R Céolin

I B Rietveld
email: ivo.rietveld@univ-rouen.fr

TOPOLOGICAL PRESSURE-TEMPERATURE STATE DIAGRAM OF THE CRYSTALLINE DIMORPHISM OF 2,4,6-TRINITROTOLUENE

Keywords: TNT, thermodynamics, phase behavior, phase diagram

The phase behavior of explosive substances is important for the proper design of stable explosive devices. However, the equilibrium behavior of chemical compounds can be difficult to assess, because thermodynamic and kinetic behaviors are generally convoluted in the experimental results. The phase behavior of TNT is a case in point. A thorough review of the literature data demonstrates that the orthorhombic polymorph is the most stable under ambient conditions. Using the topological approach for the construction of a pressure-temperature phase diagram, it can be shown that all data is consistent with an overall enantiotropic system. Nonetheless, it is also clear that the differences between the orthorhombic and the monoclinic polymorphs are relatively small and that the driving force of interconversion between the two under ambient conditions is therefore limited.

INTRODUCTION

2,4,6-trinitrotoluene or TNT (C7H5N3O6, M = 227.13 g mol -1 ) possesses two crystalline polymorphs that can be obtained by slow evaporation at room temperature; one form is monoclinic and the other orthorhombic. According to [START_REF] Vrcelj | Polymorphism in 2-4-6 trinitrotoluene[END_REF], the orthorhombic form is metastable and converts to the stable monoclinic form [START_REF] Vrcelj | Polymorphism in 2,4,6-trinitrotoluene crystallized from solution[END_REF][START_REF] Vrcelj | Polymorphism in 2-4-6 trinitrotoluene[END_REF]. Bowden et al. added to this in 2014: "the orthorhombic phase is metastable at ambient pressure/temperature and was observed at high pressure" [START_REF] Bowden | The high-pressure phase stability of 2,4,6-trinitrotoluene (TNT)[END_REF], while referring to Stevens et al, who in fact had mentioned: "the high pressure-temperature(P-T) stability of TNT has not been investigated in detail" [START_REF] Stevens | The high-pressure phase behavior and compressibility of 2,4,6-trinitrotoluene[END_REF].

Considering the foregoing information, TNT appears to be an easy case for the construction of a topological pressure-temperature phase diagram to confirm the phase behavior and stability ranking of the two polymorphs found in the literature. The construction will be carried out in this paper.

AVAILABLE DATA ON TNT PHASE BEHAVIOR IN THE LITERATURE

CRYSTALLINE POLYMORPHISM

In the literature three polymorphs of TNT have been described of which two have been confirmed by crystal structure resolution. These are a monoclinic phase, form M, considered to be the more stable phase and an orthorhombic phase, form O. TNT melts at about 81°C.

CRYSTALLOGRAPHIC DATA

In 1936, Hultgren reported values for room-temperature lattice parameters for the orthorhombic phase leading to a density of 1.726 g cm -3 with Z = 16 molecules per unit-cell (see Table 1) [START_REF] Hultgren | An X-ray study of symmetrical trinitrotoluene and cyclo trimethylenetrinitramine[END_REF]. This may have been reproduced by Winchell, as in his compilation, it is written that TNT is orthorhombic with a melting temperature of 81°C [START_REF] Winchell | The optical properties of organic compounds[END_REF]. In 1982, Carper et al. reported the crystal and molecular structure of orthorhombic TNT at 23°C, space group Pca21, V = 1823.6 Å 3 , and Z = 8 (Table 1) [START_REF] Carper | Molecular-Structure of 2,4,6-Trinitrotoluene[END_REF]. This leads to a density of 1.655 g cm - 3 , which is considerably lower than that of the structure of Hultgren. In 1994, Golovina et al. obtained three kinds of crystals and two of those led to structures solved at room temperature [START_REF] Golovina | Kinetics and Mechanism of Phase-Transitions in the Crystals of 2,4,6-Trinitrotoluene and Benzotrifuroxane[END_REF]. The first one has an orthorhombic system, space group P21ca, V = 1830.41 Å 3 , Z = 8 and d = 1.6485 g cm -3 , which is clearly similar to the structure found by Carper et al. (Table 1). The second form crystallizes in a monoclinic system, space group P21/b, with V = 1828.92 Å 3 , Z = 8 and d = 1.650 g cm -3 . A final form was found to be orthorhombic with a volume of 3627 Å 3 (Table 1), however, the structure has not been solved. This latter form resembles the one initially found by Hultgren. In 1996, Gallagher et al. reported that the crystal structures of the monoclinic and orthorhombic phases had been solved previously by Duke, who could not publish the results, because they had been classified [START_REF] Gallagher | Polymorphism, twinning and morphology of crystals of 2,4,6-trinitrotoluene grown from solution[END_REF]. The authors provided the lattice parameters of the two structures communicated by Duke in 1981 [START_REF] Gallagher | Polymorphism, twinning and morphology of crystals of 2,4,6-trinitrotoluene grown from solution[END_REF]: monoclinic P21/c, with V = 1827.52 Å 3 and Z = 8 leading to d = 1.6511 g cm -3 and the orthorhombic form Pb21a with V = 1843.47 Å 3 and Z = 8 giving rise to d = 1.6368 g cm -3 . In the following years Gallagher et al. produces more studies on the crystallization behavior of TNT and they come to the conclusion that even if the monoclinic form contains the lowest internal energy following lattice energy calculations, twinning of the monoclinic crystal tends to occur to a great extent and is only slightly more energetically unfavorable. The form highest in lattice energy according to the calculations is the orthorhombic form [START_REF] Gallagher | Polymorphism, twinning and morphology of crystals of 2,4,6-trinitrotoluene grown from solution[END_REF][START_REF] Gallagher | A theoretical examination of the molecular packing, intermolecular bonding and crystal morphology of 2,4,6-trinitrotoluene in relation to polymorphic structural stability[END_REF][START_REF] Gallagher | The crystal growth and perfection of 2,4,6-trinitrotoluene[END_REF].

In 2003, Vrcelj et al. reexamined the structures of the two polymorphs at 100 and 123 K [START_REF] Vrcelj | Polymorphism in 2-4-6 trinitrotoluene[END_REF]. The monoclinic form, P21/a, was found to possess a volume of 1761.37 Å 3 leading to a density of 1.713 g cm -3 at 100 K. The orthorhombic form, Pca21, has a volume of V = 1770.58 Å 3 and a density of 1.704 g cm -3 at 123 K. They also determined the expansivities of the two phases between 123 and 300K and found αM = 2.04 ´10 -4 K -1 for the monoclinic phase and αO = 1.95 ´10 -4 K -1 for the orthorhombic one [START_REF] Vrcelj | Polymorphism in 2,4,6-trinitrotoluene crystallized from solution[END_REF][START_REF] Vrcelj | Polymorphism in 2-4-6 trinitrotoluene[END_REF]. These expansivities are very close to the mean value of 2.21 ´ 10 -4 K -1 found for solids made up of small molecules [START_REF] Céolin | The topological pressure-temperature phase diagram of ritonavir, an extraordinary case of crystalline dimorphism[END_REF][START_REF] Rietveld | Phenomenology of crystalline polymorphism: overal monotropic behavior of the cardiotonic agent FK664 forms A and B[END_REF][START_REF] Céolin | The topological phase diagram of cimetidine: A case of overall monotropy[END_REF]. Already in 1969 it had been shown that an orthorhombic TNT polymorph on heating transforms endothermically to a monoclinic form before melting [START_REF] Grabar | Observation of a Solid-Solid Polymorphic Transformation in 2,4,6-Trinitrotoluene[END_REF]. The enthalpy associated to this transition was found to be 0.27 kcal mol -1 (1.13 kJ mol -1 ; 4.97 J g -1 ) [START_REF] Grabar | Observation of a Solid-Solid Polymorphic Transformation in 2,4,6-Trinitrotoluene[END_REF]. Furthermore, the authors reported three different sequences of thermal behavior reflected in the DSC curves (Figure 1 and Table 2). The onset of the orthorhombic to monoclinic transition was observed in the temperature range of 63-64°C (336-337 K, peak a in Figure 1), whereas the onset temperature of the fusion of the monoclinic polymorph was found in the range of 78-80°C (351 -353 K, peak b in Figure 1) [START_REF] Grabar | Observation of a Solid-Solid Polymorphic Transformation in 2,4,6-Trinitrotoluene[END_REF]. Specimens "Q1" and "Q2", which resulted in different thermal behavior (left-hand panel and center panel in Figure 1) possessed virtually the same X-ray diffraction pattern as the orthorhombic form solved by Golovina et al. [START_REF] Golovina | Kinetics and Mechanism of Phase-Transitions in the Crystals of 2,4,6-Trinitrotoluene and Benzotrifuroxane[END_REF] (See Table S1 in the supplementary Materials), indicating that they must consist of the same orthorhombic polymorph, whereas specimen "An" (right-hand panel in Figure 1) was identified by the authors as the monoclinic polymorph. It is therefore likely that the differential thermal analysis (DTA) curve in the center panel in Figure 1 corresponds to the following process: melting of the orthorhombic form (peak c, onset 350 K or 77°C), recrystallization into the monoclinic form, which melts in turn (peak b in the center panel of Figure 1). An overview of this data can be found in Table 2, where for the sake of comparison and the calculations later on in the text all data have been provided in kelvin for the temperatures or in joule per gram for the enthalpy changes.

Figure 1. Differential thermal analysis curves of TNT modifications recorded at 10 K min -1 by Grabar et al. [START_REF] Grabar | Observation of a Solid-Solid Polymorphic Transformation in 2,4,6-Trinitrotoluene[END_REF]. Specimens Q1 and Q2 correspond to the orthorhombic (O) modification (see Table T2) and specimen An is identified by the authors as being the monoclinic (M) polymorph. Peak a = O®M (onset at 336.6 K), peaks c + b = O®liquid®M®liquid, peak b = M®liquid (onset at 353 K). Figures from reference [START_REF] Grabar | Observation of a Solid-Solid Polymorphic Transformation in 2,4,6-Trinitrotoluene[END_REF] and adapted for this paper.

Simultaneously, Connick at al. carried out calorimetric and crystallographic studies that revealed two kinds of thermal behavior (see Figure S1 in the supplementary materials) [START_REF] Connick | Polymorphism in 2,4,6-Trinitrotoluene[END_REF]. Single-peak DTA curves with an onset at about 354 K were ascribed to the melting of the monoclinic polymorph by the authors who observed that 'single crystals grown from toluene solutions have a single peak melting endotherm and are monoclinic'. By contrast, 'Double peaked endotherms are indicative of a mixture of the monoclinic and another polymorphic form, possibly orthorhombic. The proportion of each polymorph is variable and dependent on sample history' according to the authors [START_REF] Connick | Polymorphism in 2,4,6-Trinitrotoluene[END_REF]. The melting of the orthorhombic form occurred in these measurements between 353 and 353.5 K (See Table 2).

