The Impact of Liquid Crystalline Phase Ordering on the

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C: Physical Processes in Nanomaterials and Nanostructures

The Impact of Liquid Crystalline Phase Ordering on the Thermodynamic Scaling of Itraconazole Dawid Heczko, Ewa Kaminska, Magdalena Tarnacka, Kajetan Koperwas, Andrzej Dzienia, Miroslaw Adam Chorazewski, Kamil Kaminski, and Marian Paluch J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b12074 • Publication Date (Web): 28 Jan 2019 Downloaded from http://pubs.acs.org on February 3, 2019

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The Journal of Physical Chemistry

The impact of liquid crystalline phase ordering on the thermodynamic scaling of itraconazole Dawid Heczko1*, Ewa Kamińska1*, Magdalena Tarnacka2,3*, Kajetan Koperwas2,3, Andrzej Dzienia4, Miroslaw Adam Chorazewski4, Kamil Kamiński2,3, Marian Paluch2,3

1

Department of Pharmacognosy and Phytochemistry, Medical University of Silesia in Katowice, School of

Pharmacy with the Division of Laboratory Medicine in Sosnowiec, ul. Jagiellonska 4, 41-200 Sosnowiec, Poland 2 Institute 3

of Physics, University of Silesia, ul. 75 Pulku Piechoty 1, 41-500 Chorzów, Poland

Silesian Center for Education and Interdisciplinary Research, University of Silesia, ul. 75 Pulku Piechoty 1A,

41-500 Chorzów, Poland 4 Institute

of Chemistry, University of Silesia, ul. Szkolna 9, 40-003 Katowice, Poland

* Corresponding authors: (DH) [email protected]; (EK) [email protected]; (MT) [email protected]

ABSTRACT Herein, we tested the validity of the thermodynamic scaling of two (α and δ) relaxation processes observed in the isotropic and nematic phases of itraconazole, that is classified as a liquid crystal (LC). As illustrated, relaxation times of both processes obtained at various thermodynamic conditions can be successfully superposed over 1/TV with different scaling exponents, γ, satisfying the thermodynamic scaling law. However, it was found that γ parameters determined in the isotropic phase are higher than those estimated for respective relaxation processes in the nematic state [J. Chem. Phys. 2015, 142, 224507]. It seems that differences in the arrangements of molecules within LC phases significantly affect the effective intermolecular potential resulting in the variation of scaling exponent and disagreement between γ and γEOS (estimated from the equation of state). The observed behavior suggests that both variables depend not only on the intermolecular potential but also on the degree of molecular ordering. 1 ACS Paragon Plus Environment

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I.

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INTRODUCTION

The concept of thermodynamic scaling of structural relaxation times () was initially studied by Tölle1,2 and later on by Dreyfus et al.3 for ortho-terphenyl (OTP). They have shown that  obtained at various thermodynamics conditions can be superposed onto single master curve as a function of 1/TV4 independently on (p,T) conditions, where T is a temperature, V describes a specific volume of the system and 4 is a scaling exponent. This relation implies that the thermodynamic scaling (TS) might provide a direct connection between the thermodynamic properties of the system and its dynamics as well as intermolecular interactions. Although at first the authors correlated the value of the scaling exponent with the repulsive part of LenardJones (LJ) potential for which m = 12 (m/3 = 4),4,5,6 further comprehensive studies performed for various glass formers, i.e., liquid crystals, ionic liquids and polymers,7,8,9,10 revealed that this assignment is not valid for the other materials. Since extensive theoretical and computational studies have demonstrated that attractive forces between molecules influence the potential shape and distance at which repulsive intermolecular interactions dominate, the scaling parameter was connected to the exponent of the effective approximation of the LJ potential at small distances, by the inverse power law (IPL) potential. Parameter mIPL obtained in that way generally differs from 12. Thus, the TS can be treated more universally as 1/TV, where the scaling exponent, γ (mIPL/3 = γ), is a material constant and may vary in a wide range from 0.1 to 9.11 As shown, the major advantage of thermodynamic scaling is that the intermolecular potential, or its repulsive part, can be determined from the analysis of macroscopic properties of the liquids, making this concept scientifically interesting. Note that the relationship between the scaling exponent and the potential is a matter of an open debate and so we refer interested readers to other articles, see Ref. 12,13,14,15,16. Also, one can also mention the isomorph theory,17,18,19,20 that explains why the thermodynamics scaling concept works well in many glass-forming systems. It postulates that so-called Roskilde-simple liquids 2 ACS Paragon Plus Environment

