# Overt and hidden polymorphism in the binary system involving the Z- and E- isomers of broparestrol

Siro Toscani, Hassan Allouchi, René Ceolin, Laia Villalobos, Maria Barrio, Josep-Lluis Tamarit, Ivo Rietveld

► To cite this version:

Siro Toscani, Hassan Allouchi, René Ceolin, Laia Villalobos, Maria Barrio, et al.. Overt and hidden polymorphism in the binary system involving the Z- and E- isomers of broparestrol. International Journal of Pharmaceutics, 2025, 669, pp.125060. 10.1016/j.ijpharm.2024.125060. hal-04865623

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# Overt and hidden polymorphism in the binary system involving the Z- and E-isomers of broparestrol

Siro Toscani<sup>a</sup>, Hassan Allouchi<sup>b</sup>, René Ceolin<sup>c</sup>, Laia Villalobos<sup>c</sup>, Maria Barrio<sup>c</sup>,
Josep-Lluis Tamarit<sup>c</sup>, Ivo B. Rietveld<sup>d,*</sup>

<figure><img src="image_3.png" /></figure>

## ARTICLE INFO

### Keywords:

Broparestrol

Polymorphism

Stereoisomers

Phase behaviour

Binary mixtures

Thermodynamics

Crystal structure

## ABSTRACT

Broparestrol has been used as a drug to treat acne in the form of a mixture of its two stereoisomers. Although it has been withdrawn from the market, the binary system is rich in polymorphism and understanding the phase behaviour of the binary system involving the *E*- and *Z*-isomers is challenging. Physical mixtures do not immediately give rise to equilibrium phase behaviour, whereas recrystallization often leads to metastable phases and the appearance of stable phases can take years. A new polymorph of *E*-broparestrol has been found crystallizing in a monoclinic unit cell, space group *P*2₁/c, with lattice parameters *a* = 5.6079(4) Å, *b* = 16.1206(10) Å, *c* = 20.250 (1) Å, *β* = 100.569(4)°, *V*cell = 1799.6(2) Å³, and *Z* = 4. This polymorph, *I*<sub>E</sub>, is stable at high temperatures, whereas the published form, *II*<sub>E</sub>, is stable at room temperature. In the case of *Z*-broparestrol polymorphism has been observed too; however, it has so far only occurred within the binary phase diagram, and it has not been possible to isolate the new polymorph of *Z*-broparestrol, *II*<sub>Z</sub>. Through the phase behaviour in the binary system, it could be determined that the new *Z* polymorph, *II*<sub>Z</sub>, behaves monotropically in relation to the known triclinic polymorph of the *Z*-isomer, *I*<sub>Z</sub>. Nothing is known about its structure, and it is therefore not clear yet whether *II*<sub>Z</sub> may possess a stable domain under pressure. A stable temperature-composition phase diagram of the binary system containing *E*- and *Z*-broparestrol is proposed.

## 1. Introduction

To control the physical-chemical properties and the pharmaceutical activity of active pharmaceutical ingredients (APIs), binary or even higher multicomponent systems are important. Such systems facilitate increasing the solubility and bioavailability of the APIs in the system through cocrystals (Bolla and Nangia, 2016; Qiao et al., 2011) or glass-forming mixtures, (Kawakami et al., 2014; Kissi et al., 2019; Valenti et al., 2023; Jain et al., 2015; Nyamba et al., 2021) for example. On the other hand, in the case of enantiomers, binary systems may need to be separated into single pure antipodes because of a difference in pharmaceutical activity or undesirable side effects. (Johnston et al., 2023; Mutiti et al., 2021) In such cases, the relative stability of the equimolar composition as racemate or conglomerate is relevant, as only

conglomerates can be easily separated. (Jacques et al., 1994; Coquerel, 2006; Rietveld et al., 2012) From a more fundamental point of view, the study of multicomponent systems can reveal the existence of metastable polymorphs that do not crystallize easily or not at all in unary systems. (Haget et al., 1999; Brandel et al., 2013) In such cases, through extrapolation of two-phase equilibria in a multicomponent system, thermodynamic properties that otherwise cannot be obtained can be inferred. (Barrio et al., 2002; Pardo et al., 2001; Pardo et al., 2005).

The synthesis of broparestrol, 1-(2-bromo-1,2-diphenylethenyl)-4-ethylbenzene (C<sub>22</sub>H<sub>19</sub>Br, *M* = 363.29 g·mol<sup>-1</sup>, chemical formulas in Fig. 1) was first reported by Buu Hoï in 1946 and later by Al-Hassan in 1987. (Buu Hoï, 1946; Al-Hassan, 1987; Al-Hassan, 1987) Broparestrol possesses two isomers *E* and *Z* as indicated in Fig. 1. The *Z/E* ≈ 40/60 mixture has been used in dermatology as the active component of

<footnote><sup>a</sup> Institut des Sciences Chimiques de Rennes – UMR 6226, Faculté des Sciences, Université de Rennes 1, Batiment 10B. 263, Avenue du Général Leclerc 35042, Rennes, France</footnote>

<footnote><sup>b</sup> EA 7502 SIMBA, Laboratoire de Chimie Physique, Faculté de Pharmacie, Université de Tours 31, Avenue Monge 37200, Tours, France</footnote>

<footnote><sup>c</sup> Grup de Caracterització de Materials, Departament de Física and Barcelona Research Center in Multiscale Science and Engineering, Universitat Politècnica de Catalunya, EEBE, Campus Diagonal-Besòs, Av. Eduard Maristany 10-14 08019, Barcelona, Catalunya, Spain</footnote>

<footnote><sup>d</sup> Laboratoire SMS, UR 3233, Université de Rouen Normandie, Normandie Université, F76000, Rouen, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: ivo.rietveld@univ-rouen.fr (I.B. Rietveld).</footnote>
<figure><img src="image_4.png" /><figcaption>**Fig. 1.** Molecular structures of the Z-(cis) and E-(trans) isomers of broparestrol (C22H19Br, M = 363.31 g/mol). The unsubstituted phenyl rings (pink surfaces) are located on the same side of the (red) C = C double bond in the Z-isomer and on the opposite side of the C = C bond in the E-isomer. The Z- and E-isomers have been drawn using the SAXGED and BEPPET files of the Cambridge Structural Database, respectively.</figcaption></figure>

ointments and solutions against acne. The isomers were isolated by fractional crystallization (Laroche, 1978) but never marketed, although the *E*-isomer was shown to inhibit prolactin-induced mammary cancer. (Laroche, 1978; Drosdowsky et al., 1980) Broparestrol has eventually been withdrawn from the European market.