Much later, in 1996, Gallagher et al, combining DSC, single-crystal and powder X-ray diffraction measurements found that the orthorhombic phase exhibits an endothermic transition into the monoclinic form at about 343 K on heating with an enthalpy of DO®MH = 0.22 kcal mol -1 (0.92 kJ mol -1 ; 4.05 J g -1 ) [START_REF] Gallagher | Polymorphism, twinning and morphology of crystals of 2,4,6-trinitrotoluene grown from solution[END_REF]. The monoclinic form melted at about 351 or 352 K on further heating (see Figure S2 in the supplementary materials). Moreover, these authors reported that: "After an interval of two months all of the samples were reexamined and were found to be identical, and to yield powder pattern II [monoclinic]. This indicates that the solid associated with powder pattern I [orthorhombic] had undergone a structural transformation to the polymorphic form corresponding to material of powder pattern II during the intervening period" [START_REF] Gallagher | Polymorphism, twinning and morphology of crystals of 2,4,6-trinitrotoluene grown from solution[END_REF]. Nonetheless, no explicit storage conditions were provided by the authors. One year later, the same authors in a theoretical study concluded that the lattice energy of the monoclinic form is lower than that of the orthorhombic form [START_REF] Gallagher | A theoretical examination of the molecular packing, intermolecular bonding and crystal morphology of 2,4,6-trinitrotoluene in relation to polymorphic structural stability[END_REF]. In 2001 and 2003, Vrcelj et al. published DSC curves of the orthorhombic and monoclinic polymorphs [START_REF] Vrcelj | Polymorphism in 2,4,6-trinitrotoluene crystallized from solution[END_REF][START_REF] Vrcelj | Polymorphism in 2-4-6 trinitrotoluene[END_REF]. They have been reproduced in Figure S3 in the supplementary materials. It can be seen that a single melting endotherm is recorded on heating the monoclinic phase with an onset at 351-352 K (peak b), whereas on heating the orthorhombic phase, the melting peak of the monoclinic phase is preceded by another endothermic event with an onset at 340.6 K (peak a) ascribed to the orthorhombic to monoclinic transition. These authors also reported the related enthalpy change of this small event of 0.11 kcal mol -1 (2.02 J g -1 ). The kinetics of the O®M transition were studied by [START_REF] Golovina | Kinetics and Mechanism of Phase-Transitions in the Crystals of 2,4,6-Trinitrotoluene and Benzotrifuroxane[END_REF] and they observed this transition starting from a temperature of 55°C [START_REF] Golovina | Kinetics and Mechanism of Phase-Transitions in the Crystals of 2,4,6-Trinitrotoluene and Benzotrifuroxane[END_REF].

Other melting points of TNT have been reported in the literature. Chang et al. in 1987 found a value of 354.55K [17]. In 1990, Hwang et al. reported a melting point for TNT of 352 K (79 °C) with a melting enthalpy of DfusH = 5.8 kcal mol -1 (24.27 kJ mol -1 ; 106.84 J g -1 ) [START_REF] Hwang | Estimation of ∆H°f of nitro derivatives of benzene and toluene using AM1 and DSC[END_REF] . The authors also determined the heat of vaporization DvapH = 19.5 kcal mol -1 (81.59 kJ mol -1 ) at a boiling point of 202°C and a heat of sublimation of DsubH = 25.1 kcal mol -1 (105.02 kJ mol -1 ; 462.36 J g -1 ) [START_REF] Hwang | Estimation of ∆H°f of nitro derivatives of benzene and toluene using AM1 and DSC[END_REF]. In the same year, Hu et al. found a melting point for TNT of Tfus = 80.6°C (353.75 K) with a melting enthalpy of DfusH = 22.41 kJ mol -1 (98.66 J g -1 ) [START_REF] Hu | Thermal-Behavior on 2,2,2-Trinitroethyl-4,4,4-Trinitrobutyrate[END_REF]. In 2014, Kumar and Rao found a melting point of Tfus = 80.6°C (353.75 K) and a melting enthalpy of DfusH = 25.1 kcal mol -1 (22.36 kJ mol -1 ; 98.45 J g -1 ) [START_REF] Kumar | Modeling of Cooling and Solidification of TNT based Cast High Explosive Charges[END_REF]. In addition, they determined the heat capacity of TNT in the solid state from 17 to 67 °C leading to Cp,solid/J g -1 °C-1 = 1.063 + 3.14 ´10 -3 (T/°C) and that of the liquid state in the range from 97 to 150°C: Cp,liquid/J g -1 °C-1 = 1.293 + 1.46 ´10 -3 T/°C, however, the authors did not specify the polymorph they used for the Cp measurements [START_REF] Kumar | Modeling of Cooling and Solidification of TNT based Cast High Explosive Charges[END_REF]. A glass transition of TNT was reported at a temperature of 258 K by [START_REF] May | A glass transition in trinitrotoluene[END_REF] in addition to a melting enthalpy of 23.53 cal g -1 (22.36 kJ mol -1 ; 98.45 J g -1 ) [START_REF] May | A glass transition in trinitrotoluene[END_REF]. Shamim et al, used a flash DSC and found Tg values ranging from 239.3 to 247.5 K by heating the glass at rates from 10 to 1000 K s -1 [START_REF] Shamim | The glass transition of trinitrotoluene (TNT) by flash DSC[END_REF].

The vapor pressure of solid TNT was measured in the range from 327 K to 349 K by Lenchitz and Velicky, leading to the following expression [START_REF] Lenchitz | Vapor Pressure and Heat of Sublimation of 3 Nitrotoluenes[END_REF]: The main calorimetric data mentioned here have been summarized in Table 2. From the data, it can be tentatively concluded that two polymorphs of TNT are confirmed: a monoclinic phase (form I), that melts at about 352.9 ±1.3 K and which tends to form heavily twinned crystals, and an orthorhombic phase, form II, that transforms endothermically to the monoclinic one and for which the lowest transformation has been observed at 328 K. [START_REF] Hwang | Estimation of ∆H°f of nitro derivatives of benzene and toluene using AM1 and DSC[END_REF] 353.75 98.66 [START_REF] Hu | Thermal-Behavior on 2,2,2-Trinitroethyl-4,4,4-Trinitrobutyrate[END_REF] 353.75 98.45 [START_REF] Kumar | Modeling of Cooling and Solidification of TNT based Cast High Explosive Charges[END_REF] 98.45 [START_REF] May | A glass transition in trinitrotoluene[END_REF] 455.21 [START_REF] Lenchitz | Vapor Pressure and Heat of Sublimation of 3 Nitrotoluenes[END_REF] 439.24 [START_REF] Pella | Measurement of Vapor-Pressures of TNT, 2,4-DNT, 2,6-DNT, and EGDN[END_REF] 497.3 [START_REF] Cundall | Vapor-Pressure Measurements on Some Organic High Explosives[END_REF] a All data has been converted into kelvin for the transition temperatures and into joule per gram for the enthalpy changes to facilitate the calculations below in the text, M: monoclinic, O: orthorhombic

Log (P/mmHg) = -5400.536/(T/K) + 13.077 (1a)

LIQUID DENSITY

Moore et al measured the density of liquid TNT as a function of temperature and found that "density was a linear function of temperature over a 20-40° range including 10-20° of supercooling". They expressed dependence of the liquid density on the temperature with the following equation: rL (g cm -3 ) = r0 -b T/°C, in which r0, the liquid density at 0°C, and β, the thermal expansion, are 1.5450 g cm -3 and 1.0244 ´10 -3 g cm - 3 K -1 , respectively [START_REF] Moore | Viscosity and Density of the Liquid System Tnt-Picric Acid and 4 Related Pure Materials[END_REF]. This dependence of the liquid (L) density on the temperature can be converted to the specific volume:

vL/cm 3 g -1 = 0.52170 + 0.0004596 T/K (2)
The expansivity aV,L related to this expansion is 8.81 ´10 -4 K -1 , which is near the value of 11.9´ 10 -4 K -1 , found for the liquid expansivity of molecular compounds [START_REF] Céolin | The topological pressure-temperature phase diagram of ritonavir, an extraordinary case of crystalline dimorphism[END_REF][START_REF] Rietveld | Phenomenology of crystalline polymorphism: overal monotropic behavior of the cardiotonic agent FK664 forms A and B[END_REF][START_REF] Céolin | The topological phase diagram of cimetidine: A case of overall monotropy[END_REF].

3 DATA ANALYSIS

THE SPECIFIC VOLUMES OF THE DIFFERENT PHASES

The values of specific volumes from Duke [START_REF] Gallagher | Polymorphism, twinning and morphology of crystals of 2,4,6-trinitrotoluene grown from solution[END_REF], from Golovina et al. [START_REF] Golovina | Kinetics and Mechanism of Phase-Transitions in the Crystals of 2,4,6-Trinitrotoluene and Benzotrifuroxane[END_REF], and from Vrcelj et al. [START_REF] Vrcelj | Polymorphism in 2-4-6 trinitrotoluene[END_REF] indicate that vM < vO at room temperature. It is significant that these three independent measurements come to the same conclusion even if the specific volumes of the two polymorphs are very close. Simply calculating the average of the difference, one obtains ∆O®Mv = -3.0 (±2.4) ×10 -3 cm 3 g -1 . Nonetheless, if one uses the expansivities of the two phases together with their specific volume determined at low temperature by Vrcelj [START_REF] Vrcelj | Polymorphism in 2-4-6 trinitrotoluene[END_REF] and one determines the respective thermal expansion of the orthorhombic and the monoclinic form as a function of temperature, using vphase/cm 3 g -1 = v0 + αphasev0 T/K on finds for the orthorhombic form vO = 0.57306 + 1.117×10 -4 T and for the monoclinic form vM = 0.57208 + 1.167×10 -4 T. Using these equations to determine the specific volumes of the two forms at room temperature, the difference ∆O®Mv has become positive. Apparently, the expansivities are not accurate enough to be used for the determination of the difference in specific volume between the two polymorphs at room temperature. In particular because two of the direct determinations of the specific volume clearly indicate that polymorph O has a slightly larger volume than polymorph M at room temperature. To correct for this, the average of the thermal expansivity for both forms is taken, 1.995 ´10 -4 K -1 , to calculate the two thermal expansions leading to the equations for the specific volume as a function of temperature in the following way:

vO = 0.57275 + 1.143×10 -4 T (3) vM = 0.57233 + 1.142×10 -4 T (4).
In this way the thermal expansion is reasonably well accounted for, while the specific volumes do not cross each other. Based on the available information in the literature, it can thus be concluded that the specific volume of the monoclinic form is (only slightly) smaller than that of the orthorhombic one, i.e. DO®Mv = vM -vO < 0.