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(i.e., liquids which at the condition of constant temperature and volume are characterized by a strong correlation between fluctuations of virial and potential energy)21 exhibit states, denoted as isomorphs, at which some structure and dynamics are invariant in reduced units.17,18,19,20 Consequently, structural and dynamic characteristics of those states, i.e., structural relaxation times or the radial-distribution functions, are identical. It should also be mentioned that for the associating compounds, the population of H bonds strongly depends on the thermodynamic, their internal structures are much different at various T, V and p conditions. Therefore, in these liquids, the TS is generally not fulfilled.22,23,24,25 Although, it should be stressed that it is not a rule. Recently, it has been shown that in the strongly hydrogen-bonded ternidazole drug (3-(2methyl-5-nitroimidazol-1-yl)-propan-1-ol), the TS is satisfied with γ = 2.26 One of the most interesting materials for which thermodynamic scaling have been applied is liquid crystals (LC),27,28,29,30,31,32 which share the properties of both solid crystals, exhibiting a unique molecular ordering, and conventional liquids. LC mesophases are longrange (orientationally) ordered (and/or translationally disordered) states. For example, in the nematic phase, molecules have no positional order, but they are randomly aligned along their long axes, averagely parallel. While in the smectic state, there are parallel layers of ordered molecules characterized by different types and degrees of positional and orientational order, see Ref. 33,34,35,36,37,38. The formation of different LC phases is mainly observed in molecules with strong anisotropic shapes (mostly disclike or rodlike). Consequently, in these materials, two different kinds of relaxation processes are usually observed being associated with the rotation of the molecule around its short (often called flip-flop motions or δ-relaxation) and long molecular axes. Due to the higher sensitivity to the molecular rearrangements within LC phases, the former mobility is considered to be crucial for the deeper understanding of molecular interactions in LC phases.39,40,41 Therefore, the majority of papers devoted to liquid crystals is focused on the dynamic behavior of the δ-relaxation process. As shown in the

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literature, the TS works pretty well for most of these systems. Interestingly, the scaling exponent obtained for the reorientation of the molecules around short exes in liquid crystals is rather small, γ ~ 2-4, and seems to depend on the chemical structure of the examined material weakly. For example, in the case of nCB’s (4-n-alkyl-4’-cyano-biphenyls), where n stands for the number of carbon atoms in the alkyl chain, γ is equal to 4.1, 4.1 and 4.2 for 5CB, 6CB and 8CB, respectively, while for nPCH’s (trans-4-n-alkyl-(4-cyanophenyl)cyclohexanes) and nBT’s (n-alkyl-isothiocyanato-biphenyls), it reaches 3.5 – 3.9 and 2.3 – 4.1, respectively (see Ref. 27,28 and references therein). Additionally, there is no significant correlation between the scaling exponent and the length of the alkyl chain. Moreover, one can add that for the liquid-crystalline compounds, for which LC transitions occur at constant relaxation times, the scaling γ parameter is reported to be in a good agreement with the thermodynamic ratio (or thermodynamic potential parameter), Г, which describes the volume dependency of the orientational contribution to the internal energy and can be calculated as follows:42

d log Tcl   , d log Vc

(1)

where Tcl is a clearing temperature, and Vc is a specific volume at Tcl. Although primary Г was introduced by Maier and Saupe for the description of the nematic phase,39 it was also used for the characterization of other LC transitions.43,44 Typically, Г parameter reaches values Г= 2-8,44,45,46 where an increase of Г leads to an increase of steric repulsion relative to the attractive interactions. Note that the above-mentioned agreement between Г and γ is a result of the linear relationship, which directly results from the TS. According to the thermodynamic scaling, TV is constant at constant relaxation times, which implies that: log T    log V  C ,

(2)

where C is a constant, and should eventually lead to γ = Γ. 4 ACS Paragon Plus Environment

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As discussed above, LC materials satisfy the TS law. Importantly, papers published so far clearly indicated that only one scaling exponent is enough to rescale the times of given relaxation process measured at different phases in liquid crystals onto the single master curve, see Ref. 27,29. These results seem to be quite intriguing since the change in molecular ordering should also affect the anisotropy of the system and the manner of intermolecular interactions, therefore the scaling exponent. To verify this hypothesis, we carried out high pressure dielectric studies on itraconazole that forms isotropic, nematic as well as Smectic A order. In each mentioned above phases, two well-visible relaxation processes can be observed. Accordingly to the previous studies,47,48 the faster process observed at high frequency region is related to the tumbling motions around a long molecular axis, having similar relaxation times. For this paper, we label this mode as α or structural. The second relaxation process detected at the low frequency side of the primary one is due to the reorientation of the molecules around a short axis and is called the flip-flop rotation or δ-mode.49,50 To the best of our knowledge, it is a first paper exploring the thermodynamic scaling concept for two different kinds of mobility (α and δ-relaxation) during isotropic-nematic phase transition in liquid crystals. It is worth mentioning that recently Romanini et al. have shown that double primary relaxation process (α and α’) detected in the orientationally disordered molecular crystal pentachloronitrobenzene, PCNB, scaled with the use of two different scaling exponents (γα = 7.60 and γα’ = 7.81).51 II. EXPERIMENTAL SECTION 2.1. Material Itraconazole

(IUPAC

Name:

(2R,4S)-rel-1-(butan-2-yl)-4-{4-[4-(4-{[(2R,4S)-2-(2,4-

dichlorophenyl)-2-(1H-1,2,4-triazol-1-ylmethyl)-1,3-dioxolan-4 yl]methoxy}phenyl)piperazin-1-yl]phenyl}-4,5-dihydro-1H-1,2,4-triazol-5-one, C35H38Cl2N8O4, Mw= 705.64g/mol), was supplied from Sigma Aldrich with purity greater than



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99%, and used without further purification. Its chemical structure is shown in Scheme 1. The dipole moment distribution in ITZ molecule is presented in Scheme 2. 2.2. Methods 2.2.1. Differential Scanning Calorimetry (DSC) Thermodynamic properties of crystalline and glassy forms of considered active substance were investigated by DSC technique. Calorimetric measurements were carried out using 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 using indium and zinc standards, while heat capacity Cp calibration was carried out using a sapphire disc. The crystalline sample in an aluminum crucible (40µL) was heated inside the DSC apparatus, and next immediately cooled to vitrify the liquid sample (10 K/min). Crucibles with such prepared glassy samples as well as their crystalline counterparts were sealed with the top with one puncture. Crystalline and amorphous samples were scanned at a rate of 10 K/min over a temperature range of 298 K to well above the glass transition point. 2.2.2. Broadband Dielectric Spectroscopy (BDS) Isobaric measurements of the dielectric permittivity ε*(ω) = ε’(ω)–iε”(ω) at ambient pressure were performed using the dielectric spectrometer (Novo-Control Alpha) over a frequency range from 1·10-2 to 3·106 Hz at ambient pressure. The sample was placed between two stainless-steel electrodes (diameter: 15 mm, gap: 0.14 mm) and mounted on a cryostat. During measurement, it was maintained under dry nitrogen gas flow. The temperature was controlled by Quatro System using a nitrogen gas cryostat, with stability better than 0.1 K. The dielectric measurements were performed for supercooled sample and carried out in the temperature range from 331 K to 383 K.


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For dielectric measurements at elevated pressure, we used a high pressure chamber with a special homemade flat parallel capacitor. Thin teflon spacers were applied to maintain a fixed distance between the plates. The sample capacitor was sealed and mounted inside a teflon capsule to separate it from the silicon liquid. Pressure was measured by a Nova Swiss tensometric meter with a resolution of 0.1 MPa. Temperature was adjusted with a precision of 0.1 K using refrigerated and heating circulator. Complex dielectric permittivity was measured within the frequency range from 10-2 up to 106 Hz. The obtained dielectric data (collected at both ambient and high pressure) were analyzed with the Havriliak-Negami (HN) function with an additional term describing the dc conductivity:52

 * ( ) 

2   dc  i  Im       0 [1  (i HNi ) ] i 1  HNi

HNi

 , 

(3)

where αHN and βHN are the shape parameters representing the symmetric and asymmetric broadening of relaxation peaks, respectively, Δε is the dielectric relaxation strength, τHN is the HN relaxation time, ε0 is the vacuum permittivity and  is an angular frequency ( =2πf). Note that the relaxation times of both processes: structural, τα, and , τ, were estimated from τHN accordingly to the equation given in Ref. 53. The distribution parameters, αHN and βHN, of the relaxation times for the structural process, differed in the range ~ 0.7-0.8 in the isotropic phase at ambient pressure and decreased with decreasing temperature.50 2.2.3. Pressure-Volume-Temperature measurements

The specific volume V of the materials in the isotropic and nematic phases was analyzed by pressure-volume-temperature

(PVT)

experiments

using

a

GNOMIX

high-pressure

dilatometer.54 The originally crystalline samples were compressed to plates at 303 K under a pressure of 90 kN. First, some isothermal heating at T = 293 – 318 K in steps of ΔT = 5 K were 7 ACS Paragon Plus Environment


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performed to calibrate the specific volume of the sample according to the literature data.55 Then, isobaric heating and cooling runs at pressures from p = 10 MPa to p = 200 MPa were performed with a rate of 2.5 K/min, in the temperature range T = 298 – 450 K. Itraconazole was completely molten during the first isobaric heating run and did not show any sign of recrystallization during the PVT measurement. The data presented here are for supercooled materials obtained during isobaric heating. PVT data were taken from Ref. 49.

III.