The binary system formed by *E*- and *Z*-broparestrol mixtures is investigated in the current paper for two reasons. First, it is an interesting example to demonstrate the influence of metastable polymorphs on binary phase equilibria. Secondly, it appears that the isomer mixtures facilitate the appearance and possible stabilization of metastable polymorphs.

This paper contains two parts. The first part demonstrates and characterizes the dimorphism of the *E*-isomer of broparestrol, and the second part is devoted to the phase equilibria in the binary *T*-x phase diagram involving the two isomers. Three partially metastable phase diagrams are found with which a stable phase diagram is constructed. Moreover, the existence of a metastable polymorph of the *Z*-isomer is demonstrated.

Two crystal structures of broparestrol have been previously determined: *E*- and *Z*-broparestrol have been found to crystallize in the monoclinic system, space group *P*2₁/c, (Fornies-Marquina et al., 1972) and the triclinic system, space group *P*-1, (Rodier et al., 1989) for form *II*<sub>E</sub> and form *I*<sub>Z</sub>, respectively. In both structures, molecules are held together by van der Waals interactions and, at room temperature, their specific volumes are virtually the same: 441.1 Å³ and 441.6 Å³ per molecule for the *E*- and *Z*-isomers, respectively.

## 2. Materials and methods

### 2.1. Broparestrol

Pure form $II_E$ and form $I_Z$ of broparestrol isomers (purities > 99 %) were supplied by Devimy Laboratory (France) and used as such after X-ray diffraction showed experimental patterns in fair agreement with the ones calculated from the crystal structures present in the Cambridge Crystallographic Database (CSD): BEPPET (E-isomer) and SAXGET (Z-isomer) (Figure S1 in the Supplementary Materials).

### 2.2. High-resolution powder X-ray diffraction

Powder X-ray diffraction (PXRD) patterns have been obtained in transmission mode with two high-resolution diffractometers from INEL (France) equipped with position sensitive detectors CPS120 in the Debye-Scherrer geometry. Monochromatic Cu-Kα₁ (λ = 1.54056 Å)

radiation was selected by means of a focusing incident-beam germanium monochromator. Samples were introduced in 0.5 mm-diameter Linde-mann capillaries, which were rotated perpendicularly to the X-ray beam during the data acquisition to improve the averaging over the crystallite orientations. Cubic Na₂Ca₃Al₂F₄ was used for external calibration.

Long acquisitions were carried out at 293 K, while measurements as a function of temperature were carried out using a liquid nitrogen 700 series Cryostream Cooler from Oxford Cryosystems. 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 130 K up to the melting points. The PEAKOC application from the DIFFRACTINEL software was used for the calibration as well as for the peak position determinations after pseudo-Voigt fittings. Lattice parameters were refined using TOPAS-Academic. (Coelho, 2007; Coelho, 2018).

### 2.3. Structure solution from powder diffraction

For structure solution of a new *E*-broparestrol polymorph, form $I_E$, with a pattern obtained at 293 K, the programs *DASH* (David et al., 2006) and *TOPAS-Academic* (Coelho, 2007; Coelho, 2018) were employed, and the powder pattern was truncated to 29.6° in 2θ (Cu Kα₁), corresponding to a real-space resolution of 3.01 Å. The background was subtracted with a Bayesian high-pass filter. (David and Sivia, 2001) Peak positions for indexing were obtained by fitting with an asymmetry-corrected pseudo-Voigt function. (Finger et al., 1994; Thompson et al., 1987) 21 peaks were indexed with the program *DIC-VOL*91. (Boultif and Louër, 1991) This did not lead to any promising unit cell. With TOPAS, (Coelho, 2003) several different settings of a monoclinic unit cell (P2₁) with a volume of 1802 Å³ were obtained with the highest probability, similar to the volume of the known structure (BEPPET). Pawley refinement was carried out with DASH to extract integrated intensities and their correlations, from which the space group was determined using Bayesian statistical analysis. (Markvardsen et al., 2001) P2₁/c was returned as the most probable space group. It was the space group with the highest symmetry and the other known structure of *E*-broparestrol (BEPPET) has this space group too. (Fornies-Marquina et al., 1972) It resulted in a Pawley χ² of 17.88. The high value for the Pawley χ² may be due to phase impurity. Simulated annealing was used to solve the crystal structure from the powder pattern in direct space. The starting molecular geometry was taken from the published polymorph from the CSD (reference code BEPPET). (Fornies-Marquina et al., 1972) This geometry was then optimized using the COMPASS forcefield (v2.8) in the Materials Studio Forcite Geometry Optimization module with the extrafine setting and Ewald summation. In 30 simulated annealing runs, the same crystal structure was found 30 times. The profile χ² of the best solution was 67.66, which is less than four times the Pawley χ²; this is a good indication that the correct solution has been found.

For the Rietveld refinement, data out to 75 °2θ were used, which corresponds to 1.27 Å real-space resolution. The Rietveld refinement was carried out with *TOPAS-Academic*. (Coelho, 2007; Coelho, 2018) Bond lengths, bond angles and planar groups were subjected to suitable restraints, including bonds to H atoms. A global $B_{iso}$ was refined for all non-hydrogen atoms, with the $B_{iso}$ of the hydrogen atoms constrained at 1.2 times the value of the global $B_{iso}$. The molecular geometry was checked with *Mogul*, (Bruno et al., 2004) which compares each bond length and bond angle to corresponding distributions from single-crystal data. A final optimization of the molecule was carried out with the COMPASS (v2.8) force field. A fit of the powder data is provided in Figure S2 in the Supplementary Materials.

Supplementary crystallographic data can be found in the CCDC, deposition number 2393322, and obtained free of charge from the Cambridge Crystallographic Data Centre via https://www.ccdc.cam.ac.uk/structures/.
## 2.4. Differential scanning calorimetry

### 2.4.1. Equipment

Differential scanning calorimetry (DSC) experiments have been performed with the DSC-cell of a TA2000 thermal analyzer from TA-Instruments (USA), calibrated using the temperature and heat of fusion of indium.

### 2.4.2. Study of the binary system involving the Z- and E-isomers of broparestrol

To explore the binary system involving the two isomers, physical mixtures in different ratios, weighed using a balance sensitive to 0.01 mg, were introduced in aluminum pans with which three series of DSC experiments were performed:

(1) First, after a one-week annealing at 323 K, the samples, $II_E$ and $I_Z$, were heated at a rate of 5 K min$^{-1}$ under a nitrogen flux from room temperature up to complete melting, leading to a first temperature-composition ($T-x$) phase diagram exhibiting a eutectic equilibrium $\varepsilon_1$ with an onset temperature at 363 K.