Another observation, which may be deceptive, is the paper by Stevens et al. on the behavior of TNT under pressure [START_REF] Stevens | The high-pressure phase behavior and compressibility of 2,4,6-trinitrotoluene[END_REF]. It is shown in the paper that when TNT is subjected to pressures above 23 GPa and in particular up to [START_REF] Céolin | Phenomenology of Polymorphism, III:p,TDiagram and Stability of Piracetam Polymorphs[END_REF] GPa, it has turned into the orthorhombic form on returning to zero pressure [START_REF] Stevens | The high-pressure phase behavior and compressibility of 2,4,6-trinitrotoluene[END_REF]. Although, it is tempting to conclude that the orthorhombic phase forms under pressure, the observation in the paper is made at zero pressure. Therefore, it may be suggested that TNT has merely amorphized under pressure, as is not uncommon for organic substances [START_REF] Hedoux | Evidence for a high-density amorphous form in indomethacin from Raman scattering investigations[END_REF][START_REF] Hedoux | Pressure-induced transformations and high-pressure behaviour in cyanoadamantane plastic crystal[END_REF], and when returning back to zero pressure, it has recrystallized into one of its available polymorphs. In that respect, Vrcelj already states that both the monoclinic and orthorhombic structures are closely related, so that slight amorphization may distort the structure enough to cause it to recrystallize in the different form [START_REF] Vrcelj | Polymorphism in 2,4,6-trinitrotoluene crystallized from solution[END_REF][START_REF] Vrcelj | Polymorphism in 2-4-6 trinitrotoluene[END_REF]. Taking into consideration that three independent X-ray diffraction measurements indicate that the monoclinic form is the densest form of the two polymorphs [START_REF] Vrcelj | Polymorphism in 2-4-6 trinitrotoluene[END_REF][START_REF] Golovina | Kinetics and Mechanism of Phase-Transitions in the Crystals of 2,4,6-Trinitrotoluene and Benzotrifuroxane[END_REF][START_REF] Gallagher | Polymorphism, twinning and morphology of crystals of 2,4,6-trinitrotoluene grown from solution[END_REF], the pathway of formation of the orthorhombic form under ambient pressure after amorphization of the monoclinic form under pressure seems the most likely, in particular, because it is thermodynamically impossible that a system spontaneously expands, while a pressure is being applied.

THE ENTHALPY CHANGES OF THE DIFFERENT PHASE TRANSITIONS

The four enthalpies of fusion in Table 2 which can be ascribed to the melting of the monoclinic form, lead to a mean value of 100.6 ±4.2 J g -1 . Four values for the heat of sublimation have been found in the literature (Table 1). Their mean value equals 463 ±25 J g -1 . Hwang et al. also determined the enthalpy of vaporization with a value of 360.57 J g -1 . The difference between the two vapor pressure enthalpies should again be equal to the heat of fusion, DM®LH = DM®VH -DL®VH (with V: vapor phase) and leads to 103 J g -1 , very similar to the mean value of the direct measurements, which confirms the vapor pressure enthalpies.

The orthorhombic-to-monoclinic phase transition (peak 'a' in Figure 1 [START_REF] Grabar | Observation of a Solid-Solid Polymorphic Transformation in 2,4,6-Trinitrotoluene[END_REF] and in Figures S2 [START_REF] Gallagher | Polymorphism, twinning and morphology of crystals of 2,4,6-trinitrotoluene grown from solution[END_REF] and S3 [START_REF] Vrcelj | Polymorphism in 2,4,6-trinitrotoluene crystallized from solution[END_REF][START_REF] Vrcelj | Polymorphism in 2-4-6 trinitrotoluene[END_REF]) is endothermic in all the different papers demonstrating that heating favors the equilibrium to shift to the monoclinic polymorph. This proves that the two polymorphs have an enantiotropic phase relationship and that, in accordance with the Le Chatelier principle, the orthorhombic form must be stable somewhere at low temperature. This assessment is in conflict with the conclusions drawn in previous papers [START_REF] Vrcelj | Polymorphism in 2,4,6-trinitrotoluene crystallized from solution[END_REF][START_REF] Vrcelj | Polymorphism in 2-4-6 trinitrotoluene[END_REF][START_REF] Bowden | The high-pressure phase stability of 2,4,6-trinitrotoluene (TNT)[END_REF]. However, the value of the enthalpy change associated with the transition is less clear, because the three observed values range from 2 to 4.9 J g -1 (Table 1). To verify the enthalpies, the areas of peaks 'a' and 'b' in Figure 1 and in Figures S2 andS3 in the supplementary materials have been remeasured using the peak delimitation as defined in Figure S5 in the supplementary materials. The enthalpy change related to peak 'a' was determined assuming that the area of peak 'b' corresponds to DM®LH = 100.6 J g -1 . Whereas DO®MH values of about 5 J g -1 were found with the 'a' peaks from Figure 1 [18] and Figure S2 [START_REF] Gallagher | Polymorphism, twinning and morphology of crystals of 2,4,6-trinitrotoluene grown from solution[END_REF] agreeing with the results published by these authors (see Table 1), a value as high as 11 J g -1 was found for peak 'a' in Figure S3 and it disagrees with the value of 2.02 J g -1 reported by the authors [START_REF] Vrcelj | Polymorphism in 2,4,6-trinitrotoluene crystallized from solution[END_REF][START_REF] Vrcelj | Polymorphism in 2-4-6 trinitrotoluene[END_REF]. Therefore discarding the latter reported value, the mean transition enthalpy has been determined based on the values from references [START_REF] Gallagher | Polymorphism, twinning and morphology of crystals of 2,4,6-trinitrotoluene grown from solution[END_REF][START_REF] Grabar | Observation of a Solid-Solid Polymorphic Transformation in 2,4,6-Trinitrotoluene[END_REF] resulting in a value of DO®MH = 4.5 J g -1 .

Solid-solid transition temperatures are known to be delayed and may be observed at a higher temperature, when measured by DSC, than the real equilibrium temperature [START_REF] Rietveld | Dimorphism of the Prodrug L-Tyrosine Ethyl Ester: Pressure-Temperature State Diagram and Crystal Structure of Phase II[END_REF][START_REF] Barrio | Pressure-temperature state diagram for the phase relationships between benfluorex hydrochloride forms I and II: a case of enantiotropic behavior[END_REF][START_REF] Toscani | Stability hierarchy between piracetam forms I, II, and III from experimental pressure-temperature diagrams and topological inferences[END_REF]. In the available literature, the lowest temperature for the observation of the O®M transition has been reported by Golovina et al. at 328 K (Table 1) [START_REF] Golovina | Kinetics and Mechanism of Phase-Transitions in the Crystals of 2,4,6-Trinitrotoluene and Benzotrifuroxane[END_REF]. Related to the position of the solid-solid equilibrium, is the question where the melting point of form O can be found. In this respect, it is clear that the melting point of form O cannot be positioned at a lower temperature than where the O®M transitions have been observed, otherwise O would have molten instead of transformed into M. It being clear from the literature that form M is the highest melting form, the melting equilibrium of form O must be found between the melting point of M and the observations of the O®M transition in the solid. This brings us to Figure S1 in the supplementary materials, which indicates that form O melts about one degree lower than form M [START_REF] Connick | Polymorphism in 2,4,6-Trinitrotoluene[END_REF]. Taking this temperature difference and applying that to the average melting temperature determined for form M of 352.9 ±1.3 K, form O would be expected to melt at 352 K. The melting points can be used to determine the solid-solid transition temperature using eq. 5 [START_REF] Yu | Inferring Thermodynamic Stability Relationship of Polymorphs from Melting Data[END_REF]:

(5)

The melting enthalpy of the orthorhombic phase can be found by adding the difference in enthalpy between the two solid phases DO®LH = DM®LH + DO®MH = 105.1 J g -1 . Then with the melting points found just above, one finds for the transition point 330.9 K, which confirms the transition temperature observed by Golovina of 328 K [START_REF] Golovina | Kinetics and Mechanism of Phase-Transitions in the Crystals of 2,4,6-Trinitrotoluene and Benzotrifuroxane[END_REF]. Thus, as is clear from the literature, the orthorhombic form can either transform to the monoclinic one through a solid-to-solid endothermic transition, melt, or melt and convert into the monoclinic form on heating as illustrated in Figure S1 in the supplementary materials [START_REF] Connick | Polymorphism in 2,4,6-Trinitrotoluene[END_REF]. Similar thermal behavior has been observed previously with piracetam phase III that either transforms to phase I or melts without transformation depending on the presence of traces of residual solvent [START_REF] Toscani | Stability hierarchy between piracetam forms I, II, and III from experimental pressure-temperature diagrams and topological inferences[END_REF][START_REF] Céolin | Phenomenology of Polymorphism, III:p,TDiagram and Stability of Piracetam Polymorphs[END_REF].

CONSTRUCTION OF THE PRESSURE-TEMPERATURE TOPOLOGICAL PHASE DIAGRAM

The construction of pressure-temperature phase diagrams through the Clapeyron equation has been described previously [START_REF] Céolin | The topological phase diagram of cimetidine: A case of overall monotropy[END_REF][START_REF] Céolin | Phenomenology of polymorphism and topological pressure-temperature diagrams[END_REF][START_REF] Ceolin | The topological pressure-temperature phase diagram of fluoxetine nitrate: monotropy unexpectedly turning into enantiotropy[END_REF]. The Clapeyron equation: [START_REF] Winchell | The optical properties of organic compounds[END_REF], can be used to calculate the slopes of the two-phase equilibrium curves using the enthalpy and volume changes of the related phase transitions. In particular solid-solid phase equilibria are straight lines over extensive temperature and pressure ranges [START_REF] Ceolin | Pitfalls and feedback when constructing topological pressure-temperature phase diagrams[END_REF]; therefore, the slope can be used to describe such a phase transition with a straight line.

PRESSURE-TEMPERATURE MELTING CURVES FOR THE TWO POLYMORPHS

Summarizing the conclusions of the foregoing paragraphs, the temperatures and the heats of fusion of the two polymorphs are: TM®L = 352.9 K, DM®LH =100.6 J g -1 and TO®L = 351.9 K, and DO®LH =105.1 J g -1 . At the melting point of the monoclinic form, the specific volumes of the solid and the liquid can be calculated using eqs. 4 and 2: vM(352.9 K) = 0.612625 cm 3 g -1 and vL(352.9 K) = 0.683896 cm 3 g -1 leading to a change in volume on melting of DM®Lv = 0.071271 cm 3 g -1 . In the case of the orthorhombic solid, eqs. 3 and 2 lead to: vO(351.9 K) = 0.612955 cm 3 g -1 , vL(351.9 K) = 0.683436 cm 3 g -1 , and DO®Lv = 0.070482 cm 3 g -1 . These values can be used to evaluate the slopes of the two melting equilibria with the Clapeyron equation, leading to dP/dTM-L = 4.00 MPa K -1 and dP/dTO-L = 4.24 MPa K -1 .

T O→M = Δ M →L H -Δ O→L H Δ M →L H T M →L - Δ O→L H T O→L = Δ M →L H -Δ O→L H Δ M →L S -Δ O→L S ≈ Δ O→M H Δ O→M S dP dT = ΔH T ΔV
Using the slopes, the pressure-temperature melting curves can be obtained by approximating them by straight lines. The melting point of the respective polymorphs can be considered a triple point, because the vapor pressure of the condensed phases around the melting temperature is in the order of 0.68 Pa, obtained with the equation reported by Pella [START_REF] Pella | Measurement of Vapor-Pressures of TNT, 2,4-DNT, 2,6-DNT, and EGDN[END_REF] at 353 K. Such a pressure can be safely neglected by using 0 MPa for the pressure of the respective triple points with temperatures equivalent to the melting points. Using expressions of the form PM®L/MPa = 4.00 T/K + BM®L, the constants are found to be: BM®L = -1411.5 and BO®L = -1491.0. This results in the following equations for the melting curves with pressure in MPa and temperature in K:

PM®L = 4.00 T -1411.5 (7)
PO®L = 4.24 T -1491.0 (8)
With these two melting curves the triple point O-M-L, their intersection, can be determined and its coordinates can be calculated by setting eqs. 7 and 8 equal to each other: TO-M-L = 335 K and PO-M-L = -71 MPa.