RESULTS AND DISCUSSION

Itraconazole (ITZ) is an active pharmaceutical ingredient (API) with broad-spectrum antifungal activity and poor water solubility, which can be easily supercooled to the glassy state. Surprisingly, it also undergoes two additional transitions (at T1 = 345.7 K and T2 = 362.5 K, see Figure 1a). Note that both endothermic events are observed on heating the glassy sample as well as on cooling the liquid ITZ.56 The nature of these two transitions has been widely discussed in the literature.55,57 Nevertheless, comprehensive FTIR studies and the analysis of the order parameter eventually confirmed that, in fact, ITZ forms two LC phases: Smectic A (below T = 346 K) and nematic (at T from 346 – 363 K).50 One can recall that in the nematic phase, the molecules have no positional order, but they are randomly aligned along their long axes. On the other hand, in the Smectic A phase, the molecules are oriented in parallel layers with respect to their long axes.33,34,35,36,37,38 Complementary dielectric measurements have revealed the presence of two relaxation processes far above the glass transition temperature, Tg (at T > 326 K). In the high frequency region, the structural (α) process related to the various tumbling fluctuation of the molecules around long axes is detected. The distribution of relaxation times of this mode is clearly nonexponential. It might be due to variation in the relaxation rates of the reorientational motions contributing to this mode. At low frequency side of the α-process an additional, Debye-like 8 ACS Paragon Plus Environment

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process can be found in the loss spectra, see Figure 1b. This slower relaxation is connected to the motions along the short molecular axis of ITZ, which in the case of LC materials is called the flip-flop rotation or δ-mode.50,56 One can observe that the temperature evolution of the relaxation times of δ-process differs in a more significant way with respect to τα(T)-dependence, when isotropic-nematic as well as nematic-Smectic A transitions take place, see Figure 1c. Note that the details concerning the following steps of the analysis together with the description of the applied experimental techniques can be found in the Experimental Section and Ref. 50. It is worth mentioning that this behavior is in agreement with previous studies on LCs, where rotations of the molecules around short axis were reported to be more sensitive to arrangements of molecules and thus, were considered to be crucial for a deeper understanding of the LC ordering.39,40 Moreover, one can mention that, as presented in Figure 1c, the dynamics of the slow mode in the isotropic phase of ITZ is much slower (10-3-10-5 s) with respect to the flip-flop rotation observed in other classical LCs (10-5-10-7 s). The studied isotropic-nematic transition occurs at relatively long δ-relaxation times, when compared to the data published by Roland et al.31 Therefore, one can suppose that the timescale limit of this characteristic motion around the clearing point may vary and strongly depend on the chemical structure of the molecule, which furthermore determines the intermolecular interactions. To test the validity of the TS in itraconazole, the PVT data were analyzed. The focus was placed on the isotropic phase regime located above Tcl, marked herein as a point, where a change in the slope of V(T)-dependences can be seen due to the nematic-isotropic phase transition, see Figure 2. It should be stressed that PVT data collected in the latter state have not been studied before. Briefly, one can see that V increases with increasing temperature at constant pressure. Moreover, two marked changes in the V(T)-dependences can be detected, which could be assigned to the glass formation and nematic-isotropic phase transition. Interestingly, we did not 9 ACS Paragon Plus Environment


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observe any transition to Smectic A phase in the presented PVT data.50 Note that in the case of LC compounds, the trend in V(T)-dependences seems to depend on the examined material strongly. For example, in the case of nBT’s, the formation of Smectic E phase was accompanied with the dramatic change in the specific volume;31 while, in 2-(4-hexyloxyphenyl)-5-octylpyrimidine, 6OPB8,29 and 4(trans-4 ′ -n hexylcyclohexyl)-isothiocyanatobenzene, 6CHBT,32 Smectic C-smectic A, Smectic A-nematic and nematic-isotropic transitions occurred with a similar small variation of this parameter. As mentioned above, PVT data in the isotropic regime (above Tcl, see Figure 2) were analyzed with the use of the equation of state (EOS):58 V T , p  

A0  A1 T  T0   A2 T  T0  , 1/  1   p  p0 b1 expb2 T  T0  EOS 2





(4)

where V is a specific volume, A0, A1, A2, b1, b2 and γEOS are fitting parameters; while, p0 and T0 are fixed constants corresponding to pressure (p = 0.1 MPa) and temperature (T0 = 370 K), where the nematic-isotropic transition occurs. Values of the parameters determined from the global fitting of V(T,p) dependences in the isotropic phase with the use of Eq. (4) are listed in Table 1. Note that we obtained a completely new set of parameters with respect to the ones published earlier by some of us,49 as the fitting procedure was performed for PVT data measured in a different phase of ITZ. As shown in Figure 2, the applied equation describes V(T,p) dependences quite well. At this point, it is also worthwhile to note that Eq. (4) was derived on the base of IPL intermolecular potential, related to the TS. This formula implies that the parameter γEOS is directly related to the exponent of the repulsive intermolecular interactions of IPL potential and that γEOS should be equal to γ. However, it was shown that the equality between both parameters takes place only for some model systems, whereas in the case of supercooled liquids γEOS>γ. Moreover, we would like to draw the attention of the readers to the