(2) Second, after cooling to 298 K and storing the samples for three years at room temperature, they were reheated at the same rate, leading to a second $T-x$ phase diagram exhibiting the eutectic equilibrium $\varepsilon_2$ with an onset temperature at 358 K.

(3) A third series of experiments was carried out with mixtures of forms $II_E$ and $I_Z$ that were first molten and subsequently cooled to room temperature. Soon after recrystallization had taken place, they were reheated, leading to a third $T-x$ phase diagram exhibiting the eutectic equilibrium $\varepsilon_3$ with an onset at 340 K. Moreover, some specimens stored for three years at room temperature (series 2) also exhibited the same eutectic equilibrium $\varepsilon_3$.

The temperatures of the invariant (eutexy) and monovariant (liq-uidus) equilibria were taken at the onset and the maximum of the related DSC peaks, respectively.

# 3. Results and discussion

## 3.1. Dimorphism of E-broparestrol

### 3.1.1. Calorimetric studies of E-broparestrol

DSC experiments were performed using the as-received form $II_E$, which was found to melt at $T_{fus}$, $II_E = 385.4(1.0)$ K (onset) with a melting enthalpy of $\Delta_{fus}H_{II_E} = +90.8(1.8)$ J/g. By slowly cooling the melt, recrystallization was found to occur at $T_{cryst} = 360.3$ K (onset) with a crystallization enthalpy of $\Delta_{cryst}H = -66.6$ J/g. Heating again, the melting temperature was found to be 386.7(1.0) K, which is close to the value obtained previously; however, the value of the melting enthalpy

was + 79.4(1.6) J/g, i. e. smaller than the initial melting enthalpy by 11.4 J/g (see Fig. 2A).

Because these results could be related to dimorphism, a powder of form $II_E$ was introduced in a Lindemann capillary for an examination by powder X-ray diffraction. After heating the sample up to fusion and slow cooling to room temperature, recrystallization occurred within a few minutes. The X-ray pattern, obtained after about 1 h of data collection, was different from that of the as-received form $II_E$, thus structurally corroborating the existence of dimorphism for E-broparestrol (Fig. 2B). However, further X-ray diffraction experiments performed 24 h later showed that the new phase slowly reverted to the known phase $II_E$ upon standing at room temperature.

In a different experiment, the melt is reheated from the glassy state after quenching it at 213 K, which results in the DSC curve presented in Fig. 3. In the resulting DSC curve, first, a glass transition at $T_g = 264$ K (midpoint) can be observed. It is followed by an exothermic effect 'a' with an onset at 300.5 K indicating a recrystallization process and subsequently by a broad endothermic peak 'b' starting at about 310 K ($\Delta_{a+b}H = 12.8$ J/g). Finally, a double melting peak 'c1 + c2' is observed with onsets at 384.4 K and 386 K, respectively, corresponding to a heat of fusion of $\Delta_{c1+c2}H = 84.5$ J/g, i.e. a value ranging between those of the known $II_E$ form and the new $I_E$. Moreover, the glass transition temperature obeys the empirical Tammann rule according to which the ratio

<figure><img src="image_5.png" /><figcaption>Fig. 3. DSC curve recorded on reheating from the glass phase obtained after quenching a molten sample of E-broparestrol at 213 K at a heating rate of 5 K min$^{-1}$ ($T_g$ = glass transition).</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**Fig. 2.** Confirmation of the dimorphism of E-broparestrol. (A) DSC curves (a) obtained on heating an as-received monoclinic $II_E$ form (4.71 mg) of E-broparestrol at 5 K min$^{-1}$ and (b) obtained on reheating the same sample at the same rate after recrystallisation on slow cooling. (B) Room temperature X-ray diffraction patterns for (a) the as-received form $II_E$ (BEPPET), and (b) the new phase, form $I_E$, recrystallized while slowly cooling the melt to room temperature.</figcaption></figure>
$T_g/T_{fus}$ is in the order of 2/3. In the present case, the ratio equals 0.683.

To verify the hypothesis of a possible recrystallization of a mixture of phases that could explain the double melting peak in Fig. 3, the following X-ray diffraction experiment was performed several times: form $II_E$ in a capillary was molten in situ then quickly cooled to room temperature and, when recrystallization started, the recorded X-ray patterns demonstrated the existence of a mixture of two phases, the known form $II_E$ and the new form $I_E$ in various ratios (Figure S3 in the Supplementary Materials). Because the melting temperature of the new phase was found to be higher, this phase was labelled ‘form $I_E$’ and the known monoclinic phase ‘form $II_E$’. From these experiments, it was also concluded that on slow cooling the melt crystallizes into form $I_E$, while on quenching and reheating the glass phase, mixtures of the two forms in various ratios are obtained.

To investigate whether these polymorphs are enantiotropically or monotropically related, the temperature of transition from form $II_E$ to form $I_E$ was calculated with the formula proposed by Yu, (Yu, 1995) neglecting the contribution of the specific heats:

$$T_{II \to I} = \frac{\Delta_{fus}H_I - \Delta_{fus}H_{II}}{\frac{\Delta_{fus}H_I}{T_{fus,I}} - \frac{\Delta_{fus}H_{II}}{T_{fus,II}}} \quad (1)$$

With $\Delta_{fus}H_{I-E} = 79.4$ J/g, $\Delta_{fus}H_{II-E} = 90.8$ J/g, $T_{fus,I-E} = 386.7$ K and $T_{fus,II-E} = 385.4$ K, one obtains $T_{II-E \to I-E} = 376.6$ K with $\Delta_{II-E \to I-E}H = +11.4$ J/g deduced from Hess’ law. Using the Clausius-Clapeyron equation, the same result of 376.6 K is found for the temperature of the $I_E-\overline{II_E}$ vapour triple point (Table S1 in the Supplementary Materials) together with an estimate of the vapour pressure.

It can therefore be concluded that the $II_E \to I_E$ transition occurs endothermically on heating below the melting temperature, thus indicating that the two forms are enantiotropically related: form $I_E$ being more stable at high temperature and form $II_E$ being more stable at low temperature.

### 3.1.2. Crystal structure of the E-broparestrol high-temperature form $I_E$

The Rietveld refinement of the high-resolution powder X-ray diffraction pattern obtained at 293 K progressed smoothly and produced a good fit with $\chi^2 = 4.322$, $R_p = 20.413$, $R_{wp} = 22.321$ (values after background correction), $R_p = 6.300$ and $R_{wp} = 8.786$ (values before background subtraction). $B_{iso}$ refined to $11.3(3)$ Å$^2$. Additional refinement information can be found in Table S2 in the Supplementary Materials.