THE PRESSURE-TEMPERATURE EQUILIBRIUM CURVE BETWEEN THE TWO SOLIDS

Solid-solid equilibria in a P-T diagram are usually found to be straight lines [START_REF] Ceolin | Pitfalls and feedback when constructing topological pressure-temperature phase diagrams[END_REF][START_REF] Gana | An Integrated View of the Influence of Temperature, Pressure, and Humidity on the Stability of Trimorphic Cysteamine Hydrochloride[END_REF][START_REF] Gana | Benzocaine polymorphism: Pressuretemperature phase diagram involving forms II and III[END_REF]. The O-M equilibrium curve passes through the O-M-vapor triple point, whose coordinates are 330.9 K and 0 MPa, and the O-M-L triple point, whose coordinates can be found just above. With these two sets of coordinates, the equation of the O-M equilibrium curve is found to be (P/MPa, T/K):

PO-M = -17.2 T + 5690 (9)
The slope of the O-M equilibrium can also be calculated with the Clapeyron equation using the data at its transition temperature calculated above: TO®M = 330.9 K, ∆O®MH = 4.5 J g -1 , ∆O®Mv = -4.42 ´10 -4 cm 3 g -1 . In that case one obtains PO-M = -30.7 T + 10159, a line that is even steeper. One has to realize that in this respect -17.2 or -30.7 only indicates that the slope of the equilibrium line is negative and very steep; the actual value of the slope is of very little importance. It can be seen that the dP/dT slope of the O-M equilibrium line is far greater than those of the melting curves and is due to the minute difference between the specific volumes of the polymorphs. The O-M transition is therefore mainly entropy driven and that also implies that increasing the pressure will have very little effect in transforming the stability conditions between the polymorphs. In fact, at room temperature, where the orthorhombic form is stable, following eq. 9, the monoclinic form would only become stable above -17.2 ´298 + 5690 = 564 MPa. This would in principle still be in contradiction with the observation of Stevens et al. [START_REF] Stevens | The high-pressure phase behavior and compressibility of 2,4,6-trinitrotoluene[END_REF] of the formation of the orthorhombic polymorph at or below a pressure of 34 GPa,; however, because the observation was carried out under atmospheric pressure, the pressure range from 564 to 0 MPa, would leave the system with a considerable pressure window to crystallize in the orthorhombic system either from the amorphous state or even from the monoclinic form damaged by the pressure.

EQUILIBRIA INVOLVING THE VAPOR PHASE

When vapor (V) is produced in the presence of condensed phases, phase changes between the condensed phases will approximate triple points. For TNT, this would be the case for transitions M®L, O®L, and O®M, whose temperatures are those of triple points M-L-V, O-L-V, and O-M-V, respectively. Because sublimation and vaporization curves are usually described by Clausius-Clapeyron type equations: ln(PV) = -DVH/(RT) + B, in which PV is the vapor pressure and ∆VH is the enthalpy change of either sublimation or vaporization. All two-phase equilibria of TNT involving the vapor phase can be obtained through eqs. 1a, 1b, or 1c. Other necessary data is the enthalpy change for the solid-solid transition or for both melting transitions. It should be realized that the vapor pressures of two condensed phases in equilibrium are equal and due to the fact that enthalpy is a state function, its algebraic sum of a change cycling around a triple point and returning to the initial state will equal 0.

If eq. 1b is used for the sublimation of the orthorhombic form, ∆L®VH = ∆O®VH -∆O®LH = 439.24 -105.09 = 334.15 J g -1 = 75896 J mol -1 . The vapor pressures of O and L are equal at the triple temperature TO-L-V and therefore using eq. 1b, one gets: ln(PO) = 33.513 -11999/T = ln(PL) = BL -9128/T. With TO®L = 351.9 K and R = 8.3145 J mol -1 K -1 , constant BL is found to be 25.35 and for ln(PL/Pa), this leads to: ln(PL) = 25.35 -9128/T with T in K [START_REF] Gallagher | A theoretical examination of the molecular packing, intermolecular bonding and crystal morphology of 2,4,6-trinitrotoluene in relation to polymorphic structural stability[END_REF] Using equation [START_REF] Gallagher | A theoretical examination of the molecular packing, intermolecular bonding and crystal morphology of 2,4,6-trinitrotoluene in relation to polymorphic structural stability[END_REF], the sublimation curve for the M-phase melting at 352.9 K can be found following the

CONCLUDING REMARKS

The topological pressure-temperature diagram for the dimorphism of TNT, constructed using data available from the literature, is found to be a case of overall enantiotropic behavior corresponding to Bakhuis-Roozeboom's case 2 [START_REF] Roozeboom | Die heterogenen Gleichgewichte vom Standpunkte der Phasenlehre[END_REF][START_REF] Ceolin | Overall monotropic behavior of a metastable phase of biclotymol, 2,2'-methylenebis(4-chloro-3-methyl-isopropylphenol), inferred from experimental and topological construction of the related P-T state diagram[END_REF][START_REF] Ceolin | X-ray crystallography, an essential tool for the determination of thermodynamic relationships between crystalline polymorphs[END_REF].

It has been demonstrated in this article in accordance with observation [START_REF] Vrcelj | Polymorphism in 2,4,6-trinitrotoluene crystallized from solution[END_REF][START_REF] Vrcelj | Polymorphism in 2-4-6 trinitrotoluene[END_REF][START_REF] Golovina | Kinetics and Mechanism of Phase-Transitions in the Crystals of 2,4,6-Trinitrotoluene and Benzotrifuroxane[END_REF][START_REF] Gallagher | Polymorphism, twinning and morphology of crystals of 2,4,6-trinitrotoluene grown from solution[END_REF][START_REF] Grabar | Observation of a Solid-Solid Polymorphic Transformation in 2,4,6-Trinitrotoluene[END_REF] that the orthorhombic form endothermically transforms to the monoclinic form at about 331 K on heating. Although the temperature of a solid-solid equilibrium remains difficult to determine [START_REF] Barrio | Pressure-temperature state diagram for the phase relationships between benfluorex hydrochloride forms I and II: a case of enantiotropic behavior[END_REF], considering the reported data and the outcome of the topological phase diagram, the orthorhombic form is most likely the stable form at room temperature. The spontaneous transformation of the orthorhombic form into the monoclinic form observed in samples left for two months [START_REF] Gallagher | Polymorphism, twinning and morphology of crystals of 2,4,6-trinitrotoluene grown from solution[END_REF] appears difficult to explain; however, storage conditions were not clearly defined in the paper and samples could have been subjected to temperature fluctuations. In addition, impurities could have been present, which is known to affect the stability behavior of chemical substances due to the formation of solid solutions.

The accuracy of the topological phase diagram improves if the dependence of the specific volumes on the temperature is known, as is the case for the data on TNT. The specific volume of crystalline molecular solids can nowadays be determined over a large temperature interval of 100 to 473 K thanks to the coupling of Xray diffractometry and commercially available devices for temperature control. Nonetheless, this is not the case for the specific volumes of molecular compounds in the molten state, because such compounds decompose while melted and because the available methods are seldomly employed.

In previous papers, the volume change on melting for a number of molecular compounds has been reported at their respective temperatures of fusion. Interestingly, the ratio vliquid/vsolid on melting is rather constant and equals 1.11 ±0.04 [START_REF] Céolin | The topological pressure-temperature phase diagram of ritonavir, an extraordinary case of crystalline dimorphism[END_REF][START_REF] Rietveld | Phenomenology of crystalline polymorphism: overal monotropic behavior of the cardiotonic agent FK664 forms A and B[END_REF][START_REF] Ceolin | The topological phase diagram of cimetidine: A case of overall monotropy[END_REF]. TNT confirms this ratio, as using eqs. ( 2) and ( 4), leads to vliquid/vsolid = 1.116, thus reinforcing the predictive character of this statistical value. However, in the case that multiple polymorphs exist, the ratio should be applied to the highest melting polymorph. Therefore, the dependence of the specific volume of the liquid should be known if the volume change on melting of other polymorphs is required for the calculation of the dP/dT slopes of the melting curves with the Clapeyron equation. Statistical analysis has shown that the expansivity of molecular liquids possesses an average value of 1.19 10 -3 K -1 [START_REF] Céolin | The topological pressure-temperature phase diagram of ritonavir, an extraordinary case of crystalline dimorphism[END_REF][START_REF] Rietveld | Phenomenology of crystalline polymorphism: overal monotropic behavior of the cardiotonic agent FK664 forms A and B[END_REF][START_REF] Ceolin | The topological phase diagram of cimetidine: A case of overall monotropy[END_REF]. For TNT, an experimental value of about 0.9 10 -3 K -1 has been found, which is on the small side, but still near the average value.

Finally, another important ratio for the determination of topological phase diagrams is the vliquid/vsolid ratio between the metastable liquid and the crystalline phase at the temperature of the glass transition. For TNT, whose glass transition temperature was found ranging from 239 to 258 K, the ratio lies between 1.052 and 1.063 depending on the Tg value used in eqs. 2 and 3. Unfortunately, not enough data exists so far to judge its statistical importance.

Supplementary Material

  It results in a sublimation enthalpy for TNT of DsubH = 103.39 kJ mol -1 (455.21 J g -1 ) with R = 8.31446 J mol - 1 K -1 . Pella obtained the vapor pressure values of solid TNT in the 287-330 K range leading to the expression [26]: Ln (P/Pa) = -11999/(T/K)+ 33.513 R 2 = 0.984 (1b) This leads to a sublimation enthalpy of DsubH = 99.765 kJ mol -1 (439.24 J g -1 ). Finally, Cundall et al. determined the vapor pressure in the range of 301.4-346.1 K [27]: Log10 (P/N m -2 ) = -5900/(T/K) + 12.60 (1c), resulting in a DsubH = 113.0 kJ mol -1 (497.3 J g -1 ).

  same procedure: ∆M®VH =∆L®VH + ∆M®LH = 334.15 + 100.6 = 434.75 J g -1 = 98745 J mol -1 . At triple point M-L-V, the vapor pressures PL and PM are equal and therefore, ln PL = 25.35 -9128/T = ln PM = BM -11876/T, which leads to BM = 33.14 and ln(PM) = 33.14 -11876.19/T with PM in Pa and T in K (11) With eqs. 1b and 11, the vapor pressures of phases O and M can be compared at room temperature (298 K).It can be seen that PO (298 K) = 1.17 ´10 -3 Pa is smaller than PM (298 K) = 1.22 ´ 10 -3 Pa. The difference reflects the thermodynamic stability ranking with the more stable phase possessing a smaller vapor pressure.

Figure 2 .