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fact that the value of γEOS changes (increases) only slightly (within the experimental error) due to the transition from isotropic (γEOS = 8.34) to the nematic phase (γEOS = 8.55, see Figure 2). Taking advantage of our PVT data, we also calculated the thermodynamic ratio, Г, at Tcl. One can recall that it quantifies the strength of the steric repulsions relative to the attractive part of the potential, where the higher Г, the stronger steric repulsions.31 Moreover, in the LC phases, occurring at constant relaxation times, the Г parameter is supposed to be the same as the scaling  exponent. The estimated value of Г of the isotropic-nematic transition was equal to Г = 3.76, see the inset in Figure 2. Note that accordingly to the model proposed by Maier and Saupe for nematic phase, Г = 2 mainly due to anisotropic dispersion forces,39 while the additional contributions to the volume dependence of the radial distribution function lead to Г = 3.59 Therefore, one can assume that the obtained value of Г (= 3.76) might indicate the presence of pronounced steric repulsions. It should be stressed that the Г parameter estimated at Tcl is significantly higher than the ones evaluated, i.e., for nBT’s, where Г = 2.22 for 5BT and 7BT.31 However, it is comparable to that determined at Tg (Г = 3.69), suggesting similar intermolecular interactions in the nematic phase of itraconazole and at Tcl.49 One can add that in the case of the glass transition of ITZ, the determined Г was in perfect agreement with the γ exponent (γ = 3.69).49 Nevertheless, as it would be presented later on, although the isotropicnematic transition of ITZ (at Tcl) also occurs at constant relaxation times (τα ≈ 10-5 s),50 this rule is not satisfied. Next, we carried out complementary high pressure dielectric measurements in the limited isotropic regime. Collected dielectric spectra displayed the presence of two well-visible relaxation processes: α and δ, see Figure 3. Note that the behavior of the latter mode has not been previously analyzed due to difficulties with the sample preparation and significant contribution of the dc conductivity.49 In this paper, we were able to overcome these difficulties and study the impact of LC ordering, especially molecule rearrangements, on the validity of the 11 ACS Paragon Plus Environment


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thermodynamic scaling of both distinguishable relaxations (α and δ). Also, it is worthwhile to stress that in the loss spectra measured in the smectic A phase, also a change on the high frequency side of the structural process, so-called an excess wing, has been detected. According to the literature data, this phenomenon is generally connected to the increasing separation between structural and secondary relaxation processes.60,61 Moreover, it was found that normalized loss peaks measured at different thermodynamic conditions, but at constant τα, collapse perfectly onto one master curve, indicating that the position of the slow Debye process with respect to the structural relaxation is independent on T and p conditions, see Figure 3. Note that for comparison also the data collected for the nematic phase were added. As it was shown for the isotropic phase, both processes, α and δ, superpose at constant structural relaxation time, for different thermodynamic conditions. Although in this phase, a visible variation in the dielectric strength of δ-process with respect to the structural relaxation can be observed, the shape of the α-process seems to be almost the same at various thermodynamic conditions, suggesting that they are characterized by similar pressure sensitivity as their separation is constant under pressure. Therefore, one can assume that both α- and δ-relaxations fulfill the temperature-pressure-superposition (TPS) rule in the examined T and p range. Nevertheless, it should be stressed that both processes obey thermodynamic scaling, but they scale with significantly different γ parameters. Among many different approaches, which can be applied to determine the scaling exponent,62,63,64,65,66 we have chosen a method proposed by Casalini and Roland,62,67 where the γ parameter can be directly obtained from the fitting of experimental data plotted as a function of temperature and volume (see Figure 4): D

 A  , log T ,V   log 0      TV 

(5)


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where logτ0, A, D, and γ are fitting parameters. The best fit was achieved with γ parameters equal to 5.52±0.23 and 6.50±0.25 for α and -process, respectively, in the isotropic phase (see Figure 4). Values of the obtained fitting parameters are presented in Table 2. It is worthwhile to stress that they are significantly higher than those determined for both processes in the nematic phase (where γα = 3.69±0.0449 and γ =4.53±0.08) and other LC materials (i.e., γ=2.3 – 4.1 for nBT’s31 and nPCH’s30). Nevertheless, despite quite large values of determined scaling exponents, relaxation times of α and -processes obtained at different thermodynamic conditions in the isotropic and nematic phases superposed onto single master curve when plotted versus 1/TV (see Figure 5a,b). A similar scenario has been reported previously by some of us for the structural relaxation times obtained for ITZ in the nematic phase49 (Figure 5b). It is worth mentioning that so far all works devoted to LC systems have indicated that the density scaling is satisfied for these materials. Taking into account the above analysis, we would like to discuss four problems. First, despite the fact that the isotropic-nematic transition of ITZ (at Tcl) occurs at constant relaxation times (τα = 10-5 s),50 the estimated γ parameters are significantly higher with respect to the thermodynamic ratio Г (where Г = 3.76, see inset in Figure 2). However, there is a perfect agreement between Г estimated at Tcl and both γ exponents of nematic phase as well as Г obtained at Tg.49 Note that the agreement between both parameters (Γ and γ) observed for some LC materials, i.e., for 6CHBT32 and nBT’s,31 is considered to affirm the connection between the rotational motions and the repulsive part of the interaction potential. Moreover, it indicates that the longitudinal relaxation time must be invariant to thermodynamic conditions along the clearing line.32 In this context, one can assume that for some reasons these rules are not satisfied. Second, both examined relaxation processes (α and δ) are described by different scaling exponents. In this context, one can mention the paper by Romanini et al.51 Authors showed that relaxation times of double primary relaxation process (α and α’) detected in loss spectra 13 ACS Paragon Plus Environment