The crystal structure of form $I_E$ was found to be monoclinic, space group $P2_1/c$, with lattice parameters $a = 5.6079(4)$ Å, $b = 16.1206(10)$ Å, $c = 20.250(1)$ Å, $\beta = 100.569(4)°$, $V_{cell} = 1799.6(2)$ Å$^3$, and $Z = 4$. A projection of the unit-cell on the bc plane is shown in Figure S4a and the atom numbering in Figure S4b. Atom coordinates and atomic displacement parameters have been compiled in Table S3 in the Supplementary Materials. Bond lengths, bond angles, and torsion angles can be found in Tables S4, S5 and S6, respectively.

The lattice parameters of the low-temperature form $II_E$ were determined by Rietveld refinement using a PXRD pattern recorded at the same temperature of 293 K with the same diffractometer as used for form $I_E$. Starting from the previously reported structure, (Fornies-Marquina et al., 1972) results were as follows: $a = 8.5774(6)$ Å, $b = 35.819$ (3) Å, $c = 5.7545(4)$ Å, $\beta = 86.151(6)°$, $V_{cell} = 1764.0(2)$ Å$^3$, and $Z = 4$. Comparing the cell volumes of forms $I_E$ and $II_E$ demonstrates that the low-temperature form $II_E$ has a higher density than form $I_E$. In both cases, intermolecular interactions consist mainly of van der Waals interactions, while the polymorphism is the result of conformational changes, as shown in Fig. 4, in which the substituted phenyl-rings of the two forms are superimposed.

### 3.1.3. Thermal expansion of the E-broparestrol polymorphs and of the triclinic Z-broparestrol isomer

Lattice parameters, volumes of the asymmetric unit, and specific

<figure><img src="image_7.png" /><figcaption>Fig. 4. Overlay of the E-broparestrol molecules of form $I_E$ (blue) and form $II_E$ (grey) with C-Br bonds in pink. The substituted central phenyl rings are superimposed.</figcaption></figure>

volumes of E-broparestrol forms I and II, together with those of the triclinic Z-broparestrol as a function of temperature have been compiled in Tables S7, S8 and S9 in the Supplementary Materials, respectively.

The curves of the specific volumes of the E-broparestrol polymorphs as a function of temperature are almost parallel (see Fig. 5) and can be described by quadratic functions:

$$v_{I-E}/\text{cm}^3\text{g}^{-1} = 0.7149 + 5.610 \times 10^{-5} \times T/K + 1.739 \times 10^{-7} \times (T/K)^2 (r^2 = 0.999) \quad (2)$$

<figure><img src="image_8.png" /><figcaption>Fig. 5. Partial projection of the Helmholtz function on the v-T plane presenting the temperature dependence of the specific volumes of the condensed phases of E-broparestrol in equilibrium with their vapour. Blue: form $I_E$, red: form $II_E$, dark green: liquid, vertical bars: volume changes, dashed curves: metastable, solid curves: stable. $T_K$: Kauzmann temperature (216 K). Inset: detail of the volume changes between 370 K and 390 K.</figcaption></figure>
$$v_{II-E}/cm^3g^{-1} = 0.6953 + 6.626 \times 10^{-5} \times T/K + 1.643 \times 10^{-7} \times (T/K)^2(r^2 = 0.999) \quad (3)$$

They can also be fitted by straight lines:

$$v_{I-E}/cm^3g^{-1} = 0.7029 + 0.0001512 \times T/K(r^2 = 0.993)$$

$$v_{II-E}/cm^3g^{-1} = 0.6846 + 0.0001537 \times T/K(r^2 = 0.993)$$

Using equations (2)' and 3', the expansivities of forms $I_E$ and $II_E$ are: $\alpha_{V,I-E} = 2.15 \times 10^{-4} K^{-1}$ and $\alpha_{V,II-E} = 2.25 \times 10^{-4} K^{-1}$, close to the value of about $2 \times 10^{-4} K^{-1}$ usually found for molecular solids. (Céolin and Rietveld, 2015; Rietveld and Céolin, 2015; Gavezzotti, 2013).

### 3.1.4. Topological pressure–temperature phase diagram accounting for the dimorphism of E-broparestrol

According to the Le Chatelier principle, the $II_E \to I_E$ transition, which occurs endothermically on heating, should be favored by a temperature increase. In addition, since the specific volume of form $II_E$ is smaller than that of form $I_E$, the $I_E \to II_E$ transition should be favored by an increase of pressure. In other words, the slope $dP/dT$ of the $I_E-II_E$ equilibrium should be positive with form $I_E$ stable at high temperature and low pressure, while form $II_E$ is the low-temperature, high-pressure phase. Two cases among the four pressure–temperature phase diagrams formerly drawn by Bakhuis-Roozeboom (Bakhuis Roozeboom, 1901) can accommodate such phase behaviour leading to two possible topological phase diagrams: either the $I_E$-liquid curve is steeper than the $II_E-I_E$ curve (Roozeboom's case I, in which monotropic behavior replaces enantiotropic behavior on increasing pressure), or the $II_E-I_E$ curve is steeper than the $I_E$-liquid curve (Roozeboom's case 2, which corresponds to an overall enantiotropic behavior). In the latter case, both polymorphs exhibit their own stable phase region irrespective of the pressure.

To determine which case is applicable for the dimorphism of E-broparestrol, a topological P-T phase diagram is constructed using the Clapeyron equation:

$$\frac{dP}{dT} = \frac{\Delta H}{T \Delta \nu} \quad (4)$$

and the following assumptions:

(1) The expansivity, $\alpha_v$, of a molecular liquid is in the order of $1.2 \times 10^{-3} K^{-1}$. (Céolin and Rietveld, 2015; Rietveld and Céolin, 2015; Gavezzotti, 2013).

(2) Molecular liquids expand or shrink linearly: $v(T) = v_0 (1 + \alpha_v \times T)$, with $T$ in K, near the melting temperature, $T_{fus}$, and below while cooling the metastable liquid.

(3) The ratio $v_{liquid}/v_{cryst}$ is 1.11 at the melting temperature, approximating the solid–liquid-vapour triple point temperature. (Céolin and Rietveld, 2015; Rietveld and Céolin, 2015; Barrio et al., 2019; Goodman et al., 2004).

(4) The ratio $v_{glass}/v_{cryst}$ is 1.06 at the glass transition temperature $T_g$. (Barrio et al., 2019).

Using Eq. (2), the specific volume of form $I_E$ at $T_{fus,I-E} = 386.7$ K is $v_{I-E} = 0.7626 cm^3 g^{-1}$. With assumption (3), the specific volume of the liquid at the melting point is found to be $v_{liq} = 0.8465 cm^3 g^{-1}$ leading to a volume change of $v_{liq} - v_{I-E} = 0.0839 cm^3 g^{-1}$ at $T_{fus,I-E}$.