 2 Figure 2. Topological pressure-temperature phase diagram of TNT representing the stability regions of forms O and M, the liquid (L) and the vapor (V) phase. Triple points: 1: M-L-V, 2: O-L-V, 3: O-M-L, 4: O-M-V. Stability ranking: solid black lines: stable, dashed lines: metastable, white lines: supermetastable

Figure S1 .

 S1 Figure S1. Differential thermal analysis curves for TNT reported by Connick et al.[START_REF] Connick | Polymorphism in 2,4,6-Trinitrotoluene[END_REF]. It was observed that monoclinic single crystals recrystallized from toluene solutions exhibited a single melting peak (peak 'b', panel a). However, convoluted peaks were observed in the case of mixtures of polymorphs (monoclinic and most likely the orthorhombic one) in various ratios (panels b -d). Thus peak 'c' is most likely the melting of the orthorhombic polymorph occurring at about one degree lower than the monoclinic one.

Figure S2 .

 S2 Figure S2. DSC curves by Gallagher et al. for the orthorhombic (left-hand panel) and monoclinic (right-hand panel) polymorphs of 2,4,6-trinitrotoluene [9].

Figure S3 .

 S3 Figure S3. DSC curves of TNT published by Vrcelj et al. [1, 2]: panel A monoclinic form (M) and panel B orthorhombic form (O). Peak 'a' = O®M (onset at 340.6 K), peak 'b' = M®liquid (onset at 351-352 K).

Figure S4 .

 S4 Figure S4. Delimitation of peaks 'a' and 'b' for Figure 1 in the text and Figures S2 and S3 in the supplementary materials. The yellow area is ascribed to the heat of fusion of the monoclinic polymorph and the blue area to the transition of form O into form M.

Table 1 . Crystallographic data on 2,4,6-trinitrotoluene in the literature and in the CSD

 1

	Lattice	T	a /Å	b /Å	c /Å	β /°	V /Å 3	Z	d /g	Ref a
	system	/K							cm -3
	Orthorhombic RT	14.85	39.5	5.96	90	3496	16 1.726	[5]
										ZZZMUC03
	Orthorhombic RT	40.0	14.89	6.09	90	3627	16? 1.66?	[8]
										ZZZMUC07
	Orthorhombic	296 14.991(1)	6.077(1)	20.017(2)	90	1823.6	8	1.655	[7]
	P21ca									ZZZMUC01
	Orthorhombic	RT 20.041(20) 15.013(8) 6.0836(5)	90	1830.41	8	1.648	[8]
	P21ab									ZZZMUC05
	Orthorhombic	RT?	15.075	20.024	6.107	90	1843.5	8	1.637	[9]
	Pb21a
	Orthorhombic	123 14.910(2) 6.034(18) 19.690(4)	90	1770.58	8	1.704	[2]
	Pca21									ZZZMUC09
	Monoclinic	RT 21.407(20) 15.019(8) 6.0932(5) 111.005(20)	1828.86	8	1.650	[8]
	P21/b					(γ)				ZZZMUC06
	Monoclinic	RT?	21.275	6.093	15.025	110.23	1827.5	8	1.651	[9]
	P21/c
	Monoclinic	100 14.9113(1) 6.0340(1) 20.8815(3) 110.365(1) 1761.37	8	1.713	[2]
	P21/a									ZZZMUC08
	Monoclinic	RT	20.2	6.2	7.7	90.0	964.3	4	1.56	[15]
	P21/*									ZZZMUC
	Monoclinic	RT	40.5	6.19	15.2	90.52	3810.4	16	1.58	[16]
	C2/c									ZZZMUC02
	Monoclinic	RT	21.230(5)	6.081(2)	14.958(5)	110.12(2)	1813.23	8	1.664	[17]
	P21/c									ZZZMUC04
	a Literature reference and refcode of the Cambridge Structural Database (CSD)
	2.1.2 CALORIMETRIC DATA

Table 2 . Available calorimetric data for TNT from the literature a

 2

	TO®M/K	DO®MH/J g -1	TS®L/K	DS®LH/J g -1	DS®VH/J g -1 DL®VH/J g -1	Ref
	336-337	4.93	351-353 (M)	-		[18]
			350 (O)
			354 (M)			[19]
			353-353.5 (O)

Table S1 . Comparison of the X-ray diffraction pattern of specimen Q used by Grabar et al. [18] with the pattern calculated from the crystal structure of the orthorhombic polymorph solved by Golovina et al. (ZZZMUC05 [8]).

 S1

	Grabar (exp)		Golovina (calc)
	dhkl	I/I1	dhkl	I/I0 (%)
	10.2	20	10.02	1.5
	7.08	50	7.03	40
	6.02	10	6.008	3
	5.71	40	5.638	35
	5.43	40	5.428	26
	5.01	40	5.000	21
	4.77	10	4.720	2
	4.31	60	4.304	16
			4.264	25
	3.88	100	3.862	100
	3.72	30	3.741	14.5
			3.688	12
	3.56	20	3.530	11
	3.45	20	3.433	14
	3.28	40	3.260	36
	3.16	10	3.150	5
	3.05	50	3.050	11
			2.992	25
	2.89	40	2.875	24

Competing Interests

No competing interests to declare

Supplementary Materials

Table comparing experimental X-ray patterns, several annotated DSC curves.


Ismet Addoui

Tarek Chouaki

Ambrogio Delli Colli

Generating relevant scenarios for intelligent transportation service

This paper addresses risk assessment issues while conceiving complex systems. Indeed, project stakeholders have to share the same problems understanding allowing to undertake rational and optimal decisions. We propose an approach based on Natural Language Processing (NLP) techniques to improve systems quality requirements such as consistency and completeness. We assess the relevancy of our approaches through experimentations and highlighted feedbacks from project stakeholders and players.

Introduction

Requirements Engineering aims to define documents and maintain requirements [1]. The number and nature of activities characterizing any process for managing requirements is correlated with the target domain (software, real-time embedded systems, automotive or railway), as well as the importance of the project, its innovative nature and other considerations such as human factors, standards or technologies. Any requirements engineering process includes at least activities of elicitation, specification, validation and change management. These activities are supported by different techniques such as interviews, knowledge engineering, modelling and analysis or simulation.

Having a clear understanding of the customer's needs is not an easy task. The goal of the requirements engineer is to help customers to clarify and to frame the requirements of the system under construction. Building a complete, consistent and feasible requirements base is a challenging issue and a timely research topic. Moreover, the quality of the requirements is of a high importance to avoid snowball effects leading to misinterpretation and ineffective realizations.

Without a shared vision, chances to converge quickly to a requirement base that is complete, consistent and feasible are negligible or would require many iterations leading to higher costs, delays and competitiveness. This comes besides with no guarantee on the quality of the requirements. To improve the quality of the requirements, one can consider scenarios with important advantages already addressed in the literature [START_REF] Do Prado Leite | Enhancing a requirements baseline with scenarios[END_REF][START_REF] Glinz | Improving the quality of requirements with scenarios[END_REF]. For instance, scenarios tend to adopt the user's viewpoint, which is a key feature to validate the adequacy between the requirements and the user's needs. Considering the complexity of large systems, the number of scenarios needed to effectively help practitioners to design a system that fits the needs of the customers can be important. The selection of relevant scenarios among possible ones to cover the user's need is not obvious. Today, this task is generally performed in ad-hoc manner by experts that consider the system only through their prism, generally limited to their concerns. We think there is a need to improve this situation and to generate more relevant scenarios considering the full coverage of users' needs and required analysis to be performed to validate their adequacy, their completeness or their feasibility.

Motivations and our contribution

Several studies highlighted recurrent problems that occur when large scale projects fail. For instance, the CHAOS Report [START_REF] Group | The chaos report into project failure, the standish group international inc[END_REF]  Lack of relevant metrics to take rational decisions In practice, most of problems issued from bad decision making are discovered during verification and validation activities. When the first versions of the system have been implemented and deployed. Those late discoveries require most of time re-engineering the system at several levels: operational, functional or physical; or reconsidering the strategy of the enterprise in terms of partnerships or skills to be developed.

From a technical perspective, the design of a complex system driven by scenarios can be helpful if it allows the consideration of any relevant combination of features (events, behaviours, conditions) to really get a deeper understanding of how the system should behave and what it should be made of. The question we shall consider are as follows:

 How many scenarios do we need to consider to embrace all user's needs?

 What are the combinations of events, behaviours or conditions do we need to analyse in priority according to initial hypotheses?

The previous questions are important and necessitate detailed responses. Nevertheless, there are no explicit answers and we propose some experiments with prominent preliminary results providing some hints.

Application

We aim to design and implement a mobility service where systems must cooperate to fulfil the expected operation capabilities. We consider five capabilities described in the following:

 Enhance personal mobility: this can be measured through user interviews about comfort or quality of service. Related metrics are the average time of waiting to access the transportation service or the mean time delay to reach the desired destination.  Ensure the System of System (SoS) integrity: it is about the physical integrity of any human being involved in operational scenarios (user, pedestrian, cyclist, etc.). This latter could be corrupted in many ways: physical attacks on roadside units or vehicles, or cyber-attacks. Meeting this capability can be measured by the reduction of any kind of accidents. This implies also a good crisis management in case of accident, in order to not deteriorate the situation and not create congestions.  Improve environment impact: this is related to the transportation efficiency and effectiveness of the cooperation between vehicles and roadside units.

Meeting this capability can be measured by the reduction of fuel consumption or lower emission of CO2 fine particles.  Ensure service continuity: this allows to avoid malicious acts that could lead to corruption of human beings, vehicles or roadside units' integrities. It also tries to anticipate damages. Its satisfaction can be measured by the reduction of malicious acts or their associated costs.  Reduce of congestion. It can be measured by the reduction of occupation rates of roads, or by the reduction of annual mean time spent on the roads by users.

Our analysis is driven by usage scenarios leading to ask the following questions:

 How systems implied in the scenarios shall behave and cooperate to fulfil each of those operational capabilities?  What are the data they shall exchange?

Through which media and what quality of service?

Depending on a described situation, the set of behaviours and interactions that shall be considered can be very large. Hence, this cannot be considered and managed easily at design time. Nevertheless, in this paper, we propose to generate a set of representative scenarios to cover a maximum number of cases, leading to a consistent and complete specification. The quality and the accuracy of simulations' results of the generated scenarios have an important impact on the ability to proceed to relevant architecture choices.

Generation of scenarios

Figure 1 depicts and illustrates our approach to generate scenarios. Note that, the definition of scenarios considered is "sequence of events that occurs during a particular execution of a group of objects implied in the system of system". The set of scenarios to drive the analyses at system level, is performed by experts. This is a manual activity relying on the knowledge of these experts and their ability to imagine key scenarios to validate users' needs. Pragmatically, the required number as well as the relevancy of scenarios defined by our experts cannot be measured accurately. Knowing that this set of scenarios is produced by humans, we can assume that there are omissions due to the large scope of features. For instance, experts have defined over 50 scenarios ranging from the highest probability of occurrence to the most critical. Are those scenarios enough to cover all the needs? Considering the complexity of the SoS, the answer is obviously no. Then there is a need to assist expert to elicit more relevant scenarios.

