999, 11, A175.

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Molecular Dynamics of the Supercooled Pharmaceutical Agent

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