Using Eq. (3), the specific volume of form $II_E$ is found to be 0.7242 $cm^3 g^{-1}$ at $T_g = 264$ K, the glass transition temperature, where form $II_E$ is stable. With assumption (4), the specific volume of the metastable liquid at $T_g$ is found to be 0.7677 $cm^3 g^{-1}$.

With these two values of the specific volume of the liquid and assumption (2), linear expansion, the dependence of the specific volume of the liquid on the temperature is found to be:

$$v_{liq}/cm^3g^{-1} = 0.598 + 0.000642 \times T/K \quad (5)$$

which leads, for the liquid, to an expansivity $\alpha_v, \text{liq}$ of $1.07 \times 10^{-3} K^{-1}$, which is reasonably close to the generally admitted value of about $1.2 \times 10^{-3} K^{-1}$ (assumption (1)).

Because the specific volumes are determined for conditions under which the condensed phases are in equilibrium with the vapour phase, it can be inferred that Fig. 5 is a partial projection of the Helmholtz function of the free energies of the condensed phases of E-broparestrol in equilibrium with the vapour on the T-v plane. With the volume changes at the phase equilibrium temperatures from this projection and the Clapeyron equation (Eq. (4)), the Helmholtz projection can be changed into a P-T projection of the Gibbs function.

The initial value of the $dP/dT$ slope of the $I_E$-liquid equilibrium curve is found to be 2.45 MPa/K. Similarly, the initial value of the slope for the melting equilibrium of $II_E$ is 2.35 MPa/K. Using Eqs. (2) and (3) to determine the volume change associated with the $II_E \to I_E$ transition at 376.6 K, one obtains: $v_{I-E} - v_{II-E} = 0.7607 - 0.7435 = 0.0172 cm^3 g^{-1}$. Incorporating this value into the Clapeyron equation (Eq. (4)) together with the transition enthalpy $\Delta H = 11.4$ J/g and the transition temperature, leads to $dP/dT = 1.76$ MPa/K for the slope of the II-I equilibrium curve.

Because the vapour pressures at triple points $I_E$-liquid-vapour, $II_E$-liquid-vapour and $I_E-II_E$-vapour are very small, their values can be taken equal to 0 MPa. It follows that the equations for the $I_E$-liquid, $II_E$-liquid and $I_E-II_E$ equilibria, which are usually straight over for several hundreds of MPa, are:

$$I_E - liquid : P/MPa = 2.45 \times T/K - 947 \quad (6)$$

$$II_E - liquid : P/MPa = 2.35 \times T/K - 904 \quad (7)$$

$$I_E - II_E : P/MPa = 1.78 \times T/K - 664 \quad (8)$$

Setting Eqs. (6) and (7) equal, leads to the coordinates of the $I_E-II_E$-liquid triple point, since it is the point at which the $I_E$-liquid and $II_E$-liquid equilibrium curves cross. The values are $T(I_E-II_E$-liquid) = 417$ K and $P(I_E-II_E$-liquid) = 73$ MPa.

Since a third equilibrium curve, $II_E-I_E$, passes through triple point $I_E-II_E$-liquid, the $P = f(T)$ equation for this curve can be determined using the coordinates of triple points $I_E-II_E$-liquid above and $I_E-II_E$-vapour ($T = 376.6$ K, $P \approx 0$). One obtains $P_{I-II}/MPa = 1.83 \times T/K - 688/MPa$, i.e. an equation close to Eq. (8). Although these calculations have been carried out using approximations, it is clear that $\Delta H$ and $\Delta v$ are both positive in going from form $II_E$ to form $I_E$ leading to a positive slope for the $II_E-I_E$ phase equilibrium in the pressure–temperature phase diagram. Moreover, the enthalpy difference being relatively small and the specific volume difference relatively large, the slope of the $II_E-I_E$ equilibrium is expected to be shallow, as the calculations demonstrate. The observation that the $I_E-II_E$-liquid triple point occurs at positive pressure is demonstrated by the shallower slope of the $II_E-I_E$ equilibrium versus both the $I_E-L$ and the $II_E-L$ equilibria and by the observation that the two equilibria $I_E$-liquid and $II_E$-liquid intersect at positive pressure as calculated above.

From these results, it can be inferred that the P-T phase diagram for the dimorphism of E-broparestrol corresponds to the first case of Bakhuis-Roozeboom, which can be found in Figure S5 in the Supplementary Materials. (Bakhuis Roozeboom, 1901) On increasing pressure, enantiotropic behaviour turns into monotropic behavior, with form $II_E$ the sole stable solid phase at high pressure.

### 3.2. Thermodynamic studies of the binary phase diagram between the E- and Z-isomers of broparestrol

#### 3.2.1. Preliminary studies of the triclinic form $I_Z$ of Z-broparestrol

A specimen of triclinic Z-broparestrol form $I_Z$ was heated at a rate of $5$ K min$^{-1}$ up to the molten state. The DSC curve (Fig. 6, curve A) contains only an endothermic effect ‘a’ with an onset at $T_{fus,I-Z} = 385.5$ (1.0) K and a melting enthalpy of $\Delta_{fus}H_{I-Z}$ of 91.4(1.8) J/g. By quenching the melt at 223 K, and immediately reheating at the rate of 5 K min$^{-1}$, a new DSC curve was recorded (Fig. 6, curve B), which contains a glass transition at $T_g = 267$ K (midpoint), followed by an exothermic
<figure><img src="image_9.png" /><figcaption>Fig. 6. DSC curves of Z-broparestrol recorded on heating at a rate of 5 K min⁻¹ with (A) a sample of triclinic Z-broparestrol of which only the fusion was observed (endothermic peak ‘a’) and (B) immediately reheating the glass phase obtained after quenching a molten sample at 223 K. A glass transition, Tg, is recorded followed by an exothermic recristallisation ‘b’ and fusion ‘a’ at the same onset temperature as in (A).</figcaption></figure>

recrystallization, event ‘b’ with an onset at 303.5 K (ΔcrystH = -61.3 J/g), and the melting peak ‘a’ at the same temperature and with the same melting enthalpy as obtained in the first run (curve A).

To confirm that the initial phase and the recrystallized one are the same, a powder of Z-broparestrol form IZ was molten in a capillary tube then quickly cooled into the glass state. The X-ray diffraction pattern recorded immediately after recrystallization unambiguously demonstrated that the so-obtained solid was the same IZ form as the initial one. Therefore, by contrast with the E-isomer, thermal treatment does not reveal any polymorphism for Z-broparestrol. It can be concluded however that the glass transition at 267 K for the Z-isomer agrees rather well with the empirical Tammann rule since it is found at Tg/Tfus = 0.69.