Knowledge Extraction

To improve the quality and the accuracy of scenarios driving key decisions, we have used an approach using knowledge extraction from the dedicated literature in order to capitalize it into an ontology. This ontology classifies all key features characterizing any scenario: users, vehicles, roadside units, road types or traffic conditions. For instance, our ontology describes all kind of:  Climatic conditions: brightness, rain, snow, wind, fog  The various roads the vehicles can take; sloppy, curving, muddy or icy  The taxonomy of all behaviours that can be expected from drivers or pedestrians: careful, distracted or dangerous This knowledge has been extracted from a set of corpuses using Natural Language Processing with the NLTK framework [START_REF] Bird | [END_REF]. The obtained results using NLP are completed with expert recommendations.

As illustrated in Figure 2. We extract key terms from the documents of the mobility corpus after tokenizing, cleaning and lemmatizing content. We rely on the computation of semantic similarities using WordNet [START_REF] Fellbaum | Wordnet[END_REF] to reduce the resulting set of words. Key terms extraction relies on the frequency distribution of remaining words. Finally, we use tags from POS (Part of Speech) Tagging to determine the role of corresponding

Generation of scenarios

The extracted ontology is exhaustive and can be used for a huge number of scenarios. Since our experimentation concerns a specific zone in Paris area, we extracted the relevant subset for achieving deeper analyses considering experts' recommendations. For this purpose, we relied on data we collected according to our experimentation: climate, hazards, topology of road, localization of roadside units, etc. We selected 45 features regarding the operational capabilities we wanted to reach. Then, each feature is annotated with a level of probability of occurrence ranging from A (the most probable) to E (the less probable). The features are also annotated with a level of criticality ranging from A (the most critical) to C (the less critical). Table 1 shows the list of selected features along with their respective levels of probability of occurrence and criticality regarding the scope of our experimentation.

¬(cross_road ∧ round_about) (1) Fog → Low_grip (2)
Formula ( 1) is used to avoid scenarios with both crossroads and roundabouts. Aware that (in our study) it is impossible to have simultaneously a crossroad and a roundabout.

Formula ( 2) is used to force the presence of low grip in case of fog. Adding those constraints allow us to avoid having inconsistent scenarios.

It is important to mention that with 45 selected features and 22 specified constraints; the total number of possible scenarios remains very high (one can consider an exponential number of combinatorial cases scenarios).

Since we cannot afford to analyse all these scenarios, we have investigated a new approach to prioritize these scenarios using two metrics such as criticality and probability of occurrence. For this purpose, and for each generated scenario, we also propose two scores as indicated by equations ( 3) and (4):

𝑃 𝑔 = ∏ 𝑃 𝑖 𝑛 𝑖=1 (3) 𝐶 𝑔 = ∏ 2 𝐶 𝑖 𝑛 𝑖=1 (4)
Equations ( 3) and ( 4) provide the global probability (resp. criticality) of a scenario for each of them using the probability of occurrence (resp. criticality) of each feature.

Equation ( 4) uses an exponential law as it fosters highest levels of criticality. Once a global score for each scenario has been computed in terms of probability of occurrence and criticality, we represent these scenarios in Figure 3. This figure represents the criticality's behaviour according to probability of occurrence variations.

Before going through the details of Figure 3, we propose the following definition [7] The definition by [7] set of non-dominated solutions, being chosen as optimal, if no objective can be improved without sacrificing at least one other objective. On the other hand, a solution x * is referred to as dominated by another solution x if, and only if, x is equally good or better than x * with respect to all objectives. The Pareto front points (see figure 3) are the non-dominated solutions.

Figure 3 depicts the Pareto front allowing us to extract the most representative scenarios represented by non-dominated points according to the two identified criteria (criticality and probability of occurrence). This Pareto front is an efficient approach to considerably reduce the total number of scenarios and exhibits only the non-dominated points or scenarios that we consider the most important to be investigated. From this 1134 scenarios have been selected from the Pareto front for analysis and study. Items below represent features of a single scenario to be prioritized for analysis: Note that items of this example precise only the features that shall appear into the same scenario. They do not reveal information about the causality links between events or behaviours. To cope with this issue, we appealed experts to recommend and select the most relevant scenarios depicted by Pareto front approach.

For instance, we provide in the following an example illustrating a right interpretation of features into a realistic scenario: "The autonomous vehicle drives on a sloppy slippery road with low visibility because of the fog. Electromagnetic disturbances cause a loss of communication with the control / command center. The road taken is often crossed by wild animals." Such situation can cause the immediate stop of the transportation service otherwise, it can put the life of users in danger. In this case, we need a set of functions ensuring the good coordination between vehicles and roadside units. This situation requires also a function for the vehicle to park in a safe area and notify the control-command operator as soon as the communication is fully restored. This analysis indeed impacts behaviours and interactions required to ensure safer transportation services.

Conclusion

In this paper, we presented some achievements of a novel approach making use of techniques from AI (NLP for instance) to elicit requirements for a mobility service. Compared to traditional approaches, we took the advantage of AI techniques to help practitioner to focus on the most important features when designing a complex system. This approach allows us to select the nature of the scenarios needed. The generation of scenario could focus on the criticity, the probability of occurrence or both. The feedback we had from the experts is considered to improve the quality of the obtained results. Besides, most of techniques presented in this paper have been automated (knowledge extraction, scenario generation, exploitation of results) which is a key point for dynamically managing changes. Obviously, our approach suffers from several limitations in terms of techniques or application that shall be addressed by further works. For instance, we did not take account the strategic aspects of the enterprise into the elicitation of requirements and we do not generate the story of the scenario. Finally, the temporality of the appearance of event (features) is not specified in our method.

Figure 1 :

 1 Figure 1: Overview of the scenarios generation

Figure 2 :

 2 Figure 2: Ontology extraction using NLP

Figure 3 :

 3 Figure 3: Pareto front of the generated scenarios criticity over probability of occurence

Table 1 .

 1 Scenario Features

	Features	Criticality Probability
	Curved Road	B	A
	Speed Bump	B	C
	Teleoperation Hacking	A	D
	CEM	A	E
	Cut Out	B	B
	Equipements Supervision Hacking	A	C
	Impaired Walking Pedestrian	A	C
	Overtaking	A	A


M Barrio

H Allouchi

J.-Ll Tamarit

R Ceolin

L Berthon-Cédille

I B Rietveld
email: ivo.rietveld@univ-rouen.fr

EXPERIMENTAL AND TOPOLOGICAL DETERMINATION OF THE PRESSURE-TEMPERATURE PHASE DIAGRAM OF RACEMIC ETIFOXINE, A PHARMACEUTICAL INGREDIENT WITH ANXIOLYTIC PROPERTIES

Keywords: active pharmaceutical ingredient, thermodynamic properties, crystallographic properties, solid state, phase diagram, melting, vitreous state

Information about the solid-state properties of etifoxine has been lacking, even if the active pharmaceutical ingredient has been used for its anxiolytic properties for decennia. The crystal structure of the racemic compound possesses a monoclinic space group P21/n with cell parameters a = 8.489(2) Å, b = 17.674(2) Å, c = 20.883(3) Å, b = 98.860(10)° and a unit-cell volume of 3095.8(9) Å 3 at 293 K. The unit cell contains 8 molecules, while 2 independent molecules with different conformations are present in the asymmetric unit. The density of the crystal is 1.291 g/cm 3 and its melting point was found at 362.6 ±0.3 K with a melting enthalpy of 85.6 ±3.0 J g -1 . Its thermal expansion in the liquid and the solid state and the change in volume on melting and between the vitreous state and the crystalline solid have been studied. The results confirm the tendency of small organic molecules to increase about 11% in volume on melting, while the volume difference between the glass and the crystal at the glass transition temperature is about half this value at 6%. These values can be used in the construction of phase diagrams in the case that the experimental data for a given system is incomplete.

INTRODUCTION

The active pharmaceutical ingredient (API) etifoxine (Figure 1) was developed about 60 years ago and the racemic compound is marketed for its anxiolytic properties. [START_REF] Kuch | benzothiazines and[END_REF][START_REF] Choi | Etifoxine for Pain Patients with Anxiety[END_REF][START_REF] Besnier | Étifoxine: études cliniques récentes[END_REF] Its anxiolytic effect is comparable with that of some benzodiazepine drugs such as lorazepam, but it has less side effects. [START_REF] Choi | Etifoxine for Pain Patients with Anxiety[END_REF][START_REF] Girard | Etifoxine improves peripheral nerve regeneration and functional recovery[END_REF][START_REF] Nguyen | Efficacy of etifoxine compared to lorazepam monotherapy in the treatment of patients with adjustment disorders with anxiety: a double-blind controlled study in general practice[END_REF] Etifoxine is prescribed in France and in some other countries, considering this drug as a safe alternative to benzodiazepine drugs.

Although it has been marketed for years, structural and thermodynamic solid-state studies remain inadequate, even if its unit cell has previously been published in the CSD. [START_REF] Paulus | CSD entry ECMPBX[END_REF][START_REF] Paulus | CSD Entry ECMPBX01[END_REF] The main purpose of the present study was to provide this data and the results are presented hereafter. Besides the API-specific use of the properties determined in this paper, the data also contribute to statistical information that can be used to study the general solid-state behavior of small organic molecules, which make up a large part of the present-day marketed oral drugs. In this light, the thermal expansion of the solid and of the liquid of etifoxine will be compared to that of other APIs. Moreover, the experimental thermal expansion will be used to determine the change in volume of the compound on melting and the difference in volume between the crystalline solid and the vitreous state. This kind of data appears to be relatively constant among small organic molecules and that knowledge is important because the data can therefore be used to construct phase diagrams of APIs such as volume-against-temperature representative of the Helmholtz free energy and the better-known pressure-against-temperature representative of the Gibbs free energy. Thus, even if very little is known about the specific volume of a given API, because it has not been determined or cannot be determined due to decomposition, it will still be possible to determine its phase behavior and with it the stability hierarchy between different solid phases of an API.

MATERIALS AND METHODS

ETIFOXINE SAMPLE

A sample of racemic etifoxine powder of medicinal grade (D4223) was kindly provided by Biocodex, France. It was used as such, while for single crystal X-ray diffraction studies suitable crystals were obtained by slow evaporation from n-hexane solutions at room temperature (see Figure 2).

SINGLE CRYSTAL X-RAY DIFFRACTION.

X-ray diffraction intensities were collected at room temperature up to q = 65° (qmax) with an Enraf-Nonius CAD4 diffractometer using Cu-Ka radiation (l = 1.54178 Å) and equipped with a graphite monochromator. [START_REF]Enraf-Nonius CAD4 Express Software[END_REF] Unit cell determination, data collection, and data reduction were carried out with the CAD4 Express Enraf-Nonius programs package and XCAD4. [START_REF] Harms | XCAD-CAD4 Data reduction[END_REF] All data were corrected for Lorentz polarization effects. The structure was solved by direct methods using the SHELXS-97 package with which most non-hydrogen atoms were located. [START_REF] Sheldrick | SHELXL97: Program for crystal structure refinement[END_REF][START_REF] Sheldrick | A short history of SHELX[END_REF] The remaining atoms were located after successive Fourier synthesis runs. The atomic parameters were refined by a least-squares method on F 2 with SHELXL-97. [START_REF] Sheldrick | SHELXL97: Program for crystal structure refinement[END_REF][START_REF] Sheldrick | A short history of SHELX[END_REF] The coordinates of all non-hydrogen atoms were refined with anisotropic thermal parameters. Hydrogen atoms were placed at calculated positions generated according to stereochemistry and refined using a riding model in SHELXL-97.