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measured above the Tg at various (p,T) conditions in dipolar benzene derivative, PCNB, also scale with the use of two different scaling parameters (γα = 7.60 and γα’ = 7.81). They postulated that the change in γ must originate from the different molecular mobility underlying both analyzed relaxation processes.51 In the case of ITZ, both γ exponents differ in a more significant way when compared to PCNB, what might also indicate their various molecular origin.50 Third, the γ parameters change dramatically with the transition from isotropic to nematic phase. In this context, it is worth mentioning that the scaling exponent is considered to be a parameter characterizing the impact of temperature or volume on the molecular dynamics, where γ = 0 indicates that the molecular dynamics is governed by the thermal energy, while the higher scaling exponent means the greater impact of free volume in controlling dynamics of given relaxation process.11 Thus, it seems that not only both processes have a different molecular origin, but also various sensitivity to the density fluctuations. The slower one, δrelaxation, related to the rotation of ITZ molecules along its short molecular axis, is much more sensitive to variation in molecular packing with respect to the α-process. Nevertheless, this property also strongly depends on the arrangements of molecules within LC phases, since a reduction of the γ-exponent is observed during isotropic-nematic phase transition. Note that the same drop of scaling parameter can be seen for both processes, α and δ, what might indicate that despite different molecular origins, changes occurring within the system due to the nematic ordering (within rearrangement of molecules) has a similar effect on the dynamics of these two relaxations. Finally, we also noted that during the transition from isotropic to nematic phase, γ parameter decreases, whereas γEOS increases, which enhances the discrepancy between γ and γEOS. By taking into account that in both of the phases the interactions between molecules are identical, so the shape of the potential remains unchanged (because the molecular structure is not modified), the changes of γ and γEOS parameters seem to be induced by the degree of 14 ACS Paragon Plus Environment

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molecular ordering of the structure. Hence, their values depend on the intermolecular interactions as well as the structure of the system. As a consequence, the discrepancy between γ and γEOS becomes higher for more anisotropic systems. In this context, we would like to mention our very recent work, which shed new light on the problem of estimation of intermolecular potential between molecules interacting in the anisotropic manner. In Ref. 68, it was presented that the effective intermolecular potential between two model molecules of anisotropic shape depends on the distance between molecules and more importantly on the character of the examined (scaled) process (γ – structural relaxation, γEOS - compressibility) as well. Since the dynamical properties of the process are strongly affected by the mutual orientation between interacting molecules, the change of γ and γEOS during the transition from isotropic to nematic phase could be still understood on the most fundamental level of intermolecular interactions. The structural molecular arrangement, which is characteristic for the nematic phase and not observed in the isotropic phase, modifies the shape of the effective intermolecular potential and then results in different values of discussed parameters. In this context, we would like to draw the attention of readers to the fact that the results presented for ITZ are in accordance with those obtained for model systems.68 In both cases, the increment of intermolecular interaction anisotropy causes the increase in γ and the drop in γEOS values. Consequently, the difference between discussed parameters is smaller in the case of the systems interacting in the less anisotropic manner. Summarizing, the data collected in two phases of ITZ are experimental validation of γ and γEOS dependences with respect to the system molecular arrangement. It is important to note that those parameters cannot be simply identified with the repulsive term of intermolecular potential. Instead, some effective intermolecular interaction potential should be estimated considering the internal structure or possibly molecular ordering of the studied system. IV. CONCLUSIONS 15 ACS Paragon Plus Environment


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Combination of PVT data with the results of high pressure dielectric measurements allowed for the validation of the thermodynamic scaling of two relaxation processes observed in the isotropic and nematic phases of itraconazole. We found that α- and δ-relaxation times determined at various thermodynamic conditions can be successfully superposed over 1/TV. Nevertheless, surprisingly, both examined processes scale with different γ exponents. Moreover, obtained scaling parameters were significantly different from the ones estimated for respective relaxation processes in the nematic phase. The observed unique behavior seems to be a result of a difference in the arrangements of molecules, which influence the effective intermolecular potential. Consequently, the variation in γ parameters in both the isotropic and nematic phases and the lack of agreement between γ and Γ in the isotropic phase can be noted. Moreover, the presented experimental results suggest that γ and γEOS parameters do not depend only on the intermolecular potential but also on the degree of molecular order in the system. This fact makes the studied liquid crystal (ITZ) an exciting candidate for further studies on this issue. AUTHOR INFORMATION Corresponding Author * (DH) e-mail: [email protected], (EK) e-mail: [email protected], (MT) e-mail: [email protected] Notes There are no conflicts to declare. ACKNOWLEDGMENT D. H. and E. K. are thankful for the financial support from the National Science Center based on decision DEC-2016/22/E/NZ7/00266. M.T. and K.K. are thankful for financial support from 16 ACS Paragon Plus Environment

Page 17 of 27 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


the Foundation for Polish Science (FNP). K. K., A. D. and M. T. are thankful for financial support from the Polish National Science Centre within the SONATA BIS 5 project (Dec 2015/18/E/ST4/00320). The authors would like to thank Alexander Rowland Lowe for the valuable discussion and language assistance during the manuscript preparation. Figures: N

Itraconazole N

Cl

N

O

O

Cl

O

N O

N

N

N N

Scheme 1. The chemical structure of itraconazole (ITZ).