The temperature dependence of the lattice parameters of Z-broparestrol form IZ has been determined between 130 K and 375 K (see Table S9 in the Supplementary Materials), leading to the following specific volume as a function of the temperature:

$$v_{I-Z} = 0.6989 + 4.112 \times 10^{-5} \times T/K + 2.578 \times 10^{-7} \times (T/K)^2 (r^2 = 0.998) \quad (9)$$

From 130 K to 350 K, the temperature dependence of the specific volume can also be described by a linear function:

$$v_{I-Z} = 0.6858 + 0.0001624 \times T/K (r^2 = 0.994) \quad (10)$$

from which the expansivity αv₁·Z of 2.4 × 10⁻⁴ K⁻¹ is obtained. It is near the usual value of 2 × 10⁻⁴ K⁻¹. (Céolin and Rietveld, 2015; Rietveld and Céolin, 2015; Gavezzotti, 2013)

### 3.2.2. The T-x phase diagram between forms I<sub>E</sub> and I<sub>Z</sub> of broparestrol

DSC curves from the first series of experiments obtained with physical mixtures of forms I<sub>E</sub> and I<sub>Z</sub> annealed for one weak at 323 K are shown in Figure S6a in the Supplementary Materials together with the Tammann plot (Figure S6b) of the eutectic equilibrium ε₁ at 363(0.5) K. The related data have been compiled in Table S10, while the temperature-composition (T-x) phase diagram is presented in Fig. 7.

To determine the mole fraction x<sub>e1</sub> of the eutectic liquid, the intersection of the Tammann plot was determined using Eqs. S1a and b in the Supplementary Materials. By setting these equations equal, the mole fraction x<sub>e1</sub> of the eutectic liquid is found to be 0.423 (at T<sub>e1</sub> = 363 K). Using the Schröder equation:

<figure><img src="image_10.png" /><figcaption>Fig. 7. T-x phase diagram involving form I<sub>E</sub> and form I<sub>Z</sub> of broparestrol after annealing one week at 323 K. Open crosses and open circles: experimental liquidus temperatures (Table S10 in the Supplementary Materials), solid circles: experimental eutectic temperatures, solid curves: experimental liquidus curves rich in E (red) or Z (blue), dashed curves: ideal liquidus curves calculated by the Schröder equation (Eq. (11)) and straight horizontal line: eutectic equilibrium ε₁.</figcaption></figure>

$$\ln x = \frac{\Delta_{\text{fus}}H}{R} \left( \frac{1}{T_{\text{fus}}} - \frac{1}{T_{x}} \right) \quad (11)$$

and the melting temperatures and melting enthalpies of the pure isomers, the two ideal liquidus curves (dashed lines in Fig. 7) have been determined. They cross at the ideal eutectic liquid coordinates: x<sub>ideal</sub> = 0.50 and T<sub>ideal</sub> = 361 K. The Z-rich liquidus curve does not behave ideally, whereas the E-rich liquidus remains near ideality.

### 3.2.3. The T-x phase diagram between forms I<sub>E</sub> and I<sub>Z</sub> of broparestrol

DSC curves obtained from this second series of experiments, obtained with samples homogenized by melting and recrystallisation on annealing for three years at room temperature, are available in the Supplementary Materials Figure S7a together with the Tammann plot (Figure S7b in the Supplementary Materials) of the eutectic equilibrium ε₂ at 358.1(1.1) K. The related data have been compiled in Table S11 and the T-x phase diagram is shown in Fig. 8.

To determine the mole fraction x<sub>e2</sub> of the eutectic liquid, the intersection of the Tammann plot was determined with Eqs. S2a and b in the Supplementary Materials. By setting the two equations equal, the mole fraction x<sub>e2</sub> of the eutectic liquid is found to be 0.444. Using the Schröder equation (Eq. (11)) and the melting temperatures and melting enthalpies of the pure isomers, the two ideal liquidus curves (dashed curves in Fig. 8) have been determined. They cross at the ideal eutectic liquid coordinates: x<sub>e2-ideal</sub> = 0.49 and T<sub>e2-ideal</sub> = 360 K. It can be seen that the E-rich liquidus curve does not behave ideally. It may be tentatively ascribed to a narrow solid-solution range for form I<sub>E</sub> as demonstrated by the DSC curve with sample x<sub>I-Z</sub> = 0.03 (see Figure S8a in the Supplementary Materials) for which no eutectic peak is recorded.

### 3.2.4. The T-x phase diagram between forms I<sub>E</sub> and I<sub>Z</sub> of broparestrol

DSC curves obtained from the third series of experiments, obtained with samples homogenized by melting and recrystallisation during a few days at room temperature, are available in the Supplementary
<figure><img src="image_11.png" /></figure>

**Fig. 8.** T-x phase diagram involving forms $I_E$ and $I_Z$ after recrystallization for three years at room temperature. Open crosses and open circles: experimental liquidus temperatures (Table S11 in the Supplementary Materials), solid squares: experimental eutectic temperatures, solid curves: experimental liquidus curves rich in *E* (red) or *Z* (blue), dashed curves: ideal liquidus curves calculated by the Schröder equation (Eq. (11)) and straight horizontal line: eutectic equilibrium $\varepsilon_2$. The tentative solid solution range involving high-temperature form $I_E$ is shown in light blue, which may explain the non-ideality of the liquidus curve.

**Materials:** Figure S8a and close-ups of recrystallisation events in Figure S8b. The Tammann plot can be found in Figure S8c of the Supplementary Materials. It involves the eutectic equilibrium $\varepsilon_3$ at 340.2 K (onset). The related data have been compiled in Table S12 in the Supplementary Materials and the T-x phase diagram is shown in Fig. 9.

To determine the mole fraction $x_{\varepsilon_3}$ of the eutectic liquid, the intersection of the Tammann plot was determined with Eqs. S3a and b in the Supplementary Materials. By setting the two equations equal, the mole fraction $x_{\varepsilon_3}$ of the eutectic liquid is found to be 0.684. The corresponding melting enthalpy, $\Delta H_{\varepsilon_3}$, of 58.52 J/g is found at the intersection of the two lines in the Tammann plot (see Figure S8c in the Supplementary Materials).

The third T-x phase diagram in Fig. 9 demonstrates that the *E*-rich liquidus curve related to form $I_E$ behaves almost ideally since the experimental curve and the ideal one, calculated with the Schröder equation (Eq. (11)), are in close proximity. Moreover, the ideal liquidus curves for the *E*-rich parts in the first (Fig. 7) and in the third (Fig. 9) T-x phase diagrams cross at 377.7 K (see Figure S9 in the Supplementary Materials), which is virtually the same temperature as 376.6 K, calculated for the transition from form $II_E$ to the high-temperature form $I_E$ in section 3.1.1.