HIGH-RESOLUTION POWDER X-RAY DIFFRACTION

PXRD measurements were performed with a vertically mounted INEL cylindrical position-sensitive detector (CPS-120) using the Debye-Scherrer geometry and transmission mode. Monochromatic Cu-Ka1 (l = 1.54056 Å) radiation was selected by means of an asymmetrically focusing incident-beam curved quartz monochromator. Measurements as a function of temperature were carried out using a liquid nitrogen 700 series Cryostream Cooler from Oxford Cryosystems. Cubic Na2Ca3Al2F4 was used for external calibration. The PEAKOC application from DIFFRACTINEL software was used for the calibration as well as for the peak position determinations after pseudo-Voigt fittings and lattice parameters were refined by way of the leastsquares option of the FullProf suite. [START_REF] Rodriguez-Carvajal | Recent advances in magnetic structure determination by neutron powder diffraction[END_REF][START_REF] Rodriguez-Carvajal | Full-Prof suite version[END_REF] Specimens were introduced in a Lindemann capillary (0.5-mm diameter) and rotate perpendicularly to the X-ray beam during the experiments to improve the averaging of the crystallite orientations. Before each isothermal data acquisition, the specimen was allowed to equilibrate for about 10 min, and each acquisition time was no less than 1 h. The heating rate in-between data collection was 1.33 K min -1 . Patterns were recorded on heating in the temperature range from 100 K up to the melting point.

DIFFERENTIAL SCANNING CALORIMETRY (DSC)

Temperature (onset) and heat of fusion were obtained with a Q100 thermal analyzer from TA Instruments at a 10 K min -1 heating rate. The analyzer was calibrated using the melting point of indium (Tfus = 429.75 K and DfusH = 28.45 J g -1 ). The specimens were weighed using a microbalance sensitive to 0.01 mg and sealed in aluminum pans.

DENSITOMETRY OF THE MELT AS A FUNCTION OF TEMPERATURE

Liquid density as a function of temperature was measured with a DMA-5000 Density Meter from Anton-Paar. A melted specimen was introduced in the apparatus equilibrated at a temperature above the temperature of fusion. Data were obtained at isothermal steps while slowly cooling in the temperature range from 363 to 323 K. Dry air and bi-distilled water were used as calibration standards in the temperature range. The temperature was controlled at ±1 mK and measurements were performed when temperature fluctuations were smaller than ± 0.5 mK.

HIGH-PRESSURE DIFFERENTIAL THERMAL ANALYSIS (HP-DTA)

HP-DTA measurements have been carried out at a heating rate of 2 K min -1 using an in-house constructed high-pressure differential thermal analyzer similar to Würflinger's apparatus and operating in the 298 -473 K and 0 -250 MPa ranges. [START_REF] Würflinger | Differential thermal-analysis under high-pressure IV. Lowtemperature DTA of solid-solid and solid-liquid transitions of several hydrocarbons up to 3 kbar[END_REF] To determine the melting temperature as a function of pressure and to ascertain that in-pan volumes were free from residual air, specimens were mixed with an inert perfluorinated liquid (Galden ® , from Bioblock Scientifics, Illkirch, France) as a pressure-transmitting medium, and the mixtures were sealed into cylindrical tin pans. To verify that the perfluorinated liquid was chemically inactive and did not interfere with the melting temperature of etifoxine, preliminary DSC measurements were carried out with a Galden ® -etifoxine mixture on a Q100 analyzer of TA instruments without applied pressure.

RESULTS

CRYSTAL STRUCTURE

Racemic etifoxine was found to be monoclinic, space group P21/n (n°14), with unit-cell parameters a = 8.489( 2 9) Å 3 at 293 K containing Z = 8 molecules per unit-cell and Z' = 2 molecules in the asymmetric unit. The unit cell is in accordance with the unit-cell data published previously. [START_REF] Paulus | CSD entry ECMPBX[END_REF][START_REF] Paulus | CSD Entry ECMPBX01[END_REF] Crystal-and structure-refinement data have been compiled in Table 1 and non-H atom coordinates have been listed in Table 2. Other data (fractional coordinates for H-atoms, bond lengths, bond angles, anisotropic displacement parameters, and torsion angles) can be found in Tables S1 to S5 of the Supplementary Information. The atom labelling is shown in Figure 3. The Cambridge Crystallographic Data Centre deposit (CCDC 1943706) contains the supplementary crystallographic data for this paper. It can be obtained free of charge from the CCDC via www.ccdc.cam.ac.uk/data_request/cif. The last digit of the atom numbering (1 or 2) corresponds to either of molecules 1 or 2, respectively. c U(eq) is defined as one third of the trace of the orthogonalized U ij tensor.

THE SPECIFIC VOLUME OF RACEMIC ETIFOXINE AS A FUNCTION OF TEMPERATURE

An experimental and a calculated X-ray powder diffraction pattern are shown in Figure S1 of the supplementary materials for comparison. It can be seen that the two patterns are virtually the same, although some differences in peak intensities indicate the presence of preferred orientation. High resolution X-ray diffraction patterns have been collected from 100 to 340 K to determine the lattice parameters of the unit cell as a function of temperature by least-squares refinement. The results have been compiled in Table S6 in the supplementary materials. The specific volumes (v /cm 3 g -1 ) have been fitted to the following quadratic equation as a function of temperature (T /K): vs = 0.74375(73) + 4.38(71)´10 -5 T + 2.24(16)´10 -7 T 2 (r 2 =0.9995)

The specific volume of molten etifoxine from experimental density measurements have been reported in Table S7 of the supplementary materials and have been fitted as a function of the temperature to the following equation:

vliq = 0.6359(29) + 0.0006181(85) T (r 2 = 0.9993) (2)
CALORIMETRIC BEHAVIOR Specimens of the as-received sample were subjected to differential scanning calorimetry in closed pans.

Heating from 213 K led to a single endothermic effect ascribed to a melting transition with a mean onset at 362.6 ±0.3 K. The mean value of the melting enthalpy was found to be 85.6 ±3.0 J g -1 (25.75 ±0.90 kJ mol -1 ). On reheating after quick or slow cooling of the melt to 213 K, a midpoint glass transition was observed at 297.2 ±0.8 K. Data from 16 experiments have been compiled in Table S8 of the supplementary materials. S10 in the supplementary materials.

THERMAL EXPANSION OF THE SOLID AND THE LIQUID

Although the thermal expansion of the solid is best fitted by a quadratic equation (eq. 1), it can be approximated by a linear expression: vs(T) = 0.7343(11) + 0.0001426(46) T (r 2 = 0.9887) (4).

An average expansivity of the solid av,s of 1.94 ´ 10 -4 K -1 can be obtained by rewriting eq. 4 in the form of vs(T) = v0 ´ (1+av,s T). This solid expansivity is very close to the mean value for molecular organic solids of 2.21 ´ 10 -4 K -1 that has been reported previously. [START_REF] Gavezzotti | Molecular Aggregation. Structure Analysis and Molecular Simulation of Crystals and Liquids[END_REF][START_REF] Céolin | The topological pressure-temperature phase diagram of ritonavir, an extraordinary case of crystalline dimorphism[END_REF][START_REF] Rietveld | Phenomenology of crystalline polymorphism: overal monotropic behavior of the cardiotonic agent FK664 forms A and B[END_REF] The expansivity of liquid etifoxine is found to be 0.97 ´10 -3 K -1 obtained from eq. 2. This is smaller than the mean value of 1.20 ±0.25 ´10 -3 K -1 found previously for the expansivity of molten active pharmaceutical ingredients; [START_REF] Céolin | The topological pressure-temperature phase diagram of ritonavir, an extraordinary case of crystalline dimorphism[END_REF][START_REF] Rietveld | Phenomenology of crystalline polymorphism: overal monotropic behavior of the cardiotonic agent FK664 forms A and B[END_REF] however, it still falls within the range of experimental uncertainty of 0.25 ´10 -3 K -1 .

VOLUME CHANGE ON MELTING AND VOLUME DIFFERENCE AT THE GLASS TRANSITION

It has been previously reported that, in the case of molecular organic solids, the change in the specific volume on melting is about 11 ±3 %, [START_REF] Céolin | The topological pressure-temperature phase diagram of ritonavir, an extraordinary case of crystalline dimorphism[END_REF][START_REF] Rietveld | Phenomenology of crystalline polymorphism: overal monotropic behavior of the cardiotonic agent FK664 forms A and B[END_REF][START_REF] Barrio | Experimental and topological determination of the pressure temperature phase diagram of morniflumate, a pharmaceutical ingredient with anti-inflammatory properties[END_REF] i.e. slightly smaller than the 12 % value found previously by Goodman et al. [START_REF] Goodman | A note on the relationship between organic solid density and liquid density at the triple point[END_REF] Calculating the specific volumes of the solid and of the liquid using eqs. 1 and 2 at Tfus = 362.6 K, it is found that the volume change on melting is in the present case 0.0709 cm 3 g -1 , leading to the value of 1.090 ±0.010 for the vliq/vs ratio at Tfus, in fair agreement with the above-mentioned value.

At the glass transition, the metastable undercooled melt rigidifies, i.e. becomes as viscous as the crystalline solid. The glass transition temperature has been found at 297.2 K (10 K min -1 ). The specific volume of the melt at Tg can be calculated with eq. 2 and is found to be 0.8196 cm 3 g -1 , while that of the crystalline solid at this temperature is 0.7766 cm 3 g -1 from eq. 1. Thus, the ratio vglass/vs at Tg equals 1.055 ±0.010, i.e. the volume difference between the crystalline and the amorphous phase is approximately half that of the difference at the melting point. With this information, one can draw the temperature -(specific) volume diagram, shown in Figure 8, which is a partial projection of F(v,T), the Helmholtz function of the system, on a T-v plane, one of the four thermodynamically equivalent energy functions of the system. vglass/vs ratios have been found for other cases, which have been compiled in Table 3.

SLOPE OF THE SOLID-LIQUID EQUILIBRIUM IN THE PRESSURE-TEMPERATURE DIAGRAM

Using eq. 3, it is found that the slope of the melting equilibrium of racemic etifoxine at P = 0 MPa equals 3.29 ±0.06 MPa K -1 (Figure 5b). This slope can also be determined through the Clapeyron equation dP/dT = DfusH/(Tfus Dv) in which DfusH is the melting enthalpy (85.60 J g -1 ), Tfus the melting temperature (362.6 K), and Dv the volume change on melting (0.07094 cm 3 g -1 ). With these experimental values, the value of dP/dT is found to be 3.33 ±0.12 MPa K -1 , i.e. extremely close to the direct experimental value of 3.29 MPa K -1 , indicating that at least in the case of etifoxine, the Clapeyron equation is a good alternative for direct measurements to obtain the response of the system to pressure.