Scheme 2. The presentation of dipole moment distribution in ITZ molecule.



Itraconazole

(b)

Tg = 329.6 K

DC

100

T2 = 362.5 K

T1 = 345.7 K

(c)

glass heating, rate 10 K/min

10-1 315

330

345

360

375

390

Temp. [K]

T = 383 K T = 363 K T = 8K T = 363 K T = 331 K T = 4 K

Heating of crystal sample, 10 K/min 320

340

360

380

400

10 420

10-2

440

10-1

-process

100

101

102

-process -process VFT fit

0

103

104

105

106

Tg VFT = 326.25 K

-2

-4

-6

Smectic A nematic isotropic phase phase phase

isotropic nematic phase phase 107

2,6

2,7

freq. [Hz]

Temp. [K]

2,8

2,9

(the blue curve) ITZ with a heating rate of 10 K/min. In the inset, the DSC curve obtained in the vicinity of the glass transition temperature has been enlarged; (b) Dielectric spectra of studied compound collected on heating; (c) Temperature dependences of relaxation times of two processes: α and . The red solid line represents the VFT fit. Data were taken from Ref. 50. 2.62

0.82

2.61

log 10 Tcl

0.80

p = 10 MPa p = 20 MPa p = 40 MPa p = 80 MPa p = 120 MPa p = 160 MPa p = 200 MPa EOS global fit EOS global fit

2.60 2.59 2.58

 = 3.76

2.57

0.78

2.56

-0.135

-0.130

-0.125

log 10 Vc

-0.120

isotropic phase EOS = 8.34

-0.115

Tcl

nematic phase EOS = 8.55

0.76

Tg 0.74

0.72

300

320

340

360

380

400

420

440

Temp. [K] 18 ACS Paragon Plus Environment

Smectic A phase

1000/T [K-1]

Figure 1. (a) DSC thermograms obtained during heating the crystal (the black curve) and glassy

V [cm3/g]

300

-2

p = 0.1 MPa

-process

''

HF [a.u]

Tm = 439 K

p = 0.1 MPa

log10 (  /s)

(a)

Heat Flow [a.u.]

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

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3,0

Page 19 of 27

Figure 2. Temperature dependences of the specific volume for various isobars in the wide pressure range (p = 10 – 200 MPa). Solid lines represent the best global fit using EOS equation (Eq. (4)). As an inset, dependence of log10Tcl versus log10Vc. The solid line represents a linear fit. PVT data were taken from Ref. 49. itraconazole isotropic phase 0.764  0.002 (4.828  0.014)·10-4 (2.051  1.844)·10-7 (2.957  0.386)·10-3 (4.24  0.39)·10-3 8.34  0.46

Parameters A0 [cm3/g] A1 [cm3/(g·K)] A2 [cm3/(g·K2)]] b1 [MPa-1] b2 [K-1] γEOS

Table 1. The parameters of the equation of state (EOS) in the isotropic phase of itraconazole.

(b) Itraconazole at the nematic phase

(a) Itraconazole at the isotropic phase

-process

10

-process

100

''/''max

100

''/''max

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


-process -1

-process

10-1

p=0.1 MPa, T=371.0 K p=1 MPa,T=374.0 K p= 7 MPa,T=382.0 K p=30 MPa,T=382.7 K

10-2

102

103

104

105

106

p=0.1 MPa,T= 353.0 K p=30 MPa,T=362.6 K p=50 MPa,T=372.0 K p=66 MPa,T=374.5 K 100

freq. [Hz]

101

102

103

104

105

freq. [Hz]

Figure 3. The superimposed dielectric loss spectra obtained for ITZ at various thermodynamic conditions (for the same ) in the isotropic (a) and nematic (b) phases. The spectra were normalized with respect to the maximum of dielectric loss (ε”max).



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Figure 4. Isothermal and isobaric relaxation times of α (a) and -processes (b) plotted as a function of both temperature and volume. Blue areas represent surface fits to the Casalini and Roland equation (Eq. (5)). Isotropic phase Nematic phase parameters α-process α-process -process -process log(τ0/s) -9.35±0.99 -6.05±0.44 -7.67±0.31 -3.69±0.47 A [K· (cm3 / g) ] 182.72±11.47 97.88±10.69 176.60±6.84 117.27±9.67 D 2.83±0.76 4.41±0.78 6.07±0.38 8.53±1.97 γ 5.52±0.23 6.50±0.25 3.69±0.04 4.53±0.08 Table 2. The parameters of Eq. (5) for both α- and -processes in the isotropic phase of itraconazole. Fit parameters of α-process in the nematic phase were taken from Ref. 49.