### 3.2.5. Evidence for the dimorphism of Z-broparestrol

The Z-rich liquidus in Fig. 9 behaves differently than the *E*-rich side: from the composition of the eutectic liquid $x_{\varepsilon_3} = 0.684$, a liquidus curve is observed (violet circles in Fig. 9) up to $x_Z = 0.795$. Then, it can be seen in Figures S8a and b of the Supplementary Materials that exothermic recrystallization occurs leading to the stable liquidus curve related to form $I_Z$.

Therefore, it can be concluded from the third T-x phase diagram that the Z-broparestrol isomer is at least dimorphic and that the new form ($II_Z$) melts at a lower temperature than the triclinic form. This is shown

<figure><img src="image_12.png" /></figure>

**Fig. 9.** Third T-x phase diagram involving form $I_E$ and the metastable form $II_Z$ of Z-broparestrol that recrystallizes into $I_Z$ on the Z-rich side of the diagram. Open crosses and open circles: stable experimental liquidus temperatures (Table S12 in the Supplementary Materials), solid violet circles: metastable experimental liquidus temperatures of Z-probarestrol, solid squares: experimental eutectic temperatures, solid curves: experimental liquidus curves rich in *E* (red) or *Z* (blue), dashed curves: ideal liquidus curves calculated by the Schröder equation (Eq. (11)) and straight horizontal line: eutectic equilibrium $\varepsilon_3$, violet dashed line: tentative representation of the liquidus curve involving the metastable polymorph of Z-broparestrol.

by the **tentatively** drawn liquidus curve (violet dashed line in Fig. 9 (see also values in bold italics in Table S12 in the Supplementary Materials) which extrapolates to $T \approx 366$ K at $x_Z = 1$ using a linear fit. It demonstrates that the new form, which could not be isolated for further characterization, is highly metastable.

Moreover, the total enthalpies reported in bold in Table S12 (in the Supplementary Materials) correspond to the change between an initial state consisting of solid forms $I_E + II_Z$ in fixed ratios and a final state consisting of an isotropic liquid with the same chemical composition. Therefore, Hess' law applies and the line that describes the total enthalpy as a function of $x_Z$ (see the equation in the caption of Figure S8c in the Supplementary Materials) can be extrapolated to $x_Z = 1$ leading to a value of 68.1 J/g, which can be **tentatively** considered as the enthalpy of fusion of the new metastable form $II_Z$ of Z-broparestrol.

Concerning the transition from the stable triclinic form $I_Z$ to the metastable form $II_Z$, it is inferred from Hess' law that it endothermically shifts right on heating with $\Delta I_Z - I_Z H = +23.3$ J/g. In addition, using the formula proposed by Yu (Eq. (1), (Yu, 1995) it is found that the equilibrium is located at about 466–471 K K. In other words, this indicates that the $I_Z - II_Z$-vapour triple point is in a region of the P-T phase diagram of Z-broparestrol where the liquid phase is stable. Unfortunately, it cannot be determined whether form $II_Z$ becomes stable on increasing the pressure, or whether it is a case of overall metastability, since nothing is known about the specific volume of form $II_Z$. In contrast to the case the *E*-isomer dimorphism, it can be concluded that form $II_Z$ behaves monotropically at ordinary pressure.

## 4. Concluding remarks

The physicochemical study of the two isomers of broparestrol has revealed dimorphism for both isomers in contrast to the results reported by Dvolaitzky and Jacques who did not demonstrate any polymorphism
of the components while studying similar binary systems by DSC. (Dvolaitzky and Jacques, 1958).

The crystal structure of the *E*-isomer form *I*<sub>E</sub> was solved at room temperature with the help of high-resolution X-ray powder diffraction. It was demonstrated that it corresponds to a high-temperature form that persists at room temperature for several days. In addition, the phase relationship between the two forms was inferred from the topological pressure–temperature phase diagram, which was found to be similar to the case of sulfur, i.e. enantiotropic behavior that turns monotropic on increasing pressure.

By contrast, the existence of the dimorphism of the *Z*-isomer was unexpectedly revealed by a DSC study of *Z*-rich mixtures in the *T*-x binary phase diagram between the two isomers. Although the polymorph could not be isolated for crystal structure determination, it was inferred that it melts at a lower temperature than the known form *I*<sub>Z</sub> and that it possesses a monotropic relationship with this form at ordinary pressure. An overview of the available thermodynamic and crystallographic information of the two series of broparestrol polymorphs have been compiled in Table 1.

Three experimental *T*-x phase diagrams have been established each with an invariant eutectic equilibrium at 363 K, 358 K, and 340 K. None of these three diagrams fully represents stable behaviour as explained below.

The *T*-x phase diagram in section 3.2.2 exhibits a eutectic equilibrium between the low-temperature form $\Pi_E$ and form $I_Z$. Since the fusion of form $\Pi_E$ is metastable and it does not transform endothermically into form $I_E$ on heating, the diagram cannot be fully stable. Moreover, it is not clear whether the *Z*-rich liquidus curve is in equilibrium since preliminary annealing took only a short time, which may not have been enough to properly homogenize the *Z*-rich mixtures.

The *T*-x phase diagram in section 3.2.3 exhibits a eutectic mixture of the high-temperature form $I_E$ and form $I_Z$. This indicates that recrystallization after melting leads to the high-temperature form $I_E$, which did not transform back to the stable room-temperature form $\Pi_E$ on cooling. Therefore, this second *T*-x phase diagram is not fully stable either. Moreover, the *Z*-rich liquidus is found to be different from that of the first *T*-x diagram and close to ideality.

The *T*-x phase diagram in section 3.2.4 exhibits a eutectic equilibrium between the high-temperature form $I_E$ and the metastable form $I_Z$ with recrystallization into the stable form $I_Z$ in the *Z*-rich liquidus region. Again, this third *T*-x phase diagram cannot represent a stable diagram.

To sum up, (1) three partly metastable phase diagrams have been obtained from the four possible combinations involving one of the following isomeric polymorph pairs: $I_E-I_Z$, $I_E-\Pi_Z$, $\Pi_E-I_Z$, and $\Pi_E-\Pi_Z$. (2) The stable phase diagram exhibits the $\Pi_E-I_E$ transition at about 366 K, as

<caption>**Table 1**</caption>

Thermodynamic and crystallographic information on the four solid phases found in Broparestrol.