ISOBARIC THERMAL EXPANSION TENSOR FOR THE SOLID

The anisotropy of the intermolecular interactions can be accounted for by the isobaric thermal expansion tensor, which shows the influence of these interactions in the crystal on heating. [START_REF] Salud | Anisotropy of intermolecular interactions from the study of the thermal-expansion tensor[END_REF] The eigenvalues and the eigenvectors of the tensor specify the strongest and the weakest directions for the intermolecular interactions, commonly referred to as "hard" and "soft" directions, respectively. [START_REF] Salud | Anisotropy of intermolecular interactions from the study of the thermal-expansion tensor[END_REF] The lattice parameters as a function of temperature have been determined (see supplementary materials, Table S6) and fitted using the least-squares method. The coefficients of the related polynomial equations have been compiled in Table S11 in the supplementary materials, together with the reliability factor, defined as R=S(yoi -yci) 2 /yci 2 , where yoi and yci are the measured and calculated lattice constants, respectively.

The procedure to determine the eigenvalues and eigenvectors of the second-rank aij thermal expansion tensor has been detailed previously. [START_REF] Salud | Anisotropy of intermolecular interactions from the study of the thermal-expansion tensor[END_REF] For monoclinic symmetry, the tensor is fully defined by three eigenvalues ai (i = 1,2,3) and by an angle between the direction of one of the eigenvectors (a1 in the present case) and the crystallographic axis a, the a2 direction being parallel to the two-fold axis b. Figure 9 depicts the variation of the eigenvalues of the thermal-expansion tensor as a function of temperature as well as the 3D-tensor within the orthogonal frame of eigenvectors together with the crystallographic axes at 140 K. The tensor is rather anisotropic and this anisotropy increases with temperature. The thermal expansion within the ab plane is the highest ("soft" plane) while the lowest deformation (a3 direction) corresponding to a "hard direction" is found within the ac plane as a consequence of the intermolecular hydrogen bonding (N2-H•••N1).

CONCLUDING REMARKS

The crystal structure of racemic etifoxine has been solved at room temperature and thermal expansion studies in the range from 100 K to 340 K as well as differential scanning calorimetry did not reveal any crystalline polymorphism. However the crystal structure contains two independent molecules (Z' = 2) with different conformations, which implies a possibility for etifoxine to exhibit conformational polymorphism as previously defined by Bernstein and Hagler. [START_REF] Bernstein | Conformational polymorphism. The influence of crystalstructure on molecular-conformation[END_REF] It has been shown that the thermal expansion of etifoxine is very similar to that of small organic molecules in general, for the solid as well as for the liquid. As far as the volume change on melting is concerned, it has been found that, again in the present case, it agrees with the average value of 11% within an error of less than 3%. In addition, the volume difference between the crystal and the metastable liquid at the temperature of the glass transition is found to be about 6 %, in close accordance with previously found data.

Further case studies are still needed before one can conclude that these volume changes for molecular organic compounds are more or less independent of the chemical composition and thus 'statistically' and possibly in a deeper sense universal.

Figure 1 .

 1 Figure 1. Chemical formula of racemic etifoxine. C17H17ClN2O, M = 300.786 g mol -1 . IUPAC name: 6-chloro-N-ethyl-4-methyl-4-phenyl-3,1-benzoxazin-2-amine. The stereogenic center is indicated by an asterisk.

Figure 2 .

 2 Figure 2. Optical microscopy photograph of single crystals of racemic etifoxine, obtained by slow evaporation of a solution in n-hexane at room temperature. The biggest crystals measure 1 to 3 mm in length.

  ) Å, b = 17.674(2) Å, c = 20.88(3) Å, b = 98.86(1)°, and Vcell = 3095.8(

Figure 3 .

 3 Figure 3. Molecular structure of R-etifoxine with atom identification. The hydrogen atoms are labelled with the same numbers as the atoms to which they are linked. When more than one H is linked to a C-atom, these H-atoms are labelled with supplementary letters A, B and C. The presented molecule is 2(R) in the racemate and the same labelling has been applied to molecule 1(R). The stereogenic center is atom C1.

Figure 4

 4 contains typical DSC curves, one for the crystalline powder and one for the glass.

Figure 4 . 3 )Figure 5 .

 435 Figure 4. Differential scanning calorimetry curves of racemic monoclinic etifoxine obtained at 10 K min -1 . (a) First heating of the crystalline commercial product, Tm: melting temperature, (b) second heating after quenching the melt to 213 K in which a glass transition (Tg: glass transition temperature) can be observed.

Figure 6 .

 6 Figure 6. Monoclinic unit-cell of racemic etifoxine with the two independent molecules 1 (red) and 2 (blue).

Figure 7 .

 7 Figure 7. Superposition showing the difference in conformation of molecules 1 (red) and 2 (blue)

Figure 8 .

 8 Figure 8. Specific volumes of solid (S) and liquid (L) etifoxine as a function of temperature with extrapolation to the Kauzmann temperature Tk = 204.6 K using eqs. 1 and 2.

Figure 9 .

 9 Figure 9. ai eigenvalues of the thermal-expansion tensor as a function of temperature for the P21/n monoclinic phase of etifoxine with the a2 eigenvector parallel to the two-fold crystallographic axis b, as evidenced in the tensor representation at 140 K in the inset (full length scale of the ai eigenvectors corresponds to 10 -4 K -1 ).

Table 1 . Crystal-and structure-refinement data for racemic etifoxine a

 1

	Identification code / Empirical formula	etifoxine / C17H17ClN2O
	Formula weight	300.786 g mol -1
	Temperature	293(2) K
	Wavelength	1.5418 Å
	Crystal system (Space group)	Monoclinic (P 21/n)
		a = 8.489(2) Å,
	Unit-cell dimensions	b = 17.674(2) Å,
		c = 20.883(3) Å,
		b = 98.860(10)°
	Cell volume	3095.8(9) Å 3
	Z, Z'	8, 2
	Density (calculated)	1.291 g/cm 3
	Absorption coefficient	2.178 mm -1
	F(000)	1264
	Crystal size	0.550 x 0.200 x 0.100 mm 3
	Theta range for data collection	3.292 to 64.944°.
	Limiting indices	0 ≤ h ≤ 9, 0 ≤ k ≤ 20, -24 ≤ l ≤ 24
	Reflections collected / independent	5239 / 5239 [R(int) = 0.0162]
	Completeness to theta = 64.944°	99.9 %
	Absorption correction	Psi-scan
	Max. and min. transmission	0.9971 and 0.8015
	Refinement method	Full-matrix least-squares on F 2
	Data / restraints / parameters	5239 / 0 / 382
	Goodness-of-fit on F 2	1.131
	Final R indices [I>2sigma(I)]	R1 = 0.0488, wR2 = 0.1272
	R indices (all data)	R1 = 0.0589, wR2 = 0.1347
	Extinction coefficient	0.0088(4)
	Largest diff. peak and hole	0.3304 and -0.348 e.Å -3
	a esd's in parentheses

Table 2 . Atom coordinates and equivalent isotropic displacement parameters U(eq) for racemic etifoxine a

 2

	Atom	x	y	z	U(eq) c
	Identification b	(´ 10 4 )	(´ 10 4 )	(´ 10 4 )	(Å 2 ´ 10 3 )
	Cl1_1	6465(1)	-3857(1)	-2(1)	70(1)
	O1_1	10100(2)	-992(1)	1252(1)	46(1)
	N1_1	7329(2)	-788(1)	1138(1)	43(1)
	N2_1	9235(2)	147(1)	1445(1)	51(1)
	C1_1	9944(2)	-1798(1)	1358(1)	45(1)
	C2_1	8401(2)	-2046(1)	953(1)	42(1)
	C3_1	7130(2)	-1531(1)	902(1)	40(1)
	C4_1	8797(2)	-558(1)	1281(1)	42(1)
	C5_1	8191(3)	-2753(1)	667(1)	50(1)
	C6_1	6699(3)	-2964(1)	356(1)	51(1)
	C7_1	5407(3)	-2484(1)	332(1)	51(1)
	C8_1	5632(3)	-1769(1)	600(1)	48(1)
	C9_1	9901(2)	-1946(1)	2075(1)	47(1)
	C10_1	10259(3)	-1390(1)	2539(1)	60(1)
	C11_1	10199(4)	-1536(2)	3183(1)	75(1)
	C12_1	9808(4)	-2247(2)	3373(2)	85(1)
	C13_1	9513(4)	-2808(2)	2921(2)	88(1)
	C14_1	9546(4)	-2664(2)	2276(1)	71(1)
	C15_1	8156(3)	784(1)	1421(1)	55(1)
	C16_1	7782(5)	1125(2)	776(2)	105(1)
	C17_1	11436(3)	-2134(2)	1149(1)	62(1)
	Cl1_2	3065(1)	1044(1)	4949(1)	70(1)
	O1_2	5459(2)	78(1)	2363(1)	48(1)
	N1_2	2674(2)	253(1)	2174(1)	42(1)
	N2_2	4203(3)	28(1)	1358(1)	53(1)
	C1_2	5449(2)	-179(1)	3024(1)	44(1)
	C2_2	4151(2)	258(1)	3282(1)	41(1)
	C3_2	2779(2)	412(1)	2835(1)	39(1)
	C4_2	4022(2)	113(1)	1975(1)	43(1)
	C5_2	4233(3)	454(1)	3928(1)	46(1)
	C6_2	2917(3)	780(1)	4137(1)	49(1)
	C7_2	1525(3)	904(1)	3713(1)	50(1)
	C8_2	1458(3)	724(1)	3069(1)	46(1)
	C9_2	5090(3)	-1030(1)	3011(1)	46(1)
	C10_2	5444(3)	-1480(2)	2514(1)	66(1)
	C11_2	5062(4)	-2243(2)	2495(2)	79(1)
	C12_2	4337(4)	-2561(2)	2976(2)	73(1)
	C13_2	4047(4)	-2124(2)	3483(2)	73(1)
	C14_2	4418(3)	-1361(1)	3501(1)	61(1)
	C15_2	2978(3)	200(2)	807(1)	58(1)
	C16_2	2579(4)	1026(2)	744(2)	81(1)
	C17_2	7132(3)	-9(2)	3364(1)	58(1)
	a esd's in parentheses
	b

Table 3 . Experimental volume changes for molecular compounds and pharmaceuticals at their melting point and glass transition temperature

 3

	compound	vL/vI at Tfus	Tfus/K	vL/vI at Tg	Tg /K	Tg/Tfus	Reference
	paracetamol	1.15	442.3	1.07	298	0.673	20
	prilocaine	1.13	311.5	1.07	218	0.700	21
	rimonabant	1.11	429.2	1.04	350	0.820	22
	biclotymol	1.13	400.5	1.05	294	0.734	23
	ternidazole	1.11	333.0	1.07	235	0.706	24
	morniflumate	1.12	348.1	1.06	249	0.715	18
	etifoxine	1.09	362.4	1.055	297.2	0.820	This work
	Mean	1.12(2)		1.06(1)

Funding: This work was supported by the MINECO, Project No. FIS2017-82625-P, and AGAUR, DGU Project No. 2017SGR-42