Page 21 of 27

(a) Itraconazole at the isotropic phase

-4

Isobars st: 0.1MPa 30MPa Isotherms at: 374.0K 377.7K 382.0K

 - process

0

 = 6.50

-5

 - process -6

 = 5.52

0,011

1

0,012

0,013

0,014

Izobars at: 0.1 MPa 30 MPa Izoterms at: 374.0 K 377.7 K

0,015

log10 /s)

-3

log10 /s)

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


-1 -2

(b) Itraconazole at the nematic phase Isobars at: 0.1 MPa 75 MPa 155 MPa Isotherms at: 343.0 K 359.0 K 377.0 K

 - process  = 4.53

-3 -4

 - process

-5

0,016

 = 3.69 0,008

0,009

Isobars at: 0.1 MPa 30 MPa Isotherms at: 372.0 K 374.5 K 380.7 K

0,010

1/TV

1/TV

Figure 5. Relaxation times of α- and -processes obtained in the isotropic (a) and nematic phases (b) of ITZ plotted versus 1/TVγ. The scaling exponent γ was determined from Eq. (5). Data of the α-process in the nematic phase were taken from Ref. 49.

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(57) Six, K.; Verreck, G.; Peeters, J.; Binnemans, K.; Berghmans, H.; Augustins, P.; Kinget, R.; Van der Mooter, G. Investigation of Thermal Properties of Glassy Itraconazole: Identification of a Monotropic Mesophase. Thermochim. Acta, 2001, 376, 175–181. (58) Grzybowski, A.; Grzybowska, K.; Paluch, M.; Swiety, A.; Koperwas, K. Density Scaling in Viscous Systems Near the Glass Transition. Phys. Rev. E, 2011, 83, 041505. (59) Chandrasekhar, S.; Madhusudana, N. W. Molecular Statistical Theory of Nematic Crystals. Acta Crystallogr. A, 1971, A27, 303. (60) Hensel-Bielowka, S.; Paluch, M. Origin of the High-Frequency Contributions to the Dielectric Loss in Supercooled Liquids. Phys. Rev. Lett., 2002, 89, 025704. (61) Kaminska, E.; Kaminski, K.; Hensel-Bielowka, S.; Paluch, M.; Ngai, K. L. Characterization and Identification of the Nature of Two Different Kinds of Secondary Relaxation in One Glass-Former. J. Non-Cryst. Solids, 2006, 352, 4672–4678. (62) Casalini, R.; Mohanty, U.; Roland, C. M. Thermodynamic Interpretation of the Scaling of the Dynamics of Supercooled Liquids. J. Chem. Phys., 2006, 125, 014505. (63) Roland, C. M.; Feldman, J. L.; Casalini, R. Scaling of the Local Dynamics and the Intermolecular Potential. J. Non-Cryst. Solids, 2006, 352, 4895–4899. (64) Paluch, M.; Grzybowska, K.; Grzybowski, A. Effect of High Pressure on the Relaxation Dynamics of Glass-Forming Liquids. J. Phys.: Condens. Matter, 2007, 19, 205117. (65) Roland, C. M.; Casalini, R. Density Scaling of the Dynamics of Vitrifying Liquids and its Relationship to the Dynamic Crossover. J. Non-Cryst. Solids, 2005, 251, 2581–2587. (66) Casalini, R.; Roland, C. M.; Capaccioli, S. Effect of Chain Length on Fragility and Thermodynamic Scaling of the Local Segmental Dynamics in Poly(methylmethacrylate). J. Chem. Phys., 2007, 126, 184903. (67) Casalini, R.; Roland, C. M. An Equation for the Description of Volume and Temperature Dependences of the Dynamics of Supercooled Liquids and Polymer Melts. J. Non-Cryst. Solids, 2007, 353, 3936–3939. (68) Koperwas, K.; Grzybowski, A.; Paluch, M. The Effect of Molecular Architecture on the Physical Properties of Supercooled Liquids Studied by MD Simulations: Density Scaling and its Relation to the Equation of State. J. Chem. Phys., 2018, 150, 014501. TOC Graphic


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Itraconazole at the isotropic phase -3

log10 /s)

Page 27 of 27

-4

 - process

Isobars st: 0.1MPa 30MPa Isotherms at: 374.0K 377.7K 382.0K

 = 6.50

-5

 - process -6

 = 5.52 0,011

0,012

0,013

0,014

1/TV

Izobars at: 0.1 MPa 30 MPa Izoterms at: 374.0 K 377.7 K 0,015

0,016




The Impact of Liquid Crystalline Phase Ordering on the

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