<table><thead><tr><th rowspan="2">Property</th><th colspan="2">E-broparestrol</th><th colspan="2">Z-broparestrol</th></tr><tr><th>Form I<sub>E</sub></th><th>Form Π<sub>E</sub></th><th>Form I<sub>Z</sub></th><th>Form Π<sub>Z</sub></th></tr></thead><tbody><tr><td>Formula, Molar mass M/ g/mol</td><td colspan="4">C<sub>22</sub>H<sub>19</sub>Br, 363.31</td></tr><tr><td>T<sub>fus</sub>/K</td><td>386.7</td><td>385.4</td><td>385.5</td><td>363.366<sup>a</sup></td></tr><tr><td>Δ<sub>fus</sub>H /J/g</td><td>79.4</td><td>90.8</td><td>91.4</td><td>68.1<sup>a</sup></td></tr><tr><td>T<sub>g</sub>/K</td><td>264</td><td></td><td>267</td><td></td></tr><tr><td>Δ<sub>II-1</sub>H /J/g</td><td>11.4<sup>b</sup></td><td></td><td>23.3<sup>a</sup></td><td></td></tr><tr><td>T<sub>II-1</sub>/K</td><td>376.6<sup>b</sup></td><td></td><td>466.471<sup>a</sup></td><td></td></tr><tr><td>System, space group</td><td>Monoclinic P2<sub>1</sub>/c</td><td>Monoclinic P2<sub>1</sub>/c,</td><td>Triclinic P-1</td><td>unknown</td></tr><tr><td>V<sub>cell</sub>/Å<sup>3</sup>, Z, T /K</td><td>1799.6, 4, 293</td><td>1784.0, 4, 293</td><td>883.2, 2, 293</td><td>unknown</td></tr><tr><td>Density /g cm<sup>-3</sup> (293 K)</td><td>1.341</td><td>1.372</td><td>1.366</td><td>unknown</td></tr><tr><td>Expansivity α<sub>V</sub>/ K<sup>-1</sup></td><td>2.15 × 10<sup>-4</sup></td><td>2.25 × 10<sup>-4</sup></td><td>2.4 × 10<sup>-4</sup></td><td>unknown</td></tr></tbody></table>

shown in Fig. 10 (see also Eqs. S4 and S5 and Figure S10 in the Supplementary Materials), and the *E*-sided liquidus curve consists of two parts: at lower temperatures, a liquid in equilibrium with form $\Pi_E$ and at higher temperatures a liquid in equilibrium with form $I_E$. With the empirical equations of the experimental liquidus curves $L_{II-E}$ and $L_{I-E}$, one finds that they cross at $x_Z = 0.391$ and $T = 365.7$ K (Eqs. S4 and S5).

Since the observed temperature is lower by about 10 degrees than the calculated one for the phase transition involving the pure polymorphs (376.6 K, cf Figure S9 in the Supplementary Materials), two conclusions can be drawn:

(1) The invariant equilibrium involving forms $I_E$, $\Pi_E$, and the liquid $L_μ$ ($x_Z = 0.391$) is a metatectic equilibrium (see Figure S10 in the Supplementary Materials), written as: (Hillert, 2008).

$$ \Pi_E + \text{Liquid } L_\mu \Leftrightarrow \Pi_E, \text{ on heating.} $$

(2) The inequality in the extent of the limited thermodynamic solid solutions at the invariant temperature shows that the amount of Z molecules as an impurity in form $I_E$ should be larger than for form $\Pi_E$ (Figure S10 in the Supplementary Materials). It entails that the specific volume of form $I_E$ is greater than that of form $\Pi_E$. This coincides with the inequality in the specific volumes $V_{cell}(I_E) = 1800 \AA^3 > V_{cell}(\Pi_E) = 1764 \AA^3$ at 293 K and strengthens the assumption that the less dense phase can incorporate a larger amount of impurities.

The absence of a eutectic peak in the DSC curve of the sample $x_Z = 0.03$ (see Figure S8a in the Supplementary Materials) is an experimental indication in favor of the existence of a limited solid solution for form $I_E$, while this is not the case in the DSC curve of specimen $x_Z = 0.96$ which clearly exhibits a weak endotherm accounting for a eutectic equilibrium (Figures S8a and b in the Supplementary Materials). By contrast, on the *Z*-rich side, only a liquidus curve in equilibrium with form $I_Z$ (as in Fig. 8) is found due to the monotropic behavior of form $\Pi_Z$.

By setting the equations of the experimental low-temperature *E*-sided and *Z*-sided liquidus curves equal, one finds the coordinates $x_{Zc} =$

<figure><img src="image_13.png" /><figcaption>**Fig. 10.** Stable *T*-x phase diagram between *E*- and *Z*-isomers of broparestrol. Blue area: form $I_E$ and liquid, red area: form $\Pi_E$ and liquid, violet area: form $I_Z$ + liquid, green area: liquid, yellow area: form $\Pi_E$ and form $I_Z$, dashed curves are metastable, metatexy = invariant equilibrium [form $\Pi_E$ + Liquid $L_μ$ ⇔ form $I_E$], on heating and eutexy = invariant equilibrium [form $\Pi_E$ + form $I_Z$ ⇔ liquid $L_E$] on heating. For the sake of clarity, the limited solid solutions on the *E*-rich side have not been represented in the graph. A graph in which the domain with solid solutions has been enlarged is available in Figure S10 in the Supplementary Materials.</figcaption></figure>

<footnote>a by 'tentative' extrapolation</footnote>

<footnote>b calculated.</footnote>
0.470 and $T_e = 360.6$ K for the eutectic liquid $L_e$ of the invariant eutectic equilibrium on heating:

$$ \text{form } I_{II_e} + \text{form } I_{Z} \rightleftharpoons \text{liquid } L_e. $$

### CRediT authorship contribution statement

**Siro Toscani:** Writing – review & editing, Validation, Investigation, Formal analysis. **Hassan Allouchi:** Validation, Investigation, Formal analysis. **René Ceolin:** Writing – review & editing, Writing – original draft, Investigation, Formal analysis, Conceptualization. **Laia Villalobos:** Investigation. **Maria Barrio:** Supervision, Methodology, Investigation, Formal analysis. **Josep-Lluis Tamarit:** Writing – review & editing, Supervision, Resources, Funding acquisition. **Ivo B. Rietveld:** Writing – review & editing, Writing – original draft, Validation, Investigation, Conceptualization.

### Declaration of competing interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: J.-Ll. Tamarit reports financial support was provided by Spanish ministry of science and innovation. J.-Ll. Tamarit reports financial support was provided by Government of Catalonia. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgements

This work was partially supported by the Spanish Ministry of Science and Innovation under projects PID2023-146623NB-I00 and CEX2023-001300 and by the Generalitat de Catalunya (2021SGR00343).

### Appendix A. Supplementary material

Supplementary data to this article can be found online at https://doi.org/10.1016/j.ijpharm.2024.125060.

### Data availability

Data will be made available on request.

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